Related papers: Scaling Function, Universality and Analytical Solu…
Recent years have seen a lot of progress in algorithms for learning parameters of spreading dynamics from both full and partial data. Some of the remaining challenges include model selection under the scenarios of unknown network structure,…
There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis…
Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…
The extinction of species is a core process that affects the diversity of life on Earth. One way of investigating the causes and consequences of extinctions is to build conceptual ecological models, and to use the dynamical outcomes of such…
The evolution model with parallel mutation-selection scheme is solved for the case when selection is accompanied by base substitutions, insertions, and deletions. The fitness is assumed to be either a single-peak function (i.e., having one…
The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for…
Rare trajectories of stochastic systems are important to understand -- because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their…
We review recent work aimed at modeling species extinction over geological time. We discuss a number of models which, rather than dealing with the direct causes of particular extinction events, attempt to predict overall statistical trends,…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
Mass extinction is a phenomenon in the history of life on Earth when a considerable number of species go extinct over a relatively short period of time. The magnitude of extinction varies between the events, the most well known are the…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
We investigate scaling and universality in nonequilibrium spin correlation functions in the presence of uncorrelated noise. In the absence of noise, spin correlation functions exhibit a crossover from monotonic decay at fast sweep…
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is…
The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this…
A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The…
We describe a method for approximating the universal scaling functions for the Ising model in a field. By making use of parametric coordinates, the free energy scaling function has a polynomial series everywhere. Its form is taken to be a…
We analyze mathematical models of the global human population growth and compare them to actual dynamics of the world population and of the world surplus product. We consider a possibility that the so-called world's demographic transition…
This paper is concerned with an analysis of the dynamics of a non-autonomous, single population age based growth model with harvesting formulation. First, we derive sufficient conditions for permanence and positive invariance. Then, by…