Related papers: Subexponential growth of early Christianity
A continuum growth model is introduced. The state at time $t$, $S_t$, is a subset of $\mathbb{R}^d$ and consists of a connected union of randomly sized Euclidean balls, which emerge from outbursts at their center points. An outburst occurs…
Macroscopic, phenomenological models have proven useful as concise framings of our understandings in fields from statistical physics to economics to biology. Constructing a phenomenological model for development would provide a framework…
Using Rees index, the subsemigroup growth of free semigroups is investigated. Lower and upper bounds for the sequence are given and it is shown to have superexponential growth of strict type $n^n$ for finite free rank greater than 1. It is…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
A simplified method to compute $R_t$, the Effective Reproduction Number, is presented. The method relates the value of $R_t$ to the estimation of the doubling time performed with a local exponential fit. The condition $R_t = 1$ corresponds…
The system of equations for parametric sub-resonant growth of the amplitude of oscillations was obtained. The time of turning point from the growing of the amplitude to the bounded oscillations in the slow variable was found. The comparison…
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…
Solar models through evolutionary phases of gravitational contraction, pre-main sequence and MS phases, up to current age 4.5E9 yr. and 4.57E9 yr., were studied adopting different prescriptions for the equation of state (EOS) and different…
We consider a model of asexually reproducing individuals. The birth and death rates of the individuals are affected by a fitness parameter. The rate of mutations that cause the fitnesses to change is proportional to the population size, N.…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
The expansion rate of `Intermediate inflation' lies between the exponential and power law expansion but corresponding accelerated expansion does not start at the onset of cosmological evolution. Present study of `Intermediate inflation'…
Despite internal complexity, tumor growth kinetics follow relatively simple macroscopic laws that have been quantified by mathematical models. To resolve this further, quantitative and discriminant analyses were performed for the purpose of…
We present a new simple functional form to model the evolution of a spherical mass distribution in a cosmological context. Two parameters control the growth of the system and this is modelled using a redshift dependent exponential for the…
We model the growth of a cell population by a piecewise deterministic Markov branching tree. Each cell splits into two offsprings at a division rate $B(x)$ that depends on its size $x$. The size of each cell grows exponentially in time, at…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…
The Lotka-Euler equation is a mathematical expression used to study population dynamics and growth, particularly in the context of demography and ecology. The growth rate $\lambda$ is the speed at which an individual produce their…
Mathematical methods of analysis of data and of predicting growth are discussed. The starting point is the analysis of the growth rates, which can be expressed as a function of time or as a function of the size of the growing entity.…
Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction.The…