Related papers: Continuum Cascade Model: Branching Random Walk for…

Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…

We build a model of information cascades on feed-based networks, taking into account the finite attention span of users, message generation rates and message forwarding rates. Using this model, we study through simulations, the effect of…

We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability…

We investigate the directed random walk on hierarchic trees. Two cases are investigated: random variables on deterministic trees with a continuous branching, and random variables on the trees constructed trough the random branching process.…

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…

A probabilistic framework is introduced that represents stylized banking networks and aims to predict the size of contagion events. In contrast to previous work on random financial networks, which assumes independent connections between…

Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…

In this paper we define direct product of graphs and give a recipe for obtained probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on…

There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time $t$. In…

Food webs are networks describing who is eating whom in an ecological community. By now it is clear that many aspects of food-web structure are reproducible across diverse habitats, yet little is known about the driving force behind this…

We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our…

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…

We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours…

The networks of predator-prey interactions in ecological systems are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole. In order to understand the mechanism driving the…

Uncovering the mechanism behind the scaling law in human trajectories is of fundamental significance in understanding many spatio-temporal phenomena. In combination of the exploration and the preferential returns, we propose a simple…

The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…

One important task in the study of information cascade is to predict the future recipients of a message given its past spreading trajectory. While the network structure serves as the backbone of the spreading, an accurate prediction can…

We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…

We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…

We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a…