Related papers: Index theorems for graph-parametrized optimal cont…
Gaussian graphical models are nowadays commonly applied to the comparison of groups sharing the same variables, by jointy learning their independence structures. We consider the case where there are exactly two dependent groups and the…
We find various lower and upper bounds for the index of Wente tori that contain a continuous family of planar principal curves. We then prove a result that gives an algorithm for computing the index sharply.
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
We study a metric on the set of finite graphs in which two graphs are considered to be similar if they have similar bounded dimensional "factors". We show that limits of convergent graph sequences in this metric can be represented by…
We consider the spectral structure of indefinite second order boundary-value problems on graphs. A variational formulation for such boundary-value problems on graphs is given and we obtain both full and half-range completeness results. This…
The strong geodetic problem on a graph $G$ is to determine a smallest set of vertices such that by fixing one shortest path between each pair of its vertices, all vertices of $G$ are covered. To do this as efficiently as possible, strong…
We use probabilistic methods to find lower bounds on the maximum number, in a graph with domination number \gamma, of dominating sets of size \gamma. We find that we can randomly generate a graph that, w.h.p., is dominated by almost all…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
The ring of graph invariants is spanned by the basic graph invariants which calculate the number of subgraphs isomorphic to a given graph in other graphs. These subgraphs counting invariants are not algebraically independent. In our view…
This survey on graphs of large girth consists of two parts. The first deals with some aspects of algebraic and extremal graph theory loosely related to the Moore bound. Our point of departure for the second, Ramsey theoretic, part are some…
This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent…
We consider the problem of damping a control system with delay, described by first-order functional-differential equations on a temporal star graph. The delay in the system is time-proportional and propagates through the internal vertex. We…
A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
Algebraic curves have a discrete analogue in finite graphs. Pursuing this analogy we prove a Torelli theorem for graphs. Namely, we show that two graphs have the same Albanese torus if and only if the graphs obtained from them by…
Consider a graph on the non-singular matrices over a finite field, in which two distinct non-singular matrices are joined by an edge whenever their sum is singular. We prove an upper bound for the independence number of this graph. As a…
A mixed graph $G$ can contain both (undirected) edges and arcs (directed edges). Here we derive an improved Moore-like bound for the maximum number of vertices of a mixed graph with diameter at least three. Moreover, a complete enumeration…
Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…
This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Mat\'ern-type Gaussian field priors that enable flexible modeling…