Computational Harmonic Analysis

Functional harmonic analysis is an important task in music composition, accompaniment, arrangement and others. However, the solutions are still not satisfactory. The proposed process is divided into two levels: the first one extends one of previous works in the domain to carry out a richer analysis of chord grids and is where the very analysis is performed, and the second one is devoted to correct some conceptual inconsistencies concerning enharmonic spelling of chords. Both levels use an engine to make inferences on some rule bases, which can be easily improved by addition of new rules.

In this article, we discuss a parallel implementation of efficient algorithms for computation of Legendre polynomial transforms and other orthogonal polynomial transforms. We develop an approach to the Driscoll-Healy algorithm using polynomial arithmetic and present experimental results on the accuracy, efficiency, and scalability of our implementation. The algorithms were implemented in ANSI C using the BSPlib communications library. We also present a new algorithm for computing the cosine transform of two vectors at the same time.

An explicit determination of the Petrov type N spacetimes on which the conformally invariant scalar wave equation satisfies Huygens' principle Annales de l'I. H. P., section A, tome 44, n o 2 (1986), p. 115-153 <http://www.numdam.org/item?id=AIHPA_1986__44_2_115_0> © Gauthier-Villars, 1986, tous droits réservés. L'accès aux archives de la revue « Annales de l'I. H. P., section A » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

Surface reconstruction from unorganized point set is a common problem in computer graphics. Generation of the signed distance field from the point set is a common methodology for the surface reconstruction. The reconstruction of implicit surfaces is made with the algorithm of marching cubes, but the distance field of a point set can not be processed with marching cubes because the unsigned nature of the distance. We propose an extension to the marching cubes algorithm allowing the reconstruction of 0-level iso-surfaces in an unsigned distance field. We calculate more information inside each cell of the marching cubes lattice and then we extract the intersection points of the surface within the cell then we identify the marching cubes case for the triangulation. Our algorithm generates good surfaces but the presence of ambiguities in the case selection generates some topological mistakes.

Technological Advances in Medical Imaging have enabled the acquisition of images accurately describing biological tissues. Finite Element (FE) methods on these images provide the means to simulate biological phenomena such as brain shift registration, respiratory organ motion, blood flow pressure in vessels, etc. FE methods require the domain of tissues be discretized by simpler geometric elements, such as triangles in two dimensions, tetrahedra in three, and pentatopes in four. This exact discretization is called a mesh. The accuracy and speed of FE methods depend on the quality and fidelity of the mesh used to describe the biological object. Elements with bad quality introduce numerical errors and slower solver convergence. Also, analysis based on poor fidelity meshes do not yield accurate results specially near the surface. In this dissertation, we present the theory and the implementation of both a sequential and a parallel Delaunay meshing technique for 3D and —for the first ti...

An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III : Petrov type III space-times Annales de l'I. H. P., section A, tome 48, n o 1 (1988), p. 77-96 <http://www.numdam.org/item?id=AIHPA_1988__48_1_77_0> © Gauthier-Villars, 1988, tous droits réservés. L'accès aux archives de la revue « Annales de l'I. H. P., section A » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

Recientemente se ha observado que para un peso w la desigualdad puntual para operadores de Hardy-Littlewood  Mf (x)^p ≤ C · M_w (| f |^p| ) (x), que es consecuencia del tipo débil (p, p) respecto de un peso w en realidad es equivalente a la acotación débil (p, p). Aquí proporcionamos una demostración nueva y elemental de dicha equivalencia que, a diferencia de las demostraciones existentes, no requiere apoyarse en resultados de cubrimientos.   The inequality Mf (x)p C Mw (j f jp) (x), for a weight function w, is a consequence of the weak type (p; p) for the Hardy-Littlewood maximal operator from Lp (w). A recent result shows that the inequality also implies the weak type(p; p) so, in fact, both conditions are equivalent. Here we give a new an elementary proof of the equivalence that, unlike existing demonstrations, it requires no covering properties

In this paper, we proposed an effective method based on the scaling function of Daubechies wavelets for the solution of the brachistochrone problem. An analytic technique for solving the integral of Daubechies scaling functions on dyadic intervals is investigated and these integrals are used to reduce the brachistochrone problem into algebraic equations. The error estimate for the brachistochrone problem is proposed and the numerical results are given to verify the effectiveness of our method.

Usually, the gaussian beam modes are assumed to be solutions of the wave equation in the free space. Nevertheless, these modes are obtained suppo sing some paraxial restrictions. Therefore, we will have to check if our working conditions are obeying or not these paraxial restrictions to consider the se beam modes as really solutions in free space. In other hand, applications of processing materials , surface coating, etc can use these beam modes to simplify considerably the transmision line betwe en the generator and the final cavity. In this paper, an original study of paraxial consid erations for the higher order gaussian modes is presented. 1.- INTRODUCCIÓN

We present spline wavelets of class C n (R) supported by sequences of aperiodic discretizations of R. The construction is based on multiresolution analysis recently elaborated by G. Bernuau. At a given scale, we consider discretizations that are sets of left-hand ends of tiles in a self-similar tiling of the real line with finite local complexity. Corresponding tilings are determined by two-letter Sturmian substitution sequences. We illustrate the construction with examples having quadratic Pisot-Vijayaraghavan units (like τ = (1 + √ 5)/2 or τ 2 = (3 + √ 5)/2) as scaling factor. In particular, we present a comprehensive analysis of the Fibonacci chain and give the analytic form of related scaling functions and wavelets. We also give some hints for the construction of multidimensional spline wavelets based on stone-inflation tilings in arbitrary dimension.

En este artículo se presentan los polinomios de Laguerre complejo L(α−k)(z), junto con algunas expresiones que resultan k a partir de ellos, que aparecen utilizando definiciones mencionadas en el texto. Además, se realiza una revisión de las propiedades de los polinomios de Laguerre y su convergencia en media, estudiada por varios autores a lo largo de la historia. La convergencia de los polinomios de Laguerre empieza con los estudios de Pollard, que plantea que para que se Rb PN pcumpla limN−→∞ a f(x) − 0 anPn(x) dF(x) = 0, entonces p = 2, luego Askey y Wainger plantean una función de Laguerre Lαn (x) = xα/2 rn exp(−x/2)Lαn (x) que converge si 4/3 &lt; p &lt; 4. En la siguiente investigacion, Muckenhoupt indica que en los polinomios de Laguerre, los términos no convergerán a 0 en la media si p no está entre 4/3 y 4, pero esta vez probando que p es un número fijo que satisface 1 ≤ p ≤ 4/3 o 4 ≤ p ≤ ∞. Luego, el mismo Muckenhoupt generaliza los resultados de Askey y Wainger p...

Resumen. Lo que se pretende en este artículo es relacionar las formas de Dirichlet y los procesos de Markov de manera analítica y probabilística. Se encuentran Procesos de Markov fuertes y movimientos Brownianos en espacios de dimensión infinita a través de las formas de Dirichlet.

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWTwas compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many free parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation> algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWTnetwork or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. Human Performance Monitoring 4 The efficiency of the DWTis discussed in terms of its decorrelation and energy compaction properties. In addition, the DWTmodels provided evidence that a pattern of low-frequency activity (I to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance.

In this paper, a differential wavelet-based operator defined on an interval is presented and used in evaluating the electromagnetic field described by Maxwell's curl equations, in time domain. The wavelet operator has been generated by using Daubechies wavelets with boundary functions. A spatial differential scheme has been performed and it has been applied in studying electromagnetic phenomena in a lossless medium. The proposed approach has been successfully tested on a bounded axial-symmetric cylindrical domain.

It is shown that the conformally invariant scalar wave equation on a general Petrov type-N space-time satisfies Huygens&#39; principle if and only if the space-time is conformally related to an exact plane wave space-time. Some related intermediate results on the validity of Huygens&#39; principle for Maxwell&#39;s equations and for Weyl&#39;s equation are also given On demontre que l&#39;equation invariante conforme des ondes scalaires sur un espace-temps general de type N de Petrov satisfait au principe d&#39;Huygens si et seulement si l&#39;espace-temps est conforme a l&#39;espace-temps des ondes planes. On donne quelques resultats partiels de nature analogue sur la validite du principe d&#39;Huygens pour les equations de Maxwell et pour l&#39;equation de Weyl

Figure 1: We present improved subdivision and isosurface reconstruction algorithms for polygonizing implicit surfaces and performing accurate geometric operations. We highlight its performance on the "gun model" of the Bradley Fighting Vehicle which is generated using 8 Boolean operations. The leftmost and center left images show an iso-surface reconstruction using the dual contouring algorithm [Ju et al. 2002] on a distance field sampled on a uniform 64 × 64 × 64(≈ 262K) and 256 × 256 × 256(≈ 16.7M) grid, respectively. The center right image shows the improved iso-surface generated from our new reconstruction on the uniform 64 × 64 × 64 grid. It can reconstruct thin features without creating additional handles, but cannot reconstruct all the sharp features. We also present an algorithm to detect multiple sharp features in a cell and use it to generate an adaptive grid. The rightmost image shows our reconstruction applied to a grid generated by our subdivision algorithm. It can reconstruct all the sharp features, does not create any additional handles and uses only 313, 168 voxels.

In this paper we present a novel shape from silhouette algorithm. For an object to be modeled, the algorithm first computes a cloud of points located on a pencil of rays and distributed evenly on the visual hull surface, inside and outside the visual hull. Then Delaunay tetrahedrization is applied to the point cloud to partition its convex hull into a set of tetrahedrons. Finally, outlier tetrahedrons are removed by tetrahedron peeling, and a mesh model of the visual hull is extracted. The algorithm is robust, free from discretization artifacts, and produces a mesh model composed of wellshaped triangles.

cuadrados. Se encontró una marea con características mixta principalmente diurna conformada por 12 constituyentes, de ellos seis son de carácter diurno (K1, O1, P1, Q1, J1, OO1) y cinco de carácter semidiurno (M2, S2, K2, N2, Mu2) además de la Componente lunisolar sinódica quincenal (Msf).

Triangular meshes play critical roles in many applications, such as numerical simulation and additive manufacturing. However, the triangular meshes transformed from computer-aided design models using common algorithms may have many undesirable narrow triangles, which tends to affect the downstream applications. In this paper, we proposed two algorithms for Delaunay mesh construction and simplification to improve the quality of the triangular meshes. Two improved mesh operations of inserting vertices and collapsing vertices based on the principle of minimum volume destruction were designed. The improved vertex inserting operation is able to modify the local mesh so that it will conform to the local Delaunay property. The improved vertex collapsing operation can realize the simplification of the original mesh while maintaining the local Delaunay property. The results of visualized rendering and thermal diffusion simulations verified the improvement of the proposed algorithms in the as...

Image snapping is the technique to move a cursor position to a nearby feature such as edges in a 2D image when the cursor is located by a user. This paper proposes a new snapping technique called the geometric snapping that naturally moves the cursor position to a geometric feature in 3D meshes. The cursor movement is based on the approximate curvatures defined for measuring the geometric characteristics of the 3D meshes. The proposed geometric snapping can be applied to extracting geometric features of 3D mesh models in many CAD and graphics systems.

In order to consider some ordered structures (X,;S) as being isotonic to subsets of the realline (R,$;) we introdu­ ce bivariate functions F: X x X -7R and study which pro­ perties of the ordered structure can be reflected by proper­ ties of the functions F. We apply this idea to the study of the representability of ordered semigroups as

The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating the resulting potential inefficiency of such preconditioners. Consequences of these results in the context of the weakly-constrained 4D-Var data assimilation problem are finally discussed.

Subdivision surfaces are an established modeling tool in computer graphics and computer-aided design. While the theoretical foundations of subdivision surfaces are well studied, the correlation between a control mesh and its subdivided limit surface still has some open-ended questions: Which topology should a control mesh have? Where should control vertices be placed? A modeler - human or software - is confronted with these questions and has to answer them. In this paper we analyze four characteristic situations. Each one consists of an analytical reference surface S and several variants of control meshes Ci. In order to concentrate on the topology of the control meshes, the geometrical positions of their control vertices have been determined and optimized automatically. As a result we identified the best topology of all Ci to represent the given surface S. Based on these results we derived heuristics to model with subdivision surfaces. These heuristics are beneficial for all modelers.

cuadrados. Se encontró una marea con características mixta principalmente diurna conformada por 12 constituyentes, de ellos seis son de carácter diurno (K1, O1, P1, Q1, J1, OO1) y cinco de carácter semidiurno (M2, S2, K2, N2, Mu2) además de la Componente lunisolar sinódica quincenal (Msf).

In this paper we introduce a new class of Gaussian singular integrals, the general alternative Gaussian singular integrals and study the boundedness of them in L p (d), 1 < p < 1 and its weak (1, 1) boundedness with respect to the Gaussian measure following [7] and [1], respectively.

Translationally invariant integro-differential equations are a common choice of model in neuroscience for describing the coarse-grained dynamics of cortical tissue. Here we analyse the propagation of travelling wavefronts in models of neural media that incorporate some form of modulation or randomness such that translational invariance is broken. We begin with a study of neural architectures in which there is a periodic modulation of the neuronal connections. Recent techniques from two-scale convergence analysis are used to construct a homogenized model in the limit that the spatial modulation is rapid compared with the scale of the long range connections. For the special case that the neuronal firing rate is a Heaviside we calculate the speed of a travelling homogenized front exactly and find how the wave speed changes as a function of the amplitude of the modulation. For this special case we further show how to obtain more accurate results about wave speed and the conditions for propagation failure by using an interface dynamics approach that circumvents the requirement of fast modulation. Next we turn our attention to forms of disorder that arise via the variation of firing rate properties across the tissue. To model this we draw parameters of the firing rate function from a distribution with prescribed spatial correlations and analyse the corresponding fluctuations in the wave speed. Finally we consider generalisations of the model to incorporate adaptation and stochastic forcing and show how recent numerical techniques developed for stochastic partial differential equations can be used to determine the wave speed by minimising the L 2 norm of a travelling disordered activity profile against a fixed test function.

In this paper, we present and discuss the NFTOOLS package written for the computer algebra system Maple. The package contains the main routines "nulltran", "inv", "nullor", "omull" and "pptype". The routine "nulltran" is an implementation of the 6-parameter Lorentz group in the Newman-Penrose (null tetrad) formalism, and "inv" checks for invariance of equations under subgroups of the Lorentz group. The routines "nullor" and "omull" provide a translation between the Newman-Penrose quantities associated with the null tetrad and the orthonormal tetrad quantities associated with the Ellis-MacCallum formalism. Finally, "pptype" determines the Petrov-Plebanski type of the Ricci tensor. @ 1998 Elsevier Science B.V.

An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III : Petrov type III space-times Annales de l'I. H. P., section A, tome 48, n o 1 (1988), p. 77-96 <http://www.numdam.org/item?id=AIHPA_1988__48_1_77_0> © Gauthier-Villars, 1988, tous droits réservés. L'accès aux archives de la revue « Annales de l'I. H. P., section A » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

En el presente trabajo estudiamos la ecuación visco elástica unidimensional definida sobre el intervalo [0, L]. Dividimos el estudio en dos partes: En la primera analizamos la existencia y unicidad de soluciones usando la teoría de los semigrupos lineales, aplicando en el problema de Cauchy o y en la segunda parte vemos la estabilidad exponencial del C0- semigrupo de contracciones asociado al sistema viscoelástica lineal.

30 digitization devices produce very large sets of 3 0 points sampled from the suqaces of the objects being scanned. A mesh construction procedure needs to be: upplied to derive polygon mesh from the 3 0 point sets\ As ts derived from.. digitization devices based on in8 technologies are inhsaenrly distributed over regions that may contain surface discontinuities, existing methods are not suitable ,for polygonizing them. This paper describes a novel polygonization algorithm,for constructing triangle mesh from unorganized 3D points. In contrast to existing methods, this a1gorith.m begins the mesh construction processsrom 3 0 points lying on smooth suqaces, and advances the mesh frontier towards 30 points lying near surjGace discontinuities. I f 30 points along the edges and at the corners are sampled, then the algorithm will form an edge where two advancing frontiers meet, and a corner where three or niore.frontiers meet. Otherwise, the algorithm constructs approximations of the edges and corners. It can be shown that thi.y frontier advancing algorithm peg0rm.r 2 0 Delaunay triangulation of 3Dpoints 1.Ying on a plane in 30 space.

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWTwas compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many free parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation> algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWTnetwork or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. Human Performance Monitoring 4 The efficiency of the DWTis discussed in terms of its decorrelation and energy compaction properties. In addition, the DWTmodels provided evidence that a pattern of low-frequency activity (I to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance.

This paper introduces a two non-invasive electrode based electroencephalography (EEG) scheme to pick-up the biopotential (generated by the neuron network of human brain) for the assessment of consciousness level. With the help of a suitable algorithm (developed by us), processed in LabVIEW environment, real-time β-wave (frequency range 13-30 Hz.) is extracted (representing the consciousness level of the brain activities) from the complex bio-signal and reproduced on the computer monitor. The data array is further processed in MATLAB platform using Daubechies wavelet transform (dB 6, level 9) to cross check the results of interpretation of one‘s awareness level as obtained from LabVIEW environment. The results provided by our proposed device are in good agreements with the actual physiological actions of the subjects‘ brain and supported by the clinicians. Key-Words: Electrodes, EEG,β-wave , consciousness ,Level of consciousness, Daubechies wavelet transform, dB6.

This paper presents several improvements to the marching triangles algorithm for general implicit surfaces. The original method generates equilateral triangles of constant size almost everywhere on the surface. We present several modifications to adapt the size of the triangles to the curvature of the surface. As cracks may arise in the resulting polygonization, we propose a specific crack-closing method invoked at the end of the mesh growing step. Eventually, we show that the marching triangles can be used as an incremental meshing technique in an interactive modeling environment. In contrast to existing incremental techniques based on spatial sudvision, no extra datastructure is needed to incrementally edit skeletal implicit surfaces, which saves both memory and computation time.

This paper introduces a unified and general tesselation algorithm for parametric and implicit surfaces. The algorithm produces a hierarchial mesh that is adapted to the surface geometry and has a multiresolution and progressive structure. The representation can be exploited with advantages in several applications.

Figure : We present improved subdivision and isosurface reconstruction algorithms for polygonizing implicit surfaces and performing accurate geometric operations. We highlight its performance on the "gun model" of the Bradley Fighting Vehicle which is generated using 8 Boolean operations. The leftmost and center left images show an iso-surface reconstruction using the dual contouring algorithm on a distance field sampled on a uniform 64 × 64 × 64(≈ 262K) and 256 × 256 × 256(≈ 16.7M ) grid, respectively. The center right image shows the improved iso-surface generated from our new reconstruction on the uniform 64 × 64 × 64 grid. It can reconstruct thin features without creating additional handles, but cannot reconstruct all the sharp features. We also present an algorithm to detect multiple sharp features in a cell and use it to generate an adaptive grid. The rightmost image shows our reconstruction applied to a grid generated by our subdivision algorithm. It can reconstruct all the sharp features, does not create any additional handles and uses only 313, 168 voxels.

A number of techniques have been developed for the polygonization of implicit surfaces or isosurfaces. Two approaches for generating polyhedral approximations of implicit models are presented. The first method produces finite element meshes. The second algorithm is based on a P1 (linear) surface approximation from volumetric datasets. Applications examples of discrete constructive solid geometry objects are given.