Related papers: Diffusive transport on networks with stochastic re…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…
We study the diffusion process in the presence of stochastic resetting inside a two-dimensional wedge of top angle $\alpha$, bounded by two infinite absorbing edges. In the absence of resetting, the second moment of the first-passage time…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
Will the strategy of resetting} help a stochastic process to reach its target efficiently, with its environment continually toggling between a strongly favourable and an unfavourable (or weakly favourable) state? A diffusive run-and-tumble…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Transport phenomena are ubiquitous in nature and known to be important for various scientific domains. Examples can be found in physics, electrochemistry, heterogeneous catalysis, physiology, etc. To obtain new information about diffusive…
Random walks are gaining much attention from the networks research community. They are the basis of many proposals aimed to solve a variety of network-related problems such as resource location, network construction, nodes sampling, etc.…
Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic…
When navigating complex environments, animals often combine multiple strategies to mitigate the effects of external disturbances. These modalities often correspond to different sources of information, leading to speed-accuracy trade-offs.…
Stochastic resetting is a powerful strategy known to accelerate the first-passage time statistics of stochastic processes. While its effects on Markovian systems are well understood, a general framework for non-Markovian dynamics is still…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…
Random search processes are instrumental in studying and understanding navigation properties of complex networks, food search strategies of animals, diffusion control of molecular processes in biological cells, and improving web search…
A self-repelling random walk of a token on a graph is one in which at each step, the token moves to a neighbor that has been visited least often (with ties broken randomly). The properties of self-repelling random walks have been analyzed…
Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an…
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking…
We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient $D(t) \sim t^{\alpha -1}$ with $\alpha > 0$ (scaled Brownian motion) is stochastically reset to its initial position,…
We look into the problem of stochastic resetting with refractory periods. The model dynamics comprises diffusive and motionless phases. The diffusive phase ends at random time instants, at which the system is reset to a given position --…