Related papers: Fermi statistics method applied to model macroscop…
Generating function equation has been derived for the probability distribution of the number of nodes with $k \ge 0$ outgoing lines in randomly evolving special trees. The stochastic properties of end-nodes (k=0) have been analyzed, and it…
Lifetime distributions of social entities, such as enterprises, products, and media contents, are one of the fundamental statistics characterizing the social dynamics. To investigate the lifetime distribution of mutually interacting…
Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the…
The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth…
Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the…
Motivated by a host of empirical evidences revealing the bursty character of human dynamics, we develop a model of human activity based on successive switching between an hesitation state and a decision-realization state, with residency…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the…
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…
Correlated sampling has wide-ranging applications in Monte Carlo calculations. When branching random walks are involved, as commonly found in many algorithms in quantum physics and electronic structure, population control is typically not…
We explore the fractional advection-diffusion equation and rare events associated with the ACTRW model. When waiting times have a finite mean but infinite variance, and the displacements follow a narrow distribution, the fractional operator…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements -…
The Josephus problem is a well--studied elimination problem consisting in determining the position of the survivor after repeated applications of a deterministic rule removing one person at a time from a given group. A natural probabilistic…
Some populations, such as red blood cells (RBCs), exhibit a pattern of population decline that is closer to linear rather than exponential, which has proven to be unexpectedly challenging to describe with a single simple mathematical model.…
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially-growing…
This note presents an Agent-Based Model (ABM) with Monte Carlo sampling, designed to simulate the behaviour of a population of objects over time. The model incorporates damage functions with the risk parameters of the ABC framework to…
Modern developments in population dynamics emphasize the role of the turnover of individuals. In the new approaches stable population size is a dynamic equilibrium between different mortality and fecundity factors instead of an arbitrary…
The diameter distribution of a given species of deciduous trees in mature, temperate zone forests is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data…