Related papers: Statistical aspects of birth--and--growth stochast…
The effects of stochastic apppearence of embryos of a new phase are analyzed analytically. A new approach by the similarity of nucleation conditions is proposed. Corrections for a number of droplets are estimated. A comparison with…
We review models of compositional growth, which were introduced to explain the growth statistics of various quantities ranging from firm sizes to GDP. In these models, entities are decomposed into units that grow independently. Thus, the…
Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
We develop a stochastic approach for describing 3D-phase transformations ruled by time-dependent correlated nucleation at solid surfaces. The kinetics is expressed as a series of correlation functions and, at odds with modeling based on…
We present two approaches to study invasion in growth-fragmentation-death mod- els. The first one is based on a stochastic individual based model, which is a piecewise deterministic branching process with a continuum of types, and the…
It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
Many spatio-temporal data record the time of birth and death of individuals, along with their spatial trajectories during their lifetime, whether through continuous-time observations or discrete-time observations. Natural applications…
We study the nucleation and growth of flame fronts in slow combustion. This is modeled by a set of reaction-diffusion equations for the temperature field, coupled to a background of reactants and augmented by a term describing random…
Understanding if and how mutants reach fixation in populations is an important question in evolutionary biology. We study the impact of population growth has on the success of mutants. To systematically understand the effects of growth we…
A feature of human creativity is the ability to take a subset of existing items (e.g. objects, ideas, or techniques) and combine them in various ways to give rise to new items, which, in turn, fuel further growth. Occasionally, some of…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
A mixture of two or more count distributions has become deeply embedded in the analysis of excess counts, often relative to the stationary (equilibrium) distributions of birth-death processes such as the geometric, Poisson, Poisson-Lindley…
Modern generative models can be understood as probability transport from a simple base distribution to a target data distribution. Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic…
We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture,…
It is argued that the present log-normal distribution of language sizes is, to a large extent, a consequence of demographic dynamics within the population of speakers of each language. A two-parameter stochastic multiplicative process is…
A class of nucleation and growth models of a stable phase (S-phase) is investigated for various different growth velocities. It is shown that for growth velocities $v\sim s(t)/t$ and $v\sim x/\tau(x)$, where $s(t)$ and $\tau$ are the mean…