Related papers: Absorption and fixation times for evolutionary pro…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
We consider the class of conditional graph patterns (\emph{CGPs}) that allow user to query data graphs with complex patterns that contain negation and predicates. To overcome the prohibitive cost of subgraph isomorphism, we consider…
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…
We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. Using structure coefficients defined for configurations describing such arrangements of any number…
We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend…
We study the graph alignment problem over two independent Erd\H{o}s-R\'enyi graphs on $n$ vertices, with edge density $p$ falling into two regimes separated by the critical window around $p_c=\sqrt{\log n/n}$. Our result reveals an…
Many mathematical models of evolution assume that all individuals experience the same environment. Here, we study the Moran process in heterogeneous environments. The population is of finite size with two competing types, which are exposed…
Evolutionary graph theory is the study of evolutionary dynamics in structured populations. A well-known problem in evolutionary graph theory is that the spread of mutation (measured by fixation probability) is impacted by the graph type…
Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic…
We consider random sequential adsorption processes where the initially empty sites of a graph are irreversibly occupied, in random order, either by monomers which block neighboring sites, or by dimers. We also consider a process where…
The voter process is a classic stochastic process that models the invasion of a mutant trait $A$ (e.g., a new opinion, belief, legend, genetic mutation, magnetic spin) in a population of agents (e.g., people, genes, particles) who share a…
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…
We study a branching random walk on $\r$ with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law,…
In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyze how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes…
We study a majority based preference diffusion model in which the members of a social network update their preferences based on those of their connections. Consider an undirected graph where each node has a strict linear order over a set of…
We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…
We study the contact process on random graphs with low infection rate $\lambda$. For random $d$-regular graphs, it is known that the survival time is $O(\log n)$ below the critical $\lambda_c$. By contrast, on the Erd\H{o}s-R\'enyi random…
Let $P(n,M)$ be a graph chosen uniformly at random from the family of all labeled planar graphs with $n$ vertices and $M$ edges. In the paper we study the component structure of $P(n,M)$. Combining counting arguments with analytic…