European Journal of Applied Mathematics最新文献_第3页

Slow passage through the Busse balloon – predicting steps on the Eckhaus staircase 缓慢通过布塞气球 - 预测埃克豪斯楼梯的台阶

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-04-16 DOI: 10.1017/s0956792524000160

Anna Asch, Montie Avery, Anthony Cortez, Arnd Scheel

引用次数: 0

Consensus-based optimisation with truncated noise 基于共识的优化与截断噪声

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-04-05 DOI: 10.1017/s095679252400007x

Massimo Fornasier, Peter Richtárik, Konstantin Riedl, Lukang Sun

{"title":"Consensus-based optimisation with truncated noise","authors":"Massimo Fornasier, Peter Richtárik, Konstantin Riedl, Lukang Sun","doi":"10.1017/s095679252400007x","DOIUrl":"https://doi.org/10.1017/s095679252400007x","url":null,"abstract":"Consensus-based optimisation (CBO) is a versatile multi-particle metaheuristic optimisation method suitable for performing non-convex and non-smooth global optimisations in high dimensions. It has proven effective in various applications while at the same time being amenable to a theoretical convergence analysis. In this paper, we explore a variant of CBO, which incorporates truncated noise in order to enhance the well-behavedness of the statistics of the law of the dynamics. By introducing this additional truncation in the noise term of the CBO dynamics, we achieve that, in contrast to the original version, higher moments of the law of the particle system can be effectively bounded. As a result, our proposed variant exhibits enhanced convergence performance, allowing in particular for wider flexibility in choosing the noise parameter of the method as we confirm experimentally. By analysing the time evolution of the Wasserstein- $2$ distance between the empirical measure of the interacting particle system and the global minimiser of the objective function, we rigorously prove convergence in expectation of the proposed CBO variant requiring only minimal assumptions on the objective function and on the initialisation. Numerical evidences demonstrate the benefit of truncating the noise in CBO.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140576290","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

A data-driven kinetic model for opinion dynamics with social network contacts – ADDENDUM 数据驱动的社交网络联系人舆论动态模型 - 增补

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-04-02 DOI: 10.1017/s0956792524000159

G. Albi, Elisa Calzola, Giacomo Dimarco

引用次数: 0

Measuring multidimensional heterogeneity in emergent social phenomena 测量新兴社会现象的多维异质性

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-03-25 DOI: 10.1017/s0956792524000081

Giuseppe Toscani

引用次数: 0

Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion 癌症侵袭表型结构游走模型的推导和游走波分析

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-02-27 DOI: 10.1017/s0956792524000056

Tommaso Lorenzi, Fiona R. Macfarlane, Kevin J. Painter

{"title":"Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion","authors":"Tommaso Lorenzi, Fiona R. Macfarlane, Kevin J. Painter","doi":"10.1017/s0956792524000056","DOIUrl":"https://doi.org/10.1017/s0956792524000056","url":null,"abstract":"We formulate haptotaxis models of cancer invasion wherein the infiltrating cancer cells can occupy a spectrum of states in phenotype space, ranging from ‘fully mesenchymal’ to ‘fully epithelial’. The more mesenchymal cells are those that display stronger haptotaxis responses and have greater capacity to modify the extracellular matrix (ECM) through enhanced secretion of matrix-degrading enzymes (MDEs). However, as a trade-off, they have lower proliferative capacity than the more epithelial cells. The framework is multiscale in that we start with an individual-based model that tracks the dynamics of single cells, which is based on a branching random walk over a lattice representing both physical and phenotype space. We formally derive the corresponding continuum model, which takes the form of a coupled system comprising a partial integro-differential equation for the local cell population density function, a partial differential equation for the MDE concentration and an infinite-dimensional ordinary differential equation for the ECM density. Despite the intricacy of the model, we show, through formal asymptotic techniques, that for certain parameter regimes it is possible to carry out a detailed travelling wave analysis and obtain invading fronts with spatial structuring of phenotypes. Precisely, the most mesenchymal cells dominate the leading edge of the invasion wave and the most epithelial (and most proliferative) dominate the rear, representing a bulk tumour population. As such, the model recapitulates similar observations into a front to back structuring of invasion waves into leader-type and follower-type cells, witnessed in an increasing number of experimental studies over recent years.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140002500","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

A data-driven kinetic model for opinion dynamics with social network contacts 数据驱动的社交网络联系人舆论动态模型

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-02-20 DOI: 10.1017/s0956792524000068

Giacomo Albi, Elisa Calzola, Giacomo Dimarco

{"title":"A data-driven kinetic model for opinion dynamics with social network contacts","authors":"Giacomo Albi, Elisa Calzola, Giacomo Dimarco","doi":"10.1017/s0956792524000068","DOIUrl":"https://doi.org/10.1017/s0956792524000068","url":null,"abstract":"Opinion dynamics is an important and very active area of research that delves into the complex processes through which individuals form and modify their opinions within a social context. The ability to comprehend and unravel the mechanisms that drive opinion formation is of great significance for predicting a wide range of social phenomena such as political polarisation, the diffusion of misinformation, the formation of public consensus and the emergence of collective behaviours. In this paper, we aim to contribute to that field by introducing a novel mathematical model that specifically accounts for the influence of social media networks on opinion dynamics. With the rise of platforms such as Twitter, Facebook, and Instagram and many others, social networks have become significant arenas where opinions are shared, discussed and potentially altered. To this aim after an analytical construction of our new model and through incorporation of real-life data from Twitter, we calibrate the model parameters to accurately reflect the dynamics that unfold in social media, showing in particular the role played by the so-called influencers in driving individual opinions towards predetermined directions.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139921894","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

The turnpike property for mean-field optimal control problems 均场优化控制问题的岔道特性

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-02-12 DOI: 10.1017/s0956792524000044

Martin Gugat, Michael Herty, Chiara Segala

引用次数: 0

From NeurODEs to AutoencODEs: A mean-field control framework for width-varying neural networks 从 NeurODEs 到 AutoencODEs：宽度可变神经网络的均场控制框架

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-02-08 DOI: 10.1017/s0956792524000032

Cristina Cipriani, Massimo Fornasier, Alessandro Scagliotti

{"title":"From NeurODEs to AutoencODEs: A mean-field control framework for width-varying neural networks","authors":"Cristina Cipriani, Massimo Fornasier, Alessandro Scagliotti","doi":"10.1017/s0956792524000032","DOIUrl":"https://doi.org/10.1017/s0956792524000032","url":null,"abstract":"The connection between Residual Neural Networks (ResNets) and continuous-time control systems (known as NeurODEs) has led to a mathematical analysis of neural networks, which has provided interesting results of both theoretical and practical significance. However, by construction, NeurODEs have been limited to describing constant-width layers, making them unsuitable for modelling deep learning architectures with layers of variable width. In this paper, we propose a continuous-time Autoencoder, which we call AutoencODE, based on a modification of the controlled field that drives the dynamics. This adaptation enables the extension of the mean-field control framework originally devised for conventional NeurODEs. In this setting, we tackle the case of low Tikhonov regularisation, resulting in potentially non-convex cost landscapes. While the global results obtained for high Tikhonov regularisation may not hold globally, we show that many of them can be recovered in regions where the loss function is locally convex. Inspired by our theoretical findings, we develop a training method tailored to this specific type of Autoencoders with residual connections, and we validate our approach through numerical experiments conducted on various examples.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765980","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

Network-based kinetic models: Emergence of a statistical description of the graph topology 基于网络的动力学模型：图拓扑统计描述的出现

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-02-02 DOI: 10.1017/s0956792524000020

Marco Nurisso, Matteo Raviola, Andrea Tosin

引用次数: 0

The dynamical analysis of a nonlocal predator–prey model with cannibalism 带有食人现象的非局部捕食者-猎物模型的动力学分析

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-01-29 DOI: 10.1017/s0956792524000019

Daifeng Duan, Ben Niu, Junjie Wei, Yuan Yuan

引用次数: 0