European Journal of Applied Mathematics最新文献

英文中文

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 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-02-27 DOI: 10.1017/s0956792524000056

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

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.

我们提出了癌症侵袭的游走模型，其中浸润的癌细胞可以在表型空间中占据一系列状态，从 "完全间质 "到 "完全上皮 "不等。间质细胞越多，就越能表现出更强的牵引反应，并且通过增强基质降解酶（MDEs）的分泌来改变细胞外基质（ECM）的能力也就越强。然而，作为一种权衡，它们的增殖能力低于上皮细胞。该框架是多尺度的，我们从基于个体的模型开始，跟踪单个细胞的动态，该模型基于代表物理空间和表型空间的晶格上的分支随机行走。我们正式推导出相应的连续模型，该模型采用耦合系统的形式，包括局部细胞群密度函数偏积分微分方程、MDE 浓度偏微分方程和 ECM 密度无穷维常微分方程。尽管模型错综复杂，但我们通过形式渐近技术表明，在某些参数情况下，可以进行详细的行波分析，并获得表型空间结构的入侵前沿。确切地说，大部分间质细胞占据入侵波的前沿，而大部分上皮细胞（和增殖能力最强的细胞）则占据后方，这代表了大量肿瘤细胞。因此，该模型再现了近年来越来越多的实验研究中观察到的入侵波由前向后分为领导型细胞和追随者型细胞的类似结构。

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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 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-02-20 DOI: 10.1017/s0956792524000068

Giacomo Albi, Elisa Calzola, Giacomo Dimarco

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.

舆论动力学是一个重要且非常活跃的研究领域，它深入探讨了个人在社会环境中形成和改变其观点的复杂过程。理解和揭示舆论形成的驱动机制对于预测政治极化、错误信息的传播、公众共识的形成和集体行为的出现等一系列社会现象具有重要意义。在本文中，我们引入了一个新颖的数学模型，专门考虑社交媒体网络对舆论动态的影响，旨在为这一领域做出贡献。随着 Twitter、Facebook、Instagram 等平台的兴起，社交网络已成为分享、讨论并可能改变观点的重要场所。为此，我们在对新模型进行分析构建后，结合 Twitter 上的真实数据，对模型参数进行了校准，以准确反映社交媒体中的动态，尤其是所谓的 "影响者 "在推动个人意见向预定方向发展方面所发挥的作用。

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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 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-02-12 DOI: 10.1017/s0956792524000044

Martin Gugat, Michael Herty, Chiara Segala

We study the turnpike phenomenon for optimal control problems with mean-field dynamics that are obtained as the limit

$Nrightarrow infty$

of systems governed by a large number

$N$

of ordinary differential equations. We show that the optimal control problems with large time horizons give rise to a turnpike structure of the optimal state and the optimal control. For the proof, we use the fact that the turnpike structure for the problems on the level of ordinary differential equations is preserved under the corresponding mean-field limit.

我们研究了具有均场动力学的最优控制问题的拐点现象，这些问题是由大量 $N$ 常微分方程控制的系统的极限 $Nrightarrow infty$。我们证明，具有大时间跨度的最优控制问题会产生最优状态和最优控制的岔道结构。为了证明这一点，我们利用了常微分方程层面问题的岔道结构在相应的均场极限下得以保留这一事实。

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 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-02-08 DOI: 10.1017/s0956792524000032

Cristina Cipriani, Massimo Fornasier, Alessandro Scagliotti

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.

残差神经网络（ResNets）与连续时间控制系统（称为 NeurODE）之间的联系促成了对神经网络的数学分析，并提供了具有理论和实践意义的有趣结果。然而，从结构上看，NeurODEs 一直局限于描述恒定宽度的层，因此不适合对具有可变宽度层的深度学习架构进行建模。在本文中，我们提出了一种连续时间自动编码器，我们称之为 AutoencODE，它基于对驱动动力学的受控场的修改。这种调整可以扩展最初为传统神经编码器设计的均值场控制框架。在这种情况下，我们解决了低 Tikhonov 正则化的问题，这可能会导致成本景观不凸。虽然在高 Tikhonov 正则化条件下获得的全局结果可能无法在全局范围内成立，但我们证明，其中许多结果可以在损失函数为局部凸的区域内恢复。受理论发现的启发，我们开发了一种针对这种具有残差连接的特定类型自动编码器的训练方法，并通过在各种示例上进行的数值实验验证了我们的方法。

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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 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-02-02 DOI: 10.1017/s0956792524000020

Marco Nurisso, Matteo Raviola, Andrea Tosin

In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific classes of interactions a statistical description of the graph topology, given in terms of the degree distribution embedded in a Boltzmann-type kinetic equation, is sufficient to capture the collective trends of networked interacting systems. This proves the validity of a commonly accepted heuristic assumption in statistically structured graph models, namely that the so-called connectivity of the agents is the only relevant parameter to be retained in a statistical description of the graph topology. Then, we validate our results by testing them numerically against real social network data.

在本文中，我们提出了一种新方法，即利用动力学方程来描述多代理系统中以图为媒介的成对交互所产生的集体动力学。我们正式证明，对于大型图和特定类别的相互作用，以嵌入波尔兹曼式动力学方程的度分布给出的图拓扑统计描述，足以捕捉网络互动系统的集体趋势。这证明了统计结构图模型中一个普遍接受的启发式假设的有效性，即所谓的代理连通性是图拓扑统计描述中唯一需要保留的相关参数。然后，我们通过对真实社交网络数据进行数值测试来验证我们的结果。

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。

IF 2.3 4区数学 Q1 MATHEMATICS, APPLIED

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

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.

研究目的本研究旨在分析特发性炎症性肌病（IIM）中抗线粒体抗体（AMA）与心脏受累之间的关联，并评估AMA对IIM患者心脏受累的诊断价值：我们在 PubMed、Web of Science、EMBASE 和 Cochrane Library 中进行了全面检索，以确定 2021 年 11 月 19 日之前发表的英文研究。统计分析使用 Stata 12.0 软件（Stata Corp., College Station, TX, USA）。我们使用敏感性、特异性、阳性似然比（PLR）、阴性似然比（NLR）和接收者操作特征曲线（SROC）来评估AMA对IIM患者心脏受累的诊断价值。使用 I2 统计量和 95% 置信区间 (95% CI) 评估研究的统计异质性：最终分析共纳入了七项研究，共计2308例IIM患者（包括171例AMA阳性和2137例AMA阴性患者）。AMA对IIM患者心脏受累的汇总敏感性为0.29（95% CI：0.19-0.43），特异性为0.92（95% CI：0.88-0.96）。汇总的 PLR 为 3.9（95% CI：2.82-5.38），NLR 为 0.76（95% CI：0.66-0.88），诊断几率比（DOR）为 5（95% CI：3-7）。SROC曲线下面积为0.76（95% CI：0.72-0.79）：AMA对IIM患者心脏受累的总体诊断价值可能不是很高。

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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 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-01-29 DOI: 10.1017/s0956792524000019

Daifeng Duan, Ben Niu, Junjie Wei, Yuan Yuan

Cannibalism is often an extreme interaction in the animal species to quell competition for limited resources. To model this critical factor, we improve the predator–prey model with nonlocal competition effect by incorporating the cannibalism term, and different kernels for competition are considered in this model numerically. We give the critical conditions leading to the double Hopf bifurcation, in which the gestation time delay and the diffusion coefficient were selected as the bifurcation parameters. The innovation of the work lies near the double Hopf bifurcation point, and the stable homogeneous and inhomogeneous periodic solutions can coexist. The theoretical results of the extended centre manifold reduction and normal form method are in good agreement with the numerical simulation.

在动物物种中，为平息对有限资源的竞争，食人往往是一种极端的相互作用。为了模拟这一关键因素，我们改进了具有非局部竞争效应的捕食者-猎物模型，加入了食人项，并在该模型中数值地考虑了不同的竞争核。我们给出了导致双霍普夫分岔的临界条件，其中选择了妊娠时间延迟和扩散系数作为分岔参数。工作的创新点在于双霍普夫分岔点附近，稳定的同质和非同质周期解可以共存。扩展中心流形还原法和法线形式法的理论结果与数值模拟结果十分吻合。

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 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-01-26 DOI: 10.1017/s0956792523000347

Chunlai Mu, Weirun Tao, Zhi-An Wang

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.

传统的捕食者捕猎系统假定捕食者的运动速度与捕食者的密度梯度成正比。然而，许多探索捕食者与猎物相互作用的实验表明，在捕食者与猎物的接触运动中，与猎物密度梯度成正比的是捕食者的加速度而不是速度，我们称之为具有猎物诱导加速度的捕食者大同（preytaxis with prey-induced acceleration）。Arditi 等（（2001）Theor.Popul.59(3), 207-221) 和 Sapoukhina 等（（2003）Am.Nat.162(1)，61-76）来解释实验中观察到的捕食者和猎物的空间异质性。本文致力于探索这种具有猎物诱导加速度的猎物-大溪地系统的定性行为，并在所有空间维度上建立了具有均匀时间界限的经典解的全局存在性。此外，我们还证明了在系统参数的特定条件下，空间均质的纯猎物稳态和共存稳态的全局稳定性及衰减率。对于稳定机制之外的参数，我们进行了线性稳定性分析，以找到可能的模式机制，并通过数值模拟证明，具有猎物诱导加速度的捕食-大同系统通常会产生空间非均质时间周期模式。我们注意到传统的猎物大同系统无法产生空间模式，因此我们的结果表明，具有猎物诱导加速度的猎物大同系统确实比传统的猎物大同系统更适合解释捕食者与猎物相互作用产生的空间异质性。

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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 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-01-22 DOI: 10.1017/s0956792523000359

Rachidi B. Salako, Yixiang Wu

In this paper, we consider reaction-diffusion epidemic models with mass action or standard incidence mechanism and study the impact of limiting population movement on disease transmissions. We set either the dispersal rate of the susceptible or infected people to zero and study the corresponding degenerate reaction-diffusion model. Our main approach to study the global dynamics of these models is to construct delicate Lyapunov functions. Our results show that the consequences of limiting the movement of susceptible or infected people depend on transmission mechanisms, model parameters and population size.

在本文中，我们考虑了具有大规模行动或标准发病机制的反应扩散流行病模型，并研究了限制人口流动对疾病传播的影响。我们将易感人群或感染人群的扩散率设为零，并研究相应的退化反应-扩散模型。我们研究这些模型全局动力学的主要方法是构建微妙的 Lyapunov 函数。我们的研究结果表明，限制易感者或感染者的移动所产生的后果取决于传播机制、模型参数和人口规模。

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 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-01-19 DOI: 10.1017/s0956792523000372

Ke Lin

This article is devoted to the analysis of the parabolic–parabolic chemotaxis system with multi-components over $mathbb{R}^2$. The optimal small initial condition on the global existence of solutions for multi-species chemotaxis model in the fully parabolic situation had not been attained as far as the author knows. In this paper, we prove that under the sub-critical mass condition, any solutions to conflict-free system exist globally. Moreover, the global existence of solutions to system with strong self-repelling effect has been discussed even for large initial data. The proof is based on the modified free energy functional and the Moser–Trudinger inequality for system.

本文主要分析了$mathbb{R}^2$上多成分的抛物-抛物线趋化系统。据笔者所知，关于全抛物线情况下多物种趋化模型全局存在解的最优小初始条件还没有得到。本文证明了在亚临界质量条件下，无冲突系统的任何解都是全局存在的。此外，还讨论了即使初始数据很大，具有强自斥效应的系统解的全局存在性。证明基于修正的自由能函数和系统的 Moser-Trudinger 不等式。

引用次数: 0

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