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Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative…
During neurodevelopment, neuronal axons navigate through the extracellular environment, guided by various cues to establish connections with distant target cells. Among other factors, axon trajectories are influenced by heterogeneities in…
This paper presents a rigorous mathematical analysis, alongside simulation studies, of a spatially extended stochastic electrophysiology model, the Hodgkin-Huxley model of the squid giant axon being a classical example. Although most…
The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in $\R^n$. Our primary contribution is a stochastic homogenization result that characterizes the effective…
The formation of neuron networks is a process of fundamental importance for understanding the development of the nervous system and for creating biomimetic devices for tissue engineering and neural repair. The basic process that controls…
We study a minimal lattice model which describes bidirectional transport of "particles" driven along a one dimensional track, as is observed in microtubule based, motor protein driven bidirectional transport of cargo vesicles, lipid bodies…
Inverse optimal control can be used to characterize behavior in sequential decision-making tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce…
We present a study of exclusion processes on networks as models for complex transport phenomena and in particular for active transport of motor proteins along the cytoskeleton. We argue that active transport processes on networks…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
Extending deterministic compartments pharmacokinetic models as diffusions seems not realistic on biological side because paths of these stochastic processes are not smooth enough. In order to extend one compartment intra-veinous bolus…
We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties…
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…
We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
We consider random search processes alternating stochastically between diffusion and ballistic motion, in which the distribution function of ballistic motion directions varies from point to point in space. The specific space dependence of…
The spatial localization or sequestering of motile cargo and their dispersal within cells is an important process in a number of physiological contexts. The morphology of the cytoskeletal network, along which active, motor-driven…
Mathematical models of biological neural networks are associated to a rich and complex class of stochastic processes. In this paper, we consider a simple {\em plastic} neural network whose {\em connectivity/synaptic strength} $(W(t))$…
Molecular motors are specialized proteins which perform active, directed transport of cellular cargoes on cytoskeletal filaments. In many cases, cargo motion powered by motor proteins is found to be bidirectional, and may be viewed as a…
We present a derivation of a multidomain model for the electric potential in bundles of randomly distributed axons with different radii. The FitzHugh-Nagumo dynamics is assumed on the axons' membrane, and the conductivity depends…
In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly…