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We introduce and study an evolutionary complementarity game where in each round a player of population 1 is paired with a member of population 2. The game is symmetric, and each player tries to obtain an advantageous deal, but when one of…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial…
Whether in search of better trade opportunities or escaping wars, humans have always been on the move. For almost a century, mathematical models of human mobility have been instrumental in the quantification of commuting patterns and…
We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths, entry and exit rates, competing for a finite reservoir of particles. We present…
We study the performance of general dynamic matching models. This model is defined by a connected graph, where nodes represent the class of items and the edges the compatibilities between items. Items of different classes arrive one by one…
We provide an explicit algorithm to solve the idempotent analogue of the discrete Monge-Kantorovich optimal mass transportation problem with the usual real number field replaced by the tropical (max-plus) semiring, in which addition is…
The collective strength of a system of fibers, each having a failure threshold drawn randomly from a distribution, indicates the maximum load carrying capacity of different disordered systems ranging from disordered solids, power-grid…
The complex interplay between population movements in space and non-homogeneous mixing patterns have so far hindered the fundamental understanding of the conditions for spatial invasion through a general theoretical framework. To address…
This research paper talks about using complex mathematical tools to study and figure out the behavior of biological populations in porous media. Porous media offer a unique environment where various factors, including fluid flow and…
The propagation of infectious diseases and its impact on individuals play a major role in disease dynamics, and it is important to incorporate population heterogeneity into efforts to study diseases. As a simplistic but illustrative…
We study the population genetics of Evolution in the important special case of weak selection, in which all fitness values are assumed to be close to one another. We show that in this regime natural selection is tantamount to the…
This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong…
This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed…
The capacitated location-routing problem involves determining the depots from a set of candidate capacitated depot locations and finding the required routes from the selected depots to serve a set of customers whereas minimizing a cost…
We consider a population spreading across a finite number of sites. Individuals can move from one site to the other according to a network (oriented links between the sites) that vary periodically over time. On each site, the population…
In equilibrium systems, the conservation of the number of particles (or mass) leads to the equalization of the chemical potential throughout the system. Using a non-equilibrium generalization of the notion of chemical potential, we…