Related papers: Information-Theoretic Thresholds for Planted Dense…
Information theory is gaining popularity as a tool to characterize performance of biological systems. However, information is commonly quantified without reference to whether or how a system could extract and use it; as a result,…
Consider a tree network T, where each edge acts as an independent copy of a given channel M, and information is propagated from the root. For which T and M does the configuration obtained at level n of T typically contain significant…
Multilayer networks are used to represent the interdependence between the relational data of individuals interacting with each other via different types of relationships. To study the information-theoretic phase transitions in detecting the…
Adaptively monitoring the states of nodes in a large complex network is of interest in domains such as national security, public health, and energy grid management. Here, we present an information theoretic adaptive tracking and sampling…
We develop an analytical approach to the susceptible-infected-susceptible (SIS) epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
We develop a consolidated theory for the detectability of network-borne attacks under two canonical observation models: (i) a static graph drawn from an Erdos-Renyi background with a planted anomalous community, and (ii) a temporal…
In order to conduct analyses of networked systems where connections between individuals take on a range of values - counts, continuous strengths or ordinal rankings - a common technique is to dichotomize the data according to their…
The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most…
In a recent letter (cond-mat/9903108), Barthelemy and Nunes Amaral discuss the crossover phenomenon between regular and ``small-world'' networks, as a function of the network size $n$ and of the disorder $p$. They claim that the average…
A significant generalization of the Erd\"os-R\'enyi random graph model is an `inhomogeneous' random graph where the edge probabilities vary according to vertex types. We identify the threshold value for this random graph with a finite…
We study the problem of detecting or recovering a planted ranked subgraph from a directed graph, an analog for directed graphs of the well-studied planted dense subgraph model. We suppose that, among a set of $n$ items, there is a subset…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
The bandwidth theorem [Mathematische Annalen, 343(1):175--205, 2009] states that any $n$-vertex graph $G$ with minimum degree $\big(\tfrac{k-1}{k}+o(1)\big)n$ contains all $n$-vertex $k$-colourable graphs $H$ with bounded maximum degree and…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
Local thresholding algorithms were first presented more than a decade ago and have since been applied to a variety of data mining tasks in peer-to-peer systems, wireless sensor networks, and in grid systems. One critical assumption made by…
Epidemic modeling has been extensively used in the last years in the field of telecommunications and computer networks. We consider the popular Susceptible-Infected-Susceptible spreading model as the metric for information spreading. In…
We study the behavior of untrained neural networks whose weights and biases are randomly distributed using mean field theory. We show the existence of depth scales that naturally limit the maximum depth of signal propagation through these…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…