Related papers: Codes on Graphs: Observability, Controllability an…
Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the…
Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…
Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity…
Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…
A graph G is called "minimalizable" if a diagram with minimal crossing number can be obtained from an arbitrary diagram of G by crossing changes. If, furthermore, the minimal diagram is unique up to crossing changes then G is called…
This paper proposes a notion termed perturbation-tolerant structural controllability (PTSC) to study the generic property of controllability preservation/resilience of structured linear systems under structured perturbations. A structured…
Dynamic graph theory is a novel, growing area that deals with graphs that change over time and is of great utility in modelling modern wireless, mobile and dynamic environments. As a graph evolves, possibly arbitrarily, it is challenging to…
For arrays of identical linear systems coupled through relative actuation four problems are studied: controllability, positive controllability, pairwise controllability, and positive pairwise controllability. To this end, related to the…
In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs.…
The parameterized complexity of counting minimum cuts stands as a natural question because Ball and Provan showed its #P-completeness. For any undirected graph $G=(V,E)$ and two disjoint sets of its vertices $S,T$, we design a…
A (2-dimensional) realisation of a graph $G$ is a pair $(G,p)$, where $p$ maps the vertices of $G$ to $\mathbb{R}^2$. A realisation is flexible if it can be continuously deformed while keeping the edge lengths fixed, and rigid otherwise. We…
There is a graph reduction system so that every optimal 1-planar graph can be reduced to an irreducible extended wheel graph, provided the reductions are applied such that the given graph class is preserved. A graph is optimal 1-planar if…
Let $\mathbf G$ be a graphing, that is a Borel graph defined by $d$ measure preserving involutions. We prove that if $\mathbf G$ is {\em treeable} then it arises as the local limit of some sequence $(G_n)_{n\in\mathbb{N}}$ of graphs with…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of…
We say that a control system is locally controllable if the attainable set from any state $x$ contains an open neighborhood of $x$, while it is controllable if the attainable set from any state is the entire state manifold. We show in this…
Distributed networks are prone to errors so verifying their output is critical. Hence, we develop LOCAL certification protocols for graph properties in which nodes are given certificates that allow them to check whether their network as a…