Related papers: Estimation of Parameter Distributions for Reaction…
Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…
The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…
Medical image segmentation is a challenging task, made more difficult by many datasets' limited size and annotations. Denoising diffusion probabilistic models (DDPM) have recently shown promise in modelling the distribution of natural…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
We introduce the state-of-the-art deep learning Denoising Diffusion Probabilistic Model (DDPM) as a method to infer the volume or number density of giant molecular clouds (GMCs) from projected mass surface density maps. We adopt…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
We review different models used for reactions involved in nuclear astrophysics. The reaction rate is defined for resonant as well as for non-resonant processes. For low-density nuclei, we describe the DWBA method, the potential model, the…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics. Based on the fluctuation-dissipation theory, this problem is reformulated as an unsupervised learning task…
This paper investigates the problem of distributed stochastic approximation in multi-agent systems. The algorithm under study consists of two steps: a local stochastic approximation step and a diffusion step which drives the network to a…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
Multicellular systems play a key role in bioprocess and biomedical engineering. Cell ensembles encountered in these setups show phenotypic variability like size and biochemical composition. As this variability may result in undesired…
Models for human choice prediction in preference learning and psychophysics often consider only binary response data, requiring many samples to accurately learn preferences or perceptual detection thresholds. The response time (RT) to make…
A central problem in data analysis is the low dimensional representation of high dimensional data, and the concise description of its underlying geometry and density. In the analysis of large scale simulations of complex dynamical systems,…