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We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…

Numerical Analysis · Mathematics 2020-03-31 S. Armstrong , A. Hannukainen , T. Kuusi , J. -C. Mourrat

Graph generative model evaluation necessitates understanding differences between graphs on the distributional level. This entails being able to harness salient attributes of graphs in an efficient manner. Curvature constitutes one such…

Machine Learning · Computer Science 2023-10-27 Joshua Southern , Jeremy Wayland , Michael Bronstein , Bastian Rieck

The Convex Hull algorithm is one of the most important algorithms in computational geometry, with many applications such as in computer graphics, robotics, and data mining. Despite the advances in the new algorithms in this area, it is…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-03-21 Roberto Carrasco , Héctor Ferrada , Cristóbal A. Navarro , Nancy Hitschfeld

The classical Whitney formula relates the number of times an oriented plane curve cuts itself to its rotation number and the index of a base point. In this paper we generalize Whitney's formula to curves on an oriented punctured surface. To…

Geometric Topology · Mathematics 2019-02-06 Yurii Burman , Michael Polyak

We study two different types of gluing for graphs: interface (obtained by choosing a common subgraph as the gluing component) and bridge gluing (obtained by adding a set of edges to the given subgraphs). We introduce formulae for computing…

Mathematical Physics · Physics 2018-05-07 Ivan Contreras , Michael Toriyama , Chengzheng Yu

One of the difficulties in doing noncommutative projective geometry via explicitly presented graded algebras is that it is usually quite difficult to show flatness, as the Hilbert series is uncomputable in general. If the algebra has a…

Algebraic Geometry · Mathematics 2022-02-18 Eric M. Rains

This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…

Graphics · Computer Science 2021-05-05 Hsueh-Ti Derek Liu , Jiayi Eris Zhang , Mirela Ben-Chen , Alec Jacobson

We consider H(curl)-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by…

Numerical Analysis · Mathematics 2009-01-08 Ralf Hiptmair , Weiying Zheng

We investigate how to make the surface of a convex polyhedron (a polytope) by folding up a polygon and gluing its perimeter shut, and the reverse process of cutting open a polytope and unfolding it to a polygon. We explore basic enumeration…

Computational Geometry · Computer Science 2007-05-23 Erik D. Demaine , Martin L. Demaine , Anna Lubiw , Joseph O'Rourke

We define strict confluent drawing, a form of confluent drawing in which the existence of an edge is indicated by the presence of a smooth path through a system of arcs and junctions (without crossings), and in which such a path, if it…

Computational Geometry · Computer Science 2016-08-12 David Eppstein , Danny Holten , Maarten Löffler , Martin Nöllenburg , Bettina Speckmann , Kevin Verbeek

We investigate the Hilbert scheme of points on curves with n-fold singularities, that is curves that look locally around their singular points as the axis in an affine space. We describe the structure and number of its irreducible…

Algebraic Geometry · Mathematics 2025-11-06 Ángel David Ríos Ortiz , Javier Sendra-Arranz

Understanding whether deep neural networks are effectively optimized remains challenging, as training occurs in highly nonconvex landscapes and standard metrics provide limited visibility into layer-wise learning quality. This challenge is…

Machine Learning · Computer Science 2026-05-05 Arian Eamaz , Farhang Yeganegi , Mojtaba Soltanalian

Consider a configuration of pebbles distributed on the vertices of a connected graph of order $n$. A pebbling step consists of removing two pebbles from a given vertex and placing one pebble on an adjacent vertex. A distribution of pebbles…

Combinatorics · Mathematics 2012-04-12 Melody Chan , Anant P. Godbole

We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of…

Differential Geometry · Mathematics 2020-07-14 Brendan Guilfoyle , Wilhelm Klingenberg

Brushing of graphs is a graph searching process in which the searching agents are called brushes. We focus on brushing directed graphs based on a new model in which the brushes can only travel in the same direction as the orientation of the…

Combinatorics · Mathematics 2024-10-08 Jared Howell , Sulani D. Kavirathne , David A. Pike

The 3-Decomposition Conjecture states that every connected cubic graph can be decomposed into a spanning tree, a 2-regular subgraph and a matching. We show that this conjecture holds for the class of connected plane cubic graphs.

Combinatorics · Mathematics 2017-10-31 Arthur Hoffmann-Ostenhof , Tomáš Kaiser , Kenta Ozeki

The paper presents a new model for single channel images low-level interpretation. The image is decomposed into a graph which captures a complete set of structural features. The description allows to accurately identify every edge location…

Computer Vision and Pattern Recognition · Computer Science 2019-04-23 Alessandro Dal Palu'

The functionality of adhesives relies on their response under the application of a load. Yet, it has remained a challenge to quantitatively relate the macroscopic dynamics of peeling to the dissipative processes inside the adhesive layer.…

Soft Condensed Matter · Physics 2019-09-04 Hugo Perrin , Antonin Eddi , Stefan Karpitschka , Jacco H. Snoeijer , Bruno Andreotti

A normal partition of the edges of a cubic graph is a partition into trails (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition. We investigate this notion and give some results and problems.

Discrete Mathematics · Computer Science 2009-11-06 Jean-Luc Fouquet , Jean-Marie Vanherpe

The conchoid of a plane curve $C$ is constructed using a fixed circle $B$ in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves $B$ and $C$ in the projective plane. We present two…

Algebraic Geometry · Mathematics 2014-06-25 Alberto Albano , Margherita Roggero