Related papers: Individual based and mean-field modelling of direc…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
A time- and space-discrete model for the growth of a rapidly saturating local biological population $N(x,t)$ is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant…
Computational models of infectious disease can be broadly categorized into two types: individual-based (Agent-based), or compartmental models. While compartmental models can be structured to separate distinct sectors of a population, they…
A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed…
We consider the $N$-particle noncolliding Bernoulli random walk --- a discrete time Markov process in $\mathbb{Z}^{N}$ obtained from a collection of $N$ independent simple random walks with steps $\in\{0,1\}$ by conditioning that they never…
Uncovering human mobility patterns is of fundamental importance to the understanding of epidemic spreading, urban transportation and other socioeconomic dynamics embodying spatiality and human travel. According to the direct travel diaries…
We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framework: contacts between people are not anticipated and avoided, they actually occur, and they are explicitly taken into account in the model. We…
In the present note we analyze the one-dimensional multi-particle diffusion limited aggregation (MDLA) model: the initial number of particles at each positive integer site has Poisson distribution with mean $\mu$, independently of all other…
We consider a space structured population model generated by two point clouds: a homogeneous Poisson process $M$ with intensity $n\to\infty$ as a model for a parent generation together with a Cox point process $N$ as offspring generation,…
In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for…
Traditional approaches to ecosystem modelling have relied on spatially homogeneous approximations to interaction, growth and death. More recently, spatial interaction and dispersal have also been considered. While these leads to certain…
We study a random walk driven by a particle system from a generic class, and establish a law of large numbers for the walk for almost all densities of the environment. To do so, we exploit the finite-ranged approximations of the environment…
We investigate the effect of groups on a bi-directional flow, by using novel computational methods. Our focus is on self-organisation phenomena, and more specifically on the time needed for the occurrence of pedestrian lanes, their…
Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random…
This paper introduces a system of stochastic differential equations (SDE) of mean-field type that models pedestrian motion. The system lets the pedestrians spend time at, and move along, walls, by means of sticky boundaries and boundary…
We consider two (off-lattice) varieties of out-of-equilibrium systems, viz., granular and active matter systems, that, in addition to displaying velocity ordering, exhibit fascinating pattern formation in the density field, similar to those…
Relying on random and purposive moving agents, we simulated human movement in large street networks. We found that aggregate flow, assigned to individual streets, is mainly shaped by the underlying street structure, and that human moving…
We run stochastic simulations of the spatial version of the rock-paper-scissors game, considering that individuals use sensory abilities to scan the environment to detect the presence of enemies. If the local dangerousness level is above a…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…
Motivated by better modeling of intra-individual variability in longitudinal data, we propose a class of location-scale mixed effects models, in which the data of each individual is modeled by a parameter-varying generalized hyperbolic…