the eigenvalues of second order spectral differentiation matrices the eigenvalues of the pseudospectral second derivative matrix with homogeneous dirichlet boundary conditions are important in many applications of spectral methods this paper investigates some of their properties numerical results show that a certain fraction of the eigenvalues approximate the eigenvalues of the continuous operator very accurately but the errors in the remaining ones are large it is demonstrated that the inaccurate eigenvalues correspond to those eigenfunctions of the continuous operator that cannot be resolved by polynomial interpolation in the spectral grid in particular it is proved that 7r points on average per wavelength are sufficient for successful interpolation of the eigenfunctions of the continuous operator in a chebyshev distribution of nodes and six points per wavelength for a uniform distribution these results are in agreement with the observed fractions of accurate eigenvalues by using the characteristic polynomial a bound on the spectral radius of the differentiation matrix is derived that is accurate to 2 or better the effect of filtering on the eigenvalues is studied numerically

empirical bayes hierarchical models for regularizing maximum likelihood estimation in the matrix gaussian procrustes problem procrustes analysis involves finding the optimal superposition of two or more forms via rotations translations and scalings procrustes problems arise in a wide range of scientific disciplines especially when the geometrical shapes of objects are compared contrasted and analyzed classically the optimal transformations are found by minimizing the sum of the squared distances between corresponding points in the forms despite its widespread use the ordinary unweighted least squares ls criterion can give erroneous solutions when the errors have heterogeneous variances heteroscedasticity or the errors are correlated both common occurrences with real data in contrast maximum likelihood ml estimation can provide accurate and consistent statistical estimates in the presence of both heteroscedasticity and correlation here we provide a complete solution to the nonisotropic ml procrustes problem assuming a matrix gaussian distribution with factored covariances our analysis generalizes simplifies and extends results from previous discussions of the ml procrustes problem an iterative algorithm is presented for the simultaneous numerical determination of the ml solutions

pivotal bootstrap methods for k sample problems in directional statistics and shape analysis we propose a novel bootstrap hypothesis testing approach for the problem of testing a null hypothesis of a common mean direction mean polar axis or mean shape across several populations of real unit vectors the directional case or complex unit vectors the two dimensional shape case multisample testing problems of this type arise frequently in directional statistics and shape analysis as in other areas of statistics but to date there has been relatively little discussion of nonparametric bootstrap approaches to this problem the bootstrap approach described here is based on a statistic that can be expressed as the smallest eigenvalue of a certain positive definite matrix we prove that this statistic has a limiting chi squared distribution under the null hypothesis of equality of means across populations although we focus mainly on the version of the statistic in which neither isotropy within populations nor constant dispersion structure across populations is assumed we explain how to modify th

intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth for planar landmark based shapes taking into account the non euclidean geometry of the shape space a statistical test for a common mean first geodesic principal component gpc is devised which rests on one of two asymptotic scenarios for both scenarios strong consistency and central limit theorems are established along with an algorithm for the computation of a ziezold mean geodesic in application this allows to verify the geodesic hypothesis for leaf growth of canadian black poplars and to discriminate genetically different trees by observations of leaf shape growth over brief time intervals with a test based on procrustes tangent space coordinates not involving the shape space s curvature neither can be achieved

the spectrum of the chebyshev collocation operator for the heat equation it is shown that the eigenvalues of the pseudospectral chebyshev second derivative operator with separated boundary conditions are real negative and distinct an application to the full potential equation is also presented

large sample theory of intrinsic and extrinsic sample means on manifolds ii this article develops nonparametric inference procedures for estimation and testing problems for means on manifolds a central limit theorem for frechet sample means is derived leading to an asymptotic distribution theory of intrinsic sample means on riemannian manifolds central limit theorems are also obtained for extrinsic sample means w r t an arbitrary embedding of a differentiable manifold in a euclidean space bootstrap methods particularly suitable for these problems are presented applications are given to distributions on the sphere s d directional spaces real projective space rp n 1 axial spaces complex projective space cp k 2 planar shape spaces w r t veronese whitney embeddings and a three dimensional shape space 4 3

modeling network traffic using generalized cauchy process abstract processes with long range dependence lrd have gained wide applications in many fields of science and technologies ranging from hydrology to network traffic two key properties of such processes are lrd that is characterized by the hurst parameter h and self similarity ss that is measured by the fractal dimension d however in the popular traffic model using fractional gaussian noise fgn these two parameters are linearly related this may be regarded as a limitation of fgn in traffic modeling from the point of view of either accurately fitting real traffic or appropriately explaining the particular multi fractal phenomena of traffic in this paper we discuss recent results in traffic modeling from a view of the generalized cauchy gc process the gc process is indexed by two parameters d and h the parameter d in the gc model is independent of h hence it provides a more flexible way to describe the multi fractal phenomena of traffic in addition to accurately modeling traffic for both short term lags and long term ones

an algorithm for the evaluation of multidimensional direct and inverse discrete chebyshev transforms abstract a method is presented for the efficient computation of n d n dimensional imbricated sums of direct and inverse discrete chebyshev transforms the algorithm consists essentially in the generalization of well known onedimensional procedures which are fitted together in order to perform the pre and post processing of the chebyshev coefficients array

linear array thinning exploiting almost difference sets this paper describes a class of linear thinned arrays with predictable and well behaved sidelobes the element placement is based on almost difference sets and the array power pattern is forced to pass through n uniformly spaced values that although neither equal nor constant as for difference sets are a priori known from the knowledge of the aperture size the number of active array elements k and the features of the correlation function such a property allows one to predict the bounds of the confidence range of the peak sidelobe of the admissible arrays obtainable through simple shift operations on a binary sequence the expected peak sidelobe performances turn out to be comparable with those from difference sets even though obtainable in a wider set of array configurations and improved in comparison with cut and try random placements

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

invariance identifiability and morphometrics the form of an object is that characteristic that remains invariant under a group of transformations comprising translation rotation and possibly reflection group invariance thus naturally plays an important role in the statistical analysis of forms we examine the existing methods for the statistical analysis of form from the invariance perspective we begin with a review of the important basic ideas behind invariance and derive a maximal invariant under the group of transformations consisting of rotation reflection and translation and its distribution under the gaussian and elliptically symmetric perturbation models we first consider the single sample case and discuss the issue of identifiability of the parameters we show that method of moments estimators based on the distances between landmarks and maximum likelihood estimators mles based on the size and shape coordinates are invariant and estimate identifiable parameters however a number of commonly used methods do not we compare the stati

hybrid design of non regular linear arrays with accurate control of the pattern sidelobes the hybridization of an analytical thinning technique based on almost difference sets adss and a convex programming cp strategy is proposed for designing non regular linear arrays over a half wavelength lattice that fit arbitrary upper bounds on the far field pattern the proposed approach combines the efficiency of the ads procedure in defining a low sidelobe thinned arrangement with the effectiveness of the cp approach in deducing the optimal tapering to control the beam shape a set of numerical results is presented to assess features and potentialities of the ads cp method

consistency of procrustes estimators lele has shown that the procrustes estimator of form is inconsistent and raised the question about the consistency of the procrustes estimator of shape in this paper the consistency of estimators of form and shape is studied under various assumptions in particular it is shown that the procrustes estimator of shape is consistent under the assumption of an isotropic error distribution and that consistency breaks down if the assumption of isotropy is relaxed the relevance of these results for practical shape analysis is discussed as a by product some new results are derived for the offset uniform distribution from directional data

chebyshev 3 d spectral and 2 d pseudospectral solvers for the helmholtz equation two chebyshev solvers are presented for the linear helmholtz equation the first algorithm is a 3 d direct spectral solver based on a diagonalization technique whilst the second performs an iterative pseudospectral 2 d calculation with finite difference preconditioning both techniques handle general nonhomogeneous boundary conditions computing times and accuracies of the two methods are compared

autocorrelation driven synthesis of antenna arrays the case of ds based planar isophoric thinned arrays a new methodology for the design of isophoric thinned arrays with a priori controlled pattern features is introduced a fully analytical and general i e valid for any lattice and set of weights relationship between the autocorrelation of the array excitations and the power pattern samples is first derived binary 2 d sequences with known autocorrelation properties namely the difference sets ds s are then chosen as a representative benchmark to prove that it is possible to deduce closed form synthesis formulas that a priori guarantee to fit requirements on the sidelobe level sll the directivity the half power beamwidth and the power pattern in user defined directions the selected results from a wide numerical assessment which also includes full wave simulations with realistic radiators are illustrated to validate the reliability and the accuracy of the proposed design equations and the associated performance bounds

an effective approach for the optimal focusing of array fields subject to arbitrary upper bounds a new approach to the optimal focusing of array fields subject to arbitrary upper bounds is presented the approach formulates the problem as the minimization of a linear function in a convex set unlike other approaches this one guarantees the achievement of the global optimum by using local optimization techniques and can moreover deal with any convex constraint on the unknowns such as near field constraints optimization is performed by two ad hoc developed solution algorithms which exploit the geometrical characteristics of the problem at hand thus leading to extremely effective and computationally efficient numerical codes an extensive numerical analysis has been performed in all cases of linear planar and circular arc arrays the enhanced performance of the proposed technique with respect to the solution algorithms available in the literature fully confirms the effectiveness of the approach

morphometric tools for landmark data geometry and biology 1 introduction 2 preliminaries 3 landmarks 4 distance measures 5 shape coordinates 6 principal axes of shape change for triangles 7 features of shape comparison 8 retrospect and prospect

generalized whittle matern random field as a model of correlated fluctuations this paper considers a generalization of the gaussian random field with covariance function of the whittle matern family such a random field can be obtained as the solution to the fractional stochastic differential equation with two fractional orders asymptotic properties of the covariance functions belonging to this generalized whittle matern family are studied which are used to deduce the sample path properties of the random field the whittle matern field has been widely used in modeling geostatistical data such as sea beam data wind speed field temperature and soil data in this paper we show that the generalized whittle matern field provides a more flexible model for wind speed data

design of subarrayed linear and planar array antennas with sll control based on an excitation matching approach in this paper the synthesis of subarrayed antennas with subarrays having different weights and dimensions is considered the problem is formulated as the definition of the element clustering into spatially contiguous subarrays and the corresponding weights to obtain a pattern with the lowest i e minimum achievable sidelobe level sll the problem is addressed with an unconstrained approach based on an excitation matching method where the synthesis of subarray weights and sizes is simultaneously carried out successively a hybrid version of such an approach is proposed to directly enforce into the optimization procedure the sll constraints a set of representative results concerned with both sum and difference patterns are shown furthermore some comparisons with state of the art hybrid evolutionary based techniques are reported as well

an informational measure of association and dimension reduction for multiple sets and groups with applications in morphometric analysis in this article we propose a new general index that measures relationships between multiple sets of random vectors this index is based on kullback leibler kl information which measures linear or nonlinear dependence between multiple sets using joint and marginal densities of affine transformations of the random vectors estimates of the matrixes are obtained by maximizing the kl information and are shown to be consistent the motivation for introducing such an index comes from morphological integration studies a topic in biological science as a special case of this index we define an overall measure of association and two other measures for dimension reduction the use of these measures is illustrated through real data analysis in morphometric studies and extensive simulations and their performance is compared with that of approaches based on canonical correlation analysis extensions of the aforementioned measures to multiple groups are also discussed in contrast to canonical correlation analysi

complex weight sparse linear array synthesis by bayesian compressive sampling an innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed in the framework of sparseness constrained optimization the approach exploits the multi task mt bayesian compressive sensing bcs theory to enable the design of complex non hermitian layouts with arbitrary radiation and geometrical constraints by casting the pattern matching problem into a probabilistic formulation a relevance vector machine rvm technique is used as solution tool the numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability flexibility and numerical efficiency of the mt bcs approach also in comparison with state of the art sparse arrays synthesis methods