Related papers: Spatial birth-death-move processes : basic propert…
Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics…
Understanding the statistical properties of a collection of individuals subject to random displacements and birth-and-death events is key to several applications in physics and life sciences, encompassing the diagnostic of nuclear reactors…
In spatio-temporal point pattern analysis, one of the main statistical objectives is to estimate the first-order intensity function, i.e., the expected number of points per unit area and unit time. This estimation is usually carried out…
In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death processes. Interactions can manifest through the birth dynamics,…
This paper is devoted to the long-term dynamics of solutions to the Gurtin-MacCamy population model with a bistable birth function. We consider a one-parameter monotone family of initial distributions for the population such that for small…
Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, because the likelihood can become numerically…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Here we tackle the problem of determining the distribution of the population density of a social space…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
Many important stochastic counting models can be written as general birth-death processes (BDPs). BDPs are continuous-time Markov chains on the non-negative integers and can be used to easily parameterize a rich variety of probability…
Human travelling behaviours are markedly regular, to a large extent, predictable, and mostly driven by biological necessities (\eg sleeping, eating) and social constructs (\eg school schedules, synchronisation of labour). Not surprisingly,…
The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work we study population survival or extinction using a stochastic, discrete…
Understanding how natural selection unfolds across space and time is a central problem in evolutionary biology. Classic models such as the Moran process capture stochastic birth-death dynamics in structured populations, while…
This work presents a non-parametric spatio-temporal model for mapping human activity by mobile autonomous robots in a long-term context. Based on Variational Gaussian Process Regression, the model incorporates prior information of spatial…
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…
Individual-level human mobility prediction has emerged as a significant topic of research with applications in infectious disease monitoring, child, and elderly care. Existing studies predominantly focus on the microscopic aspects of human…
A Feller's Brownian motion is a diffusion process on the half-line with general boundary behavior at the origin, described by four parameters. A birth-death process, on the other hand, is a continuous-time Markov chain on the nonnegative…
Understanding the spread of any disease is a highly complex and interdisciplinary exercise as biological, social, geographic, economic, and medical factors may shape the way a disease moves through a population and options for its eventual…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…