Related papers: On Finite Exchangeability and Conditional Independ…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
An independent set in a graph G is a set of vertices no two of which are joined by an edge. A vertex-weighted graph associates a weight with every vertex in the graph. A vertex-weighted graph G is called a unique independence…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. In particular, we are interested in…
The article addresses the problem of strong structural controllability of structured networks with multi-input multi-output (MIMO) node systems. The authors first present necessary and sufficient conditions for strong structural…
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…
In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…
The shift-enabled property of an underlying graph is essential in designing distributed filters. This article discusses when a random graph is shift-enabled. In particular, popular graph models ER, WS, BA random graph are used, weighted and…
Various social, financial, biological and technological systems can be modeled by interdependent networks. It has been assumed that in order to remain functional, nodes in one network must receive the support from nodes belonging to…
A modern binary executable is a composition of various networks. Control flow graphs are commonly used to represent an executable program in labeled datasets used for classification tasks. Control flow and term representations are widely…
A set $S$ of vertices of a graph $G$ is exponentially independent if, for every vertex $u$ in $S$, $$\sum\limits_{v\in S\setminus \{ u\}}\left(\frac{1}{2}\right)^{{\rm dist}_{(G,S)}(u,v)-1}<1,$$ where ${\rm dist}_{(G,S)}(u,v)$ is the…
This paper studies distribution-free inference in settings where the data set has a hierarchical structure -- for example, groups of observations, or repeated measurements. In such settings, standard notions of exchangeability may not hold.…
A recently proposed axiom system for Andr\'e's central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed…
We explore conditions on the covariance matrices of a consistent chain of mean zero finite mode Gaussian states in order that the chain may be exchangeable or stationary. For an exchangeable chain our conditions are necessary and…
Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Recently much attention has been paid to the study of the robustness of interdependent and multiplex networks and, in particular, networks of networks. The robustness of interdependent networks can be evaluated by the size of a mutually…
A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, as for…
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight…