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We consider an agent who represents uncertainty about the environment via a possibly misspecified model. Each period, the agent takes an action, observes a consequence, and uses Bayes' rule to update her belief about the environment. This…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic…
The limiting stability of invariant probability measures of time homogeneous transition semigroups for autonomous stochastic systems has been extensively discussed in the literature. In this paper we initially initiate a program to study…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
In this paper we consider mathematical modeling of the dynamics of self-organized patterning of spatially confined human embryonic stem cells (hESCs) treated with BMP4 (gastruloids) described in recent experimental works. In the first part…
Stochastic reaction networks are mathematical models frequently used in, but not limited to, biochemistry. These models are continuous-time Markov chains whose transition rates depend on certain parameters called rate constants, which…
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state…
This paper is concerned with a quantitative analysis of asymptotic behaviors of (possibly sign-changing) solutions to the Cauchy-Dirichlet problem for the fast diffusion equation posed on bounded domains with Sobolev subcritical exponents.…
Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this Letter we propose a global…
One of the aims of systems biology is to build multiple layered and multiple scale models of living systems which can efficiently describe phenomena occurring at various level of resolution. Such models should consist of layers of various…
We demonstrate aging behavior in a simple non-linear system. Our model is a chaotic map which generates deterministically sub-diffusion. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks,…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
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…
Parrondo's paradox is extended to regime switching random walks in random environments. The paradoxical behavior of the resulting random walk is explained by the effect of the random environment. Full characterization of the asymptotic…