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Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However,…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
In this paper, we propose a novel approach to obtaining a reliable and simple mathematical model of a dielectrophoretic force for model-based feedback micromanipulation. Any such model is expected to sufficiently accurately relate the…
Approximate mean-field equations of motion for the classical chiral field are developed within the linear sigma model by means of a Hartree factorization. Both the approximate and the unapproximated equations of motion are augmented with a…
Droplet-based interphase synthesis provides means to produce nanoparticles with low polydispersity by controlling mass transport through droplet dynamics. An experimentally validated model, based on coupled computational fluid dynamics with…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
An electric-field-induced phase transition and pattern formation in a binary dielectric fluid layer are studied using a coarse-grained free energy functional. The electrostatic part of the free energy is a nonlinear functional of the…
In this paper we study a two dimensional crowd model where pedestrian velocity consists of two elements: a non--local interaction term, modeling the effect of other walkers on each individual, and a control term. This latter term can be…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
Given a set of collective variables, a method is proposed to obtain the associated conjugated collective momenta and masses starting from a microscopic time-dependent mean-field theory. The construction of pairs of conjugated variables is…
In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Measurement-induced phase transitions (MIPTs) in monitored quantum dynamics are non-equilibrium phase transitions between quantum-chaotic (volume-law entangled) and entanglement-suppressed, area-law phases. We reveal how monitored dynamics…
We investigate the complex spatiotemporal dynamics of an ecological network with species dispersal mediated via a mean-field coupling. The local dynamics of the network are governed by the Truscott--Brindley model, which is an important…
A phase field approach is proposed to model the chemotaxis of Dictyostelium discoideum. In this framework, motion is controlled by active forces as determined by the Meinhardt model of chemical dynamics which is used to simulate directional…
A conservative Feller evolution on continuous bounded functions is constructed from a weakly continuous, time-inhomogeneous transition function describing a pure jump process on a locally compact Polish space. The transition function is…
We investigate pump-driven droplet electrohydrodynamics with an emphasis on deformation, pinch-off, and recoalescence. A thermodynamically consistent phase-field framework is developed that couples Nernst--Planck--Poisson electrodiffusion…
We show that the continuous-time gradient descent in Rn can be viewed as an optimal controlled evolution for a suitable action functional; a similar result holds for stochastic gradient descent. We then provide an analogous characterization…
Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular…
While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these…