Related papers: The Birth-Death-Mutation process: a new paradigm f…

Standard evolutionary theories of aging and mortality, implicitly based on assumptions of spatial averaging, hold that natural selection cannot favor shorter lifespan without direct compensating benefit to individual reproductive success.…

Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have disproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers…

Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated…

Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models…

(The third edition corrects minor typos and adds 3 chapters synthesized from published papers plus an appendix on maximum entropy distributions.) The monograph investigates the misapplication of conventional statistical techniques to fat…

Diffusion-based models have shown the merits of generating high-quality visual data while preserving better diversity in recent studies. However, such observation is only justified with curated data distribution, where the data samples are…

Genetic mutations are footprints of tumour growth. While mutation data in bulk samples has been used to infer evolutionary parameters hard to measure in vivo, the advent of single-cell data has led to strong interest in the mutational…

The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…

Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…

We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0,1,...,L} and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation…

We study a fractional birth-death process with state dependent birth and death rates. It is defined using a system of fractional differential equations that generalizes the classical birth-death process introduced by Feller (1939). We…

Evolutionary graph theory models the effects of natural selection and random drift on structured populations of competing mutant and non-mutant individuals. Recent studies have found that fixation times in such systems often have…

We study the dynamics of an age-structured population in which the life expectancy of an offspring may be mutated with respect to that of its parent. When advantageous mutation is favored, the average fitness of the population grows…

Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…

The mutual fund industry manages about a quarter of the assets in the U.S. stock market and thus plays an important role in the U.S. economy. The question of how much control is concentrated in the hands of the largest players is best…

While wealth distribution in the world is highly skewed and heavy-tailed, human talent - as the majority of individual features - is normally distributed. In a recent computational study by Pluchino et al [Talent vs luck: The role of…

Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher order taxa, such as families or genera, follow a…

In search of many social and economical systems, it is found that node strength distribution as well as degree distribution demonstrate the behavior of power-law with droop-head and heavy-tail. We present a new model for the growth of…

Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer…

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…