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Opinion disparity in hypergraphs with community structure

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arXiv 2023年

作者： Landry, Nicholas W. Restrepo, Juan G. Vermont Complex Systems Center University of Vermont BurlingtonVT United States Department of Mathematics and Statistics University of Vermont BurlingtonVT United States Department of Applied Mathematics University of Colorado at Boulder BoulderCO United States

The division of a social group into subgroups with opposing opinions, which we refer to as opinion disparity, is a prevalent phenomenon in society. This phenomenon has been modeled by including mechanisms such as opinion homophily, bounded confidence interactions, and social reinforcement mechanisms. In this paper we study a complementary mechanism for the formation of opinion disparity based on higher-order interactions, i.e., simultaneous interactions between multiple agents. We present an extension of the planted partition model for uniform hypergraphs as a simple model of community structure and consider the hypergraph SIS model on a hypergraph with two communities where the binary ideology can spread via links (pairwise interactions) and triangles (three-way interactions). We approximate this contagion process with a mean-field model and find that for strong enough community structure, the two communities can hold very different average opinions. We determine the regimes of structural and infectious parameters for which this opinion disparity can exist and find that the existence of these disparities is much more sensitive to the triangle community structure than to the link community structure. We show that the existence and type of opinion disparities are extremely sensitive to differences in the sizes of the two communities. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean field theory

Dynamic Modelling of a Controlled Orthotropic Plate: Analytic and Data-Driven Approaches in the Frequency Domain

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arXiv 2024年

作者： Zuyev, Alexander Pellicano, Francesco Zippo, Antonio Iarriccio, Giovanni Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Department of Engineering "Enzo Ferrari" University of Modena and Reggio Emilia Modena Italy Institute of Applied Mathematics and Mechanics National Academy of Sciences Ukraine

This paper is devoted to the mathematical modelling of a vibrating orthotropic plate equipped with a laminated piezosensor, under the influence of a lumped force actuation. We employ the Kirchhoff plate theory to derive the corresponding partial differential equation, assuming free boundary conditions. Analytical solutions for this boundary value problem are explored in the form of series expansions, using products of Krylov functions. Utilizing Galerkin’s method, this mathematical model is transformed into an infinite-dimensional control system characterized by modal coordinates. The transfer function of such a system is explicitly evaluated in the single-input single-output case. The computation of coefficients for finite-dimensional approximate systems is formalized in an algorithm with an arbitrary number of degrees of freedom. Our numerical study confirms that the modeled input-output behavior shows acceptable agreement over the given frequency *** Codes 74K20, 93C20, 93D25, 65N30 © 2024, CC BY.

关键词： Transfer functions

Harvesting random embedding for high-frequency change-point detection in temporal complex systems

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National Science Review 2022年第4期9卷 92-104页

作者： Jia-Wen Hou Huan-Fei Ma Dake He Jie Sun Qing Nie Wei Lin Research Institute of Intelligent Complex Systems Fudan University Centre for Computational Systems Biology Institute of Science and Technology for Brain-Inspired IntelligenceFudan University School of Mathematical Sciences Soochow University Xinhua Hospital Affiliated to Shanghai Jiao Tong University School of Medicine School of Mathematical Sciences and Shanghai Center for Mathematical Sciences Fudan University Department of Mathematics Department of Developmental and Cell Biologyand NSF-Simons Center for Multiscale Cell Fate ResearchUniversity of California Shanghai Key Laboratory for Contemporary Applied Mathematics LNMS (Fudan University)and LCNBI (Fudan University) State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain ScienceInstitutes of Brain ScienceFudan University

Recent investigations have revealed that dynamics of complex networks and systems are crucially dependent on the temporal structures. Accurate detection of the time instant at which a system changes its internal structures has become a tremendously significant mission, beneficial to fully understanding the underlying mechanisms of evolving systems, and adequately modeling and predicting the dynamics of the systems as well. In real-world applications, due to a lack of prior knowledge on the explicit equations of evolving systems, an open challenge is how to develop a practical and model-free method to achieve the mission based merely on the time-series data recorded from real-world systems. Here, we develop such a model-free approach, named temporal change-point detection(TCD), and integrate both dynamical and statistical methods to address this important challenge in a novel way. The proposed TCD approach, basing on exploitation of spatial information of the observed time series of high dimensions, is able not only to detect the separate change points of the concerned systems without knowing, a priori, any information of the equations of the systems, but also to harvest all the change points emergent in a relatively high-frequency manner, which cannot be directly achieved by using the existing methods and *** effectiveness is comprehensively demonstrated using the data from the representative complex dynamics and real-world systems from biology to geology and even to social science.

关键词： temporal systems time series change-point detection complex dynamical systems

Adaptive-triggered H∞ sliding-mode optimal control for nonlinear input-limited systems

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SSRN

SSRN 2024年

作者： Zhang, Hongxu Wang, Honggui Department of Applied Mathematics Harbin University of Science and Technology Harbin150080 China Heilongjiang Provincial Key Laboratory of Optimization Control and Intelligent Analysis for Complex Systems Harbin University of Science and Technology Harbin150080 China

This paper concentrates on the H∞ sliding mode optimal control (SMOC) problem for nonlinear systems with mismatched inter ference and constrained input. Firstly, an adaptive-triggered strategy with respect to discontinuous control part is employed which can suppress input interference and the separated matched disturbances. Also, the system trajectories are guaranteed to converge to the sliding manifold. Moreover, the adaptive-triggered strategy is optimized to self-triggered strategy with aim to avoid the real-time measurement of triggered conditions, and the minimum time interval is obtained to keep away from Zeno phenomenon. Subsequently, the optimal H∞ control problem of sliding motion turns into a two-person ZS game issue. To derive the solutions of event-trigger HJI equation, an adaptive dynamic programming (ADP) algorithm with critic-only structure is implemented to obtain the optimal control online. Furthermore, by utilizing the Lyapunov technique, the uniformly ultimately bounded (UUB) conditions about system state and the weight estimation error are obtained. At last, simulation outcomes are analyzed to validate the effectiveness of the control strategy. © 2024, The Authors. All rights reserved.

关键词： Sliding mode control

Modified BDF2 schemes for subdiffusion models with a singular source term

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arXiv 2022年

作者： Chen, Minghua Shi, Jiankang Zhou, Zhi School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Lanzhou730000 China Department of Applied Mathematics The Hong Kong Polytechnic University Kowloon Hong Kong

The aim of this paper is to study the time stepping scheme for approximately solving the subdiffusion equation with a weakly singular source term. In this case, many popular time stepping schemes, including the correction of high-order BDF methods, may lose their high-order accuracy. To fill in this gap, in this paper, we develop a novel time stepping scheme, where the source term is regularized by using a k-fold integral-derivative and the equation is discretized by using a modified BDF2 convolution quadrature. We prove that the proposed time stepping scheme is second-order, even if the source term is nonsmooth in time and incompatible with the initial data. Numerical results are presented to support the theoretical results. Copyright © 2022, The Authors. All rights reserved.

关键词： Partial differential equations

A strategy to control synchronized dynamics in swarmalator systems

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arXiv 2024年

作者： Sar, Gourab Kumar Anwar, Md Sayeed Moriamé, Martin Ghosh, Dibakar Carletti, Timoteo Physics and Applied Mathematics Unit Indian Statistical Institute 203 B. T. Road Kolkata700108 India Department of Mathematics Namur Institute for Complex Systems naXys University of Namur 2 rue Grafé NamurB5000 Belgium

Synchronization forms the basis of many coordination phenomena in natural systems, enabling them to function cohesively and support their fundamental operations. However, there are scenarios where synchronization disrupts a system’s proper functioning, necessitating mechanisms to control or suppress it. While several methods exist for controlling synchronization in non-spatially embedded oscillators, to the best of our knowledge no such strategies have been developed for swarmalators (oscillators that simultaneously move in space and synchronize in time). In this work, we address this gap by introducing a novel control strategy based on Hamiltonian control theory to suppress synchronization in a system of swarmalators confined to a one-dimensional space. The numerical investigations we performed, demonstrate that the proposed control strategy effectively suppresses synchronized dynamics within the swarmalator population. We studied the impact of the number of controlled swarmalators as well as the strength of the control term, in its original form and in a simplified one. © 2024, CC BY.

关键词： Synchronization

Wasserstein-1 distance and nonuniform Berry-Esseen bound for a supercritical branching process in a random environment

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arXiv 2023年

作者： Wu, Hao Fan, Xiequan Gao, Zhiqiang Ye, Yinna Center for Applied Mathematics Tianjin University Tianjin300072 China School of Mathematics and Statistics Northeastern University at Qinhuangdao Qinhuangdao066004 China Laboratory of Mathematics and Complex Systems School of Mathematical Sciences Beijing Normal University Beijing100875 China Department of Applied Mathematics School of Mathematics and Physics Xi'an Jiaotong-Liverpool University Suzhou215123 China

Let (Zn)n≥0 be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-1 distance for the process (Zn)n≥0, which completes a result of Grama et al. [Stochastic Process. Appl., 127(4), 1255-1281, 2017]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size Zn are *** Codes 60J80, 60K37, 60F05, 62E20 Copyright © 2023, The Authors. All rights reserved.

关键词： Random processes

Bifurcation Analysis of Incompressible Fluid Flow by a High Order Mesh-Free Indicator with Padé Approximants 15th

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Bifurcation Analysis of Incompressible Fluid Flow by a Hi...

15th International Moroccan Congress of Mechanics, CMM 2022

作者： Rammane, M. Mesmoudi, S. Askour, O. Tri, A. Braikat, B. Damil, N. Laboratory of Materials Signals Systems and Physical Modeling Department of Physics Faculty of Sciences Agadir University Ibn Zohr BP 8106 Agadir80000 Morocco Hassan First University of Settat National School of applied Sciences LISA Laboratory Berrechid26100 Morocco Mathematics Computer Science and Communication Systems Laboratory National School of Applied Sciences of Safi Cadi Ayyad University BP 63 Safi Sidi Bouzid46000 Morocco Laboratory of Mechanics Faculty of Sciences Ain Chock Hassan II University of Casablanca Casablanca Morocco Km 7 Route d’El Jadida Casablanca Morocco Laboratory of Engineering and Materials Faculty of Sciences Ben M’sik Hassan II University of Casablanca B.P 7955 Sidi Othman Casablanca Morocco Central Casablanca Complex Systems and Interactions Research Center Green City Bouskoura27182 Morocco

ISBN: (纸本)9783031469725

In this work, a mesh-free indicator is proposed to detect the bifurcation points of incompressible viscous fluid flow in a 2D sudden expansion. This indicator is mainly based on the high order mesh-free algorithm (HO-MFA) to solve the nonlinear problems obtained from the linear stability analysis. The Padé approximants are then used to improve the validity range of the HO-MFA and to determinate the roots of the indicator. The combination of these mathematical tools allows us to determine the zero of the indicator corresponding to the critical point. The Lyapunov-Schmidt reduction is used to search all the bifurcated branches from the critical point. To show the accuracy of our model, comparisons of the obtained results with those of the literature are made. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Linear stability analysis

Finite-size scaling on the torus with periodic projected entangled-pair states

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Physical Review B 2025年第16期111卷 165124-165124页

作者： Gleb Fedorovich Lukas Devos Jutho Haegeman Laurens Vanderstraeten Frank Verstraete Atsushi Ueda Department of Physics and Astronomy Ghent University Krijgslaan 281 9000 Gent Belgium Center for Nonlinear Phenomena and Complex Systems Université Libre de Bruxelles Belgium Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road Cambridge CB3 0WA United Kingdom

An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e., from L→L+1. The numerical accuracy is comparable to state-of-the-art tensor network methods, while giving access to much more data points, and at a lower computational cost. Combining this contraction routine with the use of automatic differentiation, we arrive at an efficient algorithm for optimizing fully translation-invariant projected entangled-pair states on the torus. Our benchmarks show that this method yields finite-size energy results that are comparable to those from quantum Monte Carlo simulations. When combined with field-theoretical scaling techniques, our approach enables accurate estimates of critical properties for two-dimensional quantum lattice systems.

关键词： Tensors