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Quantum computing has emerged as a promising avenue for achieving significant
speedup, particularly in large-scale PDE simulations, compared to classical
computing. One of the main quantum approaches involves utilizing Hamiltonian
simulation, which is directly applicable only to Schr\"odinger-type equations.
To address this limitation, Schr\"odingerisation techniques have been
developed, employing the warped transformation to convert general linear PDEs
into Schr\"odinger-type equations. However, despite the development of
Schr\"odingerisation techniques, the explicit implementation of the
corresponding quantum circuit for solving general PDEs remains to be designed.
In this paper, we present detailed implementation of a quantum algorithm for
general PDEs using Schr\"odingerisation techniques. We provide examples of the
heat equation, and the advection equation approximated by the upwind scheme, to
demonstrate the effectiveness of our approach. Complexity analysis is also
carried out to demonstrate the quantum advantages of these algorithms in high
dimensions over their classical counterparts.
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We introduce a method for computing interfacial motions governed by curvature
dependent acceleration. Our method is a thresholding algorithm of the BMO-type
which, instead of utilizing a diffusion process, thresholds evolution by the
wave equation to obtain the desired interfacial dynamics. We also develop the
numerical method and present results of its application, including an
investigation of the volume preserving and multiphase motions.
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A scalar model of gravity is considered. We propose Lorentz invariant field
equation $\square f = k\eta_{ab}f_{,a}f_{,b}$. The aim of this model is to get,
approximately, Newton's law of gravity. It is shown that $f=-\frac
1k\ln(1-k\frac mr)$ is the unique spherical symmetric static solution of the
field equation. $f$ is taken to be the field of a particle at the origin,
having the mass $m$. The field of a particle moving with a constant velocity is
taken to be the appropriate Lorentz transformation of $f$. The field $F$ of $N$
particles moving on trajectories ${\psi_j(t)}$ is taken to be, to first order,
the superposition of the fields of the particles, where the instantaneous
Lorentz transformation of the fields pertaining to the $j$-th particle is
${\dot\psi_j(t)}$. When this field is inserted to the field equation the
outcome is singular at $({\psi_j(t)},t)$. The singular terms of the l.h.s. and
of the r.h.s. are both $O(R^{-2})$. The only way to reduce the singularity in
the field equation is by postulating Newton's law of force. It is hoped that
this model will be generalized to system of equations that are covariant under
general diffeomorphism.
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Zipf's law predicts a power-law relationship between word rank and frequency
in language communication systems and has been widely reported in a variety of
natural language processing applications. However, the emergence of natural
language is often modeled as a function of bias between speaker and listener
interests, which lacks a direct way of relating information-theoretic bias to
Zipfian rank. A function of bias also serves as an unintuitive interpretation
of the communicative effort exchanged between a speaker and a listener. We
counter these shortcomings by proposing a novel integral transform and kernel
for mapping communicative bias functions to corresponding word frequency-rank
representations at any arbitrary phase transition point, resulting in a direct
way to link communicative effort (modeled by speaker/listener bias) to specific
vocabulary used (represented by word rank). We demonstrate the practical
utility of our integral transform by showing how a change from bias to rank
results in greater accuracy and performance at an image classification task for
assigning word labels to images randomly subsampled from CIFAR10. We model this
task as a reinforcement learning game between a speaker and listener and
compare the relative impact of bias and Zipfian word rank on communicative
performance (and accuracy) between the two agents.
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One of the distinctive features of Information Retrieval systems comparing to
Database Management systems, is that they offer better compression for posting
lists, resulting in better I/O performance and thus faster query evaluation. In
this paper, we introduce database representations of the index that reduce the
size (and thus the disk I/Os) of the posting lists. This is not achieved by
redesigning the DBMS, but by exploiting the non 1NF features that existing
Object-Relational DBM systems (ORDBMS) already offer. Specifically, four
different database representations are described and detailed experimental
results for one million pages are reported. Three of these representations are
one order of magnitude more space efficient and faster (in query evaluation)
than the plain relational representation.
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We introduce SelfExplain, a novel self-explaining model that explains a text
classifier's predictions using phrase-based concepts. SelfExplain augments
existing neural classifiers by adding (1) a globally interpretable layer that
identifies the most influential concepts in the training set for a given sample
and (2) a locally interpretable layer that quantifies the contribution of each
local input concept by computing a relevance score relative to the predicted
label. Experiments across five text-classification datasets show that
SelfExplain facilitates interpretability without sacrificing performance. Most
importantly, explanations from SelfExplain show sufficiency for model
predictions and are perceived as adequate, trustworthy and understandable by
human judges compared to existing widely-used baselines.
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Location trajectories provide valuable insights for applications from urban
planning to pandemic control. However, mobility data can also reveal sensitive
information about individuals, such as political opinions, religious beliefs,
or sexual orientations. Existing privacy-preserving approaches for publishing
this data face a significant utility-privacy trade-off. Releasing synthetic
trajectory data generated through deep learning offers a promising solution.
Due to the trajectories' sequential nature, most existing models are based on
recurrent neural networks (RNNs). However, research in generative adversarial
networks (GANs) largely employs convolutional neural networks (CNNs) for image
generation. This discrepancy raises the question of whether advances in
computer vision can be applied to trajectory generation. In this work, we
introduce a Reversible Trajectory-to-CNN Transformation (RTCT) that adapts
trajectories into a format suitable for CNN-based models. We integrated this
transformation with the well-known DCGAN in a proof-of-concept (PoC) and
evaluated its performance against an RNN-based trajectory GAN using four
metrics across two datasets. The PoC was superior in capturing spatial
distributions compared to the RNN model but had difficulty replicating
sequential and temporal properties. Although the PoC's utility is not
sufficient for practical applications, the results demonstrate the
transformation's potential to facilitate the use of CNNs for trajectory
generation, opening up avenues for future research. To support continued
research, all source code has been made available under an open-source license.
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Spherically symmetric cosmological equations in the usual FLRW coordinates
are explored, with different sources. The first couples a perfect fluid with a
quintessence scalar field and the second couples a perfect fluid to a tachyonic
scalar field. In both cases, in the inflationary regime, the scale factor a(t)
and its first two time derivatives are positive definite. Both sources in the
matter phase yield a scale factor and its first derivative as positive
definite. In both cases and in each phase, the general solutions of the
differential equations together with the algebraic and differential
inequalities are obtained. As special cases, exponential, hyperbolic, and power
law inflation, as well as power law expansion for the matter phase are all
derived from the general solutions. With recent data on baryonic matter, Hubble
parameter and deceleration parameter, the relative percentages of baryonic
matter, daek matter and dark energy are calculated. The quintessence model
yields: 4% baryonic matter, 18% dark matter, and 78% dark energy. The tachyonic
model gives: 4% baryonic matter, 36% dark matter, and 60% dark energy.
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In this paper, we study the asymptotic behavior of the normalized cadlag
functions generated by the discrete Fourier transforms of a stationary centered
square-integrable process, started at a point.
We prove that the quenched invariance principle holds for averaged
frequencies under no assumption other than ergodicity, and that this result
holds also for almost every fixed frequency under a certain generalization of
the Hannan condition and a certain rotated form of the Maxwell and Woodroofe
condition which, under a condition of weak dependence that we specify, is
guaranteed for a.e. frequency. If the process is in particular weakly mixing,
our results describe the asymptotic distributions of the normalized discrete
Fourier transforms at every frequency other than $0$ and $\pi$ under the
generalized Hannan condition.
We prove also that under a certain regularity hypothesis the conditional
centering is irrelevant for averaged frequencies, and that the same holds for a
given fixed frequency under the rotated Maxwell and Woodroofe condition but not
necessarily under the generalized Hannan condition. In particular, this implies
that the hypothesis of regularity is not sufficient for functional convergence
without random centering at a.e. fixed frequency.
The proofs are based on martingale approximations and combine results from
Ergodic theory of recent and classical origin with approximation results by
contemporary authors and with some facts from Harmonic Analysis and Functional
Analysis.
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We study strongly graded vertex algebras and their strongly graded modules,
which are conformal vertex algebras and their modules with a second, compatible
grading by an abelian group satisfying certain grading restriction conditions.
We consider a tensor product of strongly graded vertex algebras and its tensor
product strongly graded modules. We prove that a tensor product of strongly
graded irreducible modules for a tensor product of strongly graded vertex
algebras is irreducible, and that such irreducible modules, up to equivalence,
exhaust certain naturally defined strongly graded irreducible modules for a
tensor product of strongly graded vertex algebras. We also prove that certain
naturally defined strongly graded modules for the tensor product strongly
graded vertex algebra are completely reducible if and only if every strongly
graded module for each of the tensor product factors is completely reducible.
These results generalize the corresponding known results for vertex operator
algebras and their modules.
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We study the monodromy operators on the betti cohomologies associated to a
good degeneration of irreducible symplectic manifold and we show that the
unipotency of the monodromy operator on the middle cohomology is at least the
half of the dimension.
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We point out that the recent excess observed in searches for a right-handed
gauge boson W_R at CMS can be explained in a left-right symmetric model with D
parity violation. In a class of SO(10) models, in which D parity is broken at a
high scale, the left-right gauge symmetry breaking scale is naturally small,
and at a few TeV the gauge coupling constants satisfy g_R ~ 0.6 g_L. Such
models therefore predict a right-handed charged gauge boson W_R in the TeV
range with a suppressed gauge coupling as compared to the usually assumed
manifest left-right symmetry case g_R = g_L. The recent CMS data show excess
events which are consistent with the cross section predicted in the D parity
breaking model for 1.9 TeV < M_{W_R} < 2.4 TeV. If the excess is confirmed, it
would in general be a direct signal of new physics beyond the Standard Model at
the LHC. A TeV scale W_R would for example not only rule out SU(5) grand
unified theory models. It would also imply B-L violation at the TeV scale,
which would be the first evidence for baryon or lepton number violation in
nature and it has strong implications on the generation of neutrino masses and
the baryon asymmetry in the Universe.
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We introduce a novel approach to reveal ordering fluctuations in sheared
dense suspensions, using line scanning in a combined rheometer and laser
scanning confocal microscope. We validate the technique with a moderately dense
suspension, observing modest shear-induced ordering and a nearly linear flow
profile. At high concentration ($\phi = 0.55$) and applied stress just below
shear thickening, we report ordering fluctuations with high temporal
resolution, and directly measure a decrease in order with distance from the
suspension's bottom boundary as well as a direct correlation between order and
particle concentration. Higher applied stress produces shear thickening with
large fluctuations in boundary stress which we find are accompanied by dramatic
fluctuations in suspension flow speeds. The peak flow rates are independent of
distance from the suspension boundary, indicating that they likely arise from
transient jamming that creates solid-like aggregates of particles moving
together, but only briefly because the high speed fluctuations are interspersed
with regions flowing much more slowly, suggesting that shear thickening
suspensions possess complex internal structural dynamics, even in relatively
simple geometries.
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Consider a uniformly distributed random linear subspace $L$ and a
stochastically independent random affine subspace $E$ in $\mathbb{R}^n$, both
of fixed dimension. For a natural class of distributions for $E$ we show that
the intersection $L\cap E$ admits a density with respect to the invariant
measure. This density depends only on the distance $d(o,E \cap L)$ of $L\cap E$
to the origin and is derived explicitly. It can be written as the product of a
power of $d(o,E \cap L)$ and a part involving an incomplete beta integral.
Choosing $E$ uniformly among all affine subspaces of fixed dimension hitting
the unit ball, we derive an explicit density for the random variable $d(o,E
\cap L)$ and study the behavior of the probability that $E \cap L$ hits the
unit ball in high dimensions. Lastly, we show that our result can be extended
to the setting where $E$ is tangent to the unit sphere, in which case we again
derive the density for $d(o,E \cap L)$. Our probabilistic results are derived
by means of a new integral-geometric transformation formula of
Blaschke--Petkantschin type.
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We introduce a Hartmann system in the generalized Taub-NUT space with Abelian
monopole interaction. This quantum system includes well known Kaluza-Klein
monopole and MIC-Zwanziger monopole as special cases. It is shown that the
corresponding Schrodinger equation of the Hamiltonian is separable in both
spherical and parabolic coordinates. We obtain the integrals of motion of this
superintegrable model and construct the quadratic algebra and Casimir operator.
This algebra can be realized in terms of a deformed oscillator algebra and has
finite dimensional unitary representations (unirreps) which provide energy
spectra of the system. This result coincides with the physical spectra obtained
from the separation of variables.
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We produce YbF molecules with a density of 10^18 m^-3 using laser ablation
inside a cryogenically-cooled cell filled with a helium buffer gas. Using
absorption imaging and absorption spectroscopy we study the formation,
diffusion, thermalization and optical pumping of the molecules. The absorption
images show an initial rapid expansion of molecules away from the ablation
target followed by a much slower diffusion to the cell walls. We study how the
time constant for diffusion depends on the helium density and temperature, and
obtain values for the YbF-He diffusion cross-section at two different
temperatures. We measure the translational and rotational temperatures of the
molecules as a function of time since formation, obtain the characteristic time
constant for the molecules to thermalize with the cell walls, and elucidate the
process responsible for limiting this thermalization rate. Finally, we make a
detailed study of how the absorption of the probe laser saturates as its
intensity increases, showing that the saturation intensity is proportional to
the helium density. We use this to estimate collision rates and the density of
molecules in the cell.
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From Galactic binary sources, to extragalactic magnetized neutron stars, to
long-duration GRBs without associated supernovae, the types of sources we now
believe capable of producing bursts of gamma-rays continues to grow apace. With
this emergent diversity comes the recognition that the traditional (and newly
formulated) high-energy observables used for identifying sub-classes does not
provide an adequate one-to-one mapping to progenitors. The popular
classification of some > 100 sec duration GRBs as ``short bursts'' is not only
an unpalatable retronym and syntactically oxymoronic but highlights the
difficultly of using what was once a purely phenomenological classification to
encode our understanding of the physics that gives rise to the events. Here we
propose a physically based classification scheme designed to coexist with the
phenomenological system already in place and argue for its utility and
necessity.
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We classify central extensions of a reductive group $G$ by $\mathcal{K}_3$
and $B\mathcal{K}_3$, the sheaf of third Quillen $K$-theory groups and its
classifying stack. These turn out to be parametrized by the group of
Weyl-invariant quadratic forms on the cocharacter lattice valued in $k^\times$
and the group of integral Weyl-invariant cubic forms on the cocharacter lattice
respectively.
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This paper investigates the reconfigurable intelligent surface (RIS) assisted
spatial scattering modulation (SSM) scheme for millimeter-wave (mmWave)
multiple-input multiple-output (MIMO) systems, in which line-of-sight (LoS) and
non-line-of-sight (NLoS) paths are respectively considered in the
transmitter-RIS and RIS-receiver channels. Based on the maximum likelihood
detector, the conditional pairwise error probability (CPEP) expression for the
RIS-SSM scheme is derived under the two cases of received beam correct and
demodulation error. Furthermore, we derive the closed-form expressions of the
unconditional pairwise error probability (UPEP) by employing two different
methods: the probability density function and the moment-generating function
expressions with a descending order of scatterer gains. To provide more useful
insights, we derive the asymptotic UPEP and the diversity gain of the RIS-SSM
scheme in the high SNR region. Depending on UPEP and the corresponding
Euclidean distance, we get the union upper bound of the average bit error
probability (ABEP). A new framework for ergodic capacity analysis is also
provided to acquire the proposed system's effective capacity. Finally, all
derivation results are validated via extensive Monte Carlo simulations,
revealing that the proposed RIS-SSM scheme outperforms the benchmarks in terms
of reliability.
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Nested weighted automata (NWA) present a robust and convenient
automata-theoretic formalism for quantitative specifications. Previous works
have considered NWA that processed input words only in the forward direction.
It is natural to allow the automata to process input words backwards as well,
for example, to measure the maximal or average time between a response and the
preceding request. We therefore introduce and study bidirectional NWA that can
process input words in both directions. First, we show that bidirectional NWA
can express interesting quantitative properties that are not expressible by
forward-only NWA. Second, for the fundamental decision problems of emptiness
and universality, we establish decidability and complexity results for the new
framework which match the best-known results for the special case of
forward-only NWA. Thus, for NWA, the increased expressiveness of
bidirectionality is achieved at no additional computational complexity. This is
in stark contrast to the unweighted case, where bidirectional finite automata
are no more expressive but exponentially more succinct than their forward-only
counterparts.
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In the context of damage to DNA by low-energy electrons, we carry out
calculations of electron scattering from tetrahydrofuran and phosphoric acid,
models of the subunits in the DNA backbone, as a first step in simulating the
electron capture process that occurs in the cell. In the case of
tetrahydrofuran, we also compare with previous theoretical and experimental
data. A comparison of the shape of the resonant structures to virtual orbitals
is also performed to gain insight into the systematic connections with electron
scattering from similar molecules and dissociative electron attachment
experiments.
|
We have determined the metallicity of the $z_{abs} = 1.0093$ damped Lyman
alpha system in the bright QSO EX 0302-223; this is only the third such
measurement at redshifts $z \simlt 1$. Unlike the previous two cases, we find
that the abundance of Zn is only a factor of $\sim 2$ lower than in the
Galactic interstellar medium today and is entirely compatible with the typical
metallicity of stars in the Milky Way disk at a look-back time of 9.5 Gyrs.
Although the galaxy responsible for producing the absorption system has yet to
be positively identified, our observations show that galaxies on a chemical
evolution path similar to that of the Milky Way do contribute to the damped
Lyman alpha population at intermediate redshifts. Cr is 2.5 times less abundant
than Zn, presumably because of depletion onto dust; however, the degree of
depletion is less severe than in diffuse interstellar clouds in the disk of our
Galaxy and in the Magellanic Clouds. Evidently, the interstellar environment in
damped Lyman alpha galaxies is less conducive to the formation and survival of
dust grains (and molecular hydrogen), but the physical processes at the root of
this effect have yet to be clarified.
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We present an explicit representation for the matrix product ansatz for some
two-species TASEP with open boundary conditions. The construction relies on the
integrability of the models, a property that constrains the possible rates at
the boundaries. The realisation is built on a tensor product of copies of the
DEHP algebras. Using this explicit construction, we are able to calculate the
partition function of the models. The densities and currents in the stationary
state are also computed. It leads to the phase diagram of the models. Depending
on the values of the boundary rates, we obtain for each species shock waves,
maximal current, or low/high densities phases.
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We report the discovery of 47 low surface brightness objects in deep images
of a 3 x 3 degree field centered on the Coma cluster, obtained with the
Dragonfly Telephoto Array. The objects have central surface brightness mu(g,0)
ranging from 24 - 26 mag/arcsec^2 and effective radii r_e = 3"-10", as measured
from archival Canada France Hawaii Telescope images. From their spatial
distribution we infer that most or all of the objects are galaxies in the Coma
cluster. This relatively large distance is surprising as it implies that the
galaxies are very large: with r_e = 1.5 - 4.6 kpc their sizes are similar to
those of L* galaxies even though their median stellar mass is only ~6 x 10^7
Solar masses. The galaxies are relatively red and round, with <g-i> = 0.8 and
<b/a> = 0.74. One of the 47 galaxies is fortuitously covered by a deep Hubble
Space Telescope ACS observation. The ACS imaging shows a large spheroidal
object with a central surface brightness mu(g,0) = 25.8 mag/arcsec^2, a Sersic
index n=0.6, and an effective radius of 7", corresponding to 3.4 kpc at the
distance of Coma. The galaxy is not resolved into stars, consistent with
expectations for a Coma cluster object. We speculate that UDGs may have lost
their gas supply at early times, possibly resulting in very high dark matter
fractions.
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In this paper we simulated self- and mutual- acoustic impedances of guided
modes at the aperture and estimated accuracy of the piston radiation
approximation. We used the Rayleigh integral to simulate the interactions
between different guided modes at the aperture, with low time-consuming. This
kind of guided-wave technique can be utilized to solve problems in diverse
fields of wave science such as acoustics, electromagnetism and optics. For
acoustic waves emitted through a horn or a waveguide with an aperture much
smaller than the wavelength, there are only plane wave modes in the waveguide
and the aperture of horn can therefore be considered as a piston radiator.
However if an acoustic wave with high frequency such as ultrasonic wave is
radiated, there can exist several guided modes in the duct. For arbitrary shape
and size of waveguide, interactions between different modes must be taken into
account to evaluate sound field in the duct and total acoustic power from its
aperture. In this paper we simulated self- and mutual- acoustic impedances of
guided modes at the aperture and estimated accuracy of the piston radiation
approximation. We used the Rayleigh integral to simulate the interactions
between different guided modes at the aperture, with low time-consuming. This
kind of guided-wave technique can be utilized to solve problems in diverse
fields of wave science such as acoustics, electromagnetism and optics.
|
Recent strides in neural speech synthesis technologies, while enjoying
widespread applications, have nonetheless introduced a series of challenges,
spurring interest in the defence against the threat of misuse and abuse.
Notably, source attribution of synthesized speech has value in forensics and
intellectual property protection, but prior work in this area has certain
limitations in scope. To address the gaps, we present our findings concerning
the identification of the sources of synthesized speech in this paper. We
investigate the existence of speech synthesis model fingerprints in the
generated speech waveforms, with a focus on the acoustic model and the vocoder,
and study the influence of each component on the fingerprint in the overall
speech waveforms. Our research, conducted using the multi-speaker LibriTTS
dataset, demonstrates two key insights: (1) vocoders and acoustic models impart
distinct, model-specific fingerprints on the waveforms they generate, and (2)
vocoder fingerprints are the more dominant of the two, and may mask the
fingerprints from the acoustic model. These findings strongly suggest the
existence of model-specific fingerprints for both the acoustic model and the
vocoder, highlighting their potential utility in source identification
applications.
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Toroidal carbon nanotubes can serve as hosts for encapsulated loops of atomic
metal wires. Such composite structures have been analyzed using density
functional theory for a semiconducting C$_{120}$ torus encapsulating chains of
Fe, Au and Cu atoms. The sheathed metal necklaces form a zigzag structure and
drops the HOMO/LUMO bandgap to less than 0.1 eV. The iron composite is
ferromagnetic with a magnetic moment essentially the same as that of bcc iron.
The azimuthal symmetry of these toroidal composites suggests that they may
offer novel elecromagnetic properties not associated with straight,
metal-encapsulated carbon nanotubes.
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The edit distance is a fundamental measure of sequence similarity, defined as
the minimum number of character insertions, deletions, and substitutions needed
to transform one string into the other. Given two strings of length at most
$n$, simple dynamic programming computes their edit distance exactly in
$O(n^2)$ time, which is also the best possible (up to subpolynomial factors)
assuming the Strong Exponential Time Hypothesis (SETH). The last few decades
have seen tremendous progress in edit distance approximation, where the runtime
has been brought down to subquadratic, near-linear, and even sublinear at the
cost of approximation.
In this paper, we study the dynamic edit distance problem, where the strings
change dynamically as the characters are substituted, inserted, or deleted over
time. Each change may happen at any location of either of the two strings. The
goal is to maintain the (exact or approximate) edit distance of such dynamic
strings while minimizing the update time. The exact edit distance can be
maintained in $\tilde{O}(n)$ time per update (Charalampopoulos, Kociumaka,
Mozes; 2020), which is again tight assuming SETH. Unfortunately, even with the
unprecedented progress in edit distance approximation in the static setting,
strikingly little is known regarding dynamic edit distance approximation.
Utilizing the off-the-shelf tools, it is possible to achieve an
$O(n^{c})$-approximation in $n^{0.5-c+o(1)}$ update time for any constant $c\in
[0,\frac16]$. Improving upon this trade-off remains open.
The contribution of this work is a dynamic $n^{o(1)}$-approximation algorithm
with amortized expected update time of $n^{o(1)}$. In other words, we bring the
approximation-ratio and update-time product down to $n^{o(1)}$. Our solution
utilizes an elegant framework of precision sampling tree for edit distance
approximation (Andoni, Krauthgamer, Onak; 2010).
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Several models for the Monte Carlo simulation of Compton scattering on
electrons are quantitatively evaluated with respect to a large collection of
experimental data retrieved from the literature. Some of these models are
currently implemented in general purpose Monte Carlo systems; some have been
implemented and evaluated for possible use in Monte Carlo particle transport
for the first time in this study. Here we present first and preliminary results
concerning total and differential Compton scattering cross sections.
|
We demonstrate the growth of Co-doped BaFe2As2 (Ba-122) thin films on AEF2
(001) (AE: Ca, Sr, Ba) single crystal substrates using pulsed laser deposition.
All films are grown epitaxially despite of a large misfit of -10.6% for BaF2
substrate. For all films a reaction layer is formed at the interface confirmed
by X-ray diffraction and by transmission electron microscopy. The
superconducting transition temperature of the film on CaF2 is around 27 K,
whereas the corresponding values of the other films are around 21 K. The Ba-122
on CaF2 shows identical crystalline quality and superconducting properties as
films on Fe-buffered MgO.
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WD0810-353 is a white dwarf within the 20pc volume around the Sun. Using Gaia
astrometric distance and proper motions, and a radial velocity derived from
Gaia spectroscopy, it has been predicted that this star will pass within 1pc of
the Solar System in about 30kyr. However, WD0810-353 has been also shown to
host a magnetic field with strength of the order of 30MG. Its spectrum is
therefore not like those of normal DA stars of similar effective temperature.
We have obtained and analysed new polarised spectra of the star around Halpha.
Our analysis suggests that the visible surface of the star shows two regions of
different field strength (~30 and ~45MG, respectively), and opposite polarity.
The spectra do not change over a 4 year time span, meaning that either the
stellar rotation period is no shorter than several decades, or that the field
is symmetric about the rotation axis. Taking into account magnetic shift and
splitting, we obtain an estimate of the radial velocity of the star (+83+/-
140km/s); we reject both the value an the claimed precision deduced from the
Gaia DR3 spectroscopy (-373.7+/- 8.2km/s), and we conclude that there will
probably be no close encounter between the Solar System and WD0810-353. We also
reject the suggestion that the star is a hypervelocity runaway star, a survivor
of a Type Ia Supernova explosion. It is just a stellar remnant in the Solar
neighborhood with a very strong and complex magnetic field.
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Gravitational-wave (GW) data contains non-Gaussian noise transients called
"glitches". During the third LIGO-Virgo observing run about 24% of all
gravitational-wave candidates were in the vicinity of a glitch, while even more
events could be affected in future observing runs due to increasing detector
sensitivity. This poses a problem since glitches can affect the estimation of
GW source parameters, including sky localisation, which is crucial to identify
an electromagnetic (EM) counterpart. In this paper we present a study that
estimates how much sky localisation is affected by a nearby glitch in low
latency. We injected binary black hole (BBH), binary neutron star (BNS) and
neutron star-black hole (NSBH) signals into data containing three different
classes of glitches: blips, thunderstorms and fast scatterings. The impact of
these glitches was assessed by estimating the number of tile pointings that a
telescope would need to search over until the true sky location of an event is
observed. We found that blip glitches affect the localisation of BBH mergers
the most; in the most extreme cases a BBH event is completely missed even by a
20 deg$^2$ field-of-view (FOV) telescope. Thunderstorm glitches have the
biggest impact on BBH and NSBH events, especially if there is no third
interferometer, while BNS events appear to be not affected. Fast scattering
glitches impact low latency localisation only for NSBH signals. For
two-interferometer network small (FOV=1 deg$^2$) and large (FOV=20 deg$^2$)
telescopes are affected, whereas three-interferometer localisation bias is
small enough not to affect large (FOV=20 deg$^2$) telescopes.
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Unambiguous identification of the Kitaev quantum spin liquid (QSL) in
materials remains a huge challenge despite many encouraging signs from various
measurements. To facilitate the experimental detection of the Kitaev QSL, here
we propose to use remnant charge response in Mott insulators hosting QSL to
identify the key signatures of QSL. We predict an emergent orbital
magnetization in a Kitaev system in an external magnetic field. The direction
of the orbital magnetization can be flipped by rotating the external magnetic
field in the honeycomb plane. The orbital magnetization is demonstrated
explicitly through a detailed microscopic analysis of the multiorbital
Hubbard-Kanamori Hamiltonian and also supported by a phenomenological picture.
We first derive the localized electrical loop current operator in terms of the
spin degrees of freedom. Thereafter, utilizing the Majorana representation, we
estimate the loop currents in the ground state of the chiral Kitaev QSL state,
and obtain the consequent current textures, which are responsible for the
emergent orbital magnetization. Finally, we discuss the possible experimental
techniques to visualize the orbital magnetization which can be considered as
the signatures of the underlying excitations.
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In this short note I speculate on some consequences of the high energy
collision picture in which the orbital angular momentum of the colliding
hadrons can be converted into secondary particle angular spin momentum via some
spin-orbital interaction. In particular I discuss a possibility to observe a
non-zero polarization of secondary particles (e.g. hyperons) at midrapidity
($x_F=0$) and at low transverse momentum. I also speculate that such effects
could contribute to the produced particle directed and elliptic flow observed
in relativistic nuclear collisions.
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The production of dijets in diffractive deep inelastic scattering has been
measured with the ZEUS detector at HERA using an integrated luminosity of $61
\pbi$. The dijet cross section has been measured for virtualities of the
exchanged virtual photon, $5 < Q^2 < 100 \gev^2$, and $\gamma^{*} p$
centre-of-mass energies, 100 < W < 250 GeV. The jets, identified using the
inclusive k_{T} algorithm in the $\gamma^* p$ frame, were required to have a
transverse energy $E^*_{T, \rm jet} > 4 \gev$ and the jet with the highest
transverse energy was required to have $E^*_{T,\rm jet} > 5 \gev$. All jets
were required to be in the pseudorapidity range $-3.5 < \eta^*_{\rm jet} < 0$.
The differential cross sections are compared to leading-order predictions and
next-to-leading-order QCD calculations based on recent diffractive parton
densities extracted from inclusive diffractive deep inelastic scattering data.
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We introduce a new space IDA of locally integrable functions whose integral
distance to holomorphic functions is finite, and use it to completely
characterize boundedness and compactness of Hankel operators on weighted Fock
spaces. As an application, for bounded symbols, we show that the Hankel
operator $H_f$ is compact if and only if $H_{\bar f}$ is compact, which
complements the classical compactness result of Berger and Coburn. Motivated by
recent work of Bauer, Coburn, and Hagger, we also apply our results to the
Berezin-Toeplitz quantization.
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We propose a new phase detection technique based on a flux-switchable
superconducting circuit, the Josephson digital phase detector (JDPD), which is
capable of discriminating between two phase values of a coherent input tone.
When properly excited by an external flux, the JDPD is able to switch from a
single-minimum to a double-minima potential and, consequently, relax in one of
the two stable configurations depending on the phase sign of the input tone.
The result of this operation is digitally encoded in the occupation probability
of a phase particle in either of the two JDPD wells. In this work, we
demonstrate the working principle of the JDPD up to a frequency of 400 MHz with
a remarkable agreement with theoretical expectations. As a future scenario, we
discuss the implementation of this technique to superconducting qubit readout.
We also examine the JDPD compatibility with the single-flux-quantum
architecture, employed to fast-drive and measure the device state.
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In this paper, we present a thorough theoretical analysis of the default
implementation of LIME in the case of tabular data. We prove that in the large
sample limit, the interpretable coefficients provided by Tabular LIME can be
computed in an explicit way as a function of the algorithm parameters and some
expectation computations related to the black-box model. When the function to
explain has some nice algebraic structure (linear, multiplicative, or sparsely
depending on a subset of the coordinates), our analysis provides interesting
insights into the explanations provided by LIME. These can be applied to a
range of machine learning models including Gaussian kernels or CART random
forests. As an example, for linear functions we show that LIME has the
desirable property to provide explanations that are proportional to the
coefficients of the function to explain and to ignore coordinates that are not
used by the function to explain. For partition-based regressors, on the other
side, we show that LIME produces undesired artifacts that may provide
misleading explanations.
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Speculative execution which is used pervasively in modern CPUs can leave side
effects in the processor caches and other structures even when the speculated
instructions do not commit and their direct effect is not visible. The recent
Meltdown and Spectre attacks have shown that this behavior can be exploited to
expose privileged information to an unprivileged attacker. In particular, the
attack forces the speculative execution of a code gadget that will carry out
the illegal read, which eventually gets squashed, but which leaves a
side-channel trail that can be used by the attacker to infer the value. Several
attack variations are possible, allowing arbitrary exposure of the full kernel
memory to an unprivileged attacker. In this paper, we introduce a new model
(SafeSpec) for supporting speculation in a way that is immune to side-channel
leakage necessary for attacks such as Meltdown and Spectre. In particular,
SafeSpec stores side effects of speculation in a way that is not visible to the
attacker while the instructions are speculative. The speculative state is then
either committed to the main CPU structures if the branch commits, or squashed
if it does not, making all direct side effects of speculative code invisible.
The solution must also address the possibility of a covert channel from
speculative instructions to committed instructions before these instructions
are committed. We show that SafeSpec prevents all three variants of Spectre and
Meltdown, as well as new variants that we introduce. We also develop a cycle
accurate model of modified design of an x86-64 processor and show that the
performance impact is negligible. We build prototypes of the hardware support
in a hardware description language to show that the additional overhead is
small. We believe that SafeSpec completely closes this class of attacks, and
that it is practical to implement.
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In this paper, we consider the finite time blow-up results for a parabolic
equation coupled with superlinear source term and local linear boundary
dissipation. Using a concavity argument, we derive the sufficient conditions
for the solutions to blow up in finite time. In particular, we obtain the
existence of finite time blow-up solutions with arbitrary high initial energy.
We also derive the upper bound and lower bound of the blow up time.
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The World Space Observatory-Ultraviolet (WSO-UV) will provide access to the
UV range during the next decade. The instrumentation on board will allow to
carry out high resolution imaging, high sensitivity imaging, high resolution
(R~55000) spectroscopy and low resolution (R~2500) long slit spectroscopy. In
this contribution, we briefly outline some of the key science issues that
WSO-UV will address during its lifetime. Among them, of special interest are:
the study of galaxy formation and the intergalactic medium; the astronomical
engines; the Milky Way formation and evol ution, and the formation of the Solar
System and the atmospheres of extrasolar p lanets.
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I briefly discuss three topics related to the hadroproduction of jets: jet
definitions; jet structure; and the underlying event.
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We review different constructions of the supersymmetry subalgebras of the
chiral de Rham complex on special holonomy manifolds. We describe the
difference between the holomorphic-anti-holomorphic sectors based on a local
free ghost system vs the decomposition in left-right sectors from a local
Boson-Fermion system. We describe the topological twist in the case of $G_2$
and $Spin_7$ manifolds. We describe the construction of these algebras as
quantum Hamiltonian reduction of Lie superalgebras at the minimal or
superprincipal nilpotent.
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The nuclear modification factor $R_{AA}$ for $\pi_0$ production in Au+Au
collisions at $\sqrt{s}=200$ AGeV is calculated, and studied at high transverse
momenta $p_T$. The soft thermalized nuclear medium is described within the
framework of relativistic ideal three-dimensional hydrodynamics. The energy
loss of partonic jets is evaluated in the context of gluon bremsstrahlung in
the thermalized partonic matter. We provide a systematic analysis of the
azimuthal asymmetry of $\pi_0$ suppression at high $p_T$ in central and
non-central collisions, at mid and forward rapidity. The determination of
$R_{AA}$ as a function of $p_T$, at different azimuthal angles, and different
rapidities makes for a stringent test of our theoretical understanding of jet
energy loss over a variety of in-medium path lengths, temperatures and initial
partonic jet energies. This lays the groundwork for a precise tomography of the
nuclear medium.
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I review recent progress on understanding QCD dynamics involved in exclusive
$B$ meson decays. Different frameworks, including light-cone sum rules, QCD
factorization, perturbative QCD, soft-collinear effective theory, light-front
QCD, are discussed. Results from lattice QCD are quoted for comparison. I point
out the important issues in the above QCD methods, which require further
investigation.
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Superconductor/ferromagnet/superconductor Josephson junctions are
paradigmatic systems for studying the delicate interplay of superconductivity
and magnetism via proximity effects as well as their composite excitations.
Here, we analyse the collective modes (CM) in such a heterostructure by taking
into account the interplay between the de-magnetisation field $H_{dem}$ and the
field caused by the anisotropy of the ferromagnet $H_{an}$, which was
previously neglected. It turns out that the spectrum of composite collective
modes, $\omega(k)$, has a qualitatively different form in the case of
$H_{dem}<H_{an}$ and of $H_{dem}>H_{an}$. In the first case, the dependence
$\omega(k)$ has the same form as in previous studies, whereas in the second
case, the spectrum looks completely different. In particular, for moderate or
weak anisotropy in ferromagnet the group velocity of collective modes
demonstrates inflection point where the group velocity become infinite and is
superluminal. Furthermore, this point separates purely real and
complex-conjugate solutions for the collective modes and is also {\it exception
point}. We show that the difference of the CMs spectra can be revealed by Fiske
experiment, i.\,e.\,by measuring the $I-V$ characteristics in the presence of
magnetic field and voltage.
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We consider the visual feature selection to improve the estimation quality
required for the accurate navigation of a robot. We build upon a key property
that asserts: contributions of trackable features (landmarks) appear linearly
in the information matrix of the corresponding estimation problem. We utilize
standard models for motion and vision system using a camera to formulate the
feature selection problem over moving finite time horizons. A scalable
randomized sampling algorithm is proposed to select more informative features
(and ignore the rest) to achieve a superior position estimation quality. We
provide probabilistic performance guarantees for our method. The
time-complexity of our feature selection algorithm is linear in the number of
candidate features, which is practically plausible and outperforms existing
greedy methods that scale quadratically with the number of candidates features.
Our numerical simulations confirm that not only the execution time of our
proposed method is comparably less than that of the greedy method, but also the
resulting estimation quality is very close to the greedy method.
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We give a new proof of Chung and Graham's ``G-descent expansion'' of the
classical chromatic polynomial, as well as a special case of the
quasi-symmetric function expansion of the path-cycle symmetric function Xi_D.
Both proofs rely on Stanley's quasi-symmetric function expansion of the
chromatic symmetric function X_G. We also show that Stanley's expansion
suggests that a Robinson-Schensted algorithm for (3+1)-free posets---something
that has been sought for unsuccessfully for some time---ought to ``respect
descents'' in a certain precise sense.
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A non-standard teleportation scheme is proposed, wherein probabilistic
teleportation is achieved in conventionally non-teleporting channels. We make
use of entanglement monogamy to incorporate an unknown state in a multipartite
entangled channel, such that the receiver partially gets disentangled from the
network. Subsequently, the sender performs local measurement based
teleportation protocol in an appropriate measurement basis, which results with
the receiver in the possession of an unknown state, connected by local unitary
transformation with the state to be teleported. This procedure succeeds in a
number of cases, like that of W and other non-maximally entangled four qubit
states, where the conventional measurement based approach has failed. It is
also found that in certain four particle channels, the present procedure does
not succeed, although the conventional one works well.
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In this paper, we focus on the local convergence rate analysis of the
proximal iteratively reweighted $\ell_1$ algorithms for solving $\ell_p$
regularization problems, which are widely applied for inducing sparse
solutions. We show that if the Kurdyka-Lojasiewicz (KL) property is satisfied,
the algorithm converges to a unique first-order stationary point; furthermore,
the algorithm has local linear convergence or local sublinear convergence. The
theoretical results we derived are much stronger than the existing results for
iteratively reweighted $\ell_1$ algorithms.
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In this paper, a new structure of cooperative learning automata so-called
extended learning automata (eDLA) is introduced. Based on the proposed
structure, a new iterative randomized heuristic algorithm for finding optimal
sub-graph in a stochastic edge-weighted graph through sampling is proposed. It
has been shown that the proposed algorithm based on new networked-structure can
be to solve the optimization problems on stochastic graph through less number
of sampling in compare to standard sampling. Stochastic graphs are graphs in
which the edges have an unknown distribution probability weights. Proposed
algorithm uses an eDLA to find a policy that leads to an induced sub-graph that
satisfies some restrictions such as minimum or maximum weight (length). At each
stage of the proposed algorithm, eDLA determines which edges to be sampled.
This eDLA-based proposed sampling method may result in decreasing unnecessary
samples and hence decreasing the time that algorithm requires for finding the
optimal sub-graph. It has been shown that proposed method converge to optimal
solution, furthermore the probability of this convergence can be made
arbitrarily close to 1 by using a sufficiently small learning rate. A new
variance-aware threshold value was proposed that can be improving significantly
convergence rate of the proposed eDLA-based algorithm. It has been shown that
the proposed algorithm is competitive in terms of the quality of the solution
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A large number of models which address the dynamics of particle-laden
turbulent flows have been developed based on the assumption of local isotropy
and use the Kolmogorov constant that correlates the spectral distribution of
turbulent kinetic energy with the turbulent dissipation rate. Many turbulence
models (Stochastic and LES models) use the Kolmogorov constant in the
formulation. Compilation of a large number of experimental data for different
flow configurations has revealed that the Kolmogorov constant is independent of
Reynolds number in the limit of high Reynolds number (Sreenivasan, 1995).
However, several numerical studies at low and intermediate Reynolds numbers
which address the flow situations of practical importance consider that the
Kolmogorov constant remains unchanged irrespective of whether the flow is
single phase or multiphase. In the present work, we assess the variation of
local isotropy of fluid fluctuations with the increase in particle loading in
particle-laden turbulent channel flows. We also estimate the Kolmogorov
constant using second-order velocity structure functions and compensated
spectra in case of low Reynolds number turbulent flows. Our study reveals that
the Kolmogorov constant decreases in the channel center with an increase in the
particle volume fraction for the range of Reynolds number investigated here.
The estimated variation of the Kolmogorov constant is used to express the
Smagorinsky coefficient as a function of solid loading in particle-laden flows.
Then, a new modeling technique is adopted using the large eddy simulation (LES)
to predict the fluid phase statistics without solving simultaneous particle
phase equations. This new methodology also helps understand the drastic
decrease in turbulence intensity at critical particle volume loading.
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We introduce and study multivariate zeta functions enumerating
subrepresentations of integral quiver representations. For nilpotent such
representations defined over number fields, we exhibit a homogeneity condition
that we prove to be sufficient for local functional equations of the generic
Euler factors of these zeta functions. This generalizes and unifies previous
work on submodule zeta functions including, specifically, ideal zeta functions
of nilpotent (Lie) rings and their graded analogues.
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We propose a method for identifying holographic chemical potentials of
conserved charges. The guiding principle is the consistency of the
identification with the thermodynamic relations and the Legendre
transformation. We consider the baryon-charge chemical potential as an example,
and explain why the degree of freedom of the constant shift of the bulk U(1)
gauge field is absent when the Legendre transformation is well-defined. The
method proposed here suggests that the definition of the chemical potential may
be more complicated compared with the case of localized charge if we have a
nontrivial charge distribution along the radial direction of the bulk geometry.
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We describe the second version (v2.0.0) of the code ADG that automatically
(1) generates all valid off-diagonal Bogoliubov many-body perturbation theory
diagrams at play in particle-number projected Bogoliubov many-body perturbation
theory (PNP-BMBPT) and (2) evaluates their algebraic expression to be
implemented for numerical applications. This is achieved at any perturbative
order $p$ for a Hamiltonian containing both two-body (four-legs) and three-body
(six-legs) interactions (vertices). All valid off-diagonal BMBPT diagrams of
order $p$ are systematically generated from the set of diagonal, i.e.,
unprojected, BMBPT diagrams. The production of the latter were described at
length in https://doi.org/10.1016/j.cpc.2018.11.023 dealing with the first
version of ADG. The automated evaluation of off-diagonal BMBPT diagrams relies
both on the application of algebraic Feynman's rules and on the identification
of a powerful diagrammatic rule providing the result of the remaining $p$-tuple
time integral. The new diagrammatic rule generalizes the one already identified
in https://doi.org/10.1016/j.cpc.2018.11.023 to evaluate diagonal BMBPT
diagrams independently of their perturbative order and topology. The code ADG
is written in Python3 and uses the graph manipulation package NetworkX. The
code is kept flexible enough to be further expanded throughout the years to
tackle the diagrammatics at play in various many-body formalisms that already
exist or are yet to be formulated.
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The dependence of macroscopic detonation properties of a two-dimensional
diatomic (AB) molecular system on the fundamental properties of the molecule
were investigated. This includes examining the detonation velocity, reaction
zone thickness, and critical width as a function of the exothermicity of the
gas-phase reaction and the gas-phase dissociation energy for. Following
previous work, molecular dynamics (MD) simulations with a reactive empirical
bond-order potential were used to characterize the shock-induced response of a
diatomic AB molecular solid, which exothermically reacts to produce gaseous
products. MD simulations reveal that there is a linear dependence between the
square of the detonation velocity and each of these molecular parameters. The
detonation velocities were shown to be consistent with the Chapman-Jouguet
model, demonstrating that these dependencies arise from how the Equation of
State of the products and reactants are affected.
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We study the chirally symmetric continuum model (CS-CM) of the twisted
bilayer graphene. The equation on a flat band could be interpreted as a Dirac
equation on a torus in the external non-abelian magnetic field. We prove that
the existence of the flat band implies that the wave-function has a zero and
vice verse. We found a hidden solution in the CS-CM model that has a pole
instead of a zero. Our main result is that in the basis of the flat band and
hidden wave functions the flat band could be interpreted as Landau level in the
external magnetic field. From that interpretation we show the existence of
extra flat bands in the magnetic field.
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Type Ia supernovae (SNe Ia) play an important role in diverse areas of
astrophysics, from the chemical evolution of galaxies to observational
cosmology. However, the nature of the progenitors of SNe Ia is still unclear.
In this paper, according to a detailed binary population synthesis study, we
obtained SN Ia birthrates and delay times from different progenitor models, and
compared them with observations. We find that the Galactic SN Ia birthrate from
the double-degenerate (DD) model is close to those inferred from observations,
while the birthrate from the single-degenerate (SD) model accounts for only
about 1/2-2/3 of the observations. If a single starburst is assumed, the
distribution of the delay times of SNe Ia from the SD model is a weak
bimodality, where the WD + He channel contributes to the SNe Ia with delay
times shorter than 100Myr, and the WD + MS and WD + RG channels to those with
age longer than 1Gyr.
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In this paper we consider special linear Fuchsian systems of rank $2$ on a
$4-$punctured sphere and the corresponding parabolic structures. Through an
explicit abelianization procedure we obtain a $2-$to$-1$ correspondence between
flat line bundle connections on a torus and these Fuchsian systems. This
naturally equips the moduli space of flat $SL(2,\mathbb C)-$connections on a
$4-$punctured sphere with a new set of Darboux coordinates. Furthermore, we
apply our theory to give a complex analytic proof of Witten's formula for the
symplectic volume of the moduli space of unitary flat connections on the
$4-$punctured sphere.
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According to Bestvina-Bromberg-Fujiwara, a finitely generated group is said
to have property (QT) if it acts isometrically on a finite product of
quasi-trees so that orbital maps are quasi-isometric embeddings. We prove that
the fundamental group $\pi_1(M)$ of a compact, connected, orientable 3-manifold
$M$ has property (QT) if and only if no summand in the sphere-disc
decomposition of $M$ supports either Sol or Nil geometry. In particular, all
compact, orientable, irreducible 3-manifold groups with nontrivial torus
decomposition and not supporting Sol geometry have property (QT). In the course
of our study, we establish property (QT) for the class of Croke-Kleiner
admissible groups and of relatively hyperbolic groups under natural assumptions
has property (QT).
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Empirically, neural networks that attempt to learn programs from data have
exhibited poor generalizability. Moreover, it has traditionally been difficult
to reason about the behavior of these models beyond a certain level of input
complexity. In order to address these issues, we propose augmenting neural
architectures with a key abstraction: recursion. As an application, we
implement recursion in the Neural Programmer-Interpreter framework on four
tasks: grade-school addition, bubble sort, topological sort, and quicksort. We
demonstrate superior generalizability and interpretability with small amounts
of training data. Recursion divides the problem into smaller pieces and
drastically reduces the domain of each neural network component, making it
tractable to prove guarantees about the overall system's behavior. Our
experience suggests that in order for neural architectures to robustly learn
program semantics, it is necessary to incorporate a concept like recursion.
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We study the dynamics of cosmological phase transitions in the case of small
velocities of bubble walls, $v_w<0.1$. We discuss the conditions in which this
scenario arises in a physical model, and we compute the development of the
phase transition. We consider different kinds of approximations and refinements
for relevant aspects of the dynamics, such as the dependence of the wall
velocity on hydrodynamics, the distribution of the latent heat, and the
variation of the nucleation rate. Although in this case the common
simplifications of a constant wall velocity and an exponential nucleation rate
break down due to reheating, we show that a delta-function rate and a velocity
which depends linearly on the temperature give a good description of the
dynamics and allow to solve the evolution analytically. We also consider a
Gaussian nucleation rate, which gives a more precise result for the bubble size
distribution. We discuss the implications for the computation of cosmic
remnants.
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We present an updated list of direct strong evidence in favour of kicks being
imparted to newborn neutron stars. In particular we discuss the new cases of
evidence resulting from recent observations of the X-ray binary Circinus X-1
and the newly discovered binary radio pulsar PSR J1141-6545. We conclude that
the assumption that neutron stars receive a kick velocity at their formation is
unavoidable (van den Heuvel & van Paradijs 1997).
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A method to construct interior axially symmetric metrics that appropriately
match with any vacuum solution of the Weyl family is developed in
Hernandez-Pastora etal. (Class Quantum Gravity 33:235005, 2016). It was
shown,for the case of some vacuum solutions, that the simplestsolution for the
interior metric leads to sources with well behaved energy conditions. Now, we
integrate the field equa-tions to obtain the interior metric functions in terms
of theanisotropies and pressures of the source. As well, the compatible
equations of state for these global models are calculated. The interior metric
and the suitable energy momentum tensor describing the source are constructed
in terms of the exterior metric functions. At the boundary of the compact
object,the behaviour of a pressure Tm, defined from the energy momentum tensor,
is shown to be related with the exterior gravitational field. This fact allows
us to explore the differences arising at the matter distribution when the
sphericalsymmetry of the global metric is dropped. Finally, an equation derived
from the matching conditions is obtained whichallows us to calculate the Weyl
coefficients of the exteriormetric as source integrals. Hence the Relativistic
MultipoleMoments of the global model can be expressed in terms ofthe matter
distribution of the source.
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As infamous invaders to the North American ecosystem, the Asian giant hornet
(Vespa mandarinia) is devastating not only to native bee colonies, but also to
local apiculture. One of the most effective way to combat the harmful species
is to locate and destroy their nests. By mobilizing the public to actively
report possible sightings of the Asian giant hornet, the governmentcould timely
send inspectors to confirm and possibly destroy the nests. However, such
confirmation requires lab expertise, where manually checking the reports one by
one is extremely consuming of human resources. Further given the limited
knowledge of the public about the Asian giant hornet and the randomness of
report submission, only few of the numerous reports proved positive, i.e.
existing nests. How to classify or prioritize the reports efficiently and
automatically, so as to determine the dispatch of personnel, is of great
significance to the control of the Asian giant hornet. In this paper, we
propose a method to predict the priority of sighting reports based on machine
learning. We model the problem of optimal prioritization of sighting reports as
a problem of classification and prediction. We extracted a variety of rich
features in the report: location, time, image(s), and textual description.
Based on these characteristics, we propose a classification model based on
logistic regression to predict the credibility of a certain report.
Furthermore, our model quantifies the impact between reports to get the
priority ranking of the reports. Extensive experiments on the public dataset
from the WSDA (the Washington State Department of Agriculture) have proved the
effectiveness of our method.
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A Particle Tracking Velocimetry experiment has been performed in a turbulent
flow at intermediate Reynolds number. We present experimentally obtained
stretching rates for particle pairs in the inertial range. When compensated by
a characteristic time scale for coarse-grained strain we observe constant
stretching. This indicates that the process of material line stretching taking
place in the viscous subrange has its counterpart in the inertial subrange. We
investigate both forwards and backwards dispersion. We find a faster backwards
stretching and relate it to the problem of relative dispersion and its time
asymmetry.
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We show that the strongly regular graph on non-isotropic points of one type
of the polar spaces of type $U(n, 2)$, $O(n, 3)$, $O(n, 5)$, $O^+(n, 3)$, and
$O^-(n, 3)$ are not determined by its parameters for $n \geq 6$. We prove this
by using a variation of Godsil-McKay switching recently described by Wang, Qiu,
and Hu. This also results in a new, shorter proof of a previous result of the
first author which showed that the collinearity graph of a polar space is not
determined by its spectrum. The same switching gives a linear algebra
explanation for the construction of a large number of non-isomorphic designs.
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We prove that if a linear group $G$ is almost Engel, then $G$ is
finite-by-hypercentral. If $G$ is almost nil, then $G$ is finite-by-nilpotent.
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We investigate the cosmological attractor of the minimally coupled,
self-interacting phantom field with a positive energy density but negative
pressure. It is proved that the phantom cosmology is rigid in the sense that
there exists a unique attractor solution. We plot the trajectories in the phase
space numerically for the phantom field with three typical potentials. Phase
portraits indicate that an initial kinetic term decays rapidly and the
trajectories reach the unique attractor curve. We find that the curve
corresponds to the slow-climb solution.
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Three ways of constructing a non-Hermitian matrix with possible all real
eigenvalues are discussed. They are PT symmetry, pseudo-Hermiticity, and
generalized PT symmetry. Parameter counting is provided for each class. All
three classes of matrices have more real parameters than a Hermitian matrix
with the same dimension. The generalized PT-symmetric matrices are most general
among the three. All self-adjoint matrices process a generalized PT symmetry.
For a given matrix, it can be both PT-symmetric and P'-pseudo-Hermitian with
respect to some P' operators. The relation between corresponding P and P'
operators is established. The Jordan block structures of each class are
discussed. Explicit examples in 2x2 are shown.
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We study two properties of modules over a local hypersurface $R$: decency and
rigidity. We show that the vanishing of Hochster's function $\theta^R(M,N)$,
known to imply decent intersection, also implies rigidity. We investigate the
vanishing of $\theta^R(M,N)$ to obtain new results about decency and rigidity
over hypersurfaces. We employ a mixture of techniques from Commutative Algebra
and Intersection Theory of algebraic cycles.
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This study explores the application of a wall-attached ferrofluid film to
decrease skin friction drag in turbulent channel flow. We conduct experiments
using water as a working fluid in a turbulent channel flow setup, where one
wall is coated with a ferrofluid layer held in place by external permanent
magnets. Depending on the flow conditions, the interface between the two fluids
is observed to form unstable travelling waves. While ferrofluid coating has
been previously employed in laminar and moderately turbulent flows to reduce
drag by creating a slip condition at the fluid interface, its effectiveness in
fully developed turbulent conditions, particularly when the interface exhibits
instability, remains uncertain. Our primary objective is to assess the
effectiveness of ferrofluid coating in reducing turbulent drag with particular
focus on scenarios when the ferrofluid layer forms unstable waves. To achieve
this, we measure flow velocity using two-dimensional particle tracking
velocimetry (2D-PTV), and the interface contour between the fluids is
determined using an interface tracking algorithm. Our results reveal the
significant potential of ferrofluid coating for drag reduction, even in
scenarios where the interface between the surrounding fluid and ferrofluid
exhibits instability. In particular, waves with an amplitude significantly
smaller than a viscous length scale positively contribute to drag reduction,
while larger waves are detrimental, because of induced turbulent fluctuations.
However, for the latter case, slip out-competes the extra turbulence so that
drag is still reduced.
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Several key motivations and perspectives of ground based gamma-ray astronomy
are discussed in the context of the specifics of detection techniques and
scientific topics/objectives relevant to four major energy domains -- very-low
or \textit{multi-GeV} ($E \leq$ 30 GeV), low or \textit{sub-TeV} (30 GeV - 300
GeV), high or \textit{TeV} (300 GeV - 30 TeV), and very-high or
\textit{sub-PeV} ($E \geq$ 30 TeV) intervals -- to be covered by the next
generation of IACT arrays.
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A brief summary of results on homotheties in General Relativity is given,
including general information about space-times admitting an r-parameter group
of homothetic transformations for r>2, as well as some specific results on
perfect fluids. Attention is then focussed on inhomogeneous models, in
particular on those with a homothetic group $H_4$ (acting multiply
transitively) and $H_3$. A classification of all possible Lie algebra
structures along with (local) coordinate expressions for the metric and
homothetic vectors is then provided (irrespectively of the matter content), and
some new perfect fluid solutions are given and briefly discussed.
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The emergence of biomolecular homochirality is a critically important
question about life phenomenon and the origins of life. In a previous paper
(arXiv:1309.1229), I tentatively put forward a new hypothesis that the
emergence of a single chiral form of biomolecules in living organisms is
specifically determined by the electron spin state during their
enzyme-catalyzed synthesis processes. However, how a homochirality world of
biomolecules could have formed in the absence of enzymatic networks before the
origins of life remains unanswered. Here I discussed the electron spin
properties in Fe3S4, ZnS, and transition metal doped dilute magnetic ZnS, and
their possible roles in the prebiotic synthesis of chiral molecules. Since the
existence of these minerals in hydrothermal vent systems is matter of fact, the
suggested prebiotic inorganic-organic reaction model, if can be experimentally
demonstrated, may help explain where and how life originated on early Earth.
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The European Materials and Modelling Ontology (EMMO) has recently been
advanced in the computational molecular engineering and multiscale modelling
communities as a top-level ontology, aiming to support semantic
interoperability and data integration solutions, e.g., for research data
infrastructures. The present work explores how top-level ontologies that are
based on the same paradigm - the same set of fundamental postulates - as the
EMMO can be applied to models of physical systems and their use in
computational engineering practice. This paradigm, which combines mereology (in
its extension as mereotopology) and semiotics (following Peirce's approach), is
here referred to as mereosemiotics. Multiple conceivable ways of implementing
mereosemiotics are compared, and the design space consisting of the possible
types of top-level ontologies following this paradigm is characterized.
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High-energy-density flows through dense matter are needed for effective
progress in the production of laser-driven intense sources of energetic
particles and radiation, in driving matter to extreme temperatures creating
state regimes relevant for planetary or stellar science as yet inaccessible at
the laboratory scale, or in achieving high-gain laser-driven thermonuclear
fusion. When interacting at the surface of dense (opaque) targets, intense
lasers accelerate relativistic electron beams which transport a significant
fraction of the laser energy into the target depth. However, the overall
laser-to-target coupling efficiency is impaired by the large divergence of the
electron beam, intrinsic to the laser-plasma interaction. By imposing a
longitudinal 600T laser-driven magnetic-field, our experimental results show
guided >10MA-current of MeV-electrons in solid matter. Due to the applied
magnetic field, the transported energy-density and the peak background electron
temperature at the 60micron-thick targets rear surface rise by factors 5,
resulting from unprecedentedly efficient guiding of relativistic electron
currents.
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We investigated the main prompt and afterglow emission parameters of
gamma-ray bursts detected by the Burst Alert Telescope (BAT) and X-Ray
Telescope installed on the Swift satellite. Our aim was to look for differences
or connections between the different types of gamma-ray bursts, so we compared
the BAT fluences, 1-sec peak photon fluxes, photon indices, XRT early fluxes,
initial temporal decay and spectral indices. We found that there might be a
connection between the XRT initial decay index and XRT early flux/BAT photon
index. Using statistical tools we also determined that beside the duration and
hardness ratios, the means of the \gamma- and X-ray--fluences and the
\gamma-ray photon index differ significantly between the three types of bursts.
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The splitting processes of bremsstrahlung and pair production in a medium are
coherent over large distances in the very high energy limit, which leads to a
suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. In this paper,
we continue analysis of the case when the coherence lengths of two consecutive
splitting processes overlap (which is important for understanding corrections
to standard treatments of the LPM effect in QCD), avoiding soft-gluon
approximations. In particular, this paper analyzes the subtle problem of how to
precisely separate overlapping double splitting (e.g.\ overlapping double
bremsstrahlung) from the case of consecutive, independent bremsstrahlung (which
is the case that would be implemented in a Monte Carlo simulation based solely
on single splitting rates). As an example of the method, we consider the rate
of real double gluon bremsstrahlung from an initial gluon with various
simplifying assumptions (thick media; $\hat q$ approximation; large $N_c$; and
neglect for the moment of processes involving 4-gluon vertices) and explicitly
compute the correction $\Delta\,d\Gamma/dx\,dy$ due to overlapping formation
times.
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The Super-Scaling Approach (SuSA) model, based on the analogies between
electron and neutrino interactions with nuclei, is reviewed and its application
to the description of neutrino-nucleus scattering is presented. The
contribution of both one- and two-body relativistic currents is considered. A
selection of results is presented where theoretical predictions are compared
with cross section measurements from the main ongoing neutrino oscillation
experiments.
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Visual task adaptation has been demonstrated to be effective in adapting
pre-trained Vision Transformers (ViTs) to general downstream visual tasks using
specialized learnable layers or tokens. However, there is yet a large-scale
benchmark to fully explore the effect of visual task adaptation on the
realistic and important medical domain, particularly across diverse medical
visual modalities, such as color images, X-ray, and CT. To close this gap, we
present Med-VTAB, a large-scale Medical Visual Task Adaptation Benchmark
consisting of 1.68 million medical images for diverse organs, modalities, and
adaptation approaches. Based on Med-VTAB, we explore the scaling law of medical
prompt tuning concerning tunable parameters and the generalizability of medical
visual adaptation using non-medical/medical pre-train weights. Besides, we
study the impact of patient ID out-of-distribution on medical visual
adaptation, which is a real and challenging scenario. Furthermore, results from
Med-VTAB indicate that a single pre-trained model falls short in medical task
adaptation. Therefore, we introduce GMoE-Adapter, a novel method that combines
medical and general pre-training weights through a gated mixture-of-experts
adapter, achieving state-of-the-art results in medical visual task adaptation.
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A selection of recent heavy-flavor results from OPAL using the LEP1 data
sample are presented. The average polarization of b baryons in hadronic Z^0
decay has been measured to be -0.56^{+0.20}_{-0.13} (stat.) +- 0.09(syst.)
using semileptonic decays of Lambda_b baryons. A search has been conducted for
the radially excited D*' and has produced a 95% CL upper limit on its
production of f(Z^0 -> D*'+-(2629))xBr(D*'+- -> D*+- pi+ pi-) < 2.1x10^{-3}.
Finally, the measurement of the product branching ratio $f(b ->
Lambda_b)xBr(Lambda_b -> Lambda X)= (2.67 +- 0.38 (stat)
^{+0.67}_{-0.60}(syst.))% has been made. This measurement, along with an
earlier measurement of the product branching ratio f(b -> Lambda_b)xBr(Lambda_b
-> Lambda l X), has been used to compute an updated R_{Lambda l} = Br(Lambda_b
-> Lambda l X)/Br(Lambda_b -> \Lambda X)= (8.0 +- 1.2 (stat.) +- 0.9 (syst.))%,
consistent with the expected low semileptonic branching fraction of the
Lambda_b inferred from its short lifetime compared to the other b hadrons.
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We constrain the slope of the star formation rate ($\log\Psi$) to stellar
mass ($\log\mathrm{M_{\star}}$) relation down to
$\log(\mathrm{M_{\star}/M_{\odot}})=8.4$
($\log(\mathrm{M_{\star}/M_{\odot}})=9.2$) at $z=0.5$ ($z=2.5$) with a
mass-complete sample of 39,106 star-forming galaxies selected from the 3D-HST
photometric catalogs, using deep photometry in the CANDELS fields. For the
first time, we find that the slope is dependent on stellar mass, such that it
is steeper at low masses ($\log\mathrm{\Psi}\propto\log\mathrm{M_{\star}}$)
than at high masses
($\log\mathrm{\Psi}\propto(0.3-0.6)\log\mathrm{M_{\star}}$). These steeper low
mass slopes are found for three different star formation indicators: the
combination of the ultraviolet (UV) and infrared (IR), calibrated from a
stacking analysis of Spitzer/MIPS 24$\mu$m imaging; $\beta$-corrected UV SFRs;
and H$\alpha$ SFRs. The normalization of the sequence evolves differently in
distinct mass regimes as well: for galaxies less massive than
$\log(\mathrm{M_{\star}/M_{\odot}})<10$ the specific SFR
($\Psi/\mathrm{M_{\star}}$) is observed to be roughly self-similar with
$\Psi/\mathrm{M_{\star}}\propto(1+z)^{1.9}$, whereas more massive galaxies show
a stronger evolution with $\Psi/\mathrm{M_{\star}}\propto(1+z)^{2.2-3.5}$ for
$\log(\mathrm{M_{\star}/M_{\odot}})=10.2-11.2$. The fact that we find a steep
slope of the star formation sequence for the lower mass galaxies will help
reconcile theoretical galaxy formation models with the observations. The
results of this study support the analytical conclusions of Leja et al. (2014).
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The stability and convergence rate of Olver's collocation method for the
numerical solution of Riemann-Hilbert problems (RHPs) is known to depend very
sensitively on the particular choice of contours used as data of the RHP. By
manually performing contour deformations that proved to be successful in the
asymptotic analysis of RHPs, such as the method of nonlinear steepest descent,
the numerical method can basically be preconditioned, making it asymptotically
stable. In this paper, however, we will show that most of these preconditioning
deformations, including lensing, can be addressed in an automatic, completely
algorithmic fashion that would turn the numerical method into a black-box
solver. To this end, the preconditioning of RHPs is recast as a discrete,
graph-based optimization problem: the deformed contours are obtained as a
system of shortest paths within a planar graph weighted by the relative
strength of the jump matrices. The algorithm is illustrated for the RHP
representing the Painlev\'e II transcendents.
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This work examines the accuracy and precision of X-ray absorption spectra
computed with a multireference approach that combines generalized active space
(GAS) references with the driven similarity renormalization group (DSRG). We
employ the X-ray absorption benchmark of organic molecules (XABOOM) set,
consisting of 116 transitions from mostly organic molecules [T. Fransson et
al., J. Chem. Theory Comput. 17, 1618 (2021)]. Several approximations to a
full-valence active space are examined and benchmarked. Absolute excitation
energies and intensities computed with the GAS-DSRG truncated to second-order
in perturbation theory are found to systematically underestimate experimental
and reference theoretical values. Third-order perturbative corrections
significantly improve the accuracy of GAS-DSRG absolute excitation energies,
bringing the mean absolute deviation from experimental values down to 0.32 eV.
The ozone molecule and glyoxylic acid are particularly challenging for
second-order perturbation theory and are examined in detail to assess the
importance of active space truncation and intruder states.
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Uncertainty quantification in forecasting represents a topic of great
importance in energy trading, as understanding the status of the energy market
would enable traders to directly evaluate the impact of their own offers/bids.
To this end, we propose a scalable procedure that outputs closed-form
simultaneous prediction bands for multivariate functional response variables in
a time series setting, which is able to guarantee performance bounds in terms
of unconditional coverage and asymptotic exactness, both under some conditions.
After evaluating its performance on synthetic data, the method is used to build
multivariate prediction bands for daily demand and offer curves in the Italian
gas market.
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We use projector Quantum Monte-Carlo methods to study the $S_{\rm tot}=1/2$
doublet ground states of two dimensional $S=1/2$ antiferromagnets on a $L
\times L$ square lattice with an odd number of sites $N_{\rm tot}=L^2$. We
compute the ground state spin texture $\Phi^z(\vec{r}) =
<S^z(\vec{r})>_{\uparrow}$ in $|G>_{\uparrow}$, the $S^z_{\rm tot}=1/2$
component of this doublet, and investigate the relationship between $n^z$, the
thermodynamic limit of the staggered component of this ground state spin
texture, and $m$, the thermodynamic limit of the magnitude of the staggered
magnetization vector of the same system in the singlet ground state that
obtains for even $N_{\rm tot}$. We find a univeral relationship between the
two, that is independent of the microscopic details of the lattice level
Hamiltonian and can be well approximated by a polynomial interpolation formula:
$n^z \approx (1/3 - \frac{a}{2} -\frac{b}{4}) m + am^2+bm^3$, with $a \approx
0.288$ and $b\approx -0.306$. We also find that the full spin texture
$\Phi^z(\vec{r})$ is itself dominated by Fourier modes near the
antiferromagnetic wavevector in a universal way. On the analytical side, we
explore this question using spin-wave theory, a simple mean field model written
in terms of the total spin of each sublattice, and a rotor model for the
dynamics of $\vec{n}$. We find that spin-wave theory reproduces this
universality of $\Phi^z(\vec{r})$ and gives $n^z = (1-\alpha -\beta/S)m +
(\alpha/S)m^2 +{\mathcal O}(S^{-2})$ with $\alpha \approx 0.013$ and $\beta
\approx 1.003$ for spin-$S$ antiferromagnets, while the sublattice-spin mean
field theory and the rotor model both give $n^z = 1/3 m$ for $S=1/2$
antiferromagnets. We argue that this latter relationship becomes asymptotically
exact in the limit of infinitely long-range {\em unfrustrated} exchange
interactions.
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Offline software using TCP/IP sockets to distribute particle physics events
to multiple UNIX/RISC workstations is described. A modular, building block
approach was taken, which allowed tailoring to solve specific tasks efficiently
and simply as they arose. The modest, initial cost was having to learn about
sockets for interprocess communication. This multiprocessor management software
has been used to control the reconstruction of eight billion raw data events
from Fermilab Experiment E791.
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We assess the ionising effect of low energy protostellar cosmic rays in
protoplanetary disks around a young solar mass star for a wide range of disk
parameters. We assume a source of low energy cosmic rays located close to the
young star which travel diffusively through the protoplanetary disk. We use
observationally inferred values from nearby star-forming regions for the total
disk mass and the radial density profile. We investigate the influence of
varying the disk mass within the observed scatter for a solar mass star. We
find that for a large range of disk masses and density profiles that
protoplanetary disks are "optically thin" to low energy ($\sim$3 GeV) cosmic
rays. At $R\sim10$au, for all of the disks that we consider
($M_\mathrm{disk}=6.0\times10^{-4} - 2.4\times 10^{-2}M_\odot$), the ionisation
rate due to low energy stellar cosmic rays is larger than that expected from
unmodulated galactic cosmic rays. This is in contrast to our previous results
which assumed a much denser disk which may be appropriate for a more embedded
source. At $R\sim70$au, the ionisation rate due to stellar cosmic rays
dominates in $\sim$50% of the disks. These are the less massive disks with less
steep density profiles. At this radius there is at least an order of magnitude
difference in the ionisation rate between the least and most massive disk that
we consider. Our results indicate, for a wide range of disk masses, that low
energy stellar cosmic rays provide an important source of ionisation at the
disk midplane at large radii ($\sim$70au).
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Formula for the nth prime using elementary arithmetical functions based in a
previous formula changing the characteristic function of prime numbers.
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We report inclusive and exclusive measurements for $\chi_{c1}$ and
$\chi_{c2}$ production in $B$ decays. We measure $\mathcal{B}(B \to \chi_{c1}
X)$= $(3.03 \pm 0.05(\mbox{stat}) \pm 0.24(\mbox{syst})) \times 10^{-3}$ and
$\mathcal{B}(B \to \chi_{c2} X)$= $(0.70 \pm 0.06(\mbox{stat}) \pm
0.10(\mbox{syst})) \times 10^{-3}$. For the first time, $\chi_{c2}$ production
in exclusive $B$ decays in the modes $B^0 \to \chi_{c2}\pi^- K^+$ and $B^+ \to
\chi_{c2} \pi^+ \pi^- K^+$ has been observed, along with first evidence for the
$B^+ \to \chi_{c2} \pi^+ K_S^0$ decay mode. For $\chi_{c1}$ production, we
report the first observation in the $B^+ \to \chi_{c1} \pi^+ \pi^- K^+$, $B^0
\to \chi_{c1} \pi^+ \pi^- K_S^0$ and $B^0 \to \chi_{c1} \pi^0 \pi^- K^+$ decay
modes. Using these decay modes, we observe a difference in the production
mechanism of $\chi_{c2}$ in comparison to $\chi_{c1}$ in $B$ decays. In
addition, we report searches for $X(3872)$ and $\chi_{c1}(2P)$ in the $B^+ \to
(\chi_{c1} \pi^+ \pi^-) K^+$ decay mode. The reported results use $772 \times
10^{6}$ $B\overline{B}$ events collected at the $\Upsilon(4S)$ resonance with
the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.
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For every $\theta\in(0,\pi)$, we construct a 3D steady gradient Ricci soliton
whose asymptotic cone is a sector with angle $\theta$, which is a called 3D
flying wing.
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Consider a dynamical system given by a planar differential equation, which
exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is
known that under random perturbations, the distribution of locations where the
system's first exit from the interior of the unstable orbit occurs, typically
displays the phenomenon of cycling: The distribution of first-exit locations is
translated along the unstable periodic orbit proportionally to the logarithm of
the noise intensity as the noise intensity goes to zero. We show that for a
large class of such systems, the cycling profile is given, up to a
model-dependent change of coordinates, by a universal function given by a
periodicised Gumbel distribution. Our techniques combine action-functional or
large-deviation results with properties of random Poincar\'e maps described by
continuous-space discrete-time Markov chains.
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I show how an empirical variability - luminosity relationship for prompt
gamma-ray bursts, first proposed by Fenimore and Ramirez-Ruiz, can be
understood as a special-relativistic beaming effect in the ``cannonball model''
of Dar and De R\'ujula. In this scenario the variability is a measure of the
direction of propagation and the Lorentz factor of the cannonball on which in
turn the apparent luminosity of the prompt GRB depends sensitively. The
observed absence of cosmological time dilation in the ``aligned peak test'' -
when using redshifts derived with this relation - is also explained. The most
direct evidence in favour of the cannonball model presented here is its correct
description for the observed relation between narrow-spike width and amplitude
within a given GRB. There seems to be an indication for cosmological time
dilation in the total duration of GRBs, as expected in the cannonball model.
Quantitative predictions for the luminosity function of GRBs and the
``spectral-lag luminosity relation'' are given.
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Definitions of non-relativistic conformal transformations are considered both
in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann
geometrical frameworks. The symmetry groups that come into play are exemplified
by the cosmological, and also the Newton-Hooke solutions of Newton's
gravitational field equations. It is shown, in particular, that the maximal
symmetry group of the standard cosmological model is isomorphic to the
13-dimensional conformal-Newton-Cartan group whose conformal-Bargmann extension
is explicitly worked out. Attention is drawn to the appearance of independent
space and time dilations, in contrast with the Schr{\"o}dinger group or the
Conformal Galilei Algebra.
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In these lectures the properties of magnetically charged black holes are
described. In addition to the standard Reissner-N\"ordstrom solution, there are
new types of static black holes that arise in theories containing electrically
charged massive vector mesons. These latter solutions have nontrivial matter
fields outside the horizon; i.e., they are black holes with hair. While the
solutions carrying unit magnetic charge are spherically symmetric, those with
more than two units of magnetic charge are not even axially symmetric. These
thus provide the first example of time-independent black hole solutions that
have no rotational symmetry.
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Recently, $L_1$ regularization have been attracted extensive attention and
successfully applied in mean-variance portfolio selection for promoting
out-of-sample properties and decreasing transaction costs. However, $L_1$
regularization approach is ineffective in promoting sparsity and selecting
regularization parameter on index tracking with the budget and no-short selling
constraints, since the 1-norm of the asset weights will have a constant value
of one. Our recent research on $L_{1/2}$ regularization has found that the half
thresholding algorithm with optimal regularization parameter setting strategy
is the fast solver of $L_{1/2}$ regularization, which can provide the more
sparse solution. In this paper we apply $L_{1/2}$ regularization method to
stock index tracking and establish a new sparse index tracking model. A hybrid
half thresholding algorithm is proposed for solving the model. Empirical tests
of model and algorithm are carried out on the eight data sets from OR-library.
The optimal tracking portfolio obtained from the new model and algorithm has
lower out-of-sample prediction error and consistency both in-sample and
out-of-sample. Moreover, since the automatic regularization parameters are
selected for the fixed number of optimal portfolio, our algorithm is a fast
solver, especially for the large scale problem.
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QCD contributions to the $b \to u \ell^- \bar{\nu}_\ell$ decay rate, which
are known to two-loop order in the $\bar{MS}$ scheme, exhibit sufficient
dependence on the renormalization mass $\mu$ to compromise phenomenological
predictions for inclusive semileptonic $B \to X_u$ processes. Such scale
dependence is ameliorated by the renormalization-group (RG) extraction and
summation of all leading and RG-accessible subleading logarithms occurring
subsequent to two-loop order in the perturbative series. This optimal
RG-improvement of the known portion of the perturbative series virtually
eliminates $\mu$-dependence as a source of theoretical uncertainty in the
predicted semileptonic $B \to X_u$ inclusive rate.
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Cross-Project-Defect Prediction as a sub-topic of defect prediction in
general has become a popular topic in research. In this article, we present a
systematic mapping study with the focus on CPDP, for which we found 50
publications. We summarize the approaches presented by each publication and
discuss the case study setups and results. We discovered a great amount of
heterogeneity in the way case studies are conducted, because of differences in
the data sets, classifiers, performance metrics, and baseline comparisons used.
Due to this, we could not compare the results of our review on a qualitative
basis, i.e., determine which approaches perform best for CPDP.
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We develop a matrix bordering technique that can be applied to an irreducible
spectrally arbitrary sign pattern to construct a higher order spectrally
arbitrary sign pattern. This technique generalizes a recently developed
triangle extension method. We describe recursive constructions of spectrally
arbitrary patterns using our bordering technique, and show that a slight
variation of this technique can be used to construct inertially arbitrary sign
patterns.
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Subsets and Splits