IF 1.5 3区数学

Journal of Optimization Theory and Applications Pub Date : 2026-01-01 Epub Date: 2025-09-02 DOI: 10.1007/s10957-025-02791-5

Jana Dienstbier, Frauke Liers, Jan Rolfes

{"title":"A Positive Semidefinite Safe Approximation of Multivariate Distributionally Robust Constraints Determined by Simple Functions.","authors":"Jana Dienstbier, Frauke Liers, Jan Rolfes","doi":"10.1007/s10957-025-02791-5","DOIUrl":"https://doi.org/10.1007/s10957-025-02791-5","url":null,"abstract":"Single-level reformulations of (nonconvex) distributionally robust optimization (DRO) problems are often intractable, as they contain semi-infinite dual constraints. Based on such a semi-infinite reformulation, we present a safe approximation that allows for the computation of feasible solutions for DROs that depend on nonconvex multivariate simple functions. Moreover, the approximation allows to address ambiguity sets that can incorporate information on moments as well as confidence sets. The typical strong assumptions on the structure of the underlying constraints, such as convexity in the decisions or concavity in the uncertainty found in the literature were, at least in part, recently overcome in [16]. We start from the duality-based reformulation approach in [16] that can be applied for DRO constraints based on simple functions that are univariate in the uncertainty parameters. We significantly extend their approach to multivariate simple functions, which leads to a considerably wider applicability of the proposed reformulation approach. In order to achieve algorithmic tractability, the presented safe approximation is then realized by a discretized counterpart for the semi-infinite dual constraints. The approximation leads to a computationally tractable mixed-integer positive semidefinite problem for which state-of-the-art software implementations are readily available. The tractable safe approximation provides sufficient conditions for distributional robustness of the original problem, i.e., obtained solutions are provably robust.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"208 1","pages":"1"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12405389/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145001823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The work of Pierre Magal on differential equations, functional analysis and mathematical biology. 皮埃尔·马加尔在微分方程、泛函分析和数学生物学方面的工作。

IF 2.3 4区数学

Journal of Mathematical Biology Pub Date : 2025-10-18 DOI: 10.1007/s00285-025-02273-2

Jacques Demongeot, Thomas Hillen, Shigui Ruan, Glenn Webb

引用次数: 0

Tuning the brain rhythms: How internal coherence influences network entrainment by tACS 调节大脑节奏：内部一致性如何影响网络夹带的tACS

IF 7.8 1区数学

Chaos Solitons & Fractals Pub Date : 2025-10-18 DOI: 10.1016/j.chaos.2025.117421

Saeed Taghavi, Gianluca Susi, Fernando Maestú, Alireza Valizadeh

{"title":"Tuning the brain rhythms: How internal coherence influences network entrainment by tACS","authors":"Saeed Taghavi, Gianluca Susi, Fernando Maestú, Alireza Valizadeh","doi":"10.1016/j.chaos.2025.117421","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.117421","url":null,"abstract":"Transcranial alternating current stimulation (tACS) is a promising tool for modulating brain activity, but its effects depend critically on the ongoing dynamics of the targeted networks. Here, we use a biophysically plausible model of a recurrent excitatory–inhibitory neuronal network to investigate how the endogenous coherence of neural oscillations modulates network response to external periodic inputs. By systematically varying the level of background excitation, we manipulate the synchrony and the amplitude of emergent rhythms. We then apply sinusoidal inputs with varying frequency and intensity to probe neuronal and network-level entrainment. At the single-neuron level, we assess phase locking of the spiking of the individual neurons to the stimulation; at the network level, we analyze the coherence between the population activity and the stimulation signal. Our results reveal increased phase locking in a subset of neurons, which is more pronounced in inhibitory neurons. Crucially, we observe that the Arnold tongue, which refers to the range of frequencies and intensities over which the network entrains to the external drive, broadens significantly when the network’s endogenous coherence is low. These findings suggest that the initial state of brain oscillations plays a key role in determining tACS efficacy, with implications for individualized stimulation protocols.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"160 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Polar partitioning method for the multifractal characterization of complex heterogeneous structures 复杂非均质结构多重分形表征的极性分配方法

IF 7.8 1区数学

Chaos Solitons & Fractals Pub Date : 2025-10-18 DOI: 10.1016/j.chaos.2025.117413

Matthew Woods, Paul Bogdan, Uduak Z. George

{"title":"Polar partitioning method for the multifractal characterization of complex heterogeneous structures","authors":"Matthew Woods, Paul Bogdan, Uduak Z. George","doi":"10.1016/j.chaos.2025.117413","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.117413","url":null,"abstract":"Classical Euclidean geometry effectively characterizes regular-shaped structures but often falls short when attempting to describe the intricate, irregular-shaped objects, commonly found in biological systems. Multifractal spectrum, a hump function, captures the variability of scaling behavior across an object and provides an alternative approach for analyzing complex biological structures. It is increasingly being used to link structural disorganization of biological tissues to the risk for chronic diseases. Therefore, enhancing the accuracy of existing methods for multifractal analysis may further the understanding of diseases. The box counting method which is often used for computing the multifractal spectrum requires partitioning the object in order to compute the multifractal spectrum. This study proposes a polar partitioning method for the multifractal analysis of complex structures embedded in two-dimensional (2D) space. Its performance is compared with existing methods, including radial and rectangular partitioning. The accuracy of multifractal spectrum computed by polar, radial and rectangular partitioning methods was evaluated using theoretically-derived multifractal structures for which the analytical multifractal spectra exist. The results from this study demonstrate that the polar partitioning method greatly outperforms the rectangular and radial partitioning method when analyzing objects with circular support. The radial partitioning method performs well only when analyzing objects whose scaling rate vary solely along the radial direction. This study identifies the most suitable use cases for each partitioning method to minimize errors in the computations. Instead of the rectangular and radial partitioning methods, the polar partitioning method should be used for computing the multifractal spectrum for complex objects with circular support.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"6 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Memristor neurons with symmetric activity on the edge of chaos: Mono-/biphasic complex neuromorphic behaviors 混沌边缘对称活动的忆阻器神经元：单/双相复杂神经形态行为

IF 7.8 1区数学

Chaos Solitons & Fractals Pub Date : 2025-10-18 DOI: 10.1016/j.chaos.2025.117415

Hongyan Zang, Lili Huang, Fei Gao, Tengfei Lei, Yujiao Dong, Guangyi Wang

{"title":"Memristor neurons with symmetric activity on the edge of chaos: Mono-/biphasic complex neuromorphic behaviors","authors":"Hongyan Zang, Lili Huang, Fei Gao, Tengfei Lei, Yujiao Dong, Guangyi Wang","doi":"10.1016/j.chaos.2025.117415","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.117415","url":null,"abstract":"The biphasic action potential represents a crucial neuromorphic behavior of biological neurons. However, most existing memristor-based neurons currently simulate only monophasic action potentials, and the mechanisms underlying biphasic action potential generation remain incompletely understood. To address this gap, this study proposes a novel locally active memristor (LAM) model featuring a symmetric locally active domain (LAD). Theoretical and simulation analyses are conducted to investigate its local activity, edge of chaos (EoC), and small-signal equivalent circuit. Subsequently, using locally active and EoC theories, we theoretically investigated the biphasic neuromorphic dynamics and their underlying mechanism in second-order/third-order memristor-based neuronal circuits. The results demonstrate that neurons operating near the EoC via supercritical/subcritical Hopf bifurcations can generate not only biphasic action potentials but also a wide range of monophasic spike patterns and other neuromorphic behaviors, including periodic spiking, bursting, accommodation, self-sustaining oscillations, and chaotic dynamics of aberrant neuronal firing. Furthermore, EoC theory clarifies the physical origins of these bimodal dynamics: under bidirectional input pulse perturbations, neurons exhibit both bimodal and monomodal behaviors through Hopf bifurcations occurring near the odd-symmetric EoC.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"70 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Flexible Bayesian estimation of elliptical copulas 椭圆轴的柔性贝叶斯估计

IF 2.4 2区数学

Journal of Computational and Graphical Statistics Pub Date : 2025-10-17 DOI: 10.1080/10618600.2025.2573152

Panfeng Liang, Ori Rosen

引用次数: 0

Generation of Virtual Populations for Quantitative Systems Pharmacology Through Advanced Sampling Methods. 通过先进的采样方法为定量系统药理学生成虚拟种群。

IF 2.2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-10-17 DOI: 10.1007/s11538-025-01532-z

Miriam Schirru, Tristan Brier, Maxime Petit, Didier Zugaj, Pierre-Olivier Tremblay, Fahima Nekka

{"title":"Generation of Virtual Populations for Quantitative Systems Pharmacology Through Advanced Sampling Methods.","authors":"Miriam Schirru, Tristan Brier, Maxime Petit, Didier Zugaj, Pierre-Olivier Tremblay, Fahima Nekka","doi":"10.1007/s11538-025-01532-z","DOIUrl":"https://doi.org/10.1007/s11538-025-01532-z","url":null,"abstract":"Virtual population (Vpop) generation is a central component of quantitative systems pharmacology (QSP), involving the sampling of parameter sets that represent physiologically plausible patients (PPs) and capture observed inter-individual variability in clinical outcomes. This approach poses challenges due to the high dimensionality and often non-identifiability nature of many QSP models. In this study, we evaluate the performance of the DREAM(ZS) algorithm, a multi-chain adaptive Markov chain Monte Carlo (MCMC) method for generating Vpop. Using the Van De Pas model of cholesterol metabolism as a case study, we compare DREAM(ZS) to the single-chain Metropolis-Hastings (MH) algorithm adopted by Rieger et al. Our comparison focuses on convergence behavior, parametric diversity, and posterior coverage, in relation to the ability of each method to explore complex parameter distributions and maintain outcomes correlations. DREAM(ZS) demonstrates superior exploration of the parameter space, reducing boundary accumulation effects common in traditional MH sampling, and restoring parameter correlation structures. These advantages are attributed in part to its adaptive proposal mechanism and the use of a bias-corrected likelihood formulation, which together contribute to a better parameters space sampling without compromising model fit. Our findings contribute to the ongoing development of efficient sampling methodologies for high-dimensional biological models, introducing a promising and easy to use alternative for Vpop generation in QSP, expanding the methodological approaches for in silico trial simulation.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 11","pages":"165"},"PeriodicalIF":2.2,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145312197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Fast marching to branching morphologies 快速进入分支形态

IF 7.8 1区数学

Chaos Solitons & Fractals Pub Date : 2025-10-17 DOI: 10.1016/j.chaos.2025.117388

Anna Kriuchechnikova, Alisa Tiaglik, Tatiana Levdik, Alexey Brazhe

{"title":"Fast marching to branching morphologies","authors":"Anna Kriuchechnikova, Alisa Tiaglik, Tatiana Levdik, Alexey Brazhe","doi":"10.1016/j.chaos.2025.117388","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.117388","url":null,"abstract":"Tree-like branching patterns are pervasive in nature. How branching morphology results from functional demand and in turn how space and physiological constraints shape branching patterns remains largely unclear. Applications in computational biology and biomimetics require tools to generate branching morphologies across a wide range of features. Here we propose a simple computational method to build diverse branching structures. Our method builds branches as converging gradient-descent paths in some convex potential surface. This can be regarded as growing tip instability in “reverse time”: merging points of converging gradient descent paths correspond to tip splitting for divergent branches growing from the root. In our case the potential surface is modeled as a travel-time map of a wavefront propagating from some source manifold and computed with the fast-marching algorithm over a stochastic speed field. The algorithm includes a feedback mechanism where previously built structures affect the speed field and potential minima. The speed is enhanced along the branches and the update of wave sources changes the potential minima the paths converge to. We examine how different parameters, including the speed field properties, feedback rules, the density and sampling order of seed points, affect both the resulting shapes and their transport efficiency. The main utility of the algorithm is in its simplicity and the ability to generate realistic individual 2D and 3D branching structures, as well as tiling networks similar to those formed by astrocytes in the brain.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"99 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Uniqueness, regularity, and characteristic flow for a non strictly convex singular variational problem 一类非严格凸奇异变分问题的唯一性、规律性和特征流

IF 3 1区数学

Communications on Pure and Applied Mathematics Pub Date : 2025-10-17 DOI: 10.1002/cpa.70015

Jean‐François Babadjian, Gilles A. Francfort

{"title":"Uniqueness, regularity, and characteristic flow for a non strictly convex singular variational problem","authors":"Jean‐François Babadjian, Gilles A. Francfort","doi":"10.1002/cpa.70015","DOIUrl":"https://doi.org/10.1002/cpa.70015","url":null,"abstract":"This work addresses the question of uniqueness and regularity of the minimizers of a convex but not strictly convex integral functional with linear growth in a two‐dimensional setting. The integrand – whose precise form derives directly from the theory of perfect plasticity – behaves quadratically close to the origin and grows linearly once a specific threshold is reached. Thus, in contrast with the only existing literature on uniqueness for functionals with linear growth, that is that which pertains to the generalized least gradient, the integrand is not a norm. We make use of hyperbolic conservation laws hidden in the structure of the problem to tackle uniqueness. Our argument strongly relies on the regularity of a vector field – the Cauchy stress in the terminology of perfect plasticity – which allows us to define characteristic lines and then to employ the method of characteristics. Using the detailed structure of the characteristic landscape evidenced in our preliminary study [5], we show that this vector field is actually continuous, save for possibly two points. The different behaviors of the energy density at zero and at infinity imply an inequality constraint on the Cauchy stress. Under a barrier type convexity assumption on the set where the inequality constraint is saturated, we show that uniqueness holds for pure Dirichlet boundary data devoid of any regularity properties, a stronger result than that of uniqueness for a given trace on the whole boundary since our minimizers can fail to attain the boundary data. We also show a partial regularity result for the minimizer.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"25 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145306023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Cooperative effects in feature importance of individual patterns: Application to air pollutants and Alzheimer’s disease 个体模式特征重要性的协同效应：在空气污染物和阿尔茨海默病中的应用

IF 7.8 1区数学

Chaos Solitons & Fractals Pub Date : 2025-10-16 DOI: 10.1016/j.chaos.2025.117425

M. Ontivero-Ortega, A. Fania, A. Lacalamita, R. Bellotti, A. Monaco, S. Stramaglia

{"title":"Cooperative effects in feature importance of individual patterns: Application to air pollutants and Alzheimer’s disease","authors":"M. Ontivero-Ortega, A. Fania, A. Lacalamita, R. Bellotti, A. Monaco, S. Stramaglia","doi":"10.1016/j.chaos.2025.117425","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.117425","url":null,"abstract":"Leveraging recent advances in the analysis of synergy and redundancy in systems of random variables, an adaptive version of the widely used metric Leave One Covariate Out (LOCO) has been recently proposed to quantify cooperative effects in feature importance (Hi-Fi), a key technique in explainable artificial intelligence (XAI), so as to disentangle high-order effects involving a particular input feature in regression problems. Differently from standard feature importance tools, where a single score measures the relevance of each feature, each feature is here characterized by three scores, a two-body (unique) score and higher-order scores (redundant and synergistic). This paper presents a framework to assign those three scores (unique, redundant, and synergistic) to each individual pattern of the data set, while comparing it with the well-known measure of feature importance named <ce:italic>Shapley effect</ce:italic>. To illustrate the potential of the proposed framework, we focus on a One-Health application: the relation between air pollutants and Alzheimer’s disease mortality rate. Our main result is the synergistic association between features related to <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math> and <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">NO</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> with mortality, especially in the provinces of Bergamo and Brescia; notably also the density of urban green areas displays synergistic influence with pollutants for the prediction of AD mortality. Our results place local Hi-Fi as a promising tool of wide applicability, which opens new perspectives for XAI as well as to analyze high-order relationships in complex systems.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"40 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

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