Related papers: Controllability and maximum matchings of complex n…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
The controllability of a network is a theoretical problem of relevance in a variety of contexts ranging from financial markets to the brain. Until now, network controllability has been characterized only on isolated networks, while the vast…
A dynamic bipartite matching model is given by a bipartite matching graph which determines the possible matchings between the various types of supply and demand items. Both supply and demand items arrive to the system according to a…
We establish the expressibility in fixed-point logic with counting (FPC) of a number of natural polynomial-time problems. In particular, we show that the size of a maximum matching in a graph is definable in FPC. This settles an open…
In this work, we formulate two controllability maximization problems for large-scale networked dynamical systems such as brain networks: The first problem is a sparsity constraint optimization problem with a box constraint. The second…
We study the Maximum Cardinality Matching (MCM) and the Maximum Weight Matching (MWM) problems, on trees and on some special classes of graphs, in the Online Preemptive and the Incremental Dynamic Graph models. In the {\em Online…
A matching cut in a graph G is an edge cut of G that is also a matching. This short survey gives an overview of old and new results and open problems for Maximum Matching Cut, which is to determine the size of a largest matching cut in a…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
The linear complementarity problem is a continuous optimization problem that generalizes convex quadratic programming, Nash equilibria of bimatrix games and several such problems. This paper presents a continuous optimization formulation…
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…
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 graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural-controllability theory, we continue to lack a framework to control undirected complex networks, especially…
This paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem (i) we propose a metric…
A maximum priority matching is a matching in an undirected graph that maximizes a priority score defined with respect to given vertex priorities. An earlier paper showed how to find maximum priority matchings in unweighted graphs. This…
This paper introduces a framework for quantitative characterization of the controllability of time-varying linear systems (or networks) in terms of input novelty. The motivation for such an approach comes from the study of biophysical…
The coupled problems of selecting control nodes and designing control actions for nonlinear network dynamics are fundamental scientific problems with applications in many diverse fields. These problems are thoroughly studied for linear…
We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function…
Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…
We propose a Markov Chain Monte Carlo (MCMC) algorithm based on Gibbs sampling with parallel tempering to solve nonlinear optimal control problems. The algorithm is applicable to nonlinear systems with dynamics that can be approximately…