Related papers: Pattern formation within phenotype-structured chem…
We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…
Complex spatial patterns in biological systems often arise through self-organization without a central coordination, guided by local interactions and chemical signaling. In this study, we explore how motility-dependent chemical deposition…
In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that different spatio-temporal patterns can arise due to instability of the homogeneous state in reaction-diffusion systems, but at least two species are necessary to…
We use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized…
A fundamental feature of collective cell migration is phenotypic heterogeneity which, for example, influences tumour progression and relapse. While current mathematical models often consider discrete phenotypic structuring of the cell…
We introduce a multi-species diffuse interface model for tumor growth, characterized by its incorporation of essential features related to chemotaxis, angiogenesis and proliferation mechanisms. We establish the weak well-posedness of the…
We consider a reaction-diffusion system with discontinuous reaction terms modeled by non-ideal relays. The system is motivated by an epigenetic population model of evolution of two-phenotype bacteria which switch phenotype in response to…
We study the dynamics of phenotypically structured populations in environments with fluctuations. In particular, using novel arguments from the theories of Hamilton-Jacobi equations with constraints and homogenization, we obtain results…
Molecular phenotypes link genomic information with organismic functions, fitness, and evolution. Quantitative traits are complex phenotypes that depend on multiple genomic loci. In this paper, we study the adaptive evolution of a…
An important component in studying mathematical models in many biochemical systems, such as those found in developmental biology, is phase transition. The purpose of this work is to analyze the phase transition property of a…
Here we study the emergence of spontaneous leadership in large populations. In standard models of opinion dynamics, herding behavior is only obeyed at the local scale due to the interaction of single agents with their neighbors; while at…
We propose a novel class of network models for temporal dyadic interaction data. Our goal is to capture a number of important features often observed in social interactions: sparsity, degree heterogeneity, community structure and…
The contact structure of the population shapes the progression of epidemics. Nonetheless, the joint evolution of individual behavioral adaptations and disease dynamics on networks remains poorly understood. We use a…
The self-organizing behavior of swarms of inter- acting particles or agents is a topic of intense research in fields extending from biology to physics and robotics. In this paper, we carry out a systematic study of how the stable…
The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and…
Networks of biochemical reactions, like cellular metabolic networks, are kept in non-equilibrium steady states by the exchange fluxes connecting them to the environment. In most cases, feasible flux configurations can be derived from…
In personalised decision making, evidence is required to determine whether an action (treatment) is suitable for an individual. Such evidence can be obtained by modelling treatment effect heterogeneity in subgroups. The existing…
We analyze the existence, linear stability, and slow dynamics of localized 1D spike patterns for a Keller--Segel model of chemotaxis that includes the effect of logistic growth of the cellular population. Our analysis of localized patterns…
A mechanism of sympatric speciation is presented based on the interaction-induced developmental plasticity of phenotypes. First, phenotypes of individuals with identical genotypes split into a few groups, according to instability in the…
In micro-swimmer suspensions locomotion necessarily generates fluid motion, and it is known that such flows can lead to collective behavior from unbiased swimming. We examine the complementary problem of how chemotaxis is affected by…