Related papers: Criteria for linearized stability for a size-struc…
This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both…
We consider a system of interacting Fisher-Wright diffusions with seed-bank. Individuals live in colonies and are subject to resampling and migration as long as they are active. Each colony has a structured seed-bank into which individuals…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…
This paper is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work…
Biological aggregations such as insect swarms and bird flocks may arise from a combination of social interactions and environmental cues. We focus on nonlocal continuum equations, which are often used to model aggregations, and yet which…
A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…
Motivated by data on coauthorships in scientific publications, we analyze a team formation process that generalizes matching models and network formation models, allowing for overlapping teams of heterogeneous size. We apply different…
A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
A Collision-Avoiding flocking particle system proposed in [8] is studied in this paper. The global wellposedness of its corresponding Vlasov-type kinetic equation is proved. As a corollary of the global stability result, the mean field…
We report that population dynamics in fluctuating environment accompanies mathematically equivalent structure to steady state thermodynamics. By employing the structure, population growth in fluctuating environment is decomposed into…
We consider a continuum aggregation model with nonlinear local repulsion given by a degenerate power-law diffusion with general exponent. The steady states and their properties in one dimension are studied both analytically and numerically,…
Stability selection (Meinshausen and Buhlmann, 2010) makes any feature selection method more stable by returning only those features that are consistently selected across many subsamples. We prove (in what is, to our knowledge, the first…
This paper is concerned with the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison…
We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
We consider a population dynamics model coupling cell growth to a diffusion in the space of metabolic phenotypes as it can be obtained from realistic constraints-based modelling. In the asymptotic regime of slow diffusion, that coincides…
Feynman-Kac semigroups appear in various areas of mathematics: non-linear filtering, large deviations theory, spectral analysis of Schrodinger operators among others. Their long time behavior provides important information, for example in…