Related papers: Linking age, survival and transit time distributio…
At any moment in time, evolution is faced with a formidable challenge: refining the already highly optimised design of biological species, a feat accomplished through all preceding generations. In such a scenario, the impact of random…
A class of multivariate mixed survival models for continuous and discrete time with a complex covariance structure is introduced in a context of quantitative genetic applications. The methods introduced can be used in many applications in…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
Mainstream flow matching methods typically focus on learning the local velocity field, which inherently requires multiple integration steps during generation. In contrast, Mean Velocity Flow models establish a relationship between the local…
We investigate the time evolution of disease spread on a network by using the concept of generations. We derive a set of equations, which can be used to determine the average epidemic size. We find a very good agreement between the…
We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
Consider a system evolving according to an absorbing discrete-time Markov chain with known transition matrix. The state of the system is observed at two points in time, separated by an unknown number of generations. We are interested in…
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…
Demographic data and recent experiments verify earlier predictions that mortality has short (few percent of the life span) memory of the previous life history, may be significantly decreased, reset to its value at a much younger age, and…
We study an infection-age structured epidemic model in which both the infectivity and the rate of loss of immunity depend on the time-since-infection. The model can be equivalently viewed as a nonlinear renewal equation for the incidence of…
Crossing survival curves complicate how we interpret results from a clinical trial's primary endpoint. We find the function to determine a crossing point's location depends exponentially on individual survival curves. This exponential…
Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…
We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its…
The Master equation describes the time evolution of the probabilities of a system with a discrete state space. This time evolution approaches for long times a stationary state that will in general depend on the initial probability…
We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we present a full kinetic framework for age-structured interacting populations undergoing birth, death and…
Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…
Time series data can be subject to changes in the underlying process that generates them and, because of these changes, models built on old samples can become obsolete or perform poorly. In this work, we present a way to incorporate…
In this note, we address formally the issue of symmetry for probabilities of different dynamical pathways in the forward and reverse directions of a conformational transition. Our discussion is based on a decomposition of equilibrium into…
We consider a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as…