Related papers: Delay compartment models from a stochastic process

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…

Phase-type distribution has been an important probabilistic tool in the analysis of complex stochastic system evolution. It was introduced by Neuts \cite{Neuts1975} in 1975. The model describes the lifetime distribution of a finite-state…

We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settings are analyzed: hidden…

Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…

Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to…

In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…

We present a new method for inferring hidden Markov models from noisy time sequences without the necessity of assuming a model architecture, thus allowing for the detection of degenerate states. This is based on the statistical prediction…

Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…

We explore the joint effect of the intrinsic noise and time delay on the spatial pattern formation within a multi-scale mobile lattice model of the epithelium. The protein fluctuations are driven by transcription/translation processes in…

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…

This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are…

In the field of modeling the dynamics of oncolytic viruses, researchers often face the challenge of using specialized mathematical terms to explain uncertain biological phenomena. This paper introduces a basic framework for an oncolytic…

Anticipating and recognizing surgical workflows are critical for intelligent surgical assistance systems. However, existing methods rely on deterministic decision-making, struggling to generalize across the large anatomical and procedural…

Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…

Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…

Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…

We consider previous models of Timed, Probabilistic and Stochastic Timed Automata, we introduce our model of Timed Automata with Polynomial Delay and we characterize the expressiveness of these models relative to each other.

In this note, we shall consider the existence of invariant measures for a class of infinite dimensional stochastic functional differential equations with delay whose driving semigroup is eventually norm continuous. The results obtained are…