Related papers: Nondiscriminatory Propagation on Trees
The way in which different types of dynamics unfold in complex networks is intrinsically related to the propagation of activation along nodes, which is strongly affected by the network connectivity. In this work we investigate to which…
Broadcast and consensus are most fundamental tasks in distributed computing. These tasks are particularly challenging in dynamic networks where communication across the network links may be unreliable, e.g., due to mobility or failures.…
Berry and Wang [Phys. Rev. A {\bf 83}, 042317 (2011)] show numerically that a discrete-time quantum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…
This paper presents an asynchronous distributed algorithm to manage multiple trees for peer-to-peer streaming in a flow level model. It is assumed that videos are cut into substreams, with or without source coding, to be distributed to all…
We consider labelings of a finite regular tree by a finite alphabet subject to restrictions specified by a nonnegative transition matrix, propose an algorithm for determining whether the set of possible configurations on the last row of the…
We analyse diffusion dynamics on weakly-coupled networks (interconnected networks) by means of separation of time scales. Using an adiabatic approximation we reduced the system dynamics to a Markov chain with aggregated variables and…
Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information spread over social networks and biological diseases spreading over contact networks. Often, the networks over which these…
We introduce and study the problem of posterior inference on tree-structured graphical models in the presence of a malicious adversary who can corrupt some observed nodes. In the well-studied broadcasting on trees model, corresponding to…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
Excitation waves are studied on trees and random networks of coupled active elements. Undamped propagation of such waves is observed in those networks. It represents an excursion from the resting state and a relaxation back to it for each…
The transmission of a vertex in a connected graph is the sum of distances from that vertex to all the other vertices. A connected graph is transmission irregular if any two distinct vertices have different transmissions. We present an…
We investigate space-time trade-offs for population protocols in sparse interaction graphs. In complete interaction graphs, optimal space-time trade-offs are known for the leader election and exact majority problems. However, it has…
Zero forcing (also called graph infection) on a simple, undirected graph $G$ is based on the color-change rule: If each vertex of $G$ is colored either white or black, and vertex $v$ is a black vertex with only one white neighbor $w$, then…
We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behaviours of the shattering times, defined as the first instants when all the blocks of…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…
We address the problem of representing dynamic graphs using $k^2$-trees. The $k^2$-tree data structure is one of the succinct data structures proposed for representing static graphs, and binary relations in general. It relies on compact…
Randomized gossip is one of the most popular way of disseminating information in large scale networks. This method is appreciated for its simplicity, robustness, and efficiency. In the "push" protocol, every informed node selects, at every…