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A fractional-order model of coronavirus disease 2019 (COVID-19) with governmental action and individual reaction

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A fractional-order model of coronavirus disease 2019 (COVID-...

作者： Danane, Jaouad Hammouch, Zakia Allali, Karam Rashid, Saima Singh, Jagdev Laboratory of Systems Modeling and Analysis for Decision Support National School of Applied Sciences Hassan I University Berrechid Morocco Division of Applied Mathematics Thu Dau Mot University Binh Duong Province Thu Dau Mot Viet Nam Department of Medical Research China Medical University Hospital Taichung Taiwan Département des Sciences École Normale supéieure Moulay Ismail University of Meknés Meknes Morocco Laboratory of Mathematics and Applications Faculty of Sciences and Techniques Mohammedia University Hassan II-Casablanca Mohammedia Morocco Department of Mathematics Government College University Faisalabad Pakistan Department of Mathematics JECRC University Rajasthan Jaipur India Research Group Department of Mathematics Faculty of Sciences King Abdulaziz University Jeddah Saudi Arabia

The deadly coronavirus disease 2019 (COVID-19) has recently affected each corner of the world. Many governments of different countries have imposed strict measures in order to reduce the severity of the infection. In this present paper, we will study a mathematical model describing COVID-19 dynamics taking into account the government action and the individuals reaction. To this end, we will suggest a system of seven fractional deferential equations (FDEs) that describe the interaction between the classical susceptible, exposed, infectious, and removed (SEIR) individuals along with the government action and individual reaction involvement. Both human-to-human and zoonotic transmissions are considered in the model. The well-posedness of the FDEs model is established in terms of existence, positivity, and boundedness. The basic reproduction number (BRN) is found via the new generation matrix method. Different numerical simulations were carried out by taking into account real reported data from Wuhan, China. It was shown that the governmental action and the individuals' risk awareness reduce effectively the infection spread. Moreover, it was established that with the fractional derivative, the infection converges more quickly to its steady state. © 2021 John Wiley & Sons, Ltd.

关键词： COVID-19

NEURAL NETWORKS TRAINED BY WEIGHT PERMUTATION ARE UNIVERSAL APPROXIMATORS

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arXiv 2024年

作者： Cai, Yongqiang Chen, Gaohang Qiao, Zhonghua School of Mathematical Sciences Laboratory of Mathematics and Complex Systems MOE Beijing Normal University Beijing100875 China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong Department of Applied Mathematics Research Institute for Smart Energy The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong

The universal approximation property is fundamental to the success of neural networks, and has traditionally been achieved by training networks without any constraints on their parameters. However, recent experimental research proposed a novel permutation-based training method, which exhibited a desired classification performance without modifying the exact weight values. In this paper, we provide a theoretical guarantee of this permutation training method by proving its ability to guide a ReLU network to approximate one-dimensional continuous functions. Our numerical results further validate this method’s efficiency in regression tasks with various initializations. The notable observations during weight permutation suggest that permutation training can provide an innovative tool for describing network learning *** Codes 41A30, 68T05, 68T07 Copyright © 2024, The Authors. All rights reserved.

关键词： Numerical methods

Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback controller design

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arXiv 2024年

作者： Heiland, Jan Kim, Yongho Werner, Steffen W.R. Department of Mathematics and Natural Sciences Institute of Mathematics Technische Universität Ilmenau Germany Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstraße 1 Magdeburg39106 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

Polytopic autoencoders provide low-dimensional parametrizations of states in a polytope. For nonlinear PDEs, this is readily applied to low-dimensional linear parameter-varying (LPV) approximations as they have been exploited for efficient nonlinear controller design via series expansions of the solution to the state-dependent Riccati equation. In this work, we develop a polytopic autoencoder for control applications and show how it improves on standard linear approaches in view of LPV approximations of nonlinear systems. We discuss how the particular architecture enables exact representation of target states and higher order series expansions of the nonlinear feedback law at little extra computational effort in the online phase and how the linear though high-dimensional and nonstandard Lyapunov equations are efficiently computed during the offline phase. In a numerical study, we illustrate the procedure and how this approach can reliably outperform the standard linear-quadratic regulator *** Codes 34H05, 37N35, 65F45, 76D55, 93B52 Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations

INTERPOLATORY NECESSARY OPTIMALITY CONDITIONS FOR REDUCED-ORDER modeling OF PARAMETRIC LINEAR TIME-INVARIANT systems

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arXiv 2024年

作者： Mlinarić, Petar Benner, Peter Gugercin, Serkan Department of Mathematics Virginia Tech BlacksburgVA24061 United States Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39106 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

Interpolatory necessary optimality conditions for H2-optimal reduced-order modeling of non-parametric linear time-invariant (LTI) systems are known and well-investigated. In this work, using the general framework of L2-optimal reduced-order modeling of parametric stationary problems, we derive interpolatory H2 ⊗ L2-optimality conditions for parametric LTI systems with a general pole-residue form. We then specialize this result to recover known conditions for systems with parameter-independent poles and develop new conditions for a certain class of systems with parameter-dependent poles. Copyright © 2024, The Authors. All rights reserved.

关键词： Poles

Locating Domination Set in Some Subclasses of B_1-Vpg Graphs and B_1-Epg Graphs

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SSRN

SSRN 2025年

作者： Yang, Yu Wang, Cai-Xia Xu, Shou-Jun Gutin, Gregory School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Gansu Lanzhou730000 China Department of Computer Science Royal Holloway University of London United Kingdom School of Mathematical Sciences LPMC Nankai University China

A graph G is a B_k-VPG graph if there exists an integer k such that each vertex corresponds to an orthogonal path in the plane with at most k bends. Two vertices $u$ and v in V(G) are adjacent if and only if the corresponding paths intersect.A graph G is said to be a B_k-EPG graph if there exists an integer k such that G has a string representation on a grid where each vertex corresponds to an orthogonal path (string) with at most $k$ bends. Two vertices u and v in V(G) are adjacent if and only if the corresponding paths share at least one grid *** consider the problems of finding optimal locating dominating sets, open locating dominating sets, and identifying codes of B_{k}-VPG (resp., B_{k}-EPG) graphs. We prove that the decision problems associated with these three notions are NP-complete in grid graphs (a subclass of unit B_{0}-VPG graphs). Secondly, we give an O(k^{2})-approximation algorithm for the dominating set problem on unit B_{k}-VPG graphs, improving the previous O(k^{4})-approximation algorithm of Chakraborty et al. \cite{dsj22}. Moreover, we show that the decision problem of locating dominating set is NP-complete on a subclass of B_{1}-EPG graphs, and we also show that the minimum locating dominating set problem is APX-hard on B_{1}-EPG graphs, ruling out the possibility of a PTAS unless P=***, we give a linear-time labeling algorithm for finding optimal locating dominating sets on the cactus graphs, which are a subclass of B_{1}-EPG graphs. © 2025, The Authors. All rights reserved.

关键词： Approximation algorithms

Quality of Education and Socio-Economic Development: Decision Making Approach for Assessing System Performance 8

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Quality of Education and Socio-Economic Development: Decisio...

8th IEEE International Conference on Problems of Infocommunications, Science and Technology, PIC S and T 2021

作者： Volk, Iurii Artyukhov, Artem Vasylieva, Tetiana Hordiienko, Vita Sumy State University Department of Applied Mathematics And Complex Systems Modeling Sumy Ukraine Sumy State University Department of Marketing Sumy Ukraine Sumy State University Finance And Entrepreneurship Department Sumy Ukraine Sumy State University Oleg Balatskyi Department of Management Sumy Ukraine

ISBN: (纸本)9781665406826

In this paper we propose versatile approach for evaluation of higher education institution performance in the framework of education quality. The model allows both qualitative and quantitative quality indicators to be accounted in the education quality assessment procedure. We develop two-directional testing algorithm for the proposed evaluation system and demonstrate the possibility of its further use in the decision making process. Roles of stakeholders and external factors influencing education quality are assessed via the black-gray-white box approach. © 2021 IEEE.

关键词： Decision making

Entire solutions to the parabolic Monge-Ampère equation with unbounded nonlinear growth in time

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arXiv 2023年

作者： An, Ning Bao, Jiguang Liu, Zixiao School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing100875 China Institute of Applied Mathematics Department of Mathematics Facility of Science Beijing University of Technology Beijing100124 China

MSC Codes 35A01, 35K96, 35B40The Liouville type theorem on the parabolic Monge-Ampère equation −ut det D2u = 1 states that any entire parabolically convex classical solution must be of form −t + |x|2/2 up to a re-scaling and transformation, under additional assumption that partial derivative with respect to time variable ut is strictly negative and bounded. In this paper, we study the case when ut is unbounded, prove an existence result of entire parabolically convex smooth solution and investigate the asymptotic behavior near infinity. Copyright © 2023, The Authors. All rights reserved.

关键词： Nonlinear equations

Existence of entire solutions to the Lagrangian mean curvature equations in supercritical phase

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arXiv 2023年

作者： Liu, Zixiao Wang, Cong Bao, Jiguang School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing100875 China Institute of Applied Mathematics Department of Mathematics Faculty of Science Beijing University of Technology Beijing100124 China

In this paper, we establish the existence and uniqueness theorem of entire solutions to the Lagrangian mean curvature equations with prescribed asymptotic behavior at infinity. The phase functions are assumed to be supercritical and converge to a constant in a certain rate at infinity. The basic idea is to establish uniform estimates for the approximating problems defined on bounded domains and the main ingredient is to construct appropriate subsolutions and supersolutions as barrier functions. We also prove a nonexistence result to show the convergence rate of the phase functions is *** Codes 35A01, 35J60, 35B40 Copyright © 2023, The Authors. All rights reserved.

关键词： Lagrange multipliers

Energy-Efficient and Reliable Deployment Models for Hybrid Underwater Acoustic Sensor Networks with a Mobile Gateway

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哈尔滨工程大学学报(英文版) 2024年第4期23卷 960-983页

作者： Tatiana A.Fedorova Vladimir A.Ryzhov Kirill S.Safronov Nikolay N.Semenov Shaharin A.Sulaiman Department of Applied Mathematics and Mathematical Modeling Saint Petersburg State Marine Technical UniversitySaint Petersburg 190121Russia Department of Marine Information Systems and Technologies Saint Petersburg State Marine Technical UniversitySaint Petersburg 190121Russia Department of Mechanical Engineering Universiti Teknologi PETRONASSeri Iskandar 32610Malaysia

This work proposes an innovative approach to evaluate the functional characteristics of a heterogeneous underwater wireless acoustic sensor network(UWASN)using a stochastic model and the network connectivity *** connectivity criterion is probabilistic and considers inherently distinct groups of parameters:technical parameters that determine the network function at specific levels of the communication stack and physical parameters that describe the environment in the water *** proposed approach enables researchers to evaluate the network characteristics in terms of energy efficiency and reliability while considering specific network and environmental ***,this approach is a simple and convenient tool for analyzing the effectiveness of protocols in various open systems interconnection model *** is possible to assess the potential capabilities of any protocol and include it in the proposed *** work presents the results of modeling the critical characteristics of heterogeneous three-dimensional UWASNs of different scales consisting of stationary sensors and a wave glider as a mobile gateway,using specific protocols as *** alternative routes for the wave glider are considered to optimize the network’s functional *** trajectories of the wave glider’s movement have been determined in terms of ensuring the efficiency and reliability of the hybrid UWASN at various *** the context of the problem,an evaluation of different reference node placement was to ensure message transmission to a mobile *** best location of reference nodes has been found.

关键词： Heterogeneous underwater wireless acoustic sensor network Mobile gateway Wave glider Stochastic connectivity model Probabilistic optimality criteria Network reliability Network energy consumption