433,507 research outputs found
Computational Tools for Cohomology of Toric Varieties
In this review, novel non-standard techniques for the computation of
cohomology classes on toric varieties are summarized. After an introduction of
the basic definitions and properties of toric geometry, we discuss a specific
computational algorithm for the determination of the dimension of line-bundle
valued cohomology groups on toric varieties. Applications to the computation of
chiral massless matter spectra in string compactifications are discussed and,
using the software package cohomCalg, its utility is highlighted on a new
target space dual pair of (0,2) heterotic string models.Comment: 17 pages, 4 tables; prepared for the special issue "Computational
Algebraic Geometry in String and Gauge Theory" of Advances in High Energy
Physics, cohomCalg implementation available at
http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg
Notions of optimal transport theory and how to implement them on a computer
This article gives an introduction to optimal transport, a mathematical
theory that makes it possible to measure distances between functions (or
distances between more general objects), to interpolate between objects or to
enforce mass/volume conservation in certain computational physics simulations.
Optimal transport is a rich scientific domain, with active research
communities, both on its theoretical aspects and on more applicative
considerations, such as geometry processing and machine learning. This article
aims at explaining the main principles behind the theory of optimal transport,
introduce the different involved notions, and more importantly, how they
relate, to let the reader grasp an intuition of the elegant theory that
structures them. Then we will consider a specific setting, called
semi-discrete, where a continuous function is transported to a discrete sum of
Dirac masses. Studying this specific setting naturally leads to an efficient
computational algorithm, that uses classical notions of computational geometry,
such as a generalization of Voronoi diagrams called Laguerre diagrams.Comment: 32 pages, 17 figure
Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective
A unified vision of the symmetric coupling of angular momenta and of the
quantum mechanical volume operator is illustrated. The focus is on the quantum
mechanical angular momentum theory of Wigner's 6j symbols and on the volume
operator of the symmetric coupling in spin network approaches: here, crucial to
our presentation are an appreciation of the role of the Racah sum rule and the
simplification arising from the use of Regge symmetry. The projective geometry
approach permits the introduction of a symmetric representation of a network of
seven spins or angular momenta. Results of extensive computational
investigations are summarized, presented and briefly discussed.Comment: 15 pages, 10 figures, presented at ICCSA 2014, 14th International
Conference on Computational Science and Application
An Introduction to Randomization in Computational Geometry.
International audienceThis paper is not a complete survey on randomized algorithms in computational geometry, but an introduction to this subject providing intuitions and references. In a first time, some basic ideas are illustrated by the sorting problem, and in a second time few results on computational geometry are briefly explained
An exact algorithm for weighted-mean trimmed regions in any dimension
Trimmed regions are a powerful tool of multivariate data analysis. They describe a probability distribution in Euclidean d-space regarding location, dispersion, and shape, and they order multivariate data with respect to their centrality. Dyckerhoff and Mosler (201x) have introduced the class of weighted-mean trimmed regions, which possess attractive properties regarding continuity, subadditivity, and monotonicity. We present an exact algorithm to compute the weighted-mean trimmed regions of a given data cloud in arbitrary dimension d. These trimmed regions are convex polytopes in Rd. To calculate them, the algorithm builds on methods from computational geometry. A characterization of a region's facets is used, and information about the adjacency of the facets is extracted from the data. A key problem consists in ordering the facets. It is solved by the introduction of a tree-based order. The algorithm has been programmed in C++ and is available as an R package. --central regions,data depth,multivariate data analysis,convex polytope,computational geometry,algorithm,C++, R
A Simple Introduction to Grobner Basis Methods in String Phenomenology
In this talk I give an elementary introduction to the key algorithm used in
recent applications of computational algebraic geometry to the subject of
string phenomenology. I begin with a simple description of the algorithm itself
and then give 3 examples of its use in physics. I describe how it can be used
to obtain constraints on flux parameters, how it can simplify the equations
describing vacua in 4d string models and lastly how it can be used to compute
the vacuum space of the electroweak sector of the MSSM.Comment: 13 pages, Prepared for Mathematical Challenges in String
Phenomenology, ESI Vienna, Austria, Oct 6-15, 200
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