Related papers: The Stretch - Length Tradeoff in Geometric Network…
We study spatial networks that are designed to distribute or collect a commodity, such as gas pipelines or train tracks. We focus on the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of…
Most complex networks are not static, but evolve along time. Given a specific configuration of one such changing network, it becomes a particularly interesting issue to quantify the diversity of possible unfoldings of its topology. In this…
In the classic model of first passage percolation, for pairs of vertices separated by a Euclidean distance $L$, geodesics exhibit deviations from their mean length $L$ that are of order $L^\chi$, while the transversal fluctuations, known as…
Given two independent Poisson point processes $\Phi^{(1)},\Phi^{(2)}$ in $R^d$, the continuum AB percolation model is the graph with points of $\Phi^{(1)}$ as vertices and with edges between any pair of points for which the intersection of…
The reliability of a network is an important parameter to consider when building a network. Different characteristics of the network can become unreliable over time or from other outside forces. In a simple setting, we model a network as a…
Let $X:=X_n\cup\{(0,0),(1,0)\}$, where $X_n$ is a planar Poisson point process of intensity $n$. We provide a first non-trivial lower bound for the distance between the expected length of the shortest path between $(0,0)$ and $(1,0)$ in the…
We provide general formulae for the configurational exponents of an arbitrary polymer network connected to the surface of an arbitrary wedge of the two-dimensional plane, where the surface is allowed to assume a general mixture of boundary…
Let $P$ be a set of $n\geq 3$ points in general position in the plane. The edge disjointness graph $D(P)$ of $P$ is the graph whose vertices are all the closed straight line segments with endpoints in $P$, two of which are adjacent in…
We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is…
We consider navigation schemes on planar diluted lattices and semi lattices with one discrete and one continuous component. More precisely, nodes that survive inhomogeneous Bernoulli site percolation, or are placed as inhomogeneous Poisson…
We consider a fading point-to-point link with packets arriving randomly at rate $\lambda$ per slot to the transmitter queue. We assume that the transmitter can control the number of packets served in a slot by varying the transmit power for…
Xue and Kumar have established that the number of neighbors required for connectivity of wireless networks with N uniformly distributed nodes must grow as log(N), and they also established that the actual number required lies between…
In Euclidean space there is a trivial upper bound on the maximum length of a compound "walk" built up of variable-length jumps, and a considerably less trivial lower bound on its minimum length. The existence of this non-trivial lower bound…
Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complicated,…
In this paper we consider spatial networks that realize a balance between an infrastructure cost (the cost of wire needed to connect the network in space) and communication efficiency, measured by average shortest pathlength. A global…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
The topic is the average order of a connected induced subgraph of a graph. This generalizes, to graphs in general, the average order of a subtree of a tree. In 1984, Jamison proved that the average order, over all trees of order $n$, is…
We consider a communication scenario where a source communicates with a destination over a directed layered relay network. Each relay performs analog network coding where it scales and forwards the signals received at its input. In this…
We show that the local limit of the uniform spanning tree on any finite, simple, connected, regular graph sequence with degree tending to infinity is the Poisson(1) branching process conditioned to survive forever. An extension to "almost"…
In this paper, we lay the groundwork on the comparison of phylogenetic networks based on edge contractions and expansions as edit operations, as originally proposed by Robinson and Foulds to compare trees. We prove that these operations…