Related papers: Duality relations between spatial birth-death proc…
Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…
Fluctuation theorems may be partitioned into those that apply the probability measure under the original stochastic process to reversed paths, and those that construct a new, adjoint measure by similarity transform, which locally reverses…
In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the…
This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current…
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…
Dislocation-assisted phase separation processes in binary systems subjected to irradiation effect are studied analytically and numerically. Irradiation is described by athermal atomic mixing in the form of ballistic flux with spatially…
We derive and test a novel holographic duality in the B-model topological string theory. The duality relates the B-model on certain Calabi-Yau three-folds to two-dimensional chiral algebras defined as gauged $\beta\gamma\,$ systems. The…
Scalar sector offers a valuable avenue to explore its implications in the particle physics phenomenology for new physics and several model dependent phenomena. Two Higgs doublet models are among the promising models for such explorations.…
We show for the moduli space of rank-2 coherent sheaves on an algebraic surface that there exists a 'dual' moduli space. This dual space allows a construction of the first one without using the GIT construction. Furthermore, we obtain a…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
Some of the most important results in prediction theory and time series analysis when finitely many values are removed from or added to its infinite past have been obtained using difficult and diverse techniques ranging from duality in…
Motivated by recent experiments with two-component Bose-Einstein condensates, we study fully-connected spin models subject to an additional constraint. The constraint is responsible for the Hilbert space dimension to scale only linearly…
We develop a Hilbert-space approach to the diffusion process of the Brownian motion in a bounded domain with random jumps from the boundary introduced by Ben-Ari and Pinsky in 2007. The generator of the process is introduced by a diffusion…
Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional…
Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…
In a two species reaction diffusion system,we show that it is possible to generate a set of wavelength doubling bifuractions leading to spatially chaotic state.The wavelength doubling bifurcations are preceded by a symmetry breaking…
The goal of this work is to analyze the long-term behavior of reaction-diffusion systems arising in two-species chemical models and to identify the minimal set of modes that determine their dynamics. The models considered include, as…
A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption…