Related papers: Entropy and Distributed Source Coding of Connected…
In this paper we show how to use simple partitioning lemmas in order to embed spanning graphs in a typical member of $G(n,p)$. Let the \emph{maximum density} of a graph $H$ be the maximum average degree of all the subgraphs of $H$. First,…
We consider the problem of distributed compression for correlated quantum sources. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the…
This paper investigates the general distributed lossless/lossy source coding formulated by Jana and Blahut. Their multi-letter rate-distortion region, an alternative to the region derived by Yang and Qin, is characterized by entropy…
Consider a lossy compression system with $\ell$ distributed encoders and a centralized decoder. Each encoder compresses its observed source and forwards the compressed data to the decoder for joint reconstruction of the target signals under…
The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in…
The study of the optimality of low-complexity greedy scheduling techniques in wireless communications networks is a very complex problem. The Local Pooling (LoP) factor provides a single-parameter means of expressing the achievable capacity…
In this paper we study the random geometric graph $\mathsf{RGG}(n,\mathbb{T}^d,\mathsf{Unif},\sigma^q_p,p)$ with $L_q$ distance where each vertex is sampled uniformly from the $d$-dimensional torus and where the connection radius is chosen…
Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…
The random geometric graph $\mathsf{RGG}(n,\mathbb{S}^{d-1}, p)$ is formed by sampling $n$ i.i.d. vectors $\{V_i\}_{i = 1}^n$ uniformly on $\mathbb{S}^{d-1}$ and placing an edge between pairs of vertices $i$ and $j$ for which $\langle…
Graphical data is comprised of a graph with marks on its edges and vertices. The mark indicates the value of some attribute associated to the respective edge or vertex. Examples of such data arise in social networks, molecular and systems…
In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.
Modern compression systems use linear transformations in their encoding and decoding processes, with transforms providing compact signal representations. While multiple data-dependent transforms for image/video coding can adapt to diverse…
We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, we consider a fixed graph embedded…
This work studies the problem of distributed compression of correlated sources with an action-dependent joint distribution. This class of problems is, in fact, an extension of the Slepian-Wolf model, but where cost-constrained actions taken…
We consider the problem of distributed lossless computation of a function of two sources by one common user. To do so, we first build a bipartite graph, where two disjoint parts denote the individual source outcomes. We then project the…
We propose a framework for joint entropy coding and encryption using Chaotic maps. We begin by observing that the message symbols can be treated as the symbolic sequence of a discrete dynamical system. For an appropriate choice of the…
We consider the problem of minimizing the number of broadcasts for collecting all sensor measurements at a sink node in a noisy broadcast sensor network. Focusing first on arbitrary network topologies, we provide (i) fundamental limits on…
We propose a new proof technique that aims to be applied to the same problems as the Lov\'asz Local Lemma or the entropy-compression method. We present this approach in the context of non-repetitive colorings and we use it to improve…
We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below…
We consider uniform random cographs (either labeled or unlabeled) of large size. Our first main result is the convergence towards a Brownian limiting object in the space of graphons. We then show that the degree of a uniform random vertex…