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@@ -0,0 +1,900 @@
+INTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       29 
+Virtual Reality Photo-based Tours for Teaching Filipino Vocabulary in an 
+Online Class in Japan: Transitioning into the New Normal 
+ 
+Roberto B. Figueroa Jr.  
+robertojr.figueroa@up.edu.ph 
+University of the Philippines Open University, Philippines 
+ 
+Florinda Amparo Palma Gil  
+floripg@tufs.ac.jp 
+Tokyo University of Foreign Studies, Japan 
+ 
+Hiroshi Taniguchi  
+htaniguchi@up.edu.ph 
+University of the Philippines Open University, Philippines 
+ 
+Joshze Rica Esguerra  
+jlesguerra2@up.edu.ph 
+University of the Philippines Open University, Philippines 
+ 
+Abstract: When educational institutions worldwide scrambled for ways to continue their classes 
+during lockdowns caused by the COVID-19 pandemic, the use of information and communication 
+technology (ICT) for remote teaching has become widely considered to be a potential solution. As 
+universities raced to implement emergency remote teaching (ERT) strategies in Japan, some have 
+explored innovative interventions other than webinar platforms and learning management systems 
+to bridge the gap caused by restricted mobility among teachers and learners. One such innovation is 
+virtual reality (VR). VR has been changing the landscape of higher education because of its ability 
+to "teleport" learners to various places by simulating real-world environments in the virtual world. 
+Some teachers, including the authors of this paper, explored integrating VR into their activities to 
+address issues caused by geographical limitations brought about by the heightened restrictions in 
+2020.  Results were largely encouraging. However, rules started relaxing in the succeeding years as 
+more people got vaccinated. Thus, some fully online classes in Japan shifted to blended learning as 
+they moved toward fully returning to in-person classes prompting educators to modify how they 
+implemented their VR-based interventions. This paper describes how a class of university students 
+in Japan who were taking a Filipino language course experienced a VR-based intervention in 
+blended mode, which was originally prototyped during the peak of the ERT era. Moreover, 
+adjustments and comparisons regarding methodological idiosyncrasies and findings between the 
+fully online iteration and the recently implemented blended one are reported in detail.   
+ 
+Keywords: virtual reality, immersive open pedagogies, immersive learning 
+ 
+INTRODUCTION 
+ 
+Background of the Study 
+ 
+During lockdowns caused by the COVID-19 pandemic, universities raced to implement emergency remote 
+teaching (ERT) strategies in Japan. Some have explored innovative interventions other than webinar platforms and 
+learning management systems to bridge the gap caused by restricted mobility among teachers and learners. One such 
+innovation is virtual reality (VR). VR has been changing the landscape of higher education because of its ability to 
+"teleport" learners to various places by simulating real-world environments in the virtual world. To fill in the gap 
+brought by geographical limitations due to heightened restrictions in 2020, educators at Tokyo University of Foreign 
+Studies (TUFS) explored integrating VR in teaching the Filipino Language to first year Japanese students (Figueroa 
+et al., 2022). 
+
+INTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       30 
+ 
+The Filipino language was first taught in Japan at the Osaka University of Foreign Studies, now Osaka 
+University in 1983 followed by TUFS in 1992 (Laranjo, 2020). These universities offer an entire major course in the 
+Filipino language and Philippine-related courses. Before the pandemic, classes were held using traditional in-person 
+classroom-based or blended pedagogy using a learning management system (LMS). Students were encouraged to join 
+short-term language classes abroad during the long spring and summer vacations or to join one-year student exchange 
+programs with affiliated universities abroad. These programs not only provided a more immersive experience for the 
+learners as they used the language and interacted with the native speakers of the language they were studying, but they 
+also increased their motivation to apply and experience first-hand what they learned inside the classroom. 
+ 
+Therefore, when the short-term visits and student exchange programs were canceled due to the stricter rules 
+at the height of the pandemic in 2020, a photo-based VR tour lessons on Filipino vocabulary at TUFS was created to 
+provide students with an immersive way of learning Filipino language and experience the Filipino culture at the 
+comfort of their homes while being unable to physically visit the Philippines (Figueroa et al., 2022). However, rules 
+started relaxing in 2021 and 2022 when vaccines were introduced. Thus, some fully online classes in Japan shifted to 
+blended learning. The same happened at TUFS. With favorable feedback from students in 2020, the photo-based VR 
+tour lessons on Filipino vocabulary were consequently integrated even in the blended offering of the course in 2021 
+and 2022. 
+ 
+Research Questions  
+ 
+With the new changes, the procedure on how the photo-based VR tour lessons were incorporated into the 
+Filipino Language course at TUFS was revised to fit the course’s evolving context. This paper aims to compare 
+experience and related outcomes between the fully online classes in 2020 and the blended-learning implementation in 
+2022 by answering the following research questions. 
+ 
+1. How different were the satisfaction, presence, and interest felt and experienced by learners between 
+groups who used VR tours and those who did not in each tour in 2022?  
+2. How different were the satisfaction and presence felt by learners who used the VR tour-based lessons 
+between 2020 and 2022? 
+ 
+RESEARCH DESIGN & METHODS 
+ 
+Duration and Nature  of the Study 
+ 
+This longitudinal study compared 2020 and 2022 implementations of VR tour lessons. The lessons in both 2020 
+and 2022 spanned two months. Described as a cognitive innovation, the 2020 pilot of the VR tour lessons followed 
+the design-based research approach where iterative design and implementation cycles were adjusted and modified 
+based on the data collected and analyzed from each cycle.  
+ 
+Context Comparison 
+ 
+The two implementations had slightly different contexts.  Table 1 shows slight nuances and similarities between 
+the 2020 and 2022 implementations including the profile of students and how the classes were conducted. The 
+participants were Japanese university students who were enrolled in the Philippine Studies Program.   
+There were 15 student participants in the 2020 implementation and 12 participants in the 2022 
+implementation. In 2020, all the photo-based VR tour lessons were held online, while the 2022 classes were both held 
+online and during face-to-face classes. In the same year, students were divided into three groups - high immersion 
+group (used VR goggles), moderate immersion group (did not use VR goggles but used the VR tours) and low 
+immersion group (did not use VR goggles and VR tours; only used photo-based PowerPoint tours). In the 2022 
+implementation, the students were only divided into two groups, but both groups were able to experience the photo-
+based VR tours while using VR Goggles and the photo-based tours presented in PowerPoint presentations. 
+ 
+ 
+ 
+ 
+ 
+
+INTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       31 
+Table 1 
+ 
+Contextual Data of the 2020 and 2022 Implementations 
+ 
+Variable 
+    2020 Implementation 
+2021 Implementation 
+Number of Students 
+15  
+12 
+Year Level 
+First Year 
+First Year 
+Mode 
+ Fully Online (Synchronous) 
+Blended (Alternating Online and In-Person) 
+ Activity Groupings 
+ 3 (Immersive Tour, Non Immersive 
+Tour, PowerPoint) 
+2 (Immersive Tour, PowerPoint) 
+ Group Composition 
+Group 1: 5 students 
+Group 2: 5 students 
+Group 3: 5 students 
+Group 1: 6 students 
+Group 2: 6 students  
+ 
+Sequence of Activities 
+ 
+ 
+ 
+Figure 1. Procedural Diagram of the 2020 and 2022 Implementations as Illustrated in Figueroa et al. (2022) 
+ 
+The sequence of activities were the same in both the 2020 and 2021 implementations as shown in  Fig. 1. 
+The procedural diagram was directly lifted from Figueroa et al. (2022).  As illustrated, a survey was given to students 
+at the beginning of the semester before they could experience the VR or PowerPoint presentation tours.  The steps in 
+the darker square represent activities that are conducted in class.  There were six classes conducted in both 
+Only in 2020 
+
+Preparation
+Pre-VR Tour Survey
+Pre-Test
+LESSON
+Implementation
+x 6 times
+(*1)
+Post-Test
+After-classSurvey
+(*1) After each lesson, the teacher
+and
+two
+other
+researchers
+discussed
+and
+wrotedowntheir observations
+Post-semesterSurvey
+Reflection
+Focus Group
+DiscussionsINTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       32 
+implementations, which included a pre-test, the lesson proper that involved the tours,  a post-test, and an after class 
+survey.  At the end of the semester, students were asked to reflect on the whole experience through a post-semester 
+survey and focus group discussions.  The only difference during the 2022 implementation was that there was no more 
+focus group discussion conducted.  
+ 
+Group Configuration 
+Another major difference between the two implementations is the grouping configuration.  Three groups 
+were formed in 2020 (high, medium, and low).  The high immersion group consisted of students who experienced VR 
+tours using their smart phones with VR goggles delivered to their homes.  The medium immersion group consisted of 
+students who experienced VR tours without the VR goggles.  The low immersion group consisted of students who 
+experienced PowerPoint-based tours with the same content as the VR tours.  The grouping was only changed once, 
+after the first lesson where some students reported their smartphones not working with the goggles.  However, in the 
+five succeeding lessons, the groupings and their assigned activities did not change (Figueroa et al., 2022).  In contrast, 
+the implementation in 2022 only involved two groups. As illustrated in Fig. 2, in the first three lessons, Group 1 
+experienced VR tours with goggles (VR Group) while Group 2 experienced PowerPoint-based tours (Non-VR Group). 
+In the second three lessons, Group 2 became the VR group and Group 1 became the Non-VR Group. This was done 
+so that all the students may be able to experience both types of activities.  
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure 2. Group Configuration in 2022 Implementation 
+ 
+Platform Selection for Immersive Open Pedagogical Activities 
+ 
+In this section, we shall describe the platforms used in the two iterations of the study.  Kuula is a web-based 
+software that makes it easy to create 360° virtual tours. The free basic plan allows level correction and retouching of 
+images, while paid plans ranging from 16 to 48 US Dollars per month include audio support, unlimited uploads, 
+unlisted and password-protected tours, custom icons and fonts, and analytics (Kuula, n.d.).  
+  
+A free alternative to Kuula with audio support is StorySpheres, a website created by Grumpy Sailor with the 
+help of Google’s Creative Lab in 2014 (Story Spheres, n.d). A user must upload 1 JPG/JPEG image and at least 1 
+MP3 audio file, with the total size of all files below 15 MB. In addition to having a background sound, audio hotspots 
+can easily be added and positioned using the slider, as shown in Fig. 3. 
+ 
+
+Group 1
+Group 2
+VRTour1withVRGoggles
+PPTTour1
+VR Tour2withVRGoggles
+PPTTour2
+VRTour3withVRGoggles
+PPTTour3
+PPTTour4
+VRTour4withVRGoggles
+PPTTour5
+VR Tour5withVRGoggles
+PPTTour6
+VRTour6withVRGogglesINTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       33 
+ 
+Figure 3. Using and Positioning Hotspots to Play Audio Narrations in Story Spheres 
+  
+ 
+For those with HTML and JavaScript knowledge, A-Frame (https://aframe.io/) is a notable option for more 
+freedom in developing 360° tours. It is a web framework based on top of HTML for building VR experiences with 
+only text-editing software and a web browser needed. When developing a virtual tour, JavaScript can be used to 
+change the image, music, and hotspot locations upon the click of a user. Since it requires coding, it will allow for more 
+freedom and customization in the tours. For example, all paid features in Kuula can be done in A-Frame, with the only 
+limitation being the learning curve. A finished A-Frame project can be deployed to a user’s server for personal or 
+company branding, or online Integrated Development Environments (IDEs) with hosting such as Glitch 
+(https://glitch.com/).  Table 2 shows a comparative summary of the main features of the three platforms presented in 
+this section.  
+ 
+Converting from Kuula to A-Frame 
+ 
+ Kuula was a viable option in the 2020 implementation because of its capability to facilitate rapid prototyping.  
+However, because of the recurring costs of maintaining a paid account, A-Frame was chosen to migrate the developed 
+VR tours for sustainability and was eventually used in the 2022 implementation.  
+The first step was to retrieve the 360° images from Kuula by clicking the Download link at the bottom of the 
+Edit pane and then saving the image. Recognizable faces on all photos were blurred using Adobe Fresco. The 
+narrations had to be recorded using Audacity since the Kuula platform did not allow audio files to be downloaded 
+from its tours. 
+The index page with portals used a 360° panoramic image as the initial source of the <a-sky> element. There 
+were multiple portals, each one an <a-circle> element with its source and the image representing the destination. 
+Behind it is a white <a-circle> to mimic an outline. Since A-Frame does not have support for non-alphanumeric text, 
+Japanese characters were added by importing a Multi-channel Signed Distance Font (MSDF) file that was generated 
+online. 
+ 
+ 
+
+Upload audio
+Uploadoneormoreaudiofiles.
+Audiofilesmustbe:
+..mp3
+Tip:Trylimitingtheaudiodata
+ratetokeepyourfilessmall.
+Onceuploaded,selectafilethenchoose
+thetypeof audioto beeitherbackground
+orhotspot.
+Usethecontrolstoposition the audio
+withinthe sphere.
+Uploadaudio files*
+PositionAudioSnippet
+*requiredfield.
+AudioFileName
+1_2_3.mp3
+J1,2.3.mp3
+X
+Horizontal Angle
+0.117
+OBackground
+OHot Spot
+Vertical Angle
+1.211
+Depth
+74
+15%offileallowance
+NEXTINTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       34 
+Table 2 
+ 
+Comparison of the VR Tour Platforms 
+ 
+Platform 
+Price 
+Features 
+Limitations 
+Kuula 
+Free 
+● Retouch images 
+● Level correction 
+● Private tours 
+● Choose transition type 
+● Add images and hotspots 
+● Hotspots can open video/text 
+cards and URLs 
+● No audio support 
+● Max 100 uploads per month 
+● Max 25 images per batch upload  
+16-20 USD 
+per month 
+● Allows audio files 
+● Walkthrough mode 
+● Unlisted tours 
+● Custom icons and fonts 
+● 360° videos not supported 
+36-48 USD 
+per month 
+● Custom domain 
+● Password-protected tours 
+● Analytics 
+StorySpheres 
+Free 
+● Allows audio files in the 
+background or hotspot 
+● Stitching is not seamless 
+● Up to 15MB total file size 
+● Requires at least 1 audio file 
+● Video files are not supported 
+● Cannot add text 
+A-Frame 
+Free 
+● Allows for more freedom and 
+customization 
+● 360° videos supported 
+● Can host on own or cloud servers 
+● Requires coding 
+● Learning curve 
+ 
+When a user hovers on a portal, there will be a preview (see Fig. 4) by displaying the name of the place and 
+temporarily changing the <a-sky> source with the use of JavaScript. The animation component was utilized to make 
+the transition smoother. Clicking a portal will redirect the browser to the tour of that location. Fig. 5 shows the interface 
+of the tour when entering VR mode on a mobile browser. 
+ 
+ 
+Figure 4. The User Interface Before and After Hovering on a Portal 
+
+Aurora ForestINTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       35 
+ 
+Figure 5. Viewing the Tour on a VR-Ready Mobile Phone 
+ 
+Each tour includes multiple narrations that will play when its corresponding audio button is clicked. Audio 
+buttons are <a-image> hotspots that are mapped with the help of the A-Frame Inspector (see Fig. 6), by dragging it to 
+the corresponding position and copying the coordinates to the position attribute in the code. The look-at component is 
+used to easily change the angle so that it will always face the user. When the button is clicked, the script will change 
+the sound attribute of the a-sky to the narration and toggle the player. 
+ 
+Figure 6. Getting the Position Coordinates in A-Frame Inspector 
+ 
+While the created tours are on separate web pages for easier sharing and access, another approach would be to 
+use a single webpage to host all tours. This can be done by using JavaScript to change the source of the <a-sky> tag 
+and the coordinates and identifiers of each audio hotspot with each click on the portal. However, since the tours were 
+non-contiguous and were presented separately, they were developed as separate pages.  
+
+class
+rayclick
+position
+63.49.000-2.000
+rotation
+74.8783.107477
+1.Bayani
+scale
+6.0006.0001.000
+2
+Matapang
+visible
+3.Rebolusyunaryo
+mixins
+Addmixin.
+COMPONENTS
+Addcomponent.
+GEOMETRY
+LOOK-AT
+MATERIAL
+PLAY-MUSIC
+心INTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       36 
+Data Collection 
+ 
+The data used in this study include the results of six after-class surveys in the (1) 2020 implementation and 
+the (2) data collected during the photo-based VR tour lessons held in the first semester spanning from May to June in 
+2022. The results of the pre-test and post-test quizzes were not included as they were not included in the scope of the 
+study.  All questionnaires contain both Likert-type items and open-ended questions. Data (1) was analyzed to answer 
+RQ1 while data (1) and (2) were compared to answer RQ2. Fig. 7 was a table lifted from an appendix of the previous 
+publication (Figueroa et al., 2022), which lists the after-class survey items used in both the 2020 and 2022 
+implementations.  Among these, only items two, four, and 12 were used for this study.  Item two, which was boxed in 
+red in the figure, represented satisfaction. Item four, which was boxed in blue, represented interest and item 12, which 
+was boxed in green, represented presence.  All the items were translated in the Japanese language.  Face validity and 
+language expert consultation were conducted for the three items.  While there was no other validity and reliability 
+tests conducted for the interest and satisfaction items, the presence item was a slightly modified version of the single-
+item measure proposed and validated by Bouchard et al. (2004).  
+ 
+ 
+Figure 7. After-class Survey Questions in the 2020 and 2022 Implementations 
+Data Analysis  
+ 
+To answer the first research question, summary statistics were generated for satisfaction, presence, and 
+interest among students of the two groups in each of the six lessons to see whether there are trends regarding 
+differences. Statistical significance was determined by performing the Mann-Whitney U test in each lesson using the 
+stats library in R (R Core Team, 2012).  To answer the second question, summary statistics and boxplots were 
+
+After-classSurveyQuestions
+8.少了一体上、今俊今日語巢使确率法
+思？
+1.名前/二岁夕木一么(English:Name/Nickname
+English: How much do you see yourself using the Filipino words you
+learned today in the future after the tour?
+低(Lowest)高(Highest)
+1 ---2--- 3 --- 4 --- 5--- 6--- 7--- 8--- 9--- 10
+2.今回の体晚评俩？龙
+9VRの中良感
+English: How would you rate your experience?
+English: What were the positive feelings you had during the VR tour?
+良（Lowest））良（Highest）
+1--- 2--- 3--- 4--- 5--- 6--- 7--- 8 ---9--- 10
+3.周の俩の理由述龙
+10.VRの感
+English:What'sthereasonforvourratinginnumber2?
+English: What were the negativefeelings youhad during the VRtour?
+4.一自体面百感？
+11.一避龙English:ChooseOne
+English: How interested were you in the actual experience?
+VR中、の真の感
+面百(Lowest)面白(Highest)
+English: During the VR Tour, I felt like I was just looking at a photo.
+1---2---3---4---5---6---7.-8---9---10
+本当体の感
+English: I felt like I was in an actual tour.
+12.の享真、一本当体
+の感？
+来L龙加？
+English:Howmuch didyoufeel that youwereinthetourandnotjust
+English: How much were you interested in the lesson's content (new
+lookingataphoto?
+words)?
+感(Lowest)感(Highest
+1---2--3---4---5---6--7.-8---9---10
+1--2---3---4---5--6-7..-8---9--- 10
+6.味持部分使？当法の心遵人下龙去
+12今俊の授の一体思
+来？世走思？
+English: What were the most interesting parts?
+English: Would you like to do more of these tours in future online
+classes? Why or why not?
+7.の少了一体上、为老自身将来今日暂无
+13.老の他今回の体记阅寸多文下、提案、主老实尚等机
+语の语使の想像下享？の場面
+英语使思？
+English: Please share other comments, suggestions, or questions
+English: Do you see yourself using the Filipino words you learned
+regarding the whole experience.
+today in the future after the tour? If yes, how?INTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       37 
+generated for satisfaction, presence, and interest among students of lessons two through five in 2020 and 2022.  
+Statistical significance per lesson was determined by performing the Mann-Whitney U. 
+ 
+RESULTS 
+ 
+RQ 1: How different were the satisfaction, presence, and interest felt and experienced by learners between 
+groups who used VR tours and those who did not in each tour in 2022?  
+ 
+Lesson 1 
+ 
+Table 3 compares the medians of the satisfaction, presence, and interest ratings of students in the VR and 
+non-VR groups in lesson 1. 
+ 
+Table 3 
+ 
+Comparison of Medians of Student Ratings between 2 Groups in Lesson 1 
+Group 
+Satisfaction 
+Presence 
+Interest 
+VR  (1)  
+10 
+9.5 
+10 
+Non-VR (2)  
+8 
+6 
+7.5 
+  
+The Mann Whitney U test indicated that satisfaction ratings were greater for students in the VR group (Mdn 
+=10) than those in the non-VR group (Mdn = 8) ,U = 35, p = .006.  It also indicated that presence ratings were greater 
+for students in the VR group (Mdn = 9.5) than those in the non-VR group (Mdn = 6), U = 36, p =.004.  However, 
+interest ratings were not statistically significantly different between the two groups.  
+ 
+Lesson 2 
+ 
+Table 4 compares the medians of the satisfaction, presence, and interest ratings of students in the VR and 
+non-VR groups in lesson 2. 
+ 
+Table 4 
+ 
+Comparison of Medians of Student Ratings between 2 Groups in Lesson 2 
+Group 
+Satisfaction 
+Presence 
+Interest 
+VR (1) 
+10 
+9.5 
+10 
+Non-VR (2) 
+8 
+6 
+7.5 
+  
+ 
+The Mann Whitney U test indicated that none of the three variables were statistically different between the 
+two groups.  
+ 
+Lesson 3 
+ 
+Table 5 compares the medians of the satisfaction, presence, and interest ratings of students in the VR and 
+non-VR groups in lesson 3. 
+ 
+Table 5 
+ 
+Comparison of Medians of Student Ratings between 2 Groups in Lesson 3 
+Group 
+Satisfaction 
+Presence 
+Interest 
+VR (1) 
+10 
+10 
+10 
+Non-VR (2) 
+8 
+7 
+8 
+  
+ 
+The Mann Whitney U test indicated that presence ratings were greater for students in the VR group (Mdn 
+=10) than those in the non-VR group (Mdn = 7) ,U = 31, p = .018.   However, satisfaction and interest ratings were 
+not statistically significantly different between the two groups.  
+
+INTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       38 
+Lesson 4 
+ 
+Table 6 compares the medians of the satisfaction, presence, and interest ratings of students in the VR and 
+non-VR groups in lesson 4. 
+ 
+Table 6 
+ 
+Comparison of Medians of Student Ratings between 2 Groups in Lesson 4 
+Group 
+Satisfaction 
+Presence 
+Interest 
+VR (2) 
+9.5 
+9.5 
+9 
+Non-VR (1) 
+10 
+10 
+10 
+  
+ 
+The Mann Whitney U test indicated that none of the three variables were statistically different between the 
+two groups.  
+ 
+Lesson 5 
+ 
+Table 7 compares the medians of the satisfaction, presence, and interest ratings of students in the VR and 
+non-VR groups in lesson 5. 
+ 
+Table 7 
+ 
+Comparison of Medians of Student Ratings between 2 Groups in Lesson 5 
+Group 
+Satisfaction 
+Presence 
+Interest 
+VR (2) 
+10 
+10 
+10 
+Non-VR (1) 
+10 
+10 
+10 
+  
+ 
+The Mann Whitney U test indicated that none of the three variables were statistically different between the 
+two groups. 
+ 
+Lesson 6 
+ 
+Table 8 compares the medians of the satisfaction, presence, and interest ratings of students in the VR and 
+non-VR groups in lesson 6. 
+ 
+Table 8 
+ 
+Comparison of Medians of Student Ratings between 2 Groups in Lesson 6 
+Group 
+Satisfaction 
+Presence 
+Interest 
+VR (2) 
+8.5 
+8.5 
+8 
+Non-VR (1)  
+10 
+10 
+10 
+  
+ 
+`The Mann Whitney U test indicated that none of the three variables were statistically different between the 
+two groups. 
+ 
+RQ 2: How different were the learning outcomes and attitudes of learners who used the VR tour-based lessons 
+between 2020 and 2022? 
+ 
+ 
+Fig. 8 compares 2020 and 2022 boxplots of satisfaction, presence, and interest ratings that were aggregated 
+across lessons two to six.  It could be seen that the ratings of satisfaction, presence, and interest in 2022 were generally 
+higher than the ratings of the three variables in 2020.   
+ 
+The Mann Whitney U test conducted per lesson confirmed this trend in the second and third lessons.  In the 
+second lesson, there was a statistically significant difference in satisfaction ratings between 2020 (Mdn = 9) and 2022 
+(Mdn = 10), U = 7.5, p = .02. In the same lesson, there is a statistically significant difference in presence ratings 
+between 2020 (Mdn = 8) and 2022 (Mdn = 10), U = 9.5, p = .05.   
+
+INTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       39 
+In the third lesson, there was a statistically significant difference in satisfaction ratings between 2020 (Mdn 
+= 8) and 2022 (Mdn = 10), U = 7.5, p = .02. In the same lesson, there is a statistically significant difference in presence 
+ratings between 2020 (Mdn = 8) and 2022 (Mdn = 10), U = 9.5, p = .003.  None of the other lessons had statistically 
+significant differences in presence and satisfaction ratings.  Furthermore, there were no statistically significant 
+differences in interest ratings between the two-year offerings.  
+ 
+ 
+Figure 8. Comparative Boxplots of Aggregated Ratings of Satisfaction, Presence, and Interest in 2020 and 2022 
+ 
+ 
+DISCUSSION 
+ 
+The findings revealed very enlightening trends in similarities and differences between the activities 
+implemented in 2020 and 2022.    
+ 
+The Novelty of VR Tours 
+The statistically significant difference in presence, interest, and satisfaction between VR and Non-VR Groups 
+in the first lesson of the 2022 implementation showed that the VR tours piqued the students' interest, provided more 
+spatial presence, and gave them a better experience than in the PowerPoint-based tours. However, this was not evident 
+in the succeeding lessons.  This may be explained by novelty, which was found to increase the interest among 
+participants and viewed by motivational researchers as one of its dimensions or components (Deci, 1992; Sun et al., 
+2008).  However, novelty wanes through time (Spielberger & Starr, 1994). This may have happened in the succeeding 
+lessons.  Unlike in the 2020 implementation where data supported interest in the succeeding lessons, data which could 
+support this trend in the 2022 implementation was yet to be analyzed, thereby posing a significant limitation of this 
+study. However, the findings of this study highlighted that a VR tour is a practical activity for gaining attention, which 
+
+Satisfaction in 2020 and 2022
+Presence in 2020 and 2022
+Interest in 2020 and 2022
+0
+0
+16
+16
+1
+1
+9
+-
+1
+T8
+8
+一
+1
+ satisfaction
+8
+1
+interest
+-
+1
+1
+1
+一
+7-
+1
+1
+1
+1
+1
+1
+1
+1
+6i
+1
+1
+1
+1
+7-
+1
+1
+1
+1
+1
+6
+1
+/
+1
+1
+-
+51
+1
+1
+一
+1
+1
+1
+1
+1
+1
+19
+L
+一
+51
+4-
+1
+1
+1
+1
+1
+1
+4
+。
+31
+51
+1
+1
+1
+2020
+2022
+2020
+2022
+2020
+2022
+year
+year
+yearINTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       40 
+was recommended as an initial step in effective teaching according to Gagne’s nine events of instruction (Schunk, 
+2012). 
+ 
+In-Person Orientation Benefits 
+Another revelation was that 2022 implementation of the VR-based activities in blended mode yielded higher 
+presence and satisfaction ratings than that in the purely online mode in 2020.  These findings showed the advantage 
+of conducting VR-based activities in blended settings compared to purely remote ones. The learning curve and 
+technical challenges in training students to use a VR device in a purely remote environment may have blunted the 
+motivational benefits that could have been obtained from using these novel technologies. The blended nature of the 
+classes in 2022 enabled the teacher to support students in using the VR devices in person.  They could still access it 
+during the online sessions, but they were already well acquainted with the technology through the in-person 
+orientation.  The importance of ensuring that students are comfortable in using an instructional technology has been 
+echoed by studies in technology readiness (Hubbard, 2013; Ngampornchai & Adams, 2016; Warden et al., 2022) .  
+Therefore, having an initial in-person session to help students get acquainted with VR devices and applications for 
+VR-based learning activities even in purely online learning settings would be extremely helpful as the technology is 
+still not that common.  
+The piloting and prototyping nature of the implementation in 2020 could also be attributed for this 
+observation.  During that time, many of the problems encountered by students were still unknown and had to be 
+discovered. Those problems have already been addressed in the 2022 implementation. This confirms the practical 
+benefits of employing a design-based research approach in 2020, which was characterized by iterative cycles of design, 
+enactment, analysis, and redesign in a single setting over a period (Design-Based Research Collective [DBRC], 2003).   
+ 
+CONCLUSION  
+ 
+With many of the traditional universities embracing blended learning after implementing fully online classes 
+during the height of the COVID-19 pandemic, opportunities for improving students' experience in technology-
+enhanced learning can be explored.  In this paper, the findings from a study involving a method of learning a foreign 
+language in a remote teaching context through VR tours in 2020 and changes in the 2022 implementation were 
+presented. While limitations persist regarding generalizability and the need for qualitative data that could support 
+earlier findings, the study may provide practical insights regarding the advantage of in-person technical training and 
+the benefits of piloting a method using the design-based research approach.  
+REFERENCES 
+A-Frame. (n.d.). Retrieved September 2, 2022, from https://aframe.io/ 
+Bouchard, S., Robillard, G., St-Jacques, J., Dumoulin, S., Patry, M., & Renaud, P. (2004, November). Reliability and 
+validity of a single-item measure of presence in VR [Conference paper]. The 3rd IEEE International 
+Workshop on Haptic, Audio and Visual Environments and their Applications, Ottawa, ON, Canada. 
+Deci, E. L. (1992). The relation of interest to the motivation of behavior: A self-determination theory perspective. In 
+K.A. Renninger, S. Hidi, & A. Krapp (Eds.), The role of interest in learning and development (pp. 43-70). 
+Lawrence Erlbaum Associates. 
+Design-Based Research Collective. (2003). Designbased research: An emerging paradigm for educational inquiry. 
+Educational Researcher, 32(1), 5–8. 
+Figueroa, R. B., Palma Gil, F. A., & Taniguchi, H. (2022). Piloting virtual reality photo-based tours among students 
+of a Filipino language class: A case of emergency remote teaching in Japan. Avant: Trends in 
+Interdisciplinary Studies, 13(1). doi: 10.26913/avant.202208 
+Glitch. (n.d.). Retrieved September 2, 2022, from https://glitch.com/ 
+Hubbard, P. (2013). Making a case for learner training in technology enhanced language learning 
+environments. Calico Journal, 30(2), 163-178. 
+Kuula. (n.d.). Pricing. Retrieved September 2, 2022, from https://kuula.co/  
+
+INTERNATIONAL JOURNAL IN INFORMATION TECHNOLOGY IN  
+GOVERNANCE, EDUCATION AND BUSINESS 
+Vol. 4, No. 1, 2022  
+ISSN 2686-0694 (Print) 
+e-ISSN 2721-0030 (Online) 
+ 
+IJITGEB, Vol. 4 No.1, 2022, pp. 29-41, ISSN 2686-0694, e-ISSN 2721-0030                                                                                                       41 
+Laranjo, R. O. (2020). Mapping Philippine studies in Northeast Asia: A SWOT analysis of Southeast Asian Studies 
+programs from China, Japan and Korea. SUVANNABHUMI Multi-disciplinary Journal of Southeast Asian 
+Studies, 111-130. 
+Ngampornchai, A., & Adams, J. (2016). Students’ acceptance and readiness for E-learning in Northeastern 
+Thailand. International Journal of Educational Technology in Higher Education, 13(1), 1-13. 
+R Core Team. (2012). R: A language and environment for statistical computing. R Foundation for Statistical 
+Computing. Vienna, Austria. 
+Schunk, D. (2012). Learning theories an educational perspective (6th ed.). Pearson Education. 
+Spielberger, C. D., & Starr, L. M. (1994). Curiosity and exploratory behavior. n H. F. O'Neil Jr., & M. Drillings (Eds.), 
+Motivation: Theory and research (pp. 221-243). 
+Story Spheres. (n.d.). About. Retrieved September 2, 2022, from https://storyspheres.com/ 
+Sun, H., Chen, A., Ennis, C., Martin, R., & Shen, B. (2008). An examination of the multidimensionality of situational 
+interest in elementary school physical education. Research Quarterly for Exercise and Sport, 79(1), 62-70. 
+Warden, C. A., Yi-Shun, W., Stanworth, J. O., & Chen, J. F. (2022). Millennials’ technology readiness and self-
+efficacy in online classes. Innovations in Education and Teaching International, 59(2), 226-236. 
+ 
+

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+Strategic Environmental Corporate Social Responsibility (ECSR) Certification and 
+Endogenous Market Structure  
+ 
+Ajay Sharma 
+Indian Institute of Management, Indore (India) 
+Siddhartha K. Rastogi 
+Indian Institute of Management, Indore (India) 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Correspondence address:  
+ 
+Ajay Sharma, J-206, Academic Block, Indian Institute of Management Indore, Prabandh Shikhar, Rau-
+Pithampur Road, Indore, M.P. (India) - 453556. Ph: +91-7312439622. E-mail: ajays@iimidr.ac.in; 
+ajaysharma87@gmail.com.  
+ 
+Siddhartha K. Rastogi, B-101, Academic Block, Indian Institute of Management Indore, Rau-Pithampur 
+Road, Indore, M.P. (India) - 453556. Ph: +91-7312439534. E-mail: srastogi@iimidr.ac.in  
+ 
+ 
+ 
+ 
+ 
+
+Strategic Environmental Corporate Social Responsibility (ECSR) Certification and Endogenous 
+Market Structure  
+ 
+ 
+ 
+ 
+Abstract 
+This paper extends the findings of Liu et al. (2015, Strategic environmental corporate social 
+responsibility in a differentiated duopoly market, Economics Letters), along two dimensions. First, we 
+consider the case of endogenous market structure a la Vives and Singh (1984, Price and quantity 
+competition in a differentiated duopoly, The Rand Journal of Economics). Second, we refine the ECSR 
+certification standards in differentiated duopoly with rankings. We find that optimal ECSR certification 
+standards by NGO are the highest in Bertrand competition, followed by mixed markets and the lowest in 
+Cournot competition. Next, NGO certifier will set the ECSR standards below the optimal level. Also, we 
+show that given the ECSR certification standards, there is a possibility of both price and quantity 
+contracts choices by the firms in endogenous market structure.  
+ 
+ 
+JEL Classification: D43; L13; L22; M14  
+Keywords: Corporate social responsibility certification; Differentiated duopoly; Environmental standards; 
+Price competition; Quantity competition 
+ 
+Declaration of interest: The authors do not have any conflict of interests. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+ 
+1. Introduction 
+ 
+Corporate Social Responsibility (CSR) has become a mainstream pursuit among the business activities of 
+firms in the past few years, wherein more than 30% (71% and 90%) of companies in the US (the UK and 
+Japan, respectively) adopted CSR reporting in 2013 (Kim et al., 2017). 
+Given the strategic importance of CSR activities as a non-core business pursuit and their significant 
+implication for costs, eco-labeling, certification, hallmarking etc. are the common ways of CSR signaling 
+especially for environmental outcomes. Though certification is not a perfect mechanism, it is sufficiently 
+trustworthy to convey useful information (Auriol and Schilizzi, 2015).  
+The certification can come from self or third-party and can be mandatory or optional. The existing 
+literature on the strategic aspects of third-party certification focuses on nature of competition and third-
+party certifiers. Manasakis et al. (2013) suggest that the certification by alternative third parties differ 
+with respect to their objectives and has implications for certification standards. Liu et al. (2015) compares 
+the ECSR certification level in Cournot versus Bertrand competition and show that certification standards 
+are lower in Bertrand than Cournot competition.  
+Our contribution to this literature is two folds. First, we extend the analysis of Liu et al. (2015) by 
+endogenizing the market structure a la Singh and Vives (1984). If the firms have option of price or 
+quantity contracts, given the ECSR standards, then, what would be optimal choice for the firms? Second, 
+we refine the ECSR certification standards in this endogenous market structure by providing rankings and 
+then considering uniform standards. 
+ 
+2. The Model 
+Based on Manasakis et al. (2013) and Liu et al. (2015), the utility function of a representative consumer is 
+𝑈 = (𝐴 + 𝑒1𝛼𝑠1)𝑞1 + (𝐴 + 𝑒2𝛼𝑠2)𝑞2 − (𝑞12 + 2𝛾𝑞1𝑞2 + 𝑞22)
+2
+ 
+where 𝑞𝑖 is output and 𝑠𝑖 is the level of ECSR, for firm 𝑖 (𝑖 = 1,2). The parameter 𝛾 ∈ (0,1) measures 
+the nature of products being substitutes (𝛾 > 0). The parameter 𝛼 ∈ (0,1) indicates the consumer’s 
+preference for firm’s ECSR activities. The firms choose ECSR as a strategic variable. Based on 
+Manasakis et al. (2013), we consider that ECSR activities can be informed to consumers through a 
+
+credible signal. For the same, the firm seeks certification from a third-party NGO certifier who maximizes 
+Net Consumer Surplus (NCS). A firm can get the certification 𝑒𝑖 if it satisfies criteria of minimum level 
+of ECSR activities 𝑠 : 
+𝑒𝑖 = {0 𝑖𝑓 𝑠𝑖 < 𝑠 𝑎𝑛𝑑 𝑓𝑖𝑟𝑚 𝑖 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑟𝑒𝑐𝑒𝑖𝑣𝑒 𝑎 𝐸𝐶𝑆𝑅 𝑐𝑒𝑡𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛
+1 𝑖𝑓 𝑠𝑖 ≥ 𝑠 𝑎𝑛𝑑 𝑓𝑖𝑟𝑚 𝑖 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑠 𝑎 𝐸𝐶𝑆𝑅 𝑐𝑒𝑡𝑖𝑓���𝑐𝑎𝑡𝑖𝑜𝑛
+} 
+It is important to note that a firm will consider doing ECSR activity only if it generates net positive 
+benefits. A firm would spend at 𝑠 (minimum ECSR for certification) and not beyond that. If both firms 
+choose to get the certification by spending 𝑠 on ECSR, the representative consumer’s utility would be:  
+𝑈 = (𝐴 + 𝑒1𝛼𝑠)𝑞1 + (𝐴 + 𝑒2𝛼𝑠)𝑞2 − (𝑞12 + 2𝛾𝑞1𝑞2 + 𝑞22)
+2
+ 
+The corresponding demand functions would be 𝑞𝑖 =
+𝐴(1−𝛾)−𝑝𝑖+𝛾𝑝𝑗+𝛼𝑒𝑖𝑠−𝛼𝛾𝑒𝑗𝑠
+1−𝛾2
+  and inverse demand 
+functions 𝑝𝑖 = 𝐴 − 𝑞𝑖 − 𝛾𝑞𝑗 + 𝛼𝑒𝑖𝑠, 𝑓𝑜𝑟 𝑖, 𝑗 = 1,2; 𝑖 ≠ 𝑗. 
+We assume that firms use same technology with cost of production as zero, without loss of generalization. 
+Also, one unit of output produces one unit of pollution emission. The NGO certifier will not charge any 
+fee for certification if firm complies with ECSR standards. The cost of ECSR for firms is 𝑠𝑖2.  
+The firm’s profit function is, 𝜋𝑖 = 𝑝𝑖𝑞𝑖 − 𝑒𝑖𝑠2, 𝑖 = 1,2. NGO certifier’s objective function is 𝑁𝐶𝑆 =
+ 𝐶𝑆 −
+𝑑(𝑞1+𝑞2−𝑒1𝑠−𝑒2𝑠)2
+2
+ where 𝐶𝑆 =
+(𝑞12+2𝛾𝑞1𝑞2+𝑞22)
+2
+ ; and 𝑑 > 0 is the marginal environmental damage 
+due to emissions. 
+ 
+3. The Game 
+The game is organized as follows. In the first stage, the firm decides to choose price or quantity contracts. 
+In the second stage, the certifier decides threshold level of ECSR for certification. Firms meeting the 
+threshold condition get the certification, otherwise not. In the third stage, firms choose the level of output 
+and prices to maximize their profits.  
+We solve the game using backward induction.  
+3.1. Product market competition 
+
+In this stage, we analyze the four possible options: a) both firms choose prices (𝑝𝑝) i.e., Bertrand 
+competition; b) both firms choose quantities (𝑞𝑞) i.e., Cournot competition; c) one firm chooses price 
+(quantity) contract while the other firm chooses the quantity (price) contract i.e., 𝑝𝑞 (𝑞𝑝) outcomes. 
+We avoid providing the calculations for (a) and (b) option for the sake of brevity, as they are identical to 
+Liu et al. (2015). Please refer to the online appendix for the same.   
+Proposition 1: The NGO certifier will set the standards, 𝑠 =  𝑠𝑃𝑃𝑈 and  𝑠𝑄𝑄𝑈in the Bertrand (pp game) 
+and Cournot (qq game) respectively. 
+Proof: See online appendix. 
+ 
+Next, both (c) and (d) will be identical in nature. Therefore, we only solve the pq game. 
+ 
+𝑝𝑞 game (Price versus Quantity Contract) 
+We use the superscript PQ for price-quantity contract case i.e., firm 1 decides price while firm 2 decides 
+quantity. The outcomes in the product market with firms not adopting ECSR are 
+𝑞1
+𝑃𝑄𝑁 =
+𝐴(2−𝛾−𝛾2)
+4−3𝛾2
+;  𝑞2
+𝑃𝑄𝑁 =
+𝐴(2−𝛾)
+4−3𝛾2 ; 𝑝1
+𝑃𝑄𝑁 =
+𝐴(2−𝛾−𝛾2)
+4−3𝛾2
+;  𝑝2
+𝑃𝑄𝑁 =
+𝐴(2−𝛾)(1−𝛾)(1+𝛾)
+4−3𝛾2
+; 𝜋1
+𝑃𝑄𝑁 =
+𝐴2(2−𝛾−𝛾2)2
+(4−3𝛾2)2
+;  𝜋2
+𝑃𝑄𝑁 = 
+𝐴2(2−𝛾)2(1−𝛾2)
+(4−3𝛾2)2
+ ; NCS𝑃𝑄𝑁 =
+𝐴2(8−10𝛾2+3𝛾4−𝑑(4−𝛾(2+𝛾))2)
+2(4−3𝛾2)2
+                            (5) 
+If the firms choose to opt for ECSR activities and get certification, the equilibrium outcomes would be,  
+𝑞1
+𝑃𝑄𝐶 =
+(2−𝛾−𝛾2)(𝐴+𝛼𝑠)
+4−3𝛾2
+;  𝑞2
+𝑃𝑄𝐶 =
+(2−𝛾)(𝐴+𝛼𝑠)
+4−3𝛾2
+; 𝑝1
+𝑃𝑄𝐶 =
+(2−𝛾−𝛾2)(𝐴+𝛼𝑠)
+4−3𝛾2
+;  𝑝2
+𝑃𝑄𝐶 =
+(2−𝛾)(1−𝛾)(1+𝛾)(𝐴+𝛼𝑠)
+4−3𝛾2
+; 𝜋1
+𝑃𝑄𝐶 =
+ 
+(𝐴2+2𝐴𝛼𝑠+𝛼2𝑠2)(2−𝛾−𝛾2)2−(4−3𝛾2)
+2𝑠2
+(4−3𝛾2)2
+ ;  𝜋2
+𝑃𝑄𝐶 
+(𝐴2+2𝐴𝛼𝑠+𝛼2𝑠2)(2−𝛾)2(1−𝛾2)+((4−3𝛾2)
+2
+(4−3𝛾2)2
+ ;  NCS𝑃𝑄𝐶 =
+(2−𝛾2)(𝐴+𝛼𝑠)2
+8−6𝛾2
+−
+𝐴2𝑑(−4+𝛾(2+𝛾))2
+2(4−3𝛾2)2
+  
+
+For 𝑞1
+𝑃𝑄𝐶 > 𝑠 , 𝑠 <
+2𝐴−𝐴𝛾−𝐴𝛾2
+4−2𝛼+𝛼𝛾−3𝛾2+𝛼𝛾2  and for 𝑞2
+𝑃𝑄𝐶 > 𝑠 , 𝑠 <
+2𝐴−𝐴𝛾
+4−2𝛼+𝛼𝛾−3𝛾2 should be satisfied. For both 
+𝑞1
+𝑃𝑄𝐶 > 𝑠 𝑎𝑛𝑑 𝑞2
+𝑃𝑄𝐶 > 𝑠, 𝑠 <
+2𝐴−𝐴𝛾−𝐴𝛾2
+4−2𝛼+𝛼𝛾−3𝛾2+𝛼𝛾2 must be satisfied. Further 𝑞2
+𝑃𝑄𝐶 > 𝑞1
+𝑃𝑄𝐶 holds for all 
+parametric values. 
+Firm 1 would be willing to adopt ECSR certification if 𝜋1
+𝑃𝑄𝐶 > 𝜋1
+𝑃𝑄𝑁 i.e., 𝑠 < 𝑠𝑃𝑄𝑈1 =
+2𝐴−𝐴𝛾−𝐴𝛾2
+4−2𝛼+𝛼𝛾−3𝛾2+𝛼𝛾2 
+holds. For firm 2, decision to adopt ECSR certification is chosen if 𝜋2
+𝑃𝑄𝐶 > 𝜋2
+𝑃𝑄𝑁 i.e. 𝑠 < 𝑠𝑃𝑄𝑈2 =
+𝐴𝛼(2−𝛾−𝛾2)2
+(4−3𝛾2)2−𝛼2(2−𝛾−𝛾2)2  holds. 
+Also, comparing the upper threshold of spending on ECSR, we observe that firm 1 (choosing price) has 
+higher threshold than firm 2 (choosing quantity)’s ECSR spending, i.e., 𝑠𝑃𝑄𝑈1 > 𝑠𝑃𝑄𝑈2. 
+Lemma 1: In a price vs. quantity game, price setting firm has higher threshold for ECSR spending than 
+quantity setting firm.  
+ 
+NGO certifier 
+Coming to second stage, we obtain the optimal choice of ECSR certification standard for NGO certifier 
+by evaluating 
+𝑑 𝑁𝐶𝑆𝑃𝑄𝐶
+𝑑𝑠
+= 0. We get 
+𝑠𝑃𝑄∗ = 𝐴(𝛼(8 − 10𝛾2 + 3𝛾4) − 𝑑(−4 + 𝛾(2 + 𝛾))(8 − 6𝛾2 + 𝛼(−4 + 𝛾(2 + 𝛾))))
+𝛼2(−8 + 10𝛾2 − 3𝛾4) + 𝑑(8 − 6𝛾2 + 𝛼(−4 + 𝛾(2 + 𝛾)))2
+ 
+𝑠𝑃𝑄∗ > 0 if 𝑑 >
+𝛼2(8−10𝛾2+3𝛾4)
+(8−6𝛾2+𝛼(−4+𝛾(2+𝛾)))2  holds.  
+Further, 𝑠𝑃𝑄∗ > 𝑠𝑃𝑄𝑈1  and 𝑠𝑃𝑄∗ > 𝑠𝑃𝑄𝑈2 when 𝑑 >
+𝛼2(8−10𝛾2+3𝛾4)
+(8−6𝛾2+𝛼(−4+𝛾(2+𝛾)))2. This means that certifier’s 
+optimal level of ECSR standard would be higher than the upper limit for the firms in price vs. quantity 
+competition and any firm will not spend on ECSR if a certifier sets the standard at 𝑠𝑃𝑄∗. NGO certifier 
+can set the ECSR standard for certification at either 𝑠 = 𝑠𝑃𝑄𝑈1or 𝑠 = 𝑠𝑃𝑄𝑈2 level for participation. If 
+𝑠 = 𝑠𝑃𝑄𝑈1 is chosen as ECSR standard, then only price-setting firm 1 will get the certification and 
+quantity-setting firm 2 will not get ECSR certification.  Interestingly, profit of firm 2 will be higher than 
+firm 1.  
+
+On the other hand, 𝑠 = 𝑠𝑃𝑄𝑈2 as ECSR standard leads to both firms getting the certification. In this case 
+also, firm 1’s profit would be lower than firm 2’s. 
+This indicates that quantity setting firm 2 has net advantage over price setting firm 1 irrespective of 
+whether firm 1 unilaterally get the ECSR certification or both firms get the certification. This is a new 
+result. 
+Therefore, to induce the firms in adopting the certification, the standard would be set at 𝑠 = 𝑠𝑃𝑄𝑈. 
+Further, we find that consumers and firms would benefit from such ECSR standard as compared to no 
+ECSR at all because  NCSPQC > NCSPQN. 
+ 
+Proposition 2:  In a price vs. quantity competition,  
+a) NGO certifier will set the ECSR standard below the optimal level  
+b) if ECSR certification standard is set at 𝑠 = 𝑠𝑃𝑄𝑈1, then only price-setting firm will get the 
+certification, whereas quantity-setting firm 2 will not opt for certification.  
+c) if ECSR certification standard is set at 𝑠 = 𝑠𝑃𝑄𝑈2, then both firms will get the certification and it 
+is beneficial for both firms and consumers. 
+  
+ 
+4. Comparison of ECSR Certification Standards 
+ 
+Comparing the optimal ECSR standard, 𝑠 by the NGO certifier across endogenous market structure, we 
+observe that 𝑠𝑃𝑃∗ > 𝑠𝑃𝑄∗ > 𝑠𝑄𝑄∗ indicating Bertrand has the highest level followed by price-quantity and 
+lastly Cournot case.   
+Proposition 3: Across the spectrum of market structure, the NGO certifier’s optimal ECSR standard 
+rankings are  𝑠𝑃𝑃∗ > 𝑠𝑃𝑄∗ > 𝑠𝑄𝑄∗. 
+In all the cases, the NGO certifier is not able to implement the optimal level of ECSR standard because 
+the firms will not adopt such ECSR standards as that leads to lower profit for them. Therefore, the 
+certifier would choose a sub-optimal ECSR standard to incentivize the firms. Comparing these 
+equilibrium standards, we get the ranking in proposition 4. 
+
+Proposition 4: The NGO certifier’s equilibrium ECSR standard rankings are 𝑠𝑃𝑄𝑈1 > 𝑠𝑄𝑄𝑈 > 𝑠𝑃𝑃𝑈 >
+𝑠𝑃𝑄𝑈2. 
+ 
+5. Endogenous Market Structure: Price or Quantity Contract 
+Now, we solve the first stage of the game where firms have options to choose price or quantity contracts 
+in the product market competition. For the sake of brevity, we do not consider the case where no firm 
+chooses ECSR certification. The outcome of that subgame will be identical to Singh and Vives (1984).  
+ 
+Lemma 2 (Singh and Vives, 1984): In a product market competition for substitute goods1, with price and 
+quantity as strategic choices, firms choose quantity contracts as dominant strategies. 
+ 
+ 
+ECSR certification standards and market structure 
+ 
+If firms opt for the ECSR certification, then the outcome of the subgame can differ from Singh and Vives 
+(1984). The certifier can choose a uniform standard irrespective of the nature of market competition, or 
+different standards based on nature of competition2. We only consider possibility of uniform ECSR 
+certification standards.  
+In case of uniform ECSR standard, there are four choices, 𝑠𝑃𝑄𝑈1 > 𝑠𝑄𝑄𝑈 > 𝑠𝑃𝑃𝑈 > 𝑠𝑃𝑄𝑈2 (see 
+Proposition 4). If the NGO certifier sets the lowest three ECSR certification standard, i.e., either 𝑠𝑃𝑄𝑈2 or 
+𝑠𝑃𝑃𝑈 or 𝑠𝑄𝑄𝑈, then the Nash equilibrium outcome of the game in Table 1, is {Quantity, Quantity}. On the 
+other hand, if the ECSR certifier sets the standard at the highest level possible i.e., 𝑠𝑃𝑄𝑈1, then there are 
+two Nash equilibria outcomes of the game {Price, Quantity} and {Quantity, Price}. 
+ 
+ 
+1 In this paper, we only consider substitute goods in the market offered by competing firms. 
+2 But from a real-world point of view, such standards may not be feasible due to monitoring issues, 
+discrimination, and mimicking behavior among firms.  
+  
+
+Table 1: Price-Quantity Contract Game (with ECSR certification) 
+ 
+Firm 2 
+Firm 1 
+ 
+Price 
+Quantity 
+Price 
+𝜋1
+𝑃𝑃𝐶, 𝜋2
+𝑃𝑃𝐶 
+𝜋1
+𝑃𝑄𝐶, 𝜋2
+𝑃𝑄𝐶 
+Quantity 
+𝜋1
+𝑄𝑃𝐶, 𝜋2
+𝑄𝑃𝐶 
+𝜋1
+𝑄𝑄𝐶, 𝜋2
+𝑄𝑄𝐶 
+ 
+Proposition 5: In a price-quantity contract game,  
+a) If a certifier decides, the uniform ECSR standard at either 𝑠𝑃𝑄𝑈2 or 𝑠𝑃𝑃𝑈 or 𝑠𝑄𝑄𝑈 level, the 
+subgame perfect Nash equilibrium is {Quantity, Quantity} 
+b) If the certifier decides, the uniform ECSR standard at 𝑠𝑃𝑄𝑈1, there are two subgame perfect Nash 
+equilibria {price, Quantity}, {Quantity, Price} 
+Proof: See online appendix 
+ 
+6. Conclusion 
+In this paper, we analyze the relationship between endogenous market structure and strategic ECSR in a 
+differentiated duopoly. We show that NGO certifier will always set the ECSR standards below the 
+optimal level to ensure participation. In a price-quantity game, there is possibility of partial or full 
+compliance with ECSR standards. Lastly, while setting a uniform ECSR standards in endogenous market 
+structure, there is a possibility of Cournot outcome as well as mixed market outcome.  
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+References 
+ 
+Auriol, E. and Schilizzi, S.G.M. (2015) Quality signaling through certification in developing countries. 
+Journal of Development Economics. 116. 105-121. 
+Kim, S., Lee, S., and Matsumura, T. (2017) Corporate social responsibility and privatization policy in a 
+mixed oligopoly. MPRA Paper No. 79780.  
+Liu, C. C., Wang, L. F., and Lee, S. H. (2015) Strategic environmental corporate social responsibility in a 
+differentiated duopoly market. Economics Letters. 129. 108-111. 
+Manasakis, C., Mitrokostas, E., and Petrakis, E. (2013) Certification of corporate social responsibility 
+activities in oligopolistic markets. Canadian Journal of Economics. 46(1). 282-309. 
+Singh, N., and Vives, X. (1984) Price and quantity competition in a differentiated duopoly. The Rand 
+Journal of Economics. 546-554. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+ 
+ONLINE APPENDIX 
+ 
+ 
+A1. A 𝑝𝑝 game (Bertrand Competition) 
+We use the superscript PPN to denote equilibrium outcome for firms not adopting ECSR in 𝑝𝑝 
+game i.e., Bertrand competition, otherwise PPC. Solving the game, we get  
+𝑞1
+𝑃𝑃𝑁 = 𝑞2
+𝑃𝑃𝑁 =
+𝐴
+2+𝛾−𝛾2 ; 𝑝1
+𝑃𝑃𝑁 = 𝑝2
+𝑃𝑃𝑁 =
+𝐴(1−𝛾)
+2−𝛾 ; 𝜋1
+𝑃𝑃𝑁 = 𝜋2
+𝑃𝑃𝑁 = 
+𝐴2(1−𝛾)
+(2−𝛾)2(1+𝛾) ; NCSPPN =
+𝐴2(1−2𝑑+𝛾)
+(2+𝛾−𝛾2)2                             (1) 
+If the firms decide to adopt for ECSR and get certification for the same, the outcomes are 
+𝑞1
+𝑃𝑃𝐶 = 𝑞1
+𝑃𝑃𝐶 =
+𝐴 + 𝛼𝑠
+2 + 𝛾 − 𝛾2 ; 𝑝1
+𝑃𝑃𝐶 = 𝑝2
+𝑃𝑃𝐶 =
+(1 − 𝛾)(𝐴 + 𝛼𝑠)
+2 − 𝛾
+; 𝜋1
+𝑃𝑃𝐶 = 𝜋2
+𝑃𝑃𝐶
+=
+(1 − 𝛾)(𝐴 + 𝛼𝑠)
+2
+(2 − 𝛾)(2 + 𝛾 − 𝛾2) − 𝑠2 ;  
+NCSPPC =
+(𝐴+𝛼𝑠)2
+(2−𝛾)2(1+𝛾) −
+2𝑑(𝐴+(𝛼+(−2+𝛾)(1+𝛾))𝑠)2
+(2+𝛾−𝛾2)2
+               (2) 
+For a firm to be adopting ECSR, the certification threshold needs to be lower than the level of 
+pollution, otherwise the cost will be more than its benefits. For 𝑞𝑖
+𝑃𝑃𝐶 > 𝑠, 𝑠 <
+𝐴
+2−𝛼+𝛾−𝛾2 should 
+be satisfied. 
+Comparing the profits of firms3 with or without ECSR,  
+𝜋1
+𝑃𝑃𝐶 − 𝜋1
+𝑃𝑃𝑁 = 𝐴2(1 − 𝛾) + 2𝐴𝛼(1 − 𝛾)𝑠 − (4 − 𝛼2(1 − 𝛾) − (3 − 𝛾)𝛾2)𝑠2
+(2 − 𝛾)2(1 + 𝛾)
+ 
+ 
+3 Given the symmetry of the firms and their outcomes, we only compare the results of one firm, and it 
+holds for both of them. 
+
+We observe that 𝜋1
+𝑃𝑃𝐶 − 𝜋1
+𝑃𝑃𝑁 > 0 if 𝑠 < 𝑠𝑃𝑃𝑈 =
+2𝐴𝛼(1−𝛾)
+4−𝛼2+𝛼2𝛾−3𝛾2+𝛾3 , which provides the upper 
+bound for the ECSR spending to adopt the ECSR certification. So, firms will spend strategically 
+on ECSR and get certification if 𝑠 < 𝑠𝑃𝑃𝑈.4 
+ 
+Optimal ECSR Certification Standard 
+ 
+We obtain the optimal choice of ECSR certification standard in case of NGO certifier by 
+evaluating 
+𝑑 𝑁𝐶𝑆𝑃𝑃𝐶
+𝑑𝑠
+= 0. We get, 
+𝑠𝑃𝑃∗ = 𝐴(𝛼 + 𝛼𝛾 − 2𝑑(𝛼 − (2 − 𝛾)(1 + 𝛾)))
+2𝑑(𝛼 − (2 − 𝛾)(1 + 𝛾))2 − 𝛼2(1 + 𝛾) 
+𝑠𝑃𝑃∗ > 0 if 𝑑 >
+𝛼2+𝛼2𝛾
+2(𝛼−(2−𝛾)(1+𝛾))2 holds. Further, 𝑠𝑃𝑃∗ > 𝑠𝑃𝑃𝑈 when 𝑑 >
+𝛼2+𝛼2𝛾
+2(𝛼−(2−𝛾)(1+𝛾))2. This 
+means that an NGO certifier’s optimal level of ECSR standard would be higher that the upper 
+limit for the firms in Bertrand competition and a firm would not choose to spend on ECSR if a 
+certifier sets the standard at 𝑠𝑃𝑃∗. Therefore, to induce the firms, the standard would be set at 𝑠 =
+ 𝑠𝑃𝑃𝑈 by the NGO certifier. Further, we can also show that consumer and firms would benefit 
+from such ECSR standard as compared to no ECSR at all i.e., NCSPPC > NCSPPN. 
+ 
+Proposition A1:  An NGO certifier would set the ECSR standard below the optimal level if firms 
+engage in Bertrand competition and, it is beneficial for both firms and consumers in terms of 
+profit and net consumer surplus, respectively.  
+ 
+A2. A 𝑞𝑞 game (Cournot Competition) 
+ 
+4 Superscript U denotes upper bound. 
+
+For Cournot game, we use the superscript QQ. The outcomes of the product market competition, 
+if firms do not adopt ECSR are, 𝑞1
+𝑄𝑄𝑁 = 𝑞2
+𝑄𝑄𝑁 =
+𝐴
+2+𝛾 ; 𝑝1
+𝑄𝑄𝑁 = 𝑝2
+𝑄𝑄𝑁 =
+𝐴
+2+𝛾 ; 𝜋1
+𝑄𝑄𝑁 = 𝜋2
+𝑄𝑄𝑁 =
+ 
+𝐴2
+(2+𝛾)2 ; NCS𝑄𝑄𝑁 =
+𝐴2(1−2𝑑+𝛾)
+(2+𝛾)2
+                            (3) 
+On the other hand, if the firms decide to adopt ECSR certification, the outcomes would be, 
+𝑞1
+𝑄𝑄𝐶 = 𝑞2
+𝑃𝑃𝐶 =
+𝐴+𝛼𝑠
+2+𝛾  ; 𝑝1
+𝑄𝑄𝐶 = 𝑝2
+𝑄𝑄𝐶 =
+𝐴+𝛼𝑠
+2+𝛾 ; 𝜋1
+𝑄𝑄𝐶 = 𝜋2
+𝑄𝑄𝐶 = 
+(𝐴+𝛼𝑠)2
+(2+𝛾)2 − 𝑠2; NCS𝑄𝑄𝐶 =
+(1+𝛾)(𝐴+𝛼𝑠)
+2−2𝑑(𝐴−(2−𝛼+𝛾)𝑠)2
+(2+𝛾)2
+          (4) 
+ 
+For 𝑞𝑖
+𝑄𝑄𝐶 > 𝑠 , 𝑠 <
+𝐴
+2−𝛼+𝛾 should be satisfied. Further comparing the profits of firms with and 
+without adopting ECSR,  
+𝜋1
+𝑄𝑄𝐶 − 𝜋1
+𝑄𝑄𝑁 = 𝐴2 + 2𝐴𝛼𝑠 + (−2 + 𝛼 − 𝛾)(2 + 𝛼 + 𝛾)𝑠2
+(2 + 𝛾)2
+ 
+A firm would profit from adopting ECSR if 𝜋1
+𝑄𝑄𝐶 > 𝜋1
+𝑄𝑄𝑁 i.e., when 𝑠 < 𝑠𝑄𝑄𝑈 =
+2𝐴𝛼
+4−𝛼2+4𝛾+𝛾2. 
+This denotes the upper bound to spend on ECSR for certification. 
+ 
+Optimal ECSR Certification Standard 
+We obtain the optimal choice of ECSR certification standard in case of NGO certifier by 
+evaluating 
+𝑑 𝑁𝐶𝑆𝑄𝑄𝐶
+𝑑𝑠
+= 0. We get, 
+𝑠𝑄𝑄∗ = 𝐴(𝛼 + 𝛼𝛾 + 2𝑑(2 − 𝛼 + 𝛾))
+2𝑑(2 − 𝛼 + 𝛾)2 − 𝛼2(1 + 𝛾) 
+𝑠𝑄𝑄∗ > 0 if 𝑑 >
+𝛼2+𝛼2𝛾
+2(2−𝛼+𝛾)2 holds. Further, 𝑠𝑄𝑄∗ > 𝑠𝑄𝑄𝑈 when 𝑑 >
+𝛼2+𝛼2𝛾
+2(2−𝛼+𝛾)2. This means that a 
+certifier’s optimal level of ECSR standard would be higher than the upper limit for the firms in 
+Cournot competition and a firm would not choose to spend on ECSR if a certifier sets the 
+standard at 𝑠𝑄𝑄∗. Therefore, to induce the firms, the standard would be set at 𝑠 = 𝑠𝑄𝑄𝑈 by the 
+
+NGO certifier. Further, we can also show that consumer and firms would benefit from such 
+ECSR standard as compared to no ECSR at all i.e., NCSQQC > NCSQQN. 
+ 
+Proposition A2:  An NGO certifier would set the ECSR standard below the optimal level if firms 
+engage in Cournot competition and, it is beneficial for both firms and consumers in terms of 
+profit and net consumer surplus, respectively. 
+ 
+A3. Proof for Proposition 5 
+Proof:  
+a) In all three cases, we observe that 𝜋1
+𝑄𝑃𝐶 > 𝜋1
+𝑃𝑃𝐶 and 𝜋1
+𝑄𝑄𝐶 > 𝜋1
+𝑃𝑄𝐶 for firm 1; and 
+𝜋2
+𝑃𝑄𝐶 > 𝜋2
+𝑃𝑃𝐶 and 𝜋2
+𝑄𝑄𝐶 > 𝜋2
+𝑄𝑃𝐶 for firm 2. This makes ‘Quantity contract’ as the 
+dominant strategy for both the firms and the Nash equilibrium is {Quantity, Quantity}.  
+b) In this case, we observe that 𝜋1
+𝑄𝑃𝐶 > 𝜋1
+𝑃𝑃𝐶 and 𝜋1
+𝑄𝑄𝐶 < 𝜋1
+𝑃𝑄𝐶 for firm 1; and 𝜋2
+𝑃𝑄𝐶 >
+𝜋2
+𝑃𝑃𝐶 and 𝜋2
+𝑄𝑄𝐶 < 𝜋2
+𝑄𝑃𝐶 for firm 2. This means that there are no dominant strategies and 
+the best response of either firm is the choice of opposite strategy, and the Nash equilibria 
+are {Price, Quantity}, {Quantity Price}.  
+ 
+ 
+

3tE1T4oBgHgl3EQfmAQH/content/tmp_files/load_file.txt

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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf,len=273
+page_content='Strategic Environmental Corporate Social Responsibility (ECSR) Certification and Endogenous Market Structure  Ajay Sharma Indian Institute of Management, Indore (India) Siddhartha K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Rastogi Indian Institute of Management, Indore (India)  Correspondence address:  Ajay Sharma, J-206, Academic Block, Indian Institute of Management Indore, Prabandh Shikhar, Rau- Pithampur Road, Indore, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (India) - 453556.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Ph: +91-7312439622.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' E-mail: ajays@iimidr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='in;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' ajaysharma87@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  Siddhartha K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Rastogi, B-101, Academic Block, Indian Institute of Management Indore, Rau-Pithampur Road, Indore, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (India) - 453556.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Ph: +91-7312439534.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' E-mail: srastogi@iimidr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='in  Strategic Environmental Corporate Social Responsibility (ECSR) Certification and Endogenous Market Structure  Abstract This paper extends the findings of Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (2015, Strategic environmental corporate social responsibility in a differentiated duopoly market, Economics Letters), along two dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' First, we consider the case of endogenous market structure a la Vives and Singh (1984, Price and quantity competition in a differentiated duopoly, The Rand Journal of Economics).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Second, we refine the ECSR certification standards in differentiated duopoly with rankings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' We find that optimal ECSR certification standards by NGO are the highest in Bertrand competition, followed by mixed markets and the lowest in Cournot competition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Next, NGO certifier will set the ECSR standards below the optimal level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Also, we show that given the ECSR certification standards, there is a possibility of both price and quantity contracts choices by the firms in endogenous market structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  JEL Classification: D43;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' L13;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' L22;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' M14 Keywords: Corporate social responsibility certification;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Differentiated duopoly;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Environmental standards;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Price competition;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Quantity competition  Declaration of interest: The authors do not have any conflict of interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Introduction  Corporate Social Responsibility (CSR) has become a mainstream pursuit among the business activities of firms in the past few years, wherein more than 30% (71% and 90%) of companies in the US (the UK and Japan, respectively) adopted CSR reporting in 2013 (Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Given the strategic importance of CSR activities as a non-core business pursuit and their significant implication for costs, eco-labeling, certification, hallmarking etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' are the common ways of CSR signaling especially for environmental outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Though certification is not a perfect mechanism, it is sufficiently trustworthy to convey useful information (Auriol and Schilizzi, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The certification can come from self or third-party and can be mandatory or optional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The existing literature on the strategic aspects of third-party certification focuses on nature of competition and third- party certifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Manasakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (2013) suggest that the certification by alternative third parties differ with respect to their objectives and has implications for certification standards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (2015) compares the ECSR certification level in Cournot versus Bertrand competition and show that certification standards are lower in Bertrand than Cournot competition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Our contribution to this literature is two folds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' First, we extend the analysis of Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (2015) by endogenizing the market structure a la Singh and Vives (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  If the firms have option of price or quantity contracts, given the ECSR standards, then, what would be optimal choice for the firms?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Second, we refine the ECSR certification standards in this endogenous market structure by providing rankings and then considering uniform standards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The Model Based on Manasakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (2013) and Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (2015), the utility function of a representative consumer is 𝑈 = (𝐴 + 𝑒1𝛼𝑠1)𝑞1 + (𝐴 + 𝑒2𝛼𝑠2)𝑞2 − (𝑞12 + 2𝛾𝑞1𝑞2 + 𝑞22) 2  where 𝑞𝑖 is output and 𝑠𝑖 is the level of ECSR, for firm 𝑖 (𝑖 = 1,2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The parameter 𝛾 ∈ (0,1) measures the nature of products being substitutes (𝛾 > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The parameter 𝛼 ∈ (0,1) indicates the consumer’s preference for firm’s ECSR activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The firms choose ECSR as a strategic variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Based on Manasakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (2013), we consider that ECSR activities can be informed to consumers through a  credible signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' For the same, the firm seeks certification from a third-party NGO certifier who maximizes Net Consumer Surplus (NCS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' A firm can get the certification 𝑒𝑖 if it satisfies criteria of minimum level of ECSR activities 𝑠 : 𝑒𝑖 = {0 𝑖𝑓 𝑠𝑖 < 𝑠 𝑎𝑛𝑑 𝑓𝑖𝑟𝑚 𝑖 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑟𝑒𝑐𝑒𝑖𝑣𝑒 𝑎 𝐸𝐶𝑆𝑅 𝑐𝑒𝑡𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 1 𝑖𝑓 𝑠𝑖 ≥ 𝑠 𝑎𝑛𝑑 𝑓𝑖𝑟𝑚 𝑖 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑠 𝑎 𝐸𝐶𝑆𝑅 𝑐𝑒𝑡𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 } It is important to note that a firm will consider doing ECSR activity only if it generates net positive benefits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' A firm would spend at 𝑠 (minimum ECSR for certification) and not beyond that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' If both firms choose to get the certification by spending 𝑠 on ECSR, the representative consumer’s utility would be: 𝑈 = (𝐴 + 𝑒1𝛼𝑠)𝑞1 + (𝐴 + 𝑒2𝛼𝑠)𝑞2 − (𝑞12 + 2𝛾𝑞1𝑞2 + 𝑞22) 2  The corresponding demand functions would be 𝑞𝑖 = 𝐴(1−𝛾)−𝑝𝑖+𝛾𝑝𝑗+𝛼𝑒𝑖𝑠−𝛼𝛾𝑒𝑗𝑠 1−𝛾2 and inverse demand functions 𝑝𝑖 = 𝐴 − 𝑞𝑖 − 𝛾𝑞𝑗 + 𝛼𝑒𝑖𝑠, 𝑓𝑜𝑟 𝑖, 𝑗 = 1,2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝑖 ≠ 𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' We assume that firms use same technology with cost of production as zero, without loss of generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Also, one unit of output produces one unit of pollution emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The NGO certifier will not charge any fee for certification if firm complies with ECSR standards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The cost of ECSR for firms is 𝑠𝑖2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The firm’s profit function is, 𝜋𝑖 = 𝑝𝑖𝑞𝑖 − 𝑒𝑖𝑠2, 𝑖 = 1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' NGO certifier’s objective function is 𝑁𝐶𝑆 = 𝐶𝑆 − 𝑑(𝑞1+��2−𝑒1𝑠−𝑒2𝑠)2 2 where 𝐶𝑆 = (𝑞12+2𝛾𝑞1𝑞2+𝑞22) 2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' and 𝑑 > 0 is the marginal environmental damage due to emissions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The Game The game is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' In the first stage, the firm decides to choose price or quantity contracts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' In the second stage, the certifier decides threshold level of ECSR for certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Firms meeting the threshold condition get the certification, otherwise not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' In the third stage, firms choose the level of output and prices to maximize their profits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' We solve the game using backward induction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Product market competition  In this stage, we analyze the four possible options: a) both firms choose prices (𝑝𝑝) i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', Bertrand competition;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' b) both firms choose quantities (𝑞𝑞) i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', Cournot competition;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' c) one firm chooses price (quantity) contract while the other firm chooses the quantity (price) contract i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', 𝑝𝑞 (𝑞𝑝) outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' We avoid providing the calculations for (a) and (b) option for the sake of brevity, as they are identical to Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Please refer to the online appendix for the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Proposition 1: The NGO certifier will set the standards, 𝑠 =  𝑠𝑃𝑃𝑈 and  𝑠𝑄𝑄𝑈in the Bertrand (pp game) and Cournot (qq game) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Proof: See online appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  Next, both (c) and (d) will be identical in nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Therefore, we only solve the pq game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  𝑝𝑞 game (Price versus Quantity Contract) We use the superscript PQ for price-quantity contract case i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', firm 1 decides price while firm 2 decides quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The outcomes in the product market with firms not adopting ECSR are 𝑞1 𝑃𝑄𝑁 = 𝐴(2−𝛾−𝛾2) 4−3𝛾2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  𝑞2 𝑃𝑄𝑁 = 𝐴(2−𝛾) 4−3𝛾2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝑝1 𝑃𝑄𝑁 = 𝐴(2−𝛾−𝛾2) 4−3𝛾2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  𝑝2 𝑃𝑄𝑁 = 𝐴(2−𝛾)(1−𝛾)(1+𝛾) 4−3𝛾2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝜋1 𝑃𝑄𝑁 = 𝐴2(2−𝛾−𝛾2)2 (4−3𝛾2)2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  𝜋2 𝑃𝑄𝑁 = 𝐴2(2−𝛾)2(1−𝛾2) (4−3𝛾2)2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' NCS𝑃𝑄𝑁 = 𝐴2(8−10𝛾2+3𝛾4−𝑑(4−𝛾(2+𝛾))2) 2(4−3𝛾2)2 (5) If the firms choose to opt for ECSR activities and get certification, the equilibrium outcomes would be, 𝑞1 𝑃𝑄𝐶 = (2−𝛾−𝛾2)(𝐴+𝛼𝑠) 4−3𝛾2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  𝑞2 𝑃𝑄𝐶 = (2−𝛾)(𝐴+𝛼𝑠) 4−3𝛾2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝑝1 𝑃𝑄𝐶 = (2−𝛾−𝛾2)(𝐴+𝛼𝑠) 4−3𝛾2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  𝑝2 𝑃𝑄𝐶 = (2−𝛾)(1−𝛾)(1+𝛾)(𝐴+𝛼𝑠) 4−3𝛾2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝜋1 𝑃𝑄𝐶 =  (𝐴2+2𝐴𝛼𝑠+𝛼2𝑠2)(2−𝛾−𝛾2)2−(4−3𝛾2)  2𝑠2  (4−3𝛾2)2  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  𝜋2  𝑃𝑄𝐶  (𝐴2+2𝐴𝛼𝑠+𝛼2𝑠2)(2−𝛾)2(1−𝛾2)+((4−3𝛾2)  2  (4−3𝛾2)2  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  NCS𝑃𝑄𝐶 =  (2−𝛾2)(𝐴+𝛼𝑠)2  8−6𝛾2  −  𝐴2𝑑(−4+𝛾(2+𝛾))2  2(4−3𝛾2)2  For 𝑞1 𝑃𝑄𝐶 > 𝑠 , 𝑠 < 2𝐴−𝐴𝛾−𝐴𝛾2 4−2𝛼+𝛼𝛾−3𝛾2+𝛼𝛾2  and for 𝑞2 𝑃𝑄𝐶 > 𝑠 , 𝑠 < 2𝐴−𝐴𝛾 4−2𝛼+𝛼𝛾−3𝛾2 should be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' For both 𝑞1 𝑃𝑄𝐶 > 𝑠 𝑎𝑛𝑑 𝑞2 𝑃𝑄𝐶 > 𝑠, 𝑠 < 2𝐴−𝐴𝛾−𝐴𝛾2 4−2𝛼+𝛼𝛾−3𝛾2+𝛼𝛾2 must be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Further 𝑞2 𝑃𝑄𝐶 > 𝑞1 𝑃𝑄𝐶 holds for all parametric values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Firm 1 would be willing to adopt ECSR certification if 𝜋1 𝑃𝑄𝐶 > 𝜋1 𝑃𝑄𝑁 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', 𝑠 < 𝑠𝑃𝑄𝑈1 = 2𝐴−𝐴𝛾−𝐴𝛾2 4−2𝛼+𝛼𝛾−3𝛾2+𝛼𝛾2 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' For firm 2, decision to adopt ECSR certification is chosen if 𝜋2 𝑃𝑄𝐶 > 𝜋2 𝑃𝑄𝑁 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝑠 < 𝑠𝑃𝑄𝑈2 = 𝐴𝛼(2−𝛾−𝛾2)2 (4−3𝛾2)2−𝛼2(2−𝛾−𝛾2)2  holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Also, comparing the upper threshold of spending on ECSR, we observe that firm 1 (choosing price) has higher threshold than firm 2 (choosing quantity)’s ECSR spending, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', 𝑠𝑃𝑄𝑈1 > 𝑠𝑃𝑄𝑈2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Lemma 1: In a price vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' quantity game, price setting firm has higher threshold for ECSR spending than quantity setting firm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  NGO certifier Coming to second stage, we obtain the optimal choice of ECSR certification standard for NGO certifier by evaluating 𝑑 𝑁𝐶𝑆𝑃𝑄𝐶 𝑑𝑠 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' We get 𝑠𝑃𝑄∗ = 𝐴(𝛼(8 − 10𝛾2 + 3𝛾4) − 𝑑(−4 + 𝛾(2 + 𝛾))(8 − 6𝛾2 + 𝛼(−4 + 𝛾(2 + 𝛾)))) 𝛼2(−8 + 10𝛾2 − 3𝛾4) + 𝑑(8 − 6𝛾2 + 𝛼(−4 + 𝛾(2 + 𝛾)))2  𝑠𝑃𝑄∗ > 0 if 𝑑 > 𝛼2(8−10𝛾2+3𝛾4) (8−6𝛾2+𝛼(−4+𝛾(2+𝛾)))2  holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Further, 𝑠𝑃𝑄∗ > 𝑠𝑃𝑄𝑈1  and 𝑠𝑃𝑄∗ > 𝑠𝑃𝑄𝑈2 when 𝑑 > 𝛼2(8−10𝛾2+3𝛾4) (8−6𝛾2+𝛼(−4+𝛾(2+𝛾)))2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' This means that certifier’s optimal level of ECSR standard would be higher than the upper limit for the firms in price vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' quantity competition and any firm will not spend on ECSR if a certifier sets the standard at 𝑠𝑃𝑄∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' NGO certifier can set the ECSR standard for certification at either 𝑠 = 𝑠𝑃𝑄𝑈1or 𝑠 = 𝑠𝑃𝑄𝑈2 level for participation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' If 𝑠 = 𝑠𝑃𝑄𝑈1 is chosen as ECSR standard, then only price-setting firm 1 will get the certification and quantity-setting firm 2 will not get ECSR certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Interestingly, profit of firm 2 will be higher than firm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  On the other hand, 𝑠 = 𝑠𝑃𝑄𝑈2 as ECSR standard leads to both firms getting the certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' In this case also, firm 1’s profit would be lower than firm 2’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' This indicates that quantity setting firm 2 has net advantage over price setting firm 1 irrespective of whether firm 1 unilaterally get the ECSR certification or both firms get the certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' This is a new result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Therefore, to induce the firms in adopting the certification, the standard would be set at 𝑠 = 𝑠𝑃𝑄𝑈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Further, we find that consumers and firms would benefit from such ECSR standard as compared to no ECSR at all because  NCSPQC > NCSPQN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  Proposition 2:  In a price vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' quantity competition, a) NGO certifier will set the ECSR standard below the optimal level b) if ECSR certification standard is set at 𝑠 = 𝑠𝑃𝑄𝑈1, then only price-setting firm will get the certification, whereas quantity-setting firm 2 will not opt for certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' c) if ECSR certification standard is set at 𝑠 = 𝑠𝑃𝑄𝑈2, then both firms will get the certification and it is beneficial for both firms and consumers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Comparison of ECSR Certification Standards  Comparing the optimal ECSR standard, 𝑠 by the NGO certifier across endogenous market structure, we observe that 𝑠𝑃𝑃∗ > 𝑠𝑃𝑄∗ > 𝑠𝑄𝑄∗ indicating Bertrand has the highest level followed by price-quantity and lastly Cournot case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Proposition 3: Across the spectrum of market structure, the NGO certifier’s optimal ECSR standard rankings are  𝑠𝑃𝑃∗ > 𝑠𝑃𝑄∗ > 𝑠𝑄𝑄∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' In all the cases, the NGO certifier is not able to implement the optimal level of ECSR standard because the firms will not adopt such ECSR standards as that leads to lower profit for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Therefore, the certifier would choose a sub-optimal ECSR standard to incentivize the firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Comparing these equilibrium standards, we get the ranking in proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  Proposition 4: The NGO certifier’s equilibrium ECSR standard rankings are 𝑠𝑃𝑄𝑈1 > 𝑠𝑄𝑄𝑈 > 𝑠𝑃𝑃𝑈 > 𝑠𝑃𝑄𝑈2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Endogenous Market Structure: Price or Quantity Contract Now, we solve the first stage of the game where firms have options to choose price or quantity contracts in the product market competition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' For the sake of brevity, we do not consider the case where no firm chooses ECSR certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The outcome of that subgame will be identical to Singh and Vives (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  Lemma 2 (Singh and Vives, 1984): In a product market competition for substitute goods1, with price and quantity as strategic choices, firms choose quantity contracts as dominant strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  ECSR certification standards and market structure  If firms opt for the ECSR certification, then the outcome of the subgame can differ from Singh and Vives (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The certifier can choose a uniform standard irrespective of the nature of market competition, or different standards based on nature of competition2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' We only consider possibility of uniform ECSR certification standards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' In case of uniform ECSR standard, there are four choices, 𝑠𝑃𝑄𝑈1 > 𝑠𝑄𝑄𝑈 > 𝑠𝑃𝑃𝑈 > 𝑠𝑃𝑄𝑈2 (see Proposition 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' If the NGO certifier sets the lowest three ECSR certification standard, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', either 𝑠𝑃𝑄𝑈2 or 𝑠𝑃𝑃𝑈 or 𝑠𝑄𝑄𝑈, then the Nash equilibrium outcome of the game in Table 1, is {Quantity, Quantity}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' On the other hand, if the ECSR certifier sets the standard at the highest level possible i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', 𝑠𝑃𝑄𝑈1, then there are two Nash equilibria outcomes of the game {Price, Quantity} and {Quantity, Price}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  1 In this paper, we only consider substitute goods in the market offered by competing firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 2 But from a real-world point of view, such standards may not be feasible due to monitoring issues, discrimination, and mimicking behavior among firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  Table 1: Price-Quantity Contract Game (with ECSR certification)  Firm 2  Firm 1  Price  Quantity  Price  𝜋1  𝑃𝑃𝐶,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝜋2  𝑃𝑃𝐶  𝜋1  𝑃𝑄𝐶,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝜋2  𝑃𝑄𝐶  Quantity  𝜋1  𝑄𝑃𝐶,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝜋2  𝑄𝑃𝐶  𝜋1  𝑄𝑄𝐶,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝜋2  𝑄𝑄𝐶  Proposition 5: In a price-quantity contract game,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' a) If a certifier decides,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' the uniform ECSR standard at either 𝑠𝑃𝑄𝑈2 or 𝑠𝑃𝑃𝑈 or 𝑠𝑄𝑄𝑈 level,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' the subgame perfect Nash equilibrium is {Quantity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Quantity} b) If the certifier decides,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' the uniform ECSR standard at 𝑠𝑃𝑄𝑈1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' there are two subgame perfect Nash equilibria {price,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Quantity},' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' {Quantity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Price} Proof: See online appendix  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Conclusion In this paper, we analyze the relationship between endogenous market structure and strategic ECSR in a differentiated duopoly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' We show that NGO certifier will always set the ECSR standards below the optimal level to ensure participation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' In a price-quantity game, there is possibility of partial or full compliance with ECSR standards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Lastly, while setting a uniform ECSR standards in endogenous market structure, there is a possibility of Cournot outcome as well as mixed market outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
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+page_content=' 108-111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
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+page_content=', Mitrokostas, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', and Petrakis, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
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+page_content=' Canadian Journal of Economics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 46(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 282-309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Singh, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', and Vives, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' (1984) Price and quantity competition in a differentiated duopoly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The Rand Journal of Economics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 546-554.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  ONLINE APPENDIX  A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' A 𝑝𝑝 game (Bertrand Competition) We use the superscript PPN to denote equilibrium outcome for firms not adopting ECSR in 𝑝𝑝 game i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', Bertrand competition, otherwise PPC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Solving the game, we get 𝑞1 𝑃𝑃𝑁 = 𝑞2 𝑃𝑃𝑁 = 𝐴 2+𝛾−𝛾2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝑝1 𝑃𝑃𝑁 = 𝑝2 𝑃𝑃𝑁 = 𝐴(1−𝛾) 2−𝛾 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝜋1 𝑃𝑃𝑁 = 𝜋2 𝑃𝑃𝑁 = 𝐴2(1−𝛾) (2−𝛾)2(1+𝛾) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' NCSPPN = 𝐴2(1−2𝑑+𝛾) (2+𝛾−𝛾2)2                             (1) If the firms decide to adopt for ECSR and get certification for the same, the outcomes are 𝑞1 𝑃𝑃𝐶 = 𝑞1 𝑃𝑃𝐶 = 𝐴 + 𝛼𝑠 2 + 𝛾 − 𝛾2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝑝1 𝑃𝑃𝐶 = 𝑝2 𝑃𝑃𝐶 = (1 − 𝛾)(𝐴 + 𝛼𝑠) 2 − 𝛾 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝜋1 𝑃𝑃𝐶 = 𝜋2 𝑃𝑃𝐶 = (1 − 𝛾)(𝐴 + 𝛼𝑠) 2 (2 − 𝛾)(2 + 𝛾 − 𝛾2) − 𝑠2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' NCSPPC = (𝐴+𝛼𝑠)2 (2−𝛾)2(1+𝛾) − 2𝑑(𝐴+(𝛼+(−2+𝛾)(1+𝛾))𝑠)2 (2+𝛾−𝛾2)2 (2) For a firm to be adopting ECSR, the certification threshold needs to be lower than the level of pollution, otherwise the cost will be more than its benefits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' For 𝑞𝑖 𝑃𝑃𝐶 > 𝑠, 𝑠 < 𝐴 2−𝛼+𝛾−𝛾2 should be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Comparing the profits of firms3 with or without ECSR, 𝜋1 𝑃𝑃𝐶 − 𝜋1 𝑃𝑃𝑁 = 𝐴2(1 − 𝛾) + 2𝐴𝛼(1 − 𝛾)𝑠 − (4 − 𝛼2(1 − 𝛾) − (3 − 𝛾)𝛾2)𝑠2 (2 − 𝛾)2(1 + 𝛾)  3 Given the symmetry of the firms and their outcomes, we only compare the results of one firm, and it holds for both of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  We observe that 𝜋1 𝑃𝑃𝐶 − 𝜋1 𝑃𝑃𝑁 > 0 if 𝑠 < 𝑠𝑃𝑃𝑈 = 2𝐴𝛼(1−𝛾) 4−𝛼2+𝛼2𝛾−3𝛾2+𝛾3 , which provides the upper bound for the ECSR spending to adopt the ECSR certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' So, firms will spend strategically on ECSR and get certification if 𝑠 < 𝑠𝑃𝑃𝑈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='4  Optimal ECSR Certification Standard  We obtain the optimal choice of ECSR certification standard in case of NGO certifier by evaluating 𝑑 𝑁𝐶𝑆𝑃𝑃𝐶 𝑑𝑠 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' We get, 𝑠𝑃𝑃∗ = 𝐴(𝛼 + 𝛼𝛾 − 2𝑑(𝛼 − (2 − 𝛾)(1 + 𝛾))) 2𝑑(𝛼 − (2 − 𝛾)(1 + 𝛾))2 − 𝛼2(1 + 𝛾) 𝑠𝑃𝑃∗ > 0 if 𝑑 > 𝛼2+𝛼2𝛾 2(𝛼−(2−𝛾)(1+𝛾))2 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Further, 𝑠𝑃𝑃∗ > 𝑠𝑃𝑃𝑈 when 𝑑 > 𝛼2+𝛼2𝛾 2(𝛼−(2−𝛾)(1+𝛾))2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' This means that an NGO certifier’s optimal level of ECSR standard would be higher that the upper limit for the firms in Bertrand competition and a firm would not choose to spend on ECSR if a certifier sets the standard at 𝑠𝑃𝑃∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Therefore, to induce the firms, the standard would be set at 𝑠 = 𝑠𝑃𝑃𝑈 by the NGO certifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Further, we can also show that consumer and firms would benefit from such ECSR standard as compared to no ECSR at all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', NCSPPC > NCSPPN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  Proposition A1:  An NGO certifier would set the ECSR standard below the optimal level if firms engage in Bertrand competition and, it is beneficial for both firms and consumers in terms of profit and net consumer surplus, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' A 𝑞𝑞 game (Cournot Competition)  4 Superscript U denotes upper bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  For Cournot game, we use the superscript QQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' The outcomes of the product market competition, if firms do not adopt ECSR are, 𝑞1 𝑄𝑄𝑁 = 𝑞2 𝑄𝑄𝑁 = 𝐴 2+𝛾 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝑝1 𝑄𝑄𝑁 = 𝑝2 𝑄𝑄𝑁 = 𝐴 2+𝛾 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝜋1 𝑄𝑄𝑁 = 𝜋2 𝑄𝑄𝑁 =  𝐴2 (2+𝛾)2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' NCS𝑄𝑄𝑁 = 𝐴2(1−2𝑑+𝛾) (2+𝛾)2 (3) On the other hand, if the firms decide to adopt ECSR certification, the outcomes would be, 𝑞1 𝑄𝑄𝐶 = 𝑞2 𝑃𝑃𝐶 = 𝐴+𝛼𝑠 2+𝛾  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝑝1 𝑄𝑄𝐶 = 𝑝2 𝑄𝑄𝐶 = 𝐴+𝛼𝑠 2+𝛾 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' 𝜋1 𝑄𝑄𝐶 = 𝜋2 𝑄𝑄𝐶 = (𝐴+𝛼𝑠)2 (2+𝛾)2 − 𝑠2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' NCS𝑄𝑄𝐶 = (1+𝛾)(𝐴+𝛼𝑠) 2−2𝑑(𝐴−(2−𝛼+𝛾)𝑠)2 (2+𝛾)2 (4)  For 𝑞𝑖 𝑄𝑄𝐶 > 𝑠 , 𝑠 < 𝐴 2−𝛼+𝛾 should be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Further comparing the profits of firms with and without adopting ECSR, 𝜋1 𝑄𝑄𝐶 − 𝜋1 𝑄𝑄𝑁 = 𝐴2 + 2𝐴𝛼𝑠 + (−2 + 𝛼 − 𝛾)(2 + 𝛼 + 𝛾)𝑠2 (2 + 𝛾)2  A firm would profit from adopting ECSR if 𝜋1 𝑄𝑄𝐶 > 𝜋1 𝑄𝑄𝑁 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', when 𝑠 < 𝑠𝑄𝑄𝑈 = 2𝐴𝛼 4−𝛼2+4𝛾+𝛾2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' This denotes the upper bound to spend on ECSR for certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  Optimal ECSR Certification Standard We obtain the optimal choice of ECSR certification standard in case of NGO certifier by evaluating 𝑑 𝑁𝐶𝑆𝑄𝑄𝐶 𝑑𝑠 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' We get, 𝑠𝑄𝑄∗ = 𝐴(𝛼 + 𝛼𝛾 + 2𝑑(2 − 𝛼 + 𝛾)) 2𝑑(2 − 𝛼 + 𝛾)2 − 𝛼2(1 + 𝛾) 𝑠𝑄𝑄∗ > 0 if 𝑑 > 𝛼2+𝛼2𝛾 2(2−𝛼+𝛾)2 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Further, 𝑠𝑄𝑄∗ > 𝑠𝑄𝑄𝑈 when 𝑑 > 𝛼2+𝛼2𝛾 2(2−𝛼+𝛾)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' This means that a certifier’s optimal level of ECSR standard would be higher than the upper limit for the firms in Cournot competition and a firm would not choose to spend on ECSR if a certifier sets the standard at 𝑠𝑄𝑄∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Therefore, to induce the firms, the standard would be set at 𝑠 = 𝑠𝑄𝑄𝑈 by the  NGO certifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Further, we can also show that consumer and firms would benefit from such ECSR standard as compared to no ECSR at all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=', NCSQQC > NCSQQN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  Proposition A2:  An NGO certifier would set the ECSR standard below the optimal level if firms engage in Cournot competition and, it is beneficial for both firms and consumers in terms of profit and net consumer surplus, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content='  A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' Proof for Proposition 5 Proof: a) In all three cases, we observe that 𝜋1 𝑄𝑃𝐶 > 𝜋1 𝑃𝑃𝐶 and 𝜋1 𝑄𝑄𝐶 > 𝜋1 𝑃𝑄𝐶 for firm 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' and 𝜋2 𝑃𝑄𝐶 > 𝜋2 𝑃𝑃𝐶 and 𝜋2 𝑄𝑄𝐶 > 𝜋2 𝑄𝑃𝐶 for firm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' This makes ‘Quantity contract’ as the dominant strategy for both the firms and the Nash equilibrium is {Quantity, Quantity}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' b) In this case, we observe that 𝜋1 𝑄𝑃𝐶 > 𝜋1 𝑃𝑃𝐶 and 𝜋1 𝑄𝑄𝐶 < 𝜋1 𝑃𝑄𝐶 for firm 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' and 𝜋2 𝑃𝑄𝐶 > 𝜋2 𝑃𝑃𝐶 and 𝜋2 𝑄𝑄𝐶 < 𝜋2 𝑄𝑃𝐶 for firm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}
+page_content=' This means that there are no dominant strategies and the best response of either firm is the choice of opposite strategy, and the Nash equilibria are {Price, Quantity}, {Quantity Price}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfmAQH/content/2301.03291v1.pdf'}

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+‘Good job!’ The impact of positive and negative
+feedback on performance.
+Daniel Goller1,2, Maximilian Späth3*
+1 Centre for Research in Economics of Education, University of Bern
+2 Swiss Institute for Empirical Economic Research, University of St.Gallen
+3 Department of Economics, University of Potsdam
+This version: January 30, 2023
+Abstract
+We analyze the causal impact of positive and negative feedback on professional
+performance. We exploit a unique data source in which quasi-random, naturally
+occurring variations within subjective ratings serve as positive and negative feed-
+back. The analysis shows that receiving positive feedback has a favorable impact
+on subsequent performance, while negative feedback does not have an effect. These
+main results are found in two different environments and for distinct cultural back-
+grounds, experiences, and gender of the feedback recipients. The findings imply
+that managers should focus on giving positive motivational feedback.
+Keywords: Feedback, Performance, Causal Analysis, Cultural Background
+∗Preliminary version. Do not quote or circulate without permission of one of the authors. Comments
+are very welcome. We like to thank Swiss-ski (Swiss ski federation), Michel Roth, David Morris, Alexan-
+der Mesch, and the DSV (German swimming federation) for valuable insights into the sports contests
+from the perspective of (former) professional athletes. Also, we thank participants of the ESEA Confer-
+ence, 2022, and the Berlin School of Economics Workshop, 2022, as well as Enzo Brox, Lisa Bruttel, and
+Sandro Heiniger for their helpful comments and suggestions.
+arXiv:2301.11776v1  [econ.GN]  27 Jan 2023
+
+1
+Introduction
+Providing performance feedback is one of the main tasks of managers and leaders (Morgeson,
+DeRue, & Karam, 2010). One important aim of feedback is to create a favorable emotional
+response.
+At best, positive or negative feedback can motivate employees and increase their
+productivity. In the worst case, it leaves the employees frustrated and unproductive. Therefore,
+the question of how feedback impacts subsequent performance is of tremendous importance.
+Consequently, numerous studies investigating the impact of feedback on creativity (Harrison
+& Rouse, 2015; Itzchakov & Latham, 2020; Kim & Kim, 2020), the learning process of indi-
+viduals and firms (Hattie & Timperley, 2007; Lee, Lee, & Kim, 2021) or motivation (Deci &
+Casico, 1972; Fong, Patall, Vasquez, & Stautberg, 2019) emerged. In particular for positive and
+negative feedback on performance or productivity, studies show the full range from favorable
+to unfavorable effects (Eggers & Suh, 2019; Kluger & DeNisi, 1996; Podsakoff & Farh, 1989;
+Sleiman, Sigurjonsdottir, Elnes, Gage, & Gravina, 2020; Waldersee & Luthans, 1994, etc).
+The two major difficulties when investigating the impact of feedback on performance are
+(1) observing truthful and trustworthy feedback in real-incentive situations and (2) quantifying
+feedback and performance. While observational studies typically fail to satisfactorily tackle the
+second difficulty, experimental studies cannot fulfill the first requirement. We are not aware of
+any causal study in which both requirements are met together.
+To address this common shortcoming, we exploit a unique setting to estimate the causal effect
+of positive and negative feedback on subsequent performance. For this purpose, we use data
+from professional sports: diving as the primary data source, and ski jumping for supplementary
+analyses. In these sports, individuals’ performance is evaluated subjectively by a jury of seven
+(or five) experienced judges according to precise rules. Each judge independently issues one
+rating for the task performance (hereafter, "judges rating" or “rating”). Discarding the highest
+and lowest rating(s), the common assessment of the jury is calculated from the average of the
+three remaining ratings (hereafter, “jury performance assessment”).1
+Following the definition in Kluger and DeNisi (1996), stating that feedback is information
+about one’s task performance provided by an external agent, we consider the deviation of the
+discarded (highest and lowest) ratings from the jury’s performance assessment as feedback on
+1Receiving the jury performance assessment can already be seen as a knowledge of results (Kluger
+& DeNisi, 1996) intervention. The analysis of this knowledge of results, however, is beyond the scope of
+this paper.
+2
+
+task performance. The discarded ratings are not relevant to the assessment of task performance,
+but this additional information about judges’ general perceptions of performance provides feed-
+back that can only work through the motivational channel on subsequent performance. Kluger
+and DeNisi (1996) argue that the feedback sign depends on the relation between the performance
+rating and a benchmark. In line with this, discarded ratings define quasi-randomly occurring
+positive (negative) deviations from the jury performance evaluation that serve as positive (neg-
+ative) feedback. No deviation from the benchmark implies neutral feedback. We describe the
+evaluation and feedback process in more detail in Section 3.2, Figure 1.
+We test several of the propositions from the model of the seminal work by Kluger and
+DeNisi (1996) within a single framework.
+In our setup, the feedback is truthful, accurately
+observable, and from an external source. Feedback can impact subsequent performance only
+through its motivational impact.
+Performance is strongly incentivized and can be precisely
+quantified. The performance is measured in non-artificial tasks that individuals are not only
+familiar with but that are routine aspects of their work. What is particularly valuable from a
+management perspective is that we can investigate the impact of feedback in an international
+context.
+Theoretically guided by the feedback intervention model (Kluger & DeNisi, 1996), we inves-
+tigate the effect of positive and negative feedback on performance. Further, we investigate the
+internal and external generalizability of the results. To assess internal generalizability, we can
+use our extensive data to analyze whether situational (or personal) variables and task charac-
+teristics moderate the effects of the feedback intervention on performance. The international
+sample covering female and male individuals from more than 50 nations from 6 continents offer
+the unique opportunity to analyze feedback effects for different cultural backgrounds and gender
+within the same framework. To investigate external generalizability, we complement the main
+findings with a second, independent setting. We investigate these aspects using both classical
+statistical and causal machine learning methods. This is followed by analyses examining the
+feedback interventions’ long-term, repetition, and spill-over effects.
+Our analysis shows a performance-enhancing causal effect of positive feedback. The favorable
+effect of positive feedback is found for recipients from different cultural backgrounds, experience
+levels, and gender. We observe favorable effects even when individuals repeatedly receive positive
+feedback. The impact of positive feedback is stronger when the relevance of the task is high.
+3
+
+In contrast to all this, negative feedback on average does not have an impact on performance.
+Merely, the subgroup of the more experienced individuals benefits from negative feedback.
+Our findings imply that managers can use positive feedback to enhance the performance of
+their employees. Importantly, positive feedback can be given repeatedly on a regular basis. It
+has a favorable impact irrespective of several relevant characteristics of the recipient and can be
+universally applied in an international context. With our main finding we are in line with the
+studies conducted by Azmat and Iriberri (2010), Bandiera, Larcinese, and Rasul (2015), Choi,
+Johnson, Moon, and Oah (2018), and Itzchakov and Latham (2020) for positive feedback and
+the meta-study by Fong et al. (2019) for negative feedback. We complement decades of research
+that provides guidelines on how to optimally give feedback (Balcazar, Hopkins, & Suarez, 1985;
+Alvero, Bucklin, & Austin, 2001; Sleiman et al., 2020).
+2
+Theoretical framing
+To provide a theoretical foundation for the later empirical analysis, we begin by describing the
+concept of feedback. Then, we collect relevant empirical research and form predictions based on
+propositions stated by Kluger and DeNisi (1996).
+2.1
+The concept of feedback
+Feedback exists in many forms. Kluger and DeNisi (1996) define feedback as "[...] actions taken
+by (an) external agent (s) to provide information regarding some aspect (s) of one’s task per-
+formance" (p. 255). Burgers, Eden, van Engelenburg, and Buningh (2015) distinguish between
+elaborate and simple feedback. Elaborate feedback typically includes a lengthy explanation,
+which provides a guide for learning. Simple feedback merely gives information, about whether
+something was done right or wrong. Burgers et al. (2015) further distinguish between descrip-
+tive, comparative, and evaluative feedback. Descriptive feedback – sometimes called objective
+feedback (Johnson, 2013) – merely sums up behavior shown by the agent. Comparative feedback
+uses the performance of other individuals as a reference. Evaluative feedback provides a judg-
+ment of the performance. Villeval (2020) distinguishes between a cognitive and a motivational
+perspective. The cognitive perspective rests on the assumption that individuals have imperfect
+knowledge about their skills. Here, feedback serves as a signal used in an information-updating
+4
+
+process. The motivational perspective focuses on the impact of feedback on intrinsic motivation.
+Individuals might receive feedback from one agent or several agents. Stone and Stone (1984)
+find that receiving feedback from two sources instead of one source increases self-perceived task
+competence. Related, there is a strand of literature analyzing multi-source feedback (Bailey
+& Fletcher, 2002; Smither, London, & Reilley, 2005), also called 360 degree feedback (DeNisi
+& Kluger, 2000). Finally, feedback can be with direct consequences or inconsequential. Often
+feedback comes without direct (monetary) consequences. Still, research shows that agents also
+react to irrelevant information (Abeler, Falk, Goette, & Huffman, 2011; Cason & Mui, 1998).
+The focus of our paper lies on the impact of simple and evaluative feedback on subsequent
+performance. The feedback is subjective in the sense that is created by subjective evaluation
+based on objective guidelines. Our study focuses on the impact of single feedback embedded
+in a multi-source evaluative process. The feedback has no further consequences besides that
+it can motivate or demotivate the recipient.
+One important distinction is between positive
+and negative feedback.
+We define positive feedback, sometimes called promotion-orientated
+feedback (Carpentier & Mageau, 2013), as the expression that the evaluated performance is
+above a certain reference point. We define negative feedback, sometimes called change-orientated
+feedback (Carpentier & Mageau, 2013) or corrective feedback (Waldersee & Luthans, 1994), as
+the expression that the rated performance is below the reference.
+2.2
+Review and hypotheses
+In their influential model, Kluger and DeNisi (1996) assume that there are no behavioral effects
+when there is no discrepancy between the rating and the reference. Positive feedback increases
+effort if the agent has the possibility to set new self-goals. Likewise, negative feedback leads
+to an increase in effort. Similarly, Villeval (2020) argues that positive and negative feedback
+fosters motivation. On the other hand, positive feedback can lead to a decrease in efforts, when
+individuals have no possibility to set new goals (Kluger & DeNisi, 1996). Negative feedback can
+discourage individuals when it threatens the self-perception of their competence (Fong et al.,
+2019).
+Some empirical studies show a favorable impact of positive feedback. Choi et al. (2018) find
+a better performance in a computerized task after purely positive feedback than in a baseline
+treatment. Itzchakov and Latham (2020) report better performance in a brainstorming task
+5
+
+after positive than after neutral feedback. Bandiera et al. (2015) report that positive feedback
+improves the performance of university students and Azmat and Iriberri (2010) that positive
+relative rank feedback enhances the performance of high school students. Other studies, such
+as Podsakoff and Farh (1989) reporting no impact of positive feedback on performance in an
+object-listing task, find no influence of positive feedback. Waldersee and Luthans (1994) even
+report an adverse impact of positive feedback on the performance of employees of fast food
+restaurants.
+Empirical work on the effect of negative feedback provides an ambiguous picture. Several
+studies show a favorable impact of negative feedback.
+As for positive feedback, Choi et al.
+(2018) find an improved performance after purely negative feedback in comparison to a baseline
+treatment. Azmat and Iriberri (2010) find a favorable effect of negative relative rank feedback.
+Itzchakov and Latham (2020) report a positive impact of negative feedback on performance in a
+brainstorming task. Podsakoff and Farh (1989) report a favorable impact of negative feedback
+in an object-listing task. Waldersee and Luthans (1994) find a performance-enhancing effect of
+negative feedback for employees of fast food restaurants. Some research, such as the meta-study
+by Fong et al. (2019), shows no impact of negative feedback. Other studies show an unfavorable
+impact. For example, Deci and Casico (1972) observe that a negative feedback group shows
+lower motivation to conduct a puzzle task than a control group.
+A reason for the ambiguity in reaction to negative feedback might be heterogeneity in the way
+how individuals update their perception after receiving self-relevant information. Some research
+finds that agents do not fully update their self-perception after negative information, while they
+update their self-perception after observing a positive signal (Eil & Rao, 2011; Kuzmanovic,
+Jefferson, & Vogeley, 2015; Möbius, Niederle, Niehaus, & Rosenblat, 2022; Sharot et al., 2012).
+This would imply to find no reaction to negative feedback. Yet, other studies observe a rational
+updating of beliefs for positive and negative information (Barron, 2021) or even an overweighting
+of negative information (Coutts, 2019; Ertac, 2011), leaving this strand of empirical research
+inconclusive.
+We build our hypotheses on the theoretical model by Kluger and DeNisi (1996). We argue
+that in the domain of professional performance, there is always the possibility to set more am-
+bitious goals. This indicates that positive feedback might have a favorable impact.
+6
+
+Hypothesis 1 - Positive Feedback:
+The performance is better after receiving positive feedback than after receiving
+neutral feedback.
+We follow Kluger and DeNisi (1996) and Villeval (2020) by assuming that also negative feed-
+back has a performance-enhancing effect. We argue that in the field of professional performance,
+individuals have a rather stable self-perception of confidence.
+Hypothesis 2 - Negative Feedback:
+The performance is better after receiving negative feedback than after receiving
+neutral feedback.
+A vital aspect that most empirical studies usually can barely answer is the question of the
+generalizability of these hypotheses. Here, it is useful to distinguish between the two superor-
+dinate layers of personal and task-specific characteristics by which effects could be moderated
+(compare Fong et al. (2019), for example).
+For task characteristics, our hypotheses more readily generalize when individuals’ responses
+to feedback are inherently similar irrespective of the difficulty and importance of the task.
+Difficult and easy tasks might be perceived differently (Moore & Healy, 2008), which can lead to
+different perceptions of feedback (Pulford & Colman, 1997) and varying subsequent performance
+(Vancouver & Tischner, 2004). Kluger and DeNisi (1996) argue that the reaction to feedback
+is stronger the fewer cognitive resources are needed to perform the task. Likewise, performance
+might differ depending on the importance of the task (Goller & Heiniger, 2022). Here, Kluger
+and DeNisi (1996) argue that the effectiveness of feedback increases the more attention is on
+the task.
+Guided by the model predictions of Kluger and DeNisi (1996), we do not expect
+generalizability across task characteristics. Accordingly, we expect stronger feedback effects on
+performance for (relatively) easier tasks needing fewer cognitive resources and more important
+tasks that require more attention.
+Within the personal domain, three potential moderators seem highly relevant in modern
+workplaces: cultural background, gender, and experience of the feedback recipients. The litera-
+ture acknowledges that despite the high relevance of cultural differences in a globalized world,
+non-WEIRD (not coming from Western, Educated, Industrialized, Rich, and Democratic coun-
+tries) individuals are largely underrepresented in behavioral research (Henrich, Heine, & Noren-
+zayan, 2010). For example, authors postulate differences in self-construals (Markus & Kitayama,
+7
+
+1991), in feedback seeking of individuals (Sully De Luque & Sommer, 2000) and in feedback re-
+action of firms (Rhee, Alexandra, & Powell, 2020) between collectivistic and individualistic
+cultures.
+Bear, Cushenbery, London, and Sherman (2017) postulate and Berlin and Dargnies (2016),
+respectively, Roberts and Nolen-Hoeksema (1994) observe different feedback reactions for women
+than for men. Eggers and Suh (2019) find that the reaction of organizations to negative feedback
+depends on the experience in the business area. Kluger and DeNisi (1996) propose differential
+effects for individuals’ behavioral or psychological traits.
+More relevant from a managerial
+perspective is if those potentially moderating traits are associated with directly observable char-
+acteristics of individuals in a company’s diverse context. We refrain from forming explicit ex-
+pectations and leave the question of generalizability for different cultural backgrounds, genders,
+and experience levels exploratory.
+3
+Setting and data
+We collect data on international competitions of two competitive sports. In the two sports,
+namely, ski jumping and diving, athletes compete individually in multi-round competitions. In
+each round, the athletes’ task execution is evaluated by multiple professional judges.
+Besides the similarities, there are several specifics to each of the sports. In diving, athletes
+acrobatically jump into the water. We use data on individual performances in three different
+types of competitions: 1m springboard, 3m springboard, and 10m platform. The scoring consists
+of two elements. First, each jump is rated by seven judges with respect to the proper execution.
+Each judge can reward up to 10 style points (in increments of 0.5). The two highest and the two
+lowest judges’ ratings are discarded for the jury performance assessment of the jump, for which
+the remaining three judges’ ratings are summed up. Second, the jury performance assessment
+is multiplied by the difficulty coefficient, which depends on the complexity of the jump and is
+assigned to the jump according to the official rules.2 In competitions between women, points
+are accumulated over five jumps, and in competitions between men, over six jumps. Depending
+on the contest there are preliminary rounds and/or semi-finals and the final round.
+2See
+https://resources.fina.org/fina/document/2021/01/12/916f78f6-2a42-46d6-bea8
+-e49130211edf/2017-2021_diving_16032018.pdf for a current version of the rules (last accessed on
+01/23/2023).
+8
+
+In the winter sport of ski jumping, athletes jump on skis after sliding down a ramp. Scoring
+consists of four components. First, athletes receive points for the length of their jump. Second,
+there are compensation points for the force and direction of the wind. Third, scoring depends on
+the length of the ramp (gate points). Fourth, athletes receive up to 20 style points (in increments
+of 0.5) for the flight and landing of the jump. The (style) ratings are independently rewarded by
+five judges according to official rules.3 The worst and the best rating are discarded and the other
+three are accounted for the athletes’ score of the round. In a typical competition, 50 athletes
+start in the first round, of which the 30 best reach the final round. After the final round, both
+jumps’ total scores are added to determine the winner and the succeeding rankings.
+3.1
+Data sets
+Table 1: Descriptive statistics
+Diving
+Ski jumping
+Mean
+Std. dev.
+Mean
+Std. dev.
+Panel A: Treatments
+Positive Feedback (deviation positive)
+0.426
+(0.286)
+0.316
+(0.262)
+Negative Feedback (deviation negative)
+0.477
+(0.320)
+0.357
+(0.290)
+Panel B: Outcomes
+Score
+68.737
+(14.557)
+118.647
+(16.204)
+Performance (rem. 3 judges’ ratings)
+7.119
+(1.189)
+17.771
+(0.744)
+Performance (all 5 / 7 judges’ ratings)
+7.110
+(1.182)
+17.765
+(0.741)
+Panel C: Covariates
+Compatriot judge
+0.248
+0.457
+Home event
+0.099
+0.127
+Experience (Age in years)
+22.429
+(3.789)
+26.836
+(4.949)
+Female
+0.450
+Difficulty
+3.211
+(0.331)
+Distance
+122.608
+(11.837)
+Prev. Distance
+123.940
+(11.143)
+Prev. Difficulty
+3.166
+(0.317)
+Prev. Performance
+7.270
+(0.958)
+17.854
+(0.580)
+N
+13075
+4529
+Notes: Mean and standard deviation (in parentheses; for non-binary variables). rem. =
+remaining. Some variables were only observed in one of the data sets. Full descriptive
+statistics in Appendix Table 6.
+3See
+https://assets.fis-ski.com/image/upload/v1665482445/fis-prod/assets/ICR_Ski
+_Jumping_2022_marked-up.pdf for a current version of the rules (last accessed on 01/23/2023).
+9
+
+The main analysis is conducted using data on official diving competitions from 2013 through
+2017. This includes special events such as World Championships and the Summer Olympics.
+Except for the first jump, each jump constitutes one observation. We exclude observations where
+the rating points of the current or subsequent jump are at the lower or upper bound.4 Athletes
+who stop competing during the contest are excluded, e.g., due to injury.
+We conduct the analysis based on 13075 observations.
+The data consists of the jumps
+performed by 434 athletes from 54 countries in Africa, Asia, Europe, North America, Oceania,
+and South America.
+As visible in panel C of Table 1, roughly one-half of the athletes are
+female and on average 22.4 years old. In 25 percent of the cases, at least one of the judges
+has the same nationality as the task taker and about 10 percent of observations are at a home
+event. Difficulty and previous difficulty of the jump are on average around 3.2, and (current and
+previous) performance are on average around 7.1 to 7.3.
+For our analysis on ski jumping, we have 4529 observations on events from the 2010/11
+through 2016/17 season (based on a collection conducted by Krumer, Otto, and Pawlowski
+(2022)). Each observation refers to a second jump. Athletes who fail to qualify for the second
+round are excluded. In 13 percent of the cases, athletes perform in their respective country of
+birth. In 45 percent of the cases, one of the judges is of the same nationality as the performing
+athlete. The average age is about 26.8 years. Jumps are on average about 123 meters and
+(current and previous) performance are on average around 17.7 (see panels B and C of Table 1).
+4To put it more concretely: We remove observations that have received an average score of 9.5 or
+higher (19.5 in ski jumping), as well as those with an average score of less than 5 (14 in ski jumping).
+Furthermore, we remove observations with individual scores of 3 or lower (14 in ski jumping), as these
+are most likely to be crashes. All of these choices are robust to changes, and we show the robustness of
+the results to data pre-processing in the results section.
+10
+
+3.2
+Variables
+Figure 1: Illustration of the evaluation and feedback process
+Notes: For a current task (on the right), feedback is given for the previous task (left). The broken
+arrows represent our main hypotheses, i.e., the potential influence of feedback on performance
+in the subsequent task. Task and individual characteristics (dotted square) potentially
+moderate this effect. In the case of seven judges, the two highest and lowest ratings are
+discarded, and only the most extreme ratings are used. See Section 5.5 for other specifications
+used in the robustness checks.
+Figure 1 describes the evaluation and feedback process in our setup. For the task execution
+evaluation, each judge in the jury independently gives a numerical rating for the task execution
+of the task taker.
+The largest and smallest of those judges’ ratings are discarded and the
+jury performance assessment is the mean of the remaining (three) judges’ ratings. The task
+performance assessment quantifies the task performance result.
+In our study, we focus on the discarded judges’ ratings that are not regarded for the jury’s
+performance assessment and can affect subsequent performance only through their motivational
+impact. Our treatment variables are constructed as deviations of the discarded judges’ ratings
+from the jury performance assessment. More concrete, Deviation positive is constructed by sub-
+tracting the jury performance assessment (the mean of the ratings in absence of the discarded
+ratings) from the largest discarded judges’ rating. Deviation negative is constructed by sub-
+tracting the smallest discarded judges’ rating from the jury performance assessment.5 We define
+5Additionally, we construct and test two alternative specifications. All specifications can be found in
+the full descriptive statistics in Appendix Table 6. Especially, for diving, there are two (highest/lowest)
+judges’ ratings discarded. The base specification uses the most extreme judges’ ratings. Other specifi-
+11
+
+Highest
+rating
+Deviation
+Taskandindividual
+Positive
+characteristics
+Jury=
+ratings
+feedback
+Panel
+Jury
+of
+Y
+Ratings
+Judges'
+performance
+Judges
+remaining
+assessment
+Deviation
+(5 or 7)
+Negative
+feedback
+Lowest
+rating
+Task
+Task
+taker
+Taskexecution
+performance
+Feedback
+Taskexecution
+result
+Previoustask
+Current taskDeviation positive as positive feedback and Deviation negative as negative feedback. Panel A
+in Table 1 provides an overview of the main treatment variables. Both feedback variables, with
+mean values of 0.426 (0.316) for positive feedback and 0.477 (0.357) for negative feedback, range
+from 0 (for neutral feedback) to 2.5 (for increasingly positive/negative feedback).
+To measure the effect of feedback on subsequent task execution, we use the jury’s perfor-
+mance assessment that the task takers receive for their subsequent performance (hereafter, "Per-
+formance") as our outcome variable. An alternative variable to measure subsequent performance
+is the mean of the ratings from all (5 or 7) judges.
+4
+Empirical strategy
+We study how positive and negative feedback affect subsequent performance. To this end, our
+identification strategy relies on conditional idiosyncratic variations in the differences between
+the jury performance assessment and the discarded ratings. This positive (negative) deviation
+is irrelevant to the assessment of the task performance but provides feedback in the form of
+additional information about the judges’ general perception of the performance.
+The identification strategy presumes that, once we condition on a few observable character-
+istics, there are no omitted influences that are correlated with both outcome, i.e., performance
+in the task, and treatment, i.e., the positive/negative deviation (feedback for the previous task).
+Our approach formalizes to the following linear baseline model:
+Yi = α + β+A+
+i + β−A−
+i + γXi + ϵi,
+where the outcome, Yi, is the performance in the (current) task for individual i. The con-
+tinuous treatments A+/−
+i
+are defined as the positive/negative feedback for the (previous) task,
+and β+/− are the coefficients of interest to investigate our hypotheses 1 and 2. Xi contains
+(pre-determined) covariates of individual i that we need to control for. ϵi is an idiosyncratic
+error term.
+To give credence to the unconfoundedness assumption, we address concerns raised in the lit-
+erature about potential biases in subjective ratings. First, we consider nationality bias (Heiniger
+cation descriptions and results for the robustness of the alternative treatment variable specifications can
+be found in Section 5.5.
+12
+
+& Mercier, 2021; Krumer et al., 2022; Sandberg, 2018; Zitzewitz, 2006), i.e., a judge from the
+same country as the task taker rates the compatriot better than other individuals. To account
+for potentially more positive ratings from judges who are compatriots, we include a) a binary
+variable indicating whether a judge on the panel is a compatriot of the task taker, and b) an
+indicator if the individual competes in a home event in Xi.6 To alleviate remaining concerns
+about bias based on common nationality, we conduct two further checks. A balancing test in Ta-
+ble 8 shows no balancing issues related to compatriot judges. To ensure that the results are not
+driven by individuals that are potentially subject to nationality bias, we perform a robustness
+check in which the affected task takers are removed from the sample.7
+Second, there is evidence in the literature of an order of action bias (Damisch, Mussweiler,
+& Plessner, 2006; Ginsburgh & Van Ours, 2003). Subjective ratings are found to be affected by
+the order of task performance, which threatens our identification when some but not all judges
+are affected. We account for this by controlling for the order in which individuals perform tasks
+(starting order).
+Third, more difficult tasks were found to be rewarded with higher scores–
+the difficulty bias (Morgan & Rotthoff, 2014). The difficulty of a task in our case is precisely
+measurable and predetermined. Specifically, in diving, we control for the difficulty of the jump
+(chosen a priori); in ski jumping, we control for the (previous and current) wind and gate, i.e.,
+the length of the hill–both factors that can influence difficulty and subjective evaluation.
+Fourth, there could be reputation bias (Findlay & Ste-Marie, 2004). This bias can lead to
+better ratings for well-established individuals who typically have a better reputation. To ensure
+conditional independence, we take into account a) individual and individual-by-season fixed
+effects and b) current rank in the competition. Fifth, the accuracy of subjective performance
+ratings is found to vary for different performance qualities (Heiniger & Mercier, 2021). Therefore,
+we include the individual mean and standard deviation of the jury’s performance assessment of
+the previous task in Xi.
+While not testable, we are confident that the conditional independence assumption is satis-
+fied. Still, we offer two types of checks for it. First, in a total of 20 balancing checks in Table 8,
+only one statistically significant test indicates a solid balancing among observable characteristics.
+Second, with respect to unobservable characteristics, we provide an indirect approach to sup-
+6Judges’ decisions regarding possible bias in favor of compatriots might be different in front of a
+supportive crowd (Page & Page, 2010; Goller & Krumer, 2020).
+7The results for this can be found in Table 11 and hardly differ materially from the main results.
+13
+
+port the conditional independence assumption by implementing a placebo treatment test. We
+replace the treatment variable with a pseudo-treatment variable recorded in the future. The task
+performance cannot be influenced by the feedback given in the future of this task. Therefore, if
+we observe all confounding influences, the placebo treatment effect should be zero. If we reject
+this placebo null hypothesis this points to some unobserved confounding (or other issues like
+endogeneity or reverse causality), while not rejecting gives some evidence that the conditional
+independence assumption is plausible. Table 7 shows that this placebo test cannot reject our
+assumption of unconfoundedness.
+To estimate the main effects of interest, we use linear regression and cluster standard errors
+on the individual level. In the second step, we apply a method from the causal machine learning
+literature. For this research, the importance of investigating potential non-linearities in the effect
+lies in the differently observed treatment intensities, i.e., high or low quantified feedback, for
+which it is unclear if an estimated constant treatment effect reflects various treatment intensities
+properly.
+With the non-parametric kernel method for continuous treatment effects introduced by
+Kennedy, Ma, McHugh, and Small (2017) we investigate the effects for different intensities
+of the treatment. The method builds on two steps. First, a (doubly-robust) pseudo-outcome is
+constructed as follows:
+ξ(π, µ) = Y − µ(X, A)
+π(A|X)
+�
+π(A|x)dP(x) +
+�
+µ(x, A)dP(x),
+where the nuisance functions π(A|X) and µ(X, A) are estimated using a random forest estimator
+(Breiman, 2001). The pseudo-outcome ξ(π, µ) is doubly-robust in the sense that only (at least)
+one of the two nuisances needs to be consistent, not both, and is free from confounding influences.
+In the second step, the average potential outcome for given treatment levels is estimated using
+a non-parametric kernel regression of the pseudo-outcome on the continuous treatment variable:
+E(Y a) = E(ξ(π, µ|A = a)).
+14
+
+5
+Results
+5.1
+Main results
+Our first main finding is that positive feedback is enhancing (subsequent) performance. Panel
+A in Table 2 shows a statistically significant and positive coefficient for positive feedback. The
+effect is robust to the inclusion of different sets of covariates. In each specification, the average
+effects are statistically significant at the 1% level. Panel B replicates this finding for our second
+data set. As our second main finding, we observe that negative feedback causes an effect close
+to zero in both panels and all specifications. We do not see any effect of negative feedback on
+performance.
+Table 2: The effect of feedback on performance – sensitivity to different specifications
+Performance
+(1)
+(2)
+(3)
+(4)
+Panel A: Diving (N=13075)
+Positive Feedback
+0.242***
+0.208***
+0.115***
+0.100***
+(0.036)
+(0.034)
+(0.032)
+(0.035)
+Negative Feedback
+0.018
+0.024
+0.001
+0.007
+(0.030)
+(0.030)
+(0.029)
+(0.030)
+Panel B: Ski jumping (N=4529)
+Positive Feedback
+0.201***
+0.180***
+0.145***
+0.107***
+(0.035)
+(0.036)
+(0.034)
+(0.034)
+Negative Feedback
+-0.063
+-0.055
+-0.049
+-0.026
+(0.043)
+(0.041)
+(0.037)
+(0.041)
+Base Covariates
+x
+x
+x
+x
+All Covariates
+x
+x
+x
+Individual Fixed Effect
+x
+Individual x Season FE
+x
+Notes: Linear regression. Full regressions in Tables 9 and 10. All regressions contain previous’
+jumps jury assessment (Base Covariates). All Covariates include prev. jumps wind and
+gate points and distance (ski jumping) or difficulty (diving). Also, points behind,
+compatriot judge, home event, current ranking, SD of previous performance, and start
+order. Standard errors are clustered on the individual level. *, **, and *** represents
+statistical significance at the 10 %, 5 %, and 1 % level, respectively.
+The performance-enhancing impact of positive feedback is rather insensitive to the inclusion
+of more covariates and fixed effects.
+We start with controlling only for performance in the
+previous task in column (1). In column (2) we add several control variables as discussed in
+15
+
+Section 4.
+Columns (3) and (4) add individual fixed effects and individual-by-season fixed
+effects to the regressions. Detailed result tables can be found in the appendix in Tables 9 and
+10, and for the sake of simplicity, all of the following regressions are based on the specification
+used in column (3).
+Figure 2: Non-linear estimation of feedback on performance
+Notes: Non-parametric kernel regression for different levels of positive (left) and negative (right).
+feedback. Expected outcomes (y-axis) and treatment levels (x-axis) are displayed.
+Kernel bandwidths are 0.300 (left) and 0.214 (right) and are determined in a data-driven
+approach using a cross-validation method. To obtain treatment effects, one might
+calculate the difference of the expected outcomes for two treatment levels and divide
+this by the difference in the treatment levels (treatment intensity). Diving data.
+The broken lines represent the 90% confidence intervals.
+Our results show that, on average, positive feedback is enhancing performance. In the fol-
+lowing, we go beyond average effects and investigate the effect of positive and negative feedback
+for different magnitudes of feedback. Figure 2 provides non-linear estimates of positive and neg-
+ative feedback showing the expected outcome (performance) against the extent of the feedback,
+i.e., the level of the treatment. The (treatment) effect of different feedback intensities can be
+calculated as the difference in expected outcomes for an increase from some treatment level to
+another.8 In the graph on the left, the effect of positive feedback is positive throughout all feed-
+8For two different treatment levels A = a1 and A = a0, the effect can be calculated as θ(a1, a0) =
+E(Y (A=a1))−E(Y (A=a0))
+a1−a0
+. The treatment intensity in this example is a1 − a0, while for a complete picture,
+it needs to be clear that the treatment level from which the treatment intensity is evaluated is a0 here.
+16
+
+Positive feedback
+E(Y(a)
+7.75
+7.50
+7.25
+7.00
+1
+6.75
+1
+1
+6.50
+1
+0.0
+0.5
+1.0
+1.5
+2.0
+Treatment level A=aNegative feedback
+E(Y(a)
+7.75
+7.50
+7.25
+7.00
+6.75
+1
+6.50
+1
+0
+2
+Treatment level A=aback intensities, i.e., the expected outcome increases almost steadily as the level of treatment
+increases. With negative feedback, on the right side of Figure 2, the effect varies slightly up
+and down for different treatment intensities – although the effect does not appear to be different
+from zero for any treatment intensity, consistent with the average effect of zero reported in Table
+2. For both estimations, we find that the linearity assumption in the regression analyses is a
+good approximation for the non-linear effect curves. Still, especially for the higher treatment
+intensities the confidence intervals become large and conclusions become imprecise–a fact to
+which global linear regression models do not give any hint.
+Overall, the results provide support for hypothesis 1: The performance is better after receiv-
+ing positive feedback than after receiving neutral feedback. Contrarily, we do not find support
+for hypothesis 2, i.e., the performance is not better after receiving negative feedback than after
+receiving neutral feedback. In the next section, we test if the positive effect of positive feedback
+and the null effect of negative feedback persists in different sub-populations and is generalizable
+for diverse personal or situational conditions.
+5.2
+Sub-population and context heterogeneity
+In the feedback-intervention model of Kluger and DeNisi (1996), as well as, for example, in
+the meta-study of Fong et al. (2019) aspects are collected for which the effects of feedback
+potentially differ. Personal characteristics, situational aspects, and task characteristics, among
+other factors, might shape the reaction of individuals to positive and negative feedback.
+A
+strength of our unique data set is that it allows us to investigate if we can generalize the results
+of our analysis.
+Panel A of Table 3 exhibits that positive feedback has a favorable impact irrespective of in-
+dividuals’ personal characteristics. We consider three categorizations of the individuals’ cultural
+backgrounds. First, we report that the favorable effect of feedback on performance is present
+for individuals from WEIRD and non-WEIRD countries. Second, we find a favorable impact
+of positive feedback irrespective of the relative cultural distance to the U.S.. Third, individuals
+coming from relatively individualistic and relatively collectivistic countries both react favorably
+to positive feedback.9
+Other personal characteristics that we investigate are experience and
+9We classify (non-)WEIRD countries according our own assessment based on Henrich et al. (2010);
+the respective list can be obtained upon request. For cultural distance to the U.S., we use the metrics
+provided in Table 1 in the research article by Muthukrishna et al. (2020).
+For individualistic and
+17
+
+gender.
+We find a performance-enhancing effect of positive feedback for both the relatively
+more and less experienced. Similar to Bear et al. (2017), we also explore whether there are
+gender differences in the reaction to feedback. We find that both sexes react favorably to posi-
+tive feedback For none of the three different definitions of cultural background, nor gender and
+experience, do the two-sample WALD tests show statistically significant differences. This leads
+to the conclusion that the effects of feedback are consistent and generalizable across these three
+personal characteristics.
+Importantly, we find some heterogeneity with respect to the characteristics of the task.
+Contested situations offer greater incentives to perform (Goller & Heiniger, 2022), with higher
+task focus and more pressure. Panel B of Table 3 shows large and positive effects for positive
+feedback in close competitions, but an insignificant effect for situations that are less competitive.
+This is in line with the argumentation by Kluger and DeNisi (1996) and our expectations.
+Contrary, we find no support for differential effects for the difficulty of the task. Positive feedback
+leads to a performance-enhancing impact for easy and hard tasks.
+The results of the heterogeneity analysis on the impact of negative feedback are largely in line
+with the main finding. The second column of Table 3 shows a null effect of negative feedback for
+most subgroups and all contexts. The only exception is the experience of the individuals, where
+we find that relatively more experienced individuals improve their performance after receiving
+negative feedback. A two-sample Wald test (in square brackets) shows that the difference in
+the reaction between the more and less experienced individuals is statistically significant. The
+favorable impact of negative ratings for experienced individuals is in line with findings by Eggers
+and Suh (2019) on the firm level.
+collectivistic countries, we use data from the index created by Hofstede (2011).
+18
+
+Table 3: Differential effects
+Positive Feedback
+Negative Feedback
+Panel A: Individuals‘ characteristics
+WEIRD1 (N=4955)
+0.086* (0.048)
+0.006 (0.049)
+Non–WEIRD (N=8120)
+0.135*** (0.043)
+0.004 (0.037)
+[0.447]
+[0.974]
+Culturally close to U.S.2 (N=6223)
+0.132*** (0.046)
+-0.007 (0.047)
+Not culturally close to U.S. (N=6852)
+0.101** (0.044)
+0.008 (0.037)
+[0.626]
+[0.802]
+Individualistic country3 (N=6013)
+0.096** (0.047)
+0.007 (0.045)
+Collectivistic country (N=6872)
+0.144*** (0.045)
+0.001 (0.040)
+[0.461]
+[0.921]
+More experienced (age ≥ 23y, N=6176)
+0.146*** (0.045)
+0.076* (0.039)
+Less experienced (age < 23y; N=6899)
+0.081* (0.047)
+-0.062 (0.044)
+[0.318]
+[0.019]
+Female (N=5885)
+0.087* (0.047)
+-0.028 (0.042)
+Male (N=7190)
+0.128*** (0.043)
+0.018 (0.039)
+[0.520]
+[0.422]
+Panel B: Task characteristics
+Tight competition4 (N=5118)
+0.173*** (0.056)
+-0.033 (0.052)
+Non–tight competition (N=7957)
+0.064 (0.039)
+0.007 (0.037)
+[0.110]
+[0.531]
+Easy task5 (N=7267)
+0.154*** (0.043)
+-0.027 (0.037)
+Hard task (N=5808)
+0.086* (0.048)
+0.025 (0.044)
+[0.291]
+[0.366]
+Notes: Linear Regression estimates. Diving data. Control variables as in column (3) in Table 2.
+Standard errors are clustered on the individual level. *, **, and *** represents statistical
+significance at the 10 %, 5 %, and 1 % level, respectively. P-value of WALD test for
+equality in square brackets. 1Western, Educated, Industrialized, Rich, Democratic. 2Cultural
+closeness is divided at the median level of an index taken Muthukrishna et al. (2020). 3Divided
+at median level of an individualism index constructed by Hofstede (2011); (some countries
+missing). 4Athlete is within ten points to first place in final, and to the cut-off in preliminary
+rounds. 5Easy and hard according to the median chosen difficulty of the (assessed) task.
+19
+
+5.3
+Repetition and long-term effects
+For practitioners, it is crucial to know about the impact of feedback when it is given repeatedly
+and about its long-term effect. Fortunately, our data allows for analyzing the impact of feedback
+on performance in a repeated setup.
+Figure 3 shows that the favorable impact of positive feedback is non-diminishing with repe-
+tition. As a benchmark, Baseline shows the average effect of receiving feedback as reported in
+Table 2, which is not conditional on further previously received feedback. We find that for those
+who have received positive feedback at least one time before, further positive feedback continues
+to have a positive impact on their performance. Similarly, we find a positive influence of positive
+feedback if the individual has received positive feedback at least two or three times before.
+Figure 3: A non-diminishing effect of positive feedback
+Notes: Linear regression estimates. Diving data. Specifications as in column (3) in Table 2.
+Standard errors are clustered on the individual level. Effect among those that
+experienced positive feedback at least one, two, or three times (in the respective
+round) before. The whiskers mark the 90 % confidence intervals.
+Table 4 shows the non-persistence of the effect of positive feedback on performance. For
+reference, column (1) reports the baseline effect for the performance in the task that is conducted
+directly after the feedback is received. Columns (2-4) provide estimates for the effect of feedback
+on performance in tasks carried out thereafter.
+For all follow-up tasks, we find statistically
+insignificant effects. This indicates that the favorable short-term effect of positive feedback does
+not carry on to future tasks. Negative feedback has no impact, neither on subsequent nor future
+tasks.
+20
+
+Positive feedback before
+0
+0.15
+Effect
+0.09
+0.03
+0.03
+Baseline
+One
+Two
+ThreeTable 4: A non-persistent effect of feedback on performance
+Performance
+(1)
+(2)
+(3)
+(4)
+Positive feedback
+0.115***
+-0.010
+0.073
+-0.062
+(0.032)
+(0.047)
+(0.050)
+(0.061)
+Negative feedback
+0.001
+-0.049
+0.023
+-0.079
+(0.029)
+(0.036)
+(0.046)
+(0.056)
+Periods after feedback:
+1
+2
+3
+4
+N
+13075
+10130
+7350
+4512
+Notes: Linear Regression on future outcomes. Diving data. Specifications as in column (3) in
+Table 2. Standard errors are clustered on the individual level. *, **, and *** represents
+statistical significance at the 10 %, 5 %, and 1 % level, respectively.
+5.4
+Spillover effects on related tasks
+Previously presented evidence shows the favorable effects of positive feedback on the task for
+which the feedback was obtained. In practice, individuals might do several tasks simultaneously,
+or a task containing different elements, that potentially influence each other. For example, Hecht,
+Tafkov, and Towry (2012) show spillover effects of incentive schemes in one task on a related,
+simultaneously conducted second task. Our settings allow us to study, both, a single-task and a
+multi-task environment.
+Panel A presents the results for the single-task setup. As presented previously in Table 2, we
+find a performance-enhancing impact of positive feedback and no impact of negative feedback
+on performance. The difficulty is fixed ex-ante. That we find no impact of feedback on the
+difficulty can be regarded as a placebo outcome test and supports our identification strategy.
+Difficulty and performance evaluation jointly determine the combined outcome. Consequently,
+we observe a favorable effect of positive feedback on the total score.
+Panel B exhibits the results for the multi-task environment. We observe favorable spillover
+effects. Receiving positive feedback in Task 1 enhances subsequent performance in Task 1 and
+the related Task 2.
+Negative feedback has no impact on either of the tasks.
+In the setup,
+performance in Task 1 and Task 2 are the most important determinants of combined success
+and the only ones that can be influenced by the task taker. Consistently, we also find a favorable
+influence of positive feedback on the total score.
+21
+
+Table 5: Spillover effects
+Panel A: One isolated task, diving
+Task 1:
+Multiplier:
+Combined:
+Performance
+Difficulty
+Total score
+Positive Feedback
+0.115***
+-0.002
+1.071***
+(0.032)
+(0.006)
+(0.324)
+Negative Feedback
+0.001
+-0.001
+-0.029
+(0.029)
+(0.005)
+(0.282)
+Panel B: Two simultaneous tasks, ski jumping
+Task 1:
+Task 2:
+Combined:
+Performance
+Distance points
+Total score
+Positive Feedback
+0.145***
+1.692***
+2.126***
+(0.034)
+(0.634)
+(0.693)
+Negative Feedback
+-0.049
+0.072
+-0.080
+(0.037)
+(0.545)
+(0.631)
+Notes: Linear Regression estimates. Control variables as in column (3) in Table 2. Feedback was
+given previously for Task 1 only. Standard errors are clustered on the individual level. *, **
+, and *** represents statistical significance at the 10 %, 5 %, and 1 % level, respectively.
+5.5
+Robustness
+To ensure that our results are robust to different specifications we conduct several supplementary
+analyses. First, we consider alternative specifications of our key variables. In a first regression,
+we take the mean of all (five or seven) judges’ ratings, instead of the performance, i.e., the
+mean of the (after discarding the extreme ratings) remaining three ratings, as an alternative
+outcome variable. With the treatment, the second key variable is (additionally) constructed
+in two different ways. Instead of subtracting the jury’s performance assessment from the most
+extreme (positive/negative) discarded rating we deduct (a) the lowest (highest) rating included
+in the jury’s performance assessment from the lowest (highest) discarded rating (Deviation
+positive/negative+) and (b) the jury’s performance assessment from the mean of the two dis-
+carded highest or lowest ratings (Deviation positive/negative++, in diving only).
+Table 11
+presents the results for these alternative specifications and shows robust estimates. We conclude
+22
+
+from this that the result does neither depend on the concrete choice of the treatment variable,
+nor on the selection of the outcome variable.
+Second, we consider different choices with respect to the sample that is used for the inves-
+tigation. Data cleaning might offer some leeway to researchers influencing results. Thus, we
+provide additional analyses in Table 11 using (a) the full sample without any data cleaning and
+(b) without excluding failed attempts (but excluding boundary values as described in Section
+3.1). We find robust results for both supplementary analyses, indicating that our data-cleaning
+step does not drive the results.
+Third, to prove that nationality bias is not responsible for the effect, i.e., judges favor their
+compatriots and potentially influence other judges on the panel, we re-estimate the results
+excluding all athletes with a compatriot judge in the panel. If the effect would be driven by
+these individuals the results might just be some mechanical effect. Though, the effect is also
+found for individuals not sharing nationality with a judge.
+6
+Managerial implications and conclusions
+Giving feedback is one of the most important tasks of managers. On a typical workday, managers
+regularly provide feedback to their teams. Some of this feedback is subconscious, such as facial
+expressions or nodding as a sign of appreciation and approval. Other feedback can be formal
+and dictated by the institution, as is the case with appraisal interviews. It can be constructive
+and substantive. But it can also be purely motivational. Common examples would be phrases
+like “Good job!” or “You can do better!” embedded in the context of everyday conversations.
+The crucial question is whether such motivational feedback, given consciously by managers,
+can serve the goal of increasing the future productivity of workers. For both valences of feedback,
+i.e. positive and negative feedback, this question is not trivial. The appreciation that positive
+feedback expresses can motivate but also cause employees to rest on their laurels. Negative
+feedback can spur on but it can also hurt and discourage.
+Our causal analysis indicates that managers can use positive feedback to enhance productiv-
+ity. Our results show a favorable impact of positive feedback on (subsequent) performance. The
+heterogeneity analysis indicates that this favorable effect of positive feedback can be found for
+feedback recipients coming from varying cultural backgrounds, for recipients of both male and
+23
+
+female gender, and for relatively more and less experienced recipients. We find that the favorable
+effect of positive feedback is short-term, repeatable, and with potentially favorable spillover to
+related tasks. The favorable impact of positive feedback is robust to the setup in which the
+activity is performed and is more pronounced in highly relevant situations. All this makes us
+confident that giving positive motivational feedback is a performance-enhancing strategy.
+Furthermore, we find no significant impact of negative feedback on performance. This null
+effect might explain why managers and other raters are often reluctant to give negative feedback
+(Fisher, 1979), a phenomenon termed as leniency bias (Cheng, Hui, & Cascio, 2017) or MUM-
+effect (Rosen & Tesser, 1970). While in other contexts the lack of negative ratings is decreasing
+efficiency (Cannon & Witherspoon, 2005; Bolton, Kusterer, & Mans, 2019; Keser & Späth,
+2021), we report no need to give negative motivational feedback.
+Despite the robustness of our results, we acknowledge some limitations of our approach.
+First, our sample consists of internationally competing athletes. While their level of profession-
+alism and self-discipline might be comparable to those of employees in highly competitive work
+environments, top athletes are not representative of the general population. Second, we consider
+an environment in which individuals receive feedback from multiple, external sources. Again,
+this is more comparable to daily life at large and competitive companies than at small firms.
+Third, we analyze a domain in which feedback recipients directly benefit from improvements in
+their performance, while feedback providers do not. In other domains, raters might be more
+prone to willfully bias their feedback.
+Therefore, we suggest that future research could contrast our results to environments, in
+which feedback providers benefit from an increased performance more than feedback recipients
+do. Employees in such environments might be prone to exploitation when employers use positive
+feedback as a substitute for more substantial improvements in the employees’ well-being. Fur-
+thermore, future research could analyze the long-term effects of positive and negative feedback.
+With this study, we contribute to the literature that provides guidelines for optimal feedback
+(Balcazar et al., 1985; Alvero et al., 2001; Sleiman et al., 2020). Our causal analysis shows that
+positive feedback is improving performance, while negative feedback has no effect.
+24
+
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+31
+
+Appendix
+Descriptive statistics
+Table 6: Full descriptive statistics
+Diving
+Ski jumping
+Mean
+Std. dev.
+Mean
+Std. dev.
+Treatments:
+Positive feedback (deviation positive)
+0.426
+(0.286)
+0.316
+(0.262)
+Negative feedback (deviation negative)
+0.477
+(0.320)
+0.357
+(0.290)
+Positive feedback+
+0.314
+(0.297)
+0.179
+(0.258)
+Negative feedback+
+0.363
+(0.328)
+0.218
+(0.289)
+Future positive feedback
+0.439
+(0.301)
+Future negative feedback
+0.489
+(0.325)
+Outcomes:
+Performance (rem. 3 judges’ ratings)
+7.119
+(1.189)
+17.771
+(0.744)
+Performance (all 5 / 7 judges’ ratings)
+7.110
+(1.182)
+17.765
+(0.741)
+Score
+68.737
+(14.557)
+118.647
+(16.204)
+Distance
+122.608
+(11.837)
+Covariates:
+Difficulty
+3.211
+(0.331)
+Compatriot judge
+0.248
+0.457
+Home event
+0.099
+0.127
+Final
+0.291
+Female
+0.450
+Age
+22.429
+(3.789)
+26.836
+(4.949)
+Current ranking
+8.490
+(9.655)
+15.357
+(8.582)
+Start order
+9.490
+(11.082)
+Points behind leader
+31.491
+(31.011)
+19.247
+(10.132)
+In range (within 5 pts. to threshold)
+0.264
+Gate points
+0.093
+(3.270)
+Wind points
+-0.291
+(8.225)
+Prev. performance
+7.270
+(0.958)
+17.854
+(0.580)
+Prev. SD performance
+0.130
+(0.151)
+0.157
+(0.159)
+Prev. wind points
+-1.685
+(8.136)
+Prev. gate points
+-0.163
+(4.386)
+Prev. distance
+123.940
+(11.143)
+Prev. difficulty
+3.166
+(0.317)
+N
+13075
+4529
+Notes: Mean and standard deviation (in parentheses; for non-binary variables). Some variables
+only observed in one of the data sets. +Alternative definition as defined in the main text.
+32
+
+Placebo and balancing tests
+Table 7: Placebo treatment regressions
+Judges’
+Judges’
+Judges’
+ratings 3
+ratings 5
+ratings 7
+Score
+Future positive feedback
+0.028
+0.030
+0.027
+-0.012
+(0.035)
+(0.035)
+(0.035)
+(0.345)
+Future negative feedback
+-0.045
+-0.043
+-0.041
+-0.437
+(0.035)
+(0.035)
+(0.035)
+(0.318)
+N
+10256
+10256
+10256
+10256
+Notes: Linear Regression on the outcome mentioned in the column header. 3, 5, and 7 refer
+to discarding four, two, or none of the extreme judges’ ratings. Diving data. Pseudo-
+treatment is the deviation of next (future) jump. Jumps 2–4/5 only. Specifications as
+in column (3) in Table 2. Standard errors are clustered on the individual level. *, **,
+and *** represents statistical significance at the 10 %, 5 %, and 1 % level, respectively.
+33
+
+Table 8: Balancing Tests
+Diving
+Compatriot judge
+Home event
+SD prev. perform.
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+Feedback positive
+-0.000
+-0.004
+0.007
+(0.014)
+(0.008)
+(0.005)
+Feedback negative
+-0.017
+-0.012
+0.002
+(0.012)
+(0.007)
+(0.005)
+Difficulty
+Final
+(1)
+(2)
+(3)
+(4)
+Feedback positive
+-0.005
+-0.018
+(0.007)
+(0.013)
+Feedback negative
+0.006
+-0.017
+(0.006)
+(0.013)
+Ski jumping
+Compatriot judge
+Home event
+Prev. distance
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+Feedback positive
+-0.045
+-0.023
+0.918
+(0.028)
+(0.018)
+(0.696)
+Feedback negative
+-0.010
+-0.048***
+0.345
+(0.022)
+(0.017)
+(0.674)
+Prev. gate
+SD prev. perform.
+(1)
+(2)
+(3)
+(4)
+Feedback positive
+-0.304
+0.024
+(0.306)
+(0.092)
+Feedback negative
+0.031
+0.018
+(0.217)
+(0.095)
+Notes: Linear Regression estimates. Each regression includes athlete fixed-effects. Standard errors
+are clustered on the individual level. *, **, and *** represents statistical significance at the
+10 %, 5 %, and 1 %, respectively.
+34
+
+Additional and full results tables
+Table 9: Feedback on performance – sensitivity to different specifications, ski jumping
+Ski jumping
+Performance
+(1)
+(2)
+(3)
+(4)
+Positive feedback
+0.201***
+0.180***
+0.145***
+0.107***
+(0.035)
+(0.036)
+(0.034)
+(0.034)
+Negative feedback
+-0.063
+-0.055
+-0.049
+-0.026
+(0.043)
+(0.041)
+(0.037)
+(0.041)
+Prev. jury assessment
+0.593***
+0.465***
+0.402***
+0.329***
+(0.027)
+(0.041)
+(0.043)
+(0.031)
+Prev. wind points
+0.044***
+0.040***
+0.036***
+(0.002)
+(0.002)
+(0.002)
+Prev. gate points
+0.003
+0.002
+0.000
+(0.003)
+(0.003)
+(0.003)
+Prev. distance
+0.002***
+0.003***
+0.002**
+(0.001)
+(0.001)
+(0.002)
+Wind points
+-0.041***
+-0.038***
+-0.036***
+(0.002)
+(0.002)
+(0.002)
+Gate points
+-0.020***
+-0.019***
+-0.019***
+(0.003)
+(0.002)
+(0.003)
+Points behind
+-0.015***
+-0.016***
+-0.015***
+(0.002)
+(0.002)
+(0.002)
+Compatriot judge
+0.021
+0.016
+0.024
+(0.020)
+(0.022)
+(0.023)
+Home event
+0.013
+0.028
+0.041
+(0.032)
+(0.032)
+(0.035)
+Start order
+0.002
+-0.003
+-0.005*
+(0.002)
+(0.002)
+(0.003)
+SD prev. judges’ ratings.
+-0.019
+-0.001
+-0.017
+(0.061)
+(0.063)
+(0.065)
+Athlete Fixed Effect
+x
+Athlete x Season FE
+x
+N
+4529
+4529
+4529
+4529
+Notes: Linear regression. Prev. (= previous) refers to a lagged variable from the previous jump.
+SD = standard deviation. Standard errors are clustered on the individual level. *, **,
+and *** represents statistical significance at the 10 %, 5 %, and 1 % level, respectively.
+35
+
+Table 10: Feedback on performance – sensitivity to different specifications, diving
+Diving
+Performance
+(1)
+(2)
+(3)
+(4)
+Positive Feedback
+0.242***
+0.208***
+0.115***
+0.100***
+(0.036)
+(0.034)
+(0.032)
+(0.035)
+Negative Feedback
+0.018
+0.024
+0.001
+0.007
+(0.030)
+(0.030)
+(0.029)
+(0.030)
+Prev. jury assessment
+0.430***
+0.284***
+0.103***
+0.073***
+(0.026)
+(0.022)
+(0.016)
+(0.016)
+Prev. difficulty
+0.794***
+0.540***
+0.147
+0.228**
+(0.079)
+(0.087)
+(0.091)
+(0.100)
+SD prev. judges’ ratings
+0.095
+0.056
+0.029
+(0.067)
+(0.067)
+(0.070)
+Compatriot judge
+-0.015
+-0.024
+-0.016
+(0.024)
+(0.022)
+(0.025)
+Home event
+0.129***
+0.164***
+0.196***
+(0.038)
+(0.045)
+(0.054)
+Current ranking
+-0.020***
+0.000
+0.011***
+(0.002)
+(0.002)
+(0.003)
+Start order
+-0.003***
+-0.006***
+-0.009***
+(0.001)
+(0.001)
+(0.001)
+Points behind
+-0.003***
+-0.000
+0.001
+(0.001)
+(0.000)
+(0.001)
+Penalty
+-0.288
+-0.362*
+-0.310
+(0.187)
+(0.187)
+(0.200)
+Jump and Event Fixed Effect
+x
+x
+x
+Athlete Fixed Effect
+x
+Athlete x Season Fixed Effects
+x
+N
+13075
+13075
+13075
+13075
+Notes: Prev. (= previous) refers to a lagged variable from the previous jump. SD = standard
+deviation. Fixed effects for Events are 1m and 3m Springboard and 10m Platform, and the
+five (female) or six (male) jumps. Standard errors are clustered on the individual level.
+*, **, and *** represents statistical significance at the 10 %, 5 %, and 1 %, respectively.
+36
+
+Table 11: Robustness Checks
+Ski jumping
+Diving
+Positive
+Negative
+Positive
+Negative
+Feedback
+Feedback
+Baseline results
+0.121***
+-0.036
+0.115***
+0.001
+(0.033)
+(0.044)
+(0.032)
+(0.029)
+Other outcome variable
+0.129***
+-0.070*
+0.111***
+0.005
+(all ratings, incl. discarded)
+(0.035)
+(0.038)
+(0.032)
+(0.029)
+Treatment definition 2
+0.119***
+-0.062
+0.109***
+0.005
+(Discarded vs. last credited)
+(0.033)
+(0.039)
+(0.032)
+(0.030)
+Treatment definition 3
+0.127***
+0.007
+(Mean discarded vs. mean credited)
+(0.043)
+(0.039)
+Without data cleaning
+0.124***
+-0.056
+0.059*
+0.017
+(0.044)
+(0.047)
+(0.035)
+(0.031)
+Without dropping failed attempts
+0.124***
+-0.042
+0.109***
+0.031
+(0.045)
+(0.042)
+(0.037)
+(0.033)
+Only athletes not sharing
+0.175***
+-0.044
+0.113***
+-0.021
+nationality with a judge
+(0.040)
+(0.053)
+(0.038)
+(0.034)
+Only jumps with no variance
+0.132***
+-0.044
+0.143***
+0.056
+in scoring ratings
+(0.043)
+(0.051)
+(0.043)
+(0.038)
+Notes: Linear regression. Every line represents two separate regressions, one in each data set.
+Specification as in column (3) in Table 2. Standard errors are clustered on the individual
+level. *, **, and *** represents statistical significance at the 10 %, 5 %, and 1 %, respectively.
+37
+

5tE2T4oBgHgl3EQfOwZB/content/tmp_files/2301.03751v1.pdf.txt

@@ -0,0 +1,1141 @@
+Generative Emotional AI for Speech Emotion Recognition:
+The Case for Synthetic Emotional Speech Augmentation
+Abdullah Shahida, Siddique Latifb,∗ and Junaid Qadirc
+aInformation Technology University (ITU),Punjab, Pakistan
+bUniversity of Southern Queensland, Australia
+cQatar University, Doha, Qatar
+A R T I C L E I N F O
+Keywords:
+Tacotron, WaveRNN, speech synthesis,
+text-to-speech, emotional speech syn-
+thesis, speech emotion recognition
+A B S T R A C T
+Despite advances in deep learning, current state-of-the-art speech emotion recognition (SER) systems
+still have poor performance due to a lack of speech emotion datasets. This paper proposes augmenting
+SER systems with synthetic emotional speech generated by an end-to-end text-to-speech (TTS) system
+based on an extended Tacotron architecture. The proposed TTS system includes encoders for speaker
+and emotion embeddings, a sequence-to-sequence text generator for creating Mel-spectrograms, and a
+WaveRNN to generate audio from the Mel-spectrograms. Extensive experiments show that the quality
+of the generated emotional speech can significantly improve SER performance on multiple datasets,
+as demonstrated by a higher mean opinion score (MOS) compared to the baseline. The generated
+samples were also effective at augmenting SER performance.
+1. Introduction
+Speech emotion recognition (SER) is a rapidly growing
+field with many applications in fields such as healthcare, cus-
+tomer service, media, education, and forensics. While deep
+learning (DL) has shown promise in developing SER sys-
+tems, their performance is still limited by the scarcity of
+emotion datasets [20, 24]. Existing SER corpora are small
+since the process of creating emotional data is costly and
+time-consuming, as multiple annotators have to manually
+listen to and annotate the material [26, 31]. To increase data
+size, some studies have used multiple corpora, but the num-
+ber of standard benchmark datasets is also limited, hindering
+progress in SER systems [19].
+Researchers have long been interested in creating natural-
+sounding TTS systems. TTS technology has come a long
+way from early TTS systems that often used pre-recorded
+waveforms pieced together based on input text [11]. Such
+systems were prone to boundary artefact issues and statis-
+tical techniques were later developed to generate smoothed
+audio features for the vocoder to synthesise speech [37, 44].
+More recently, end-to-end neural network-based approaches
+have been proposed that can synthesise more natural-sounding
+human speech [3, 34]. Current state-of-the-art TTS systems
+are trained using DL algorithms in an end-to-end fashion,
+with popular models including Tacotron [41], Deepvoice [3],
+Fastspeech [33, 34], Fastpitch [18], to name a few.
+Unlike traditional systems, end-to-end TTS models can
+learn to generate a spectrogram directly from text without
+any complex pre-processing. These models, however, are
+currently only able to synthesise natural speech. Using gen-
+erative DL techniques such as generative adversarial net-
+works (GANs) [8] for emotional speech synthesis is also
+challenging, as it requires a large amount of time-aligned
+data of a single speaker speaking the same content in dif-
+∗Corresponding author
+ORCID(s):
+ferent emotions and complex equations to guide the model
+in converting emotions using audio features. Some studies
+have achieved promising results in single-speaker emotional
+speech synthesis using TTS models [17], but the quality of
+synthetic speech in augmenting SER has not been evaluated.
+In this paper, we propose a method for augmenting SER
+systems using an emotional text-to-speech (TTS) system and
+make two main contributions. Firstly, we develop an end-to-
+end multi-speaker emotional TTS system that does not re-
+quire any alignment of audio files for emotion conversion
+or complex pre-processing of input data. Inspired by the
+success of end-to-end TTS models, we adopt a similar ar-
+chitecture to Tacotron. We propose to use a condition en-
+coder to control the speakers’ voices and emotions in the
+output speech. We generate speaker voice feature vectors
+using the encoder network. These feature vectors are modu-
+lated with one of the encoded emotional feature representa-
+tions. These modulated feature vectors are used to condition
+the Tacotron to synthesise speech in different speaker voices
+and emotions. Subjective evaluation tasks show that our pro-
+posed model improves controllability and successfully syn-
+thesises emotional speech. Secondly, we use the synthesised
+emotional speech to augment an SER system and conduct
+multiple experiments to evaluate the generated data quan-
+titatively. Results show that the synthesised data can help
+improve SER performance in both within-corpus and cross-
+corpus settings.
+The rest of the paper is organised as follows. In Section
+2, we briefly introduce the related work to change different
+features of audio. The model’s architecture, loss functions,
+and flow of our architecture are described in Section 3. The
+details of the dataset and experimental condition in which
+we trained our model and hyper-parameters are provided in
+Section 4. We report our results in Section 5. Finally, this
+paper is concluded in Section 6.
+A Shahid et al.: Preprint submitted to Elsevier
+Page 1 of 9
+arXiv:2301.03751v1  [cs.SD]  10 Jan 2023
+
+Multi-Speaker Emotional Speech Synthesis
+2. Previous Work
+In this section, we review the literature that has emerged
+around (1) the use of Tacotron for TTS, and for (2) emotional
+speech synthesis, and (3) the process of augmenting SER.
+2.1. Tacotron Based TTS Systems
+Many recent studies have focused on modifying the Tacotron
+model in order to better control the output of TTS systems.
+For instance, [13] presented a Tacotron-based model that
+synthesises multi-speaker speech by conditioning the Tacotron
+on the speaker’s voice embedding, which was generated from
+a speaker verification model [40]. [42] introduced a Tacotron
+variant that can change the speaking style, by learning dif-
+ferent styles and saving them as vectors or tokens. These
+tokens are obtained by clustering similar accents and repre-
+senting each cluster with an average. During synthesis, the
+Tacotron is conditioned on one of these tokens to produce
+speech with a specific style. [35] presented a multi-speaker
+Tacotron that can change accents (e.g., American, Indian,
+British). Their model uses two encoder networks with the
+Tacotron and requires two audio samples (one for the ac-
+cent and one for the speaker’s voice) as input to generate
+the desired output. [36] proposed a Tacotron model that is
+trained with encoded output audio from a variational autoen-
+coder as input. This not only improves the multi-speaker
+performance of Tacotron but also allows for control over the
+energy of the generated audio through the mean-variance
+property of the variational autoencoder. [43] developed a
+Tacotron model that can learn more complex vocalisations
+by using the self-attention mechanism in Tacotron to learn
+complex dependencies related to pitch in different accents.
+They claim that their model outperforms traditional end-to-
+end approaches for languages with more pitch-dependent ac-
+cents, such as Japanese. Our proposed model also gener-
+ates speech in a multi-speaker setting and includes additional
+control over the emotions in the output.
+2.2. Tacotron Based Emotional TTS Systems
+Several previous works have attempted to generate emo-
+tional speech using TTS systems. For example, [38] devel-
+oped an emotion control method for a TTS system based on
+the GST-Tacotron network [35], and demonstrated its effec-
+tiveness in synthesising emotional speech in a single-speaker
+setting in Korean. [27] also evaluated a Tacotron-based emo-
+tional speech synthesizer in Korean, and found improvements
+in the quality of the generated speech for a single speaker.
+Other studies, such as [15, 17], have also proposed meth-
+ods for controlling emotional speech synthesis, but these ap-
+proaches only synthesise emotional speech in a single speaker’s
+voice. In contrast, our proposed method achieves control
+over emotional speech synthesis for multi-speaker TTS and
+we also evaluate the quality of the synthesised data to aug-
+ment the SER system.
+2.3. Augmenting Techniques for SER
+Speed perturbation [16] is a popular data augmentation
+technique that has been widely studied in different contexts
+[2, 23]. It has been found to improve speech emotion recog-
+nition (SER) performance by creating copies of input data
+with different speed effects. Mixup [45] is another data aug-
+mentation technique that generates augmented samples as a
+linear combination of original samples from the input data.
+Several studies have demonstrated the effectiveness of mixup
+in SER, including Latif et al. [25], who used the technique to
+augment an SER system and achieve improved performance
+and robustness. A recent method called SpecAugment [30],
+originally proposed for automatic speech recognition, has
+also been applied to SER [4]. In this study, the authors aug-
+mented the SER system with duplicate samples by a factor
+of two and found that SpecAugment improved model per-
+formance. Other studies [2, 21, 23] have also achieved im-
+proved performance by using input perturbation-based data
+augmentation techniques to increase the training data.
+Further research is required to explore data-driven ap-
+proaches to increase the training data for SER. In this paper,
+we propose to explore TTS based data augmentation method
+where we explored different variations in the training data
+by changing the speaker and gender voices in different emo-
+tions.
+3. Proposed Framework
+We propose to generate synthetic speech using a Tacotron-
+based emotional TTS system. We use synthetic speech data
+to augment the speech emotion classifier. The details of both
+emotional TTS and classifier are presented next.
+3.1. Emotional Speech Synthesis
+Our model consists of an encoder which conditions Tacotron
+(as depicted in Figure 1) to alter the speaker’s voice and emo-
+tion in the output. Tacotron generates a Mel-spectrogram
+from a given text and embedding vector, while a Wave-RNN-
+based vocoder is used to generate an audio signal from the
+Mel-spectrogram
+3.1.1. Condition Encoder
+We propose using a condition encoder to create an em-
+bedding that represents both speaker identity and emotion.
+To do this, we use a speaker identification model presented
+in [40], which creates a fixed-dimensional embedding, known
+as a d-vector [10, 39], using a sequence of Mel-spectrograms
+computed from a speech signal of arbitrary length. We train
+this model using an end-to-end speaker verification loss that
+maximises the cosine similarity between utterances from the
+same speaker while minimising the cosine similarity between
+utterances from different speakers. We fine-tune this net-
+work on an emotional corpus to create an emotional embed-
+ding as well. Thus, the condition encoder is optimised to
+maximise the cosine similarity between embeddings of the
+same speaker with different emotions and to minimise the
+similarity between different emotions and different speak-
+ers. In this way, the model learns to generate a feature vector
+that contains both emotion and speaker identity information.
+The speaker’s voice audio and emotion audio are embedded
+A Shahid et al.: Preprint submitted to Elsevier
+Page 2 of 9
+
+Multi-Speaker Emotional Speech Synthesis
+Figure 1: Architectural flow diagram. The reference speaker’s voice is first encoded and then modulated to desired emotion as
+described in the model schema. The output is then passed to the Tacotron decoder with the text embedding to synthesise the
+Mel-spectrogram.
+using the condition encoder and combined to generate a fi-
+nal embedding, which is used to condition the synthesizer to
+output speech with the selected emotion and speaker’s voice.
+For each unique emotion of every speaker in dataset, a
+centroid 푐푘 is calculated by taking the average of embedding
+for each unique emotion of every unique speaker. Loss for
+an embedding 푒푖 when the embedding and the centroid 푐푘
+have the same speaker and emotion is calculated as:
+(푒푖, 푐푘) = −1 × 휎(cos(푒푖, 푐푘))
+(1)
+When 푒푖 have different emotion or different speaker for cen-
+troid 푐푘 then loss is calculated as:-
+(푒푖, 푐푘) = 휎(cos(푒푖, 푐푘))
+(2)
+퐺(푆) =
+∑
+푖,푘
+퐿(푒푖, 푐푘)
+(3)
+Equation 1 maximises the cosine similarity between em-
+beddings for the same speaker voice and same emotion. Equa-
+tion 2 represents the cosine similarity between embedding
+and centroid when they have different speaker voices or dif-
+ferent emotions or both. Equation 3 represents the final loss
+over every embedding, which is calculated as the sum of the
+loss for every embedding with every centroid.
+The condition encoder consists of three LSTM layers
+with 768 cells each, and a final 256-length fully connected
+layer. The input to the model is the Mel-spectrogram gener-
+ated from a speech utterance of a reference speaker’s audio
+sample, and its output is an embedding vector of size 256
+which represents the speaker’s identity. After training the
+model, we use it to extract speaker and emotional informa-
+tion from a given audio. To separate the emotion from the
+speaker’s voice, we generate vectors that only contain emo-
+tional information by using the trained condition encoder to
+generate embedding vectors for both the neutral and emo-
+tional voices of the same speaker. The neutral embedding
+vector is then subtracted from the emotional ones using Equa-
+tion (4), resulting in a vector that only contains emotional
+information. This vector can be used at inference time to
+control the emotion of the synthesised audio.
+푒푚푏em = (푒푚푏en − 푒푚푏neu)
+(4)
+Where 푒푚푏en represents the embedding with emotion and
+voice information generated from the emotional voice of a
+speaker; 푒푚푏neu is generated from neutral audio of the same
+speaker, and 푒푚푏em represents the embedding that only con-
+tains emotional information. During inference, reference au-
+dio embedding (voice in which we want our output sample
+to be synthesised) and emotional embedding are added to
+generate a final embedding vector.
+푒푚푏final = 푒푚푏ref + 푒푚푏em
+(5)
+Finally, the modulated embedding vector and text are fed
+to Tacotron, which generates the Mel-spectrograms. These
+Mel-spectrograms are converted to the time domain using a
+vocoder, resulting in an audio signal.
+3.1.2. Synthesizer architecture
+The synthesizer is a variation of Tacotron [41], which
+is a sequence-to-sequence model that generates output one
+frame at a time based on the input. In addition, we condition
+this synthesizer on an embedding vector generated by the
+condition encoder, which contains information about the de-
+sired output emotion and the speaker’s voice. The condition
+embedding is concatenated with the text embedding of the
+synthesizer and then passed through a decoder to synthesise
+A Shahid et al.: Preprint submitted to Elsevier
+Page 3 of 9
+
+Audio
+Reference audio
+Emotional embedding
+Speaker
+Vocoder
+Encoder
+Concatenation
+Condition encoder
+Mel
+Spectrogram
+Text
+Concatenation
+Attention
+Decoder
+embedding
+Synthesizer
+Character SeguenceMulti-Speaker Emotional Speech Synthesis
+the output Mel-spectrogram. The synthesizer was trained on
+80-channel Mel-spectrograms with a window size of 50 ms
+and a hop size of 12.5 ms. The synthesizer encodes the input
+characters into a hidden representation using three convolu-
+tion layers, which learn longer-term context like an n-gram.
+The output of these convolution layers is passed to a single
+bi-directional LSTM layer with 256 units, which learns time
+dependencies from these n-gram-like features. The LSTM
+layer returns an encoded vector that fully represents the in-
+put text sequence. This vector is concatenated with a vector
+of emotional and speaker embeddings from the encoder.
+It is worth noting that at this point, the encoder has been
+trained and its weights are not updated. The combined text,
+speaker, and emotion embedding is passed to the decoder to
+generate a Mel-spectrogram. The decoder architecture in-
+cludes a location-sensitive attention mechanism that trans-
+forms the input embedding into a fixed-length vector. The
+output frame from the previous step is passed through two
+fully connected layers and concatenated with the embedding
+vector to ensure that sequences are generated without any
+time artefacts. This vector is then passed through two LSTM
+layers, and a linear transformation is applied to generate the
+next frame of the Mel-spectrogram. The output from this
+LSTM is also projected down to a single scalar, which serves
+as a stop token and indicates when to stop generating further
+frames. Once the Mel-spectrogram has been generated, it
+is passed through a 5-layer convolution network called the
+PostNet to improve overall reconstruction.
+3.1.3. Vocoder
+Traditionally, the Griffin-Lim algorithm [9] was used to
+generate time-domain audio from a spectrogram, but it was
+slow and the output speech lacked naturalness. To address
+this, we use a vocoder based on the WaveRNN architecture
+[14], which is a faster and more powerful recurrent network
+for sequential modelling of high-fidelity audio. It employs
+residual convolutions and GRU layers to generate a time-
+domain audio signal frame by frame from a Mel-spectrogram.
+3.2. Emotion Classifier
+To evaluate the synthesised emotions, we trained a deep
+neural network (DNN) for SER. We implemented a convo-
+lutional neural network (CNN)-based classifier that consists
+of a convolutional layer, a batch normalisation layer, and a
+dense layer before the softmax layer. Mel-frequency cepstral
+coefficients (MFCCs) are used as the input to the classifier.
+The CNN layers learn high-level features from the input fea-
+tures, which are then transformed by the dense layer into a
+more discriminative space for better emotion classification
+after passing through the normalisation layer.
+4. Experimental Protocol
+This section describes the details of the dataset, input
+feature, and model training.
+4.1. Datasets
+We used the Librispeech dataset [29] to train our TTS
+model. It consists of 1000 hours of speech data from various
+speakers, sampled at 16 kHz. For the emotion embeddings,
+we used the Emotional Voices Database (EVD) [1] and the
+Toronto Emotional Speech Set (TESS) [7], which contain six
+different speakers reading different sentences with different
+emotions. We conducted multiple experiments to evaluate
+the performance of our model. For emotion classification
+experiments, we used the Ryerson Audio-Visual Database
+of Emotional Speech and Song (RAVDESS) [28] and TESS.
+For cross-corpus emotion classification, we used the CREMA-
+D [6], SAVEE [12], EmoDB [5], and synthesised audio. The
+details of these datasets are presented in Table 1. We used
+one speaker from Librispeech, as well as all the speakers
+from EVD and TESS with two samples that were not in-
+cluded in the training set, to determine the mean opinion
+score. For emotion classification experiments, we use speaker-
+independent emotion classification. We randomly select 70%
+of CREMA-D for training, 10% for validation, and 20% for
+testing. The full corpora including RAVDESS and EmoDB
+were used as the test set in the emotion classification experi-
+ments, and the SAVEE dataset was used as the test set in the
+cross-corpus emotion classification experiments.
+4.2. Input Features
+Tacotron takes text strings as input, which are sequences
+of characters. Each character is encoded into a one-hot en-
+coded vector and embedded in a continuous vector. The
+other input to Tacotron is a condition embedding vector that
+contains speaker and emotion information. This vector is
+obtained from an encoder, which takes speaker audio as in-
+put and converts it into Mel-frequency cepstral coefficients
+(MFCCs). These MFCCs have 40 log filter banks, 80 frames,
+and no overlapping window. To generate t-distributed stochas-
+tic neighbour embedding (t-SNE) plots of synthesised audio,
+we encoded our synthesised audio using the model presented
+in [13]. The input to this model is also MFCCs with 40 log
+filter banks, 80 frames, and no overlapping window, result-
+ing in an 80x40-dimensional feature vector. This model is
+also used in evaluating the equal error rate (EER) in speaker
+verification. In emotion classification and cross-corpus emo-
+tion classification, we use MFCCs with 40 log filter banks
+and a hop size of 64 milliseconds. The MFCC array is trans-
+posed and the arithmetic mean is calculated across its hori-
+zontal axis as in a previous work [32].
+4.3. Speech Synthesis Models Training
+First, the encoder is trained on the Librispeech dataset
+to learn to generate a speaker embedding that is distinct for
+each speaker. It takes a Mel-spectrogram as input and out-
+puts an embedding vector of size 256. From these embed-
+ding vectors, a similarity matrix is constructed such that each
+column contains an embedding vector for a unique speaker,
+and cosine similarity is maximised in all cells of the columns
+and minimised in all cells of the rows. Cosine similarity is
+maximised along the columns because they contain audio
+embeddings for the same person, whereas it is minimised
+A Shahid et al.: Preprint submitted to Elsevier
+Page 4 of 9
+
+Multi-Speaker Emotional Speech Synthesis
+Table 1
+Description of all the considered datasets.
+Name
+Number of
+Speakers
+Number of
+Utterances
+CREMA-D
+91
+7,442
+EmoDB
+10
+535
+EVD
+5
+7,590
+Librispeech
+2484
+281,241
+REVDESS
+24
+7,356
+SAVEE
+4
+480
+TESS
+2
+2,800
+along the rows because they contain audio embeddings for
+different people. In this way, the embeddings of the same
+people are similar and those of different people are differ-
+ent.
+After training the encoder on the Librispeech data, it is
+fine-tuned on the EVD and TESS datasets to generate dis-
+tinct embedding vectors for different emotions. This time,
+a similarity matrix is constructed such that a column con-
+tains embedding vectors generated for a single emotion for
+the same speaker, and other emotions are placed in other
+columns. This is done for all speakers, and then cosine sim-
+ilarity is maximised along a column and minimised across
+columns. This is done to increase the distance between dif-
+ferent emotions of the same person, so cosine similarity is
+minimised by adding it across columns rather than within
+the same columns. We used a batch size of 30 and a learn-
+ing rate of 10−4.
+During training, the synthesizer model is first trained on
+the Librispeech data so that it can learn to generate audio
+of different speakers from a diverse range of text. This is
+because the EVD and TESS datasets combined only have six
+speakers. Once the synthesizer is trained enough that it can
+generate audio resembling the reference speaker, we fine-
+tune it to generate different emotional Mel-spectrograms by
+training it on the EVD and TESS datasets. We use a learning
+rate of 103 that exponentially decays to 10−5, and a batch size
+of 30 for training the synthesizer. The Adam optimiser with
+훽1 = 0.9, 훽2 = 0.999, and 휖 = 10−6 is used as the optimiser.
+The teacher forcing ratio is set to 1 (meaning the original
+previous sequence is shown to the model for prediction of
+the next sequence). The mean squared error is minimised
+for the predicted Mel-spectrogram.
+5. Results
+In this section, we evaluate the performance of our pro-
+posed model in terms of the similarity of the synthesized
+speakers and the granularity of synthesized emotions.
+5.1. Evaluating Synthetic Speech Quality
+To evaluate the quality of synthetic speech, we conducted
+multiple experiments. The details of these experiments are
+presented below.
+Table 2
+Speaker verification EERs of different synthesizers.
+# of samples
+EER
+Emotion + voice conversion TTS
+100
+0.16
+Baseline Emotion conversion TTS
+100
+0.24
+Voice conversion TTS
+100
+0.10
+Real audios
+100
+0.04
+Table 3
+Mean Opinion Score (MOS) with 95% confidence interval.
+Emotion
+Angry
+Happy
+Sad
+Neutral
+Overall
+Recorded
+4.6
+4.50
+4.50
+4.60
+4.55
+Baseline
+2.80
+3.10
+2.70
+4.20
+3.20
+Proposed
+3.60
+3.70
+3.80
+4.10
+3.80
+5.1.1. Speaker Verification
+We evaluated the speaker similarity of synthesised au-
+dios with real speech using speaker verification and mea-
+sured the equal error rate (EER) following [13]. The EER
+is used to measure the performance of a speaker verification
+system by comparing the false reject rate (FRR) and false ac-
+cept rate (FAR) at different sensitivity levels. The EER is the
+point at which the FRR and FAR are equal. To calculate the
+EER, we used 100 audio samples, 40 of which were synthe-
+sised. We enrolled only synthesised speakers in the system
+and calculated the EER. We achieved an EER of 0.10% by
+performing voice conversion using a multi-speaker Tacotron
+model [13]. We also generated emotional audio samples us-
+ing a base model, and the speaker verification model gave an
+EER of 0.24% on these synthesised audios. In contrast, we
+achieved an EER of 0.16% when using the proposed model
+for both emotion and voice conversion. The EER on real
+samples using the approach in [13] was 0.04%. We have
+compared the EER of these models in Table 2.
+5.1.2. Listening Experiments
+We performed mean opinion score (MOS) evaluations
+to measure the quality of synthesised speech. We asked sub-
+jects with post-graduate exposure to give a score after listen-
+ing to the audio based on the following standard: 1 = Bad;
+2 = Poor; 3 = Fair; 4 = Good; and 5 = Excellent. The re-
+sults, shown in Table 3, indicate that the proposed model
+can synthesise high-quality emotional speech compared to
+the baseline model. The proposed model significantly im-
+proves the MOS score for emotions including angry, sad,
+and happy compared to the baseline. However, it achieves
+slightly lower MOS scores for natural speech compared to
+the baseline. This may be because the baseline model is
+specifically designed to generate natural speech and there-
+fore performs better for neutral speech. Nevertheless, our
+proposed model performs well for all emotions. Readers can
+listen to samples of the generated speech at this URL1.
+1https://emotaco.github.io/Emotional_Tacotron/
+A Shahid et al.: Preprint submitted to Elsevier
+Page 5 of 9
+
+Multi-Speaker Emotional Speech Synthesis
+Figure 2: Comparison of target and synthesized Mel-spectrograms for various emotions in Male and Female audios.
+5.1.3. Speaker and Emotion Visualisation
+During this experiment, we did not use teacher forcing
+and generated audio as described in the inference part. The
+synthesised Mel-spectrograms for different emotions by the
+baseline and proposed models were plotted in Figure 2, and
+the results were compared with the target Mel-spectrograms.
+In contrast to the baseline, our proposed model did not smooth
+the generated Mel-spectrograms that help produce a better
+quality of emotional speech using WaveRNN vocoder.
+For the purpose of evaluation, we present the t-SNE plot,
+which was generated by embedding vectors generated from
+synthesised output samples using a speaker verification model
+as the encoder. Note that the speaker encoder was not trained
+with the synthesizer, so it is not optimised for synthesizer
+output. We generated t-SNE plots for emotional audio syn-
+thesised using the model from the base papers and compared
+the results with the proposed model. These t-SNE plots for
+synthesised speech in both male and female voices are shown
+in Figure 3 and 4, respectively. These plots demonstrate that
+our model is able to synthesise distinct emotions compared
+to the base model. It can be observed that different emotions
+are separated and similar emotions are clustered together, in-
+dicating similarity between emotions.
+Since the angry emotion has more expression compared
+to the sad and happy emotions, which are tone variations,
+the cluster of angry emotions is farther from the happy emo-
+tions. We also visualise the t-SNE plot of multiple speakers
+in neutral speech using our proposed model in Figure 5. It
+shows distinct clusters for different speakers indicating that
+the model is able to learn the multiple speaker embeddings
+effectively.
+.
+5.2. Augmenting Speech Emotion Recognition
+(SER)
+In this section, we used the synthetic speech to augment
+the SER system. We performed our evaluations using corpus
+Figure 3: Comparison of t-SNE plots of male audio for various
+emotions using baseline and our proposed model shows that
+our model demonstrates better emotion performance.
+and cross-corpus settings. Results for these experiments are
+presented next.
+5.2.1. Within Corpus Evaluations
+We used the RAVDESS and TESS datasets for evalua-
+tions. We combined both datasets and then randomly split
+the data into a ratio of 70:10:20 for train, validation, and
+test sets, respectively. We trained the model for 45 epochs.
+We compared the results for speaker recognition on real and
+synthesised speech in Figure 6. We achieved an accuracy
+of 80% for synthesised speech, while the accuracy for the
+real speech test set was 92.4%. This demonstrates that our
+model can synthesise the emotional characteristics of out-
+put speech. We also augmented the classifier with synthetic
+data and performed training using both real and synthesised
+speech data. We achieved an accuracy of 94.6%, which is
+better compared to the classifier trained on real data alone.
+This experiment shows that our model can also be used to
+A Shahid et al.: Preprint submitted to Elsevier
+Page 6 of 9
+
+Female-happy
+Female-angry
+Female-sad
+ Male-happy
+Male-angry
+Male-sad
+Target
+20 
+20
+20
+20 
+20
+导
+40
+40
+40
+60
+50
+60
+25
+50
+75
+100125
+25
+50
+75
+100
+125
+50 
+100
+25
+50
+75
+100
+125
+25
+50
+75
+100
+125
+50 
+100
+Proposed
+20
+20
+20
+20
+20
+20
+导
+40
+40
+40
+60
+60
+60
+100125
+100
+50
+100
+25
+50
+100
+125
+25
+50
+75
+100
+125
+50
+100
+25
+50
+75
+25
+Baseline
+20 
+20
+2
+2
+40
+40
+40
+40
+40 
+60
+50
+60
+60
+25
+50
+100
+125
+05
+50
+100
+125
+ 50 
+100
+0
+25
+75
+100125
+0
+25
+50
+75
+100
+125
+0
+50 
+100Proposed
+Baseline
+30
+30
+20
+20
+10
+10
+0
+0
+10
+-10
+20
+20
+30
+30
+20
+20
+20
+D
+20Multi-Speaker Emotional Speech Synthesis
+Figure 4: Comparison of t-SNE plots of female audio for var-
+ious emotions using baseline and our proposed model shows
+that our model demonstrates better emotion performance.
+Figure 5: The t-SNE plot for speaker voice of synthesised re-
+sults shows that individual speakers’ voices are distinctly clus-
+tered together.
+generate additional audio data which can be used to augment
+speaker recognition systems to improve their performance.
+Figure 6: Bar plot which shows that our synthesized audio’s
+emotion and real audio emotions are almost similarly classified
+by the classification model.
+We have also plotted confusion matrices in Figure 7 for
+emotion classification on real audio, synthetic audio, and a
+combination of real and synthetic data in the training set.
+The confusion matrix shows that the model augmented with
+synthetic data is able to better classify speech emotions. The
+accuracy of other emotions has also been improved, but the
+most significant improvement can be seen in the classifica-
+tion of happy emotions.
+5.2.2. Cross-Corpus Corpus Evaluations
+We also evaluated the effect of augmenting with syn-
+thetic data by performing cross-corpus emotion classifica-
+tion. To do this, we implemented a classifier consisting of an
+LSTM layer, three dense layers, and a softmax layer for emo-
+tion classification. We also used two dropout layers between
+dense layers to learn more generalised representations. We
+selected the architecture of the model based on previous re-
+search findings [22, 23]. We trained the classifier on MFCC
+features extracted from the input audio. The model was trained
+with a sparse categorical cross-entropy loss and Adam op-
+timiser for 100 epochs. The model was trained using the
+CREMA-D dataset and the CREMA-D dataset augmented
+with synthetic data and was evaluated on the CREMA-D,
+SAVEE, and EMODB datasets. The results, shown in Figure
+8, demonstrate that adding synthesised data increases accu-
+racy not only on the SAVEE and EMODB datasets without
+fine-tuning the model but also on the CREMA-D test set as
+well.
+5.2.3. Changing Gender and Speaker Distributions
+In this experiment, we compare the results of data aug-
+mentation with new speaker voices that are not present in
+the given corpus. For instance, the SAVEE corpus has four
+male speakers, and synthetic data can be created either in the
+voices of these four male speakers or in the voices of addi-
+tional male and female speakers to bring diversity to the data
+and augment speech emotion classification. We present the
+results in Table 4. We compared the results with the baseline
+model, which was trained without any augmentation, and
+also with the application of speed perturbation to the train-
+ing data. We followed [19] and created two copies of aug-
+mented samples using the speed perturbation data augmenta-
+tion technique. We found that augmenting the data with dif-
+ferent speaker voices helps improve performance compared
+to the baseline and the widely used data augmentation tech-
+nique of speed perturbation.
+6. Conclusions
+This paper proposes to utilise an emotional text-to-speech
+(TTS) system to augment a speech emotion recognition (SER)
+system. We present a Tacotron-based multi-speaker emo-
+tional TTS system for synthetic speech generation in dif-
+ferent speaker voices and use it for data augmentation in
+speech emotion recognition to improve performance. The
+results showed that the proposed TTS system can generate
+high-quality emotionally discriminative samples. When we
+augment the SER system with these augmented samples, we
+find that using synthetic data in different emotional voices
+A Shahid et al.: Preprint submitted to Elsevier
+Page 7 of 9
+
+Proposed
+Baseline
+30
+30
+20 
+20
+10 
+10
+D
+10
+-10
+20
+-20
+-30
+-30
+20
+20
+0100
+50 
+0 
+50 
+100
+100
+50
+50
+10080
+ccuracy
+60
+40
+20
+0
+Real
+Synthetic
+Real +
+Synthetic
+augmentationMulti-Speaker Emotional Speech Synthesis
+Figure 7: Confusion matrix for the test set of real, synthetic, and combined synthetic and real audio. The addition of synthetic
+data improves emotion classification.
+Table 4
+Results using different distributions of synthetic data for speakers and gender
+Dataset
+Accuracy (%)
+Baseline
+Speed perturbation
+augmentation
+Male spakers
+synthetic data
+Female speakers
+synthetic data
+Both female and
+male synthetic data
+SAVEE
+65.4
+66.8
+68.2
+69.4
+72.3
+CREMA-D
+68.3
+70.1
+72.7
+72.9
+74.3
+Figure 8: Test results in cross-corpus setting, which shows
+improvements when the model is augmented with synthetic
+data.
+can help improve performance compared to the widely used
+speech data augmentation technique in SER. Our future work
+will focus on investigating the learning of a unified embed-
+ding for controlling style and emotions for all people, regard-
+less of age, background, and gender.
+References
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+Real
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+Synthetic + Real
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+2.8
+5.5
+70
+20
+10
+97.2
+2.8
+0
+happy
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+81.2
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+sad
+angry80
+Crema-D+Synthetic
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+Crema-D only
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+60
+57.0
+52.2
+50
+Accuracy
+45.0
+40
+37.0
+35.44
+30
+20
+10
+0
+CREAD Test set
+SAVEE
+EMOdbMulti-Speaker Emotional Speech Synthesis
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+Page 9 of 9
+

6dE2T4oBgHgl3EQfPAZa/content/tmp_files/2301.03754v1.pdf.txt

@@ -0,0 +1,1095 @@
+1 
+ 
+Inert gas as electronic impurity in semiconductors: The case for 
+active infrared absorption in silicon 
+Nian-Ke Chen1,#, Yu-Chen Gao1,#, Ji-Hong Zhao1,*, Chun-Hao Li1, Qi-Dai Chen1, 
+Hong-Bo Sun2,*, Shengbai Zhang3,*, and Xian-Bin Li1,* 
+ 
+1State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and 
+Engineering, Jilin University, Changchun 130012, China 
+2State Key Lab of Precision Measurement Technology and Instruments, Department of 
+Precision Instrument, Tsinghua University, Beijing 100084, China 
+3Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic 
+Institute, Troy, New York 12180, USA 
+Corresponding 
+authors: 
+lixianbin@jlu.edu.cn, 
+or 
+zhaojihong@jlu.edu.cn, 
+hbsun@tsinghua.edu.cn, or zhangs9@rpi.edu  
+ 
+Abstract 
+Inert (noble gas) elements are extremely inactive to surrounding chemical environment 
+and are frequently employed as protective gas in various semiconductor fabrication 
+processes. In this work, we surprisingly discover that high doses of argon up to 1017-
+1020 cm-3 can be measured in silicon exposed by laser pulses even after 1300 days. First-
+principles calculations and molecular dynamics identify a unique argon-locking-
+vacancy (ALV) defect atomic model in silicon. The ALV defect is dynamically robust 
+in contrast to the frequently moving pure Si vacancy. While argon is chemically inert, 
+it readily modulates defect states of the occupied vacancy via steric repulsion and 
+rattling motions, leading to significant band splitting within bandgap and thus strong 
+infrared absorptions. Moreover, the repulsion between substitutional argon and 
+dangling bonds results in shallow donors which explains the confusion of enhanced n-
+type carriers in experiments. The work paves a way of using noble gas element to 
+produce active infrared absorption source for the non-heteroepitaxy photonic detectors 
+directly on silicon wafer at infrared communication wavelength. 
+
+2 
+ 
+Silicon (Si) based optoelectronic devices is at the heart of optoelectronic industry owing 
+to their ability for Si integration. Among them, photodetectors working at infrared (IR) 
+communication wavelength (λ) of 1.31/1.55 μm are indispensable. However, due to the 
+well-known problem of low absorption at λ ≥ 1.1 μm, corresponding to the Si bandgap, 
+Si is powerless in communication applications. Often, a different semiconductor with a 
+suitable bandgap is heterogeneously grown on Si. However, issues with heteroepitaxy 
+such as lattice mismatch can reduce or even degrade the performance of the detectors 
+[1]. Another way is to introduce IR absorption sources in Si. For example, gap states 
+can be created inside Si by chalcogenide dopants with the help of ultrafast laser pulses 
+to result in doped black silicon [2-6]. It has a strong IR absorption at λ = 1.31/1.55 μm. 
+However, such IR sources are often not stable enough for applications. For example, 
+the IR absorption at 1.31/1.55 μm in black silicon can be significantly reduced by 
+annealing at 775 K for half an hour [4]. 
+ 
+In 2018, Zhao et al. reported a form of black Si, which was fabricated by nanosecond 
+laser pulses without any intentional element dopant except for a protective Ar gas [7,8]. 
+It was quite unexpected that the photodiode fabricated based on such a black Si has a 
+high and stable photoresponsivity of 260 mA/W at 5 V at λ  =  1.31 μm [8], which paves 
+the way for practical sensing by a Si detector at the IR communication wavelength. 
+Argon is a noble gas widely used as a protective gas in the electronic industry.  As a 
+matter of fact, the name of argon is derived from a Greek word that means lazy or 
+inactive. Due to its fully occupied valence band electronic shell with eight electrons, 
+there is little chemical reaction between argon and other elements. As such, it is also 
+expected that the Ar gas has no effect on the property of semiconductors. 
+ 
+In this work, we report the observation of very high concentration of Ar (1017-1020 cm-
+3) in ultrafast laser-modified Si using the secondary-ion mass spectrometry (SIMS) 
+measurement. First-principles calculations and molecular dynamic studies reveal the 
+unique atomic and electronic properties of the Ar-doped Si to result in an unexpected 
+and strong IR absorptions. While the pure Si vacancy can produce dangling-bond state 
+
+3 
+ 
+within bandgap, it is movable and unstable. In contrast, Ar atom can lock the Si vacancy 
+to form a dynamically stable defect complex even up to 900 K. Thanks to its full 
+electronic shell, Ar protects the dangling electrons of vacancy and retains its gap states. 
+Moreover, rattling motion and Coulomb repulsion of Ar atoms can lead to an enhanced 
+structural distortion and the further splitting of defect energy levels within the bandgap. 
+Unexpectedly, the repulsion between substitutional Ar and dangling electrons makes 
+the defect a shallow donor, which explains the confusion of laser irradiation induced n-
+type doping effect. As a result, the inert Ar atom in fact acts as an electronic impurity 
+and offers active and robust sub-bandgap IR absorption source for Si photodetector. 
+This solves the long-term difficulty of high photoresponsivity of Si based detectors at 
+IR communication wavelength. The physics behind shed new light on a general strategy 
+of employing inert elements to raise performances of semiconductor devices. 
+ 
+The concentrations of Ar atoms are measured by dynamic secondary ion mass 
+spectrometer (D-SIMS) in laser modified Si samples in argon protecting atmosphere.  
+The fabrication of such samples were reported in our previous work [8]. The D-SIMS 
+instrument is equipped with a Cameca IMS-4F device using 8 keV Cs+ primary beam. 
+Density-functional theory (DFT) calculations are performed using the VASP code 
+[9,10], where the projector-augmented wave (PAW) pseudo potential and generalized-
+gradient approximation (GGA) exchange-correlation functional developed by Perdew, 
+Burke and Ernzerh are adopted [11-13]. A Si supercell that contains 216 atoms are used 
+to describe defect effects. The energy cutoff for plane-wave expansion is 380 eV. The 
+3×3×3 Monkhorst-Pack grids are used as Brillouin-zone sampling for static energy and 
+property calculations, while the Γ point is used for structural relaxation and molecular 
+dynamic (MD) simulations. The band structures of supercells are unfolded by the 
+modified VaspBandUnfolding package [14]. Energy barriers are calculated using the 
+climbing image nudged elastic band (c-NEB) method [15,16]. The structures and 
+charge density are visualized by the VESTA code [17]. The positions of vacancy defect 
+are determined by the Wigner-Seitz method in the OVITO code [18]. 
+ 
+
+4 
+ 
+To figure out the actual role of Ar atoms in laser modified Si, we carefully analyze the 
+dose of Ar by SIMS measurements in this work. Figure 1(a) displays Ar concentration 
+for such a typical Si sample, which was fabricated previously by nanosecond laser in 
+Ar atmosphere [8]. It is unexpected that even the sample has been made over 1300 days, 
+a very high dose of Ar atoms can be detected as from ~ 4×1021 cm-3 at the surface to ~ 
+4×1017 cm-3 at 2 µm below the surface. We reevaluate the specific detectivity (D*) of 
+the photodetector based on the Si sample [8] and compare it to those of non-silicon 
+photodetectors at the IR wavelength of λ = 1.31 μm [19].  The 1.31-µm wavelength, 
+whose photonic energy is below the bandgap of Si, is out of the detecting scope of 
+detectors based on intrinsic Si. A higher D* reflects a higher signal-to-noise ratio of 
+detectors. For example, Fig. 1(b) shows that the D* of the laser modified Si in Ar 
+atmosphere here working at 295 K (1011 cmHz1/2W-1) is not only higher than those of 
+PbSe and InAs working at the same temperature but also higher than or close to those 
+of InAs and InSb working at a much lower temperature of 193 K or 77 K. All of these 
+indicate the inclusion of Ar in Si could potentially offer a highly effective IR absorption 
+source for detectors. 
+ 
+To uncover the microscopic picture and critical role of Ar in Si samples, we carry out 
+first-principles calculations. In fact, the formation energies (ΔHf) of Ar defects in 
+crystalline Si are very large. Table S1 in Supplemental Material summarizes the 
+calculated ΔHf of several defects in Si, which agrees with previous reports [20,21]. 
+The calculated ΔHf of interstitial and substitutional Ar defects are as large as 6.05-7.19 
+eV while the ΔHf of a silicon vacancy (VSi) is about 3.67 eV. Despite of the high ΔHf, 
+the Ar-related defects can still be formed under laser irradiations. A key reason is that 
+the ΔHf can be substantially reduced when Si is melted by laser irradiations, see Fig. 
+1(c). Also, compared with interstitial Ar defects, substitutional Ar defects should be 
+dominate because an interstitial Ar and a VSi will be annihilated into a substitutional Ar 
+once they encounter during the annealing process. This annihilation is obviously energy 
+favorable. Moreover, the ΔHf of substitutional Ar defects can further be lowered by 
+their accumulation [see Fig. 1(d)] because such an accumulation reduces the number of 
+
+5 
+ 
+dangling bonds. 
+ 
+   
+FIG. 1. (a) Concentration of Ar in the nanosecond-laser modified silicon sample 
+measured by the secondary ion mass spectroscopy. (b) Comparison of specific 
+detectivity (D*) between the black silicon detector [8] and other reported infrared 
+detectors at 1.31 µm [19]. (c) Formation energies of a substitutional Ar defect (ArSi) at 
+various temperatures. The energy of a high-temperature state is calculated by the 
+average free energy of the last 10 ps frames of a 20-ps NVT MD simulation. (d) 
+Formation energies of the accumulated substitutional Ar defects in Si. The formation 
+energies of the multi-substitutional defects are averaged by the number of Ar atoms. 
+ 
+Figure 2 elucidates atomic and electronic structures after an Ar atom is introduced into 
+Si. In order to study Ar induced defect states in Si, a large supercell with 216 atoms is 
+employed. Due to Brillouin Zone folding in the supercell, band structures are calculated 
+and further reanalyzed by the effective band unfolding method [22]. The unfolded band 
+structure in Fig. 2(d) reproduces the correct E-k dispersion for the intrinsic Si despite 
+of underestimating the bandgap by the GGA-DFT method. 
+ 
+Naturally, an Ar atom filling in a Si lattice vacancy (VSi) could be an ideal candidate 
+for the IR absorption. Because an intrinsic vacancy has the ability of offering defect 
+
+1E22
+(a)
+3
+Concentration (Atoms/cm
+1E13
+(b)
+1.31 μum
+InGaAs(PV,295K)
+PbS(PC,295K)
+InAs(PV,193K)
+PbS(PC,77K)
+-Black Si in this work O (PV, 295K)
+nslaserpulse
+1E21
+1E12
+InSb(PV,77K)
+InSb(PC,77K)
+InAs(PC,77K)
+lens
+Si substrate
+PbS(PC,193K)
+1E11
+1E20
+■PbSe(PC,295K)
+■ InAs(PV,295K)
+1E10
+1E19
+1E9
+1E18
+Ar (
+Intrinsic absorption
+1E8
+impurityabsorption
+0.0
+0.5
+1.0
+1.5
+2.0
+Detectors
+Depth (μm)
+(c)
+6
+(d)
+6
+H (eV per Ar)
+ (eV per Ar)
+4
+melting states
+5
+H.
+0
+4
+2Ar,si
+3Ar3si
+4Ar4si
+OK
+2000 K 2500K 3000 K
+Temperature
+Substutional Ar in Si6 
+ 
+states within the bandgap. Fig. 2(a) displays the local tetrahedral motif in intrinsic Si. 
+When a Si atom is removed to form a VSi, four dangling bonds are produced, see Fig. 
+2(b). Here, the four atoms around the vacancy are noted as atoms 1, 2, 3, 4 (Si1, Si2, Si3, 
+Si4), respectively. Li,j is the distance between any two of them. If no any atomic 
+relaxation, the vacancy with all the same Li,j = 3.87 Å holds an ideal Td local symmetry. 
+However, due to the well-known Jahn-Teller distortion effect, the four atoms are 
+relaxed closer to the center of the vacancy with L1,2 (3.03 Å) ≈ L3,4 (3.12 Å) and other 
+Li,j = 3.54 Å. The symmetry is thus lowered to a near D2d symmetry (~D2d) shown in 
+Fig. 2(b), which is consistent with a previous result [23]. Accordingly, the energy levels 
+of defect states can split into two parts: two occupied levels in the lower part within the 
+bandgap while two unoccupied levels in the upper part within the bandgap, see Fig. 2(e) 
+of the band structure and its schematic drawing [Fig. 2(h)] for Si with a ~D2d vacancy. 
+ 
+After Ar atoms are introduced into Si which is confirmed by our SIMS measurement, 
+the local structures of VSi will be changed. For example, as shown in Fig. 2(c), the 
+atomic distortion of VSi can be further enhanced to hold a C2v symmetry due to a Ar 
+atom substitutionally filled in VSi (ArSi). In this case, the Ar atom is closer to Si3 and 
+Si4, which makes Si3 and Si4 move away from each other. Meanwhile, Si1 and Si2 move 
+closer to each other. Therefore, L1,2 and L3,4 are changed to 3.46 Å and 5.40 Å, 
+respectively. The ~120°bond angles of Si3 and Si4 indicate the bonding type is changed 
+to be sp2-hybridization like while the sp3-hybridization like bonding still remains for 
+Si1 and Si2. Our calculations found that the filling of Ar into VSi costs about 2.56-eV 
+extra energy. Such large an interaction energy and the large structural distortion suggest 
+that Ar should have a significant repulsive interaction with surrounding dangling bonds 
+of Si atoms, i.e., the steric repulsion effect. The steric-repulsive induced distortion 
+(SRD) also leads to a larger bonding hierarchy and changes the defect states of VSi. 
+Accordingly, comparing to the case of VSi, defect levels of ArSi are further splitted, see 
+Figs. 2(f) and (i): the energies of highest occupied defect orbital (HODO), lowest 
+unoccupied defect orbital (LUDO) and LUDO+1 is raised and closer to conduction 
+band while the energy of HODO-1 lowers into the valence band. 
+
+7 
+ 
+ 
+FIG. 2. Local atomic structures of (a) Si, (b) VSi and (c) ArSi with the steric-repulsive 
+distortion (SRD) holding a C2v symmetry . The arrows indicate the directions of atomic 
+relaxation referred to their original positions. (d)-(f) correspondingly show the unfolded 
+band structures of the three supercell models. The size of the scatters represents the 
+atomic weight. The weights of Si1,2,3,4 (green and red scatters) are amplified by a factor 
+of 10. The green and red scatters indicate the contributions from Si1,2 and Si3,4, 
+respectively. (g)-(i) show corresponding schematic band structures. Ef is set as 0 eV. 
+ 
+In fact, the local atomic configuration of ArSi defect with SRD is not unique. It can also 
+have other structures with a C3v or ~Td symmetry, see Figs. S1(e) and (f) in 
+Supplemental Material. In both cases, the four dangling Si atoms (Si1,2,3,4)  are repulsed 
+by the Ar and thus tend to have a sp2-like bonding characteristic due to the bond angle 
+of ~120°. In the two cases, not only the defect levels but also the spin states are splitted, 
+see Figs. S2 and S3 in Supplemental Material. Three of the four electrons from dangling 
+bonds occupy three spin-up levels while one occupies a spin-down level. 
+
+(a)
+Si
+(b)
+V.
+(c)
+Ar..SRD-C
+Si
+Energy [eV]
+Energy [eV]
+Energy [eV]
+Q
+1
+-1
+2
+2
+2
+-3
+3
+xu
+K
+W
+X
+X U
+K
+L
+W
+X
+xU
+K
+L
+L
+W
+X
+(g)
+(h)
+(0)
+Conduction Band
+ConductionBand
+Conduction Band
+ValenceBand
+Valence Band
+Valence Band8 
+ 
+ 
+In fact, the three configurations of ArSi with C2v, C3v and ~Td SRDs almost have the 
+same formation energy with little differnece of 0.01-0.03 eV (see Table S1 in 
+Supplemental Material). The energy barrier of the tansition between C2v and C3v (C3v 
+and ~Td) configurations calculated by the NEB method is also as small as 0.015 (0.013) 
+eV, indicating readily transitions to each other. Defect levels always preserve inside the 
+bandgap after inert Ar doping in VSi, despite of these different Ar configurations with 
+close eneriges. Moreover, the SRD effect still stands in the accumulated substitutional 
+Ar defects (3Ar3Si and 4Ar4Si) and thus the splitted defect states also exist (see Fig. S4 
+in Supplemental Material). In addition, a bond-centered (B-C.) site interstitial Ar defect 
+also has two dangling bonds while the tetrahedral/hexagonal-site interstitial Ar defects 
+have no dangling bonds, see Figs. S1(a)-(c) in Supplemental Material. As such, the B-
+C. interstitial Ar also has two defect levels inside the bandgap, see Fig. S5 in 
+Supplemental Material. All these defect states no doubt will benefit a robust sub-
+bandgap IR absorption in Si. 
+ 
+Next, electronic bonding mechanisms of ArSi are analyzed to figure out the mechanism 
+of the Ar doping induced change of defect states. Taking the C2v configuration as an 
+example, the charge density difference (CDD) analyses [24] in Figs. 3(a)-(c) show no 
+transferred or shared electrons between Ar and its surrounding Si due to the chemical 
+inertia of Ar. Therefor, the interaction between Ar and the dangling Si atoms should be 
+Coulomb repulsion effect which agrees with the SRD of the local structure. In fact, 
+although Ar atom does not offer any defect levels but indirectly modulate defect states 
+of a Si vacancy via the repulsion. Figures 3(d)-(h) elucidate the spatial distributions of 
+defect states. The updated sp2-like configuration of Si3,4 [see the bond angles of 121° in 
+Fig. 3(a)] may release a dangling pz orbital from the orginal  sp3 orbital. Obviously, the 
+LUDO+1 and the HODO are the unoccupied  and occupied pz-like orbitals of Si3,4, 
+respectively, see Figs. 3(e) and (g). Figure 3(f) shows the LUDO corresponding to the 
+unoccupied sp3-like orbital of Si1,2. Since Si1 and Si2 has also a certain interaction due 
+to a charge accumulation between them shown in Fig. 3(b), their occupied sp3-like state 
+
+9 
+ 
+further moves below the valence band maximum. We indeed find the state by projecting 
+the orbital-decomposed partial charge density inside valence band [see Fig. 3(h)]. Such 
+a defect state will move back into bandgap in the case of C3v and ~Td SRDs due to the 
+absence of such interaction between dangling Si atoms (see Figs. S2 and S3 in 
+Supplemental Material). 
+ 
+ 
+FIG. 3. (a) The charge density difference (CDD) of ArSi with the C2v SRD. The value 
+of isosurface is 0.015 e/a03, a0 is the Bohr radius. (b) and (c) show the respective (11̅0) 
+and (110) slices of the CDD. The unit of the color bar is e/a03. (d) Schematic defect 
+levels of ArSi with C2v SRD. (e)-(h) The corresponding orbital-decomposed partial 
+charge density projected to real space. The values of isosurface are 0.005 e/a03 for (e)-
+(g) and 0.0015 e/a03 for (h). 
+ 
+To directly demonstrate the influence of the Ar-related defect on the IR absorption at λ 
+= 1.31/1.55 μm, the aobsorption coefficients are calculated [see Fig. 4(a)]. Here, the 
+meta-GGA method using the modified Becke-Johnson (MBJ) exchange potential 
+[25,26] is adopted to correct the bandgap underestimated by the traditional PBE 
+functional (see Fig. S6 in Supplemental Material for the effect of correction). Obviously, 
+
+a
+≥ 0.015
+0.006
+105°
+0.000
+121
+121°
+-0.006
+<-0.015
+e
+(d)
+Conduction
+Band
+Pz
+(g)
+(h)
+sp
+Valence
+Band10 
+ 
+a substantial enhancement of the sub-bandgap IR absorption is achieved by ArSi in great 
+contrast to the case without defect (Si) that displays almost no absoprtion. Moreover, 
+the substitutioanl defects also have stronger abosorptions compared with the interstitial 
+Ar and VSi, owing to the repulsion induced splitting of defect levels. 
+ 
+ 
+FIG. 4. (a) Calculated absorption coefficient of Si, VSi, B-C. interstitial Ar and ArSi with 
+the C2v and C3v SRDs. (b)-(d) The ΔHf of neutral and charged states of the ArSi with 
+C2v SRD, the ArSi with C3v SRD and the B-C. interstitial Ar defect, respectively. 
+ 
+In fact, the repulsion effect of Ar on dangling electrons not only changes the atomic 
+structure and the position of defect levels but also significantly affects the ionization 
+process. When the Ar is filled into the vacancy, the strong repulsive interaction between 
+Ar and dangling electrons should make the electrons be ionized easily. Figures 4(b)-(d) 
+show the calculated chemical potential dependent ΔHf of neutral and charged states of 
+the Ar defects [27,28]. According to the position of transition levels (where the ΔHf of 
+neutral and charged states equal), it is surprising that the substitutional Ar defects are 
+shallow donors but deep acceptors. In contrast, the B-C. interstitial Ar still has deep 
+donor and acceptor levels. The shallow donor effect of ArSi defects can explain the 
+
+Absorption Coefficient (cm
+6000
+(a)
+by meta-GGA
+Ar.. SRD-C
+3V
+4000
+Ar.. SRD-C
+2000
+B-C. interstitial
+Si
+0
+1.2
+1.3
+1.4
+1.5
+1.6
+Wavelength (μm)
+6.8
+(b)
+(c)
+ Ar SRD-C
+(d)B-C. interstitial
+Ar SRD-C
+IS
+2v
+1
+S
+3v
+-1
+6.4
+(eV)
+0
+0
+△H.
+0
+6.0
++1
++1
++1
+0.0
+0.3
+0.6 0.0
+0.3
+0.6 0.0
+0.3
+0.6
+E.- E
+(eV)
+E.-E
+(eV)
+E.-E
+(eV)
+f
+VBV
+VBM
+VBV11 
+ 
+confusion that the fabricated sample shows a substantially enhanced n-type carrier 
+concentration [8]. In other words, the substitutional Ar can act as an electronic impurity 
+despite of its inert chemical property. 
+ 
+  
+ 
+FIG. 5. The projected trajectories of the local structure of (a) ArSi and (b) VSi during 60-
+ps MD simulations at 500 K. The colored dots represent positions of ArSi and Vsi while 
+the grey dots indicate the ones of Si atoms with time evolution. The energy barriers for 
+a diffusion of (c) ArSi and (d) VSi calculated by c-NEB method. (e) The MSD of the VSi 
+during the MD simulation. Inset in (e) shows the schematic trajectory of diffusion of a 
+pure VSi in the simulation. 
+ 
+It worth noting that VSi has the lowest ΔHf (3.67 eV) among the defects in Si and it 
+can also offer a significant sub-bandgap IR absorption. As mentioned above, the 
+absorption of ArSi is in fact originated from defect states of dangling bonds around the 
+Ar filled vacancy. However, for practical device applications, IR absorption sources 
+should be reliable enough. Therefore, two ab initio MD simulations of 60 ps at 500 K, 
+
+ps
+(a)
+(b)
+60
+(010)
+(100)
+(100)
+40
+20
+0
+(001)
+(001)
+Si
+Si
+Z
+0.3
+Ar
+V
+Energy (eV)
+(c)
+(d)
+Si
+Si
+0.2
+0.1
+0
+0.0
+Configurations
+Configurations
+40
+(e)
+V
+MSD (A^
+Si
+4
+20
+2
+6
+8
+1.
+0
+0
+10
+20
+30
+40
+50
+60
+Time (ps)12 
+ 
+which is significantly higher than room temperature at which detector devices work, 
+are performed to compare the structural stability between ArSi and pure VSi. Figures 5(a) 
+and (b) show the projected atomic trajectories with time for the local structures of ArSi 
+and the VSi, respectively. During the MD simulations, the instant sites of the vacancy 
+are determined by the Wigner-Seitz method as implemented in the OVITO code [18]. 
+It is clear that the Ar atom in ArSi is in form of a kind of rattling motion and moves 
+much more intensely than normal Si atoms behave in lattices. The result is consistent 
+with the negligible energy barriers among different SRD configurations of a ArSi. 
+Despite of such intense motions, ArSi stays in a same lattice firmly during the whole 
+MD simulation. Note that the multi-substitutional Ar defects (e.g., 4Ar4Si) also stable 
+during a 500 K MD simulation (see Fig. S7 in Supplemental Material). In a great 
+contrast, the pure VSi shows an easy diffusion among different lattices. Next, the c-NEB 
+analyses further evaluate barriers of atomic diffusions in Si. First, the energy barrier of 
+a single VSi diffusion can be as low as 0.26 eV, see Fig. 5(d). The probability of its 
+diffusion behavior at 500 K could be simply estimated by Arrhenius equation: 𝑃 = 𝑣 ∙
+exp (−
+𝐸𝑎
+𝑘𝐵𝑇), where kB is the Boltzmann constant, T is the temperature, Ea is the energy 
+barrier of diffusion and v can be regarded as atomic vibration frequency. Using the 
+frequency of highest optical phonon of crystalline Si, i.e., ~15 THz [29], the estimated 
+characteristic time for one diffusion event is 𝜏 =
+1
+𝑃 ≈ 30 ps  for the VSi. Figure 5(e) 
+shows the mean square displacement (MSD) of VSi during the 500-K MD simulations. 
+The pure VSi can move in different lattices as many as 8 times within 60 ps, which is 
+close to the estimated characteristic time. That indicates in a practical Si sample the 
+pure VSi can readily diffuses among the lattices at the raised temperature and will be 
+eliminated when it gets to a grain boundary or a surface by an annealing process. As 
+such, the significant sub-bandgap absorption by VSi as shown in Fig. 4(f) cannot readily 
+happens. Second, in a great contrast, the energy barrier for an Ar diffusion out of a 
+vacancy (i.e., an Ar exchanges its site with an adjacent Si atom) is as high as 1.8 eV, 
+see Fig. 5(c). We have performed c-NEB calculations with other two different paths for 
+Ar diffusions and the barriers are almost the same (~1.8 eV), see Fig. S8 in 
+
+13 
+ 
+Supplemental Material. The atomic pictures of the ArSi diffusions are presented in Figs. 
+S9-S11 in Supplemental Material. According to the Arrhenius equation, the 
+characteristic time for the Ar diffusion is at least ~ 70000 s, indicating a robust stability 
+of ArSi. Moreover, in another 60-ps MD in Fig. S12 of Supplemental Material, the 
+diffusion of ArSi is still absent at a much higher temperature of 900 K, which is usually 
+as an annealing temperature for fabrications of black Si detectors. Therefore, ArSi can 
+be regarded as a kind of Ar locking vacancy (ALV) defect. 
+ 
+Finally, we discuss benefits of the ArSi or ALV doping for IR absorptions in Si detectors. 
+Firstly, the steric repulsion induced band splitting makes the ArSi defect readily 
+contribute multi defect states and thus offer effective sub-bandgap IR sources, which is 
+impossible for intrinsic Si. Secondly, due to Coulomb repulsion of the fully occupuied 
+shell of Ar, local configurations of the ALV can be dynamically adjusted by the Ar atom 
+at a raised temperature or even room temperature, see Fig. S13 in Supplemental 
+Material, which leads to a broad IR absorption band. Thirdly, Ar acts like an electronic 
+impurity with shallow donor defect levels. Then, the N+ layer can be formed which is 
+the key to construct the N+-N- junction in the device of IR detector [8]. 
+ 
+Conclusion 
+In summary, we detect an unexpected high dose of inert Ar (with 1017-1020 cm-3) by 
+SIMS measurements in laser modified Si samples at Ar protective gas even after more 
+than 1300 days from when it was fabricated. First-principles calculations and molecular 
+dynamics simulations demonstrate a mechanism of Ar locking vacancy (ALV or ArSi) 
+happening in Ar doped silicon. While the pure vacancy in silicon can readily diffuse at 
+500 K, the ALV defect is dynamically robust at the same condition even no direct 
+chemical bonding connection between Ar and its neighboring Si atoms. Despite of the 
+chemical inert property of Ar, it can still act as an electronic impurity via strong 
+Coulomb repulsion effect which leads to significant splitting of defect levels within 
+bandgap, and thus have a strong sub-bandgap IR absorption in Si. It is an impossible 
+task for intrinsic Si. Moreover, the repulsion between Ar and dangling electrons leads 
+
+14 
+ 
+to a shallow donor effect, which explains the confusion of n-type doping effect of laser 
+irradiation observed in previous experiments. It is reasonable to expect that such an 
+inert element induced IR absorption mechanism may also happen in other 
+semiconductors. Our work opens up a new door of using inert element doping 
+engineering to develop high performance IR Si detector, which is urgently required in 
+current Si based integrated optoelectronics. 
+  
+Acknowledgements 
+Work in China was supported by the National Natural Science Foundation of China 
+(Grants No. 62275098, No. 12274180, No. 12274172) and the Fundamental Research 
+Funds for the Central Universities.  S.Z. was supported by the US Department of Energy 
+under Award No. DE-SC0002623. We sincerely thank Prof. Q.Z. at USTC for his 
+supports on band-unfolding analyses. The High-Performance Computing Center 
+(HPCC) at Jilin University for computational resources is also acknowledged. 
+ 
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+ 
+
+1 
+ 
+Supplemental Material for 
+“Inert gas as electronic impurity in semiconductors: 
+The case for active infrared absorption in silicon” 
+ 
+Nian-Ke Chen1,#, Yu-Chen Gao1,#, Ji-Hong Zhao1,*, Chun-Hao Li1, Qi-Dai Chen1, 
+Hong-Bo Sun2,*, Shengbai Zhang3,*, and Xian-Bin Li1,* 
+ 
+1State Key Laboratory of Integrated Optoelectronics, College of Electronic Science 
+and Engineering, Jilin University, Changchun 130012, China 
+2State Key Lab of Precision Measurement Technology and Instruments, Department of 
+Precision Instrument, Tsinghua University, Beijing 100084, China 
+3Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic 
+Institute, Troy, New York 12180, USA 
+ 
+Corresponding 
+authors: 
+lixianbin@jlu.edu.cn, 
+or 
+zhaojihong@jlu.edu.cn, 
+hbsun@tsinghua.edu.cn, or zhangs9@rpi.edu 
+ 
+
+2 
+ 
+CONTENTS: 
+Table S1. Formation energies of different defects in crystalline Si. 
+Fig. S1. Atomic structures of different Ar defects in crystalline Si. 
+Fig. S2. Band structure of ArSi defect with the configuration of C3v symmetry. 
+Fig. S3. Band structure of ArSi defect with the configuration of ~Td symmetry. 
+Fig. S4. Band structures of the 3Ar3Si and 4Ar4Si defects. 
+Fig. S5. Band structures of the interstitial Ar defects. 
+Fig. S6 Comparison of the density of states calculated by traditional PBE functional 
+and the meta-GGA method. 
+Fig. S7. A transient structure of 4Ar4Si and the projected trajectories of the local 
+structure of the 4Ar4Si during the 60-ps MD simulations at 500 K. 
+Fig. S8. Energy barriers for the diffusion of ArSi defect calculated by c-NEB method. 
+Fig.S9-S11. Atomic pictures of ArSi diffusion corresponding to the c-NEB calculations 
+in Fig. 5(c), Fig. S8(a) and Fig. S8(b), respectively. 
+Fig. S12-S13. The projected trajectories of the local structure of ArSi during the 60-ps 
+MD simulations at 900 K and 300 K, respectively. 
+ 
+
+3 
+ 
+TABLE S1. Formation energies of the defects in crystalline Si. The unit is eV. VSi is a 
+silicon vacancy. Tetrahedral (Tetra.), hexagonal (Hex.) and bond-centered (B-C.) 
+represent three different sites of the interstitial Ar defects [see Fig. S1(a)-(c) for the 
+atomic pictures]. C2v, C3v and ~Td represent three different configurations of the 
+substitutional Ar defects as described in the main text [see Fig. S1(d)-(f) for the 
+atomic 
+pictures]. 
+2Ar2Si, 
+3Ar3Si 
+and 
+4Ar4Si 
+represent 
+the 
+accumulated 
+multi-substitutional Ar defects [see Fig. S1(g)-(i) for the atomic pictures]. The 
+formation energies of multi-substitutional Ar defects are averaged by the number of 
+Ar atoms. Under the jellium approximation, the formation energy of defect w with 
+charge q can be calculated by the following equation: 
+𝛥𝐻𝑓(𝑞, 𝑤) = 𝐸𝑡𝑜𝑡(𝑞, 𝑤) − 𝐸𝑡𝑜𝑡(ℎ𝑜𝑠𝑡) + ∑ 𝑛𝑖𝜇𝑖
+𝑖
++ 𝑞(𝜀𝑉𝐵𝑀 + 𝜀𝐹) 
+where 𝐸𝑡𝑜𝑡(𝑞, 𝑤) is the total energy of the supercell with defects, 𝐸𝑡𝑜𝑡(ℎ𝑜𝑠𝑡) is the 
+energy without the defect (i.e., bulk Si), 𝑛𝑖 is the number of atoms being exchanged 
+during the formation of the defect, 𝜇𝑖 is the atomic chemical potential of an element 
+(here we use the 𝜇𝑖 of bulk and isolated atom for Si and Ar, respectively), and 𝜀𝐹 is 
+the Fermi energy relative to the valence band maximum, 𝜀𝑉𝐵𝑀. 
+VSi 
+Interstitial 
+Substitutional 
+Multi-substitutional 
+Tetra. 
+Hex. 
+B-C. 
+C2v 
+C3v 
+~Td 
+2Ar2Si 3Ar3Si 4Ar4Si 
+3.69 
+6.05 
+7.19 
+6.10 
+6.25 
+6.24 
+6.27 
+4.97 
+4.52 
+4.28 
+ 
+ 
+
+4 
+ 
+ 
+FIG. S1. (a)-(c) Local atomic structures of three interstitial Ar defects. (d)-(f) Local 
+atomic structures of ArSi with the steric-repulsive distortion (SRD) of C2v, C3v and ~Td 
+symmetry. (g)-(i) The atomic structures of accumulated multi-Ar doping defects 
+including two-Ar-atoms substitution (2Ar2Si), three-Ar-atoms substitution (3Ar3Si) and 
+the four-Ar-atoms substitution (4Ar4Si). 
+ 
+ 
+
+(a) Tetra. interstitial
+(b) Hex. interstitial
+(c) B-C. interstitial
+(d)
+Ar..
+c
+(e)
+Ar..
+C
+(f)
+Ar.
+Si
+2v
+Si
+3v
+120°
+120°
+105
+~120°
+115°
+121
+121
+120°
+~120°
+120%
+~120°
+2Ar
+(h)
+3Ar
+(i)
+4Ar
+(g)
+2Si
+3Si
+4Si5 
+ 
+ 
+FIG. S2. Unfolded band structures of ArSi with the SRD-C3v configuration [see Fig. 
+S1(e) for the atomic structure] holding (a) spin-up and (b) spin-down polarizations. 
+The green and red scatters indicate the contributions from Si1 and Si2,3,4, respectively. 
+Lower panels show corresponding schematic band structures. Ef is set as 0 eV. 
+ 
+ 
+
+(a) Ars, SRD-C3spin个
+(b) Ars, SRD-C3 spin
+2
+1
+1
+0
+0
+Energy [eV]
+[eV]
+Energy
+2
+2
+-3
+3
+XU
+K
+L
+W
+X
+XU
+K
+L
+W
+X
+Conduction Band
+Conduction Band
+Valence Band
+Valence Band6 
+ 
+ 
+FIG. S3. The unfolded band structure of the ArSi with the ~Td configuration [see Fig. 
+S1(f) for the atomic structure], which is very similar to the ArSi SRD-C3v 
+configuration. The states contributed by the defective atoms are highlighted by red 
+color. 
+ 
+ 
+FIG. S4. The unfolded band structures of the (a) 3Ar3Si [see Fig. S1(h) for the atomic 
+structure] and (b) 4Ar4Si [see Fig. S1(i) for the atomic structure], respectively. The 
+states contributed by the defective atoms are highlighted by red color. 
+
+a
+SRD-~T
+spin个
+(b)
+Ar..
+SRD-~TspinV
+2
+7
+0
+0
+Energy [ev]
+1
+T
+2
+2
+3
+3
+.4
+5
+5
+X U
+K
+W
+X
+x U
+K
+W
+X(a)
+3Ar
+(b)
+4Ar
+3Si
+4Si
+2
+2
+1
+1
+Energy[eV]
+Energy [eV]
+0
+0
+1
+2
+-3
+3
+XU
+K
+厂
+W
+X
+XU
+K
+W
+X7 
+ 
+ 
+ 
+FIG. S5. The unfolded band structure of the (a) Tetra.-site [see Fig. S1(a) for the 
+atomic picture] and (b) B-C.-site [see Fig. S1(c) for the atomic picture] interstitial Ar 
+defects. The states contributed by the defective atoms are highlighted by red color. 
+The defect states exist in the supercell with a B-C. interstitial Ar defect because the Ar 
+atom in this case breaks a Si-Si bond. 
+ 
+ 
+FIG. S6. Comparison of the density of states (DOS) of calculated by traditional PBE 
+functional and the meta-GGA method using the modified Becke-Johnson (MBJ) 
+exchange potential. The bandgap underestimated by PBE is corrected by the 
+meta-GGA method while the defect states still retain. 
+ 
+
+(a) Tetra. interstitia
+(b)
+B-C. interstitial
+2
+Energy [eV]
+Energy [eV]
+1
+1
+2
+2
+-3
+3
+.
+X
+K
+W
+X
+XU
+K
+L
+W
+X300
+(a)
+Si
+PBE
+(b)
+PBE
+Ar..SRD-C
+PBE
+metaGGA
+metaGGA
+2
+metaGGA
+200
+DOS
+100
+0
+-3
+-2
+-1
+0
+2
+3
+.3
+-2
+1
+0
+2
+3
+2
+0
+3
+E- E, (eV)
+E- E. (ev)
+E-E.(eV)8 
+ 
+ 
+FIG. S7. (a) A snapshot of the atomic structure of the 4Ar4Si after the 60-ps MD 
+simulations at 500 K. (b) The projected trajectories of the local structure of the 4Ar4Si 
+during the 60-ps MD simulations at 500 K. The color coding is the same with that in 
+the main text. 
+ 
+ 
+ 
+FIG. S8. The energy barriers for diffusion of ArSi calculated by c-NEB method along 
+different paths. The atomic pictures of different paths are shown in Figs. S9-S11 
+below. 
+ 
+
+(a) 4Aras; after 60-ps MD at 500 K
+60 ps
+(b)
+(010)
+(100)
+40
+20
+(001)
+02
+2
+(a)
+(b)
+1
+0
+0
+Configurations
+Configurations9 
+ 
+ 
+FIG. S9. The picture of ArSi diffusion corresponding to the c-NEB calculation of the 
+path in Fig. 5(c) of the main text. The color coding is the same with that in the main 
+text. The yellow label indicates the Si atom who exchanged its position with Ar atom 
+during the diffusion. (a) and (b) show the views along [010] and [100] directions, 
+respectively. 
+ 
+ 
+FIG. S10. The picture of ArSi diffusion corresponding to the c-NEB calculation of the 
+path in Fig. S8(a). The color coding is the same with that in the main text. The yellow 
+label indicates the Si atom who exchanged its position with Ar atom during the 
+diffusion. (a) and (b) show the views along [010] and [100] directions, respectively. 
+
+aa)
+b10 
+ 
+ 
+ 
+FIG. S11. The picture of ArSi diffusion corresponding to the c-NEB calculation of the 
+path in Fig. S8(b). The color coding is the same with that in the main text. The yellow 
+label indicates the Si atom who exchanged its position with Ar atom during the 
+diffusion. (a) and (b) show the views along [010] and [100] directions, respectively. 
+ 
+ 
+FIG. S12. The projected trajectories of the local structure of ArSi during the 60-ps MD 
+simulations at 900 K. The color coding is the same with that in the main text.  
+
+a
+b60ps
+(010)
+(100)
+40
+20
+(001)
+011 
+ 
+ 
+ 
+FIG. S13. The projected trajectories of the local structure of ArSi during the 60-ps MD 
+simulations at 300 K. The color coding is the same with that in the main text. 
+ 
+ 
+
+60ps
+(010)
+(100)
+40
+20
+(001)
+0

79AyT4oBgHgl3EQfc_dz/content/tmp_files/2301.00293v1.pdf.txt

@@ -0,0 +1,1187 @@
+arXiv:2301.00293v1  [astro-ph.EP]  31 Dec 2022
+Orbital Migration of Protoplanets in a Marginally Gravitationally
+Unstable Disk. II. Migration, Merging, and Ejection
+Alan P. Boss
+Earth & Planets Laboratory, Carnegie Institution for Science, 5241 Broad Branch Road,
+NW, Washington, DC 20015-1305
+aboss@carnegiescience.edu
+ABSTRACT
+Protoplanets formed in a marginally gravitationally unstable (MGU) disk by
+either core accretion or disk instability will be subject to dynamical interactions
+with massive spiral arms, possibly resulting in inward or outward orbital migra-
+tion, mergers with each other, or even outright ejection from the protoplanetary
+system. The latter process has been hypothesized as a possible formation sce-
+nario for the unexpectedly high frequency of unbound gas giant exoplanets (free
+floating planets, FFP). Previous calculations with the EDTONS fixed grid three
+dimensional (3D) hydrodynamics code found that protoplanets with masses from
+0.01 M⊕ to 3 MJup could undergo chaotic orbital evolutions in MGU disks for
+∼ 1000 yrs without undergoing monotonic inward or outward migration. Here
+the Enzo 2.5 adaptive mesh refinement (AMR) 3D hydrodynamics code is used
+to follow the formation and orbital evolution of protoplanets in MGU disks for
+up to 2000 yrs. The Enzo results confirm the basic disk fragmentation results
+of the EDTONS code, as well as the absence of monotonic inward or outward
+orbital migration. In addition, Enzo allows protoplanet mergers to occur, unlike
+EDTONS, resulting in a significant decrease in the number of protoplanets that
+survive for 1000 to 2000 yrs in the Enzo models. These models also imply that
+gas giants should be ejected frequently in MGU disks that fragment into large
+numbers of protoplanets, supporting ejection as a possible source mechanism for
+the observed FFPs.
+Subject headings: planets and satellites: formation — protoplanetary disks
+1.
+Introduction
+Exoplanet demographics provide one of the ultimate arbiters of theories of exoplanet
+formation and evolution. Nielsen et al. (2019) used the GPI exoplanet survey to search
+
+– 2 –
+for planets with masses between 2 and 13 MJup and semimajor axes between 3 and 100 au,
+finding that the peak occurrence distance of giant planets was in the range of 1 to 10 au.
+Fulton et al. (2021) found the same peak occurrence distance of 1 to 10 au for the California
+Legacy Doppler velocities survey.
+Vigan et al.
+(2021) showed that the VLT SPHERES
+direct imaging survey of 150 stars detected 13 sub-stellar companions with masses between
+1 and 75 MJup and semimajor axes between 5 and 300 au, finding that both core accretion
+(CA; Mizuno 1980) and disk instability (DI; Boss 1997) appeared necessary to explain the
+detections for the FGK stars in their sample.
+Gas giant planets with orbital distances as large as 980 au have been discovered and
+studied (Wu et al. 2022). Forming giant exoplanets at such large distances by CA within
+the ∼ 1 Myr lifetimes of the gaseous portion of protoplanetary disks is challenging (e.g.,
+Chambers 2021), if not impossible. DI has the advantage of forming dense, self-gravitating
+clumps in a few orbital periods, relaxing the disk lifetime constraint for forming wide-orbit
+gas giants in situ (e.g., Boss 2011). Evidence for a gas giant protoplanet embedded in a spiral
+arm 93 au from AB Aurigae has been interpreted as an example of gas giant planet formation
+by DI (Currie et al. 2022; cf. Cadman et al. 2021; Zhou et al. 2022). DI has also been
+proposed as the source of the ∼ 10MJup exoplanet that orbits ∼ 560 au from the massive
+binary b Centauri (Janson et al. 2021). Goda & Matsuo (2019) examined the demographics
+of 485 planetary systems and concluded that a hybrid theory of planet formation, involving
+both CA and DI, was needed to explain the exoplanet detections.
+Miret-Roig et al. (2022) used a direct imaging survey coupled with Gaia and Hipparchos
+astrometry to search for unbound gas giant exoplanets in the Upper Scorpius and Ophiuchus
+young stellar association. Their survey yielded between 70 and 170 free floating planets
+(FFP), considerably more than might be expected to form as the tail end of the star formation
+process of molecular cloud core collapse and fragmentation, and suggested that ejection
+from unstable planetary systems might make a major contribution during the first 10 Myr.
+Gravitational microlensing has also found an abundance of likely FFPs, though these could
+also simply be bound planets with orbital distances greater than about 10 au (Mr´oz et al.
+2020; Ryu et al. 2021). Vorobyov (2016) performed numerical simulations that supported
+the hypothesis that FFPs might be the result of planets ejected from massive MGU disks.
+While exoplanet demographics reveal orbital characteristics at the present epoch, unless
+exoplanets do not undergo significant orbital evolution or migration following their formation,
+the present epoch orbital parameters are of limited usefulness in constraining their initial
+orbital distances. CA is the favored mechanism closer to the host star, as a result of shorter
+orbital periods, higher gas disk temperatures, and higher surface densities of solids, to name
+a few factors, while DI may be more effective at larger distances in suitably massive and cool
+
+– 3 –
+protoplanetary disks. For either CA or DI, a key question then becomes the extent to which
+protoplanets might migrate away from their birth orbits to their present epoch orbits.
+As noted by Boss (2013), CA and DI both require giant protoplanets to form in the
+presence of disk gas. Theoretical work on protoplanetary orbital migration (e.g., Kley &
+Nelson 2012) usually focuses on protoplanets in disks where the disk mass is low enough
+that the disk self-gravity can be neglected, greatly simplifying the analysis. Protoplanet
+evolution in MGU disk models has been calculated by Boss (2005), Baruteau et al. (2011),
+and Michael et al. (2011). These studies each considered quite different initial conditions
+and found a wide range of outcomes, ranging from large-scale inward orbital migration to
+relatively little orbital migration. Boss (2013) studied the evolution of protoplanets formed
+by either CA and DI in MGU disks, noting that while a MGU disk is essential for formation
+by DI, even a giant planet formed by CA in a quiescent, non-MGU disk can experience a
+later phase of MGU disk interactions during the periodic FU Orionis outbursts experienced
+by young solar-type protostars, which are thought to involve a phase of disk gravitational
+instability that dumps disk mass onto the protostar (e.g., Zhu et al. 2010; Kuffmeier et al.
+2018). Dunhill (2018) similarly suggested that giant planets formed by CA might undergo
+orbital migration during FU Orionis outbursts.
+The Boss (2005, 2013) models were performed using the EDTONS three dimensional
+radiative hydrodynamics code, with a spherical coordinate grid that was fixed at moderate
+spatial resolution throughout the MGU disk evolutions. Virtual protoplanets were introduced
+at the beginning of each model to represent protoplanets as point sources of gravity, able
+to interact gravitationally with the disk and with each other and to accrete mass from the
+disk by Bondi-Hoyle accretion. Boss (2013) found that protoplanets with initial masses in
+the range from 0.01 M⊕ to 3 MJup and initial orbital distances of 6 to 12 au in a MGU disk
+around a solar-mass protostar underwent chaotic orbital evolutions for ∼ 1000 yr without
+undergoing the monotonic inward or outward migration that typically characterizes the Type
+I or Type II behavior of non-self-gravitating disk models (e.g., Kley & Nelson 2012).
+The present models of protoplanet orbital evolution employ the Enzo 2.5 hydrodynamics
+code. Enzo is also a three dimensional (3D) code and uses Adaptive Mesh Refinement (AMR)
+in Cartesian coordinates to ensure that sharp gradients in fluid quantities such as shock fronts
+can be handled accurately. Enzo is able to replace exceptionally dense disk clumps with sink
+particles representing newly formed (by DI) protoplanets, which thereafter interact with each
+other and the disk while accreting disk gas, as do the virtual protoplanets in the Boss (2013)
+models. We thus seek here to use a completely different 3D hydro code to learn more about
+the possible outcomes for protoplanet orbital evolution in MGU disks, and to compare the
+results with the latest advances in exoplanet demographics.
+
+– 4 –
+2.
+Numerical Hydrodynamics Code
+As noted by Boss & Keiser (2013), the Enzo 2.5 AMR code performs hydrodynamics
+(HD) using any one of three different algorithms (Collins et al. 2010; Bryan et al. 2014): (1)
+the piecewise parabolic method (PPM) of Colella & Woodward (1984), (2) the ZEUS method
+of Stone & Norman (1992), or (3) a Runge–Kutta third-order-based MUSCL (“monotone
+upstream-centered schemes for conservation laws”) algorithm based on the Godunov (1959)
+shock-handling HD method. Enzo is designed for handling strong shock fronts by solving
+the Riemann problem (e.g., Godunov 1959) for discontinuous solutions of a fluid quantity
+that should be conserved. The PPM option was used in the current models as a result of the
+testing on mass and angular momentum conservation performed with Enzo 2.0 by Boss &
+Keiser (2013), who found that PPM was better able to conserve mass and angular momentum
+during the collapse of a rotating isothermal cloud core (Boss & Bodenheimer 1979) than
+either ZEUS or MUSCL. Enzo is designed for parallel processing on high performance clusters
+(HPC), but when run on a single, dedicated 32-core node of the Carnegie memex HPC, a
+typical model still required 7 months of continuous computation to evolve for ∼ 103 yrs of
+model time.
+The Enzo 2.5 models were initialized on a 3D Cartesian grid with 32 top grid points
+in each direction.
+A maximum of 7 levels of refinement was used, with a factor of two
+refinement occurring for each level, so that the maximum possible effective grid resolution
+was 27 = 128 times higher than the initial resolution of 323, i.e., 40963. The models with 7
+levels needed an increase in the number of cell buffer zones (NumberBufferZones) to 3 from
+the default value of 1, which was used for the lower levels of refinement, in order to maintain
+reasonable time steps. Grid refinement was performed whenever necessary to ensure that
+the Jeans length constraint (e.g., Truelove et al. 1997; Boss et al. 2000) was satisfied by a
+factor of 4 for cells with a density at least eight times the initial density. Periodic boundary
+conditions were applied on each face of the grid cubic box, with each side either 60 au or
+120 au in length. A point source of external gravity was used to represent a 1 M⊕ protostar
+at the center of the grid. The maximum number of Green’s functions used to calculate the
+gravitational potential was 10. The time step typically used was 0.15 of the limiting Courant
+time step. The results were analyzed with the yt astrophysical analysis and visualization
+toolkit (Turk et al. 2011).
+Following Boss & Keiser (2014), we used the Enzo 2.2 sink particle coding described by
+Wang et al. (2010). Sink particles are created in grid cells that have already been refined
+to the maximum extent permitted by the specified number of levels of grid refinement,
+but where the gas density still exceeds that consistent with the Jeans length criterion for
+avoiding spurious fragmentation (Truelove et al. 1997; Boss et al. 2000). As described by
+
+– 5 –
+Boss & Keiser (2014), sink particles accrete gas from their host cells at the modified Bondi-
+Hoyle accretion rate proposed by Ruffert (1994). Two parameters control the conditions
+under which sink particles can be merged together: the merging mass (SinkMergeMass) and
+the merging distance (SinkMergeDistance). The former of these two parameters is used to
+divide the sink particles into either large or small particles. Particles with less mass than
+SinkMergeMass are first subjected to being combined with any large particles that are located
+within the SinkMergeDistance. Any surviving small particles after this first step are then
+merged with any other small particles within the SinkMergeDistance. The merging process
+is performed in such a way as to ensure conservation of mass and linear momentum. Boss &
+Keiser (2014) found that their results for collapse and fragmentation of magnetic molecular
+cloud cores were not particularly sensitive to the choice of these two key parameters with
+regard to the tendency of the cores to undergo fragmentation into multiple protostar systems.
+The current paper uses the Wang et al. (2010) sink particle coding with the SinkMergeMass
+set equal to 0.01 MJup and the SinkMergeDistance set equal to 0.1 au, appropriate values
+for studying gas giant protoplanets in a 120 au-size region. Sink creation was only allowed
+for cells with densities exceeding the values listed in Table 1 (DensThresh in code units in
+the sink maker.C subroutine). These densities were chosen to be low enough that sinks do
+form in the models, as the point of the present models was to study the orbital evolution
+of sink particles representing protoplanets in MGU disks rather than to study the precise
+physics of DI-induced fragmentation and clump formation in such disks (e.g., Boss 2021a,b).
+The sink particles used in the Enzo models are similar to the virtual protoplanets (VPs)
+used in the EDTONS models: both are introduced in regions of density maxima and are
+intended to represent gravitationally bound clumps of disk gas that will contract to form
+gaseous protoplanets, as they orbit in the disk around the central protostar, interacting
+gravitationally with each other and the disk gas, even as they accrete more disk gas. There
+are several differences, however. Sink particles are created automatically by Enzo following
+the criteria noted above, sink particles with close encounters can be merged together, and
+sink particles that encounter a grid boundary reappear on the opposite boundary as a result
+of the periodic boundary conditions. VPs, on the other hand, are inserted when a density
+maximum exceeds the Jeans length or Toomre length criteria (Nelson 2006; Boss 2021a,b) for
+the current grid spatial resolution. VPs may undergo close encounters with each other but
+do not suffer mergers. VPs that strike either the inner or outer grid boundary are removed
+from the calculation.
+While it would be desirable to compare flux-limited diffusion (FLD) approximation
+radiative hydrodynamic models from the EDTONS code with FLD radiative hydrodynamic
+models calculated by Enzo, the FLD routines available in Enzo are limited to non-local
+thermodynamic equilibrium (non-LTE), as Enzo was developed primarily for cosmological
+
+– 6 –
+simulations, whereas EDTONS assumes LTE. As a result, we are limited to using a simpler
+approach to handling the disk thermodynamics with the Enzo code. Boss (1998) showed that
+disk fragmentation could occur for strongly gravitationally unstable disks with either locally
+isothermal or locally adiabatic thermodynamics, using disk gas adiabatic exponents ranging
+from γ = 1 (purely isothermal) to γ = 7/5, which is appropriate for molecular hydrogen.
+Given that disks are subject to compressional heating, γ = 1 is not strictly correct, and given
+that disks that are optically thick at their midplanes can cool from their surfaces, γ = 7/5
+is not strictly correct either. The physically correct behavior presumably lies somewhere in
+the middle of these two extremes.
+Radiative cooling in optically thin regions was employed in the Enzo models, with a
+critical density for cooling of 10−13 g cm−3; regions with densities above this critical value
+had the cooling rate decreased proportionally.
+This critical density was chosen because
+that is the disk midplane density where the dust grain opacity produces optical depths of
+order unity (e.g., Boss 1986). The cooling rates were modified from the default values in
+cool rates.in to rates consistent with molecular line cooling in optically thin regions (Boss
+et al.
+2010; Neufeld & Kaufman 1993).
+Because Enzo PPM hydrodynamics involves a
+Riemann solver that cannot be purely isothermal, i.e., γ cannot equal unity, the adiabatic
+index for the disk gas was taken to be γ = 1.001, appropriate for a nearly isothermal, but
+still adiabatic equation of state for an ideal gas. Test runs were computed for 100 yrs of
+evolution with both γ = 7/5 and γ = 5/3, but in both cases Enzo produced midplane
+disk temperatures that were over 104 K, whereas the initial disk had a maximum midplane
+temperature of 1500 K. The test runs with γ = 1.001 produced the expected maximum
+temperatures of ∼ 1500 K, and hence γ = 1.001 was adopted for the models presented here.
+The resulting temperature distributions were also affected by the assumption of radiative
+cooling; spiral features in the midplane temperature distribution accompanied spiral features
+in the midplane density distribution, as is to be expected. Finally, the mean molecular weight
+of the gas was effectively taken to be µ = 2.4, appropriate for a solar composition mixture
+of molecular hydrogen and helium.
+3.
+Initial Conditions
+Table 1 lists the models with variations in the number of levels of grid refinement,
+the outer disk and envelope temperatures, initial minimum value of the Toomre (1964) Q
+parameter, disk radius, calculational grid box size, and critical density for sink particle
+creation. A 60 au box size was used for the 20 au and 30 au radius disks, while a 120 au box
+size was used for 60 au radius disks, in order to give the disks sufficient room to evolve and
+
+– 7 –
+expand by the outward transport of angular momentum through gravitational interactions
+with the spiral arms and clumps. In the number of levels column, 34 means the model was
+initially run with 3 levels and then a fourth level of refinement was added.
+The initial disks are based on the model HR disk from Boss (2001), with an outer disk
+temperature of 40 K and and disk envelope temperature of 50 K, which has been used as a
+standard initial model for many of the author’s disk instability models (e.g., Boss 2021a,b).
+Model HR has an initial minimum Toomre Q ≈ 1.3, implying marginal stability to the
+growth of rings and spiral arms. The model HR initial disk has a mass of 0.091 M⊙ within
+an inner radius of 4 au and an outer radius of 20 au and orbits a 1 M⊙ central protostar.
+The Enzo models have have masses of 0.102 M⊙ for 20 au outer radius disks, slightly higher
+than in model HR because the Enzo models extend inward to 1 au, 0.142 M⊙ for 30 au outer
+radius disks, and 0.210 M⊙ for 60 au outer radius disks. The same disk density power-law-like
+Keplerian structure as in Boss (2001) is used for all of the models, with the structure being
+terminated at 20 au, 30 au, or 60 au. Figures 1 and 2 show cross sections of the initial disk
+density distribution for the 20 au disks, both parallel and perpendicular (i.e., disk midplane)
+to the disk rotation axis.
+4.
+Results
+Figure 3 shows the intermediate results for two of the four models that have the identical
+initial disk configuration (20 au radius) as the Boss (2001) model HR, depicted at the same
+time (190 yrs of evolution) as the same initial disk model (fldA) in Boss (2021b, cf. Figure
+2a). Figure 3 shows that both of these models (3-1K-20 and 6-1K-20) rapidly evolved into
+a configuration of multiple spiral arms interspersed with dense clumps, as expected for a
+marginally gravitationally unstable disk.
+Also as expected, the degree of fragmentation
+and clump formation increases as the numerical grid resolution increases from 3 to 6 levels.
+When sink particles are allowed to form, the number of sink particles similarly increases as
+the resolution is improved. While the background disk looks quite similar for model 3-1K-20
+with or without sink particles (Figure 3a,c), there is a clear difference in the case of model
+6-1K-20 (Figure 3b,d), where the background disk has become perturbed into a prolate
+configuration due to the formation of a massive (∼ 20MJup) secondary companion (at one
+o’clock), with its own circumplanetary disk and tertiary companion, whose combined tidal
+forces have evidently distorted the disk’s overall appearance. Model fldA of Boss (2021b)
+had fragmented into a five clumps and three virtual protoplanets (i.e., sink particles) by
+189 yrs, for a total of eight, considerably more than formed in the present model 3-1K-20,
+but not as many as in model 6-1K-20, suggesting that even with the quadrupled spatial
+
+– 8 –
+resolution of the Boss (2021b) EDTONS models, the adaptive mesh refinement feature of
+Enzo results in significantly improved numerical spatial resolution of the disk instability and
+fragmentation. Confirmation of the formation of long-lived fragments in the model HR disk
+(Boss 2001, 2021b) with the completely different hydrodynamical method used here provides
+strong support for the viability of the disk instability mechanism for the formation of gas
+giant protoplanets and higher mass companions.
+Figure 4 displays the results after 2000 yrs for the Enzo models in Figure 3.
+The
+EDTONS model fldA in Boss (2021b) was stopped after only 189 yrs of evolution, but even
+still required over 4 years of computation on a single core of a node on memex, a Carnegie
+Institution computer cluster. EDTONS is based on code initially written in the late 1970s
+and is not parallelized. Enzo, in contrast, is a modern code designed to run on parallel
+processing systems like memex, and as a result the Enzo models can be computed much
+farther in time. Even still, model 3-1K-20 required one week to run for 2000 yrs of model
+time on a dedicated single memex node with 28 cores, while model 6-1K-20 required one
+year to run 2000 yrs on a dedicated 28-core node. Three dimensional hydrodynamics at high
+spatial resolution is computationally expensive, even when a parallelized code is employed.
+Figure 4 shows that the evolution of these two models diverged considerably following
+the early fragmentation phase depicted in Figure 3. The two sink particles evident in Figure
+4a have masses of ∼ 2MJup and ∼ 0.6MJup, with a total gas disk mass of ∼ 99MJup, while
+the 13-odd sink particles in Figure 4b have masses ranging from ∼ 0.2MJup to ∼ 23MJup,
+for a total sink particle mass of ∼ 96MJup, leaving a disk gas mass of only ∼ 5MJup. Clearly,
+the final disk mass in model 3-1K-20 far outweighs the mass of the sink particles, and as
+a result the particles are unable to open gaps in the disk, though the disk has expanded
+outward to a radius of about 30 au as a result of the transport of disk mass and angular
+momentum outward, caused by the strong spiral arms evident in Figure 3a,c. The fact that
+sink particle formation has been so efficient in model 6-1K-20, with the total particle mass
+some 20 times larger than the disk mass, means that the particles rule the evolution and
+are able to clear out a distinct inner gap, centered on about 5 au (Figure 4b). In model
+6-1K-20, the sink particles gained the bulk of the disk’s mass and angular momentum, so
+that the disk is not able to expand beyond its initial radius of 20 au. Three sink particles
+were accelerated to speeds high enough at their orbital location to be ejected altogether from
+the system, but because of the periodic boundary conditions imposed on the calculations
+by the Enzo self-gravity solver, these ejectable particles were returned to the system and
+underwent further interactions with the sink particles and disk gas.
+Table 2 gives the maximum number of sink particles formed for all the models, as well
+as the number surviving at the end of the run. Table 2 shows that the maximum number of
+
+– 9 –
+sinks formed decreases as the initial disk gas temperature is increased, as this results in an
+increase in the Toomre minimum Q value (Table 1), i.e., in greater stability to the growth of
+rings and spiral arms, and hence to fragmentation and sink particle formation. By the time
+that the disk temperature is increased to 160 K, disk fragmentation is completely stifled in
+the Enzo models, consistent with the flux-limited diffusion approximation models of Boss
+(2021b), where fragmentation ceased for a minimum Toomre Q greater than 2.2.
+Models 6-2K-30 and 7-2K-30 did not form sink particles, unlike the otherwise identical,
+but lower resolutions models 3-2K-30, 4-2K-30, and 5-2K-30, because this sequence used a
+fixed critical density for sink particle formation of 10−9 g cm−3. That choice meant that
+the dense clumps formed in the two higher resolution models could always be resolved with
+more grid levels and finer spatial resolution, thereby preventing the clumps from exceeding
+the critical density required for sink particle formation, at least during the limited amount
+of model time that the 6- and 7-level models were able to be evolved (326 and 340 yrs,
+respectively).
+Small time steps prevented these two models for being evolved farther in
+time. Figure 5 shows these two models at their final times, showing that the spiral arms and
+nascent clumps become more distinct as the number of grid levels is increased, as expected
+when approaching the continuum limit of infinite spatial resolution.
+Table 2 also lists the number of sink particles mergers, where Nmerged−sinks = Nmax−sinks−
+Nfinal−sinks, and the number of times that a sink particle would have been ejected if periodic
+boundary conditions were not required. Table 2 shows that mergers of sink particles are
+quite common in all of the models that formed sink particles, and evidently are responsi-
+ble for much of the gain in mass of the particles, along with the ongoing accretion of disk
+gas, given that the number of mergers is usually comparable to, or far greater than, the final
+number of sink particles. The value Nescaped−sinks can be quite large due to the sink particles’
+inability to escape the system; often the same particle bounces in and out in orbital radius
+and achieves escape velocity multiple times. Achieving the escape velocity usually occurs for
+particle orbital distances of 30 au to 40 au, but can also occur from 10 au to 20 au in the
+more unstable disks (e.g., 5-1K-20, 6-1K-20). The large numbers of escape episodes in the
+latter two models are clearly solely a result of the periodic boundary conditions, but they
+do indicate that ejected protoplanets are to be expected as a natural outcome of a phase of
+gas disk gravitational instability. Table 2 suggests that such a phase of protoplanetary disk
+evolution should result in the ejection of several gas giant protoplanets.
+Figure 6 presents all of the sink particle masses and distances from the central star
+at the final times for the models. These distances correspond to observed separations in
+the absence of any other knowledge of the orbital parameters, i.e., the semimajor axis and
+eccentricity, The final masses range from ∼ 0.1MJup to ∼ 100MJup, i.e., sub-Jupiters to
+
+– 10 –
+brown dwarfs and late M dwarf stars. Separations range from inside 1 au to over 30 au.
+Ejected particles would be at much larger distances, were ejection permitted.
+Figure 6 shows that the black dots, representing the 20 au radius disks, tend to have
+higher masses (> 10MJup) inside 10 au than the blue dots, representing the 60 au radius
+disks, which tend to have lower masses (< 1MJup) inside 10 au. This outcome is the result
+of the 20 au radius disks all starting their evolutions from considerably more gravitationally
+unstable initial states, i.e., Toomre Qminimum = 1.3 than the 60 au radius disks, with initial
+Toomre Qminimum = 1.9 or 2.2. The 20 au radius models thus generally form more massive
+sink particles, as would be expected.
+Figure 7 shows the sink particle masses as a function of the orbital semimajor axis at the
+final times for the models, while Figure 8 depicts these properties for the known exoplanets
+on the same scales. Figure 3b shows that fragmenting dense clumps appear between about
+5 au and 20 au, which is the same distance range as most of the sink particles in Figure 7;
+only a few have migrated inside 1 au, and only a few orbit beyond about 20 au. Clearly
+the present models produce a goodly number of cool gas giants and brown dwarfs, but do
+not lend support for the formation and inward migration of the numerous hot and warm
+exoplanets evident in Figure 8: little evidence for monotonic inward orbital migration is
+seen. This result is consistent with the EDTONS models of Boss (2013).
+Finally, Figure 9 shows the sink particle masses as a function of the orbital eccentricity
+at the final times for the models, while Figure 10 depicts these properties for the known
+exoplanets on the same scales. The present models show that the processes studied here of
+fragmentation, mergers, chaotic orbits, and ejections result in the observed wide range of
+eccentricities, though not the presumably tidally damped, near-zero eccentricities of the hot
+Jupiters.
+5.
+Discussion
+Drass et al. (2016) showed that the initial mass function in the Orion nebula cloud has
+two peaks, one at 0.25 M⊙ and another at 0.025 M⊙, and suggested that the latter peak was
+composed of brown dwarfs and isolated planetary-mass objects that had been ejected from
+circumstellar disks or multiple star systems. The large number of attempted ejections in the
+Enzo models that are listed in Table 2 fully support this hypothesis.
+Feng et al. (2022) combined high-precision Doppler velocity data with Gaia and Hippar-
+cos astrometry to constrain the masses and orbital parameters of 167 sub-stellar companions
+to nearby stars. Their Figure 3 shows that these 167 companions fully populate a parameter
+
+– 11 –
+space ranging from semimajor axes of ∼ 2 au to ∼ 40 au, with masses from ∼ 4MJup to
+∼ 100MJup, much like the upper right quadrant of Figure 7. Their Figure 3 also shows orbital
+eccentricities varying from 0 to 0.75, again in basic agreement with the range evident in the
+present models in Figure 9. These Enzo models suggest a unified formation mechanism of
+the 167 sub-stellar companions studied by Feng et al. (2022): fragmentation of MGU disks.
+Galvagni et al. (2012) used a smoothed particle hydrodynamics (SPH) code to study
+clumps formed at ∼ 100 au in a MGU disk, finding that the clumps could contract and heat
+up enough to begin molecular hydrogen dissociation, resulting in a dynamical collapse phase
+that can ensure their survival to tidal forces. Their results showed that this collapse phase
+could occur within ∼ 103 yrs, shorter than the evolution times of the models considered here
+(Table 2), justifying the replacement of dense clumps with Enzo sink particles or EDTONS
+virtual protoplanets (e.g., Boss 2005, 2013).
+Lichtenberg & Schleicher (2015) used Enzo to study fragments formed by the disk in-
+stability process in isothermal disks, but did not employ sink particles or radiative transfer
+effects, finding that the clumps formed were all lost by inward migration combined with the
+tidal force of the protostar. Stamatellos (2015) used a SPH code to study disks with radii
+of 100 au and high Toomre Q values. Planets inserted at 50 au either migrated inward or
+outward over 2 × 104 yrs, depending on whether they were allowed to gain mass or not,
+respectively.
+Hall et al. (2017) used an SPH code to study the identification and interactions of disk
+fragments composed of clumps of SPH particles that formed from the fragmentation of a
+0.25M⊙ disk of radius 100 au around a 1M⊙ protostar. Their models showed that fragment-
+fragment interactions early in the evolutions led to scattering of fragments to larger semi-
+major axes, as large as 250 au, and to increased eccentricities, as high as 0.7. While the
+periodic boundary conditions used in the present models preclude an assessment of the final
+semi-major axes after close encounters, the fact that the sink particle velocities were often
+sufficiently high to predict ejection from the system is consistent with the Hall et al. (2017)
+results showing efficient scattering outward (cf., Table 2). The eccentricity pumping found
+by Hall et al. (2017) is similarly consistent with that found in the present models (cf. Figure
+9).
+Hall et al. (2017) also studied tidal downsizing and disruption of fragments that ven-
+tured too close to the tidal forces of the central protostar, finding that more clumps were
+destroyed by tidal disruption than by disappearing in a merger event. Tidal downsizing was
+proposed by Nayakshin (2010, 2017) as a means for forming inner rocky worlds from gas
+giants formed in a disk instability, following the formation of rocky inner cores by the sed-
+imentation of dust grains and pebbles to the center of the giant gaseous protoplanet (Boss
+
+– 12 –
+1997). Tidal downsizing remains as a creative means to form inner rocky worlds as a result
+of a gravitationally unstable gas disk. The present sink particle models, as well as the virtual
+protoplanet models of the EDTONS code, do not allow tidal downsizing to occur, though
+implicitly the loss of virtual protoplanets that hit the inner disk boundary in EDTONS code
+calculations could be considered the equivalent of the loss of gas giant protoplanets by tidal
+disruption. Modeling the interior structure and thermal evolution of slowly contracting gas
+giant protoplanets is a future challenge for these types of models, and tidal disruption could
+result in the loss of sink particles that pass close to the central protostar, though it can be
+seen in Figure 6 that few sink particles passed inside 1 au.
+Fletcher et al. (2019) performed a code comparison study of the orbital migration of
+protoplanets inserted at 120 au in disks of 300 au radius, finding that protoplanets of 2
+MJup migrated inward to ∼ 40 au to ∼ 60 au within ∼ 104 yr. These code comparisons
+differ considerably from the present models, as only single protoplanets were injected, the
+disks used a γ = 7/5 adiabatic index, and the disks were gravitationally stable everywhere,
+with Toomre Q ≥ 2. As a result, the evolutions did not undergo the chaotic evolutions of
+the present models, where the MGU disk produces strong spiral arms that interact with the
+numerous protoplanets that formed near the outset.
+Finally, Rowther & Meru (2020) used a SPH code to study planet survival in self-
+gravitating disks. They found that a fixed-mass planet with a range of masses would migrate
+inward in the cool outer regions of their disks, but that this migration was halted once the
+planet reached the warm inner disk. In their models, a single planet at a time is embedded
+in a disk with a mild spiral arm structure. Compared to the multiple clumps, sink particles,
+and strong spiral arms that form and interact in the present models (e.g., Figure 3), it is
+clear that the Rowther & Meru (2020) planets do not undergo the chaotic orbital motions
+experienced by the Enzo models here (or the EDTONS models of Boss 2013), which prevent
+monotonic orbital migration.
+6.
+Conclusions
+The use of a completely different three dimensional hydrodynamical code (Enzo 2.5),
+with a completely different method for handling nascent protoplanets (sink particles), has
+produced results in good agreement with those obtained by the EDTONS code and the
+virtual protoplanet method (Boss 2005). Both codes agree that with high spatial resolution,
+the standard model HR disk (Boss 2001) fragments rapidly into multiple dense clumps and
+strong spiral arms. Both codes agree that when these clumps are replaced with particles that
+can accrete mass from the disk, the particles grow in mass and can orbit chaotically for 1000
+
+– 13 –
+yrs to 2000 yrs without suffering monotonic inward or outward orbital migration. In addition,
+the Enzo models show that the protoplanets have a high probability of close encounters with
+each other, leading either to mergers, or to being ejected from the protoplanetary system.
+Comparisons with the observational data on exoplanet demographics and FFPs suggest that
+gas disk gravitational instabilities have an important role to play in explaining the formation
+of sub-stellar companions with a wide range of masses and orbital distances.
+I thank Sean Raymond for discussions about FFPs and Floyd Fayton for his invaluable
+assistance with the memex cluster. I also thank the reviewer for providing several suggestions
+for improving the manuscript. The computations were performed on the Carnegie Institu-
+tion memex computer cluster (hpc.carnegiescience.edu) with the support of the Carnegie
+Scientific Computing Committee. The computations were performed using the Enzo code
+originally developed by the Laboratory for Computational Astrophysics at the University of
+California San Diego and now available at https://enzo-project.org/.
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+
+– 16 –
+Table 1.
+Initial conditions for the models with varied maximum number of refinement
+levels, initial outer disk and envelope temperatures (K), initial minimum Toomre Q, outer
+disk radii (au), box size (au), and critical density needed for sink particle formation (cgs).
+Model
+Nlevels
+Tdisk
+Tenvelope
+Qminimum
+Rdisk
+Sbox
+ρcrit−sinks
+3-1K-20
+3
+40
+40
+1.3
+20
+60
+10−8
+4-1K-20
+4
+40
+40
+1.3
+20
+60
+10−8
+5-1K-20
+5
+40
+40
+1.3
+20
+60
+10−7
+6-1K-20
+6
+40
+40
+1.3
+20
+60
+10−7
+3-2K-30
+3
+80
+80
+1.9
+30
+60
+10−9
+4-2K-30
+4
+80
+80
+1.9
+30
+60
+10−9
+5-2K-30
+5
+80
+80
+1.9
+30
+60
+10−9
+6-2K-30
+6
+80
+80
+1.9
+30
+60
+10−9
+7-2K-30
+7
+80
+80
+1.9
+30
+60
+10−9
+3-2K-60-11
+3
+80
+120
+1.9
+60
+120
+10−11
+34-2K-60-11
+3-4
+80
+120
+1.9
+60
+120
+10−11
+4-2K-60-10
+4
+80
+120
+1.9
+60
+120
+10−10
+4-2K-60-11
+4
+80
+120
+1.9
+60
+120
+10−11
+3-3K-60-10
+3
+120
+120
+2.2
+60
+120
+10−10
+3-3K-60-11
+3
+120
+120
+2.2
+60
+120
+10−11
+34-3K-60-10
+3-4
+120
+120
+2.2
+60
+120
+10−10
+34-3K-60-11
+3-4
+120
+120
+2.2
+60
+120
+10−11
+4-3K-60-10
+4
+120
+120
+2.2
+60
+120
+10−10
+4-3K-60-11
+4
+120
+120
+2.2
+60
+120
+10−11
+3-4K-60-10
+3
+160
+120
+2.5
+60
+120
+10−10
+3-4K-60-11
+3
+160
+120
+2.5
+60
+120
+10−11
+
+– 17 –
+Table 2.
+Results for the models, showing the maximum number of sinks formed, final
+number of sinks, number of times a sink reached escape velocity, number of sinks lost to
+mergers, and final time (yrs).
+Model
+Nmax−sinks
+Nfinal−sinks
+Nescaped−sinks
+Nmerged−sinks
+tfinal
+3-1K-20
+4
+2
+0
+2
+2000
+4-1K-20
+11
+3
+0
+8
+2000
+5-1K-20
+23
+11
+130
+12
+2000
+6-1K-20
+30
+18
+540
+12
+2000
+3-2K-30
+13
+2
+6
+11
+2000
+4-2K-30
+15
+3
+50
+12
+2000
+5-2K-30
+19
+5
+110
+14
+2000
+6-2K-30
+0
+0
+0
+0
+326
+7-2K-30
+0
+0
+0
+0
+340
+3-2K-60-11
+25
+4
+0
+21
+1000
+34-2K-60-11
+12
+2
+15
+10
+1000
+4-2K-60-10
+0
+0
+0
+0
+130
+4-2K-60-11
+0
+0
+0
+0
+234
+3-3K-60-10
+12
+2
+0
+10
+1000
+3-3K-60-11
+11
+2
+0
+9
+1000
+34-3K-60-10
+10
+3
+0
+7
+890
+34-3K-60-11
+10
+5
+0
+5
+1000
+4-3K-60-10
+0
+0
+0
+0
+250
+4-3K-60-11
+0
+0
+0
+0
+268
+3-4K-60-10
+0
+0
+0
+0
+86
+3-4K-60-11
+0
+0
+0
+0
+142
+
+– 18 –
+Fig. 1.— Initial log density cross-section in a vertical section (x = 0) showing the entire
+computational grid with a maximum of three levels of refinement for the 20 au outer disk
+radius models.
+
+Density
+01-
+10°12
+C1.01
+b1.01
+ST.O1
+LI-
+3
+2
+(nv)
+0
+y
+01-
+-20
+3
+-10
+-20
+-30
+z (AU)– 19 –
+Fig. 2.— Initial log density cross-section in the disk midplane (z = 0) showing the entire
+computational grid with a maximum of three levels of refinement for the 20 au outer disk
+radius models. With six levels of refinement, the inner 1 au is better resolved, but otherwise
+the initial disk is identical.
+
+Density
+10~10
+10~12
+10~14
+1015
+10~16
+1017
+11.0
+1013
+3
+2
+(AU)
+0
+X
+-10
+-20
+0
+-10
+-20
+-30
+y (AU)– 20 –
+!
+"
+#
+$
+Fig. 3.— Log density cross-section in the disk midplane (z = 0) after 190 yr of evolution for
+model 3-1K-20 without (a) and with (c) sink particles, and model 6-1K-20 without (b) and
+with (d) sink particles.
+
+30
+104
+20
+103
+10
+102
+(nv)
+10
+0
+100
+-10
+10-1
+-20
+10-2
+-20
+-10
+0
+10
+20
+30
+X (AU)30
+109
+20
+10-10
+1011
+10
+10-12
+(nv)
+0
+1013
+Density
+10~14
+-10
+1015
+10~16
+-20
+10-17
+-30
+-30
+-10
+20
+30
+10-18
+-20
+0
+10
+X (AU)30
+10-7
+20
+10-9
+10
+10-1L
+(AU)
+0
+Density
+10-13
+-10
+10-15
+-20
+21-01
+3030
+20
+-10
+0
+10
+20
+30
+X (AU)30
+104
+20
+103
+10
+102
+10
+(AU)
+0
+-10
+10-1
+20
+102
+-30
+10-3
+-30
+-20
+-10
+0
+10
+20
+30
+X (AU)– 21 –
+!
+"
+#
+$
+!
+Fig. 4.— Log density cross-section in the disk midplane (z = 0) after 2000 yr of evolution
+for (a) model 3-1K-20 and (b) model 6-1K-20, both with sink particles.
+
+30
+30
+a
+103
+103
+20
+20
+102
+102
+10
+10
+10'
+y (AU)
+y (AU)
+101
+0
+0
+10°
+-10
+-10
+100
+10
+20
+102
+20
+10-1
+-30
+10-3
+3030
+-30
+-20
+-10
+0
+10
+20
+30
+-20
+-10
+0
+10
+20
+30
+x (AU)
+X (AU)– 22 –
+!
+"
+#
+$
+!
+Fig. 5.— Log density cross-section in the disk midplane (z = 0) for (a) model 6-2K-30 and
+(b) model 7-2K-30 after 326 yr and 340 yr of evolution, respectively.
+
+30
+30
+10-10
+20
+20
+10-10
+10
+10
+10-12
+10-12
+(nv)
+(nv)
+0
+-10
+-10
+10-16
+10-16
+20
+20
+-30
+30
+20
+-10
+0
+10
+20
+30
+-20
+-10
+0
+10
+20
+30
+X (AU)
+X (AU)– 23 –
+Fig. 6.— Sink particle masses and distances from central star at the final times for the
+models. These distances correspond to observed separations in the absence of knowledge of
+the orbital parameters, i.e., the semi-major axis and eccentricity. Black dots are for models
+that started with 20 au radius disks, red dots are for 30 au disks, and blue dots are for 60
+au radius disks (see Table 1).
+
+– 24 –
+Fig. 7.— Sink particle masses as a function of the orbital semimajor axis at the final times
+for the models. Black dots are for models that started with 20 au radius disks, red dots are
+for 30 au disks, and blue dots are for 60 au radius disks (see Table 1).
+
+– 25 –
+Fig. 8.— Exoplanet masses as a function of orbital semimajor axis from the Extrasolar
+Planets Encyclopaedia (exoplanet.eu) as of 24 August 2022.
+
+1ie+2
+.
+exoplanet.eu,
+2e+1
+.
+.
+.
+Semi-Major Axis (AU)
+.
+2e+0
+.
+.
+.
+.
+8
+.
+8
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+:
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+.
+！
+.
+.
+.
+1e+2
+1e+1
+Planetary Mass (Mjup)– 26 –
+Fig. 9.— Sink particle masses as a function of the orbital eccentricity at the final times for
+the models. Black dots are for models that started with 20 au radius disks, red dots are for
+30 au disks, and blue dots are for 60 au radius disks (see Table 1).
+
+– 27 –
+Fig. 10.— Exoplanet masses as a function of orbital eccentricity from the Extrasolar Planets
+Encyclopaedia (exoplanet.eu) as of 24 August 2022.
+
+Orbital Eccentricity
+0.5
+！
+1e+2
+1e+1
++1
+3
+Planetary Mass (Mjup)

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+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+1
+Nearest Neighbor-Based Contrastive Learning for
+Hyperspectral and LiDAR Data Classification
+Meng Wang, Feng Gao, Junyu Dong, Heng-Chao Li, Qian Du
+Abstract—The joint hyperspectral image (HSI) and LiDAR
+data classification aims to interpret ground objects at more
+detailed and precise level. Although deep learning methods have
+shown remarkable success in the multisource data classification
+task, self-supervised learning has rarely been explored. It is
+commonly nontrivial to build a robust self-supervised learning
+model for multisource data classification, due to the fact that the
+semantic similarities of neighborhood regions are not exploited
+in existing contrastive learning framework. Furthermore, the
+heterogeneous gap induced by the inconsistent distribution of
+multisource data impedes the classification performance. To
+overcome these disadvantages, we propose a Nearest Neighbor-
+based Contrastive Learning Network (NNCNet), which takes
+full advantage of large amounts of unlabeled data to learn
+discriminative feature representations. Specifically, we propose
+a nearest neighbor-based data augmentation scheme to use
+enhanced semantic relationships among nearby regions. The
+intermodal semantic alignments can be captured more accu-
+rately. In addition, we design a bilinear attention module to
+exploit the second-order and even high-order feature interactions
+between the HSI and LiDAR data. Extensive experiments on
+four public datasets demonstrate the superiority of our NNCNet
+over state-of-the-art methods. The source codes are available at
+https://github.com/summitgao/NNCNet.
+Index Terms—hyperspectral image, self-supervised learning,
+light detection and ranging, contrastive learning, image classifi-
+cation.
+I. INTRODUCTION
+R
+ECENTLY, with the rapid development of satellite sen-
+sors, an ever increasing number of multimodal im-
+ages (optical, SAR, hyperspectral and LiDAR) are obtained
+everyday [1]. Among these multimodal data, hyperspectral
+images (HSIs) provide detailed spectral information for the
+identification of specified objects on the ground, while LiDAR
+data provide elevation information of the area [2] [3] [4]. These
+HSI and LiDAR sensors are different in imaging mechanism,
+spatial resolution, and even coverage. Therefore, both sensors
+capture different properties of the earth, such as spectral
+radiance and height information. For example, there are no
+significant differences in the spectral domain between the
+“trees” on the ground and the “trees” on the hill, but they can
+This work was supported in part by the National Key Research and
+Development Program of China under Grant 2018AAA0100602, and in part
+by the National Natural Science Foundation of China under Grant 42106191.
+Meng Wang, Feng Gao, and Junyu Dong are with the School of Information
+Science and Engineering, Ocean University of China, Qingdao 266100, China.
+(Corresponding author: Feng Gao.)
+H. -C. Li is with the Sichuan Provincial Key Laboratory of Information
+Coding and Transmission, Southwest Jiaotong University, Chengdu 610031,
+China.
+Qian Du is with the Department of Electrical and Computer Engineering,
+Mississippi State University, Starkville, MS 39762 USA.
+Encoder
+Momentum
+encoder
+Similarity
+Contrastive loss
+Nearest 
+neighbor
+Encoder
+Momentum
+encoder
+Similarity
+Contrastive loss
+(a)
+(b)
+Fig. 1. Conceptual comparison of MoCo and the proposed nearest neighbor-
+based contrastive learning framework. In the proposed framework, the nearest
+neighbors are considered as positive samples. The semantic similarities among
+neighborhood regions are exploited.
+be distinguished from the LiDAR data [5]. Therefore, the joint
+exploitation of HSI and LiDAR data enables us to interpret
+ground objects at a more detailed and precise level, which can
+hardly be achieved by using single-mode data [6]. Thus, the
+classification of cross-modal data has attracted considerable
+attention and has been widely applied in multisource image
+interpretations [7] [8].
+A great deal of effort has been put into solving the problem
+of HSI and LiDAR joint classification. Traditionally, feature-
+level fusion models have been proposed, and these models
+commonly concatenate the HSI and LiDAR features for clas-
+sification [9] [10] [11]. Besides feature-level fusion, decision-
+level fusion is another popular solution for HSI and LiDAR
+classification. Several classifiers are designed for HSI and
+LiDAR data, respectively. The voting strategy is commonly
+used to obtain the final classification map [12]. Subsequently,
+to further exploit high-level semantic features, convolutional
+neural networks (CNNs) are employed for multisource data
+classification [13]. Encoder-decoder network [14], coupled
+CNNs [15], Gabor CNN [16], cross attention [17], and Trans-
+former [18] are used to extract representative multisource
+features, and these methods have achieved promising perfor-
+mance.
+In practice, deep learning models have demonstrated re-
+markable success in various multisource data joint classifi-
+cation. However, it is non-trivial to build an effective HSI
+and LiDAR classification model. One of the critical reasons is
+that the deep learning-based model commonly requires a great
+number of labeled samples to achieve satisfactory accuracy,
+which is expensive and limited in ground object modeling.
+Recent research in self-supervised learning encourages the
+deep network to learn more representative and interpretable
+arXiv:2301.03335v1  [eess.IV]  9 Jan 2023
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+2
+features in natural language processing [19] [20] and computer
+vision tasks [21] [22]. Self-supervised learning mines the
+inherent attributes and semantics of large-scale unlabeled data
+to obtain beneficial semantic representations, and it does not
+require manually annotated data [23]. After the self-supervised
+training finished, the learned features can be transferred to
+classification tasks (especially when only small training data
+is available) as pretrained models to boost the classification
+performance and alleviate overfitting [24] [25] [26] [27]. In
+HSI and LiDAR joint classification, self-supervised learning
+has rarely been explored, and in this paper, we aim to build
+an effective self-supervised model to solve the problem.
+It is commonly non-trivial to build a robust self-supervised
+learning model for the HSI and LiDAR joint classification task,
+due to the following reasons: 1) Data augmentation scheme.
+In Momentum Contrast (MoCo) for self-supervised learning
+[22], the random color jittering, random horizontal flip, and
+random grayscale conversion are used for data augmentation.
+However, such data augmentation scheme does not take the
+spatial distances between the positive and negative samples
+into account, and the semantic similarities of neighborhood
+regions are not exploited. Consequently, how to properly
+utilize the semantic similarities among nearby regions is a
+major challenge. 2) The heterogeneous gap. HSI and LiDAR
+joint classification requires a comprehensive understanding
+of complex heterogeneous data simultaneously. However, the
+heterogeneous gap induced by the inconsistent distributions of
+multisource data would greatly impedes its implementation.
+Therefore, it is vital to bridge this gap for more robust
+multisource data classification.
+To address the aforementioned challenges, we propose a
+Nearest Neighbor-based Contrast learning Network, NNCNet
+for short, which aims to learn an encoder that encodes similar
+data of the same kind and makes the encoding results of differ-
+ent classes of data as different as possible. To be more specific,
+we propose a nearest neighbor-based framework to use the
+enhanced semantic relationships among nearby regions. As
+illustrated in Fig. 1, nearest neighbors of positive samples
+are fed into the encoder for contrastive learning. The feature
+representations are learned by encouraging the proximity of
+between different views of the same sample and its nearest
+neighbors in the spatial domain. Therefore, the contrastive
+learning framework is encouraged to generalize to new feature
+embeddings that may not be covered by the data augmentation.
+In addition, we design a bilinear attention fusion module to
+exploit second-order and even higher-order feature interactions
+between the HSI and LiDAR data, and the information flow
+can be controlled more flexibly.
+The contributions of this work are as follows:
+• We propose a self-supervision contrastive learning ap-
+proach NNCNet, which integrates a nearest neighbor-
+based data augmentation scheme. The scheme can exploit
+the semantic similarities among neighborhood regions,
+and hence capture inter-modal semantic alignments more
+accurately. To our best knowledge, we are the first to
+apply self-supervised contrastive learning to HSI and Li-
+DAR joint classification, which has both great theoretical
+and practical significance.
+• We propose a bilinear attention fusion module that aims
+to enhance the contextual representation of HSI and
+LiDAR data. The module captures second-order feature
+interactions between multisource data.
+• We have conducted extensive experiments on four bench-
+mark datasets to validate the effectiveness of our NNC-
+Net. Additionally, we have released our codes and pa-
+rameters to benefit other researchers.
+II. RELATED WORK
+A. Morphological Filter-Based Methods for HSI and LiDAR
+Classification
+The joint use of HSI and LiDAR has already been in-
+vestigated for a variety of applications, such as illumination
+calibration [28], forest area analysis [29], bushfire monitoring
+[30], and urban sprawl modeling [31]. Great efforts have been
+devoted to exploiting the complementary information between
+multisource data, especially for morphological filter-based
+methods. Morphological filters are intensively used to atten-
+uate the redundant spatial details and preserve the geometric
+structures. Pedergnana et al. [9] used morphological extended
+attribute profiles to HSI and LiDAR data for classification.
+Features extracted from HSI and LiDAR data are stacked
+for classification. Liao et al. [32] computed morphological
+attribute profiles from HSI and LiDAR data, and these attribute
+profiles are fused using a generalized graph-based method.
+Khodadadzadeh et al. [33] pointed out that simple stacking
+of morphological attribute profiles from multisource data may
+contain redundant features. To solve this issue, they proposed
+a multiple feature learning approach based on the multinomial
+logistic regression classifier, which can adaptively exploit
+the spatially and spectrally derived features. Later, attribute
+profiles are considered to be complex and time-consuming
+in threshold initialization, and extinction profiles [34] are
+proposed to solve the problem. Ghamisi et al. [35] presented a
+classification framework based on extinction profiles and deep
+learning.
+B. CNN-Based Methods for HSI and LiDAR Classification
+Recently, deep CNNs have attracted extensive research
+attention in the remote sensing data fusion community, and
+many CNN-based models have been proposed for multisource
+data classification. Xu et al. [36] proposed a two-branch CNN
+model, which consists of a 2-D convolutional network and
+a 1-D convolutional network. Zhang et al. [37] presented a
+patch-to-patch CNN for the joint feature extraction of HSI
+and LiDAR data. Chen et al. [38] proposed a CNN and DNN
+hybrid model for multisource feature extraction. CNNs are
+used to extract informative features from multisource data,
+and a DNN is utilized to fuse these heterogeneous features
+for robust classification. Li et al. [39] proposed a dual-channel
+spatial, spectral and multiscale attention CNN for multisource
+data classification. Hang et al. [15] used coupled CNNs for
+multisource data classification. The coupled layers reduce the
+number of parameters and guide both networks learning from
+each other. Zhao et al. [16] proposed a fractional Gabor CNN,
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+3
+and focused on efficient feature fusion. Fractional Gabor con-
+volutional kernels are used for multiscale and multidirectional
+feature extraction and yield robust feature representations
+against semantic changes. In [40], a multisource graph fusion
+network is presented to integrate feature extraction and fusion
+into a single network. A multimodal graph is constructed to
+guide the multimodal image feature extraction. Gao et al.
+[17] proposed a deep-wise feature interaction network for
+multisource remote sensing image classification. Consistency
+loss, discrimination loss, and classification loss are designed
+for parameter optimization.
+Although CNNs have been successfully applied to HSI
+and LiDAR joint classification, its performance remains un-
+satisfactory for practical applications. An important factor
+may be the lack of sufficient annotated data. In practical
+applications, remote sensing data annotation is costly, making
+it difficult to obtain robust deep learning models. To solve this
+problem, we aim to build a simple yet effective self-supervised
+method for multisource data joint classification. It extracts the
+inherent attributes and semantics from unlabeled large-scale
+data to capture beneficial feature representations. In addition,
+a nearest-neighbor-based data augmentation scheme is used to
+exploit the semantic relationships among nearby regions.
+III. METHODOLOGY
+As shown in Fig. 2, the proposed NNCNet consists of
+three parts: nearest neighbor-based data augmentation, bilinear
+attention-based encoder, and contrastive loss computation.
+Considering that the proposed NNCNet is based on a self-
+supervised contrastive learning framework, we first introduce
+the nearest neighbor-based contrastive learning framework
+and then successively elaborate the bilinear attention-based
+encoder.
+A. Nearest Neighbor-based Momentum Contrast Learning
+Framework
+Considering that unlabeled data have no supervised infor-
+mation, we aim to extract the supervised information from
+large-scale unsupervised HSI and LiDAR data. Our goal is to
+train an encoder that keeps the different transformations from
+the same sample as close as possible and the different samples
+as far away as possible in the feature space. To solve the
+problem, He et al. [22] proposed Momentum Contrast (MoCo)
+for self-supervised learning. To be specific, a minibatch of
+samples is selected from the data. Each sample is handled
+by random data augmentation (Gaussian blur, flip, or spectral
+distortions) to generate a query sample and a key sample. The
+query and key samples are encoded separately to embedding q
+and k. The cosine similarity between q and k is computed for
+representation learning. The embedding from the same image
+is defined as the positive key, and embedding from different
+image is defined as the negative key. In MoCo, a dynamic
+dictionary is built with a queue and a dynamic encoder.
+For remote sensing data classification, we argue that random
+augmentations can hardly provide positive pairs for the same
+object representation. For the sake of covering more variance
+in a given class, we propose nearest neighbor-based contrastive
+Algorithm 1 Pseudocode of the Nearest Neighobr-Based
+Contrastive Learning in PyTorch Style.
+# f_q: encoder network for query
+# f_k: encoder network for key
+# queue: key dictionary
+# r: momentum coefficient
+f_k.param = f_q.param # initialize parameters
+# load a mini-batch x with N samples
+for x in loader:
+nn = neighbor(x) # generate neighbors of x
+x_q = augment(x) # query randomly augmentation
+x_k = augment(x) # key random augmentation
+x_n = augment(nn) # neighbors random augmentation
+# randomly substitute half samples in x_k by x_n
+x_k = substitute(x_k, x_n)
+q = f_q.forward(x_q) # queries: NxC
+k = f_k.forward(x_k) # keys: NxC
+k = k.detach() # no gradient to keys
+# positive logits: Nx1
+# bmm: batch matrix multiplication
+l_pos = bmm(q.view(N,1,C), k.view(N,C,1))
+# negative logits: NxK
+# mm: matrix multiplication
+l_neg = mm(q.view(N,C), queue.view(C,K))
+# logits: Nx(1+K)
+logits = cat([l_pos, l_neg], dim=1)
+# contrastive loss computation
+labels = zeros(N)
+loss = CrossEntropyLoss(logits/t, labels)
+# back propagation, only update the query network
+loss.backward()
+update(f_q.param)
+# dictionary update
+f_k.param = r*f_k.param+(1-r)*f_q.param
+enqueue(queue, k) # push the current key
+dequeue(queue) # pop the earliest key
+learning framework. In remote sensing images, the neighbor
+labels of one specified position tend to be the same. As
+illustrated in Fig. 3, the region within the red box is rooftop,
+and the green boxes are its nearest neighbors. Blue boxes
+denote regions far from the red box. From the visualized
+feature space, it can be observed that the features of the nearest
+neighbors are close. In this paper, we use a nearest neighbor-
+based contrastive learning framework in which the semantic
+similarities among neighborhood regions are exploited. There-
+fore, the inter-modal semantic alignments are reinforced.
+Nearest Neighbor-Based Contrastive Learning. Algo-
+rithm 1 provides the pseudo code of the proposed nearest
+neighbor-based contrastive learning. In the proposed frame-
+work, a set of sample pairs are selected from HSI and
+LiDAR data centered at the same position. During training,
+each sample pair is handled by random data augmentation
+to generate a query sample xq and a key sample xk. They
+are encoded to embeddings q and k, respectively. The em-
+beddings from the same image are defined as positive key,
+and embeddings from different images are defined as negative
+key. A large number of negative key embeddings are stored
+in a dictionary {k1, k2, k3, . . .}, while one positive key k+
+is stored separately. Furthermore, we randomly select some
+nearest neighbors of q to generate embeddings, which are
+denoted as kn+. Next, in a minibatch, half positive keys k+
+are substituted by kn+ to form new positive keys. Hence,
+nearest neighbors act small semantic perturbations. In our
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+4
+Hyperspectral image
+LiDAR
+Data 
+augmentation
+Nearest neighbor
+substitution
+Encoder
+Momentum 
+encoder
+Push
+Pop
+Positive key
+Dictionary of negative keys
+Contrastive loss
+Contrastive loss
+D
+D
+D
+D
+Similarity of positive pairs
+Similarity of negative pairs
+Slowly update
+Fig. 2. Schematic illustration of the nearest-neighbor based contrastive learning. It consists of three components: 1) Nearest neighbor-based data augmentation.
+The input samples are handled by random data augmentation to generate query and key samples. In a mini-batch, half positive key samples are substituted by
+its nearest neighbors to form new positive key samples. These nearest neighbors act small semantic perturbations. 2) Bilinear attention-based feature encoder.
+The query and key samples are fed into the encoder for feature extraction. A bilinear attention fusion module is employed to capture the second-order feature
+interactions between multisource data. 3) Contrastive loss computation. Positive and negative keys are stored in a dynamic dictionary, and contrastive loss is
+computed to assign high scores for positive keys and low scores for negative keys.
+Remote sensing images
+Visualized feature space
+Fig. 3.
+Typical regions in remote sensing images and the corresponding
+visualized features. The region within the red box is rooftop, and the green
+boxes are its nearest neighbors. Blue boxes denote regions far from the the
+red box. In the visualized feature space, it can be observed that features of the
+nearest neighbors are close. Therefore, the contextual information is critical
+in contrastive learning for remote sensing image classification.
+implementations, nearest neighbors denotes a region whose
+overlap area with xq is greater than 80%.
+We calculate the cosine similarities between q and keys
+(both the positive key and negative keys). Then, the results
+are stored as {D+, D1, D2, D3, . . . , DK}. Here D+ is the
+similarity between q and positive key k+. The rest are the
+similarities between q and negative keys. K is the number of
+negative keys.
+The objective of contrastive learning is to force the query to
+match the positive key and far apart from the negative keys. To
+be specific, the contrastive loss whose value is low when q is
+similar to the positive key k+ and dissimilar to all the negative
+keys. Therefore, the contrastive loss function is designed as
+follows:
+L = − log
+exp(D+/τ)
+�K
+i=1 exp(Di/τ)
+(1)
+where τ is a temperature hyperparameter. Intuitively, softmax
+classifier and cross-entropy loss can be combined into the
+above equation.
+Dictionary Update and Moving Average Encoder. Similar
+to MoCo [22], we maintain the dictionary as a queue which
+stores many minibatch of negative samples. The negative sam-
+ples in the dictionary are updated progressively. Specifically,
+during training, when a new minibatch is pushed into the
+dictionary, the oldest minibatch is removed. The length of the
+dictionary is flexibly set as a hyperparameter.
+Furthermore, the parameters of the encoder for the dic-
+tionary are updated slowly. Similar to MoCo, we use a
+separate moving average encoder for the key samples. During
+training, no backpropagation is done for the key encoder. The
+parameters of key encoder are updated as follows:
+θk = rθk + (1 − r)θq,
+(2)
+where θk denotes the parameters of the key encoder, and θq
+denotes the parameters of the query encoder. r is a momentum
+coefficient that controls the speed of key encoder update.
+Only θq is updated by backpropagation during training. In our
+implementations, r is set to 0.9, since a slowly evolving key
+encoder is critical for robust feature learning.
+Shuffling BN. Batch Normalization (BN) is employed in
+the encoder to speed up convergence and improve the gener-
+alization of the network. Similar to MoCo, we use the shuffling
+BN for better feature representation. In particular, we shuffle
+the sample order in the current minibatch for the key encoder.
+The sample order of the mini-batch for the query encoder is
+not changed.
+B. Bilinear Attention-Based Multisource Encoder
+In this work, the purpose of contrastive learning is to
+generate a pretrained model, and the model can be used for the
+classification task. To achieve high classification accuracy, the
+encoder is an essential part of the contrastive framework. We
+design a multisource encoder for hyperspectral and LiDAR
+feature modeling, as illustrated in Fig. 4. It contains three
+parts: HSI feature extraction, LiDAR feature extraction, and
+bilinear attention fusion.
+The detailed summary of the encoder in terms of layer
+type, kernel size, and output size is illustrated in Table I.
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+5
+LiDAR
+3DConv
+3DConv
+3DConv
+2DConv
+2DConv
+2DConv
+2DConv
+HSI
+Bilinear 
+Attention
+Output
+FC
+3DConv
+2DConv
+3D convolution
+2D convolution
+Element-wise summation
+FC
+Fully connected layer
+Fig. 4. Bilinear attention-based multisource encoder.
+TABLE I
+SUMMARY OF THE PROPOSED MULTI-SOURCE ENCODER
+HSI feature extraction subnetwork
+#
+Layer type
+Kernel number@size
+Output size
+Input
+—
+(11, 11, 30, 1)
+1
+3D Conv
+8@3×3×9
+(9, 9, 22, 8)
+2
+3D Conv
+16@3×3×7
+(7, 7, 16, 16)
+3
+3D Conv
+32@3×3×5
+(5, 5, 12, 32)
+4
+Reshape
+—
+(5, 5, 384)
+5
+2D Conv
+256@3×3
+(5, 5, 256)
+6
+Reshape
+—
+(25, 256)
+LiDAR feature extraction subnetwork
+#
+Layer type
+Kernel numbre@size
+Output size
+Input
+—
+(11, 11, 1)
+1
+2D Conv
+64@3×3
+(9, 9, 64)
+2
+2D Conv
+128@3×3
+(7, 7, 128)
+3
+2D Conv
+256@3×3
+(5, 5, 256)
+4
+Reshape
+—
+(25, 256)
+Hyperspectral data adopt a network similar to HybridSN [41],
+which uses both 3D and 2D convolutions for feature extraction.
+Three 3D convolution layers and one 2D convolution layer are
+used to derive the HSI feature FH. At the same time, three 2D
+convolution layers are used to generate the LiDAR feature
+FL. Next, FH and FL are combined to form the fused feature.
+A 2D convolution is used for feature embedding. Then, the
+fused feature Ffus has the same dimension as FH and FL.
+To effectively reduce the inherent redundancy in HSI, and
+thereby reduce the amount of data that needs to be processed
+in classification, Principal Component Analysis (PCA) is used
+to select the best 30 spectral bands for HSI feature extraction.
+Finally, FH, FL and Ffus are fed into the bilinear attention
+fusion module as Q, K, and V, respectively. The output of the
+bilinear attention fusion module is fed into a fully connected
+layer to generate the final feature for classification.
+C. Bilinear Attention Fusion Module
+The attention mechanism has made valuable breakthroughs
+in deep neural networks and has been successfully applied to
+FC
+FC
+FC
+FC
+Bilinear pooling
+FC
+softmax
+C
+FC
+S
+Gate mechanmism
+Bilinear pooling
+FC
+Fully connected layer
+Element-wise multiplication
+C
+Feature concatenation
+S
+Sigmoid activation
+Fig. 5. Bilinear attention fusion module. It can capture second-order interac-
+tions between multisource data.
+cross-modal tasks (e.g., visual question answering [42], image
+captioning [43], and image-text matching [44]). This prompts
+recent methods to adopt the attention to trigger the interaction
+between multi-modal remote sensing data [45] [46] [47] [48].
+In the conventional attention mechanism, the attention weights
+are estimated via linearly fusing the inputs. However, we
+argue that conventional attention exploits the first-order feature
+interaction and is limited in complex multisource feature
+reasoning.
+Toward this end, we propose a bilinear attention fusion mod-
+ule to exploit the second-order feature interactions between
+the hyperspectral and LiDAR data. As illustrated in Fig. 5,
+it mainly contains two parts: the multi-head bilinear attention
+and the gate mechanism.
+Multi-Head Bilinear Attention. Suppose we have query
+Q ∈ Rc×d, key K ∈ Rc×d, and value V ∈ Rc×d, where
+d denotes the feature dimension, and c is the number of
+channels. To enhance the capability of feature representation,
+the multi-head scheme is used to model feature interactions
+from different subspaces as:
+hi = BiAttention(Qi, Ki, Vi),
+(3)
+where hi is the output of the i-th head, and BiAttention
+denotes the bilinear attention. The number of heads is denoted
+by H.
+The bilinear attention first maps Qi ∈ R
+c
+H ×d and Ki ∈
+R
+c
+H ×d into a joint space as:
+B1
+i = σ(QiW1
+q) ⊙ σ(KiWk),
+(4)
+where W1
+q ∈ Rd×d and Wk ∈ Rd×d are weighting matrices,
+σ is the ReLU activation and ⊙ denotes the element-wise
+multiplication. As such, B1
+i ∈ R
+c
+H ×d denotes the second-order
+representation between query Qi and key Ki.
+Similarly, we compute the bilinear representation between
+Qi and Vi as:
+B2
+i = σ(QiW2
+q) ⊙ σ(ViWv),
+(5)
+where W2
+q ∈ Rd×d and Wv ∈ Rd×d are weighting matrices.
+B2
+i ∈ R
+c
+H ×d denotes the second-order representation between
+query Qi and value Vi.
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+6
+Next, the bilinear representation B1
+i is projected into atten-
+tion weights Watt
+i
+∈ R
+c
+H ×d via a linear layer and a softmax
+layer as follows:
+ˆB1
+i = σ(WBB1
+i ),
+(6)
+Watt
+i = softmax( ˆB1
+i ),
+(7)
+where WB ∈ R
+c
+H × c
+H is the weight matrix. Next, the attended
+feature hi ∈ R
+c
+H ×d is derived by enhancing the attention
+weights as:
+hi = Watt
+i ⊙ B2
+i
+(8)
+Gate Mechanism. The aforementioned bilinear attention
+exploits the feature interactions among Qi, Ki, and Vi.
+However, there may contain noisy information in the query
+and key. To adaptively enhance the informative parts and
+suppress the useless parts, we design a gate mechanism. To
+be specific, for the i-th head, ˆB1
+i is fed into a linear layer and
+then handled with a sigmoid function to compute a weight
+mask Gi ∈ R
+c
+H ×1 as:
+Gi = sigmoid( ˆB1
+i WB′),
+(9)
+where WB′
+∈ Rd×1 is the weight matrix. Next, Gi is
+expanded to form G′
+i ∈ R
+c
+H ×d. Then the obtained gating mask
+is applied to control the information flow of hi ∈ R
+c
+H ×d as:
+ˆhi = G′
+i ⊙ hi.
+(10)
+Finally, by concatenating the results of multiple heads, we
+obtain the fused representation of multi-source data. In this
+work, the size of Q, K and V is 25×256. The number of
+heads H is set to 5.
+IV. EXPERIMENTAL RESULTS AND ANALYSIS
+To validate the effectiveness of the proposed NNCNet, we
+conduct extensive experiments on four widely used bench-
+mark datasets: Houston 2013 dataset, Trento dataset, MUUFL
+dataset and Houston 2018 dataset. We first compare the
+proposed NNCNet with state-of-the-art methods. Then we
+implemented additional evaluations to investigate the effec-
+tiveness of each component of our method.
+A. Datasets and Evaluation Metric
+Houston 2013 dataset: The dataset was captured by the
+National Airborne Center for Laser Mapping, and it was used
+as a challenge in the 2013 GRSS Data Fusion Contest. The
+HSI was captured by the CASI sensor (144 spectral bands at a
+resolution of 2.5 m). Coregistered LiDAR data with the same
+resolution are available. A total of 15029 ground truth samples
+are distributed in 15 classes. They are divided into train and
+test sets containing 2832 and 12197 pixels, respectively. We
+used standard training and test sets, and Table II lists the
+number of training and test samples.
+Trento dataset: The dataset was collected in a rural region
+south of Trento, Italy. The HSI image consists of 63 bands with
+a wavelength range of 0.42-0.99 µm. The size of the datset
+is 166×660 pixels, and the spatial resolution of the datset is
+1.0 m. A total of 30214 ground truth samples are distributed
+TABLE II
+TRAIN-TEST DISTRIBUTION OF SAMPLES FOR THE HOUSTON 2013
+DATASET.
+No.
+Class Name
+Training
+Test
+1
+Healthy grass
+198
+1053
+2
+Stressed grass
+190
+1064
+3
+Synthetic grass
+192
+505
+4
+Tree
+188
+1056
+5
+Soil
+186
+1056
+6
+Water
+182
+143
+7
+Residential
+196
+1072
+8
+Commercial
+191
+1053
+9
+Road
+193
+1059
+10
+Highway
+191
+1036
+11
+Railway
+181
+1054
+12
+Parking lot 1
+192
+1041
+13
+Parking lot 2
+184
+285
+14
+Tennis court
+181
+247
+15
+Running track
+187
+473
+Total
+2832
+12197
+TABLE III
+TRAIN-TEST DISTRIBUTION OF SAMPLES FOR THE TRENTO DATASET.
+No.
+Class Name
+Training
+Test
+1
+Apple trees
+129
+3905
+2
+Buildings
+125
+2778
+3
+Ground
+105
+374
+4
+Wood
+154
+8969
+5
+Vineyard
+184
+10317
+6
+Roads
+122
+3052
+Total
+819
+29595
+TABLE IV
+TRAIN-TEST DISTRIBUTION OF SAMPLES FOR THE MUUFL DATASET.
+No.
+Class Name
+Training
+Test
+1
+Trees
+150
+23096
+2
+Mostly grass
+150
+4120
+3
+Mixed ground surface
+150
+6732
+4
+Dirt and sand
+150
+1676
+5
+Road
+150
+6537
+6
+Water
+150
+316
+7
+Building shadow
+150
+2083
+8
+Building
+150
+6090
+9
+Sidewalk
+150
+1235
+10
+Yellow curb
+150
+33
+11
+Cloth panels
+150
+119
+Total
+1650
+52037
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+7
+ (a) Ground truth
+ (b) FusAtNet
+ (c) TBCNN
+ (d) EndNet
+ (e) MDL
+ (f) CCNN
+ (g) S2ENet
+ (h) w/o Pretraining
+ (i) Proposed NNCNet
+Healthy grass
+Stressed grass
+Synthetic grass
+Tree
+Road
+Railway
+Soil
+Water
+Residential
+Commercial
+Highway
+Parking lot 1
+Parking lot 2
+Tennis court
+Running track
+Fig. 6.
+Classification maps for the Houston 2013 dataset. (a) Groundtruth. (b) FusAtNet. (c) TBCNN. (d) EndNet. (e) MDL. (f) CCNN. (g) S2ENet. (h)
+Proposed NNCNet without pretraining. (i) Proposed NNCNet.
+TABLE V
+TRAIN-TEST DISTRIBUTION OF SAMPLES FOR THE HOUSTON 2018
+DATASET.
+No.
+Class Name
+Training
+Test
+1
+Healthy grass
+500
+9299
+2
+Stressed grass
+500
+32002
+3
+Artificial turf
+68
+616
+4
+Evergreen trees
+500
+13095
+5
+Deciduous trees
+500
+4521
+6
+Bare earth
+451
+4065
+7
+Water
+26
+240
+8
+Residential buildings
+500
+39272
+9
+Non-residential buildings
+500
+223252
+10
+Roads
+500
+45366
+11
+Sidewalks
+500
+33529
+12
+Crosswalks
+151
+1367
+13
+Major thoroughfares
+500
+45848
+14
+Highways
+500
+9365
+15
+Railways
+500
+6437
+16
+Paved parking lots
+500
+11000
+17
+Unpaved parking lots
+14
+132
+18
+Cars
+500
+6047
+19
+Trains
+500
+4869
+20
+Stadium seats
+500
+6324
+Total
+8210
+496646
+in 6 classes. Table III lists the distribution of training and test
+samples for the Trento dataset.
+MUUFL dataset: The MUUFL dataset is captured over
+the University of Southern Mississippi Gulf Coast campus
+in November 2010. The HSI contains 72 spectral bands, but
+the first and last four bands are removed for noise reduction,
+leaving 64 bands for classification. The total size of the dataset
+is 325×220 pixels. Table IV lists the training and test samples
+available for the dataset. In our experiments, we use the entire
+data in the pretraining phase, while in the training validation
+phase, we use only the portion of the training set for which
+labels are given.
+Houston 2018 dataset: The dataset was captured by the
+Hyperspectral Image Analysis Laboratory and the National
+Center for Airborne Laser Mapping (NCALM) at the Uni-
+versity of Houston. It was originally released for the 2018
+IEEE GRSS Data Fusion Contest. Hyperspectral data covers
+380-1050 nm spectral range with 48 bands at 1.0 m ground
+sample distance. The dataset contains a total of 4768×1202
+pixels in which a piece is delineated as the training set with
+the size of 2384×601 pixels. Table V lists the distribution of
+training and test samples for the Houston 2018 dataset.
+The performance of the model is evaluated by Overall Ac-
+curacy (OA), Average Accuracy (AA), and Kappa coefficient.
+OA denotes the ratio of the model’s correct predictions to the
+overall number on all test samples. AA is the ratio between
+the number of correct predictions in each category and the
+overall number in each category, and finally the average of
+the accuracy in each category. Kappa is the percentage of
+agreement corrected by the number of agreements that would
+be expected purely by chance.
+B. Implementation Details
+The proposed contrastive learning architecture is used to
+generate a pretrained model. In the contrastive learning phase,
+we use the Adam optimizer. The mini-batch size is set to 64
+and the learning rate is set to 0.0005. The image patch of
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+8
+TABLE VI
+CLASSIFICATION ACCURACY (%) ON THE HOUSTON 2013 DATASET
+Class
+FusAtNet [49]
+TBCNN [36]
+EndNet [14]
+MDL [5]
+CCNN [15]
+S2ENet [50]
+NNCNet (ours)
+Healthy grass
+79.20
+81.01
+78.54
+83.00
+91.55
+82.72
+81.84
+Stressed grass
+96.71
+97.93
+96.33
+98.68
+99.72
+100.0
+99.72
+Synthetic grass
+97.82
+99.60
+100.0
+99.80
+99.60
+99.60
+99.80
+Tree
+97.63
+94.13
+88.26
+93.94
+97.63
+95.74
+99.43
+Soil
+100.0
+98.86
+100.0
+99.05
+100.0
+99.81
+100.0
+Water
+91.61
+97.90
+100.0
+100.0
+95.80
+97.20
+100.0
+Residential
+76.31
+80.50
+83.02
+79.66
+83.12
+91.23
+94.87
+Commercial
+74.17
+87.46
+79.96
+80.44
+94.49
+91.55
+94.78
+Road
+89.05
+86.50
+93.30
+84.70
+93.20
+95.94
+96.03
+Highway
+92.86
+64.86
+92.28
+94.88
+89.96
+84.75
+99.81
+Railway
+94.21
+93.74
+85.86
+85.67
+96.39
+94.31
+99.34
+Parking lot 1
+87.32
+74.93
+99.81
+98.75
+99.71
+97.79
+99.81
+Parking lot 2
+84.21
+85.96
+83.16
+82.46
+89.82
+89.47
+90.88
+Tennis court
+100.0
+100.0
+100.0
+100.0
+100.0
+100.0
+100.0
+Running track
+100.0
+100.0
+100.0
+100.0
+100.0
+100.0
+100.0
+OA
+89.70
+87.57
+90.71
+90.80
+94.98
+93.99
+96.77
+AA
+90.73
+89.55
+92.03
+92.06
+95.40
+94.67
+97.06
+Kappa
+88.81
+86.50
+89.92
+90.01
+94.56
+93.48
+96.49
+TABLE VII
+CLASSIFICATION ACCURACY (%) ON THE TRENTO DATASET
+Class
+FusAtNet [49]
+TBCNN [36]
+EndNet [14]
+MDL [5]
+CCNN [15]
+S2ENet [50]
+NNCNet (ours)
+Apple trees
+99.95
+99.87
+99.90
+99.90
+99.90
+99.90
+99.13
+Buildings
+98.92
+98.81
+99.03
+99.10
+99.10
+98.88
+98.92
+Ground
+85.56
+81.02
+85.83
+86.36
+86.90
+86.36
+99.73
+Wood
+100.0
+100.0
+100.0
+100.0
+100.0
+100.0
+100.0
+Vineyard
+99.68
+98.40
+99.31
+99.61
+99.67
+99.21
+100.0
+Roads
+92.07
+89.35
+90.83
+91.12
+91.25
+91.32
+91.88
+OA
+98.77
+97.96
+98.52
+98.66
+98.71
+98.53
+98.92
+AA
+96.03
+94.57
+95.81
+96.01
+96.13
+95.94
+98.26
+Kappa
+98.35
+97.27
+98.01
+98.21
+98.27
+98.03
+98.55
+11×11 pixels is randomly cropped from the dataset as training
+samples.
+After obtaining the pretrained model, training samples from
+the dataset are used for fine-tuning the model. In the fine-
+tuning phase, the mini-batch size is set to 128, and the setting
+of the optimizer is the same as that in the contrastive learning
+phase.
+C. Classification Accuracy and Discussion
+The proposed NNCNet is implemented on the Houston
+2013, Trento, MUUFL and Houston 2018 datasets. To verify
+the effectiveness of the proposed NNCNet, we compared it
+with six state-of-the-art methods, including FusAtNet [49],
+TBCNN [36], EndNet [14], MDL [5], CCNN [15], and
+S2ENet [50]. In particular, FusAtNet [49] exploits HSI and
+LiDAR features via cross-attention, and attentive spectral and
+spatial representations are combined to compute modality-
+specific feature embeddings. TBCNN [36] uses a two-branch
+CNN for HSI and LiDAR feature extraction. In EndNet [14],
+a deep encoder–decoder network is utilized for multimodal
+information fusion and classification. MDL [5] presents a
+general multimodal deep learning framework. CCNN [15]
+presents a coupled network for multimodal information fu-
+sion. Feature-level and decision-level fusion are integrated
+for heterogeneous feature representation. S2ENet [50] is a
+spatial-spectral enhancement network that improves spatial
+and spectral feature representations simultaneously. For a
+fair comparison, all the compared methods adopt the default
+parameters provided in their works.
+Table VI shows the classification results on the Houston
+2013 dataset. The proposed NNCNet achieves the best per-
+formance in terms of OA, AA and Kappa coefficients. Our
+NNCNet outperforms the competitor (CCNN and S2ENet)
+by 1.78% and 2.78% for OA, respectively. It shows that
+the proposed self-supervised framework effectively models
+the correlations between multisource samples. Furthermore,
+the accuracy for ‘highway’ class (99.81%) is significantly
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+9
+TABLE VIII
+CLASSIFICATION ACCURACY (%) ON THE MUUFL DATASET
+Class
+FusAtNet [49]
+TBCNN [36]
+EndNet [14]
+MDL [5]
+CCNN [15]
+S2ENet [50]
+NNCNet (ours)
+Trees
+95.31
+91.18
+90.86
+90.95
+92.40
+93.91
+93.09
+Mostly grass
+79.83
+83.98
+83.30
+84.54
+83.52
+88.28
+86.82
+Mixed ground surface
+83.69
+83.72
+84.27
+83.01
+84.34
+81.85
+86.29
+Dirt and sand
+97.73
+96.12
+96.00
+96.42
+96.72
+97.32
+96.18
+Road
+84.86
+91.23
+91.11
+90.44
+91.68
+91.28
+92.35
+Water
+99.68
+99.68
+99.68
+99.68
+99.68
+99.68
+99.68
+Building shadow
+83.01
+92.85
+92.61
+92.75
+92.61
+88.29
+92.75
+Building
+94.70
+96.86
+96.90
+96.70
+96.80
+95.99
+96.21
+Sidewalk
+89.80
+87.85
+88.34
+87.85
+89.23
+88.50
+91.34
+Yellow curb
+87.88
+90.91
+90.91
+90.91
+90.91
+87.88
+84.85
+Cloth panels
+99.16
+99.16
+99.16
+99.16
+99.16
+99.16
+99.16
+OA
+90.68
+90.53
+90.39
+90.27
+91.20
+91.61
+92.07
+AA
+90.51
+92.14
+92.10
+92.03
+92.45
+92.01
+92.61
+Kappa
+87.65
+87.59
+87.42
+87.26
+88.44
+88.93
+89.56
+TABLE IX
+CLASSIFICATION ACCURACY (%) ON THE HOUSTON 2018 DATASET
+Class
+FusAtNet [49]
+TBCNN [36]
+EndNet [14]
+MDL [5]
+CCNN [15]
+S2ENet [50]
+NNCNet (ours)
+Healthy grass
+89.40
+90.91
+89.55
+93.99
+93.39
+91.29
+93.36
+Stressed grass
+90.65
+88.83
+89.51
+88.95
+90.84
+91.97
+91.95
+Artificial turf
+98.54
+84.90
+75.97
+98.86
+98.38
+96.59
+98.38
+Evergreen trees
+85.30
+71.97
+67.97
+90.60
+94.25
+88.91
+92.00
+Deciduous trees
+73.15
+70.87
+66.98
+76.55
+80.62
+79.12
+76.86
+Bare earth
+100.0
+99.78
+100.0
+100.0
+99.48
+99.78
+99.98
+Water
+99.17
+96.67
+92.92
+98.75
+95.83
+93.75
+96.25
+Residential buildings
+97.29
+94.93
+92.54
+86.31
+91.43
+91.31
+87.58
+Non-residential buildings
+94.36
+95.78
+96.78
+97.75
+93.93
+95.22
+97.04
+Roads
+62.29
+53.26
+42.71
+69.65
+73.14
+70.95
+71.25
+Sidewalks
+64.00
+72.67
+71.00
+68.30
+78.85
+76.82
+70.63
+Crosswalks
+40.53
+41.84
+03.66
+49.82
+52.38
+56.18
+38.33
+Major thoroughfares
+69.77
+78.48
+71.08
+60.56
+76.08
+76.25
+81.58
+Highways
+97.16
+98.55
+96.11
+96.18
+98.70
+98.24
+98.54
+Railways
+99.43
+99.19
+98.91
+97.84
+99.52
+99.67
+99.94
+Paved parking lots
+85.68
+78.73
+75.27
+82.50
+87.32
+91.12
+95.25
+Unpaved parking lots
+100.0
+100.0
+100.0
+100.0
+100.0
+100.0
+100.0
+Cars
+56.13
+72.65
+24.77
+47.87
+89.37
+77.11
+92.16
+Trains
+91.29
+65.06
+60.67
+90.37
+76.38
+92.75
+99.01
+Stadium seats
+99.62
+99.49
+99.34
+99.59
+99.83
+99.65
+99.78
+OA
+85.98
+86.33
+83.84
+86.70
+88.64
+88.87
+89.89
+AA
+84.68
+82.72
+75.78
+84.72
+88.48
+88.33
+88.99
+Kappa
+81.46
+81.83
+78.06
+82.15
+85.19
+85.38
+86.65
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+10
+ (a) Ground truth
+ (b) FusAtNet
+ (c) TBCNN
+ (d) EndNet
+ (e) MDL
+ (f) CCNN
+ (g) S2ENet
+ (h) w/o Pretraining
+ (i) Proposed NNCNet
+Apple trees
+Buildings
+Ground
+Wood 
+Vineyard
+Roads
+Fig. 7. Classification maps for the Trento dataset. (a) Groundtruth. (b) FusAtNet. (c) TBCNN. (d) EndNet. (e) MDL. (f) CCNN. (g) S2ENet. (h) Proposed
+NNCNet without pretraining. (i) Proposed NNCNet.
+ (a) Ground truth
+(b) FusAtNet
+ (c) TBCNN
+ (d) EndNet
+ (e) MDL
+(f) CCNN
+ (g) S2ENet
+(h) w/o Pretraining
+ (i) Proposed NNCNet
+Trees
+Mostly grass
+Mixed ground 
+surface
+Dirt and sand 
+Road
+Water
+Building 
+Shadow
+Building
+Sidewalk
+Yellow curb
+Cloth panels
+Fig. 8. Classification maps for the MUUFL dataset. (a) Groundtruth. (b) FusAtNet. (c) TBCNN. (d) EndNet. (e) MDL. (f) CCNN. (g) S2ENet. (h) Proposed
+NNCNet without pretraining. (i) Proposed NNCNet.
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+11
+ (a) Group truth
+ (b) FusAtNet
+ (c) TBCNN
+ (d) EndNet
+ (e) MDL
+ (f) CCNN
+ (g) S2ENet
+ (h) w/o Pretraining
+ (i) Proposed NNCNet
+Healthy grass
+Stressed grass
+Artificial turf
+Evergreen trees
+Deciduous trees
+Bare earth
+Water
+Residential  
+buildings
+Non-residential 
+buildings
+Roads
+Sidewalks
+Crosswalks
+Major 
+thoroughfares
+Highways
+Railways
+Paved parking  
+lots
+Unpaved parking 
+lots
+Cars
+Trains
+Stadium seats
+Fig. 9.
+Classification maps for the Houston 2018 dataset. (a) Groundtruth. (b) FusAtNet. (c) TBCNN. (d) EndNet. (e) MDL. (f) CCNN. (g) S2ENet. (h)
+Proposed NNCNet without pretraining. (i) Proposed NNCNet.
+improved by our NNCNet. There are many unlabeled highway
+regions in the Houston 2013 dataset. Therefore, our NNCNet
+captured the texture and spectral features of highway via
+contrastive learning from unlabeled data. The classification
+maps are illustrated in Fig. 6. It can be observed that with-
+out pretraining, some highway regions are falsely classified
+into road. In contrast, the proposed NNCNet performs better
+through contrastive learning.
+Table VII illustrates the classification results of different
+methods on the Trento dataset. The classification maps are
+shown in Fig. 7. It can be seen that without pretraining,
+some vineyard regions are falsely classified into apple trees. In
+addition, the proposed NNCNet achieves the best performance
+in terms of OA, AA, and Kappa. The proposed method
+achieves the best OA in ‘ground’. There is only a small amount
+of labeled data in this class, but it still accounts for a large
+portion of the entire graph. It is evident that our NNCNet is
+capable to learning the robust feature representations when
+training samples are limited.
+Table VIII shows the classification results of different meth-
+ods on the MUUFL dataset. The proposed NNCNet obtains
+the best performance against the other methods. To be specific,
+the proposed method has the best OA (92.07%) and reached
+the highest accuracy in five classes (Mixed ground surface,
+Road, Water, Sidewalk and Cloth panels). The classification
+results of the proposed method for the Mostly building and
+Building shadow are quite competitive. Therefore, the com-
+parisons demonstrate the superior performance of the proposed
+NNCNet on the MUUFL dataset. The classification maps of
+the proposed NNCNet with / without pretraining are illustrated
+in Fig. 8, it can be observed that the pretraining effectively
+improved the classification performance.
+Table IX illustrates the classification results of different
+methods on the Houston 2018 dataset. Compared to other
+methods, the proposed NNCNet achieves the best perfor-
+mance. Especially for ‘cars’ and ‘paved parking lots’, our
+method achieves 92.16% and 95.25%, which is far ahead of
+other methods. The classification maps are shown in Fig. 9. It
+can be seen that the results of other methods are not smooth
+enough for car classification, while the proposed NNCNet can
+depict the clear boundaries of cars and paved parking lots. It
+is evident that the proposed NNCNet has strong capabilities
+for fine-grained feature representation.
+We find that the performance of the proposed NNCNet
+on the Houston 2013 dataset and Houston 2018 dataset far
+exceeds that on the Trento and MUUFL datasets. We believe
+it is due to the higher image resolution of both datasets
+(348×1905 and 2384×601 pixels). Therefore, the proposed
+NNCNet can exploit better feature representations on large
+dataset through contrastive learning. As a result, we believe
+that the proposed NNCNet could achieve better classification
+results in practical applications, in which more unlabeled data
+are available.
+D. Ablation Study
+To evaluate the effectiveness of different components in
+NNCNet, we conducted a series of ablation studies. The effec-
+tiveness of each proposed module for improving classification
+accuracy is verified through a series of ablation experiments,
+and the specific experimental results are listed in Table X.
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+12
+Healthy grass
+Stressed grass
+Synthetic grass
+Tree
+Soil
+Water
+Residential
+Commercial
+Road
+Highway
+Railway
+Parking lot 1
+Parking lot 2
+Tennis court
+Running track
+Features without pretraining
+Features with pretraining
+(a) Results on the Houston 2013
+Apple trees
+Features without pretraining
+Features with pretraining
+(b) Results on the Trento
+Buildings
+Ground
+Wood
+Vineyard
+Roads
+Trees
+Features without pretraining
+Features with pretraining
+(c) Results on the MUUFL
+Mostly grass
+Mixed ground surface
+Dirt and sand
+Road
+Water
+Building Shadow
+Building
+Sidewalk
+Yellow curb
+Cloth panels
+Healthy grass
+Features without pretraining
+Features with pretraining
+(d) Results on the Houston 2018
+Stressed grass
+Artificial turf
+Evergreen trees
+Deciduous trees
+Bare earth
+Water
+Residential buildings
+Non-residential buildings
+Roads
+Sidewalks
+Crosswalks
+Major thoroughfares
+Highways
+Railways
+Paved parking lots
+Unpaved parking lots
+Cars
+Trains
+Stadium seats
+Features of the final model
+Features of the final model
+Features of the final model
+Features of the final model
+Fig. 10. Feature visualizations on different datasets. (a) Results on the Houston 2013 dataset. (b) Results on the Trento dataset. (c) Results on the MUUFL
+dataset. (d) Results on the Houston 2018 dataset. The first column denotes features without pretraining, the second column denotes features with pretraining,
+the last column represents the features of our final model. The star denotes the cluster center of each class of features.
+Effectiveness of the Pretraining and Nearest Neighbor
+Learning. We adopt a vanilla convolutional neural network
+without pretraining, bilinear attention fusion, and nearest
+neighbor contrastive learning as our baseline model. As il-
+lustrated in Table X, compared with the baseline model,
+pretraining effectively improves classification performance to
+some extent on four datasets. It demonstrates that our pretrain-
+ing scheme yields parameter initialization that can boost the
+classification accuracy.
+We further examine our nearest neighbor-based contrastive
+learning scheme. As illustrated in Table X, the model with
+nearest neighbor learning significantly boosts the classification
+performance. The reason is that the semantic similarities of
+neighborhood regions are taken into account, and the inter-
+modal semantic alignments are enhanced.
+To further demonstrate the effectiveness of the pretraining
+and nearest neighbor learning, we visualized the features
+before and after pretraining in Fig. 10. We visualized the
+features without/with pretraining, together with the features in
+our final model, respectively. On the Houston 2013, Houston
+2018 and Trento datasets, we found that after pretraining, the
+features of the same class distributed close to each other and
+
+★★★IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+13
+TABLE X
+PERFORMANCE COMPARISON OF SEVERAL VARIANTS OF THE PROPOSED MODEL ON DIFFERENT DATASETS
+Variant
+Pretrain
+Bilinear
+Attention
+Gate
+Mechanism
+Nearest
+Neighbor
+Houston 2013
+Trento
+MUUFL
+Houston 2018
+1
+�
+�
+�
+�
+95.20
+98.74
+91.38
+88.21
+2
+�
+�
+�
+�
+95.57
+98.80
+91.60
+88.72
+3
+�
+�
+�
+�
+96.30
+98.88
+91.83
+89.41
+4
+�
+�
+�
+�
+95.64
+98.86
+91.68
+88.79
+5
+�
+�
+�
+�
+96.47
+98.90
+92.01
+89.76
+6
+�
+�
+�
+�
+95.84
+98.86
+91.68
+88.83
+7
+�
+�
+�
+�
+96.77
+98.92
+92.07
+89.89
+ 
+Fig. 11. Classification accuracy for different number of samples.
+ 
+Fig. 12. Performance comparison of our model using different data augmen-
+tations.
+the features of different classes moved far away from each
+other. It is evident that our unsupervised framework is effective
+on the Houston 2013 and Trento datasets. Furthermore, we
+observed that the features after pretraining do not improve
+significantly on the MUUFL dataset. The reason may be
+that there are more unlabeled data in the Houston 2013,
+Houston 2018 and Trento datasets. These unlabeled data play
+a critical role in contrastive learning. Therefore, the proposed
+contrastive learning framework performs better when more
+unlabeled data are available. It is more convenient in practical
+applications in which large amounts of unlabeled data are
+available.
+Number of Training Samples. One of the advantages of
+self-supervised learning strategy is its excellent performance in
+handling small number of training samples. Therefore, we try
+to gradually reduce the number of samples during the training
+process, and the results are shown in Fig. 11. On the Houston
+2013 dataset, when we use only 375 training samples (25
+samples for each class), the OA value of the proposed method
+is 91.86 which is satisfying and encouraging. Furthermore, the
+model with pretraining consistently outperforms that without
+pretraining on four datasets when small training sets are
+used. It is evident that the contrastive learning strategy of the
+proposed NNCNet is especially effective for small training
+sets. Moreover, we observe that the performance gain of
+pretraining on the Houston 2013 and 2018 datasets is better
+than that on the Trento and MUUFL datasets. As mentioned
+before, there are more unlabeled data on the Houston 2013
+and 2018 datasets. Therefore, the proposed nearest neighbor-
+based strategy can exploit rich feature representations on both
+datasets.
+Effectiveness of Data Augmentation. The purpose of data
+augmentation is to enhance the differences between positive
+and negative samples as a way to facilitate the training of the
+encoder. In the proposed NNCNet, we use four data augmen-
+tation schemes, including RandomResizedCrop, RandomHor-
+izontalFlip, RandomVerticalFlip and RandomGaussianNoise.
+The corresponding results are shown in Fig. 12. We found that
+RandomResizedCrop is the key to data augmentation. Since
+the image patch is cropped into 11×11 pixels, if the scale
+is set too small, the semantic information would easily be
+damaged. Therefore, in our implementations, the scale is set
+to (0.7, 1).
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+14
+ 
+Fig. 13. Classification accuracy for different spatial distances, queue sizes, and mini-batch sizes on different datasets.
+ 
+Fig. 14. Performance comparison of our model with or without 3D convo-
+lution.
+E. Parameter Sensitivity
+Minimum Spatial Distance between Positive and Neg-
+ative Samples. In order to prevent too much similarity be-
+tween positive and negative samples, we define a minimum
+distance s between them (i.e. the distances between positive
+and negative samples need to be greater than s). The results
+are shown in Fig. 13(a). In our implementations, the size of
+each sample is 11 × 11 pixels. The classification performance
+improved slightly when 4 ⩽ s ⩽ 12. It is beneficial to use a
+large distance to increase the difference between positive and
+negative samples. Therefore, in our implementations, s is set
+to 12.
+Size of the Negative Key Dictionary. Fig. 13(b) shows
+the effect of negative key dictionary size on the classification
+performance. The experiments show that a larger dictionary
+size will have a positive effect on pretraining, and it is
+consistent with our previous assumptions. We believe that the
+proposed method works better when more unlabeled data are
+available.
+Key Encoder Update Speed. We tested different key
+encoder update speeds r during pretraining. The experimental
+results are shown in Fig. 13(c). We find that the best classifi-
+cation performance is achieved when r is set to 0.9.
+Effectiveness of 3D Convolution. Inspired by HybridSN
+[41], we first use PCA for channel dimensionality reduction.
+Then, 3D and 2D convolutions are combined for feature
+extraction. To verify the effectiveness of 3D convolution,
+we design a network in which the 3D convolutions are
+replaced with 2D convolutions (“w/o Conv2d” in Fig. 14).
+The experimental results are shown in Fig. 14. We found that
+3D convolution can improve the classification performance to
+some extent. Although PCA disturbs the spectral continuity of
+the hyperspectral data, we argue that 3D convolution can still
+generate more discriminative feature maps from the spectral
+dimensions than 2D convolution. These discriminative features
+generated by 3D convolution can boost the classification
+performance.
+V. CONCLUSIONS AND FUTURE WORK
+In this paper, we propose a self-supervised NNCNet model
+to tackle the HSI and LiDAR joint classification problem.
+Specifically, we integrate a nearest neighbor-based data aug-
+mentation scheme into the contrastive learning framework. Se-
+mantic similarities among neighborhood regions are exploited.
+The intermodal semantic alignments can be captured more
+accurately. In addition, we proposed a bilinear attention fusion
+module that can capture second-order feature interactions be-
+tween HSI and LiDAR data. Therefore, the module improves
+the contextual representation of multisource data effectively.
+Extensive experiments on Houston 2013, Trento, MUUFL and
+Houston 2018 datasets have demonstrated the superiority of
+our model to a wide range of state-of-the-art methods.
+In the future, we aim to explicitly explore the semantic and
+spatial relations between HSI and LiDAR data. In addition,
+we will explore how to further enhance the feature interactions
+between HSI and LiDAR data.
+Meng Wang received the B.Sc. degree in com-
+puter science from Jinan University, Jinan, China,
+in 2020. He is currently pursuing the M.Sc. degree
+in computer science and applied remote sensing with
+the School of Information Science and Technology,
+Ocean University of China, Qingdao, China.
+His current research interests include computer
+vision and remote sensing image processing.
+
+IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
+15
+Feng Gao (Member, IEEE) received the B.Sc degree
+in software engineering from Chongqing University,
+Chongqing, China, in 2008, and the Ph.D. degree
+in computer science and technology from Beihang
+University, Beijing, China, in 2015.
+He is currently an Associate Professor with the
+School of Information Science and Engineering,
+Ocean University of China. His research interests in-
+clude remote sensing image analysis, pattern recog-
+nition and machine learning.
+Junyu Dong (Member, IEEE) received the B.Sc.
+and M.Sc. degrees from the Department of Applied
+Mathematics, Ocean University of China, Qingdao,
+China, in 1993 and 1999, respectively, and the Ph.D.
+degree in image processing from the Department
+of Computer Science, Heriot-Watt University, Ed-
+inburgh, United Kingdom, in 2003.
+He is currently a Professor and Dean with the
+School of Computer Science and Technology, Ocean
+University of China. His research interests include
+visual information analysis and understanding, ma-
+chine learning and underwater image processing.
+Heng-Chao Li (Senior Member, IEEE) received the
+B.Sc. and M.Sc. degrees from Southwest Jiaotong
+University, Chengdu, China, in 2001 and 2004, re-
+spectively, and the Ph.D. degree from the Graduate
+University of Chinese Academy of Sciences, Bei-
+jing, China, in 2008.
+He is currently a Full Professor with the School
+of Information Science and Technology, Southwest
+Jiaotong University. His research interests include
+statistical analysis of synthetic aperture radar (SAR)
+images, remote sensing image processing, and pat-
+tern recognition.
+Dr. Li is an Editorial Board Member of the Journal of Southwest Jiaotong
+University and Journal of Radars. He is an Associate Editor of the IEEE
+JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATION AND
+REMOTE SENSING.
+Qian Du (Fellow, IEEE) received the Ph.D. degree
+in electrical engineering from the University of
+Maryland at Baltimore, Baltimore, MD, USA, in
+2000.
+She is currently the Bobby Shackouls Professor
+with the Department of Electrical and Computer
+Engineering, Mississippi State University, Starkville,
+MS, USA. Her research interests include hyperspec-
+tral remote sensing image analysis and applications,
+and machine learning.
+Dr. Du was the recipient of the 2010 Best Re-
+viewer Award from the IEEE Geoscience and Remote Sensing Society
+(GRSS). She was a Co-Chair for the Data Fusion Technical Committee of
+the IEEE GRSS from 2009 to 2013, the Chair for the Remote Sensing
+and Mapping Technical Committee of International Association for Pattern
+Recognition from 2010 to 2014, and the General Chair for the Fourth IEEE
+GRSS Workshop on Hyperspectral Image and Signal Processing: Evolution
+in Remote Sensing held at Shanghai, China, in 2012. She was an Associate
+Editor for the PATTERN RECOGNITION, and IEEE TRANSACTIONS ON
+GEOSCIENCE AND REMOTE SENSING. From 2016 to 2020, she was the
+Editor-in-Chief of the IEEE JOURNAL OF SELECTED TOPICS IN APPLIED
+EARTH OBSERVATION AND REMOTE SENSING. She is currently a member of
+the IEEE Periodicals Review and Advisory Committee and SPIE Publications
+Committee. She is a Fellow of SPIE-International Society for Optics and
+Photonics (SPIE).
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@@ -0,0 +1,1287 @@
+Astronomy & Astrophysics manuscript no. JupiterTidesFinal
+©ESO 2023
+January 9, 2023
+Dynamical tides in Jupiter and the role of interior structure
+Yufeng Lin
+Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen 518055, China
+e-mail: linyf@sustech.edu.cn
+January 9, 2023
+ABSTRACT
+Context. The Juno spacecraft has obtained highly accurate tidal Love numbers, which provide important constraints on the tidal
+response and interior structure of Jupiter.
+Aims. In order to exploit these observations, it is necessary to develop an approach for accurately calculating the tidal response of
+Jupiter for a given interior model and to investigate the role of interior structure.
+Methods. We directly solve the linearized tidal equations of a compressible, self-gravitating, rotating and viscous fluid body using a
+pseudo-spectral method. The Coriolis force is fully taken into account but the centrifugal effect is neglected. We can simultaneously
+obtain the real and imaginary parts of the tidal Love numbers for a given planetary interior model.
+Results. We calculate the tidal responses for three simple interior models of Jupiter which may contain a compact rigid core or an
+extended dilute core. All of models we consider can explain the fractional correction ∆k22 ≈ −4% due to dynamical tides, but all have
+difficulties to reconcile the observed ∆k42 ≈ −11% for the high-degree tidal Love number. We show that the Coriolis force significantly
+modifies gravity modes in an extended dilute core at the tidal frequency relevant to the Galilean satellites. We demonstrate that a thin
+stable layer in the outer region, if exists, would also influence the tidal responses of Jupiter.
+Key words. giant planets – tides – internal structure
+1. Introduction
+Tidal interactions between Jupiter and the Galilean satellites play
+an important role in the orbital evolution of the system and the
+internal dynamics of the moons (Lainey et al. 2009). The highly
+active volcanic eruptions on Io are believed to be due to strong
+tides raised by Jupiter (Peale et al. 1979). Meanwhile, tides are
+also raised in Jupiter by its moons, probably dominated by Io
+(Gavrilov & Zharkov 1977). The tidal response of a gaseous
+body such as Jupiter is conventionally treated as a hydrostatic
+deformation, which acquires a small phase lag with respect to
+the tidal forcing due to dissipative processes. This is known as
+the equilibrium tide. However, the equilibrium tide alone does
+not suffice to account for the observed strong tidal dissipation in
+Jupiter (Lainey et al. 2009) and the gravitational perturbations
+recently measured by the Juno spacecraft (Durante et al. 2020).
+In fact, the equilibrium tide does not satisfy the momentum
+equation of tidal flows and thus corrections have to be made to
+fully account for the tidal response of Jupiter. The corrections to
+the equilibrium tide are collectively referred to as the dynamical
+tide, which usually involves wave-like motions in the planet and
+depends on the tidal frequency and the interior structure (Ogilvie
+2014). The dynamical tide may provide extra channels of tidal
+dissipation and produce additional gravitational perturbations on
+top of the hydrostatic deformation. The Juno spacecraft has ob-
+tained highly accurate tidal Love numbers klm (Durante et al.
+2020), which quantitatively characterize the tidal response of
+Jupiter to a tidal forcing component represented in spherical har-
+monics of degree l and order m. The observed tidal Love num-
+bers by Juno exhibit non-negligible discrepancies with respect to
+the theoretically calculated hydrostatic values (Wahl et al. 2020),
+suggesting that the dynamical tide has to be considered to ex-
+plain the observed tidal response. Specifically, Juno observations
+found ∆k22 ≈ −4% for the dominant tidal component l = 2 and
+m = 2 and ∆k42 ≈ −11% for the high-degree tidal component
+l = 4 and m = 2, where ∆klm = (klm − k(hs)
+lm )/k(hs)
+lm represents the
+fractional correction to the hydrostatic value k(hs)
+lm
+(Wahl et al.
+2020; Idini & Stevenson 2021, 2022a).
+As the dynamical tides is sensitive to the tidal frequency and
+the interior structure, the detected gravitational signatures of dy-
+namical tides may provide important constraints on the Jupiter’s
+interior (Idini & Stevenson 2021; Lai 2021; Idini & Stevenson
+2021, 2022b; Dewberry & Lai 2022). Recent studies (Idini &
+Stevenson 2021; Lai 2021) have revealed that the discrepancy in
+k22 can be mainly attributed to the Coriolis effect on the funda-
+mental modes, i.e. f−modes. More recently, Idini & Stevenson
+(2022b) proposed that the resonant locking with a gravity mode
+in an extended dilute core can explain ∆k42 ≈ −11%. This pro-
+vides an independent constraint on the existence of a dilute core
+in Jupiter, which has also been suggested by the Juno measure-
+ments of gravitational moments of Jupiter (Wahl et al. 2017; Mil-
+itzer et al. 2022). However, the tidal constraint on the existence
+of a dilute core remains some uncertainties. The calculation of
+tidal response in Idini & Stevenson (2022b) inadequately treated
+the rotational (Coriolis) effect, which plays an important role in
+Jupiter’s tidal responses because the tidal frequencies of Galilean
+satellites are comparable to the spin frequency of Jupiter. Includ-
+ing the Coriolis force introduces inertial waves in the neutrally
+buoyant regions (Ogilvie & Lin 2004; Wu 2005a) and mixed
+gravity waves and inertial waves, i.e. gravito-inertial waves, in
+the stably stratified region (Dintrans et al. 1999; Xu & Lai 2017).
+The mechanism proposed by Idini & Stevenson (2022b) is also
+struggling to reconcile both the real part (relevant to the grav-
+itational perturbation) and imaginary part (relevant to the tidal
+dissipation) of the tidal Love numbers.
+Article number, page 1 of 12
+arXiv:2301.02418v1  [astro-ph.EP]  6 Jan 2023
+
+A&A proofs: manuscript no. JupiterTidesFinal
+In this study, we develop a method to directly calculate the
+tidal response of a fully compressible, self-gravitating, rotating
+and viscous fluid body. The Coriolis force is fully taken into
+account but the centrifugal force is neglected, which allows us
+to numerically solve the problem in spherical geometry using a
+pseudo-spectral method based on spherical harmonic expansions
+(Ogilvie & Lin 2004; Lin & Ogilvie 2017). As we directly solve
+the tidally forced problem with explicit viscosity, we can simul-
+taneously obtain the real and imaginary parts of the tidal Love
+number for a given planetary interior model. Our approach is
+different from recent studies on dynamical tides of Jupiter (Lai
+2021; Idini & Stevenson 2022b; Dewberry & Lai 2022). They
+obtain the eigen modes of the inviscid fluid body first and then
+calculate the tidal Love number (only the real part) through pro-
+jecting the tidal force onto each eigen modes. We consider three
+nominal interior models of Jupiter to investigate the dependence
+of the tidal response on the tidal frequency and the interior struc-
+ture. We focus on the effect of a compact rigid core, an extended
+dilute core and a thin stably stratified layer in the outer region
+on tidal responses. All of simplified models can explain the ob-
+served ∆k22 ≈ −4% as previous studies have shown. However,
+these simplified models are difficult to account for the observed
+∆k42 ≈ −11%. Resonances with gravito-inertial modes in an ex-
+tended dilute core near the tidal frequency of Io can produce
+non-negligible dynamical correction to k42, but it is insufficient
+to explain the Juno observation based on our simplified model.
+2. Tidal model
+We consider linear tidal responses of a rotating gaseous planet
+to a tidal potential component of Ψm
+l
+= A(r/R)lYm
+l (θ, φ)e−iωt,
+where A is the tidal amplitude, R is the radius of the planet,
+Ym
+l (θ, φ) represents spherical harmonics and ω is the tidal fre-
+quency. The resulting tides of the planet produce an external
+gravitational potential perturbation Φ′ = B(R/r)l+1Ym
+l (θ, φ)e−iωt
+(and probably other spherical harmonic components). The ratio
+Km
+l (ω) = B/A defines the tidal Love number, which depends
+on the tidal frequency. The tidal Love number Km
+l is a complex
+number because there exists a phase lag between the forcing
+and the gravitational perturbations due to dissipative processes
+(Ogilvie 2014). While the real part klm = Re[Km
+l ] measures the
+in-phase gravitational perturbations with the tidal forcing, the
+imaginary part Im[Km
+l ] quantifies the out of phase tidal response
+and is related to the dissipation rate. The ratio between the real
+and imaginary parts is related to the tidal quality factor
+Q = sgn(ω)
+klm
+Im[Km
+l ],
+(1)
+where sgn(ω) = ±1 is the sign function. Because the phase lag is
+generally very small, i.e. Q ≫ 1, the magnitude of the imaginary
+part is typically much smaller than the real part. In this study, we
+develop an approach to directly and simultaneously calculate the
+real and imaginary parts of the tidal Love number for a given
+planetary model.
+2.1. Linearized equations
+For a compressible, self-gravitating and rotating fluid body
+which may contain a rigid core of radius Ri, linear perturbations
+to a tidal potential Ψ ∝ e−iωt in the rotating frame are described
+by the following equations (e.g. Ogilvie & Lin 2004):
+−iωu′ = −2Ω × u′ − 1
+ρ0
+∇P′ + ρ′
+ρ2
+0
+∇P0 − ∇Φ′ − ∇Ψ + fν,
+(2)
+−iωρ′ + ∇ · (ρ0u′) = 0,
+(3)
+−iω
+� P′
+ΓP0
+− ρ′
+ρ0
+�
++ u′ ·
+�1
+Γ∇ ln P0 − ∇ln ρ0
+�
+= 0
+(4)
+∇2Φ′ = 4πGρ′,
+(5)
+where u is the velocity, Ω the rotation rate, ρ the density, P the
+pressure, Γ the adiabatic index and G the gravitational constant.
+In the above equations, the subscript 0 denotes physical quan-
+tities in hydrostatic state (without tidal potential) and the nota-
+tions with the prime represent Eulerian perturbations induce by
+the tidal forcing. In the momentum equation (2), we explicitly
+include a viscous force fν defined as
+fν = 1
+ρ0
+∇ · (2µS),
+(6)
+where µ is the dynamic shear viscosity (we neglect the bulk vis-
+cosity) and S is the strain-rate tensor:
+S = 1
+2
+�
+∇u′ + (∇u′)T�
+− 1
+3(∇ · u′)I.
+(7)
+Note that we include the viscous force in the momentum equa-
+tion but neglect the viscous heating in the energy equation, i.e.
+the density and pressure perturbations are treated as adiabatic.
+In this study, we take fully into account the Coriolis force
+due to the rotation but neglect the centrifugal distortion for nu-
+merical convenience. The centrifugal effect can be measured by
+ϵ = Ω/ωdyn, i.e. the ratio between the spin frequency Ω and
+the dynamical frequency ωdyn = (GM/R3)1/2, which is not par-
+ticularly small for Jupiter (ϵ = 0.288). Indeed, the centrifugal
+distortion of Jupiter has non-negligible contributions to the total
+Love number klm, especially for the high-degree Love number
+k42 because the tidal response at l = m = 2 can produce a gravi-
+tational perturbation at l = 4 and m = 2 in an oblate figure (Idini
+& Stevenson 2022a). For the hydrostatic k(hs)
+42
+of Jupiter due to
+Io, 93% of the total value is actually contributed by the centrifu-
+gal coupling with k22 and only the remaining 7% is produced by
+the tidal forcing at l = 4 and m = 2 (Wahl et al. 2020; Idini
+& Stevenson 2022a). In this paper we do not aim to directly
+fit the klm observed by Juno, but rather focus on the fractional
+corrections ∆klm by the dynamical tides. In terms of the frac-
+tional correction ∆klm, the centrifugal contribution to ∆k22 can
+be neglected in leading order (Lai 2021). However, the centrifu-
+gal contribution to ∆k42 can not be neglected even in leading
+order because the k(hs)
+42
+is mostly contributed by the centrifugal
+coupling with k22. This complicates the comparison between the
+calculated ∆k42 in a spherical figure and the observation. Nev-
+ertheless, the calculated ∆k42 in a spherical figure can be multi-
+plied by the factor 0.07 to account Jupiter’s centrifugal coupling
+effect for qualitative comparisons with the observation (Idini &
+Stevenson 2022b). Such a comparison would assume that the
+tidally-excited internal modes are not significantly modified by
+the centrifugal deformation.
+By neglecting the centrifugal deformation, the unperturbed
+basic state is spherically symmetric, i.e. depends on the radius r
+only. Given the density ρ0(r) and pressure P0(r) profiles of the
+unperturbed state, the radial gravitational acceleration (inward)
+Article number, page 2 of 12
+
+Lin: Dynamical tides in Jupiter and the role of interior structure
+g(r) and the Brunt-Väisälä frequency N(r) are then determined
+by
+g = dΦ0
+dr = − 1
+ρ0
+dP0
+dr ,
+(8)
+N2 = g
+�1
+Γ
+d ln P0
+dr
+− d ln ρ0
+dr
+�
+.
+(9)
+2.2. Numerical method
+In order to obtain the complex Love numbers, we numerically
+solve Eqs. (2-5) using a pseudo-spectral method for the pre-
+scribed basic states, subject to the relevant boundary conditions.
+The numerical scheme is based on the method used in previous
+studies (Ogilvie & Lin 2004; Lin & Ogilvie 2017), but we ex-
+tend the method to solve the full set of linearized equations (2-5)
+without making a low-frequency approximation (Ogilvie 2013).
+By introducing h′ = P′/ρ0 and eliminating the density perturba-
+tion ρ′, Eqs. (2-5) can be reduced to the following equations:
+−iωρ0u′
+=
+−2ρ0Ω × u′ − ∇(ρ0h′) + g∇2ϕ′/(4πG)
+−ρ0∇ϕ′ − ∇Ψ + ∇ · (2µS),
+(10)
+−iωh′ = −c2
+s(N2u′
+r/g + ∇ · (ρ0u′)/ρ0),
+(11)
+−iω∇2ϕ′ = −4πG∇ · (ρ0u′),
+(12)
+where u′
+r is the radial velocity perturbation and c2
+s = ΓP0/ρ0 is
+the square of the adiabatic sound speed.
+We impose boundary conditions including the regularity of
+the gravitational perturbations, zero radial velocity on the rigid
+inner boundary and vanishing Lagrange pressure perturbation at
+the surface, i.e. δP = P′ + u′
+r/(−iω)∇P0 = 0. In terms of h′ and
+u′
+r, the last boundary condition can be written as (Dewberry et al.
+2021)
+�−iωh′ − gu′
+r
+� |r=R = 0.
+(13)
+As the viscous force is included, additional boundary conditions
+are required to complete the boundary value problem. We use the
+so-called stress-free conditions, i.e. the tangential stresses van-
+ish, at both boundaries.
+For a given tidal potential Ψm
+l
+= A(r/R)lYm
+l (θ, φ)e−iωt, the
+tidal perturbations (including both equilibrium and dynamical
+tides) u′, h′ and Φ′ can be expanded as
+u′ =
+L
+�
+n=m
+um
+n (r)Rm
+n +
+L
+�
+n=m
+vm
+n (r)Sm
+n +
+L
+�
+n=m
+wm
+n (r)Tm
+n ,
+(14)
+h′ =
+L
+�
+n=m
+hm
+n (r)Ym
+n (θ, φ),
+(15)
+Φ′ =
+L
+�
+n=m
+Φm
+n (r)Ym
+n (θ, φ),
+(16)
+where Rm
+n , Sm
+n , Tm
+n are vector spherical harmonics
+Rm
+n = Ym
+n (θ, φ)ˆr,
+Sm
+n = r∇Ym
+n (θ, φ),
+Tm
+n = r∇ × Rm
+n .
+(17)
+As the basic state is axisymmetric, the perturbations involve
+spherical harmonics with the same order m as the tidal potential
+Ψm
+l , but the Coriolis force would couple all spherical harmon-
+ics with degree n ≥ m. For numerical calculations, we have to
+make a truncation at certain degree L. Substituting expansions of
+Eqs. (14-16) into Eqs. (10-12) and projecting onto spherical har-
+monics, we end up with a set of ordinary differential equations
+involving um
+n (r), vm
+n (r), wm
+n (r), hm
+n (r) and Φm
+n (r) . For the radial de-
+pendence, we use Chebyshev collocation on Nr Gauss–Lobatto
+nodes (Rieutord et al. 2001). The boundary conditions are ap-
+plied through replacing the ODEs with the corresponding bound-
+ary conditions on the boundary nodes. The regularity of gravita-
+tional perturbations requires
+rdΦm
+n
+dr
++ (n + 1)Φm
+n = 0
+at r = R,
+(18)
+rdΦm
+n
+dr
+− nΦm
+n = 0
+at r = Ri.
+(19)
+The vanishing Lagrangian pressure perturbation at the surface
+and zero radial velocity at the rigid inner boundary give
+−iωhm
+n = gum
+n
+at r = R,
+(20)
+um
+n = 0
+at r = Ri.
+(21)
+The stress-free boundary condition is given as (Ogilvie 2009)
+um
+n + rdvm
+n
+dr − vm
+n = 0,
+rdwm
+n
+dr − wm
+n = 0,
+(22)
+at both boundaries.
+Using the numerical discretization described above, the
+boundary value problem becomes a linear system involving a
+large complex block-tridiagonal matrix. The solution of the lin-
+ear system is obtained using the standard direct solver. We use
+typical truncations of L = 200 and Nr = 100 in this study.
+Once the solution of the linear system is obtained numeri-
+cally, the complex tidal Love number is readily given by
+Km
+l = Φm
+l (r = R),
+(23)
+for the tidal potential component Ψm
+l = A(r/R)lYm
+l (θ, φ)e−iωt (we
+simply set A = 1 for the linear tidal response). Note that the so-
+lution includes both the equilibrium and dynamical tides. For the
+real part of Love numbers, of particular interest is the fractional
+correction of dynamical tides
+∆klm = (klm − k(hs)
+lm )/k(hs)
+lm ,
+(24)
+where k(hs)
+lm
+is the hydrostatic value and is calculated by setting
+ω = 0. As our calculations neglect the centrifugal effect which
+significantly influences the high-degree Love number k42, the
+calculated value of ∆k42 should be multiplied by the factor 0.07
+when compared with the observation as we have discussed in
+Sec. 2.1.
+We can also calculate the tidal dissipation rate Dν from the
+velocity perturbations
+Dν =
+�
+V
+2µS2dV,
+(25)
+Article number, page 3 of 12
+
+A&A proofs: manuscript no. JupiterTidesFinal
+where the integral is taken over the fluid domain. The dissipation
+rate is related to the imaginary part of the tidal Love number
+(Ogilvie 2014)
+Dν = (2l + 1)RA2
+8πG
+ωIm[Km
+l ],
+(26)
+which can be served as an independent validation of the numer-
+ical code. The above relation is satisfied to a high degree of ac-
+curacy in all of numerical calculations presented in this paper.
+2.3. Interior models
+In order to solve Eqs. (10-12), we need to prescribe basic state
+profiles ρ0(r), g(r) and N2(r) to model Jupiter’s interior. Our un-
+derstanding of Jupiter’s interior has been significantly improved
+by Juno observations (Stevenson 2020), yet it remains some de-
+grees of uncertainties. In this study, we do not aim to build a
+realistic model of Jupiter’s interior, but focus on the fractional
+contributions of dynamical tides to the tidal Love number for dif-
+ferent possible scenarios of Jupiter’s interior. We consider three
+nominal interior models (Fig. 1) based on a polytrope of index 1,
+which is a good leading order approximation for Jupiter (Steven-
+son 2020).
+For all of models used in this study, the unperturbed density
+and gravity follow a hydrostatic polytrope of index 1,
+ρ0 = πM
+4R3
+sin kr
+kr
+,
+(27)
+g = GM
+r2 [sin(kr) − kr cos(kr)] ,
+(28)
+where k = π/R. The first model consists of a small rigid core
+of radius 0.25R and an isentropic fluid envelope, i.e. Γ = 2 and
+N2 = 0 in the fluid region (Fig. 1(a)).
+The second model assumes an extended dilute core of radius
+0.7R and an isentropic envelope (Fig. 1(b)).The dilute core is
+treated as a stably stratified fluid layer with the Brunt-Väisälä
+frequency given by
+N2
+ω2
+dyn
+= ˜N2 sin
+�πr
+Rc
+�
+,
+(29)
+where ˜N2 = 0.25 and Rc = 0.7 for this model. As we fixed the
+density and pressure profiles to that of a polytrope, the strati-
+fication is effectively realized by adjusting the adiabatic index
+(Γ > 2) in the dilute core (Lai 2021). This model is similar to
+that used in Idini & Stevenson (2022b), but they adjust the den-
+sity profile to model the stable stratification in the dilute core
+while fix the adiabatic index Γ = 2.
+The third model is based on the model in Fig. 1(a), but we
+further add a stably stratified layer between 0.8R and 0.9R (Fig.
+1(c)), possibly resulting from H-He immiscibility (Debras &
+Chabrier 2019; Stevenson et al. 2022). The Brunt-Väisälä fre-
+quency in the top stable layer is prescribed as
+N2
+ω2
+dyn
+= ˜N2
+1
+[1 + e−100(r−0.8)][1 + e100(r−0.9)].
+(30)
+The degree of stratification of this layer remains uncertain, but
+it is estimated that typical values of N2/ω2
+dyn would be roughly
+between 0.1 and 0.8 for Jupiter (Christensen et al. 2020; Gastine
+& Wicht 2021). Here we set a moderate value ˜N2 = 0.5.
+Note that an interior model with the co-existence of a dilute
+core and a top stable layer is also possible (Debras & Chabrier
+2019). As this kind of model involves two different stably strat-
+ified layers, it would be difficult to characterize the role of the
+top stable layer on tides. We consider only the combination of a
+compact rigid core and a top stable layer for simplicity.
+In all of these models, we set the total mass M, the radius R
+and the spin rate Ω such that the ratio ϵ = Ω/
+�
+GM/R3 = 0.288,
+corresponding the value of Jupiter. Our calculations also require
+the fluid viscosity, which is difficult to estimate in detail for giant
+planets. We simply assume the dynamic viscosity µ is propor-
+tional to the background density ρ0, so the kinematic viscosity
+ν = µ/ρ0 is constant. The viscosity can be measured by the di-
+mensionless number Ek = ν/(ΩR2), known as the Ekman num-
+ber. We set Ek = 10−6 for most of calculations (unless otherwise
+specified), roughly corresponding to the effective viscosity based
+on mixing-length theory (Guillot et al. 2004).
+As we have mentioned that we do not aim to construct a re-
+alistic interior model for Jupiter in this study. These simplified
+models are designed to investigate the effects of a compact rigid
+core, an extended dilute core and a top stable layer on the tidal re-
+sponses of Jupiter respectively. Nevertheless, the fractional cor-
+rections ∆klm and the tidal quality factor Q for these simplified
+models can be used to make some qualitative comparisons with
+the observations (Lai 2021; Idini & Stevenson 2021, 2022b).
+3. Results
+In this paper, we focus on the dominant tidal component Ψ2
+2 and
+a high-degree tesseral component Ψ2
+4, for which non-negligible
+dynamical corrections have been detected as we have discussed
+in Sec. 1. Our calculations are limited to the frequency range of
+−2 ≤ ω/Ω ≤ −1, relevant to the tidal frequencies of the Galilean
+moons. Note that the negative tidal frequency means that the
+tidal forcing is retrograde in the co-rotating frame with the planet
+based on our convention. For the real part of Love numbers, we
+show the fractional correction ∆klm. In order to make compar-
+isons with the Juno observation, the calculated ∆k42 is multi-
+plied by 0.07 to compensate the centrifugal effect which is ne-
+glected in our calculations. Because of the negative tidal fre-
+quency, the imaginary part of Love numbers is also negative
+in our calculations and is related to the tidal quality factor by
+klm/Ql = −Im[Km
+l ] according to Eq. (1).
+3.1. Full polytrope model
+Before presenting results for the interior models in Fig. 1, we
+first show the tidal response of a full isentropic polytrope, i.e.
+neutrally buoyant in the whole fluid sphere. This model serves
+as a reference for other models and has been used to investigate
+the dynamical tides of Jupiter in recent analytical studies (Idini
+& Stevenson 2021; Lai 2021). Fig. 2 shows both the real and
+imaginary parts of the Love numbers as a function of the tidal
+frequency for the full polytrope model. We can see that ∆k22
+is negative in the frequency range we considered and smoothly
+varies as the tidal frequency except a burst around ω/Ω = −1.08,
+which corresponds to a resonance with an inertial mode. Away
+from resonances, our numerical results are consistent with recent
+theoretical calculations and produce ∆k22 ≈ −4% at the tidal fre-
+quency of Io (Lai 2021; Idini & Stevenson 2021). These studies
+also revealed that the dynamical correction ∆k22 can be attributed
+to the Coriolis effect on the f-modes. Apart from the f-modes,
+the rotating sphere of isentropic fluid also supports smooth iner-
+Article number, page 4 of 12
+
+Lin: Dynamical tides in Jupiter and the role of interior structure
+(a)
+(b)
+(c)
+Fig. 1. Three nominal models of Jupiter’s interior used in this study. The top panel shows the schematic models and the bottom panel shows the
+density (normalized by the density at the center) and the Brunt-Väisälä frequency (normalized by the dynamical frequency) as a function of the
+radius. The blue shadow in the bottom panel indicates solid regions. (a) A compact rigid core model; (b) an extended dilute core model; (c) a
+compact rigid core and an outer stable layer model.
+tial modes restored by the Coriolis force in the frequency range
+of 0 < |ω/Ω| < 2 (Greenspan 1968; Lockitch & Friedman 1999).
+The burst of ∆k22 at ω/Ω = −1.08 indeed is due to the resonant
+excitation of the inertial mode as shown in Fig. 3(a), but we no-
+tice that the resonance occurs only in a very narrow frequency
+range.
+However, this inertial mode has more significant contribu-
+tions to ∆k42. The angular structure of an inertial mode cannot be
+described by a single spherical harmonics in general (Lockitch
+& Friedman 1999), but the density perturbations (and thus the
+gravitational perturbations) are dominated by the spherical har-
+monics Y2
+4(θ, φ) for the resonant inertial mode at ω/Ω = −1.0836
+as we can see from Fig. 3(a). This suggests a likely strong cou-
+pling between the tidal potential component Ψ2
+4 and the inertial
+mode in Fig. 3(a), i.e. large tidal overlap as described in Wu
+(2005b), leading to significant dynamical corrections to k42. The
+dynamical correction can reach ∆k42 ≈ −10% (after the centrifu-
+gal correction) near the resonance at ω/Ω = −1.0836. However,
+the tidal frequencies of the Galilean satellites are too far away
+from this resonance.
+The curve of ∆k42 also shows a spike around ω/Ω = −1.51,
+corresponding to a narrow resonance with a high degree inertial
+mode (ρ′ is dominated by Y2
+6(θ, φ) as shown in Fig. 3(b)). Inter-
+estingly, the tidal frequency of Io is close to this resonance, but
+the dynamical correction caused by this resonant mode is insuffi-
+cient to account for the observed ∆k42 ≈ −11%. The frequencies
+of inertial modes in Fig. 3 are slightly shifted comparing to that
+calculated by Lockitch & Friedman (1999) for a polytrope of
+index 1 (see their table 6 and note different conventions for the
+sign of frequencies) because they assumed ϵ → 0 whereas we
+set ϵ = 0.288.
+The imaginary parts of the Love numbers in Fig. 2 show that
+resonances with inertial modes significantly enhance the tidal
+dissipation. The enhanced dissipation due to resonant inertial
+modes in a neutrally buoyant sphere has been demonstrated by
+Wu (2005b) but using different density profiles. When the tidal
+frequency is away from resonances, the dissipation rate for the
+full isentropic polytrope is too small to account for the observed
+tidal quality factor Q (Lainey et al. 2009).
+3.2. Compact rigid core model
+We now consider tidal responses for the interior model with a
+compact rigid core. Basically, the inner region (r ≤ 0.25R) of a
+whole fluid polytrope becomes solid for this model. Fig. 4 shows
+the frequency-dependence of the Love numbers for the compact
+rigid core model. We can see that the real parts are largely sim-
+ilar to that of a full polytrope, but the imaginary parts are rather
+different from that of a full polytrope, showing enhanced tidal
+dissipation by introducing the rigid core. The rigid core model
+also supports inertial waves in the fluid envelope, but these waves
+have some peculiar behaviors due to the singularity in a spher-
+Article number, page 5 of 12
+
+O1.0
+1.0
+1.0
+p/pc
+0.8
+0.8
+0.8
+0.6
+0.6
+0.6
+0.4
+0.4
+0.4
+0.2
+0.2
+0.2
+0.0
+0.0
+0.0
+0.00
+0.25
+0.50
+0.75
+1.00
+0.25
+0.50
+0.75
+1.00
+0.25
+0.50
+0.75
+1.00
+0.00
+0.00
+r/R
+r/R
+r/RA&A proofs: manuscript no. JupiterTidesFinal
+Fig. 2. Complex Love number as a function of the tidal frequency for a full isentropic polytrope of index 1. Top panel shows the fractional
+correction ∆klm of the real part of the Love numbers. The fractional correction ∆k42 (orange curve in the top panel) is multiplied by 0.07. The
+bottom panel shows the minus imaginary part −Im[Km
+l ], which is equivalent to klm/Ql. Vertical dashed lines indicate tidal frequencies of four
+Galilean Moons of Jupiter (from right to left: Io, Europa, Ganymede, Callisto). The horizontal dashed line in the bottom panel represents the
+astrometric observation of the frequency independent k2/Q2 from Lainey et al. (2009).
+(a)
+(b)
+Fig. 3. Density perturbations (left half) and radial velocity perturbations (right half) in the meridional plane to the tidal component Ψ2
+4 at two
+resonant frequencies in Fig. 2. Amplitudes are normalized by the maximum absolute values.
+ical shell (Stewartson & Rickard 1969). Smooth inertial modes
+do not exist generally in a spherical shell even with uniform den-
+Article number, page 6 of 12
+
+10
+-
+1
+K2
+I
+-
+I
+-
+5
+K?
+-
+-
+I
+I
+1
+-
+I
+Nkim(
+0
+1
+1
+-
+5
+-10
+-1.4
+-1.0
+-2.0
+-1.8
+-1.6
+-1.2
+101
+-
+-
+10-1
+-
+-
+-
+10
+3
+-
+-
+1
+-
+-
+I
+1
+-
+I
+1
+1
+10-7
+-2.0
+-1.6
+-1.0
+-1.8
+-1.4
+-1.2
+Tidal frequency 0/Q0.5
+0.5
+0
+0
+-0.5
+-0.5
+-1
+1
+/S2 =-1.0836
+Wp
+0.5
+0.5
+0
+0
+-0.5
+-0.5
+-1
+1
+3
+/S2 =-1.5117Lin: Dynamical tides in Jupiter and the role of interior structure
+Fig. 4. As for Fig. 2 but for the interior model with a compact rigid core. The fractional correction ∆k42 (orange curve in the top panel) is multiplied
+by 0.07.
+(a)
+(b)
+Fig. 5. Density perturbations (left half) and gravitational perturbations (right half) in the meridional plane to the tidal component Ψ2
+4 for the
+interior model with a compact rigid core at (a) ω/Ω = −1.5092 (resonance) and (b) ω/Ω = 1.53 (non-resonance) with Ek = 10−7. Amplitudes are
+normalized by the maximum absolute values.
+sity (Rieutord et al. 2001), and localized wave beams spawned
+from the critical latitudes propagate in the bulk along the charac-
+teristics of the inertial wave equations (e.g. Ogilvie 2009). How-
+ever, Lin & Ogilvie (2021) recently revealed that resonant tidal
+responses in a spherical shell correspond to eigen modes with
+large scale flows hidden beneath localized wave beams using a
+Article number, page 7 of 12
+
+10
+-
+K2
+5
+K?
+-
+-
+0
+-
+-
+-
+-10
+-2.0
+-1.6
+-1.8
+-1.4
+-1.2
+-1.0
+100
+-
+-
+10-4
+-2.0
+-1.8
+-1.6
+-1.2
+-1.0
+-1.4
+Tidal frequency 0/Qp
+0.5
+0.5
+0
+0
+-0.5
+-0.5
+-1
+1
+/S2 =-1.50920.5
+0.5
+0
+0
+-0.5
+-0.5
+-1
+1
+/S2 =-1.5300A&A proofs: manuscript no. JupiterTidesFinal
+uniform density model. Furthermore, it was shown that the hid-
+den large scale structures basically resemble inertial modes in a
+full sphere. This is in line with our results for the non-uniform
+density model in this study. The real parts k22 and k42 are relevant
+to only large scale density perturbations, which are similar to in-
+ertial modes in a full sphere as one can see from Fig. 5. There-
+fore, the curves of ∆klm for the rigid core model resemble that of
+a full polytrope, but note slight shifts of the resonant frequencies
+due to the presence of rigid core. As for the full polytrope, the
+compact rigid core model can produce ∆k22 = −4% as observed,
+but it cannot produce sufficient dynamical correction in the high-
+degree Love number k42 near the tidal frequency of Io to account
+for the observed ∆k42 = −11%.
+On the other hand, the imaginary parts are largely modified
+by the presence of small rigid core. We can see that the tidal dis-
+sipation is significantly enhanced by the localized wave beams
+spawned from the critical latitudes both in and out of resonances.
+The velocity perturbations in Fig. 5(b) indeed exhibit localized
+waves propagating in the bulk, which can generate significant
+viscous dissipation but do not produce much density and gravi-
+tational perturbations. In Fig. 4, we also see that several peaks in
+the tidal dissipation (bottom panel) do not lead to obvious fluc-
+tuations in ∆klm (top panel), corresponding to resonances with
+higher degree modes that have little contributions to the low de-
+gree ( i.e. l = 2 and l = 4) gravitational perturbations.
+In summary for the compact rigid core model, the tidal dis-
+sipation is significantly enhanced with respect to the full poly-
+trope case. This is in line with the early work of Ogilvie & Lin
+(2004), who have shown the enhanced tidal dissipation due to
+inertial waves in the convective envelope of rotating stars and
+planets. The averaged dissipation in the tidal frequency range of
+Galilean moons gives rise to comparable tidal quality factor as
+observed (Lainey et al. 2009). However, the fractional correction
+to the real part of Love number ∆k42 is insufficient to explain the
+observation.
+3.3. Dilute core model
+An extended dilute core rather than a compact core in Jupiter has
+been suggested recently based on Juno gravitational measure-
+ments (Wahl et al. 2017; Militzer et al. 2022). In this subsection,
+we consider tidal responses for the interior model with an ex-
+tended dilute core as shown in Fig. 1(b). The dilute core is treated
+as a stably stratified layer which supports gravity waves restored
+by the buoyancy. If the Coriolis force is fully taken into account,
+dynamical tides in the dilute core region would be in the the form
+of mixed gravity waves and inertial waves, i.e. gravito-inertial
+waves (Dintrans et al. 1999; Xu & Lai 2017). Idini & Stevenson
+(2022b) recently calculated the tidal response of Jupiter with an
+extended dilute core, but they did not fully consider the Coriolis
+effect, which turns out to important as we will show.
+Fig. 6 shows the frequency-dependence of the Love num-
+bers for the dilute core model. For the tidal component Ψ2
+2 (bule
+curves), the dynamical correction ∆k22 is generally similar to
+that of the full polytrope except the absence of obvious spikes for
+the dilute core model. However, the imaginary part exhibits sev-
+eral peaks and troughs, suggesting possible resonances with high
+degree mixed modes that enhance the tidal dissipation but do not
+significantly contribute to the l = 2 gravitational perturbations.
+The overall tidal dissipation is also enhanced with respect to the
+full polytrope due to the excitation of gravito-inertial waves in
+the dilute core and inertial waves in the convective envelope. The
+frequency-averaged tidal dissipation tends to be compatible with
+the observed tidal quality factor as we can see from Fig. 6.
+For the tidal component Ψ2
+4, Fig. 6 also shows results with-
+out including the Coriolis force (green curves) for compari-
+son. We note that the fractional correction ∆k42 is always pos-
+itive when the Coriolis force is neglected, probably because the
+pure gravity modes enhance the in-phase gravitational pertur-
+bations and thus produce positive dynamical corrections. Nev-
+ertheless, we observe distinct resonant responses at certain tidal
+frequencies from both real and imaginary parts of the Love num-
+ber for the non-Coriolis case. For instance, the resonance at
+ω/Ω = −1.5193, which is close to the tidal frequency of Io,
+corresponds to the first gravity mode of l = 4 and m = 2 as
+shown in Fig. 7 (a). Indeed, Idini & Stevenson (2022b) proposed
+the resonant locking between this gravity mode 1 (referred to as
+2
+4g1) and the Jupiter-Io orbital evolution to explain the observed
+∆k42 for Jupiter. In Idini & Stevenson (2022b), the Coriolis force
+is neglected for the calculation of gravity modes, but approxi-
+mated rotational corrections are made to obtain the Love num-
+ber. However, taking fully into account the the Coriolis force
+significantly alter the tidal responses as we can see from Fig.
+6. The dynamical correction ∆k42 exhibits several large fluctu-
+ations especially in the frequency range of −1.5 < ω/Ω < −1.
+This is due to the mixing of gravity modes and inertial modes
+in the dilute core, leading to more chances for resonances. The
+most significant dynamical corrections are produced near the
+tidal frequency ω/Ω = −1.2, which is close to the frequency
+of the purely inertial mode as shown in Fig. 3(a). Of course,
+the inertial mode is mixed with gravity modes in the dilute core
+for this model. The resonance around ω/Ω = −1.2 can pro-
+duce more than −10% dynamical corrections in k42 (after the
+centrifugal correction), but it is too far away from the tidal fre-
+quency of Io. The resonance close to the tidal frequency of Io
+(also close to the frequency of pure gravity mode 2
+4g1) occurs at
+ω/Ω = −1.4448 when the Coriolis force is considered. Fig. 7 (b)
+shows the spatial structure of this resonant response. The Cori-
+olis effect not only leads to a non-negligible shift in the mode
+frequency, but also largely modifies the mode structure. The per-
+turbations are in the from of gravito-inertial waves in the dilute
+core and become pure inertial waves in the neutrally buoyant
+envelope. Non-negligible dynamical corrections are induced by
+this resonance at ω/Ω = −1.4448, but the corrections are in-
+sufficient (after the centrifugal correction) to account for the ob-
+served ∆k42 = −11%. As the resonance is very narrow, we use
+200 equally spaced frequency points in the tidal frequency in-
+terval of [-1.45, -1.43]. The peak amplitude of ∆k42 in this fre-
+quency interval is comparable to that of using only 20 frequency
+points, suggesting that the frequency sampling points are suffi-
+cient to capture the resonant peak.
+Comparing the orange and green curves in the bottom panel
+of Fig. 6, we can see that the tidal dissipation is increased by
+about two orders of magnitude when the Coriolis force is in-
+cluded. This suggests that the excitation of pure gravity waves
+is a less efficient tidal dissipation mechanism (unless resonances
+take place) based on our linear calculations, though the nonlinear
+interaction or wave breaking of gravity waves may lead to effi-
+cient tidal dissipation (e.g. Barker 2011; Weinberg et al. 2012).
+3.4. Outer stable layer model
+We finally consider the effect of an outer stable layer, which may
+exist in Jupiter resulting from H-He immiscibility (Debras &
+Chabrier 2019). Fig. 8 shows the Love numbers as a function
+1 They used slightly different background density ρ0(r) and Brunt-
+Väisälä frequency N(r), so the mode frequency is slightly shifted.
+Article number, page 8 of 12
+
+Lin: Dynamical tides in Jupiter and the role of interior structure
+Fig. 6. As for Fig. 2 but for the interior model with an extended dilute core. Green lines represent results without including the Coriolis force. The
+fractional correction ∆k42 (orange and green curves in the top panel) is multiplied by 0.07.
+(a)
+(b)
+Fig. 7. Density perturbations (left half) and radial velocity perturbations (right half) in the meridional plane to the tidal component Ψ2
+4 for the
+interior model with an extended dilute core. (a) Without including the Coriolis force at ω/Ω = −1.5193 (resonance); (b) including the Coriolis
+force at ω/Ω = −1.4448 (resonance). Amplitudes are normalized by the maximum absolute values.
+of the tidal frequency for the interior model (c) in Fig. 1, which
+includes a compact rigid core and a top stable layer between 0.8R
+Article number, page 9 of 12
+
+p
+0.5
+0.5
+0
+0
+-0.5
+-0.5
+1
+/S2 =-1.51930.4
+0.4
+0.2
+0.2
+0
+0
+-0.2
+-0.2
+-0.4
+-0.4
+-0.6
+-0.6
+3
+/S2 =-1.4448K
+10
+-
+-
+K(Non-Coriolis)
+5
+%
+-
+Aklm(
+0
+-
+-
+-
+1
+-10
+-2.0
+-1.8
+-1.6
+-1.4
+-1.2
+-1.0
+10-1
+Q10-3
+10-5
+-
+10-7
+-2.0
+-1.8
+-1.6
+-1.4
+-1.2
+-1.0
+Tidal frequency  /QA&A proofs: manuscript no. JupiterTidesFinal
+Fig. 8. As for Fig. 2 but for the interior model with a small rigid core and a top stably stratified layer. Green lines represent results at the Ekman
+number Ek = 10−7. The fractional correction ∆k42 (orange and green curves in the top panel) is multiplied by 0.07.
+(a)
+(b)
+Fig. 9. Perturbations in the meridional plane to the tidal component Ψ2
+4 at ω/Ω = −1.1650 for the interior model (c) in Fig. 1. (a) Density (left
+half) and radial velocity (right half) perturbations; (b) gravitational (left half) and vorticity (right half) perturbations. Amplitudes are normalized
+by the maximum absolute values. The dashed lines denote r = 0.8R.
+and 0.9R. For the tidal responses to Ψ2
+2, the dynamical correction
+∆k22 is similar to the case without the stable layer, but the pres-
+ence of the thin stable layer eliminates the spike due to the res-
+onant inertial mode at the tidal frequency around ω/Ω = −1.08.
+The overall tidal dissipation due to Ψ2
+2 is comparable to the coun-
+terpart without the top stable layer (blue curve in the bottom
+panel of Fig. 4), but the fluctuation amplitudes, i.e. the differ-
+ences between peaks and troughs, are smaller.
+Article number, page 10 of 12
+
+10
+Ek = 10-6
+5
+Ek = 10-7
+-
+%
+△klm(
+0
+-
+1
+-10
+-1.8
+-1.6
+-1.2
+-1.0
+2.0
+-1.4
+100
+10
+Q
+klml
+10°
+-2.0
+-1.8
+-1.6
+-1.4
+-1.2
+-1.0p
+0.5
+0.5
+0
+0
+-0.5
+-0.5
+1
+S2 =-1.1650V
+0.4
+0.5
+0.3
+0
+0.2
+-0.5
+0.1
+-1
+0
+w/2 =-1.1650Lin: Dynamical tides in Jupiter and the role of interior structure
+For the tidal responses to Ψ2
+4, we also show results for Ek =
+10−7 (green curves) to illustrate the effect of fluid viscosity in
+Fig. 8. One can see that the viscosity has little influence on the
+real part of the Love number. The tidal dissipation weakly de-
+pends on viscosity at peaks and troughs, but the overall dissipa-
+tion tends to be insensitive to viscosity. Indeed, Ogilvie (2013)
+has shown the frequency-averaged dissipation is independent of
+viscosity.
+The dynamical correction ∆k42 is also similar to the case
+without the stable layer. We can see large variations of ∆k42 at
+the tidal frequency around ω/Ω = −1.165, which corresponds to
+a resonant mode as shown in Fig. 9. This mode is complicated
+because it involves three different layers for the interior model
+considered here. The fluid body is primarily neutrally buoyant
+and supports inertial waves. However, the fluid domain is sepa-
+rated by the thin stable layer, which suppresses radial fluid mo-
+tions and creates a "barrier" for the communication between in-
+ertial waves in the inner and outer regions (see the radial velocity
+and vorticity perturbations in Fig. 9). In addition, the thin sta-
+ble layer supports rotationally modified gravity waves. The den-
+sity perturbations are mainly restricted in the stable layer and
+the outer envelope, i.e. in the region of r > 0.8R. Despite the
+complicated velocity and density perturbations, the gravitational
+perturbations are dominated by the l = 4 component with rela-
+tively simple radial dependence. In this regard, this complicated
+mode is relevant to the l = 4 inertial mode without the stable
+layer, leading to large dynamical corrections around the tidal
+frequency at ω/Ω ≈ −1.1 as in Fig. 4. However, the dynami-
+cal correction ∆k42 is negligible after the centrifugal correction
+at the tidal frequency of Io.
+4. Conclusions
+We have developed a numerical method for calculating the tidal
+responses of a compressible, self-gravitating, rotating and vis-
+cous fluid body. We take fully into account the Coriolis force but
+neglect the centrifugal distortion, which allows us to solve the
+problem in the spherical geometry. We use the pseudo-spectral
+method based on spherical harmonics in the angular directions
+and Chebyshev collocation in the radial direction. Different from
+recent studies on Jupiter’s dynamical tides (Lai 2021; Idini &
+Stevenson 2022b; Dewberry & Lai 2022), we directly solve the
+tidally forced problem and explicitly add the fluid viscosity,
+which allows us to simultaneously obtain the real and imaginary
+parts of the tidal Love numbers for a given planetary interior
+model.
+In this study, we considered three simplified interior models
+(Fig. 1) of Jupiter based on a polytrope of index 1. We focus
+on the tidal components Ψ2
+2 and Ψ2
+4 in the frequency range of
+−2 ≤ ω/Ω ≤ −1, which is relevant to the tidal frequencies of
+Galilean moons. Our numerical results show that the dynami-
+cal correction ∆k22 is generally insensitive to the interior mod-
+els. All of models we considered can give rise to the observed
+∆k22 ≈ −4% at the tidal frequency of Io, which is also in line
+with previous studies (Idini & Stevenson 2021; Lai 2021). The
+tidal dissipation is significantly enhanced by the presence of a
+compact rigid core model or an extended dilute core with re-
+spect to the full polytrope, leading to comparable tidal quality
+factor Q as observed (Lainey et al. 2009).
+For the tidal responses to the Ψ2
+4 component, all of models
+we considered are difficult to give rise to ∆k42 ≈ −11% near
+the tidal frequency of Io. For the interior model with a com-
+pact rigid core, significant dynamical corrections are generated
+at the tidal frequency around ω/Ω ≈ −1.1 due to the resonance
+with an inertial mode whose gravitational perturbations are dom-
+inated by the spherical harmonics of l = 4 and m = 2. How-
+ever, this resonance is too far away from the tidal frequencies
+of Galilean moons. For the interior model with an extended di-
+lute core, we demonstrate that the gravity modes in the dilute
+core can be significantly modified by the Coriolis force, leading
+to the mixed gravito-inertial modes. Resonances with gravito-
+inertial modes in the dilute core can produce non-negligible dy-
+namical corrections, but they are insufficient to explain the ob-
+served ∆k42 ≈ −11% near the tidal frequency of Io based on
+our simplified model. We also briefly investigated the effect of
+a top stable layer on Jupiter’s tides. The thin stable layer acts
+as a "barrier" and tends to restrict the density and velocity per-
+turbations mainly in the outer envelope. However, our numerical
+results show that the top stable layer has little influence on the
+real part of tidal Love numbers.
+As we have mentioned, we do not aim to construct a realistic
+interior model of Jupiter in this study. These simplified models
+are designed to characterize the tidal responses of some possi-
+ble scenarios of Jupiter’s interior. Because the dynamical tides
+highly depend on the tidal frequency, the satellite dependent tidal
+Love numbers would provide more constraints on the interior of
+Jupiter (Idini & Stevenson 2022b). In addition, seismology is
+the most effective approach to determine the interior structure of
+planets, though the detection of Jupiter’s oscillations remains a
+big challenge (Gaulme et al. 2011). Nevertheless, the numerical
+scheme we developed in this study can be also used for theoreti-
+cal calculations of oscillation modes of giant planets.
+There are some caveats, which should be considered in fu-
+ture. First, we do not consider the centrifugal deformation in
+order to solve the problem in the spherical geometry. The cen-
+trifugal effect plays a significant role in the tidal Love num-
+bers of Jupiter, especially for the high-degree tidal components.
+Although we have made the centrifugal corrections when the
+numerical results are qualitatively compared with the observa-
+tions, both the Coriolis and centrifugal effects should be self-
+consistently taken into account for quantitative comparisons
+with the high precision observations in future. Second, giant
+planets exhibit differential rotations, which also influence the os-
+cillation modes and thus tidal responses (Dewberry et al. 2021).
+Finally, Jupiter has the strongest magnetic field among planets in
+the solar system and mainly consists of electrically conducting
+fluid (metallic hydrogen), so the magnetic effects (Lin & Ogilvie
+2018; Wei 2022) should also play a part in the tides of Jupiter.
+Acknowledgements. The author would like to thank an anonymous referee for
+constructive comments and Dali Kong for fruitful discussions. This study was
+supported by the B-type Strategic Priority Program of the CAS (XDB41000000),
+National Natural Science Foundation of China (grant no. 42174215) and the pre-
+research project on Civil Aerospace Technologies of CNSA (D020308). Numer-
+ical calculations were performed on the Taiyi cluster supported by the Center for
+Computational Science and Engineering of Southern University of Science and
+Technology.
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+

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+© 2023 IEEE. This is the author’s version of the work. The definitive Version of Record is published in the IEEE International
+Symposium on Circuits and Systems (ISCAS), 2023.
+TrojanSAINT: Gate-Level Netlist Sampling-Based
+Inductive Learning for Hardware Trojan Detection
+Hazem Lashen, Lilas Alrahis, Johann Knechtel, and Ozgur Sinanoglu
+New York University Abu Dhabi
+{hl3372, lma387, jk176, os22}@nyu.edu
+Abstract—We propose TrojanSAINT, a graph neural network
+(GNN)-based hardware Trojan (HT) detection scheme working at
+the gate level. Unlike prior GNN-based art, TrojanSAINT enables
+both pre-/post-silicon HT detection. TrojanSAINT leverages a
+sampling-based GNN framework to detect and also localize HTs.
+For practical validation, TrojanSAINT achieves on average (oa)
+78% true positive rate (TPR) and 85% true negative rate (TNR),
+respectively, on various TrustHub HT benchmarks. For best-case
+validation, TrojanSAINT even achieves 98% TPR and 96% TNR
+oa. TrojanSAINT outperforms related prior works and baseline
+classifiers. We release our source codes and result artifacts.
+Index Terms—Hardware Security, Trojan Detection, GNNs
+I. INTRODUCTION
+Integrated circuit (IC) design and manufacturing has become
+an increasingly outsourced process that involves various third
+parties. While this has allowed to increase both productivity
+and complexity of ICs, it has also made them more vulnerable
+to the introduction of hardware Trojans (HTs), among other
+threats. HTs are malicious circuitry, causing system failure,
+leaking sensitive information, etc [1], [2]. Thus, methods to
+accurately check for HTs become increasingly important.
+Conventional methods for HT detection include code re-
+view [3] and verification against a “golden reference”, i.e.,
+a trusted, HT-free version of the design [4]. However, the
+former is prone to errors, especially for complex ICs, and
+the latter is not always feasible, especially when untrusted
+parties are engaged in the design process [4]. Other meth-
+ods have been proposed as well, e.g., utilizing side-channel
+fingerprinting [5]; however, such are limited to post-silicon
+HT detection. Researchers have shown that machine learning
+(ML) can successfully adapt to a wide variety of HTs, without
+necessitating new techniques for detecting new HT designs [6].
+Using graph neural networks (GNNs) is an emerging and
+promising method toward this end [3], [7]–[9]. Thanks to their
+ability to work on graph-structured data – such as circuits –
+GNNs can leverage both a) the features of each gate and b)
+the overall structure of the design for the prediction of HTs.
+Still, prior art for GNN-based HT detection suffers from the
+following limitations (also summarized in Table I).
+HT Localization. State-of-the-art GNN-based detection
+schemes, GNN4TJ [3] and HW2VEC [7], predict whether
+a design contains a HT or not, but they cannot localize HTs.
+However, localizing HTs is essential to identify the part of the
+design at fault and name the responsible, malicious party.
+Scope. Earlier works [3], [7], [10] are limited to register
+transfer level (RTL), unable to handle gate-level netlists (GLNs).
+TABLE I
+COMPARISON OF GNN-BASED HT DETECTION SCHEMES
+Method
+HT
+HT
+Gate-Level
+Pre-
+Post-
+Detection
+Localization
+Netlist
+Silicon
+Silicon
+GNN4TJ [3]
+Yes
+No
+No
+Yes
+No
+HW2VEC [7]
+Yes
+No
+No
+Yes
+No
+GRFTL [10]
+Yes
+Yes
+No
+Yes
+No
+Our Work
+Yes
+Yes
+Yes
+Yes
+Yes
+Fig. 1. Concept of TrojanSAINT.
+Such methods are restricted to pre-silicon assessment; they
+cannot detect HTs in the field. Note that only schemes which
+can work on GLNs allow for pre- and post-silicon detection.
+Associated Research Challenges. Developing a GNN-based
+HT detection and localization scheme that can work on GLNs
+imposes the following research challenges (RC).
+RC1: GLN Complexity. Compared to RTL, GLN designs
+are more complex to analyze, as GLNs are flattened (i.e.,
+hierarchical information is lost) and also considerably larger,
+in the range of thousands or even millions of gates and wires.
+RC2: Imbalanced Datasets. HTs are stealthy and small in
+size; HT gates represent a very small percentage, e.g., 0.14–
+11.29% or 1.94% on average for the TrustHub suite considered
+in this work. Thus, a highly imbalanced dataset arises (e.g.,
+the ratio of regular to HT gates reaches up to 719× for the
+TrustHub suite), which is difficult to handle for any ML model.
+Our Contributions. Here, we propose TrojanSAINT, a GNN-
+based method for HT detection and localization that works
+well on large-scale GLNs. The concept is outlined in Fig. 1.
+As indicated, the graph representations of GLNs are complex
+and large, which makes them difficult to handle with traditional
+architectures such as graph convolutional networks (GCNs).
+This motivates our decision to, without loss of generality
+(w/o.l.o.g.), use GraphSAINT [11] for our methodology. Graph-
+SAINT is a well-established, sampling-based approach that
+extracts smaller sub-graphs for training from the larger original
+graph. It has shown good performance for various tasks [11]–
+arXiv:2301.11804v1  [cs.CR]  27 Jan 2023
+
+Fig. 2. Overview of TrojanSAINT. Black arrows follow the inference process,
+orange arrows follow the additional steps needed for training and validation.
+In this example, the thresholding value is 0.4.
+[13], but it has not been considered for HT detection until now.
+We summarize our contributions as follows:
+1) A parser for GLN-to-graph conversion (Sec. II-A) which
+performs feature extraction tailored for HT detection.
+2) A GNN-based method for detection and localization of
+HT in GLNs (Sec. II-B), addressing RC1.
+3) A procedure for tuning of the classification thresholds to
+obtain more accurate predictions, addressing RC2.
+4) We demonstrate that our scheme is competitive to tra-
+ditional ML baselines and prior art. We also verify the
+generalization ability of our scheme – i.e., good prediction
+accuracy for unknown HTs on unseen GLNs.
+5) We open-source our scheme and related artifacts from
+our experimental study [https://github.com/DfX-NYUAD/
+TrojanSAINT].
+II. TROJANSAINT METHODOLOGY
+An overview of our methodology is shown in Fig. 2. Next,
+we describe all relevant details.
+A. GLN Parsing and Feature Vectors
+Parser. We develop a parser that converts GLNs (given in
+Verilog format) into unweighted and undirected graphs, where
+nodes represent gates and edges represent wires. We are dis-
+carding directionality for improved representation learning [14].
+Given a set of GLNs, our parser generates one large single
+graph, consisting of multiple disjoint graphs, where nodes
+are labeled as ‘train,’ ‘validation’ or ‘test,’ depending on the
+designation of the GLN they belong to. The graph is encoded
+as an adjacency matrix A following a standard procedure.
+Feature Vectors. Our parser also generates a matrix X of
+feature vectors for all nodes. Vectors cover the following:
+• Gate type, represented via one-hot encoding. From exper-
+imentation, we are more interested in the functionality of
+the gate over the exact implementation. That is, we group
+functionally related gates together, e.g., all AND gates
+are grouped regardless of the number of inputs and the
+driver strengths that the different AND gates support.
+• Input, output degrees of gates, i.e., the number of incoming
+and outgoing connections.
+• Shortest distances to primary inputs/outputs. For gates not
+directly connected with a primary input/output, a breadth-
+first search is conducted to obtain shortest distances.
+For training and validation, we also use a binary label vector
+which marks each node as part of some HT or as regular/benign
+gate. The related information is derived during parsing.
+B. GNN Implementation and Application
+Outline. We utilize GraphSAINT [11] for sampling. Further,
+we utilize the GNN architecture of GNN-RE [15], along with
+GraphSAGE [16]. We tune the classification thresholds for more
+accurate predictions. We further utilize a practical validation.
+For training and inference, we employ standard procedures.
+GNN Architecture. We consider an undirected graph
+G (V, A) for representing a GLN, where V is the set of
+vertices/nodes/gates, and the adjacency matrix of the graph is
+A, where Au,v = 1 and Av,u = 1 if there exists an edge/wire
+from vertex/gate u to vertex/gate v. Each vertex u in the initial
+graph G has a feature vector xu. This vector represents the
+node embedding at layer zero of the GNN. The embedding of
+node u is iteratively updated by the GNN, by aggregating the
+embedding of the node and its neighbors N(u). The embedding
+of a node u after l GNN layers, h(l)
+u , is given by:
+a(l)
+u = AGGREGATE(l) ��
+h(l−1)
+v
+: v ∈ N(u)
+��
+(1)
+h(l)
+u = COMBINE(l) �
+h(l−1)
+u
+, a(l)
+u
+�
+(2)
+GNN architectures are defined by their implementation
+of AGGREGATE(·) and COMBINE(·). For example, Graph-
+SAGE [16], which we also use here, works as follows:
+h(l)
+u = σ([Wl · AGG({h(l−1)
+v
+, ∀v ∈ N(u)}), Blh(l−1)
+u
+]) (3)
+AGG =
+�
+v∈N(u)
+h(l−1)
+v
+|N(u)|
+(4)
+where σ(.) is an activation function such as ReLU and
+Wl and Bl are trainable weight matrices. In GraphSAGE, the
+embedding of node h(l)
+u is determined by first concatenating the
+node’s features from the previous layer h(l−1)
+u
+with the output
+of the AGG function. Then the Wl and Bl transformations
+learns the important components of the neighbors’ features
+and the node u, respectively. GraphSAGE is compatible with
+different AGG functions. Here, we use the mean aggregator
+as described in Equation (4).
+Thresholding. From experimentation, we observe that the
+classification threshold plays a significant role for prediction
+performance. This is because of the considerably imbalanced
+datasets (Sec. I, RC2), where the GNN model as is can predict
+the minority class, i.e., HT nodes, only with low confidence.
+The goal of thresholding is to determine a sufficiently small
+value so that HT nodes/gates are classified as such the moment
+the GNN captures any hint of malicious structures. In other
+words, thresholding allows the GNN to focus more on the
+minority class, improving the performance of the entire model.
+W/o.l.o.g., we tune the threshold between 0–0.5 in steps
+of 1,000 and select the threshold that yields the best score
+on validation. Here, best score refers to the average of true
+positive rate (TPR) and true negative rate (TNR).
+
+首Algorithm 1 TrojanSAINT training algorithm
+Input: Training graph G (V, A); Ground truth Y ; Sampler RWS
+Output: Trained GNN
+1: Compute normalization coefficients α, λ using RWS
+2: for each mini-batch do
+3:
+Gs (Vs, As) ← Sampled sub-graph of G using RWS
+4:
+Build GNN on Gs
+5:
+{yu | u ∈ Vs} ← Propagating α-normalized {xu | u ∈ Vs}
+6:
+Propagating λ-normalized loss L (yu, yu) to update weights
+7: end for
+Algorithm 2 TrojanSAINT inference algorithm
+Input: Flattened netlist N; Trained GNN; Threshold th
+Output: Trojan classification of all nodes/gates
+1: Initiate G (V, A) with V ← GLN to graph(N)
+2: for each u ∈ V do
+3:
+zu ← GNN(u)
+▷ Compute embedding
+4:
+cu ← fc(zu, th)
+▷ Classify node u based on the threshold
+5: end for
+Practical Validation. We propose an approach where pre-
+dictions are made on unknown HTs residing within circuits
+that are neither seen during training nor have golden references.
+This represents a real-world scenario, where security engineers
+do not know in advance which HT to expect, if any at all, and
+further need to test circuits without golden references. Prior
+art did not necessarily consider such practical validation.
+Training. First, we construct sub-graphs using a standard
+random-walk sampler (RWS). TrojanSAINT’s training procedure
+is shown in Algorithm 1. Due to the RWS, the network can
+become biased towards frequently sampled nodes. To alleviate
+this issue, we follow the normalization technique of [11]. We
+use stochastic gradient descent as optimizer. Gs is sampled
+for each minibatch and a GNN is built on the sub-graph. The
+cross-entropy loss is calculated for each node in the sub-graph
+and the GNN weights are then updated by backpropagation.
+Inference. See Algorithm 2. For all test nodes in the graph,
+node embeddings are calculated and passed to a fully-connected
+layer with softmax activation, to compute class probabilities.
+We then apply our thresholding technique, and finally convert
+class probabilities into labels.
+III. EXPERIMENTAL STUDY
+A. Setup
+Software. We use Python for coding and bash scripts
+for job/data management. TrojanSAINT extends on GNN-
+RE, which is obtained from [14] and is implemented in
+PyTorch. Our TrojanSAINT platform is available online [https:
+//github.com/DfX-NYUAD/TrojanSAINT]. Baseline models
+are implemented using Scikit-Learn, except the fully-connected
+neural network (FCNN) in PyTorch.
+Computation. Experiments for GNN-RE, TrojanSAINT and
+FCNN are conducted on a high-performance cluster with 4x
+Nvidia V100 GPUs and 360GB RAM; experiments for others
+are conducted on a workstation with Intel i7 CPU and 16GB
+RAM. Training of GNN-RE and TrojanSAINT takes ≈15–30
+minutes per model, FCNN ≈10 minutes per model, and all
+others ≈3 minutes in total. All inference takes few seconds.
+Benchmarks and Model Building. We use 17 exemplary
+GLN benchmarks from the TrustHub suite [17]. For each
+benchmark, a respective model is trained from scratch. For our
+practical validation, each model does not get to see the design
+to be tested at all during training.1
+We note that random seeds used in TrojanSAINT’s com-
+ponents affect performance significantly. Thus, we conduct
+w/o.l.o.g. 6 runs with different seeds and report only results
+for each model that performs best on its validation set.
+Prior Art, Comparative Study. From Table I, recall that
+none of the prior art in GNN-based HT detection works on
+GLNs. Thus, a direct comparison is not practical. However,
+we consider the following works for comparison.
+• GNN-RE [15]: Proposed for reverse engineering of GLNs,
+it could also be utilized for HT detection and localization.
+This is because GNN-RE seeks to classify gates/nodes
+from flattened GLNs into the circuit modules they belong
+to; TrojanSAINT’s task of classifying gates/nodes into
+begin or HT-infested ones is analogous.
+• Related Works [18]–[20]: ML-based, not GNN-based, HT
+detection schemes that are working on GLNs. Unlike ours,
+these works employ elaborate feature engineering. Also,
+these works do not offer native HT localization.
+We also implement and run the following well-known
+baseline classifiers for a further comparative study.
+• XGBoost: A decision tree (DT)-based model that uses
+an ensemble of sequentially added DTs. DTs are added
+aiming to minimize errors of their predecessor.
+• Random Forest: A DT-based model that uses an ensemble
+of DTs trained on subsets of the training data.
+• Logistic Regression: A classification algorithm that utilizes
+the sigmoid function on independent variables.
+• Support Vector Machine (SVM): A classification model
+that generates a hyperplane to separate different classes.
+• FCNN: We implement a three-layer network; each layer
+use the SELU activation function [21] and batch normaliza-
+tion. The final layer uses sigmoid activation to calculate
+classification probabilities.
+All these classifiers work on tabular, non-graph data; thus, we
+provide them with the feature vectors as inputs. All classifiers,
+except SVM, output probabilities; thus, we can study them
+considering our proposed thresholding as well.
+B. Results
+Practical Validation and Impact of Thresholding. In
+Table II, we report TPR/TNR results for practical validation
+across two scenarios: with thresholding versus without.2
+First, the results show that TrojanSAINT outperforms other
+methods for this realistic but challenging scenario of HT
+1For example, if rs232t1000 is to be tested, none of the other rs232 designs
+are used for training, only for validation.
+For s15850t100, the only s15850 design in the suite, we randomly select
+three other designs for validation.
+2Since thresholding is part of our proposed scheme, we do not consider
+TrojanSAINT without. We implement the same thresholding strategy (Sec. II-B)
+for all models. SVM directly separates data into classes without computing
+probabilities, making thresholding not applicable (N/A).
+
+TABLE II
+TPR/TNR RESULTS FOR PRACTICAL VALIDATION. BEST RESULTS, CONSIDERING AVERAGE OF TPR AND TNR, ARE MARKED IN BOLDFACE.
+TrustHub
+All With Thresholding
+Others Without Thresholding
+Benchmark
+TrojanSAINT
+XGBoost
+FCNN
+GNN-RE
+Logistic
+Random
+SVM
+TrojanSAINT
+XGBoost
+FCNN
+GNN-RE
+Logistic
+Random
+SVM
+Regression
+Forest
+Regression
+Forest
+rs232t1000
+1.00/0.60
+1.00/0.57
+0.85/0.64
+0.77/0.51
+1.00/0.46
+0.69/0.75
+N/A
+1.00/0.60
+0.23/0.91
+0.00/1.00
+0.00/1.00
+0.00/1.00
+0.15/0.92
+0.00/1.00
+rs232t1100
+0.92/0.68
+0.83/0.57
+1.00/0.61
+0.92/0.52
+0.83/0.61
+0.33/0.90
+N/A
+0.92/0.68
+0.08/0.91
+0.00/0.94
+0.00/0.94
+0.00/1.00
+0.08/0.92
+0.00/1.00
+rs232t1200
+0.41/0.80
+0.59/0.56
+0.59/0.91
+0.82/0.27
+0.71/0.60
+0.35/0.75
+N/A
+0.41/0.80
+0.06/0.90
+0.06/1.00
+0.06/0.93
+0.00/1.00
+0.00/0.91
+0.00/1.00
+rs232t1300
+1.00/0.74
+1.00/0.57
+1.00/0.66
+1.00/0.71
+1.00/0.43
+0.56/0.86
+N/A
+1.00/0.74
+0.22/0.91
+0.00/1.00
+0.00/0.98
+0.00/1.00
+0.00/0.92
+0.00/1.00
+rs232t1400
+0.92/0.50
+0.92/0.57
+1.00/0.56
+1.00/0.27
+1.00/0.46
+0.54/0.70
+N/A
+0.92/0.50
+0.08/0.91
+0.08/0.71
+0.62/0.94
+0.00/1.00
+0.00/0.92
+0.00/1.00
+rs232t1500
+0.71/0.82
+0.93/0.57
+0.93/0.57
+0.79/0.61
+1.00/0.46
+0.57/0.76
+N/A
+0.71/0.82
+0.21/0.91
+0.07/0.77
+0.36/0.94
+0.00/1.00
+0.14/0.91
+0.00/1.00
+rs232t1600
+0.73/0.57
+0.73/0.57
+0.91/0.49
+0.55/0.66
+0.73/0.59
+0.27/0.90
+N/A
+0.73/0.57
+0.18/0.91
+0.00/1.00
+0.00/0.83
+0.00/1.00
+0.00/0.91
+0.00/1.00
+s15850t100
+0.35/0.97
+0.77/0.94
+0.92/0.76
+0.88/0.97
+0.96/0.73
+0.85/0.94
+N/A
+0.35/0.97
+0.12/1.00
+0.00/1.00
+0.12/1.00
+0.00/1.00
+0.04/1.00
+0.04/1.00
+s35932t100
+1.00/1.00
+0.87/0.98
+0.87/0.64
+0.93/1.00
+0.93/0.44
+1.00/0.98
+N/A
+1.00/1.00
+0.20/1.00
+0.00/1.00
+0.00/0.97
+0.00/1.00
+0.13/1.00
+0.07/1.00
+s35932t200
+1.00/1.00
+1.00/0.98
+0.92/0.80
+1.00/1.00
+0.92/0.44
+1.00/0.99
+N/A
+1.00/1.00
+0.00/1.00
+0.00/1.00
+0.00/1.00
+0.00/1.00
+0.00/1.00
+0.00/1.00
+s35932t300
+0.97/1.00
+0.94/0.98
+1.00/0.81
+1.00/1.00
+0.40/0.81
+0.97/0.97
+N/A
+0.97/1.00
+0.63/1.00
+0.00/1.00
+0.09/1.00
+0.00/1.00
+0.57/1.00
+0.00/1.00
+s38417t100
+0.92/0.92
+1.00/0.82
+0.75/0.77
+1.00/0.92
+1.00/0.35
+0.75/0.90
+N/A
+0.92/0.92
+0.33/0.95
+0.00/1.00
+0.00/1.00
+0.00/1.00
+0.42/0.94
+0.00/1.00
+s38417t200
+0.40/0.99
+0.53/0.86
+0.73/0.73
+0.47/0.93
+1.00/0.35
+0.73/0.90
+N/A
+0.40/0.99
+0.27/0.95
+0.73/0.90
+0.00/1.00
+0.00/1.00
+0.27/0.94
+0.00/1.00
+s38417t300
+0.98/0.96
+0.98/0.82
+0.18/0.89
+0.98/0.91
+0.16/0.87
+0.95/0.84
+N/A
+0.98/0.96
+0.14/0.95
+0.07/1.00
+0.00/0.98
+0.02/1.00
+0.23/0.95
+0.07/1.00
+s38584t100
+1.00/0.95
+1.00/0.87
+1.00/0.87
+1.00/0.92
+1.00/0.52
+1.00/0.93
+N/A
+1.00/0.95
+0.22/1.00
+0.00/1.00
+0.00/1.00
+0.00/1.00
+0.22/1.00
+0.00/1.00
+s38584t200
+0.90/0.98
+0.49/0.87
+0.89/0.87
+0.39/0.95
+0.98/0.52
+0.84/0.94
+N/A
+0.90/0.98
+0.02/1.00
+0.00/1.00
+0.00/1.00
+0.00/1.00
+0.02/1.00
+0.02/1.00
+s38584t300
+0.13/0.98
+0.08/0.88
+0.47/0.94
+0.23/0.93
+0.94/0.52
+0.45/0.94
+N/A
+0.13/0.98
+0.01/1.00
+0.00/1.00
+0.00/1.00
+0.00/1.00
+0.01/1.00
+0.00/1.00
+Average
+0.78/0.85
+0.80/0.76
+0.82/0.74
+0.81/0.77
+0.86/0.54
+0.70/0.88
+N/A
+0.78/0.85
+0.18/0.95
+0.06/0.96
+0.07/0.97
+0.00/1.00
+0.13/0.95
+0.01/1.00
+detection considering unknown Trojans within unseen circuits.
+The GNN framework underlying of TrojanSAINT is superior to
+other models. Recall that others take the same feature vectors
+as inputs; such direct comparison is fair. Second, thresholding
+is crucial for high prediction performance for this task.
+Relaxed Validation. We also study a “best case” validation,
+using a leave-one-out split where validation and test sets are
+the same. Such setting is often considered in the literature, as
+it shows the best performance for any model and benchmark.
+As indicated, however, it is not as realistic for HT detection.
+With thresholding applied, we observe the following average
+TPR/TNR values here:3 0.98/0.96 for TrojanSAINT, 0.93/0.93
+for XGBoost, 0.91/0.89 for FCNN, 0.98/0.96 for GNN-RE,
+0.89/0.81 for logistic regression, and 0.91/0.994 for random
+forest, respectively. Without thresholding applied, we observe
+the following average TPR/TNR values: 0.41/0.99 for XGBoost,
+0.09/1.00 for FCNN, 0.07/0.97 for GNN-RE, 0.09/1.00 for
+logistic regression, 0.40/0.99 for random forest, and 0.11/1.00
+for SVM, respectively. TrojanSAINT is superior to almost all
+methods across these two cases; only GNN-RE, and only with
+thresholding applied, becomes a close contender.
+Related Works. In Table III, we compare to more loosely
+related works (Sec. III-A). Results are quoted and rounded.
+Numbers of nodes/gates are reported as obtained from our
+parser.4 The related works employ leave-one-out or “best case”
+validation schemes; thus, we also report TrojanSAINT results
+for such “best case” validation here.
+TrojanSAINT outperforms these related works for all larger
+benchmarks, where the ratio of HT gates/nodes to regular ones
+is more challenging—this demonstrates superior scalability for
+3Due to limited space, we refrain from reporting a table for this scenario.
+4Number of nodes/gates may vary across ours and related works, depending
+on parsing approach, technology library etc., but overall ranges remain similar.
+TABLE III
+BENCHMARK PROPERTIES; TPR/TNR RESULTS FOR RELATED WORKS
+TrustHub
+Benign
+HT
+Ratio of Nodes,
+R-HTD [18]
+[19]
+[20]
+TrojanSAINT
+Benchmark
+Nodes
+Nodes
+HT to Benign
+(Orig. Samples)
+rs232t1000
+202
+13
+0.064
+1.00/0.94
+1.00/0.99
+1.00/1.00
+1.00/0.94
+rs232t1100
+204
+12
+0.059
+1.00/0.93
+0.50/0.98
+1.00/1.00
+1.00/0.93
+rs232t1200
+199
+17
+0.085
+0.97/0.96
+0.88/1.00
+1.00/1.00
+0.82/0.96
+rs232t1300
+204
+9
+0.044
+1.00/0.95
+1.00/1.00
+0.86/1.00
+1.00/0.98
+rs232t1400
+202
+13
+0.064
+1.00/0.98
+0.98/1.00
+1.00/1.00
+1.00/0.96
+rs232t1500
+202
+14
+0.069
+1.00/0.94
+0.95/1.00
+1.00/1.00
+1.00/0.94
+rs232t1600
+203
+11
+0.054
+0.97/0.92
+0.93/0.99
+0.78/0.99
+1.00/0.88
+s15850t100
+2,156
+26
+0.012
+0.74/0.93
+0.78/1.00
+0.08/1.00
+0.88/0.97
+s35932t100
+5,426
+15
+0.003
+0.80/0.69
+0.73/1.00
+0.08/1.00
+1.00/0.97
+s35932t200
+5,426
+12
+0.002
+0.08/1.00
+0.08/1.00
+0.08/1.00
+1.00/1.00
+s35932t300
+5,427
+35
+0.006
+0.84/1.00
+0.81/1.00
+0.92/1.00
+1.00/1.00
+s38417t100
+5,329
+12
+0.002
+0.67/1.00
+0.33/1.00
+0.09/1.00
+1.00/0.97
+s38417t200
+5,329
+15
+0.003
+0.73/0.99
+0.47/1.00
+0.09/1.00
+1.00/0.97
+s38417t300
+5,329
+44
+0.008
+0.89/1.00
+0.75/1.00
+1.00/1.00
+1.00/0.96
+s38584t100
+6,473
+9
+0.001
+N/A
+N/A
+0.17/1.00
+1.00/0.99
+s38584t200
+6,473
+83
+0.013
+N/A
+N/A
+0.18/1.00
+1.00/0.98
+s38584t300
+6,473
+731
+0.113
+N/A
+N/A
+0.03/1.00
+0.99/0.95
+Average
+3,250
+63
+0.035∗
+0.84/0.95
+0.72/1.00
+0.55/1.00
+0.98/0.96
+0.019∗
+∗The first value is averaged across the column; the second value, more representative of
+the overall imbalance, is based on re-calculating the ratio using the average node counts.
+ours. For the smaller benchmarks, which are not representative
+of real IC designs, related works achieve better results presum-
+ably due to feature engineering. In fact, up to 76 features are
+considered in [19], [20] which reflects on considerable efforts,
+whereas for ours, some simple feature vectors suffice.
+IV. CONCLUSION
+We have developed TrojanSAINT, a GNN-based method
+for detection and localization of HTs. We overcome the HT-
+inherent issue of class imbalance through threshold tuning.
+Through practical validation, ours is capable of generalizing
+to circuits and HTs it has not seen for training. Our method
+outperforms prior art and a number of strong ML baselines.
+
+The use of a GNN framework renders TrojanSAINT simple
+yet competitive. For future work, we will study the role of
+different feature vectors in more details.
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+

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