Related papers: Observability through matrix-weighted graph
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…
This work attempts to discuss the observability of linear time-invariant systems with event-triggered measurements. A new notion of observability, namely, $\epsilon$-observability is defined with parameter $\epsilon$, which relates to the…
In this paper, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence…
In a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolation-like emergence of a macroscopic observable component in graphs in which the state of a fraction of…
In the modeling, monitoring, and control of complex networks, a fundamental problem concerns the comprehensive determination of the state of the system from limited measurements. Using power grids as example networks, we show that this…
Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social…
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. We are interested in graph-theoretic conditions…
Random walks on graphs are a fundamental concept in graph theory and play a crucial role in solving a wide range of theoretical and applied problems in discrete math, probability, theoretical computer science, network science, and machine…
This paper investigates observability/controllability of a networked dynamic system (NDS) in which system matrices of its subsystems are expressed through linear fractional transformations (LFT). Some relations have been obtained between…
Recently normalized Laplacian matrices of graphs are studied as density matrices in quantum mechanics. Separability and entanglement of density matrices are important properties as they determine the nonclassical behavior in quantum…
This paper addresses the ubiquity of remarkable measures on graphs, and their applications. In many queueing systems, it is necessary to take into account the compatibility constraints between users, or between supply and demands, and so…
Connectivity is one of the most fundamental properties of wireless multi-hop networks. A network is said to be connected if there is a path between any pair of nodes. A convenient way to study the connectivity of a random network is by…
This work addresses the design of a robust hybrid observer for discrete-time switched linear systems subject to unknown inputs and modeling errors. The observer herein proposed is synthesized, for the case when the active mode is unknown…
In this paper, we analyze timed systems with data structures, using a rich interplay of logic and properties of graphs. We start by describing behaviors of timed systems using graphs with timing constraints. Such a graph is called…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation,…
This paper provides a framework to evaluate the performance of single and double integrator networks over arbitrary directed graphs. Adopting vehicular network terminology, we consider quadratic performance metrics defined by the L2-norm of…
The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. We extend this visibility graph and create a directed limited penetrable horizontal visibility graph and an image…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
In~\cite{bgs2013}, exclusion sensitivity and exclusion stability for symmetric exclusion processes on graphs were defined as a natural analogue of noise sensitivity and noise stability in this setting. As these concepts were defined for any…