Related papers: Linear systems on graphs with a real structure

Convolutional Neural Networks are very efficient at processing signals defined on a discrete Euclidean space (such as images). However, as they can not be used on signals defined on an arbitrary graph, other models have emerged, aiming to…

We propose a statistical model for graphs with a core-periphery structure. To do this we define a precise notion of what it means for a graph to have this structure, based on the sparsity properties of the subgraphs of core and periphery…

By considering graphs as discrete analogues of Riemann surfaces, Baker and Norine (Adv. Math. 2007) developed a concept of linear systems of divisors for graphs. Building on this idea, a concept of gonality for graphs has been defined and…

Consider the scheme parametrizing non-constant morphisms from a fixed projective curve to a projective surface. There is a rational map between this scheme and the Chow variety of $1$-cycles on the surface. We prove that, if the curve is…

Inside the symmetric product of a very general curve, we consider the codimension-one subvarieties of symmetric tuples of points imposing exceptional secant conditions on linear series on the curve of fixed degree and dimension. We compute…

Motivated by a conjecture of Xiao, we study supporting divisors of fibred surfaces. On the one hand, after developing a formalism to treat one-dimensional families of varieties of any dimension, we give a structure theorem for fibred…

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…

We study spaces of realisations of linkages (weighted graphs) whose underlying graph is a series parallel graph. In particular, we describe an algorithm for determining whether or not such spaces are connected.

Recently, the deep learning community has given growing attention to neural architectures engineered to learn problems in relational domains. Convolutional Neural Networks employ parameter sharing over the image domain, tying the weights of…

We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…

Given a divisor $D$ on a tropical curve $\Gamma$, we show that reduced divisors define an integral affine map from the tropical curve to the complete linear system $|D|$. This is done by providing an explicit description of the behavior of…

Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…

In this paper we study a construction of algebraic curves from combinatorial data. In the study of algebraic curves through degeneration, graphs usually appear as the dual intersection graph of the central fiber. Properties of such graphs…

A new generalization of the classical separate algebraicity theorem is suggested and proved.

Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…

Model repair is an essential topic in model-driven engineering. Since models are suitably formalized as graph-like structures, we consider the problem of rule-based graph repair: Given a rule set and a graph constraint, try to construct a…

In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…

Detection of curvilinear structures in images has long been of interest. One of the most challenging aspects of this problem is inferring the graph representation of the curvilinear network. Most existing delineation approaches first…