Journal of Nonlinear Science最新文献_第8页

An Optimal Control Approach to the Problem of the Longest Self-Supporting Structure 最长自支撑结构问题的最优控制方法

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-02-21 DOI: 10.1007/s00332-023-10011-5

Giacomo Vecchiato, Michele Palladino, Pierangelo Marcati

引用次数: 0

Cortical Divisive Normalization from Wilson–Cowan Neural Dynamics 从威尔逊-考文神经动力学看皮层分裂归一化问题

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-02-15 DOI: 10.1007/s00332-023-10009-z

Jesús Malo, José Juan Esteve-Taboada, Marcelo Bertalmío

{"title":"Cortical Divisive Normalization from Wilson–Cowan Neural Dynamics","authors":"Jesús Malo, José Juan Esteve-Taboada, Marcelo Bertalmío","doi":"10.1007/s00332-023-10009-z","DOIUrl":"https://doi.org/10.1007/s00332-023-10009-z","url":null,"abstract":"Divisive Normalization and the Wilson–Cowan equations are well-known influential models of nonlinear neural interaction (Carandini and Heeger in Nat Rev Neurosci 13(1):51, 2012; Wilson and Cowan in Kybernetik 13(2):55, 1973). However, they have been always treated as different approaches and have not been analytically related yet. In this work, we show that Divisive Normalization can be derived from the Wilson–Cowan dynamics. Specifically, assuming that Divisive Normalization is the steady state of the Wilson–Cowan differential equations, we find that the kernel that controls neural interactions in Divisive Normalization depends on the Wilson–Cowan kernel but also depends on the signal. A standard stability analysis of a Wilson–Cowan model with the parameters obtained from our relation shows that the Divisive Normalization solution is a stable node. This stability suggests the appropriateness of our steady state assumption. The proposed theory provides a mechanistic foundation for the suggestions that have been done on the need of signal-dependent Divisive Normalization in Coen-Cagli et al. (PLoS Comput Biol 8(3):e1002405, 2012). Moreover, this theory explains the modifications that had to be introduced ad hoc in Gaussian kernels of Divisive Normalization in Martinez-Garcia et al. (Front Neurosci 13:8, 2019) to reproduce contrast responses in V1 cortex. Finally, the derived relation implies that the Wilson–Cowan dynamics also reproduce visual masking and subjective image distortion, which up to now had been explained mainly via Divisive Normalization.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139770628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Martingale Solutions in Stochastic Fluid–Structure Interaction 随机流固相互作用中的马丁格尔解

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-02-08 DOI: 10.1007/s00332-023-10012-4

Dominic Breit, Prince Romeo Mensah, Thamsanqa Castern Moyo

引用次数: 0

Applications of Nijenhuis Geometry V: Geodesic Equivalence and Finite-Dimensional Reductions of Integrable Quasilinear Systems 尼延胡斯几何的应用 V：积分准线性系统的测地等效性和有限维还原

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-01-29 DOI: 10.1007/s00332-023-10008-0

Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev

引用次数: 0

On a Chemotactic Host–Pathogen Model: Boundedness, Aggregation, and Segregation 关于趋化性宿主-病原体模型：边界、聚集和隔离

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-01-29 DOI: 10.1007/s00332-023-10010-6

Guodong Liu, Hao Wang, Xiaoyan Zhang

引用次数: 0

Vortex on Surfaces and Brownian Motion in Higher Dimensions: Special Metrics 曲面上的涡旋和高维布朗运动：特殊度量

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-01-28 DOI: 10.1007/s00332-023-10007-1

{"title":"Vortex on Surfaces and Brownian Motion in Higher Dimensions: Special Metrics","authors":"","doi":"10.1007/s00332-023-10007-1","DOIUrl":"https://doi.org/10.1007/s00332-023-10007-1","url":null,"abstract":"<h3>Abstract</h3> A single hydrodynamic vortex on a surface will in general move unless its Riemannian metric is a special “Steady Vortex Metric” (SVM). Metrics of constant curvature are SVM only in surfaces of genus zero and one. In this paper: <ol> <li> I show that K. Okikiolu’s work on the regularization of the spectral zeta function leads to the conclusion that each conformal class of every compact surface with a genus of two or more possesses at least one steady vortex metric (SVM). </li> <li> I apply a probabilistic interpretation of the regularized zeta function for surfaces, as developed by P. G. Doyle and J. Steiner, to extend the concept of SVM to higher dimensions. </li> </ol> The new special metric, which aligns with the Steady Vortex Metric (SVM) in two dimensions, has been termed the “Uniform Drainage Metric” for the following reason: For a compact Riemannian manifold ( M ) , the “narrow escape time” (NET) is defined as the expected time for a Brownian motion starting at a point ( p ) in ( M {setminus } B_epsilon (q) ) to remain within this region before escaping through the small ball ( B_epsilon (q) ) , which is centered at ( q ) with radius ( epsilon ) and acts as the escape window. The manifold is said to possess a uniform drainage metric if, and only if, the spatial average of NET, calculated across a uniformly distributed set of initial points ( p ) , remains invariant regardless of the position of the escape window ( B_epsilon (q) ) , as ( epsilon ) approaches ( 0 ) .","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139583549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions 微磁能量的随机同质化与磁天幕的出现

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-01-23 DOI: 10.1007/s00332-023-10005-3

{"title":"Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions","authors":"","doi":"10.1007/s00332-023-10005-3","DOIUrl":"https://doi.org/10.1007/s00332-023-10005-3","url":null,"abstract":"<h3>Abstract</h3> We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic energy functional with homogeneous coefficients. We provide explicit formulas for the effective magnetic properties of the composite material in terms of homogenization correctors. Additionally, the variational analysis of the two exchange energy terms is performed in the more general setting of functionals defined on manifold-valued maps with Sobolev regularity, in the case in which the target manifold is a bounded, orientable smooth surface with tubular neighborhood of uniform thickness. Eventually, we present an explicit characterization of minimizers of the effective exchange in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s predictions on the emergence of helical structures in composite ferromagnetic materials with stochastic microstructure.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139557863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Statistical Theory of the Angiogenesis Equations 血管生成方程的统计理论

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-01-22 DOI: 10.1007/s00332-023-10006-2

Björn Birnir, Luis Bonilla, Manuel Carretero, Filippo Terragni

引用次数: 0

Analysis of a Stochastic Within-Host Model of Dengue Infection with Immune Response and Ornstein–Uhlenbeck Process 具有免疫反应和 Ornstein-Uhlenbeck 过程的登革热感染随机宿主内模型分析

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-01-02 DOI: 10.1007/s00332-023-10004-4

Qun Liu, Daqing Jiang

引用次数: 0

Pullback Exponential Attractors with Explicit Fractal Dimensions for Non-Autonomous Partial Functional Differential Equations 非自治偏函微分方程的具有显式分形维数的回拉指数吸引子

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-12-30 DOI: 10.1007/s00332-023-10003-5

Wenjie Hu, Tomás Caraballo

{"title":"Pullback Exponential Attractors with Explicit Fractal Dimensions for Non-Autonomous Partial Functional Differential Equations","authors":"Wenjie Hu, Tomás Caraballo","doi":"10.1007/s00332-023-10003-5","DOIUrl":"https://doi.org/10.1007/s00332-023-10003-5","url":null,"abstract":"The aim of this paper is to propose a new method to construct pullback exponential attractors with explicit fractal dimensions for non-autonomous infinite-dimensional dynamical systems in Banach spaces. The approach is established by combining the squeezing properties and the covering of finite subspace of Banach spaces, which generalize the method established for autonomous systems in Hilbert spaces (Eden A, Foias C, Nicolaenko B, and Temam R Exponential attractors for dissipative evolution equations, Wiley, New York, 1994). The method is especially effective for non-autonomous partial functional differential equations for which phase space decomposition based on the exponential dichotomy of the linear part or variation techniques are available for proving squeezing property. The theoretical results are illustrated by applications to several specific non-autonomous partial functional differential equations, including a retarded reaction–diffusion equation, a retarded 2D Navier–Stokes equation and a retarded semilinear wave equation. The constructed exponential attractors possess explicit fractal dimensions which do not depend on the entropy number but only on some inner characteristics of the studied equations including the spectra of the linear part and the Lipschitz constants of the nonlinear terms and hence do not require the smooth embedding between two spaces in the previous work.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139063660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0