Related papers: Random walks in time-varying networks with memory

Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…

Elephant random walk is a special type of random walk that incorporates the memory of the past to determine its future steps. The probability of this walk taking a particular step (+1 or -1) at a time point, conditioned on the entire…

For random walks on networks (graphs), it is a theoretical challenge to explicitly determine the mean first-passage time (MFPT) between two nodes averaged over all pairs. In this paper, we study the MFPT of random walks in the famous…

The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…

In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…

In a recent paper [2] the author introduced and investigated a random walk model similar to a model introduced in [1]. In these models the increment of the random walk depends on the complete past of the process. In this note I will point…

We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…

The self-avoiding random walk (SARW) is a stochastic process whose state variable avoids returning to previously visited states. This non-Markovian feature has turned SARWs a powerful tool for modelling a plethora of relevant aspects in…

Random walks (RWs) are fundamental stochastic processes with applications across physics, computer science, and information processing. A recent extension, the laser chaos decision-maker, employs chaotic time series from semiconductor…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

Empirical temporal networks display strong heterogeneities in their dynamics, which profoundly affect processes taking place on these networks, such as rumor and epidemic spreading. Despite the recent wealth of data on temporal networks,…

We perform an in-depth study for mean first-passage time (MFPT)---a primary quantity for random walks with numerous applications---of maximal-entropy random walks (MERW) performed in complex networks. For MERW in a general network, we…

We introduce a general framework, applicable to a broad class of random walks on networks, that quantifies the response of the mean first-passage time to a target node to a local perturbation of the network, both in the context of attacks…

Random walks on bipartite networks have been used extensively to design personalized recommendation methods. While aging has been identified as a key component in the growth of information networks, most research has focused on the…

Random walks can be used to search complex networks for a desired resource. To reduce search lengths, we propose a mechanism based on building random walks connecting together partial walks (PW) previously computed at each network node.…

We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…

The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…

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…