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

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":"24 1","pages":""},"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":"19 1","pages":""},"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":"49 1","pages":""},"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

Associations between anti-mitochondrial antibodies and cardiac involvement in idiopathic inflammatory myopathy patients : A systematic review and meta-analysis. 特发性炎症性肌病患者抗线粒体抗体与心脏受累之间的关系：系统回顾和荟萃分析。

4区数学

European Journal of Applied Mathematics Pub Date : 2024-02-01 Epub Date: 2022-05-16 DOI: 10.1007/s00393-022-01216-2

Hui Wang, Yuan Zhu, Jingjing Hu, Jieni Jin, Jun Lu, Cong Shen, Zhaobin Cai

{"title":"Associations between anti-mitochondrial antibodies and cardiac involvement in idiopathic inflammatory myopathy patients : A systematic review and meta-analysis.","authors":"Hui Wang, Yuan Zhu, Jingjing Hu, Jieni Jin, Jun Lu, Cong Shen, Zhaobin Cai","doi":"10.1007/s00393-022-01216-2","DOIUrl":"10.1007/s00393-022-01216-2","url":null,"abstract":"Objective: The objectives of this study are to analyze the association between anti-mitochondrial antibody (AMA) and cardiac involvement in idiopathic inflammatory myopathy (IIM) and to evaluate the diagnostic value of AMA for cardiac involvement in IIM patients.Methods: We conducted a comprehensive search in PubMed, Web of Science, EMBASE, and the Cochrane Library to identify English-language studies published before November 19, 2021. Stata 12.0 software (Stata Corp., College Station, TX, USA) was used for the statistical analyses. We used the sensitivity, specificity, positive likelihood ratio (PLR), negative likelihood ratio (NLR), and summary receiver operating characteristic (SROC) curve to evaluate the diagnostic value of AMA for cardiac involvement in IIM patients. Statistical heterogeneity of studies was assessed using the I2 statistic with 95% confidence intervals (95% CIs).Results: Seven studies were included in the final analyses, with a total of 2308 IIM patients (including 171 AMA-positive and 2137 AMA-negative patients). The pooled sensitivity of AMA for cardiac involvement in IIM patients was 0.29 (95% CI: 0.19-0.43) and specificity was 0.92 (95% CI: 0.88-0.96). The pooled PLR was 3.9 (95% CI: 2.82-5.38), NLR was 0.76 (95% CI: 0.66-0.88), and the diagnostic odds ratio (DOR) was 5 (95% CI: 3-7). The area under the SROC curve was 0.76 (95% CI: 0.72-0.79).Conclusion: The overall diagnostic value of AMA may not be very high for cardiac involvement in IIM patients.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"12 1","pages":"214-221"},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78840237","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 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

Global dynamics and spatiotemporal heterogeneity of a preytaxis model with prey-induced acceleration 具有猎物诱导加速度的猎物大同模式的全局动力学和时空异质性

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-01-26 DOI: 10.1017/s0956792523000347

Chunlai Mu, Weirun Tao, Zhi-An Wang

{"title":"Global dynamics and spatiotemporal heterogeneity of a preytaxis model with prey-induced acceleration","authors":"Chunlai Mu, Weirun Tao, Zhi-An Wang","doi":"10.1017/s0956792523000347","DOIUrl":"https://doi.org/10.1017/s0956792523000347","url":null,"abstract":"Conventional preytaxis systems assume that prey-tactic velocity is proportional to the prey density gradient. However, many experiments exploring the predator–prey interactions show that it is the predator’s acceleration instead of velocity that is proportional to the prey density gradient in the prey-tactic movement, which we call preytaxis with prey-induced acceleration. Mathematical models of preytaxis with prey-induced acceleration were proposed by Arditi et al. ((2001) Theor. Popul. Biol. 59(3), 207–221) and Sapoukhina et al. ((2003) Am. Nat. 162(1), 61–76) to interpret the spatial heterogeneity of predators and prey observed in experiments. This paper is devoted to exploring the qualitative behaviour of such preytaxis systems with prey-induced acceleration and establishing the global existence of classical solutions with uniform-in-time bounds in all spatial dimensions. Moreover, we prove the global stability of spatially homogeneous prey-only and coexistence steady states with decay rates under certain conditions on system parameters. For the parameters outside the stability regime, we perform linear stability analysis to find the possible patterning regimes and use numerical simulations to demonstrate that spatially inhomogeneous time-periodic patterns will typically arise from the preytaxis system with prey-induced acceleration. Noticing that conventional preytaxis systems are unable to produce spatial patterns, our results imply that the preytaxis with prey-induced acceleration is indeed more appropriate than conventional preytaxis to interpret the spatial heterogeneity resulting from predator–prey interactions.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"35 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139587087","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

On degenerate reaction-diffusion epidemic models with mass action or standard incidence mechanism 关于具有质量作用或标准发生机制的退化反应-扩散流行病模型

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-01-22 DOI: 10.1017/s0956792523000359

Rachidi B. Salako, Yixiang Wu

引用次数: 0

The fully parabolic multi-species chemotaxis system in 中的全抛物线多物种趋化系统

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2024-01-19 DOI: 10.1017/s0956792523000372

Ke Lin

引用次数: 0