Related papers: Estimation of Parameter Distributions for Reaction…
This paper studies how patterns derived from a system of reaction-diffusion equations may vary significantly depending upon boundary and initial conditions, as well as in the spatial dependence of the coefficients involved. From an…
Daily, are reported systems in nature that present anomalous diffusion phenomena due to irregularities of medium, traps or reactions process. In this scenario, the diffusion with traps or localised--reactions emerge through various…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
Reaction-diffusion models are widely used to study spatially-extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for…
Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of…
Stochastic models play an essential role in accounting for the variability and unpredictability seen in real-world. This paper focuses on the application of the gamma distribution to analysis of the stationary distributions of populations…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
We study a stochastic model of urban growth generating spatial distributions of population densities at an intermediate mesoscopic scale. The model is based on the antagonist interplay between the two opposite abstract processes of…
The nonlocal Fisher equation is a diffusion-reaction equation with a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the…
Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available and numerical methods are the main tools for approximating the…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
Recent technological advancements have enabled detailed investigation of associations between the molecular architecture and tumor heterogeneity, through multi-source integration of radiological imaging and genomic (radiogenomic) data. In…
Heterogeneity in gene expression across isogenic cell populations can give rise to phenotypic diversity, even when cells are in homogenous environments. This diversity arises from the discrete, stochastic nature of biochemical reactions,…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…
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…
Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…
We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…