N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Complex networks arise in a wide range of biological and sociotechnical systems. Epidemic spreading is central to our understanding of dynamical processes in complex networks, and is of interest to physicists, mathematicians, epidemiologists, and computer and social scientists. This review presents the main results and paradigmatic models in infectious disease modeling and generalized social contagion processes.

Epidemic processes in complex networks

The American political science review

The mathematical theory of quantitative genetics

Neural stem and progenitor cells (NSPCs) generate neurons throughout life in the mammalian hippocampus We used chronic in vivo imaging and followed genetically labeled individual NSPCs and their progeny in the mouse hippocampus for up to 2 months We show that NSPCs targeted by the endogenous Achaete-scute homolog 1 (Ascl1) promoter undergo limited rounds of symmetric and asymmetric divisions, eliciting a burst of neurogenic activity, after which they are lost Further, our data reveal unexpected asymmetric divisions of nonradial glia-like NSPCs Cell fates of Ascl1-labeled lineages suggest a developmental-like program involving a sequential transition from a proliferative to a neurogenic phase By providing a comprehensive description of lineage relationships, from dividing NSPCs to newborn neurons integrating into the hippocampal circuitry, our data offer insight into how NSPCs support life-long hippocampal neurogenesis

/pdf/live-imaging-of-neurogenesis-in-the-adult-mouse-hippocampus-13qrou66xk.pdf

Live imaging of neurogenesis in the adult mouse hippocampus

We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical and efficient algorithm like the Gillespie algorithm for Markovian processes, with the difference being that now the occurrence rates of the events depend on the time elapsed since the event last took place. We use our non-Markovian generalized Gillespie stochastic simulation methodology to investigate the effects of nonexponential interevent time distributions in the susceptible-infected-susceptible model of epidemic spreading. Strikingly, our results unveil the drastic effects that very subtle differences in the modeling of non-Markovian processes have on the global behavior of complex systems, with important implications for their understanding and prediction. We also assess our generalized Gillespie algorithm on a system of biochemical reactions with time delays. As compared to other existing methods, we find that the generalized Gillespie algorithm is the most general because it can be implemented very easily in cases (such as for delays coupled to the evolution of the system) in which other algorithms do not work or need adapted versions that are less efficient in computational terms.

/pdf/simulating-non-markovian-stochastic-processes-17hr7zafr2.pdf

Simulating non-Markovian stochastic processes

Modellers of complex biological or social systems are often faced with an invidious choice: to use simple models with few mechanisms that can be fully analysed, or to construct complicated models that include all the features which are thought relevant. The former ensures rigour, the latter relevance. We discuss a method that combines these two approaches, beginning with a complex model and then modelling the complicated model with simpler models. The resulting “chain” of models ensures some rigour and relevance. We illustrate this process on a complex model of voting intentions, constructing a reduced model which agrees well with the predictions of the full model. Experiments with variations of the simpler model yield additional insights which are hidden by the complexity of the full model. This approach facilitated collaboration between social scientists and physicists—the complex model was specified based on the social science literature, and the simpler model constrained to agree (in core aspects) with the complicated model.

/pdf/staged-models-for-interdisciplinary-research-58vhmflp6l.pdf

Staged Models for Interdisciplinary Research

A recently proposed model of social interaction in voting is investigated by simplifying it down into a version that is more analytically tractable and which allows a mathematical analysis to be performed. This analysis clarifies the interplay of the different elements present in the system --- social influence, heterogeneity and noise --- and leads to a better understanding of its properties. The origin of a regime of bistability is identified. The insight gained in this way gives further intuition into the behaviour of the original model.

/pdf/simplification-and-analysis-of-a-model-of-social-interaction-386qvom14y.pdf

Simplification and analysis of a model of social interaction in voting

Recent theoretical studies have shown that demographic stochasticity can greatly increase the tendency of asexually reproducing phenotypically diverse organisms to spontaneously evolve into localized clusters, suggesting a simple mechanism for sympatric speciation. Here we study the role of demographic stochasticity in a model of competing organisms subject to assortative mating. We find that in models with sexual reproduction, noise can also lead to the formation of phenotypic clusters in parameter ranges where deterministic models would lead to a homogeneous distribution. In some cases, noise can have a sizable effect, rendering the deterministic modeling insufficient to understand the phenotypic distribution.

/pdf/role-of-demographic-stochasticity-in-a-speciation-model-with-4etrftm34e.pdf

Role of demographic stochasticity in a speciation model with sexual reproduction

A recently proposed model of social interaction in voting is investigated by simplifying it down into a version that is more analytically tractable and which allows a mathematical analysis to be performed. This analysis clarifies the interplay of the different elements present in the system – social influence, heterogeneity and noise – and leads to a better understanding of its properties. The origin of a regime of bistability is identified. The insight gained in this way gives further intuition into the behaviour of the original model.

/pdf/simplification-and-analysis-of-a-model-of-social-interaction-57igl5ugs9.pdf

Luis F. Lafuerza

Papers

Simulating non-Markovian stochastic processes

Staged Models for Interdisciplinary Research

Simplification and analysis of a model of social interaction in voting

Role of demographic stochasticity in a speciation model with sexual reproduction

Simplification and analysis of a model of social interaction in voting