Related papers: Layering $\partial$-Graphs and Networks
We consider a neural network architecture designed to solve inverse problems where the degradation operator is linear and known. This architecture is constructed by unrolling a forward-backward algorithm derived from the minimization of an…
We consider the distributed weight balancing problem in networks of nodes that are interconnected via directed edges, each of which is able to admit a positive integer weight within a certain interval, captured by individual lower and upper…
Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1)…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
To incorporate spatial (neighborhood) and bidirectional hierarchical relationships as well as features and priors of the samples into their classification, we formulated the classification problem on three variants of multiresolution…
Sparsification aims at extracting a reduced core of associations that best preserves both the dynamics and topology of networks while reducing the computational cost of simulations. We show that the semi-metric topology of complex networks…
We study harmonic map regression, a nonparametric estimator for manifold-valued responses, that penalizes the empirical Fr\'echet risk by the Dirichlet energy. By connecting penalized regression to the theory of harmonic maps, the estimator…
In this paper, we consider the inverse dynamic problem for the Dirac system on finite metric tree graphs. Our main goal is to recover the topology (connectivity) of a tree, lengths of edges, and a matrix potential function on each edge. We…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
The Sturm-Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the…
By employing a novel generalization of the inverse scattering transform method known as the unified transform or Fokas method, it can be shown that the solution of certain physically significant boundary value problems for the elliptic…
To perform any meaningful optimization task, power distribution operators need to know the topology and line impedances of their electric networks. Nevertheless, distribution grids currently lack a comprehensive metering infrastructure.…
We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semidefinite programming relaxation of the minimum cut problem is obtained by strengthening the known…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…
In a semi-supervised learning scenario, (possibly noisy) partially observed labels are used as input to train a classifier, in order to assign labels to unclassified samples. In this paper, we study this classifier learning problem from a…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…
In the context of holography, entanglement entropy can be studied either by i) extremal surfaces or ii) bit threads, i.e., divergenceless vector fields with a norm bound set by the Planck length. In this paper we develop a new method for…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
Finding equitable partitions is closely related to the extraction of graph symmetries and of interest in a variety of applications context such as node role detection, cluster synchronization, consensus dynamics, and network control…