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arXiv 2024年

作者： Quan, Chaoyu Wang, Xiaoming Zheng, Pinzhong Zhou, Zhi School of Science and Engineering The Chinese University of Hong Kong Guangdong Shenzhen518172 China Department of Mathematics and Statistics Missouri University of Science and Technology RollaMO65409 United States Department of Mathematics Southern University of Science and Technology Guangdong Shenzhen518055 China Department of Applied Mathematics The Hong Kong Polytechnic University Kowloon Hong Kong

The energy dissipation law and the maximum bound principle are two critical physical properties of the Allen–Cahn equations. While many existing time-stepping methods are known to preserve the energy dissipation law, most apply to a modified form of energy. In this work, we demonstrate that, when the nonlinear term of the Allen–Cahn equation is Lipschitz continuous, a class of arbitrarily high-order exponential time differencing Runge–Kutta (ETDRK) schemes preserve the original energy dissipation property, under a mild step-size constraint. Additionally, we guarantee the Lipschitz condition on the nonlinear term by applying a rescaling post-processing technique, which ensures that the numerical solution unconditionally satisfies the maximum bound principle. Consequently, our proposed schemes maintain both the original energy dissipation law and the maximum bound principle and can achieve arbitrarily high-order accuracy. We also establish an optimal error estimate for the proposed schemes. Some numerical experiments are carried out to verify our theoretical results. Copyright © 2024, The Authors. All rights reserved.

关键词： Energy dissipation

Numerical solution of the Newtonian plane Couette flow with linear dynamic wall slip

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arXiv 2024年

作者： Abou Hasan, Muner M. Ahmed, Ethar A.A. Ghaleb, Ahmed F. Abou-Dina, Moustafa S. Georgiou, Georgios C. School of Mathematics and Data Sciences EAU Dubai United Arab Emirates School of Engineering and Applied Sciences Nile University Giza12588 Egypt Department of Mathematics Faculty of Science Cairo University Giza12613 Egypt Department of Mathematics and Statistics University of Cyprus P.O. Box 20537 Nicosia1678 Cyprus

An efficient numerical approach based on weighted average finite differences is used to solve the Newtonian plane Couette flow with wall slip, obeying a dynamic slip law that generalizes the Navier slip law with the inclusion of a relaxation term. Slip is exhibited only along the fixed plate, and the motion is triggered by the motion of the other plate. Three different cases are considered for the motion of the moving plate, i.e., constant speed, oscillating speed, and a single-period sinusoidal speed. The velocity and the volumetric flow rate are calculated in all cases and comparisons are made with the results of other methods and available results in the literature. The numerical outcomes confirm the damping with time and the lagging effects arising from the Navier and dynamic wall slip conditions and demonstrate the hysteretic behavior of the slip velocity in following the harmonic boundary motion. © 2024, CC BY.

关键词： Hysteresis

HIGH-ORDER BDF CONVOLUTION QUADRATURE FOR STOCHASTIC FRACTIONAL EVOLUTION EQUATIONS DRIVEN BY INTEGRATED ADDITIVE NOISE

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arXiv 2024年

作者： Chen, Minghua Shi, Jiankang Song, Zhen Yan, Yubin Zhou, Zhi School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Lanzhou730000 China Department of Physical Mathematical and Engineering Sciences University of Chester ChesterCH1 4BJ United Kingdom Department of Applied Mathematics The Hong Kong Polytechnic University Kowloon Hong Kong

The numerical analysis of stochastic time fractional evolution equations presents considerable challenges due to the limited regularity of the model caused by the nonlocal operator and the presence of noise. The existing time-stepping methods exhibit a significantly low order convergence rate. In this work, we introduce a smoothing technique and develop the novel high-order schemes for solving the linear stochastic fractional evolution equations driven by integrated additive noise. Our approach involves regularizing the additive noise through an m-fold integral-differential calculus, and discretizing the equation using the k-step BDF convolution quadrature. This novel method, which we refer to as the IDm-BDFk method, is able to achieve higher-order convergence in solving the stochastic models. Our theoretical analysis reveals that the convergence rate of the ID2-BDF2 method is O(τα+γ-1/2) for 1 2) for 5/2 α+γ-1/2) for any α ∈ (1, 2) and γ ∈ (0, 1), if we employ the ID3-BDF3 method. The argument could be easily extended to the subdiffusion model with α ∈ (0, 1). Numerical examples are provided to support and complement the theoretical findings. Copyright © 2024, The Authors. All rights reserved.

关键词： Additive noise

HARMONIC TUTTE POLYNOMIALS OF MATROIDS III

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arXiv 2024年

作者： Britz, Thomas Chakraborty, Himadri Shekhar Miezaki, Tsuyoshi School of Mathematics and Statistics University of New South Wales SydneyNSW2052 Australia Department of Mathematics Shahjalal University of Science and Technology Sylhet3114 Bangladesh Faculty of Science and Engineering Waseda University Tokyo169-8555 Japan

In this paper, we present the harmonic generalizations of well-known polynomials of codes over finite fields, namely the higher weight enumerators and the extended weight enumerators, and we derive the correspondences between these weight enumerators. Moreover, we present the harmonic generalization of Greene’s Theorem for the higher (resp. extended) weight enumerators. As an application of this Greene’s-type theorem, we provide the MacWilliams-type identity for harmonic higher weight enumerators of codes over finite fields. Finally, we use this new identity to give a new proof of the Assmus-Mattson Theorem for subcode supports of linear codes over finite fields using harmonic higher weight enumerators. Copyright © 2024, The Authors. All rights reserved.

关键词： Harmonic functions

Navigating the Fermi Multiverse: Assessing LLMs for Complex Multi-hop Queries 7

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Navigating the Fermi Multiverse: Assessing LLMs for Complex ...

7th Workshop on Natural Language for Artificial Intelligence, NL4AI 2023

作者： Rahgouy, Mostafa Giglou, Hamed Babaei Feng, Dongji Rahgooy, Taher Dozier, Gerry Seals, Cheryl D. Department of Computer Science and Software Engineering Auburn University AuburnAL United States TIB Leibniz Information Centre for Science and Technology Hannover Germany Department of Mathematics Computer Science and Statistics Gustavus Adolphus College MN United States Meta Menlo ParkCA United States

Recently, large language models (LLMs) have gained significant attention in the field of Natural Language Processing (NLP) and have shown promise across various tasks, even when given only a few examples to learn from. However, their ability to understand and reason with natural language remains uncertain. While there have been attempts to evaluate these models using reasoning tests, these evaluations have mostly focused on models' final answers, often overlooking the step-by-step reasoning processes behind their performance. Additionally, these analyses have typically concentrated on just one or a few aspects of reasoning, especially for tasks that do not require much complex thinking to find the answer. This limits our understanding of LLMs' potential and limitations when it comes to more complex and realistic questions. To address this issue, we conduct a comprehensive analysis of LLMs using the existing Fermi reasoning challenge, a task that combines different aspects of reasoning into a single question-answering format, requiring deeper levels of reasoning. In this paper, we examine various advanced LLMs in this reasoning challenge and explore how their performance is affected by their size (i.e., the number of parameters). We also investigate how these models behave with different levels of supervision, ranging from having all the information to no evidence at all. Furthermore, we compare the two primary methods of teaching these LLMs, fine-tuning, and few-shot learning, using the Chain-of-Thought approach. We provide a detailed case study highlighting the most common limitations of these models. While our results imply that these models may have a long journey ahead to reach human-level reasoning, our work can be considered a robust baseline for the community to strive toward achieving this ambitious goal. Our code is available on GitHub https://***/MostafaRahgouy/LLMs_for_FPs for the community. © 2023 Copyright for this paper by its authors.

关键词： Natural language processing systems

A novel collocation method with a coronavirus optimization algorithm for the optimal control of COVID-19: A case study of Wuhan, China

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Computers in Biology and Medicine 2024年 178卷 108680-108680页

作者： Khanduzi, Raheleh Jajarmi, Amin Ebrahimzadeh, Asiyeh Shahini, Mehdi Department of Mathematics and Statistics Gonbad Kavous University P.O. Box 49717-99151 Gonbad Kavous Iran Department of Electrical Engineering University of Bojnord P.O. Box 94531-1339 Bojnord Iran Department of Mathematics Education Farhangian University P.O. Box 14665-889 Tehran Iran

In this study, we develop a numerical optimization approach to address the challenge of optimal control in the spread of COVID-19. We evaluate the impact of various control strategies aimed at reducing the number of exposed and infectious individuals. Our novel approach employs Legendre wavelets, their derivative operational matrix, and a collocation method to transform the COVID-19 transmission optimal control model into a nonlinear programming (NLP) problem. To solve this problem, we employ a coronavirus optimization algorithm (COVIDOA) to determine the optimal control, state variables, and objective value. We investigate three control plans for this highly contagious disease, focusing on individual protection, rapid detection and treatment, detection with delay in treatment, and environmental viral dispersion as time-based control functions. These strategies are applied within an SEIR-type control model specific to COVID-19 in China, designed to mitigate disease spread. Lastly, we analyze the effects of various parameters within the COVID-19 spread model. Our numerical results highlight the significant impact of strategies that minimize the number of exposed and infectious individuals, particularly those related to rapid detection, detection delay, and environmental viral dispersion, in controlling and preventing the transmission of the COVID-19 virus. © 2024 Elsevier Ltd

关键词： Coronavirus

DaISy: diffuser-aided sub-THz imaging system

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Optics Express 2024年第7期32卷 11092-11106页

作者： Shao-Hsuan, W.U. Zhang, Yiyao Chen, Ke Shang-Hua, Yang Institute of Electronics Engineering National Tsing Hua University Hsinchu30013 Taiwan Department of Mathematical Sciences University of Liverpool LiverpoolL69 7ZL United Kingdom Centre for Mathematical Imaging Techniques University of Liverpool LiverpoolL69 7ZL United Kingdom Department of Mathematics and Statistics University of Strathclyde GlasgowG1 1XH United Kingdom Department of Electrical Engineering National Tsing Hua University Hsinchu30013 Taiwan Terahertz Optics and Photonics Center National Tsing Hua University Hsinchu30013 Taiwan

Sub-terahertz (Sub-THz) waves possess exceptional attributes, capable of penetrating non-metallic and non-polarized materials while ensuring bio-safety. However, their practicality in imaging is marred by the emergence of troublesome speckle artifacts, primarily due to diffraction effects caused by wavelengths comparable to object dimensions. In addressing this limitation, we present the Diffuser-aided sub-THz Imaging System (DaISy), which utilizes a diffuser and a focusing lens to convert coherent waves into incoherent counterparts. The cornerstone of our progress lies in a coherence theory-based theoretical framework, pivotal for designing and validating the THz diffuser, and systematically evaluating speckle phenomena. Our experimental results utilizing DaISy reveal substantial improvements in imaging quality and nearly diffraction-limited spatial resolution. Moreover, we demonstrate a tangible application of DaISy in the scenario of security scanning, highlighting the versatile potential of sub-THz waves in miscellaneous fields. © 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement.

关键词： Imaging systems

Convolutional Neural Network Approach for Sentiment Analysis of GoFood Services

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Convolutional Neural Network Approach for Sentiment Analysis...

Computer Sciences, engineering, and Technology Innovation (ICoCSETI), International Conference on

作者： Zaenal Abidin Adzqi Aulia Ryan Randy Suryono Permata Akmal Junaidi Wamiliana Wamiliana Doctoral Program of Mathematics and Natural Sciences Universitas Lampung Bandarlampung Indonesia Faculty of Engineering and Computer Science Universitas Teknokrat Indonesia Bandarlampung Indonesia Department of Computer Science Universitas Lampung Bandarlampung Indonesia Department of Mathematics Universitas Lampung Bandarlampung Indonesia

ISBN: (数字)9798331508616

ISBN: (纸本)9798331508623

In the age of swift digital advancement, social media has emerged as a vital and readily available information source for users. Individuals utilize social media to communicate, articulate thoughts, and disseminate their viewpoints, both textually and visually. Twitter is a social media platform that people extensively utilize to disseminate both favorable and unfavorable information regarding GoFood services. This study intends to apply the Convolutional Neural Network (CNN) algorithm within the GoFood service on Twitter. This research also seeks to assess the accuracy of the CNN algorithm in relation to GoFood services. Employing deep learning techniques, particularly the convolutional neural network algorithm, to analyze Twitter user sentiment can enhance the efficiency, accuracy, and simplicity of classifying answers to GoFood services. The findings indicated that the Convolutional Neural Network technique was effectively employed to classify positive, negative, and neutral feelings. The optimal accuracy rate was attained through preprocessing with Stemming, yielding 51% accuracy for multiclass classification and 72% for binary class classification. The accuracy percentage for classification without stemming was 49% for multiclass classification and 70% for binary classification. This research holds possible consequences for Gojek firms and can serve as evaluative and assessment material for GoFood services, enabling them to implement necessary corrective measures.

关键词： Sentiment analysis Accuracy Social networking (online) Convolution Blogs Text categorization Feature extraction Classification algorithms Convolutional neural networks Testing

Riemannian geometric approach to optimal binocular rotation,pyramid based interpolation and bio-mimetic pan-tilt movement

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Autonomous Intelligent Systems 2021年第1期1卷 13-31页

作者： Bijoy KGhosh Bhagya Athukorallage Department of Mathematics and Statistics Texas Tech UniversityLubbockTexas 79409-1042USA School of Automation Engineering University of Electronic Science and Technology of ChinaChengduSichuan 610054China

Over the past several years,we have been studying the problem of optimally rotating a rigid sphere about its center,where the rotation is actuated by a triplet of external torques acting on the *** control objective is to repeatedly direct a suitable radial vector,called the gaze vector,towards a stationary point target in R^(3).The orientation of the sphere is constrained to lie in a suitable submanifold of SO(3).Historically,the constrained rotational movements were studied by physiologists in the nineteenth century,interested in eye and head *** this paper we revisit the gaze control problem,where two visual sensors,are tasked to simultaneously stare at a point target in the visual *** target position changes discretely and the problem we consider is how to reorient the gaze directions of the sensors,along the optimal pathway of the human eyes,to the new location of the *** is done by first solving an optimal control problem on the human binocular ***,we use these optimal control and show that a pan-tilt system can be controlled to follow the gaze trajectory of the human eye requiring a nonlinear static feedback of the pan and tilt angles and their *** problem formulation uses a new Riemannian geometric description of the orientation *** paper also introduces a new,pyramid based interpolation method,to implement the optimal controller.

关键词： Binocular vision Riemannian geometry Optimal control Pyramid based interpolation Bio-Mimetic Pan-Tilt rotation

ARITHMETIC PROPERTIES OF 2α−REGULAR OVERPARTITION PAIRS

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arXiv 2025年

作者： Hemanthkumar, B. Bharadwaj, H.S. Sumanth Department of Mathematics RV College of Engineering RV Vidyanikethan Post Mysuru Road Karnataka Bengaluru560 059 India Department of Mathematics and Statistics M. S. Ramaiah University of Applied Sciences RTC Campus Peenya Karnataka Bengaluru560 058 India

Recently, several mathematicians have investigated various partition functions with the goal of discovering Ramanujan-type congruences. One such function is B2α (n), which represents the number of 2α−regular overpartition pairs of n. In this context, we establish Ramanujan-type congruences modulo powers of 2 for this function. For instance, we prove that B2α (2α+β+1(n + 1)) ≡ 0 (mod 23β+5) for all n, β ≥ 0, α ∈ *** Codes 05A17, 11P83 (Primary) © 2025, CC BY-NC-ND.

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