Related papers: Path statistics, memory, and coarse-graining of co…
Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…
In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner…
Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
The Semi-Markov property of Continuous Time Random Walks (CTRWs) and their limit processes is utilized, and the probability distributions of the bivariate Markov process $(X(t),V(t))$ are calculated: $X(t)$ is a CTRW limit and $V(t)$ a…
The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and under power law regime is splitted into three distinct random walks: (rw_1), a random walk along the line of natural time, happening in operational time; (rw_2), a…
Transition Path Theory (TPT) provides a rigorous statistical characterization of the ensemble of trajectories connecting directly, i.e., without detours, two disconnected (sets of) states in a Markov chain, a stochastic process that…
Using the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road…
Transition path theory computes statistics from ensembles of reactive trajectories. A common strategy for sampling reactive trajectories is to control the branching and pruning of trajectories so as to enhance the sampling of low…
Using the continuous-time random walk (CTRW) approach, we study the phenomenon of relaxation of two-state systems whose elements evolve according to a dichotomous process. Two characteristics of relaxation, the probability density function…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
Continuous time random walks (CTRW) on finite arbitrarily inhomogeneous chains are studied. By introducing a technique of counting all possible trajectories, we derive closed-form solutions in Laplace space for the Green's function and for…
Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…
We study continuous time random walks (CTRW) with power law distribution of waiting times under resetting which brings the walker back to the origin, with a power-law distribution of times between the resetting events. Two situations are…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
As random walk is a powerful tool in many graph processing, mining and learning applications, this paper proposes an efficient in-memory random walk engine named ThunderRW. Compared with existing parallel systems on improving the…
Background: This study is mainly motivated by the need of understanding how the diffusion behaviour of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell,…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
Functional limit theorem for continuous-time random walks (CTRW) are found in general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional…
We discuss large deviation properties of continuous-time random walks (CTRW) and present a general expression for the large deviation rate in CTRW in terms of the corresponding rates for the distributions of steps' lengths and waiting…
Systems living in complex non equilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the…