Related papers: Growth rates of small cancellation groups
We study solvency of insurers in a comprehensive model where various economic factors affect the capital developments of the companies. The main interest is in the impact of real growth to ruin probabilities. The volume of the business is…
We study the evolution of the population size distribution of a critical Galton-Watson process with infinite variance of the offspring size of particles assuming that the population size is unusually small at the distant moment $n$ of…
This paper presents a simple shrinkage estimator of rates based on Bayesian methods. Our focus is on crime rates as a motivating example. The estimator shrinks each town's observed crime rate toward the country-wide average crime rate…
The rate equation for an arbitrary mth order growth or decay reaction can be expressed in terms of the q-exponential function, with q equal to m. The analysis suggests that a wide variety of reaction rate (kinetic) processes and models, in…
We continue research into the cyclically presented groups with length three positive relators. We study small cancellation conditions and SQ-universality, we obtain the Betti numbers of the groups' abelianisations, we calculate the orders…
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…
This article arises as an alternative solution to the problem of estimating the future population of some care centers for children and adolescents at social risk. The population of these centers fluctuates from month to month due to…
A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…
We finely describe the "coming down from infinity" for birth and death processes which eventually become extinct. Our biological motivation is to study the decrease of regulated populations which are initially large. Under general…
We study, both with numerical simulations and theoretical methods, a cellular automata model for continuum equations describing growth processes in the presence of an external flux of particles. As a result of local instabilities we find a…
Cluster growth in a coagulating system of active particles (such as microswimmers in a solvent) is studied by theory and simulation. In contrast to passive systems, the net velocity of a cluster can have various scalings dependent on the…
We consider a general class of Markovian models describing the growth in a randomly fluctuating environment of a clonal biological population having several phenotypes related by stochastic switching. Phenotypes differ e.g. by the level of…
We obtain characterizations of nonuniform dichotomies, defined by general growth rates, based on admissibility conditions. Additionally, we use the obtained characterizations to derive robustness results for the considered dichotomies. As…
We prove that the growth rate of an endomorphism of a finitely generated nilpotent group equals to the growth rate of induced endomorphism on its abelinization, generalizing the corresponding result for an automorphism in [14]. We also…
We consider continuous space-time decay-surge population models which are semi- stochastic processes for which deterministically declining populations, bound to fade away, are rein- vigorated at random times by bursts or surges of random…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…
We present direct numerical simulations and Lagrangian averaged (also known as alpha-model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at…
The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…
We study the rate of growth of entire functions that are frequently hypercyclic with respect to some upper weighted densities for the differentiation operator. The statements obtained show the link between the minimal growth of frequently…
The aggregation of particles in the free molecular regime is determined approximately for situations with a high degree of translational energy equilibration. The mean particle sizes develop linearly in time. Scaling relations are used to…