相关论文: Non-local Branching Superprocesses and Some Relate…

We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.

As communication networks are growing at a fast pace, the need for more scalable approaches to operate such networks is pressing. Decentralization and locality are key concepts to provide scalability. Existing models for which local…

We provide a many-to-few formula in the general setting of non-local branching Markov processes. This formula allows one to compute expectations of k-fold sums over functions of the population at k different times. The result generalises…

We establish general sufficient conditions for a sequence of controlled branching processes to converge weakly on the Skorokhod space. We focus on a class of controlled random variables that extends previous results by considering them as a…

The dynamics of a population exhibiting exponential growth can be modelled as a birth-death process, which naturally captures the stochastic variation in population size over time. In this article, we consider a supercritical birth-death…

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the…

The design and analysis of spiking neural network algorithms will be accelerated by the advent of new theoretical approaches. In an attempt at such approach, we provide a principled derivation of a spiking algorithm for unsupervised…

In this paper, we firstly give a reconstruction for Crump-Mode-Jagers processes with immigration as solutions to a class of stochastic Volterra integral equations, which offers us a new insight for the evolution dynamics of age-dependent…

We characterize recurrence and transience of nonnegative multivariate autoregressive processes of order one with random contractive coefficient matrix, of subcritical multitype Galton-Watson branching processes in random environment with…

Model merging aims to efficiently combine the weights of multiple expert models, each trained on a specific task, into a single multi-task model, with strong performance across all tasks. When applied to all but the last layer of weights,…

We review the theory of regenerative processes, which are processes that can be intuitively seen as comprising of i.i.d.\ cycles. Although we focus on the classical definition, we present a more general definition that allows for some form…

(Multi-type) branching processes are a natural and well-studied model for generating random infinite trees. Branching processes feature both nondeterministic and probabilistic branching, generalizing both transition systems and Markov…

We construct a family of processes, from a renewal process, that have realizations that converge almost surely to the Brownian motion, uniformly on the unit time interval. Finally we compute the rate of convergence in a particular case.

Diffusion and flow matching approaches to generative modeling have shown promise in domains where the state space is continuous, such as image generation or protein folding & design, and discrete, exemplified by diffusion large language…

Paraphrase generation has benefited extensively from recent progress in the designing of training objectives and model architectures. However, previous explorations have largely focused on supervised methods, which require a large amount of…

We present a progress report for studies on maxima related to offspring in branching processes. We summarize and discuss the findings on the subject that appeared in the last ten years. Some of the results are refined and illustrated with…

A branching process in random environment $(Z_n, n \in \N)$ is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several results which belong to the class of…

We would like to give an overview of results on regularity, or better to say "irregularity", properties of densities at fixed times of super-Brownian motion with $(1+\beta)$-stable branching for $\beta<1$. First, the following dichotomy for…

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…

Singularities appear in numerous important mathematical models used in Physics. And in most of such cases singularities are involved in essentially nonlinear contexts. For more than four decades, general enough nonlinear theories of…