Search results for "algebra"

"Table 1" of "Determination of $alpha_{s}$ in second order {QCD} from hadronic $Z$ decays"

1992

Experimental differential Thrust distributions.

Polynomial Spline-Wavelets

2015

This chapter presents wavelets in the spaces of polynomial splines. The wavelets’ design is based on the Zak transform, which provides an integral representation of spline-wavelets. The exponential wavelets which participate in the integral representation are counterparts of the exponential splines that were introduced in Chap. 4. Fast algorithms for the wavelet transforms of splines are presented. Generators of spline-wavelet spaces are described, such as the B-wavelets and their duals and the Battle-Lemarie wavelets whose shifts form orthonormal bases of the spline-wavelet spaces.

Zariski Closed Algebras in Varieties of Universal Algebra

2014

Highly Enantioselective Friedel−Crafts Alkylations of Indoles with Simple Enones Catalyzed by Zirconium(IV)−BINOL Complexes

2007

Complexes of BINOL-based ligands with Zr(OtBu)4 catalyze the Friedel-Crafts alkylation reaction of indoles and pyrrole with nonchelating beta-substituted alpha,beta-enones at room temperature affording the expected products with good yields and ee above 95% in most of the studied examples.

Data structures and algorithms for topological analysis

2014

International audience; One of the steps of geometric modeling is to know the topology and/or the geometry of the objects considered. This paper presents different data structures and algorithms used in this study. We are particularly interested by algebraic structures, eg homotopy and homology groups, the Betti numbers, the Euler characteristic, or the Morse-Smale complex. We have to be able to compute these data structures, and for (homotopy and homology) groups, we also want to compute their generators. We are also interested in algorithms CIA and HIA presented in the thesis of Nicolas DELANOUE, which respectively compute the connected components and the homotopy type of a set defined by…

Extending CSG with projections: Towards formally certified geometric modeling

2015

We extend traditional Constructive Solid Geometry (CSG) trees to support the projection operator. Existing algorithms in the literature prove various topological properties of CSG sets. Our extension readily allows these algorithms to work on a greater variety of sets, in particular parametric sets, which are extensively used in CAD/CAM systems. Constructive Solid Geometry allows for algebraic representation which makes it easy for certification tools to apply. A geometric primitive may be defined in terms of a characteristic function, which can be seen as the zero-set of a corresponding system along with inequality constraints. To handle projections, we exploit the Disjunctive Normal Form,…

Algebraic Properties to Optimize kNN Queries

2011

International audience; New applications that are being required to employ Database Management Systems (DBMSs), such as storing and retrieving complex data (images, sound, temporal series, genetic data, etc.) and analytical data processing (data mining, social networks analysis, etc.), increasingly impose the need for new ways of expressing predicates. Among the new most studied predicates are the similarity-based ones, where the two commonest are the similarity range and the k-nearest neighbor predicates. The k-nearest neighbor predicate is surely the most interesting for several applications, including Content-Based Image Retrieval (CBIR) and Data Mining (DM) tasks, yet it is also the mos…

Semantic aware RSS query algebra

2010

International audience; Existing XML query algebras are not fully appropriate to retrieve RSS news items mainly due to three reasons: 1) RSS is text rich and its content is dependent on the wording and verbification of the author, thus semantic aware operators are needed; 2) news items are dynamic and consequently time oriented retrieval is needed; 3) a news item may evolve through time, or overlap with other news items and hence identifying relationships between items is also needed. In this paper, we aim to solve these issues by providing a dedicated RSS algebra based on semantic-aware operators that consider RSS characteristics. The provided operators are application domain specific and …

OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS

2010

The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…

Kolmogorov Superposition Theorem and Its Application to Multivariate Function Decompositions and Image Representation

2008

International audience; In this paper, we present the problem of multivariate function decompositions into sums and compositions of monovariate functions. We recall that such a decomposition exists in the Kolmogorov's superposition theorem, and we present two of the most recent constructive algorithms of these monovariate functions. We first present the algorithm proposed by Sprecher, then the algorithm proposed by Igelnik, and we present several results of decomposition for gray level images. Our goal is to adapt and apply the superposition theorem to image processing, i.e. to decompose an image into simpler functions using Kolmogorov superpositions. We synthetise our observations, before …