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Correction to: On the numerical ranges of matrices in max algebra

Banach Journal of Mathematical Analysis 2024年第1期19卷 1-26页

作者： Thaghizadeh, Davod Zahraei, Moshen Aboutalebi, Narges Haj Peperko, Aljoša Fallat, Shaun Department of Mathematics Ahvaz Branch Islamic Azad University Ahvaz Iran Department of Mathematics Shahrood Branch Islamic Azad University Shahrood Iran Faculty of Mechanical Engineering University of Ljubljana Ljubljana Slovenia Institute of Mathematics Physics and Mechanics Ljubljana Slovenia Department of Mathematics and Statistics University of Regina Saskatchewan Canada

We correct some unfortunate mistakes that appeared in the article D. Thaghizadeh, M. Zahraei, A. Peperko, and N. H. Aboutalebi, On the numerical ranges of matrices in max algebra, Banach J. Math. Anal., 14 (2020), 1773–1792, concerning certain notions of the numerical range in the max algebra setting. Along the way we also include a study of the characteristic max polynomial and correspondingly the max k-spectrum and the k-tropical spectrum. We also pose a related and intriguing open question.

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Variational design of sensory feedback for powerstroke-recovery systems

arXiv

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arXiv 2024年

作者： Yu, Zhuojun Thomas, Peter J. Department of Mathematics Applied Mathematics and Statistics Case Western Reserve University ClevelandOH44106 United States Department of Mathematics Applied Mathematics and Statistics Department of Biology Department of Electrical Control and Systems Engineering Case Western Reserve University ClevelandOH44106 United States

Although the raison d’etre of the brain is the survival of the body, there are relatively few theoretical studies of closed-loop rhythmic motor control systems. In this paper we provide a unified framework, based on variational analysis, for investigating the dual goals of performance and robustness in powerstroke-recovery systems. To demonstrate our variational method, we augment two previously published closed-loop motor control models by equipping each model with a performance measure based on the rate of progress of the system relative to a spatially extended external substrate – such as a long strip of seaweed for a feeding task, or progress relative to the ground for a locomotor task. The sensitivity measure quantifies the ability of the system to maintain performance in response to external perturbations, such as an applied load. Motivated by a search for optimal design principles for feedback control achieving the complementary requirements of efficiency and robustness, we discuss the performance-sensitivity patterns of the systems featuring different sensory feedback architectures. In a paradigmatic half-center oscillator (HCO)-motor system, we observe that the excitation-inhibition property of feedback mechanisms determines the sensitivity pattern while the activation-inactivation property determines the performance pattern. Moreover, we show that the nonlinearity of the sigmoid activation of feedback signals allows the existence of optimal combinations of performance and sensitivity. In a detailed hindlimb locomotor system, we find that a force-dependent feedback can simultaneously optimize both performance and robustness, while length-dependent feedback variations result in significant performance-versus-sensitivity tradeoffs. Thus, this work provides an analytical framework for studying feedback control of oscillations in nonlinear dynamical systems, leading to several insights that have the potential to inform the design of control or rehabilitation sy

关键词： Efficiency

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Explain the Explainer: Interpreting Model-Agnostic Counterfactual Explanations of a Deep Reinforcement Learning Agent

IEEE Transactions on Artificial Intelligence

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IEEE Transactions on Artificial Intelligence 2024年第4期5卷 1443-1457页

作者： Chen, Ziheng Silvestri, Fabrizio Tolomei, Gabriele Wang, Jia Zhu, He Ahn, Hongshik Stony Brook University Department of Applied Mathematics and Statistics Stony BrookNY11794 United States Sapienza University of Rome Department of Computer Engineering The Department of Computer Science Rome00185 Italy Xi'An Jiaotong-Liverpool University Department of Intelligent Science Suzhou215000 China Rutgers University-New Brunswick Department of Computer Science PiscatawayNJ08854 United States

Counterfactual examples (CFs) are one of the most popular methods for attaching post hoc explanations to machine learning models. However, existing CF generation methods either exploit the internals of specific models or depend on each sample's neighborhood;thus, they are hard to generalize for complex models and inefficient for large datasets. This article aims to overcome these limitations and introduces ReLAX, a model-agnostic algorithm to generate optimal counterfactual explanations. Specifically, we formulate the problem of crafting CFs as a sequential decision-making task. We then find the optimal CFs via deep reinforcement learning (DRL) with discrete-continuous hybrid action space. In addition, we develop a distillation algorithm to extract decision rules from the DRL agent's policy in the form of a decision tree to make the process of generating CFs itself interpretable. Extensive experiments conducted on six tabular datasets have shown that ReLAX outperforms existing CF generation baselines, as it produces sparser counterfactuals, is more scalable to complex target models to explain, and generalizes to both the classification and regression tasks. Finally, we show the ability of our method to provide actionable recommendations and distill interpretable policy explanations in two practical real-world use cases. © 2020 IEEE.

关键词： Reinforcement learning

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LATTICE-VALUED BOTTLENECK DUALITY

arXiv

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arXiv 2024年

作者： Ghrist, Robert Gould, Julian Lopez, Miguel Department of Mathematics Department of Electrical & Systems Engineering and Program in Applied Mathematics & Computational Science University of Pennsylvania United States

This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive lattice. For posets, we generalize a bottleneck version of Dilworth’s theorem, again weighted in a distributive lattice. These results are applicable to a wide array of non-numerical network flow problems, as shown. All results, proofs, and applications were created in collaboration with AI language models. An appendix documents their role and *** Codes 06D05, 90C35, 06A07 © 2024, CC BY.

关键词： Combinatorial optimization

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Initial Exploration and Understanding of Parameters for Successful Enterprise Architecture Implementation 11

Initial Exploration and Understanding of Parameters for Succ...

引用

11th International Conference on ICT for Smart Society, ICISS 2024

作者： Khairina, Dyna Marisa Purwanto, Purwanto Nugraheni, Dinar Mutiara Kusumo School of Postgraduate Studies Universitas Diponegoro Program in Information Systems Semarang Indonesia Universitas Diponegoro Faculty of Engineering Department of Chemical Engineering Semarang Indonesia Universitas Diponegoro Faculty of Science and Mathematics Department of Informatics Semarang Indonesia

ISBN: (纸本)9798350389654

This study provides an initial exploration and further understanding of the factors that are parameters in evaluating the success of Enterprise Architecture (EA) implementation. An evaluation process is needed to ensure that the EA project implementation provides effectiveness, efficiency, and feasibility of the EA information system as well as assessing previous project experience to avoid future EA project risks. The research aims to present a Systematic Literature Review based on the stages of identification, screening, eligibility, and inclusion so that 14 main articles are selected for review with strong actual relevance. The study results provide insights and references that can be used to further explore key factors in evaluating the success of EA implementation in the future. It was found that there were ten factors that most influenced the evaluation of the success of EA implementation and it was concluded that two potential factors were the most influential and required further exploration in evaluating the success of EA implementation which could be applied in various sectors/dimensions. This study contributes as an initial reference for overcoming problems in investigating and exploring the factors that influence the success of EA implementation as an effort to assess the success of achieving future organizational goals. © 2024 IEEE.

关键词： Enterprise Architecture Parameters Success Factors Systematic Literature Review

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Computational Modeling of Heat Transfer from a Horizontal Array of Cylinders for Low Reynolds Numbers

Computational Modeling of Heat Transfer from a Horizontal Ar...

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AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2025

作者： Khan, Ovais U. Arshed, G.M. Raza, S.A. Ali, H. Department of Mechanical and Industrial Engineering Texas A and M University KingsvilleTX United States Department of Mechanical Engineering PNG University of Technology Morobe Province Lae411 Papua New Guinea Department of Mathematics and Statistics Wichita State University WichitaKS United States Department of Mechanical Engineering NED University of Engineering and Technology Karachi Pakistan

ISBN: (数字)9781624107238

ISBN: (纸本)9781624107238

A numerical model based on the computational fluid dynamics (CFD) approach was developed to investigate heat transfer from a horizontal row of circular cylinders in a tandem, side-by-side arrangement. The study involved solving momentum and energy equations using the finite volume method, with convective terms discretized using a second-order upwind method and diffusion terms discretized using central differencing. A second-order implicit technique was used to integrate the temporal term. The numerical simulations were run with various values of free stream Reynolds number and dimensionless longitudinal pitch ratio. The numerical results were compared with analytical findings from the literature and found in good agreement for low values of free stream Reynolds number. The maximum percentage error between the average Nusselt number obtained from the numerical and analytical solutions was less than 20% for larger free-stream Reynolds numbers;however, it decreased to less than 2% as the free-stream Reynolds number decreased. The good agreement between the two models at low free-stream Reynolds numbers suggests that the CFD model is valid in this range and can be used to study similar fluid flow and heat transfer problems. The information generated would be useful in the design of more efficient fluid systems involving arrays of cylinders. © 2025, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

关键词： Finite volume method

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ON THE NORMAL COMPLEMENT PROBLEM FOR FINITE GROUP ALGEBRAS OF ABELIAN-BY-CYCLIC GROUPS

arXiv

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arXiv 2025年

作者： Herman, Allen Kaur, Surinder Department of Mathematics and Statistics University of Regina Saskatchewan Canada Department of Mathematics School of Engineering and Sciences SRM University-AP Andhra Pradesh 522502 India

Assume F is a finite field of order pf and q is an odd prime for which pf − 1 = sqm, where m ≥ 1 and (s, q) = 1. In this article, we obtain the order of symmetric and unitary subgroup of the semisimple group algebra F Cq. Further, for the extension G of Cq = hbi by an abelian group A of order pn with CA(b) = {e}, we prove that if m > 1, or (s + 1) ≥ q and 2n ≥ f (q − 1), then G does not have a normal complement in V (F G).MSC Codes 16U60 (Primary) 20C05, 20E45 (Secondary) © 2025, CC BY-NC-ND.

关键词： Algebra

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Generalized Tribonacci Sequence and its Sum Through Third Order Difference Operator

Generalized Tribonacci Sequence and its Sum Through Third Or...

引用

2024 International Conference on Science, engineering and Business for Driving Sustainable Development Goals, SEB4SDG 2024

作者： Rajiniganth, P. Aparna, T. Oluwayemi, M.O. Oyetepo, T. Suresh, K. Dhanalakshmi Srinivasan University School of Engineering and Technology Department of Mathematics Samayapuram621112 India Margaret Lawrence University Department of Mathematics and Statistics Galilee Delta State Nigeria Landmark University SDG4 Quality Education Research Group Kwara State Omu-Aran Nigeria Landmark University Department of Physical Sciences Mathematics Programme Kwara State Omu-Aran Nigeria Federal University of Allied Health Sciences Department of Applied Sciences Enugu400001 Nigeria St. Joseph's College of Enginering Department of Mathematics Tamil Nadu Chennai119 India

ISBN: (数字)9798350358155

ISBN: (纸本)9798350358155

This study presents the generalized third-order difference operator with constant coefficients and inverse, allowing us to construct a sequence similar to the generalized k-Fibonacci sequence. We refer to this sequence as the generalized Tribonacci sequence and prove certain lemmas and theorems regarding its generalized Tribonacci sums. We have included relevant examples validated using MATLAB to demonstrate our primary findings *** Subject classification: 11B37, 11B39, 11B83, 39A70. © 2024 IEEE.

关键词： Inverse problems

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-norm Estimates of the Bergman Projection on the Monomial Polyhedra

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The Journal of Geometric Analysis 2025年第3期35卷 1-47页

作者： Qin, Chuan Wang, Maofa Zhang, Shuo Department of Mathematics School of Electronics and Information Engineering Taizhou University Taizhou China School of Mathematics and Statistics Wuhan University Wuhan China College of Science Tianjin University of Technology Tianjin China

Monomial polyhedra are a class of bounded singular Reinhardt domains defined as sublevel sets of holomorphic monomials. The purpose of this paper is twofold. We first establish an $$L^p$$ -norm estimate for the Bergman projection on the monomial polyhedra $${\mathcal {U}}_{B}$$ , which can be viewed as a complement of the recent work of the $$L^p$$ regularity for the Bergman projection on monomial polyhedra by Bender et al. (Can J Math 74:732–772, 2022). Then, if $${\mathcal {U}}_{B}$$ is a monomial polyhedron associated to the matrix $$B\in {\mathbb {Z}}^{n\times n}$$ satisfying $$\det \,B=1$$ , we obtain a sharp weighted version of $$L^p$$ -norm estimate for the Bergman projection on $${\mathcal {U}}_{B}$$ .

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Three-way trade-off in multi-objective learning: optimization, generalization and conflict-avoidance

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2024年第1期25卷 9153-9205页

作者： Lisha Chen Heshan Fernando Yiming Ying Tianyi Chen Department of Electrical Computer & Systems Engineering Rensselaer Polytechnic Institute School of Mathematics and Statistics University of Sydney NSW Australia

Multi-objective learning (MOL) often arises in machine learning problems when there are multiple data modalities or tasks. One critical challenge in MOL is the potential conflict among different objectives during the optimization process. Recent works have developed various dynamic weighting algorithms for MOL, where the central idea is to find an update direction that avoids conflicts among objectives. Albeit its appealing intuition, empirical studies show that dynamic weighting methods may not outperform static ones. To understand this theory-practice gap, we focus on a stochastic variant of MGDA, the Multi-objective gradient with Double sampling (MoDo), and study the generalization performance and its interplay with optimization through the lens of algorithmic stability in the framework of statistical learning theory. We find that the key rationale behind MGDA--updating along conflict-avoidant direction--may hinder dynamic weighting algorithms from achieving the optimal O(1/√n) population risk, where n is the number of training samples. We further demonstrate the impact of dynamic weights on the three-way trade-off among optimization, generalization, and conflict avoidance unique in MOL. We showcase the generality of our theoretical framework by analyzing other algorithms under the framework. Experiments on various multi-task learning benchmarks are performed to demonstrate the practical applicability. Code is available at https://***/heshandevaka/Trade-Off-MOL.

关键词： multi-objective optimization statistical learning theory algorithm stability Pareto stationarity gradient conflict

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