Related papers: Modeling Shortest Paths in Polymeric Networks usin…
We investigate the large deviation probabilities of first passage times (FPT) of discrete-time supercritical non-lattice branching random walks (BRWs) in $\mathbb{R}^d$ where $d\geq 1$. The FPT refers to the first time the BRW enters a ball…
Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal…
We present analytical results for the distribution of first-passage (FP) times of random walks (RWs) on random regular graphs that consist of $N$ nodes of degree $c \ge 3$. Starting from a random initial node at time $t=0$, at each time…
Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states, for example those employed in…
Randomized shortest paths (RSP) are a tool developed in recent years for different graph and network analysis applications, such as modelling movement or flow in networks. In essence, the RSP framework considers the temperature-dependent…
In a network, the shortest paths between nodes are of great importance as they allow the fastest and strongest interaction between nodes. However measuring the shortest paths between all nodes in a large network is computationally…
Highly stretchable and self-healable supramolecular elastomers are promising materials for future soft electronics, biomimetic systems, and smart textiles, due to their dynamic cross-linking bonds. The dynamic or reversible nature of the…
We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…
We study the problem of searching for a fixed path $\epsilon_0\epsilon_1\cdots\epsilon_l$ on a network through random walks. We analyze the first hitting time of tracking the path, and obtain exact expression of mean first hitting time…
The first passage time (FPT) distribution for random walk in complex networks is calculated through an asymptotic analysis. For network with size $N$ and short relaxation time $\tau\ll N$, the computed mean first passage time (MFPT), which…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
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…
Consider the following routing problem in the context of a large scale network $G$, with particular interest paid to power law networks, although our results do not assume a particular degree distribution. A small number of nodes want to…
We present analytical results for the distribution of first hitting times of random walks (RWs) on random regular graphs (RRGs) of degree $c \ge 3$ and a finite size $N$. Starting from a random initial node at time $t=1$, at each time step…
Above two dimensions, diffusion of a particle in a medium with quenched random traps is believed to be well-described by the annealed continuous time random walk (CTRW). We propose an approximate expression for the first-passage-time (FPT)…
We present analytical results for the distribution of first return (FR) times of random walks (RWs) on random regular graphs (RRGs) consisting of $N$ nodes of degree $c \ge 3$. Starting from a random initial node $i$ at time $t=0$, at each…
Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…
The shortest path problem is related to many dynamic processes on networks, ranging from routing in communication networks to signaling in molecular interaction networks. When the network is fully known, the shortest path problem can be…
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…
We present a graph random walk (GRW) method for the study of charge transport properties of complex molecular materials in the time-of-flight regime. The molecules forming the material are represented by the vertices of a directed weighted…