Related papers: Emergence of order in selection-mutation dynamics
Citizens' assemblies are a form of democratic innovation in which a randomly selected panel of constituents deliberates on questions of public interest. We study a novel goal for the selection of panel members: maximizing the entropy of the…
Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a…
Evolution of a universe with homogeneous extra dimensions is studied with the benefit of a well-chosen parameter space that provides a systematic, useful, and convenient way for analysis. In this model we find a natural evolution pattern…
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population…
We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution---a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
The interaction between natural selection and random mutation is frequently debated in recent years. Does similar dilemma also exist in the evolution of real networks such as biological networks? In this paper, we try to discuss this issue…
Aggregation of particles whose interaction potential depends on their mutual orientation is considered. The aggregation dynamics is derived using a version of Darcy's law and a variational principle depending on the geometric nature of the…
We study sorting in the evolving data model, introduced by [AKMU11], where the true total order changes while the sorting algorithm is processing the input. More precisely, each comparison operation of the algorithm is followed by a…
Dynamic processes on networks are fundamental to understanding modern-day phenomena such as information diffusion and opinion polarization on the internet or epidemics spreading through society. However, such processes are notoriously…
We consider a integro-differential nonlinear model that describes the evolution of a population structured by a quantitative trait. The interactions between traits occur from competition for resources whose concentrations depend on the…
The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…
A microscopic agent dynamical model for diploid age-structured populations is used to study evolution of polymorphism and sympatric speciation. The underlying ecology is represented by a unimodal distribution of resources of some width.…
In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…
Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for co-evolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a…
We study a recently proposed model in which an odd number of agents are competing to be in the minority. The agents have one strategy in hand which is to follow the most recent history. Each agent is also assigned a value p, which is the…
We investigate the evolution of a population of non-interacting particles which undergo diffusion and multiplication. Diffusion is assumed to be homogeneous, while multiplication proceeds with different rates reflecting the distribution of…
In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time,…
We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics,…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…