Related papers: Optimization in First-Passage Resetting
We review recent work on systems with multiple interacting-particles having the dynamical feature of stochastic resetting. The interplay of time scales related to inter-particle interactions and resetting leads to a rich behavior, both…
A new model of search based on stochastic resetting is introduced, wherein rate of resets depends explicitly on time elapsed since the beginning of the process. It is shown that rate inversely proportional to time leads to paradoxical…
In this article we study optimization problems ruled by $\alpha$-fractional diffusion operators with volume constraints. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of…
Resetting is a strategy for boosting the speed of a target-searching process. Since its introduction over a decade ago, most studies have been carried out under the assumption that resetting takes place instantaneously. However, due to its…
We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that MSD relaxes to a constant only when the distribution of reset times possess finite mean and variance. In this case, the leading…
`Gating' is a widely observed phenomenon in biochemistry that describes the transition between the activated (or open) and deactivated (or closed) states of an ion-channel, which makes transport through that channel highly selective. In…
We investigate the role of stochastic resetting in non-Markovian systems, where memory effects arise due to slow relaxation, rugged energy landscapes, disordered environments, and molecular crowding. Using the celebrated continuous-time…
We investigate a class of diffusion-controlled reactions that are initiated at the time instance when a prescribed number $K$ among $N$ particles independently diffusing in a solvent are simultaneously bound to a target region. In the…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
During a random search, resetting the searcher's position from time to time to the starting point often reduces the mean completion time of the process. Although many different resetting models have been studied over the past ten years,…
Classical reverse diffusion is generated by changing the drift at fixed noise. We show that the quantum version of this principle obeys an exact law with a sharp phase boundary. For Gaussian pure-loss dynamics, the canonical model of…
Algorithms for computing equilibria, optima, and fixed points in nonconvex problems often depend sensitively on practitioner-chosen initial conditions. When uniqueness of a solution is of interest, a common heuristic is to run such…
We have studied anomalous diffusion of a particle in a random medium in which the passage of the particle may modify the state of the visited sites. The simplicity of the dynamics allows analytic solution. Interesting propagation and…
Many chemical reactions can be formulated in terms of particle diffusion in a complex energy landscape. Transition path theory (TPT) is a theoretical framework for describing the direct (reaction) pathways from reactant to product states…
We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model where the drift and volatility coefficients are general functions of the level of surplus and the external…
Particle filtering is a Bayesian inference method and a fundamental tool in state estimation for dynamic systems, but its effectiveness is often limited by the constraints of the initial prior distribution, a phenomenon we define as the…
This paper considers a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of a related stochastic processes called penalties. We…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…