Journal ArticleDOI
From first-passage times of random walks in confinement to geometry-controlled kinetics
TLDR
In this article, the authors present a general theory which allows one to accurately evaluate the mean first-passage time (FPT) for regular random walks in bounded domains, and its extensions to related firstpassage observables such as splitting probabilities and occupation times.About:
This article is published in Physics Reports.The article was published on 2014-06-30. It has received 249 citations till now. The article focuses on the topics: Random walk & Stochastic process.read more
Citations
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Random walks and diffusion on networks
TL;DR: The theory and applications of random walks on networks are surveyed, restricting ourselves to simple cases of single and non-adaptive random walkers, and three main types are distinguished: discrete-time random walks, node-centric continuous-timerandom walks, and edge-centric Continuous-Time random walks.
Journal ArticleDOI
Random walks and diffusion on networks
TL;DR: Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures as discussed by the authors, and they are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can extract information about important entities or dense groups of entities in networks.
Journal Article
The yeast coexpression network has a small-world, scale-free architecture and can be explained by a simple model
TL;DR: A new model is derived based on the observation that there is a positive correlation between the sequence similarity of paralogues and their probability of coexpression or sharing of transcription factor binding sites (TFBSs) that reproduces the scale‐free, small‐world architecture of the coregulation network and the homology relations between coregulated genes without the need for selection.
Journal ArticleDOI
Universal proximity effect in target search kinetics in the few-encounter limit.
Aljaž Godec,Ralf Metzler +1 more
TL;DR: The behavior of smooth FPT densities, for which all moments are finite, is explained and universal yet generally non-Poissonian long-time asymptotics for a broad variety of transport processes are demonstrated.
Journal ArticleDOI
Diffusion-limited reactions in dynamic heterogeneous media
TL;DR: A general mathematical framework is proposed to compute the distribution of first-passage times in a dynamically heterogeneous medium and shows how the dynamic disorder broadens the distribution and increases the likelihood of both short and long trajectories to reactive targets.
References
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Journal ArticleDOI
Collective dynamics of small-world networks
TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Journal ArticleDOI
Statistical mechanics of complex networks
TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
Book
Stochastic processes in physics and chemistry
TL;DR: In this article, the authors introduce the Fokker-planck equation, the Langevin approach, and the diffusion type of the master equation, as well as the statistics of jump events.
Journal ArticleDOI
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Journal ArticleDOI
Comprehensive mapping of long-range interactions reveals folding principles of the human genome.
Erez Lieberman Aiden,Nynke L. van Berkum,Louise Williams,Maxim Imakaev,Tobias Ragoczy,Tobias Ragoczy,Agnes Telling,Agnes Telling,Ido Amit,Bryan R. Lajoie,Peter J. Sabo,Michael O. Dorschner,Richard Sandstrom,Bradley E. Bernstein,Bradley E. Bernstein,Michaël Bender,Mark Groudine,Mark Groudine,Andreas Gnirke,John A. Stamatoyannopoulos,Leonid A. Mirny,Eric S. Lander,Eric S. Lander,Job Dekker +23 more
TL;DR: Hi-C is described, a method that probes the three-dimensional architecture of whole genomes by coupling proximity-based ligation with massively parallel sequencing and demonstrates the power of Hi-C to map the dynamic conformations of entire genomes.