Related papers: A Path Integral Approach to Age Dependent Branchin…
Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart. We use the constraint phase space developed in J. Chem. Phys.…
In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and…
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…
There has been growing interest on forecasting mortality. In this article, we propose a novel dynamic Bayesian approach for modeling and forecasting the age-at-death distribution, focusing on a three-components mixture of a Dirac mass, a…
Mechanistic statistical models are commonly used to study the flow of biological processes. For example, in landscape genetics, the aim is to infer spatial mechanisms that govern gene flow in populations. Existing statistical approaches in…
We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next generation. For any specific characteristic of…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
Using the age-structure formalism, we definitely establish connections between semi-Markov processes and the dynamics of open quantum systems that satisfy the Markov quantum master equations. A generalized Feynman-Kac formula of the…
The generalized Fleming-Viot processes were defined in 1999 by Donnelly and Kurtz using a particle model and by Bertoin and Le Gall in 2003 using stochastic flows of bridges. In both methods, the key argument used to characterize these…
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 paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by [17]. Moreover, its multiplicative structure and the multiplicative…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random…
We investigate jointly modeling Age-specific rates of various causes of death in a multinational setting. We apply Multi-Output Gaussian Processes (MOGP), a spatial machine learning method, to smooth and extrapolate multiple cause-of-death…
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on…
This paper is devoted to the study of an age-structured SIRS epidemic model, in which a population affected by a disease is divided into susceptible, infected, and removed individuals. We assume that the force of infection may be nonlinear…
Ageing's sensitivity to natural selection has long been discussed because of its apparent negative effect on individual's fitness. Thanks to the recently described (Smurf) 2-phase model of ageing we were allowed to propose a fresh angle for…
Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. Despite the existence of…
Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…