arXiv subjects

Bastian Wiederhold

Publications and source records attributed to Bastian Wiederhold.

5 recordsLinked to original sources

arXiv2026

A new stochastic SIS-type modelling framework for analysing epidemic dynamics in continuous space

We propose a new stochastic epidemiological model defined in a continuous space of arbitrary dimension, based on SIS dynamics implemented in a spatial $Λ$-Fleming-Viot (SLFV) process. The model can be described by as little as three parameters, and is dual to a spatial branching process with competition linked to genealogies of infected individuals. Therefore, it is a possible modelling framework to develop computationally tractable inference tools for epidemics in a continuous space using demographic and genetic data.We provide mathematical constructions of the process based on well-posed martingale problems as well as driving space-time Poisson point processes. With these devices and the duality relation in hand, we unveil some of the drivers of the transition between extinction and survival of the epidemic. In particular, we show that extinction is in large parts independent of the initial condition, and identify a strong candidate for the reproduction number R 0 of the epidemic in such a model.

math.PR↗

arXiv2025

An introduction to memory competitions, records and techniques

Anyone who has tried to memorize a one-hundred-digit number can attest that the human brain acquires abstract information slowly. However, following a three-decade increase of results at memory competitions, the best competitors manage to memorize a one-hundred-digit number in under 15 seconds. This documents explores the origins of this trend: how competitions, records and techniques have evolved. In the process several phenomena are discussed: the actual process of memorization is likely even faster, records are governed by a power law, numbers are easier than playing cards and associations are at the core of memory.

q-bio.NC↗

arXiv2025

Central limit theorems describing isolation by distance under various forms of power-law dispersal

In this paper, we uncover new asymptotic isolation by distance patterns occurring under long-range dispersal of offspring. We extend a recent work of the first author, in which this information was obtained from forwards-in-time dynamics using a novel stochastic partial differential equations approach for spatial $Λ$-Fleming-Viot models. The latter were introduced by Barton, Etheridge and Véber as a framework to model the evolution of the genetic composition of a spatially structured population. Reproduction takes place through extinction-recolonisation events driven by a Poisson point process. During an event, in certain ball-shaped areas, a parent is sampled and a proportion of the population is replaced. We generalize the previous approach of the first author by allowing the area from which a parent is sampled during events to differ from the area in which offspring are dispersed, and the radii of these regions follow power-law distributions. In particular, while in previous works the motion of ancestral lineages and coalescence behaviour were closely linked, we demonstrate that local and non-local coalescence is possible for ancestral lineages governed by both fractional and standard Laplacians.

math.PR↗

arXiv2025

Central limit theorems describing isolation by distance under varying population size

We derive a central limit theorem for a spatial $Λ$-Fleming-Viot model with fluctuating population size. At each reproduction, a proportion of the population dies and is replaced by a not necessarily equal mass of new individuals. The mass depends on the local population size and a function thereof. Additionally, as new individuals have a single parental type, with growing population size, events become more frequent and of smaller impact, modelling the successful reproduction of a higher number of individuals. From the central limit theorem we derive a Wright-Malécot formula quantifying the asymptotic probability of identity by descent and thus isolation by distance. The formula reflects that ancestral lineages are attracted by centres of population mass and coalesce with a rate inversely proportional to the population size. Notably, we obtain this information despite the varying population size rendering the dual process intractable.

math.PR↗

arXiv2023

A $Λ$-Fleming-Viot type model with intrinsically varying population size

We propose an extension of the classical $Λ$-Fleming-Viot model to intrinsically varying population sizes. During events, instead of replacing a proportion of the population, a random mass dies and a, possibly different, random mass of new individuals is added. The model can also incorporate a drift term, representing infinitesimally small, but frequent events. We investigate elementary properties of the model, analyse its relation to the $Λ$-Fleming-Viot model and describe a duality relationship. Through the lookdown framework, we provide a forward-in-time analysis of fixation and coming down from infinity. Furthermore, we present a new duality argument allowing one to deduce well-posedness of the measure-valued process without the necessity of proving uniqueness of the associated lookdown martingale problem.

math.PR↗