Related papers: Realizability of Rectangular Euler Diagrams
Diagrams matter. Unfortunately, the deep learning community has no standard method for diagramming architectures. The current combination of linear algebra notation and ad-hoc diagrams fails to offer the necessary precision to understand…
Octupolar order is described in two space dimensions in terms of the maxima (and conjugated minima) of the probability density associated with a third-rank, fully symmetric and traceless tensor. Such a representation is shown to be…
A rectangular partition is the partition of an (axis-aligned) rectangle into interior-disjoint rectangles. We ask whether a rectangular partition permits a "nice" drawing of its dual, that is, a straight-line embedding of it such that each…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of motivations for this study is to understand how neural networks work on the example of a problem for which…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
It is well known that the incompressible Euler equations can be formulated in a very geometric language. The geometric structures provide very valuable insights into the properties of the solutions. Analogies with the finite-dimensional…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This generalizes existing results, such as the enumeration of graphs…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…
Given n data points in R^d, an appropriate edge-weighted graph connecting the data points finds application in solving clustering, classification, and regresssion problems. The graph proposed by Daitch, Kelner and Spielman (ICML~2009) can…
Some graphs admit drawings in the Euclidean k-space in such a (natu- ral) way, that edges are represented as line segments of unit length. Such drawings will be called k dimensional unit distance representations. When two non-adjacent…
A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
Higher-order diagrams required for radiative corrections to mixed electroweak and QCD processes at the LHC and anticipated future colliders will require numerically stable representations of the associated Feynman diagrams. The…
Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these…
In this brief paper, a simple and fast computational method, the Planar Visibility Graph Networks Algorithm was proposed based on the famous Visibility Graph Algorithm, which can fulfill converting two dimensional timeseries into a planar…
A rectangle visibility representation (RVR) of a graph consists of an assignment of axis-aligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its…