Related papers: Reciprocal symmetry breaking in Pareto sampling
We examine the problem of family size statistics (the number of individuals carrying the same surname, or the same DNA sequence) in a given size subsample of an exponentially growing population. We approach the problem from two directions.…
We consider a neutral haploid population whose generations are not overlapping and whose size is large and constantly of $N$ individuals. Any generation is replaced by a new one and any individual has a single parent. We do not choose the…
A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constiyuent molecules in each generation,i.e., linkage…
Under random mating, a progeny's alleles are independently sampled from the parental gene pools. Here is a new proof which avoids the usual algebraic complexity, based on a restated Mendel's First Law. Another simplified proof along the old…
Metapopulation theory for a long time has assumed dispersal to be symmetric, i.e. patches are connected through migrants dispersing bi-directionally without a preferred direction. However, for natural populations symmetry is often broken,…
We find the perhaps surprising inequality that the weighted average of independent and identically distributed Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic…
Considering two random variables with different laws to which we only have access through finite size iid samples, we address how to reweight the first sample so that its empirical distribution converges towards the true law of the second…
The white dwarf mass distribution has been studied primarily at two extremes: objects that presumably evolved as single stars and members of close binaries that likely underwent substantial interaction. This work considers the intermediate…
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…
Understanding the interplay between recombination and resampling is a significant challenge in mathematical population genetics and of great practical relevance. Asymptotic results about the distribution of samples when recombination is…
We consider weighted particle systems in which new generations are re-sampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo methods, widely used in applied…
We consider generic optimal Bayesian inference, namely, models of signal reconstruction where the posterior distribution and all hyperparameters are known. Under a standard assumption on the concentration of the free energy, we show how…
A computational model for the distribution of wealth among the members of an ideal society is presented. It is determined that a realistic distribution of wealth depends upon two mechanisms: an asymmetric flux of wealth in trading…
Developments in genome-wide association studies and the increasing availability of summary genetic association data have made the application of two-sample Mendelian Randomization (MR) with summary data increasingly popular. Conventional…
In this chapter we report on the measurements of the overlap distribution of the replica symmetry breaking solution in complex disordered systems. After a general introduction to the problem of the experimental validation of the Parisi…
Reciprocity, or the tendency of individuals to mirror behavior, is a key measure that describes information exchange in a social network. Users in social networks tend to engage in different levels of reciprocal behavior. Differences in…
Commonly recognized evolutionarily relevant effects of sexual reproduction include increased diversity, accelerated adaptation, and constrained accumulation of deleterious mutations, along with a secondary effect of species genotype…
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…
Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…