Related papers: Distance Distributions in Finite Uniformly Random …
We consider a random variable expressed as the Euclidean distance between an arbitrary point and a random variable uniformly distributed in a closed and bounded set of a three-dimensional Euclidean space. Four cases are considered for this…
Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently…
We investigate the heterogeneity of outcomes of repeated instances of percolation experiments in complex networks using a message passing approach to evaluate heterogeneous, node dependent probabilities of belonging to the giant or…
We apply statistical physics to study the task of resource allocation in random networks with limited bandwidths along the transportation links. The mean-field approach is applicable when the connectivity is sufficiently high. It allows us…
In this paper, we investigate the transmission range assignment for N wireless nodes located on a line (a linear wireless network) for broadcasting data from one specific node to all the nodes in the network with minimum energy. Our goal is…
We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…
Rapid progress made in the field of sensor technology, wireless communication, and computer networks in recent past, led to the development of wireless Ad-hoc sensor networks, consisting of small, low-cost sensors, which can monitor wide…
We investigate entanglement distribution in pure-state quantum networks. We consider the case when non-maximally entangled two-qubit pure states are shared by neighboring nodes of the network. For a given pair of nodes, we investigate how…
Wireless networks are fundamentally limited by the intensity of the received signals and by their inherent interference. It is shown here that in finite ad hoc networks where node placement is modelled according to a Poisson point process…
A wireless sensor network comprises of small sensor nodes each of which consists of a processing device, small amount of memory, battery and radio transceiver for communication. The sensor nodes are autonomous and spatially distributed in…
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or matrix distances may fail to capture underlying subtle…
Many analytic results for the connectivity, coverage, and capacity of wireless networks have been reported for the case where the number of nodes, $n$, tends to infinity (large-scale networks). The majority of these results have not been…
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
This paper analyzes the outage performance in finite wireless networks. Unlike most prior works, which either assumed a specific network shape or considered a special location of the reference receiver, we propose two general frameworks for…
The edges in networks are not only binary, either present or absent, but also take weighted values in many scenarios (e.g., the number of emails between two users). The covariate-$p_0$ model has been proposed to model binary directed…
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad-hoc networks "soft" or "probabilistic"…
Dynamical processes taking place on networks have received much attention in recent years, especially on various models of random graphs (including small world and scale free networks). They model a variety of phenomena, including the…