Related papers: Linear pencils on graphs and on real curves
We develop the first parallel graph coloring heuristics with strong theoretical guarantees on work and depth and coloring quality. The key idea is to design a relaxation of the vertex degeneracy order, a well-known graph theory concept, and…
We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in…
We use fine curve graph tools to prove that there exist parabolic isometries of graphs of curves associated to surfaces of infinite type.
Aiming at a generalization of a classical theorem of Moebius, we study maps that take line intervals to plane curves, and also maps that take line intervals to conics from certain linear systems.
While convolutional neural networks (CNNs) have recently made great strides in supervised classification of data structured on a grid (e.g. images composed of pixel grids), in several interesting datasets, the relations between features can…
This paper studies syzygies of curves that have been embedded in projective space by line bundles of large degree. The proofs take advantage of the relationship between syzygies and spaces of section of vector bundles associated to the…
Network representation learning and node classification in graphs got significant attention due to the invent of different types graph neural networks. Graph convolution network (GCN) is a popular semi-supervised technique which aggregates…
It has often been conjectured that the effectiveness of line drawings can be explained by the similarity of edge images to line drawings. This paper presents several problems with explaining line drawing perception in terms of edges, and…
Linear connections are introduced on a series of noncommutative geometries which have commutative limits. Quasicommutative corrections are calculated.
The purpose of this review is to introduce the reader to graph kernels and the corresponding literature, with an emphasis on those with direct application to chemoinformatics. Graph kernels are functions that allow for the inference of…
We consider hypergraph visualizations that represent vertices as points in the plane and hyperedges as curves passing through the points of their incident vertices. Specifically, we consider several different variants of this problem by (a)…
We prove that any graph of multicurves satisfying certain natural properties is either hyperbolic, relatively hyperbolic, or thick. Further, this geometric characterization is determined by the set of subsurfaces that intersect every vertex…
A general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations, is presented. We emphasize the use of several types of dynamical variables : branches, power sums and…
We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.
Linearization is a standard method in the computation of eigenvalues and eigenvectors of matrix polynomials. In the last decade a variety of linearization methods have been developed in order to deal with algebraic structures and in order…
Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the…
We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.
A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained results contain as special cases the…
We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs.
In this paper, we give a simple definition of tangents to a curve in elementary geometry. From which, we characterize the existence of the tangent to a curve at a point.