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We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
Pitman~(1999) describes a duality relationship between fragmentation and coagulation operators. An explicit relationship is described for the two-parameter Poisson-Dirichlet laws, with parameters {\footnotesize $(\alpha,\theta)$} and…
In this work we present a reduction result for discrete time systems with two time scales. In order to be valid, previous results in the field require some strong hypotheses that are difficult to check in practical applications. Roughly…
Galaxies and clusters distributions show two major properties: (i) the positions of galaxies and clusters are characterized by a power law distribution indicating properties with respect to their positions. (ii) The distribution of masses…
This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state…
We link optimal filtering for hidden Markov models to the notion of duality for Markov processes. We show that when the signal is dual to a process that has two components, one deterministic and one a pure death process, and with respect to…
We use a geometric method to derive (two-dimensional) separation functions amongst pairs of objects within populations of specified position function $\mathrm{d} N/\mathrm{d} \vec{R}$. We present analytic solutions for separation functions…
The two-dimensional cell-sorting problem is found to be mathematically equivalent to the one-dimensional random walk problem with pair creations and annihilations, i.e. the adhesion probabilities in the cell-sorting model relate…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
We explore the usage of meta-learning to derive the causal direction between variables by optimizing over a measure of distribution simplicity. We incorporate a stochastic graph representation which includes latent variables and allows for…
By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of…
A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
We give an account of matter and (basically) a solution of a new class of problems synthesizing percolation theory and branching diffusion processes. They led us to realizing a novel type of stochastic processes, namely branching processes…
Stunning progresses in the experimental resolution and control of natural or man-made complex systems at the level of their quantum mechanical constituents raises the question, across diverse subdisciplines of physics, chemistry and…