Related papers: Stochastic Reaction-Diffusion Systems in Biophysic…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
Discrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years severalmethods for accurately…
Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…
Motivated by investigating spatio-temporal patterns of the distribution of continuous variables, we consider describing the conditional distribution function of the response variable incorporating spatio-temporal components given…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
Diffusion models have shown a great ability at bridging the performance gap between predictive and generative approaches for speech enhancement. We have shown that they may even outperform their predictive counterparts for non-additive…
Modeling transformations between arbitrary data distributions is a fundamental scientific challenge, arising in applications like drug discovery and evolutionary simulation. While flow matching offers a natural framework for this task, its…
We investigate a recently proposed cross-diffusion system modelling the growth of gliobastoma taking into account size exclusion both in the migration and proliferation process. In addition to degenerate nonlinear cross-diffusion the model…
Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic Thermodynamics uses Markovian jump processes to model the random transitions between the chemical and configurational…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…
Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection-diffusion model, describing the spatio-temporal dynamics of a population in different human behaviors (alert, panic and control)…
We establish results for the first sensitivity analysis of the stochastic fluid models (SFMs). We derive expressions for the sensitivity analysis of the key stationary and transient (time-dependent) quantities of this class of models. We…
Statistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment.…
Stochasticity in gene expression can give rise to fluctuations in protein levels and lead to phenotypic variation across a population of genetically identical cells. Recent experiments indicate that bursting and feedback mechanisms play…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…