相关论文: Another view of sequential sampling in the birth p…

Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by…

This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…

We aim at modelling the appearance of distinct tags in a sequence of labelled objects. Common examples of this type of data include words in a corpus or distinct species in a sample. These sequential discoveries are often summarised via…

Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…

Under a fourth order moment condition on the branching and a second order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous state and continuous…

We study the random times between successive cases in a transmission chain of infectious diseases with asymptomatic carriers. We derive the probability distribution of this generation time (in days) from a discrete-time epidemic model with…

Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…

We propose a simple model for sample space reducing (SSR) stochastic process, where the dynamical variable denoting the size of the state space is continuous. In general, one can view the model as a multiplicative stochastic process, with a…

This work is a continuation of [7]. We consider a continuous-time birth-and-death process in which the transition rates have an asymptotical power-law dependence upon the position of the process. We establish rough exponential asymptotic…

Count data modeling has been extensively applied in medical sciences to analyze various healthcare datasets. Numerous probability models have been developed to address diverse aspects of healthcare data. In this study, we propose a novel…

Compartment models with delay terms are widely used across a range of disciplines. The motivation to include delay terms varies across different contexts. In epidemiological and pharmacokinetic models, the delays are often used to represent…

The deluge of single-cell data obtained by sequencing, imaging and epigenetic markers has led to an increasingly detailed description of cell state. However, it remains challenging to identify how cells transition between different states,…

At least one unusual event appears in some count datasets. It will lead to a more concentrated (or dispersed) distribution than the Poisson, the gamma, the Weibull, and the Conway-Maxwell-Poisson (CMP) can accommodate. These well-known…

The growing popularity of wearable sensors has generated large quantities of temporal physiological and activity data. Ability to analyze this data offers new opportunities for real-time health monitoring and forecasting. However, temporal…

In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…

In vitro cell biology experiments are routinely used to characterize cell migration properties under various experimental conditions. These experiments can be interpreted using lattice-based random walk models to provide insight into…

Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…

To forecast the time dynamics of an epidemic, we propose a discrete stochastic model that unifies and generalizes previous approaches to the subject. Viewing a given population of individuals or groups of individuals with given health state…

The population protocol model describes collections of distributed agents that interact in pairs to solve a common task. We consider a dynamic variant of this prominent model, where we assume that an adversary may change the population size…

Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated…