Related papers: Connectivity in Sub-Poisson Networks
This paper proposes a communication strategy for decentralized learning on wireless systems. Our discussion is based on the decentralized parallel stochastic gradient descent (D-PSGD), which is one of the state-of-the-art algorithms for…
In recent times, the use of stochastic geometry has become a popular and important tool for performance analysis of next-generation dense small cell wireless networks. Usually, such networks are modeled using 2 dimensional spatial Poisson…
We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…
We study a model for coupled networks introduced recently by Buldyrev et al., Nature 464, 1025 (2010), where each node has to be connected to others via two types of links to be viable. Removing a critical fraction of nodes leads to a…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
Geographic locations of cellular base stations sometimes can be well fitted with spatial homogeneous Poisson point processes. In this paper we make a complementary observation: In the presence of the log-normal shadowing of sufficiently…
Given a quasi-transitive infinite graph $G$ with volume growth rate ${\rm gr}(G),$ a transient biased electric network $(G,\, c_1)$ with bias $\lambda_1\in (0,\,{\rm gr}(G))$ and a recurrent biased one $(G,\, c_2)$ with bias $\lambda_2\in…
Spatial Poisson Point Process (PPP) network, whose Base Stations (BS)s are distributed according to a Poisson distribution, is currently used as a accurate model to analyse the performance of a cellular network. Most current work on…
The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory.…
A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…
This paper introduces a general theoretical framework to analyze noise limited networks. More precisely, we consider two homogenous Poisson point processes of base stations and users. General model of radio signal propagation and effect of…
In the present work we demonstrate the use of a parcellation free connectivity model based on Poisson point processes. This model produces for each subject a continuous bivariate intensity function that represents for every possible pair of…
We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…
Site percolation in a distorted simple cubic lattice is characterized numerically employing the Newman-Ziff algorithm. Distortion is administered in the lattice by systematically and randomly dislocating its sites from their regular…
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…
We study a stable partial matching $\tau$ of the (possibly randomized) $d$-dimensional lattice with a stationary determinantal point process $\Psi$ on $\mathbb{R}^d$ with intensity $\alpha>1$. For instance, $\Psi$ might be a Poisson…
We first study crossing statistics in random connection models (RCM) built on marked Poisson point processes on $\mathbb R^d$. Under general assumptions, we show exponential tail bounds for the number of crossings of a box contained in the…
In this paper we will consider the contact process in a very simple type of random environment that physicists call the random dilution model. We start with the contact process on a graph, here either $\mathbb{Z}^d$, a $d$-dimensional torus…
In this letter, we introduce a general cellular network model where i) users and BSs are distributed as two general point processes that may be coupled, ii) pathloss is assumed to follow a multi-slope power-law pathloss model, and iii)…
Percolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density $\lambda_c^{(d)}$ for $d$-dimensional Poisson random geometric…