Related papers: Sensing and Control in Symmetric Networks
This paper investigates the problem of consensus-based distributed control of linear time-invariant multi-channel systems subject to unknown inputs. A distributed observer-based control framework is proposed, within which observer nodes and…
The lack of studying the complex organization of directed network usually limits to the understanding of underlying relationship between network structures and functions. Structural controllability and structural predictability, two…
This document explores structural controllability of polynomial dynamical systems or polysystems. We extend Lin's concept of structural controllability for linear systems, offering hypergraph-theoretic methods to rapidly assess strong…
Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and…
Synchronization is of central importance in power distribution, telecommunication, neuronal, and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these…
Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…
Network visualization is essential for many scientific, societal, technological and artistic domains. The primary goal is to highlight patterns out of nodes interconnected by edges that are easy to understand, facilitate communication and…
We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
In this paper, we consider composite networks formed from the Kronecker product of smaller networks. We find the observability and controllability properties of the product network from those of its constituent smaller networks. The overall…
We give algorithms for designing near-optimal sparse controllers using policy gradient with applications to control of systems corrupted by multiplicative noise, which is increasingly important in emerging complex dynamical networks.…
Previously, the controllability problem of a linear time-invariant dynamical system was mapped to the maximum matching (MM) problem on the bipartite representation of the underlying directed graph, and the sizes of MMs on random bipartite…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
This paper introduces and solves a structural controllability problem for ensembles of switched linear systems. All individual systems in the ensemble are sparse and governed by the same sparsity pattern, and undergo switching among…
In this paper, we propose to study on sufficient control of complex networks which is to control a sufficiently large portion of the network, where only the quantity of controllable nodes matters. To the best of our knowledge, this is the…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the…