Related papers: On the last digits of consecutive primes
In a recent joint work with D.A. Goldston and C.Y. Yildirim we just missed by a hairbreadth a proof that bounded gaps between primes occur infinitely often. In the present work it is shown that adding to the primes a much thinner set,…
Strong positive feedback is considered a necessary condition to observe abrupt shifts of ecosystems. A few previous studies have shown that demographic noise -- arising from the probabilistic and discrete nature of birth and death processes…
We represent a process of learning by using bit strings, where 1-bits represent the knowledge acquired by individuals. Two ways of learning are considered: individual learning by trial-and-error; and social learning by copying knowledge…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
In this paper, we study a finite population undergoing discrete, nonoverlapping generations, that is structured into $D$ demes, each containing $N$ individuals of two possible types, $A$ and $B$, whose viability coefficients, $s_A$ and…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
Infinite Leslie matrices, introduced by Demetrius forty years ago are mathematical models of age-structured populations defined by a countable infinite number of age classes. This article is concerned with determining solutions of the…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
A permutiple is the product of a digit preserving multiplication, that is, a number which is an integer multiple of some permutation of its digits. Certain permutiple problems, particularly transposable, cyclic, and, more recently,…
Evolutionary synthesis models have been used to study the physical properties of unresolved populations in a wide range of scenarios. Unfortunately, their self-consistency are difficult to test and there are some theoretical open questions…
In 1930, G. H. Hardy and J. E. Littlewood derived results concerning rates of divergence of certain series involving cosecants. In more recent terminology, one of their results can be interpreted in terms of the behaviour of orbits in a…
Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
We discuss recent observational data on the transverse and radial velocities, as well as on the masses of the main components of the Orion Trapezium. Based on the most reliable values of these quantities we study the dynamical evolution of…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
The use of algorithmic predictions in decision-making leads to a feedback loop where the models we deploy actively influence the data distributions we see, and later use to retrain on. This dynamic was formalized by Perdomo et al. 2020 in…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
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…
Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates.…
Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others.…