178 research outputs found
A generalized flat extension theorem for moment matrices
In this note we prove a generalization of the flat extension theorem of Curto and Fialkow [4] for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free setting, this gives an equivalent result for truncated Hankel operators
Fast algorithm for border bases of Artinian Gorenstein algebras
Given a multi-index sequence , we present a new efficient algorithm
to compute generators of the linear recurrence relations between the terms of
. We transform this problem into an algebraic one, by identifying
multi-index sequences, multivariate formal power series and linear functionals
on the ring of multivariate polynomials. In this setting, the recurrence
relations are the elements of the kerne l\sigma of the Hankel operator
$H$\sigma associated to . We describe the correspondence between
multi-index sequences with a Hankel operator of finite rank and Artinian
Gorenstein Algebras. We show how the algebraic structure of the Artinian
Gorenstein algebra \sigma\sigma yields the
structure of the terms $\sigma\alpha N nAK[x 1 ,. .. , xnIHIA$ and the tables of multiplication by the variables in these
bases. It is an extension of Berlekamp-Massey-Sakata (BMS) algorithm, with
improved complexity bounds. We present applications of the method to different
problems such as the decomposition of functions into weighted sums of
exponential functions, sparse interpolation, fast decoding of algebraic codes,
computing the vanishing ideal of points, and tensor decomposition. Some
benchmarks illustrate the practical behavior of the algorithm
Efficient and robust reconstruction of botanical branching structure from laser scanned points
This paper presents a reconstruction pipeline for recovering branching structure of trees from laser scanned data points. The process is made up of two main blocks: segmentation and reconstruction. Based on a variational k-means clustering algorithm, cylindrical components and ramified regions of data points are identified and located. An adjacency graph is then built from neighborhood information of components. Simple heuristics allow us to extract a skeleton structure and identify branches from the graph. Finally, a B-spline model is computed to give a compact and accurate reconstruction of the branching system. © 2009 IEEE.published_or_final_versionThe 11th IEEE International Conference on Computer-Aided Design and Computer Graphics (CAD/Graphics '09), Huangshan, China, 19-21 August 2009. In Proceedings of 11th CAD/Graphics, 2009, p. 572-57
Resultant-based methods for plane curves intersection problems
http://www.springeronline.com/3-540-28966-6We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials and the Sylvester or Bezout resultant constructions. We propose a new method to treat multiple roots, detail its numerical aspects and describe experiments on tangential problems, which show the efficiency of the approach. An industrial application of the method is presented at the end of the paper. It consists in recovering cylinders from a large cloud of points and requires intensive resolution of polynomial equations
SYNAPS: A library for dedicated applications in symbolic numeric computing,
International audienceWe present an overview of the open source library synaps. We describe some of the representative algorithms of the library and illustrate them on some explicit computations, such as solving polynomials and computing geometric information on implicit curves and surfaces. Moreover, we describe the design and the techniques we have developed in order to handle a hierarchy of generic and specialized data-structures and routines, based on a view mechanism. This allows us to construct dedicated plugins, which can be loaded easily in an external tool. Finally, we show how this design allows us to embed the algebraic operations, as a dedicated plugin, into the external geometric modeler axel
Guidelines of the French Society of Otorhinolaryngology (SFORL), short version. Extension assessment and principles of resection in cutaneous head and neck tumors
AbstractCutaneous head and neck tumors mainly comprise malignant melanoma, squamous cell carcinoma, trichoblastic carcinoma, Merkel cell carcinoma, adnexal carcinoma, dermatofibrosarcoma protuberans, sclerodermiform basalioma and angiosarcoma. Adapted management requires an experienced team with good knowledge of the various parameters relating to health status, histology, location and extension: risk factors for aggression, extension assessment, resection margin requirements, indications for specific procedures, such as lateral temporal bone resection, orbital exenteration, resection of the calvarium and meningeal envelopes, neck dissection and muscle resection
Numeric and Certified Isolation of the Singularities of the Projection of a Smooth Space Curve
International audienceLet CP ∩Q be a smooth real analytic curve embedded in R 3 , defined as the solutions of real analytic equations of the form P (x, y, z) = Q(x, y, z) = 0 or P (x, y, z) = ∂P ∂z = 0. Our main objective is to describe its projection C onto the (x, y)-plane. In general, the curve C is not a regular submanifold of R 2 and describing it requires to isolate the points of its singularity locus Σ. After describing the types of singularities that can arise under some assumptions on P and Q, we present a new method to isolate the points of Σ. We experimented our method on pairs of independent random polynomials (P, Q) and on pairs of random polynomials of the form (P, ∂P ∂z) and got promising results
Symbolic Methods for Solving Algebraic Systems of Equations and Applications for Testing the Structural Stability
International audienceIn this work, we provide an overview of the classical symbolic techniques for solving algebraic systems of equations and show the interest of such techniques in the study of some problems in dynamical system theory, namely testing the structural stability of multidimensional systems
Ideal Interpolation, H-Bases and Symmetry
International audienceMultivariate Lagrange and Hermite interpolation are examples ofideal interpolation. More generally an ideal interpolation problemis defined by a set of linear forms, on the polynomial ring, whosekernels intersect into an ideal.For an ideal interpolation problem with symmetry, we addressthe simultaneous computation of a symmetry adapted basis of theleast interpolation space and the symmetry adapted H-basis ofthe ideal. Beside its manifest presence in the output, symmetry isexploited computationally at all stages of the algorithm
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