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Durban businessman Thoshan Panday and his co-accused in the R47 million Fifa World Cup tender scandal urged the State to disclose transcripts of tapped mobile telephone conversations in the Durban High Court on Monday.

Thoshan Panday, co-accused urged to disclose transcripts of ‘tapped’ phone conversations

The AGM also saw other appointments to the executive committee, including Tomasz Orkiszewski of Goldcast Academy, Alison Foster of C Foster Plant Hire and Bryan Shilliday of Tam Shilliday Plant ...

New president for the Scottish Plant Owners Association

Zero-Knowledge Hackathon Insights and Recommendations

জিরো-নলেজ হ্যাকাথন অন্তর্দৃষ্টি এবং সুপারিশ

Erkenntnisse und Empfehlungen zum Zero-Knowledge-Hackathon

Ideas y recomendaciones del Hackathon de conocimiento cero

Perspectives et recommandations du Zero-Knowledge Hackathon

शून्य-ज्ञान हैकाथॉन अंतर्दृष्टि और सिफारिशें

ゼロ知識ハッカソンの洞察と推奨事項

영지식 해커톤 통찰력 및 권장 사항

Insights e recomendações do Zero-Knowledge Hackathon

Анализ и рекомендации хакатона с нулевым разглашением

Sıfır Bilgi Hackathonu İçgörüleri ve Önerileri

Thông tin chi tiết và đề xuất về Hackathon không có kiến thức

零知识黑客马拉松的见解和建议

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London;
(4) DANIEL GRIN, Haverford College;
(5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro
Methods
Phenomenology
Discussion and Future Work
Conclusion
Acknowledgments and References ABSTRACT 1. INTRODUCTION Axion-like particles (ALPs) are a broad class of dark matter (DM) particle candidates that possess both a strong theoretical justification and a variety of potentially observable signatures. While the traditional quantum chromodynamics (QCD) axion is a pseudo-Nambu-Goldstone boson arising from a broken Peccei-Quinn symmetry (Peccei & Quinn 1977), ALPs can arise from broken symmetries more generally, and are produced naturally from a variety of string theories as a result of compactified higher dimensions, making them a well-motivated DM particle candidate (Dine & Fischler 1983; Preskill et al. 1983; Abbott & Sikivie 1983; Svrcek & Witten 2006; Duffy & van Bibber 2009; Arvanitaki et al. 2010; Marsh 2016; Adams et al. 2022). Throughout this work, we will use axion and ALP interchangeably to refer to this broad class of low-mass pseudo-Nambu-Goldstone boson DM candidates. Some work has been done to model the evolution of the axion field with these extreme starting angles, such as the works of Cedeno et al. ˜ (2017); Zhang & Chiueh (2017b); Leong et al. (2019); Zhang & Chiueh (2017a). However, the rapidly-oscillating nature of these axion fields (both at the background and perturbation level) necessitates extremely high temporal resolution for the computations, requiring long computation times for a brute force solution Zhang & Chiueh (2017b,a). This makes running repeated estimates of the axion evolution, of the sort required for a Markov Chain Monte Carlo (MCMC) or other likelihood sampler method, prohibitively expensive. In this work, we present a novel method of efficiently and accurately modeling the behaviour of these extreme axions as a cosmological fluid. We follow the structure of the vanilla axion modeling code axionCAMB, explained in more detail in Hlozek et al. ˇ (2015). We implement a number of innovations and improvements to axionCAMB compute predictions for cosmological observables such as the linear MPS. These innovations, described in more detail in the Section 2, include a restructuring of the initial conditions, and a novel effective sound speed of the extreme axion fluid. All of these innovations reduce the runtime to model extreme axions down to ∼ 7 seconds. This opens up new opportunities to put observational constraints on extreme axion models with higher-dimensional MCMC algorithms that require tens of thousands of calls to the axion evolution code. This paper is available on arxiv under CC 4.0 license. Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro Methods Phenomenology Discussion and Future Work Conclusion Acknowledgments and References Abstract and Intro Abstract and Intro Methods Methods Phenomenology Phenomenology Discussion and Future Work Discussion and Future Work Conclusion Conclusion Acknowledgments and References Acknowledgments and References ABSTRACT 1. INTRODUCTION Axion-like particles (ALPs) are a broad class of dark matter (DM) particle candidates that possess both a strong theoretical justification and a variety of potentially observable signatures. While the traditional quantum chromodynamics (QCD) axion is a pseudo-Nambu-Goldstone boson arising from a broken Peccei-Quinn symmetry (Peccei & Quinn 1977), ALPs can arise from broken symmetries more generally, and are produced naturally from a variety of string theories as a result of compactified higher dimensions, making them a well-motivated DM particle candidate (Dine & Fischler 1983; Preskill et al. 1983; Abbott & Sikivie 1983; Svrcek & Witten 2006; Duffy & van Bibber 2009; Arvanitaki et al. 2010; Marsh 2016; Adams et al. 2022). Throughout this work, we will use axion and ALP interchangeably to refer to this broad class of low-mass pseudo-Nambu-Goldstone boson DM candidates. Some work has been done to model the evolution of the axion field with these extreme starting angles, such as the works of Cedeno et al. ˜ (2017); Zhang & Chiueh (2017b); Leong et al. (2019); Zhang & Chiueh (2017a). However, the rapidly-oscillating nature of these axion fields (both at the background and perturbation level) necessitates extremely high temporal resolution for the computations, requiring long computation times for a brute force solution Zhang & Chiueh (2017b,a). This makes running repeated estimates of the axion evolution, of the sort required for a Markov Chain Monte Carlo (MCMC) or other likelihood sampler method, prohibitively expensive. In this work, we present a novel method of efficiently and accurately modeling the behaviour of these extreme axions as a cosmological fluid. We follow the structure of the vanilla axion modeling code axionCAMB, explained in more detail in Hlozek et al. ˇ (2015). We implement a number of innovations and improvements to axionCAMB compute predictions for cosmological observables such as the linear MPS. These innovations, described in more detail in the Section 2, include a restructuring of the initial conditions, and a novel effective sound speed of the extreme axion fluid. All of these innovations reduce the runtime to model extreme axions down to ∼ 7 seconds. This opens up new opportunities to put observational constraints on extreme axion models with higher-dimensional MCMC algorithms that require tens of thousands of calls to the axion evolution code.

Extreme Axions Unveiled: A Novel Fluid Approach for Cosmological Modeling - Abstract and Intro

চরম অক্ষরেখা উন্মোচন: মহাজাগতিক মডেলিংয়ের জন্য একটি অভিনব তরল পদ্ধতি - বিমূর্ত এবং ভূমিকা

Extreme Axionen enthüllt: Ein neuartiger Fluidansatz für die kosmologische Modellierung - Zusammenfassung und Einführung

Se revelan los axiones extremos: un nuevo enfoque fluido para el modelado cosmológico: resumen e introducción

Extreme Axions dévoilé : une nouvelle approche fluide pour la modélisation cosmologique - Résumé et introduction

एक्सट्रीम एक्सियंस का अनावरण: ब्रह्माण्ड संबंधी मॉडलिंग के लिए एक नवीन द्रव दृष्टिकोण - सार और परिचय

極限アクシオンの解明: 宇宙論モデリングのための新しい流体アプローチ - 概要と序文

Extreme Axions 공개: 우주론적 모델링을 위한 새로운 유체 접근 방식 - 요약 및 소개

Extreme Axions revelados: uma nova abordagem fluida para modelagem cosmológica - Resumo e introdução

Представлены экстремальные аксионы: новый жидкостный подход к космологическому моделированию – Аннотация и введение

Extreme Axions Ortaya Çıktı: Kozmolojik Modelleme için Yeni Bir Akışkan Yaklaşımı - Özet ve Giriş

Ra mắt các trục cực mạnh: Một phương pháp tiếp cận chất lỏng mới cho mô hình vũ trụ - Tóm tắt và giới thiệu

揭秘极端轴子：一种用于宇宙学建模的新型流体方法 - 摘要和简介

This paper is under CC 4.0 license. available on arxiv Authors: (1) Zhe Liu, State Key Laboratory of Intelligent Game, Beijing, China Institute of Software Chinese Academy of Sciences, Beijing, China; University of Chinese Academy of Sciences, Beijing, China; (2) Chunyang Chen, Monash University, Melbourne, Australia; (3) Junjie Wang, State Key Laboratory of Intelligent Game, Beijing, China Institute of Software Chinese Academy of Sciences, Beijing, China; University of Chinese Academy of Sciences, Beijing, China & Corresponding author; (4) Mengzhuo Chen, State Key Laboratory of Intelligent Game, Beijing, China Institute of Software Chinese Academy of Sciences, Beijing, China; University of Chinese Academy of Sciences, Beijing, China; (5) Boyu Wu, State Key Laboratory of Intelligent Game, Beijing, China Institute of Software Chinese Academy of Sciences, Beijing, China; University of Chinese Academy of Sciences, Beijing, China; (6) Zhilin Tian, State Key Laboratory of Intelligent Game, Beijing, China Institute of Software Chinese Academy of Sciences, Beijing, China; University of Chinese Academy of Sciences, Beijing, China; (7) Yuekai Huang, State Key Laboratory of Intelligent Game, Beijing, China Institute of Software Chinese Academy of Sciences, Beijing, China; University of Chinese Academy of Sciences, Beijing, China; (8) Jun Hu, State Key Laboratory of Intelligent Game, Beijing, China Institute of Software Chinese Academy of Sciences, Beijing, China; University of Chinese Academy of Sciences, Beijing, China; (9) Qing Wang, State Key Laboratory of Intelligent Game, Beijing, China Institute of Software Chinese Academy of Sciences, Beijing, China; University of Chinese Academy of Sciences, Beijing, China & Corresponding author. Table of Links Abstract and Introduction Motivational Study and Background Approach Experiment Design Results and Analysis Discussion and Threats to Validity Related Work Conclusion and References 4 EXPERIMENT DESIGN 4.1 Research Questions • How effective of InputBlaster in detecting bugs related to text input widgets? RQ1: (Bugs Detection Performance) For RQ1, we first present some general views of InputBlaster for bug detection, and then compare it with commonly-used and state-of-the-art baseline approaches. • What is the contribution of the (sub-) modules of InputBlaster for bug detection performance? RQ2: (Ablation Study) For RQ2, We conduct ablation experiments to evaluate the impact of each (sub-) module on the performance. • How does our proposed InputBlaster work in real-world situations? RQ3: (Usefulness Evaluation) For RQ3, we integrate InputBlaster with the GUI testing tool to make it automatically explore the app and detect unseen inputrelated bugs, and issue the detected bugs to the development team. 4.2 Experimental Setup we crawl 200 most popular open-source apps from F-Droid [3], and only keep the latest ones with at least one update after September 2022 (this ensures the utilized apps are not overlapped with the ones in Sec 3.3). Then we collect all their issue reports on GitHub, and use keywords (e.g., EditText) to filter those related to text input. Finally, we obtain 126 issue reports related to 54 apps. Then we manually review each issue report and the mobile app, and filter it according to the following criteria: (1) the app wouldn’t constantly crash on the emulator; (2) it can run all baselines; (3) UIAutomator [65] can obtain the view hierarchy file for context extraction; (4) the bug is related to text input widgets; (5) the bug can be manually reproduced for validation; (6) the app is not used in the motivational study or example dataset construction. Please note that we follow the name of the app to ensure that there is no overlap between the datasets. Finally, 31 apps with 36 buggy text inputs remain for further experiments. For RQ1 and RQ2, We measure the bug detection rate, i.e., the ratio of successfully triggered crashes in terms of all the experimental crashes (i.e., buggy inputs), which is a widely used metric for evaluating GUI testing [8, 27, 43]. Specifically, with the generated unusual input, we design an automated test script to input it into the text input widgets, and automatically run the “submit” operation to check whether a crash occurs. If no, use the script to go back to GUI page with the input widget if necessary, and try the next generated unusual input. As long as a crash is triggered for a text input widget, we treat it as successful bug detection and will stop the generation for this widget. Note that our generated unusual input is not necessarily the same as the one provided in the issue report, e.g., -18 vs. -20, as long as a crash is triggered after entering the unusual inputs, we treat it as a successful crash detection. For a fair comparison with other approaches, we employ two experimental settings, i.e., 30 attempts (30 unusual inputs) and 30 minutes. We record the bug detection rate under each setting (denoted as “Bug (%)” in Table 2 to Table 5), and also record the actual number of attempts (denoted as “Attempt (#)”) and the actual running time (denoted as “Min (#)”) when the crash occurs to fully understanding the performance. we further evaluate the usefulness of InputBlaster in detecting unseen crash bugs related to text input. A total of 131 apps have been retained. We run Ape [26] (a commonly-use automated GUI testing tool) integrated with InputBlaster, for exploring the mobile apps and getting the view hierarchy file of each GUI page. For RQ3, We use the same configurations as the previous experiments. Once a crash related to text input is spotted, we create an issue report by describing the bug, and report them to the app development team through the issue reporting system or email. 4.3 Baselines Since there are hardly any existing approaches for the unusual input generation of mobile apps, we employ 18 baselines from various aspects to provide a thorough comparison. First, we directly utilize ChatGPT [58] as the baseline. We provide the context information of the text input widgets (as described in Table 1 P1), and ask it to generate inputs that can make app crash. Fuzzing testing and mutation testing can be promising techniques for generating invalid inputs, and we apply several related baselines. Feldt et al. [24] proposed a testing framework called GoldTest, which generates diverse test inputs for mobile apps by designing regular expressions and generation strategies. In 2017, they further proposed an invalid input generation method [55] based on probability distribution (PD) parameters and regular expressions, and we name this baseline as PDinvalid. Furthermore, we reuse the idea of traditional random-based fuzzing [13, 41], and develop a RandomFuzz for generating inputs for text widgets. In addition, based on the 50 buggy text inputs from the GitHub dataset in Section 3.3.1, we manually design 50 corresponding mutation rules to generate the invalid input, and name this baseline as ruleMutator. Furthermore, we include the string analysis methods as the baselines, i.e., OSTRICH [15] and Sloth [14]. They aim at generating the strings that violate the constraints (e.g., string length, concatenation, etc), which is similar to our task. OSTRICH’s key idea [15] is to generate the test strings based on heuristic rules. Sloth [14] proposes to exploit succinct alternating finite-state automata as concise symbolic representations of string constraints. There are constraint-based methods, i.e., Mobolic [8] and TextExerciser [27], which can generate diversified inputs for testing the app. For example, TextExerciser utilizes the dynamic hints to guide it in producing the inputs. We also employ two methods (RNNInput [43] and QTypist [44]) which aim at generating valid inputs for passing the GUI page. In addition, we use the automated GUI testing tools, i.e., Stoat [61], Droidbot [39], Ape [26], Fastbot [12], ComboDroid [67], TimeMachine [23], Humanoid [40], Q-testing [53], which can produce inputs randomly or following rules to make app running automatically. We design the script for each baseline to ensure that it can reach the GUI page with the text input widget, and run them in the same experimental environment (Android x64) to mitigate potential bias.

Leveraging LLMs for Generation of Unusual Text Inputs in Mobile App Tests: Experiment Design

This is paper is available on arxiv under CC 4.0 DEED license. Authors: (1) Leah Chrestien, Czech Technical University in Prague; (2) Tomá˘s Pevný, Czech Technical University in Prague, and Gen Digital, Inc.; (3) Stefan Edelkamp, Czech Technical University in Prague; (4) Antonín Komenda, Czech Technical University in Prague. Table of Links Abstract & Introduction Preliminaries Conditions on strictly optimally efficient heuristic Loss functions Related Work Experiments Conclusion and References Appendix 7 Conclusion The motivation of this paper stemmed from the observation that even the cost-to-goal, considered to be an optimal heuristic, fails to guarantee a strictly optimally efficient search. Since a large body of existing research optimizes this quantity, we are effectively lost with respect to what should be optimized. To fill this gap, we have stated the necessary and sufficient conditions guaranteeing the forward search to be strictly optimally efficient. These conditions show that the absolute value of the heuristic is not important, but that the ranking of states in the Open list is what controls the efficiency. Ranking can be optimized by minimizing the ranking loss functions, but its concrete implementation needs to correspond to a variant of the forward search. In case of mismatch, the resulting heuristic can perform poorly, which has been demonstrated when the heuristic optimized for BGFS search was used with A* search. The other benefit of ranking losses is that from the point of view of statistical learning theory, they solve a simpler problem than ubiquitous regression in estimating the cost-to-goal. We do not question the existence of a strictly optimally efficient heuristic. 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Optimize Planning Heuristics to Rank, not to Estimate Cost-to-Goal: Conclusion and References

What are ZK Proofs and How are They the Future of Verifiability

This paper is available on under CC 4.0 license. Arxiv Authors: (1) Md Masud Rana, Department of Mathematics, University of Kentucky; (2) Duc Duy Nguyen, Department of Mathematics, University of Kentucky & ducnguyen@uky.edu. Table of Links Abstract & Introduction Datasets and Results Methods Conclusion, Data and Software Availability, Competing interests, Acknowledgments & References 4 Conclusion The study of protein-protein interactions (PPIs) and the prediction of mutation-induced binding free energy changes are of great importance in understanding the molecular basis of biological processes. The application of geometric graph theory and atom-level graph coloring techniques provides a powerful framework for analyzing biomolecules and capturing their intricate relationships. By utilizing the concept of geometric subgraphs and constructing multi-scale weighted colored geometric subgraphs (MWCGS), we can effectively represent the structural and functional properties of PPIs. The site-specific MWCGS features allow us to extract meaningful patterns and characteristics, shedding light on the effects of mutations and the underlying molecular interactions. In this work, we developed a mutation-induced binding free energy change predictor, called GGL-PPI, by incorporating site-specific MWCGS features for PPIs and gradient-boosting trees. Our method demonstrates superior performance compared to existing methods. The model was validated on three datasets: AB-Bind S645, SKEMPI 1.0 S1131, and SKEMPI 2.0 S4169 and S8338, showcasing its robustness and effectiveness. Furthermore, GGL-PPI was evaluated on a blind test set, the Ssym dataset. To prevent data leakage between the test and training sets, the model was trained on a homology-reduced balanced training set Q3488. This approach ensures the reliability and fairness of the evaluation process. GGL-PPI exhibits the most unbiased and superior performance in predicting binding free energy changes for both direct and reverse mutations, outperforming other existing methods, particularly for reverse mutations. Overall, the results highlight the potential of the GGL-PPI approach in accurately predicting mutation-induced binding free energy changes in protein-protein interactions, providing valuable insights into the molecular mechanisms underlying protein-protein interactions and facilitating drug design and discovery efforts. 5 Data and Software Availability The source code is available at Github: https://github.com/NguyenLabUKY/GGL-Mutation. 6 Competing interests No competing interest is declared. 7 Acknowledgments This work is supported in part by funds from the National Science Foundation (NSF: # 2053284, # 2151802, and # 2245903), and the University of Kentucky Startup Fund. References [1] Dana Chuderland and Rony Seger. 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PPIs and the Prediction of Mutation-Induced Binding Free Energy Changes: What It All Means

This paper is CC 4.0 license. available on arxiv under Authors: (1) Amir Noorizadegan, Department of Civil Engineering, National Taiwan University; (2) D.L. Young, Core Tech System Co. Ltd, Moldex3D, Department of Civil Engineering, National Taiwan University & dlyoung@ntu.edu.tw; (3) Y.C. Hon, Department of Mathematics, City University of Hong Kong; (4) C.S. Chen, Department of Civil Engineering, National Taiwan University & dchen@ntu.edu.tw. Table of Links Abstract & Introduction Neural Networks PINN for Solving Inverse Burgers’ Equation Residual Network Numerical Results Results, Acknowledgments & References 6 Conclusion Throughout this study, we conducted a series of experiments to assess how different neural network setups, including Plain NN and SQR-SkipResNet, perform when it comes to interpolating both smooth and complex functions. Our findings consistently showed that SQR-SkipResNet outperforms other architectures in terms of accuracy. This was especially evident when dealing with non-smooth functions, where SQR-SkipResNet displayed improved accuracy, although it might take slightly more time to converge. We also applied our approach to real-world examples, like interpolating the shape of a volcano and the Stanford bunny. In both cases, SQR-SkipResNet exhibited better accuracy, convergence, and computational time compared to Plain NN. Furthermore, while opting for a deeper network might at times lead to reduced accuracy for both Plain NN and SQR-SkipResNet, we observed that this outcome is influenced by the specific problem. For instance, when dealing with the complicated geometry of the Stanford Bunny and its smooth function, we noticed that deeper networks yielded enhanced accuracy, quicker convergence, and improved CPU efficiency. Regardless of whether deeper networks are suitable, the proposed method demonstrated superior performance. As the effectiveness of network depth varies based on the problem, our approach offers a more favorable architecture choice for networks of different depths. Additionally, when applied to solve the inverse Burgers’ equation using a physicsinformed neural network, our proposed architecture showcased significant accuracy and stability improvements across different numbers of hidden layers, unlike Plain NN. Prospective studies might delve into further optimizations, extensions, and applications of the SQR-SkipResNet framework across diverse domains, particularly for addressing a broad range of inverse problems coupled with PINN methodologies. Acknowledgments Authors gratefully acknowledge the financial support of the Ministry of Science and Technology (MOST) of Taiwan under grant numbers 111-2811-E002-062, 109-2221-E002- 006-MY3, and 111-2221-E-002 -054 -MY3. References [1] Raissi, M., P. Perdikaris, and G.E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378: p. 686-707, 2019. [2] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. arXiv preprint arXiv:1512.03385, 2015. [3] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual networks. arXiv preprint arXiv:1603.05027, 2016. [4] Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, Tom Goldstein: Visualizing the Loss Landscape of Neural Nets, arxiv.1712.09913v3, 2018. [5] Veit, A., M. Wilber, and S. Belongie, Residual networks behave like ensembles of relatively shallow networks, in Proceedings of the 30th International Conference on Neural Information Processing Systems. Curran Associates Inc.: Barcelona, Spain. p. 550–558, 2016. [6] S. Jastrzębski, Arpit D, Ballas N, Verma V, Che T, Bengio Y: Residual Connections Encourage Iterative Inference. arXiv:1710.04773, 2017. [7] Lu, Lu., M. Dao, P. Kumar, U. Ramamurty, G.E. Karniadakis, and S. Suresh, Extraction of mechanical properties of materials through deep learning from instrumented indentation. Proceedings of the National Academy of Sciences, 117(13): p. 7052-7062, 2020. [8] Wang, S., Y. Teng, and P. Perdikaris, Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks. SIAM Journal on Scientific Computing, 43(5): p. A3055-A3081, 2021. [9] R. Franke, Scattered data interpolation: tests of some methods, Mathematics of Computation 38 , 181–200, 1982. [10] C.-S. Chen, A. Noorizadegan, C.S. Chen, D.L. Young, On the selection of a better radial basis function and its shape parameter in interpolation problems, Applied Mathematics and Computation 442, 12771, 2023. [11] denizunlusu / Getty Images. (n.d.). Mt Eden, or Maungawhau, is a significant M¯aori site. Retrieved from https://www.lonelyplanet.com/articles/top-things-to-doin-auckland [12] Mira Bozzini, Milvia Rossini. Testing methods for 3d scattered data interpolation. Multivariate Approximation and Interpolation with Applications, 20, 2002.

Physics-Informed with Power-Enhanced Residual Network: Results, Acknowledgments & References

Authors: (1) Eugene Y. S. Chua, Division of the Humanities and Social Sciences, California Institute of Technology; (2) Eddy Keming Chen, ‡Department of Philosophy, University of California. Table of Links Abstract & Introduction Decoherence and Branching The Born Rule Discussion Conclusion and References 5 Conclusion We suggest that the Evereian understanding of decoherence and branching, as well as the justifications for the Born rule, apply to both WFRE and DMRE. Hence, the theoretical benefits of DMR are available on EQM. Another consequence is that Everettians face a choice between two types of theories, one allowing only pure states for the multiverse and the other allowing mixed states also. The choice will not be based on different understandings of the branching structure or the Born rule, as the Everettian justifications equally apply in both theories, but must involve some other theoretical considerations. 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Decoherence, Branching, and the Born Rule in a Mixed-State Everettian Multiverse: Conclusion

Older and Younger Adults Are Influenced Differently by Dark Pattern Designs: Conclusion & References

Authors: (1) Chenhao Shi, Shanghai Jiao Tong University; (2) Ruibang Liu, Shanghai Jiao Tong University; (3) Guoqiang Li†, Shanghai Jiao Tong University. Table of Links Abstract & Introduction Preliminaries Normalization Algorithm Evaluation Conclusion & References V. CONCLUSION In this paper, we propose an algorithm based on data flow analysis to construct a paradigm for R1CS. The correctness and equivalence of R1CS have long been challenging to study due to the diversity and flexibility of constraint construction methods. Our algorithm aims to eliminate the differences between equivalent R1CS constraint systems through a series of abstraction processes. We introduce ordering methods for internal variables and constraints in R1CS, which provide reference information for the final paradigm generation. Through experimental results, we demonstrate that our algorithm can identify equivalent R1CS resulting from constraint merging, intermediate variable selection, and variable and constraint reordering, and transform them into a unique paradigm. Therefore, R1CS plays an indispensable part in zk-SNARKS. Further work includes establishing rules for merging constraints and a more comprehensive benchmark. This requires us to conduct more in-depth research and exploration of the generation rules of R1CS to improve the algorithm. REFERENCES [1] S. Goldwasser, S. Micali, and C. Rackoff, “The knowledge complexity of interactive proof-systems,” in Providing Sound Foundations for Cryptography: On the Work of Shafi Goldwasser and Silvio Micali, 2019, pp. 203–225. [2] Zcash company, https://z.cash/, 2014. [3] E. B. Sasson, A. Chiesa, C. Garman, et al., “Zerocash: Decentralized anonymous payments from bitcoin,” in 2014 IEEE symposium on security and privacy, IEEE, 2014, pp. 459–474. [4] G. Drevon, J-r1cs – a json lines format for r1cs, 2019. [5] E. Albert, M. Belles-Mu ´ noz, M. Isabel, C. Rodrı ˜ eguez- ´ Nu´nez, and A. Rubio, “Distilling constraints in zero- ˜ knowledge protocols,” in Computer Aided Verification: 34th International Conference, CAV 2022, Haifa, Israel, August 7–10, 2022, Proceedings, Part I, Springer, 2022, pp. 430–443. [6] E. Ben-Sasson, A. Chiesa, M. Riabzev, N. Spooner, M. Virza, and N. P. Ward, “Aurora: Transparent succinct arguments for r1cs,” in Advances in Cryptology– EUROCRYPT 2019: 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Darmstadt, Germany, May 19–23, 2019, Proceedings, Part I 38, Springer, 2019, pp. 103–128. [7] J. Lee, S. Setty, J. Thaler, and R. Wahby, “Lineartime and post-quantum zero-knowledge snarks for r1cs,” Cryptology ePrint Archive, 2021. [8] A. Golovnev, J. Lee, S. Setty, J. Thaler, and R. S. Wahby, “Brakedown: Linear-time and post-quantum snarks for r1cs,” Cryptology ePrint Archive, 2021. [9] Y. Muzi, F. Muyue, B. Gu, et al., Semantic comparison method and device between a kind of source code and binary code, 2019. [10] G. Li, L. Zhongqi, Y. Dongsheng, and Y. Liu, Compiling method from intermediate language (il) program to c language program of instruction list, 2013. [11] Z. Yongsheng, C. Zhiyong, C. Rongtao, and W. Zhili, A kind of assembly language is to the code conversion method of higher level language and device, 2015. [12] E. Ben-Sasson, A. Chiesa, E. Tromer, and M. Virza, “Succinct {non-interactive} zero knowledge for a von neumann architecture,” in 23rd USENIX Security Symposium (USENIX Security 14), 2014, pp. 781–796. [13] V. Buterin, “Quadratic arithmetic programs: From zero to hero,” URl: https://medium. com/@ VitalikButerin/quadratic-arithmetic-programs-fromzero-to-hero-f6d558cea649, 2016. [14] H. Vollmer, Introduction to circuit complexity: a uniform approach. Springer Science & Business Media, 1999. [15] J. Groth, “On the size of pairing-based non-interactive arguments,” in Advances in Cryptology–EUROCRYPT 2016: 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Vienna, Austria, May 8-12, 2016, Proceedings, Part II 35, Springer, 2016, pp. 305–326. [16] J. B. Dennis, “First version of a data flow procedure language,” in Programming Symposium: Proceedings, Colloque sur la Programmation Paris, April 9–11, 1974, Springer, 2005, pp. 362–376. [17] P. C. Treleaven, D. R. Brownbridge, and R. P. Hopkins, “Data-driven and demand-driven computer architecture,” ACM Computing Surveys (CSUR), vol. 14, no. 1, pp. 93–143, 1982. [18] W. Xing and A. Ghorbani, “Weighted pagerank algorithm,” in Proceedings. Second Annual Conference on Communication Networks and Services Research, 2004., IEEE, 2004, pp. 305–314. [19] L. Page, S. Brin, R. Motwani, and T. Winograd, “The pagerank citation ranking: Bring order to the web,” Technical report, stanford University, Tech. Rep., 1998. This paper is under CC BY 4.0 DEED license. available on arxiv

Data-Flow-Based Normalization Generation Algorithm of R1CS: Conclusion & References

This paper is available on arxiv under CC 4.0 license. Authors: (1)Eason Chen, Carnegie Mellon University; (2) Justa Liang, Bucket Protocol; (3) Ray Huang, Bucket Protocol; (4) Pierce Hung, Bucket Protocol; (5) Damien Chen, Bucket Protocol; (6) Ashley Hsu, Bucket Protocol; (7) Konstantinos Chalkias, Mysten Labs; (8) Stefanos Pleros Mysten Labs. TABLE OF LINKS Abstract and Introduction Background Randomness Practice in Blockchain System Development Transaction Fee Comparison Discussion Conclusion and References 7. CONCLUSION This paper explained how to build a fair, verifiable, efficient random raffle on the Sui Network. We investigate a range of smart contract design methodologies for constructing chance-based games through smart contracts, identify their inherent constraints, and propose remedies. Furthermore, we furnish insights drawing from the advantages and limitations of different design choices. Through these insights, we provide valuable guidance to researchers and developers engaged in randomness games using smart contracts. REFERENCES [1] Sam Blackshear, Evan Cheng, David L Dill, Victor Gao, Ben Maurer, Todd Nowacki, Alistair Pott, Shaz Qadeer, Dario Russi Rain, Stephane Sezer, et al. 2019. Move: A language with programmable resources. Libra Assoc (2019), 1. [2] Joseph Bonneau, Jeremy Clark, and Steven Goldfeder. 2015. On bitcoin as a public randomness source. Cryptology ePrint Archive (2015). [3] Joseph Bonneau and Valeria Nikolaenko. 2022. Public Randomness and Randomness Beacons. https://a16zcrypto.com/posts/article/public-randomness-andrandomness-beacons/. (Accessed on 10/10/2023). [4] Chainlink. 2023. Chainlink VRF | Chainlink Documentation. https://docs.chain. link/vrf. (Accessed on 10/07/2023). [5] Kostas Kryptos Chalkias. 2022. Fair Randomness in Decentralized Games. https://docs.google.com/presentation/d/ 1a9wddWhqKM4GXMV1UrhrpaH1sBMUxZWI. 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[11] Ethereum Foundation. 2023. Zero-Knowledge rollups | ethereum.org. https:// ethereum.org/en/developers/docs/scaling/zk-rollups/. (Accessed on 10/09/2023). [12] Sara Gherghelas. 2023. State of the Dapp Industry in Q2 2023. https://dappradar. com/blog/state-of-the-dapp-industry-in-q2-2023. [13] Shafi Goldwasser, Silvio Micali, and Chales Rackoff. 2019. The knowledge complexity of interactive proof-systems. In Providing sound foundations for cryptography: On the work of shafi goldwasser and silvio micali. 203–225. [14] The News Lense. 2023. Dinter’s "Lineage M" Purple Cloth Incident: The fair will fine Gamania 2 million TWD, legislators and the public call for the promotion of the "Gashapon Law" - The News Lens Key Comment Network. https://www. thenewslens.com/article/168188. (Accessed on 10/07/2023). [15] Ralph C Merkle. 1987. A digital signature based on a conventional encryption function. In Conference on the theory and application of cryptographic techniques. Springer, 369–378. [16] Satoshi Nakamoto. 2008. Bitcoin: A peer-to-peer electronic cash system. Decentralized business review (2008). [17] Newzoo. 2023. Newzoo Global Games Market Report 2023 | Free Version. https://newzoo.com/resources/trend-reports/newzoo-global-gamesmarket-report-2023-free-version. (Accessed on 10/07/2023). [18] Rune Kristian Lundedal Nielsen and Pawel Grabarczyk. 2019. Are Loot Boxes Gambling?: Random reward mechanisms in video games. Transactions of the Digital Games Research Association 4 (2019), 171–207. [19] League of Entropy. 2023. Drand - Distributed Randomness Beacon. https: //drand.love. (Accessed on 10/07/2023). [20] League of Entropy. 2023. Specification | Drand - Distributed Randomness Beacon. https://drand.love/docs/specification/. (Accessed on 10/07/2023). [21] Stefanos Pleros and Konstantinos Chalkias. 2023. Time-locked Satoshi Coin Flip. https://github.com/MystenLabs/satoshi-coin-flip. (Accessed on 10/10/2023). [22] Yolan Romailler. 2022. Multi Frequency Support and Timelock Encryption Capabilities are coming in drand! https://drand.love/blog/2022/02/21/multi-frequencysupport-and-timelock-encryption-capabilities/. (Accessed on 10/10/2023). [23] The MystenLabs Team. 2022. The Sui Smart Contracts Platform. https://docs.sui. io/paper/sui.pdf. (Accessed on 10/04/2023). [24] Zhipeng Wang, Stefanos Chaliasos, Kaihua Qin, Liyi Zhou, Lifeng Gao, Pascal Berrang, Benjamin Livshits, and Arthur Gervais. 2023. On how zero-knowledge proof blockchain mixers improve, and worsen user privacy. In Proceedings of the ACM Web Conference 2023. 2022–2032. [25] Zibin Zheng, Shaoan Xie, Hongning Dai, Xiangping Chen, and Huaimin Wang. 2017. An overview of blockchain technology: Architecture, consensus, and future trends. In 2017 IEEE international congress on big data (BigData congress). Ieee, 557–564. This paper is under CC 1.0 license. available on arxiv

Designing Fair and Efficient Blockchain Games: Conclusion and References

185 Stories To Learn About Ai Applications

Verifiable Privacy-Preserving Computing: Conclusion & References

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Shanshan Han & Qifan Zhang, UCI; (2) Wenxuan Wu, Texas A&M University; (3) Baturalp Buyukates, Yuhang Yao & Weizhao Jin, USC; (4) Salman Avestimehr, USC & FedML. Table of Links Abstract and Introduction Problem Setting The Proposed Two-Stages Anomaly Detection Verifiable Anomaly Detection using ZKP Evaluations Related Works Conclusion & References 7 CONCLUSION We present a cutting-edge anomaly detection technique specifically designed for the real-world FL systems. Our approach utilizes an early cross-round check that activates subsequent anomaly detection exclusively in the presence of attacks. When attacks happen, our approach removes anomaly client models efficiently, ensuring that the local models submitted by benign clients remain unaffected. Further, by leveraging ZKPs, participating clients get to verify the integrity of the anomaly detection and removal performed by the server. The practical design and the inherent efficiency of our approach make it well-suited for real-world FL systems. Our plans for future works include extending our approach to asynchronous FL and vertical FL scenarios. REFERENCES T. Aoki. On the stability of the linear transformation in banach spaces. Journal of the Mathematical Society of Japan, 2(1-2):64–66, 1950. E. Bagdasaryan, A. Veit, Y. Hua, D. Estrin, and V. Shmatikov. How to backdoor federated learning. In AISTATS, 2020a. Eugene Bagdasaryan, Andreas Veit, Yiqing Hua, Deborah Estrin, and Vitaly Shmatikov. How to backdoor federated learning. In International Conference on Artificial Intelligence and Statistics, pp. 2938–2948. PMLR, 2020b. Arjun Nitin Bhagoji, Supriyo Chakraborty, Prateek Mittal, and Seraphin Calo. Analyzing federated learning through an adversarial lens. In International Conference on Machine Learning, pp. 634– 643. PMLR, 2019. P. Blanchard, E. M. El Mhamdi, R. Guerraoui, and J. Stainer. Machine learning with adversaries: Byzantine tolerant gradient descent. In NeurIPS, 2017. David Byrd and Antigoni Polychroniadou. Differentially private secure multi-party computation for federated learning in financial applications. In Proceedings of the First ACM International Conference on AI in Finance, pp. 1–9, 2020. Sebastian Caldas, Sai Meher Karthik Duddu, Peter Wu, Tian Li, Jakub Konecnˇ y, H Brendan McMa- ` han, Virginia Smith, and Ameet Talwalkar. Leaf: A benchmark for federated settings. arXiv preprint arXiv:1812.01097, 2018. Xiaoyu Cao and Neil Zhenqiang Gong. Mpaf: Model poisoning attacks to federated learning based on fake clients. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 3396–3404, 2022. Xiaoyu Cao and Neil Zhenqiang Gong. Mpaf: Model poisoning attacks to federated learning based on fake clients. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 3396–3404, 2022. Xiaoyu Cao, Zaixi Zhang, Jinyuan Jia, and Neil Zhenqiang Gong. Flcert: Provably secure federated learning against poisoning attacks. IEEE Transactions on Information Forensics and Security, 17: 3691–3705, 2022. Mingqing Chen, Rajiv Mathews, Tom Ouyang, and Franc¸oise Beaufays. Federated learning of outof-vocabulary words. arXiv preprint arXiv:1903.10635, 2019. Y. Chen, L. Su, and J. Xu. Distributed statistical machine learning in adversarial settings: Byzantine gradient descent. ACM on Measurement and Analysis of Computing Systems, 1(2):1–25, 2017. Alexander Chowdhury, Hasan Kassem, Nicolas Padoy, Renato Umeton, and Alexandros Karargyris. A review of medical federated learning: Applications in oncology and cancer research. In Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain Injuries: 7th International Workshop, BrainLes 2021, Held in Conjunction with MICCAI 2021, Virtual Event, September 27, 2021, Revised Selected Papers, Part I, pp. 3–24. Springer, 2022. M. Fang, X. Cao, J. Jia, and N. Gong. Local model poisoning attacks to Byzantine-robust federated learning. In USENIX Security, 2020. B. Feng, L. Qin, Z. Zhang, Y. Ding, and S. Chu. ZEN: An optimizing compiler for verifiable, zero-knowledge neural network inferences. 2021. Cryptology ePrint Archive. Grant S Fletcher. Clinical epidemiology: the essentials. Lippincott Williams & Wilkins, 2019. R. Freivalds. Probabilistic machines can use less running time. In IFIP Congress, 1977. Shuhao Fu, Chulin Xie, Bo Li, and Qifeng Chen. Attack-resistant federated learning with residualbased reweighting. arXiv preprint arXiv:1912.11464, 2019. Clement Fung, Chris JM Yoon, and Ivan Beschastnikh. The limitations of federated learning in sybil settings. In RAID, pp. 301–316, 2020. S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems. SIAM Jour. on Comp., 18(1):186–208, 1989. J. Groth. On the size of pairing-based non-interactive arguments. In Eurocrypt, 2016. 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Advances in Neural Information Processing Systems, 34:12613–12624, 2021. Ziteng Sun, Peter Kairouz, Ananda Theertha Suresh, and H Brendan McMahan. Can you really backdoor federated learning? arXiv preprint arXiv:1911.07963, 2019. Circom Contributors. Circom zkSNARK ecosystem, 2022. https://github.com/iden3/circom. Vale Tolpegin, Stacey Truex, Mehmet Emre Gursoy, and Ling Liu. Data poisoning attacks against federated learning systems. In European Symposium on Research in Computer Security, pp. 480– 501. Springer, 2020. Richard Tomsett, Kevin Chan, and Supriyo Chakraborty. Model poisoning attacks against distributed machine learning systems. In Artificial Intelligence and Machine Learning for Multi-Domain Operations Applications, volume 11006, pp. 481–489. SPIE, 2019. H. Wang, K. Sreenivasan, S. Rajput, H. Vishwakarma, S. Agarwal, J. Sohn, K. Lee, and D. Papailiopoulos. Attack of the tails: Yes, you really can backdoor federated learning. In NeurIPS, 2020. Jianhua Wang. Pass: Parameters audit-based secure and fair federated learning scheme against free rider. arXiv preprint arXiv:2207.07292, 2022. S. Weisberg. Yeo-Johnson power transformations. 2001. Available at https://www.stat.umn.edu/arc/yjpower.pdf. Cong Xie, Oluwasanmi Koyejo, and Indranil Gupta. SLSGD: Secure and Efficient Distributed Ondevice Machine Learning. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 213–228. Springer, 2020. H. Yang, X. Zhang, M. Fang, and J. Liu. Byzantine-resilient stochastic gradient descent for distributed learning: A Lipschitz-inspired coordinate-wise median approach. In IEEE CDC, 2019. Dong Yin, Yudong Chen, Kannan Ramchandran, and Peter Bartlett. Byzantine-robust distributed learning: Towards optimal statistical rates. In International Conference on Machine Learning, pp. 5650–5659. PMLR, 2018. Zaixi Zhang, Xiaoyu Cao, Jinyuan Jia, and Neil Zhenqiang Gong. Implementation of fldetector. https://github.com/zaixizhang/FLDetector, 2022a. Zaixi Zhang, Xiaoyu Cao, Jinyuan Jia, and Neil Zhenqiang Gong. Fldetector: Defending federated learning against model poisoning attacks via detecting malicious clients. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 2545–2555, 2022b. Zhengming Zhang, Ashwinee Panda, Linyue Song, Yaoqing Yang, Michael W. Mahoney, Joseph Gonzalez, Kannan Ramchandran, and Prateek Mittal. Neurotoxin: Durable backdoors in federated learning. In International Conference on Machine Learning, 2022c. URL https: //api.semanticscholar.org/CorpusID:249889464. A APPENDIX A.1 PROOF OF THE RANGE OF PPV B ZKP IMPLEMENTATION B.1 CHOICE OF THE ZKP SYSTEM In our implementation, we use the Groth16 (Groth, 2016) zkSNARK scheme implemented in the Circom library (Circom Contributors, 2022) for all the computations described above. We chose this ZKP scheme because its construction ensures constant proof size (128 bytes) and constant verification time. Because of this, Groth16 is popular for blockchain application due to small on-chain computation. There are other ZKP schemes based on different construction that can achieve faster prover time (Liu et al., 2021), but the proof size is too big and verification time is not constant, which is a problem if verifier lacks computational power. The construction of a ZKP scheme that is efficient for both prover and verifier is still an open research direction. B.2 SUPPLEMENTARY EXPERIMENTS FOR IMPORTANCE LAYER

Zero-Knowledge-Proof-Based Anomaly Detection: Conclusion & References

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Shanshan Han & Qifan Zhang, UCI; (2) Wenxuan Wu, Texas A&M University; (3) Baturalp Buyukates, Yuhang Yao & Weizhao Jin, USC; (4) Salman Avestimehr, USC & FedML. Table of Links Abstract and Introduction Problem Setting The Proposed Two-Stages Anomaly Detection Verifiable Anomaly Detection using ZKP Evaluations Related Works Conclusion & References 2 PROBLEM SETTING In this section we present our threat model along with some preliminaries that we leverage in the proposed anomaly detection mechanism. 2.1 ADVERSARY MODEL We consider an FL system where some subset of the clients might be malicious, while most of the clients (i.e., more than 50%) are honest. The clients would like to collaboratively train a model, however, malicious clients may conduct attacks to achieve some adversarial goals, including: i) planting a backdoor to misclassify a specific set of samples while minimally impacting the overall performance of the global model, i.e., backdoor attacks (Bagdasaryan et al., 2020b; Wang et al., 2020); ii) altering the local models to prevent the global model from converging, i.e., Byzantine attacks (Chen et al., 2017; Fang et al., 2020); and iii) randomly submitting contrived models without actual training, i.e., free riders (Wang, 2022). Clients are aware that the FL server may take some defensive measures for their submissions to mitigate potential attacks, and they want to verify the integrity of these defensive measures, to ensure correct operation at the server. 2.2 PRELIMINARIES Krum (Blanchard et al., 2017) is a well-known distance-based anomaly detection method in distributed learning that accepts local models that deviate less from the majority based on their pairwise distances. Given that there are f byzantine clients (i.e., malicious clients) among L clients in the FL system, where the server receives L local models as w1, w2, . . . , wL in each training round, Krum selects one of these models, i.e., the one that is the most likely to be benign, as the global model. An optimization of Krum is m-Krum (Blanchard et al., 2017) that selects m local models, instead of one, with the m smallest scores, to compute an average model when aggregating local models. Algorithms for Krum and m-Krum is shown in Algorithm 1. Krum. The three sigma rule is an empirical rule stating that almost all of the population lies within three standard deviations of the mean in normal distributions. Specifically, in normal distributions N (µ, σ), the percentage of values within one, two, and three standard deviations of the mean are 68%, 95%, and 99.7%, respectively. This rule can be widely applied in real-world applications, since normal distributions are consistent with real-world data distributions (Lyon, 2014), and according to the central limit theorem (Rosenblatt, 1956), when aggregating independent random variables, even if the variables are generated by various distributions, the aggregation tends towards a normal distribution. Further, when the data are not normally distributed, we can transform the distribution to a normal distribution (Aoki, 1950; Osborne, 2010; Sakia, 1992; Weisberg, 2001). The three sigma rule has been used in anomaly detection (Han et al., 2019) since data outside two or three standard deviations of the mean take a very limited proportion; see Figure 2. Three Sigma Rule. Zero-Knowledge Proofs (ZKPs)(Goldwasser et al., 1989) is a proof system that allow a prover to convince a verifier that a function on prover’s secret input (witness) is correctly computed. ZKPs ensures three properties: correctness, soundness, and zero-knowledge. Correctness means that if the prover is honest, then the proof they produce should check out (integrity property). Soundness ensures that a cheating prover will not convince verifier with overwhelming probability. Zero-knowledge guarantees that prover’s winess will be not learned by the verifier (privacy). Due to these properties, ZKP has been widely used in machine learning and blockchain applications (Lee et al., 2020; Feng et al., 2021; Liu et al., 2021; Sasson et al., 2014). Zero-knowledge proofs.

Zero-Knowledge-Proof-Based Anomaly Detection: Problem Setting

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Shanshan Han & Qifan Zhang, UCI; (2) Wenxuan Wu, Texas A&M University; (3) Baturalp Buyukates, Yuhang Yao & Weizhao Jin, USC; (4) Salman Avestimehr, USC & FedML. Table of Links Abstract and Introduction Problem Setting The Proposed Two-Stages Anomaly Detection Verifiable Anomaly Detection using ZKP Evaluations Related Works Conclusion & References ABSTRACT Federated learning (FL) systems are vulnerable to malicious clients that submit poisoned local models to achieve their adversarial goals, such as preventing the convergence of the global model or inducing the global model to misclassify some data. Many existing defense mechanisms are impractical in real-world FL systems, as they require prior knowledge of the number of malicious clients or rely on re-weighting or modifying submissions. This is because adversaries typically do not announce their intentions before attacking, and re-weighting might change aggregation results even in the absence of attacks. To address these challenges in real FL systems, this paper introduces a cutting-edge anomaly detection approach with the following features: i) Detecting the occurrence of attacks and performing defense operations only when attacks happen; ii) Upon the occurrence of an attack, further detecting the malicious client models and eliminating them without harming the benign ones; iii) Ensuring honest execution of defense mechanisms at the server by leveraging a zero-knowledge proof mechanism. We validate the superior performance of the proposed approach with extensive experiments. 1 INTRODUCTION Federated Learning (FL) (McMahan et al., 2017a) enables clients to collaboratively train machine learning models without sharing their local data with other parties, maintaining the privacy and security of their local data. Due to its privacy-preserving nature, FL has attracted considerable attention across various domains and has been utilized in numerous areas (Hard et al., 2018; Chen et al., 2019; Ramaswamy et al., 2019; Leroy et al., 2019; Byrd & Polychroniadou, 2020; Chowdhury et al., 2022). However, even though FL does not require sharing raw data with others, its decentralized and collaborative nature inadvertently introduces privacy and security vulnerabilities (Cao & Gong, 2022; Bhagoji et al., 2019; Lam et al., 2021; Jin et al., 2021; Tomsett et al., 2019; Chen et al., 2017; Tolpegin et al., 2020; Kariyappa et al., 2022; Zhang et al., 2022c). Malicious clients in FL systems can harm training by submitting spurious models to disrupt the global model from converging (Fang et al., 2020; Chen et al., 2017), or planting backdoors to induce the global model to perform wrongly for certain samples (Bagdasaryan et al., 2020b;a; Wang et al., 2020). Existing literature on robust learning and mitigation of adversarial behaviors includes Blanchard et al. (2017); Yang et al. (2019); Fung et al. (2020); Pillutla et al. (2022); He et al. (2022); Cao et al. (2022); Karimireddy et al. (2020); Sun et al. (2019); Fu et al. (2019); Ozdayi et al. (2021); Sun et al. (2021), etc. These approaches exhibit shortcomings, making them less suitable for real FL systems. Some of these strategies require prior knowledge about the number of malicious clients within the FL system (Blanchard et al., 2017), even though in practice an adversary would not notify the system before attacking. Also, some of these methods mitigate impacts of potential malicious client submissions by re-weighting the local models (Fung et al., 2020), retaining only several local models that are most likely to be benign while removing others (Blanchard et al., 2017), or modifying the aggregation function (Pillutla et al., 2022). These methods have the potential to unintentionally alter the aggregation results in the absence of deliberate attacks, considering attacks happen infrequently in real-world scenarios. While the defense mechanisms can mitigate the impact of potential attacks, they can inadvertently compromise the result quality when applied to benign cases. Moreover, existing defense mechanisms are deployed at the FL server without any verification procedures to ensure their correct execution. While most of the clients are benign and wish to collaboratively train machine learning models, they can also be skeptic about the server’s reliability due to the execution of the defense mechanisms that modify the original aggregation procedure. Thus, a successful anomaly detection approach should simultaneously satisfy the following: i) It should be able to detect the occurrence of attacks and exclusively handle the cases when attacks happen. ii) If an attack is detected, the strategy must further detect malicious client submissions and accordingly mitigate (or eliminate) their adversarial impacts without harming the benign client models. iii) There should be a robust mechanism to corroborate the honest execution of defense mechanisms. In this work, we propose a novel anomaly detection mechanism that is specifically tailored to address genuine challenges faced by real-world FL systems. Our approach follows a two-stage scheme at the server to filter out malicious client submissions before aggregation. It initiates with a crossround check based on some cache called “reference models” to determine whether any attacks have occurred. In case of attacks, a subsequent cross-client detection is executed to eliminate malicious clients models without harming the benign client models. Meanwhile, the reference models in the cache is renewed. We provide an overview in Figure 1. Our contributions are summarized as follows: Our strategy is equipped with an initial cross-round check to detect the occurrence of potential attacks, ensuring that defensive methods are only activated in response to the presence of attacks, thereby maintaining the sanctity of the process in attack-free scenarios. ) Proactive attack detection. i By coupling the cross-round check with a subsequent crossclient detection, our approach efficiently eliminates malicious client submissions without harming the benign local submissions. ) Enhanced anomaly detection. ii Our method operates effectively without any prerequisites such as data distribution or the number of malicious clients. Such autonomous nature ensures widespread applicability and adaptability of our approach across different FL tasks, regardless of the data distribution and the selection of models. ) Autonomy from prior knowledge. iii Incorporating Zero-Knowledge Proof (ZKP) (Goldwasser et al., 1989) methodologies, our approach guarantees that the elimination of malicious client models is executed correctly, ensuring that clients can place trust in the defense mechanism in the FL system. ) Rigorous verification protocol. iv

A Zero-Knowledge Anomaly Detection Approach for Robust Federated Learning

শক্তিশালী ফেডারেটেড লার্নিংয়ের জন্য একটি শূন্য-জ্ঞান অসঙ্গতি সনাক্তকরণ পদ্ধতি

Ein wissensfreier Anomalieerkennungsansatz für robustes föderiertes Lernen

Un enfoque de detección de anomalías sin conocimiento para un aprendizaje federado sólido

Une approche de détection des anomalies sans connaissance pour un apprentissage fédéré robuste

मजबूत फ़ेडरेटेड लर्निंग के लिए एक शून्य-ज्ञान विसंगति का पता लगाने का दृष्टिकोण

堅牢なフェデレーテッド ラーニングのためのゼロ知識異常検出アプローチ

강력한 연합 학습을 위한 영지식 이상 탐지 접근 방식

Uma abordagem de detecção de anomalias de conhecimento zero para aprendizagem federada robusta

Подход к обнаружению аномалий с нулевым разглашением для надежного федеративного обучения

Güçlü Birleştirilmiş Öğrenme için Sıfır Bilgi Anormallik Tespiti Yaklaşımı

Phương pháp phát hiện bất thường không có kiến thức để học tập liên kết mạnh mẽ

用于鲁棒联邦学习的零知识异常检测方法

This paper is available on arxiv under CC 4.0 license. Authors: (1) Ruta Jawale; (2) Dakshita Khurana. Table of Links Abstract and Introduction Technical Overview Preliminaries Unclonable Non-Interactive Zero-Knowledge in the CRS Model Unclonable NIZK in the Quantum Ramdon Oracle Model Unclonable Signatures of Knowledge References References [Aar09] Scott Aaronson. Quantum copy-protection and quantum money. In Proceedings of the 24th Annual IEEE Conference on Computational Complexity, CCC 2009, Paris, France, 15-18 July 2009, pages 229–242. IEEE Computer Society, 2009. [AC13] Scott Aaronson and Paul F. Christiano. Quantum money from hidden subspaces. Theory Comput., 9:349–401, 2013. [AGKZ20] Ryan Amos, Marios Georgiou, Aggelos Kiayias, and Mark Zhandry. One-shot signatures and applications to hybrid quantum/classical authentication. 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Garay and Roberto De Prisco, editors, Security and Cryptography for Networks, 7th International Conference, SCN 2010, Amalfi, Italy, September 13-15, 2010. Proceedings, volume 6280 of Lecture Notes in Computer Science, pages 454–471. Springer, 2010. [CL06] Melissa Chase and Anna Lysyanskaya. On signatures of knowledge. In Cynthia Dwork, editor, Advances in Cryptology - CRYPTO 2006, 26th Annual International Cryptology Conference, Santa Barbara, California, USA, August 20-24, 2006, Proceedings, volume 4117 of Lecture Notes in Computer Science, pages 78–96. Springer, 2006. [CLLZ21] Andrea Coladangelo, Jiahui Liu, Qipeng Liu, and Mark Zhandry. Hidden cosets and applications to unclonable cryptography. In Tal Malkin and Chris Peikert, editors, Advances in Cryptology - CRYPTO 2021 - 41st Annual International Cryptology Conference, CRYPTO 2021, Virtual Event, August 16-20, 2021, Proceedings, Part I, volume 12825 of Lecture Notes in Computer Science, pages 556–584. Springer, 2021. 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[Por22] Alexander Poremba. Quantum proofs of deletion for learning with errors. Cryptology ePrint Archive, Report 2022/295, 2022. https://ia.cr/2022/295. [PS19] Chris Peikert and Sina Shiehian. Noninteractive zero knowledge for NP from (plain) learning with errors. In Alexandra Boldyreva and Daniele Micciancio, editors, Advances in Cryptology - CRYPTO 2019 - 39th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 18-22, 2019, Proceedings, Part I, volume 11692 of Lecture Notes in Computer Science, pages 89–114. Springer, 2019. [Sah99] Amit Sahai. Non-malleable non-interactive zero knowledge and adaptive chosenciphertext security. In 40th Annual Symposium on Foundations of Computer Science, FOCS ’99, 17-18 October, 1999, New York, NY, USA, pages 543–553. IEEE Computer Society, 1999. [SCO+01] Alfredo De Santis, Giovanni Di Crescenzo, Rafail Ostrovsky, Giuseppe Persiano, and Amit Sahai. Robust non-interactive zero knowledge. In Joe Kilian, editor, Advances in Cryptology - CRYPTO 2001, 21st Annual International Cryptology Conference, Santa Barbara, California, USA, August 19-23, 2001, Proceedings, volume 2139 of Lecture Notes in Computer Science, pages 566–598. Springer, 2001. [SCP00] Alfredo De Santis, Giovanni Di Crescenzo, and Giuseppe Persiano. Necessary and sufficient assumptions for non-iterative zero-knowledge proofs of knowledge for all NP relations. In Ugo Montanari, Jos´e D. P. Rolim, and Emo Welzl, editors, Automata, Languages and Programming, 27th International Colloquium, ICALP 2000, Geneva, Switzerland, July 9-15, 2000, Proceedings, volume 1853 of Lecture Notes in Computer Science, pages 451–462. Springer, 2000. [SP92] Alfredo De Santis and Giuseppe Persiano. Zero-knowledge proofs of knowledge without interaction (extended abstract). In 33rd Annual Symposium on Foundations of Computer Science, Pittsburgh, Pennsylvania, USA, 24-27 October 1992, pages 427–436. IEEE Computer Society, 1992. [Unr14] Dominique Unruh. Revocable quantum timed-release encryption. In Phong Q. Nguyen and Elisabeth Oswald, editors, Advances in Cryptology - EUROCRYPT 2014 - 33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Copenhagen, Denmark, May 11-15, 2014. Proceedings, volume 8441 of Lecture Notes in Computer Science, pages 129–146. Springer, 2014. [Unr17] Dominique Unruh. Post-quantum security of fiat-shamir. In Tsuyoshi Takagi and Thomas Peyrin, editors, Advances in Cryptology - ASIACRYPT 2017 - 23rd International Conference on the Theory and Applications of Cryptology and Information Security, Hong Kong, China, December 3-7, 2017, Proceedings, Part I, volume 10624 of Lecture Notes in Computer Science, pages 65–95. Springer, 2017. [Wie83] Stephen Wiesner. Conjugate coding. SIGACT News, 15(1):78–88, 1983. [Zha19a] Mark Zhandry. How to record quantum queries, and applications to quantum indifferentiability. In Alexandra Boldyreva and Daniele Micciancio, editors, Advances in Cryptology - CRYPTO 2019 - 39th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 18-22, 2019, Proceedings, Part II, volume 11693 of Lecture Notes in Computer Science, pages 239–268. Springer, 2019. [Zha19b] Mark Zhandry. Quantum lightning never strikes the same state twice. In Yuval Ishai and Vincent Rijmen, editors, Advances in Cryptology - EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Darmstadt, Germany, May 19-23, 2019, Proceedings, Part III, volume 11478 of Lecture Notes in Computer Science, pages 408–438. Springer, 2019. A A Reduction Between Unclonability Definitions A.1 In the CRS model For completeness, here we repeat the definitions of unclonability. Definition A.1. (Unclonable Security for Hard Instances). A proof (Setup, Prove,Verify) satisfies unclonable security if for every language L with corresponding relation RL, for every polynomialsized quantum circuit family {Cλ}λ∈N, and for every hard distribution {Xλ,Wλ}λ∈N over RL, there exists a negligible function negl(·) such that for every λ ∈ N, Definition A.2. (1-to-2 Unclonable Extractability) A proof (Setup, Prove,Verify) satisfies unclonable security there exists a QPT extractor E which is an oracle-aided circuit such that for every language L with corresponding relation RL and for every non-uniform polynomial-time quantum adversary A, for every instance-witness pair (x, w) ∈ RL and λ = λ(|x|), such that there is a polynomial p(·) satisfying: there is also a polynomial (·) such that q Any protocol satisfying Definition A.2 also satisfies Definition A.1. Claim A.3. . Suppose there exists a protocol Π = ( ) satisfying Definition A.2. Proof Setup, Prove, Verify Consider the extractor E guaranteed by Definition A.2. Given a sample (x, w) ← (X ,W), we will show that there is a polynomial p ′ (·) such that which suffices to contradict hardness of the distribution (X ,W), as desired. Towards showing that Equation (37) holds, recall by Definition A.2 that for every NP instance-witness pair (x, w) such that there is a polynomial p(·) satisfying: there is also a polynomial (·) such that q This implies that there is a polynomial (·) such that for every (x, w) ∈ S, q This, combined with Equation (36) implies that which proves Equation (37) as desired. A.2 In the QRO model For completeness, here we repeat the definitions of unclonability. Definition A.4. (Unclonable Security for Hard Instances). A proof ( ) satisfies unclonable security with respect to a quantum random oracle O if for every language L with corresponding relation RL, for every polynomial-sized quantum oracle-aided circuit family {Cλ}λ∈N, and for every hard distribution {Xλ,Wλ}λ∈N over RL, there exists a negligible function l(·) such that for every λ ∈ N, Prove, Verify neg Definition A.5. (1-to-2 Unclonable Extractability) A proof ( ) satisfies unclonable security with respect to a quantum random oracle O there exists a QPT extractor E which is an oracle-aided circuit such that for every language L with corresponding relation RL and for every non-uniform polynomial-time quantum adversary A, for every instance-witness pair (x, w) ∈ RL and λ = λ(|x|), such that there is a polynomial p(·) satisfying: Prove, Verify there is also a polynomial (·) such that q Any protocol satisfying Definition A.5 also satisfies Definition A.4. Claim A.6. Suppose there exists a protocol Π = (Prove,Verify) satisfying Definition A.5. Proof. Let S denote the set of instance-witness pairs {(x, w) ∈ (X ,W)} that satisfy First, we claim that Suppose not, then by Equation (41), contradicting Equation (40). Thus, Equation (42) must be true. Consider the extractor E guaranteed by Definition A.5. Given a sample (x, w) ← (X ,W), we will show that there is a polynomial p ′ (·) such that which suffices to contradict hardness of the distribution (X ,W), as desired. Towards showing that Equation (43) holds, recall by Definition A.5 that for every NP instance-witness pair (x, w) such that there is a polynomial p(·) satisfying: there is also a polynomial (·) such that q This along with Equation (40) implies that there is a polynomial (·) such that for every (x, w) ∈ S, q This, combined with Equation (42) implies that which proves Equation (43) as desired.

Unclonable Non-Interactive Zero-Knowledge: References

For the past few years, I've been studying economics. This spring, I focused on Behavioral Economics and Behavioral Design. Both areas have a lot in common with my primary profession, . I've decided to dig deeper into these fields and share the fundamental principles and processes here. I'll also provide resources below for those interested in a more thorough exploration of the subject. Product Management Let's start with definitions: this is a scientific discipline within economics that studies the influence of psychological, cognitive, emotional, and social factors on the economic decisions made by individual persons and institutions, as well as their implications for market prices, returns, and resource allocation. Behavioral Economics: this involves the application of insights from human behavior (derived from Behavioral Economics) to design products, services, systems, or spaces that help people to make better decisions and act in their own best interests. Behavioral Design: Behavioral Economics The traditional schools of economics - that we all studied in schools and universities - are built on the premise that humans make decisions rationally and act in their personal interests (homo economicus). Adam Smith laid the foundation for classical economics in his work “ ” (1776), introducing the idea of the “invisible hand” that regulates the market and promotes societal well-being through individual actions aimed at personal gain. An Inquiry into the Nature and Causes of the Wealth of Nations That's all well and good. But there's a catch. While we all aspire to exercise, read books, buy healthy products, and avoid sugar, Coca-Cola's annual revenue stands at $44.140B, with a growth of 6.82% year-over-year. Unlike the theoretical homo economicus, real people: Process information imperfectly Are emotional Are influenced by context and environment Are short-sighted Are inconsistent Are mentally lazy All of this leads to the Intention — Action Gap: a disparity between intention and action. “I have three main flaws — 1) lack of willpower, 2) irritability, and 3) laziness, which I need to get rid of.” — Leo Tolstoy, 1854 Context Effect Let's now examine how, for example, the Context Effect influences choice and decision-making. The Compromise Effect Options are more often chosen when they give us a compromise among a set of alternatives. A middle-of-the-road choice appears to be a good compromise between options that might be perceived as too extreme. For instance, if a local store sells bicycles priced between $50 and $75, the average buyer who's not looking for a luxury bike will typically choose a $60 bicycle, as it's moderate and matches their expertise level. However, if a $100 bicycle is added to the mix, most average buyers will opt for the more expensive $75 bicycle. This demonstrates the compromise effect on bicycle choice, which aligns with their expectations about average prices. MIT Paper on the Compromise Effect: https://web.mit.edu/bwerner/www/papers/ARationalReconstructionoftheCompromiseEffect-UsingMarketDatatoInferUtilities.pdf The Attractiveness Effect The second contextual effect on consumer behavior claims that one item will enhance the appeal of another one that is similar but superior. By showing that one item surpasses a similar one, the likability and potential purchasing power of the superior item can be increased. SAGE Journal on Attractiveness Effect: https://journals.sagepub.com/doi/10.1509/jmkr.46.1.1 The Similarity Effect The third contextual effect on consumer behavior states that a product will do more damage to the sales of a similar product than to a dissimilar one. When two or more products, that are alike, compete for consumer attention, they will only diminish interest in each other in the market. SAGE Journal on Similarity Effect: https://journals.sagepub.com/doi/10.1509/jmkr.48.4.767 Default Effect The Default Effect explains an agent's tendency to typically accept the default option. A no-action default is the outcome when an individual fails to make a decision. E. Johnson and D. Goldstein (2003), Science. Endogenous Default Effects The likelihood of selecting an option is higher when it is set as the standard or default. For example, different countries have various rules regarding organ donor registration. In those with a donor opt-in policy, all citizens are automatically considered non-donors unless they are registered as such. In countries with an opt-out system, all citizens are automatically deemed donors unless they actively choose to be excluded from the registry. It's argued that this policy difference is the main reason for the huge disparity in donor rates among these nations. Exogenous Default Effects Normative choice (what others do) might unconsciously be adopted as a social default effect. Thus, people are more likely to choose what they perceive as the choice of others, even if they don't view the other person as more competent. People also tend to consider options that require less justification as defaults. For example, the standard procedure in parole hearings is to decline to release inmates (we all want to be the good guys and press the blue button). The Allais paradox The paradox demonstrates the inapplicability of the expected utility maximization theory under real-world conditions of risk and uncertainty. From a mathematical standpoint, the author shows that a real economic agent doesn't maximize expected utility but strives for maximum reliability. Allais, a well-known French economist, conducted a psychological experiment described below and got paradoxical results. Individuals were offered a choice between one decision out of two sets of risky decisions. In the first set, there was situation A, where there was a 100% certainty of winning 1 million francs, and situation B, where there was a 10% chance of winning 5 million francs, an 89% chance of winning 1 million francs, and a 1% chance of winning nothing. Here, X is an unknown amount to the chooser. Let's make a choice too. Which option seems better to you? But which choice would be optimal in reality? Will the result remain the same if the “unknown amount” X changes from zero to 100 million? Most people choose option A. The mathematical expectation for the first option equals: For the second option, it is: Thus, mathematically, option B is more profitable regardless of the value of X. However, people fear the zero outcome in option B and therefore often choose A. Alright, we understand that people make irrational decisions. What next? How can we help ourselves and others narrow this Intention — Action Gap? This is where the practical aspect of behavioral economics comes into play — Behavioral Design. Behavioral Design 4 strategies of Behavioral Design As you can see, we've mentioned Nudging for the first time, but it's worth noting that it's just one of the strategies and not necessarily the dominant one. Who decides what choice is correct in the development of Behavioral Design? The highest authority — the government, non-profit organizations (for example, a cancer-fighting foundation), or expert councils on a specific topic (like the WHO). Social norms and socially acceptable outcomes. The person. White Behavioral Design planning, especially when using Nudging, it's important to remember that we shouldn't change what people want. Instead, we should help them achieve their goals. An alternative to Nudging is the toxic Sludge. The New York Times has a neat test to check it out for yourself. Stages of Behavioral Design At this stage, we study and describe the current behavior of a group of people and identify the target behavior. For example, we are concerned that people are not inclined to save, posing risks for themselves (like not being able to cover emergency medical expenses or future educational expenses for their kids) and contributing to broader economic issues (increased budget for social subsidies, less educated population, etc). The target behavior is for people to save for their children's education and have reserves for emergency expenses. Behavior. We analyze why people act in a particular way. We identify cognitive biases that affect monthly decisions to avoid saving money in deposit accounts. These may be a combination of biases, some of which could include: Obstacles. In this example, we see Cognitive Load (too busy to figure out types of saving accounts), Overconfidence (thinking they will save in the future or earn more soon), and Present Bias (the desire to buy a new phone now outweighs hypothetical future problems). We identify potential tools (Constraints, Monetary Incentives, Information, and Persuasion, Nudging) that could offset the biases identified in the previous stage's research. We end up with a prioritized set of tools for further testing. Prioritizing in Behavioral Design is quite similar to product prioritization. Operational costs of implementation must also be considered, along with: 3. Design. Choosing interventions that address problems at earlier stages of the decision-making process. Reach: Individual choices have less reach than default options, for example. Long-term effectiveness in forming new, better habits. So, in our example, potential tools might include: Simplifying banking products with fewer or no options. One-click online deposit opening. Default saving goals like “Education”, “Retirement”, “Travel” (addressing the Cognitive Load issue). Auto-deductions from each paycheck into a deposit account (addressing Overconfidence and the Present Bias). We test our hypotheses on a subset of the target group. While I won't go into details on how to conduct randomized studies, select test groups, or calculate statistical significance, the goal is to find the most cost-effective combination of tools that lead to the target behavior. Testing. We roll out the chosen strategies to the entire target group and monitor the results. Scaling. Behavioral Design and Product Management We’ve already got an overview of what Behavioral Design entails, and its similarities to the tasks of product management are evident, particularly in stages 2 to 5 (from Obstacles to Scaling). The main differences I see are these: The choice of target behavior in Behavioral Design implies improving the quality of life of research participants (users). In Product Management, it's about generating profit for a commercial organization. Sometimes the objectives align, but more often, they don't. Even services from EdTech / HealthTech, which aim to help people with their habits and motivation, mainly focus on optimizing purchase conversion because retention in these services often doesn't allow for commercial success in the market without Sludging. Professionalism and expertise. Scientists working in Behavioral Design focus on a deep understanding of the problem and finding suitable solutions. In contrast, Product Managers explore market-known options and conduct many tests: quickly and, often, under pressure Courses on Behavioral Economics & Design Courses on Behavioral Design: Motivation & Reward Loops Masterclass — by Behavior Institute Behavioral Design Course — by Irrational Labs Behavioural Science & Gamification for Product Design — MakeIt Masterclass : Courses on Behavioral Economics Behavioral Economics & Psychology in Marketing Behavioural Economics in Action BETA Behavioural insights for public policy (Materials from the courses Behavioral Economics in Action and Designing Nudges were used in this article.) Designing Nudges Useful Impactually Articles: Behavioral Science Reading List — <https://impactually.se/your-essential-behavioral-economics-reading-list/](https://impactually.se/your-essential-behavioral-economics-reading-list/) Where to get started in your organization — <https://impactually.se/where-to-start-nudging-in-your-organization/](https://impactually.se/where-to-start-nudging-in-your-organization/) Don’t trust your gut! Why data is king — <https://impactually.se/dont_trust_your_gut/](https://impactually.se/dont_trust_your_gut/)

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