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We study how stochastic resetting affects first-passage processes in systems of many interacting particles. While resetting is well understood for single-particle dynamics, its consequences for collective behavior remain less clear. We…

Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of L\'evy walks, a specific range of optimal efficiencies was suggested under variation of search…

We review some representative results for first-passage problems involving so-called mortal or evanescent walkers, i.e., walkers with a finite lifetime. The mortality constraint plays a key role in the modeling of many real scenarios, as it…

Stochastic resets have lately emerged as a mechanism able to generate finite equilibrium mean square displacement (MSD) when they are applied to diffusive motion. Furthermore, walkers with an infinite mean first arrival time (MFAT) to a…

Machine learning (ML) is probably the first and foremost used technique to deal with the size and complexity of the new generation of data. In this paper, we analyze one of the means to increase the performances of ML algorithms which is…

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…

This paper considers simulation-based optimization of the performance of a regime-switching stochastic system over a finite set of feasible configurations. Inspired by the stochastic fictitious play learning rules in game theory, we propose…

Many physical, chemical, and biological systems depend on the first passage time (FPT) of a diffusive searcher to a target. Typically, this FPT is much slower than the characteristic diffusion timescale. For example, this is the case if the…

We study the effect of a resetting point randomly distributed around the origin on the mean first passage time of a Brownian searcher moving in one dimension. We compare the search efficiency with that corresponding to reset to the origin…

In this paper, we conduct a literature review of laws of motion based on stochastic search strategies which are mainly focused on exploring highly dynamic environments. In this regard, stochastic search strategies represent an interesting…

In this paper, we analyze the mean first passage time (MFPT) for a single Brownian particle to find a stochastically-gated target under the additional condition that the position of the particle is reset to a fixed position $\x_r$ at a rate…

How long a stochastic process survives before leaving a domain depends not only on its intrinsic dynamics but also on how it is observed. Classical first-passage theory assumes continuous monitoring with absorbing boundaries…

Pushdown systems (PDSs) and recursive state machines (RSMs), which are linearly equivalent, are standard models for interprocedural analysis. Yet RSMs are more convenient as they (a) explicitly model function calls and returns, and (b)…

A striking feature of our universe is its near criticality. The cosmological constant and weak hierarchy problems, as well as the metastability of the electroweak vacuum, can all be understood as problems of criticality. This suggests a…

In this chapter, we consider the problem of a non-Markovian random walker (displaying memory effects) searching for a target. We review an approach that links the first passage statistics to the properties of trajectories followed by the…

Retrieval data structures are data structures that answer key-value queries without paying the space overhead of explicitly storing keys. The problem can be formulated in four settings (static, value-dynamic, incremental, or dynamic), each…

We study random walks with stochastic resetting to the initial position on arbitrary networks. We obtain the stationary probability distribution as well as the mean and global first passage times, which allow us to characterize the effect…

The spectral theory of random walks on networks of arbitrary topology can be readily extended to study random walks and L\'evy flights subject to resetting on these structures. When a discrete-time process is stochastically brought back…

In this paper we consider the one-dimensional dynamical evolution of a particle traveling at constant speed and performing, at a given rate, random reversals of the velocity direction. The particle is subject to stochastic resetting,…

In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a…