Related papers: Introducing Loopedia
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…
Encyclopedic queries express the intent of obtaining information typically available in encyclopedias, such as biographical, geographical or historical facts. In this paper, we train a classifier for detecting the encyclopedic intent of web…
We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally arise from classical knot and link diagrams. In fact, the graphs…
Although RDF graphs have schema information associated with them, in practice it is very common to find cases in which data do not fully conform to their schema. A prominent example of this is DBpedia, which is RDF data extracted from…
The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the…
Neighborhood graphs and clustering algorithms are fundamental structures in both computational geometry and data analysis. Visualizing them can help build insight into their behavior and properties. The Ipe extensible drawing editor,…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
The aim of XLOOPS is to calculate one-particle irreducible Feynman diagrams with one or two closed loops for arbitrary processes in the Standard model of particles and related theories. Up to now this aim is realized for all one-loop…
Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…
We review the recent developments of the Loop-Tree Duality method, focussing our discussion on the first numerical implementation and its use in the direct numerical computation of multi-leg Feynman integrals. Non-trivial examples are…
Creating graph visualizations involves many decisions, such as layout, node and edge appearance, and color choices. These decisions are challenging due to the multitude of options available. For instance, graph layout can be force-directed…
The index of a seaweed Lie algebra can be computed from its associated meander graph. We examine this graph in several ways with a goal of determining families of Frobenius (index zero) seaweed algebras. Our analysis gives two new families…
A numerical parameter, referred to as a topological index, is used to represent the molecular structure of a compound by analyzing its graph-theoretical characteristics. Topological indices are predictive methods for the physicochemical…
New criteria for which Cayley graphs of cyclic groups of any order can be completely determined--up to isomorphism--by the eigenvalues of their adjacency matrices is presented. Secondly, a new construction for pairs of nonisomorphic Cayley…
To realize the premise of the Semantic Web towards knowledgeable machines, one might often integrate an application with emerging RDF graphs. Nevertheless, capturing the content of a rich and open RDF graph by existing tools requires both…
Attack graphs provide compact representations of the attack paths that an attacker can follow to compromise network resources by analysing network vulnerabilities and topology. These representations are a powerful tool for security risk…
We present a new formula for the coaction of a large class of integrals. When applied to one-loop (cut) Feynman integrals, it can be given a diagrammatic representation purely in terms of pinches and cuts of the edges of the graph. The…
Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such…
Keeping abreast of current trends, technologies, and best practices in visualization and data analysis is becoming increasingly difficult, especially for fledgling data scientists. In this paper, we propose Lodestar, an interactive…
Visual comparison is an important task in the analysis of multivariate graphs. However, comparison of topological features of a graph with respect to its data attributes for different portions of the data remains challenging because there…