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Data-Driven Learning of the Generalized Langevin Equation with State-Dependent Memory

Physical Review Letters 2024年第7期133卷 077301-077301页

作者： Pei Ge Zhongqiang Zhang Huan Lei Department of Computational Mathematics Science and Engineering Department of Mathematical Sciences Department of Statistics and Probability

We present a data-driven method to learn stochastic reduced models of complex systems that retain a state-dependent memory beyond the standard generalized Langevin equation with a homogeneous kernel. The constructed model naturally encodes the heterogeneous energy dissipation by jointly learning a set of state features and the non-Markovian coupling among the features. Numerical results demonstrate the limitation of the standard generalized Langevin equation and the essential role of the broadly overlooked state-dependency nature in predicting molecule kinetics related to conformation relaxation and transition.

关键词： Coarse graining Machine learning Multiscale modeling

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Paradoxical roles of inhibitory autapse and excitatory synapse in formation of counterintuitive anticipated synchronization

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Chinese Physics B 2023年第8期32卷 499-509页

作者：丁学利古华光李玉叶贾雁兵 Department of Public Basic Education Fuyang Institute of TechnologyFuyang 236031China School of Aerospace Engineering and Applied Mechanics Tongji UniversityShanghai 200092China College of Mathematics and Computer Science Chifeng UniversityChifeng 024000China School of Mathematics and Statistics Henan University of Science and TechnologyLuoyang 471000China

Different from the common delayed synchronization(DS)in which response appears after stimulation,anticipated synchronization(AS)in unidirectionally coupled neurons denotes a counterintuitive phenomenon in which response of the receiver neuron appears before stimulation of the sender neuron,showing an interesting function of brain to anticipate the *** dynamical mechanism for the AS remains unclear due to complex dynamics of inhibitory and excitatory *** this article,the paradoxical roles of excitatory synapse and inhibitory autapse in the formation of AS are ***,in addition to the common roles such that inhibitory modulation delays and excitatory modulation advances spike,paradoxical roles of excitatory stimulation to delay spike via type-II phase response and of inhibitory autapse to advance spike are obtained in suitable parameter regions,extending the dynamics and functions of the excitatory and inhibitory ***,AS is related to the paradoxical roles of the excitatory and inhibitory modulations,presenting deep understandings to the *** autapse induces spike of the receiver neuron advanced to appear before that of the sender neuron at first,and then excitatory synapse plays a delay role to prevent the spike further advanced,resulting in the AS as the advance and delay effects realize a dynamic ***,inhibitory autapse with strong advance,middle advance,and weak advance and delay effects induce phase drift(spike of the receiver neuron advances continuously),AS,and DS,respectively,presenting comprehensive relationships between AS and other *** results present potential measures to modulate AS related to brain function.

关键词： anticipated synchronization inhibitory autapse excitatory synapse paradoxical firing

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Numerical Procedure for Fractional HBV Infection with Impact of Antibody Immune

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Computers, Materials & Continua 2023年第2期74卷 2575-2588页

作者： Sakda Noinang Zulqurnain Sabir Muhammad Asif Zahoor Raja Soheil Salahshour Wajaree Weera Thongchai Botmart Department of Mathematics Statistics and Computer Faculty of ScienceUbon Ratchathani UniversityUbon Ratchathani34190Thailand Department of Mathematics and Statistics Hazara UniversityMansehra21120Pakistan Future Technology Research Center National Yunlin University of Science and TechnologyDouliouYunlin64002Taiwan Faculty of Engineering and Natural Sciences Bahcesehir UniversityIstanbul34494Turkey Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand

The current investigations are presented to solve the fractional order HBV differential infection system(FO-HBV-DIS)with the response of antibody immune using the optimization based stochastic schemes of the Levenberg-Marquardt backpropagation(LMB)neural networks(NNs),i.e.,*** FO-HBV-DIS with the response of antibody immune is categorized into five dynamics,healthy hepatocytes(H),capsids(D),infected hepatocytes(I),free virus(V)and antibodies(W).The investigations for three different FO variants have been tested numerically to solve the nonlinear *** data magnitudes are implemented 75%for training,10%for certification and 15%for testing to solve the FO-HBV-DIS with the response of antibody *** numerical observations are achieved using the stochastic LMBNNs procedures for soling the FO-HBV-DIS with the response of antibody immune and comparison of the results is presented through the database Adams-Bashforth-Moulton *** authenticate the validity,competence,consistency,capability and exactness of the LMBNNs,the numerical presentations using the mean square error(MSE),error histograms(EHs),state transitions(STs),correlation and regression are accomplished.

关键词： Fractional order HBV differential infection system artificial neural networks nonlinear Levenberg-Marquardt backpropagation Adams-Bashforth-Moulton

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Swarm intelligent computing procedures to solve the novel precautionary measures in the nonlinear HIV system

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Multimedia Tools and Applications 2024年 1-21页

作者： Umar, Muhammad Amin, Fazli Ali, Mohamed R. Department of Mathematics and Statistics Hazara University Mansehra Pakistan Faculty of Engineering and Natural Sciences Istanbul Okan University Istanbul Turkey Al Obour Egypt Basic Engineering Science Department Benha Faculty of Engineering Benha University Benha Egypt

The current investigations present a novel prevention dynamic in the Human immunodeficiency virus (HIV) system, which is one of the deathly, convertible and unsafe viruses that arise almost the entire world. Since there is currently no confirmed remedy or medication, therefore the researchers are motivated to offer a mathematical preventive group in HIV, which makes this system HIPV. This novel category includes the injectable medicine, avoid getting pregnant, safety precautions, and contact frequency. The numerical solutions of the HIPV model are presented by applying the artificial neural networks (ANNs), while the hybridization of global particle swarm optimization (PSO) and local interior-point algorithm (IPA) approaches are used in the optimization process. The correctness of the solver ANNs-PSO-IPA is observed by using the comparison of the results, which are based on proposed and reference Runge–Kutta scheme as well as minor absolute error, while some statistical measures are performed in order to get the reliability of the designed solver. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

关键词： Diseases

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Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

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Chinese Physics B 2022年第10期31卷 331-340页

作者： Li-Ping Zhang Yang Liu Zhou-Chao Wei Hai-Bo Jiang Wei-Peng Lyu Qin-Sheng Bi Faculty of Civil Engineering and Mechanics Jiangsu UniversityZhenjiang 212013China School of Mathematics and Statistics Yancheng Teachers UniversityYancheng 224002China Engineering Department Mathematics and Physical SciencesUniversity of ExeterExeter EX44QFUK School of Mathematics and Physics China University of GeosciencesWuhan 430074China

We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction,bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multistability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially,this work can be used for some real applications in secure communication, such as data and image encryptions.

关键词： two-dimensional maps memristive maps hidden attractors bifurcation analysis extremely hidden multi-stability

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The mathematics of mathematics: Using mathematics and Data Science to Analyze the Mathematical Sciences Community and Enhance Social Justice

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Matematica 2025年第1期4卷 110-125页

作者： Buckmire, Ron Hibdon, Joseph E. Lewis, Drew Ortega, Omayra Pabón, José L. Roca, Rachel Vindas-Meléndez, Andrés R. Mathematics Department Occidental College Los Angeles CA United States Department of Mathematics Northeastern Illinois University Chicago IL United States Independent Mathematician and Education Researcher Palo Alto CA United States Department of Mathematics & Statistics Sonoma State University Rohnert Park CA United States Mathematical Sciences Department New Jersey Institute of Technology Newark NJ United States Department of Computational Mathematics Science and Engineering Michigan State University East Lansing MI United States Department of Mathematics University of California Berkeley CA United States Department of Mathematics Harvey Mudd College Claremont CA United States

We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community. We engage in this project with a focus on including research that highlights, documents, or quantifies inequality that exists in the mathematical sciences, specifically, and STEM (science, technology, engineering, and mathematics) more broadly. We seek to enhance social justice in the mathematics and data science communities by providing numerous examples of the ways in which the mathematical sciences fails to meet standards of equity, equal opportunity, and inclusion. We introduce the term “mathematics of mathematics” for this project, explicitly building upon the growing, interdisciplinary field known as “Science of Science” to interrogate, investigate, and identify the nature of the mathematical sciences itself. We aim to promote, provide, and posit sources of productive collaborations and we invite interested researchers to contribute to this developing body of work. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

关键词： Data science quantitative justice Diversity Inequities Mathematical sciences community Social justice

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Large-Scale Swarm Control in Cluttered Environments 15th

Large-Scale Swarm Control in Cluttered Environments

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15th International Conference on Social Robotics, ICSR 2023

作者： Elsayed, Saber Mabrok, Mohamed School of Systems and Computing University of New South Wales Canberra Australia Mathematics Program Department of Mathematics Statistics and Physics College of Arts and Sciences Qatar University P.O. Box 2713 Doha Qatar

ISBN: (纸本)9789819987146

In the evolving era of social robots, managing a swarm of autonomous agents to perform particular tasks has become essential for numerous industries. The task becomes more challenging for large-scale swarms and complex environments, which have not been fully explored yet. Therefore, this research introduces a methodology incorporating multiple coordinated robotic shepherds to effectively guide large-scale agent swarms in obstacle-laden terrains. The proposed framework commences with deploying an unsupervised machine-learning algorithm to categorise the swarm into clusters. Then, a shepherding algorithm with coordinated robotic shepherds drives the sub-swarms towards the goal. Also, a path planner based on an evolutionary algorithm is proposed to help robotic shepherds move in a way that minimises the dispersion of each sub-swarm and avoids potential hazards and obstructions. The proposed approach is tested on different scenarios, with the results showing a success rate of 100% in guiding swarms with sizes up to 3000 agents. © 2024, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Motion planning

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Influences of double diffusion upon radiative flow of thin film Maxwell fluid through a stretching channel

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Chinese Physics B 2023年第8期32卷 327-335页

作者： Arshad Khan Ishtiaq Ali Musawa Yahya Almusawa Taza Gul Wajdi Alghamdi College of Aeronautical Engineering National University of Sciences and Technology(NUST)Sector H-12Islamabad 44000Pakistan Department of Mathematics and Statistics College of ScienceKing Faisal UniversityAl-Ahsa 31982Saudi Arabia Department of Mathematics Faculty of ScienceJazan UniversityJazanSaudi Arabia Department of Mathematics City University of Science and Information TechnologyPeshawar 25000Pakistan Department of Information Technology Faculty of Computing and Information TechnologyKing Abdulaziz UniversityJeddah 80261Saudi Arabia

This work explores the influence of double diffusion over thermally radiative flow of thin film hybrid nanofluid and irreversibility generation through a stretching *** nanoparticles of silver and alumina have mixed in the Maxwell fluid(base fluid).Magnetic field influence has been employed to channel in normal *** that are going to administer the fluid flow have been converted to dimension-free notations by using appropriate *** analysis method is used for the solution of the resultant *** this investigation it has pointed out that motion of fluid has declined with growth in magnetic effects,thin film thickness,and unsteadiness *** of fluid has grown up with upsurge in Brownian motion,radiation factor,and thermophoresis effects,while it has declined with greater values of thermal Maxwell factor and thickness factor of the thin *** distribution has grown up with higher values of thermophoresis effects and has declined for augmentation in Brownian motion.

关键词： Maxwell fluid flow magnetohydrodynamic(MHD) hybrid nano fluid flow stretching channel double diffusion entropy generation HAM technique

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Advanced SMS Spam Detection using Deep Complex Models and Sine-Cosine Algorithm 14

Advanced SMS Spam Detection using Deep Complex Models and Si...

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14th International Conference on Information and Knowledge Technology, IKT 2023

作者： Rezaei, Sepehr Shams, Mohammadreza Meybodi, Mohsen Alambardar University of Isfahan Faculty of Mathematics and Statistics Department of Applied Mathematics and Computer Science Isfahan Iran University of Isfahan Shahreza Campus Department of Computer Engineering Isfahan Iran

ISBN: (纸本)9798350349412

With the increasing use of mobile phones and messaging services, SMS spam has become a significant issue for users. In this paper, we propose a novel approach1 to tackle this problem by using Sine-Cosine Algorithm (SCA) and Complex Multi-Layer Perceptron (C-MLP). Specifically, we apply the SCA method to reduce the dimensionality of the feature space and CMLP to improve the performance of spam detection. Also, in this paper, we investigate the effectiveness of different classification algorithms, including Support Vector Machines, Random Forests, K-nearest neighbors, Naive Bayes, bagging, and voting approaches. Our experimental results show that the proposed approach achieves high accuracy and outperforms existing methods in terms of both accuracy and F-measure. The proposed approach can be helpful in designing effective SMS spam filters and improving the overall user experience.1All the code used in this research is publicly available on the first author's GitHub repository: https://***/seper-sw/*** © 2023 IEEE.

关键词： Support vector machines

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Asymptotic coefficients and errors for Chebyshev polynomial approximations with weak endpoint singularities: Effects of different bases

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Science China mathematics 2023年第1期66卷 191-220页

作者： Xiaolong Zhang John P.Boyd MOE-LCSM School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China Department of Climate&Space Sciences and Engineering University of MichiganAnn ArborMI 48109USA

When one solves differential equations by a spectral method,it is often convenient to shift from Chebyshev polynomials Tn(x) with coefficients anto modified basis functions that incorporate the boundary *** homogeneous Dirichlet boundary conditions,u(±1)=0,popular choices include the "Chebyshev difference basis" ζn(x)≡Tn+2(x)-Tn(x) with coefficients here denoted by bnand the "quadratic factor basis" Qn(x)≡(1-x2)Tn(x) with coefficients *** u(x) is weakly singular at the boundary,then the coefficients andecrease proportionally to O(A(n)/nκ) for some positive constant κ,where A(n) is a logarithm or a *** prove that the Chebyshev difference coefficients bndecrease more slowly by a factor of 1/n while the quadratic factor coefficients cndecrease more slowly still as O(A(n)/nκ-2).The error for the unconstrained Chebyshev series,truncated at degree n=N,is O(|A(N)|/Nκ) in the interior,but is worse by one power of N in narrow boundary layers near each of the *** having nearly identical error norms in interpolation,the error in the Chebyshev basis is concentrated in boundary layers near both endpoints,whereas the error in the quadratic factor and difference basis sets is nearly uniformly oscillating over the entire interval in ***,for Chebyshev polynomials,the values of their derivatives at the endpoints are O(n2),but only O(n) for the difference ***,we give the asymptotic coefficients and rigorous error estimates of the approximations in these three bases,solved by the least squares *** also find an interesting fact that on the face of it,the aliasing error is regarded as a bad thing;actually,the error norm associated with the downward curving spectral coefficients decreases even faster than the error norm of infinite *** the premise is under the same basis,and when involving different bases,it may not be established yet.

关键词： Chebyshev polynomial interpolation endpoint singularities least squares method

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