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Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
The interplay between stochastic chemical reactions and diffusion can generate rich spatiotemporal patterns. While the timescale for individual reaction or diffusion events may be very fast, the timescales for organization can be much…
Risk specialists are trying to understand risk better and use complex models for risk assessment, while many risks are not yet well understood. The lack of empirical data and complex causal and outcome relationships make it difficult to…
We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare,…
Coarse-graining of fully atomistic molecular dynamics simulations is a long-standing goal in order to allow the description of processes occurring on biologically relevant timescales. For example, the prediction of pathways, rates and…
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…
Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into…
Mathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings. While a variety of models are now available, their…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
Presently, it is well established that fission of excited nuclei is a dynamical process being a subject of fluctuations and dissipation. In the literature, there are indications that, at the compact nucleus shapes, the strength of nuclear…
Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
In a data matrix, we may distinguish between cases, each represented by a row vector for a statistical unit, and cells, which correspond to single entries of the data matrix. Recent developments in Robust Statistics have introduced the…
The escape of the randomly accelerated undamped particle from the finite interval under action of stochastic resetting is studied. The motion of such a particle is described by the full Langevin equation and the particle is characterized by…