Related papers: A simple algorithm for automatic Feynman diagram g…
Using Symbolic Dynamic Programming we describe algorithms, fully implemented in Maple, for automatically generating generating functions introduced by Richard Stanley in his study of generalized Stern arrays, generalized even further, to…
This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.…
This text reviews, hopefully in a pedagogical manner, a series of work on the automatic calculations of Feynman diagrams in the context of quantum nanoelectronics (Keldysh formalism) with an application to the Kondo effect in the…
Three programs are presented for automatically generating and calculating Feynman diagrams: the diagrams are generated with FeynArts, algebraically simplified with FormCalc, and finally evaluated numerically using the LoopTools package. The…
We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to…
We investigate a class of random graph ensembles based on the Feynman graphs of multidimensional integrals, representing statistical-mechanical partition functions. We show that the resulting ensembles of random graphs strongly resemble…
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…
Feynmf is a LaTeX package for easy drawing of professional quality Feynman diagrams with Metafont (or Metapost). Feynmf lays out most diagrams satisfactorily from the structure of the graph without any need for manual intervention.…
A computer program for evaluating colour factors of QCD Feynman diagrams is presented, and illustrative examples on how to use the program to calculate non trivial colour factors are given. The program and the discussion in this paper is…
In the first part of the paper we present a short review of applications of digital differential analyzers (DDA) to generation of circles showing that they can be treated as one-step numerical schemes. In the second part we present and…
We develop the first theory of control-flow graphs from first principles, and use it to create an algorithm for automatically synthesizing many variants of control-flow graph generators from a language's operational semantics. Our approach…
We introduce a new method for deriving Feynman integral symmetry relations. By solving the ansatz of momentum transformation in the field of rational functions rather than constants, this method can sometimes find more symmetry relations,…
We show that momentum space Feynman diagrams involving internal massless fields can be cast as conformal integrals. This leads to a classification of all Feynman diagrams into conformal families, labelled by conformal integrals. Computing…
Differential flatness enables efficient planning and control for underactuated robotic systems, but we lack a systematic and practical means of identifying a flat output (or determining whether one exists) for an arbitrary robotic system.…
In the very near future the first data from LHC will be available. The searches for the Higgs boson and for new physics will require precise predictions both for the signal and the background processes. Tree level calculations typically…
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm designed for practical use both because of its ability to…
In this contribution the matrix element generator AMEGIC++ will be presented. It automatically generates Feynman diagrams, helicity amplitudes, and suitable phase space mappings for processes involving multi-particle final states within the…
Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates. Here we restrict to planar trees since each…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…