Related papers: Numerical Aspects of Computing Possible Equilibria…
Let $(X_1, \xi_1), (X_2,\xi_2),\ldots$ be i.i.d.~copies of a pair $(X,\xi)$ where $X$ is a random process with paths in the Skorokhod space $D[0,\infty)$ and $\xi$ is a positive random variable. Define $S_k := \xi_1+\ldots+\xi_k$, $k \in…
This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID random environments. The key assumptions of the…
We consider branching particle processes on discrete structures like the hypercube in a random fitness landscape (i.e., random branching/killing rates). The main question is about the location where the main part of the population sits at a…
Immigration can rescue local populations from extinction, helping to stabilise a metapopulation. Local population dynamics is important for determining the strength of this rescue effect, but the mechanistic link between local demographic…
We consider a branching process with Poissonian immigration where individuals have inheritable types. At rate theta, new individuals singly enter the total population and start a new population which evolves like a supercritical,…
The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
A well known result states that stability criterion for matchings in two-sided markets doesn't ensure uniqueness. This opens the door for a moral question with regard to the optimal stable matching from a social point of view. Here, a new…
The use of emergent constraints to quantify uncertainty for key policy relevant quantities such as Equilibrium Climate Sensitivity (ECS) has become increasingly widespread in recent years. Many researchers, however, claim that emergent…
This paper is a supplement to the paper "Interactions between Human Populations and Related Problems of Optimal Transport" written by the same author in honour of Marc Hallin, Universit\'e Libre de Bruxelles, at the occasion of Hallin's…
A number of simplified dynamical problems is studied in an attempt to clarify some of the mechanisms leading to turbulence and the existing proposals to control this transition. A simplified set of boundary layer equations displays a…
We study the optimization of the stable marriage problem. All individuals attempt to optimize their own satisfaction, subject to mutually conflicting constraints. We find that the stable solutions are generally not the globally best…
We consider a population constituted by two types of individuals; each of them can produce offspring in two different islands (as a particular case the islands can be interpreted as active or dormant individuals). We model the evolution of…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…
The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…
The asymptotic normality of conditional least squares estimators for the offspring variance in critical branching processes with non-homogeneous immigration is established, under moment assumptions on both reproduction and immigration. The…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
We consider population dynamics on a network of patches, each of which has a the same local dynamics, with different population scales (carrying capacities). It is reasonable to assume that if the patches are coupled by very fast migration…
Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…