spatiospectral concentration on a sphere we pose and solve the analogue of slepian s time frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere or alternatively of strictly spacelimited functions that are optimally concentrated in the spherical harmonic domain such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications as well as in medical imaging computer science cosmology and numerical analysis the spherical slepian functions can be found by solving either an algebraic eigenvalue problem in the spectral domain or a fredholm integral equation in the spatial domain the associated eigenvalues are a measure of the spatiospectral concentration when the concentration region is an axisymmetric polar cap the spatiospectral projection operator commutes with a sturm liouville operator this enables the eigenfunctions to be computed extremely accurately and efficiently even when their area bandwidth product or shannon number is large in the asymptotic limit of a small spatial region and a large spherical harmonic bandwidth the spherical concentration problem reduces to its planar equivalent which exhibits self similarity when the shannon number is kept invariant

super resolution on the sphere using convex optimization this paper considers the problem of recovering an ensemble of diracs on a sphere from its low resolution measurements the diracs can be located at any location on the sphere not necessarily on a grid we show that under a separation condition one can recover the ensemble with high precision by a three stage algorithm which consists of solving a semi definite program root finding and least square fitting the algorithm s computation time depends solely on the number of measurements and not on the required solution accuracy we also show that in the special case of non negative ensembles a sparsity condition is sufficient for recovery furthermore in the discrete setting we estimate the recovery error in the presence of noise as a function of the noise level and the super resolution factor

double fourier series on a sphere the solution of elliptic and vorticity equations on a sphere is studied using double fourier series as orthogonal basis functions the basis functions incorporate sine series weighted by cosine latitude as meridional basis functions for even zonal wavenumbers other than zero to meet the pole condition as to the solution of poisson s equation it is found that the new method gives improved accuracy compared to the method of yee mon weather rev 109 501 1981 due to the absence of constraints imposed on spectral coefficients with the operation number being slightly increased the new method is applied to the vorticity equation along with the use of fourier and spherical harmonics filters and its accuracy is tested for the rotated rossby haurwitz wave it is shown that the basis functions adopted here provide high accuracy for all tests used numerical integration without spherical harmonics filters indicates that they are necessary for stable and accurate time integration comparison with the spherical harmonics model reveals that the present method is more accurate by a factor of order 112 for the test case further application to the advection equation is carried out the error measure for the strong advection of the cosine bell with various rotation angles indicates that the present method is capable of producing accurate and stable calculations without the pole problem suggesting that it could be applied to the numerical weather prediction model including shallow water equations without difficulty extension to the shallow water equations with accuracy tests as in williamson et al j comput phys 102 211 1992 will be given in the future additional time could be saved by introducing the reduced grids near poles in the present method besides the advantage of applying fft to both longitudinal and latitudinal directions

rank preserving regression a more robust rank regression model against outliers mean based semi parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models unfortunately such models are quite sensitive to outlying observations the wilcoxon score based rank regression rr provides more robust estimates over generalized estimating equations against outliers however the rr and its extensions do not sufficiently address missing data arising in longitudinal studies in this paper we propose a new approach to address outliers under a different framework based on the functional response models this functional response model based alternative not only addresses limitations of the rr and its extensions for longitudinal data but with its rank preserving property even provides more robust estimates than these alternatives the proposed approach is illustrated with both real and simulated data copyright 2016 john wiley sons ltd

expansion maximization compression algorithm with spherical harmonics for single particle imaging with x ray lasers in three dimensional 3d single particle imaging with x ray free electron lasers particle orientation is not recorded during measurement but is instead recovered as a necessary step in the reconstruction of a 3d image from the diffraction data here we use harmonic analysis on the sphere to cleanly separate the angular and radial degrees of freedom of this problem providing new opportunities to efficiently use data and computational resources we develop the expansion maximization compression algorithm into a shell by shell approach and implement an angular bandwidth limit that can be gradually raised during the reconstruction we study the minimum number of patterns and minimum rotation sampling required for a desired angular and radial resolution these extensions provide new avenues to improve computational efficiency and speed of convergence which are critically important considering the very large datasets expected from experiment

a performance comparison of associated legendre projections the associated legendre projection provides a means for accelerating the dynamical core of a global weather or climate model therefore the goal is to determine the fastest possible projection algorithm of which this paper compares six the standard method which computes the projection using a forward and backward associated legendre transform the direct method which uses a single projection matrix when this approach results in fewer operations the fast multipole method the weighted orthogonal complement method the seminaive method and a projection based on transforms proposed by mohlenkamp timing results indicate that all the projections behave like o n3 algorithms up to at least n 200 spectral truncation for this range of resolutions the weighted orthogonal complement has the lowest operation count best cache utilization and best overall timings

exact wavelets on the ball we develop an exact wavelet transform on the three dimensional ball i e on the solid sphere which we name the flaglet transform for this purpose we first construct an exact transform on the radial half line using damped laguerre polynomials and develop a corresponding quadrature rule combined with the spherical harmonic transform this approach leads to a sampling theorem on the ball and a novel three dimensional decomposition which we call the fourier laguerre transform we relate this new transform to the well known fourier bessel decomposition and show that band limitedness in the fourier laguerre basis is a sufficient condition to compute the fourier bessel decomposition exactly we then construct the flaglet transform on the ball through a harmonic tiling which is exact thanks to the exactness of the fourier laguerre transform from which the name flaglets is coined the corresponding wavelet kernels are well localised in real and fourier laguerre spaces and their angular aperture is invariant under radial translation we introduce a multiresolution algorithm to perform the flaglet transform rapidly while capturing all information at each wavelet scale in the minimal number of samples on the ball our implementation of these new tools achieves floating point precision and is made publicly available we perform numerical experiments demonstrating the speed and accuracy of these libraries and illustrate their capabilities on a simple denoising example

an estimating equations approach for the liscomp model maximum likelihood estimation is computationally infeasible for latent variable models involving multivariate categorical responses in particular for the liscomp model a three stage generalized least squares approach introduced by muthen 1983 1984 can experience problems of instability bias non convergence and non positive definiteness of weight matrices in situations of low prevalence small sample size and large numbers of observed indicator variables we propose a quadratic estimating equations approach that only requires specification of the first two moments by performing simultaneous estimation of parameters this method does not encounter the problems mentioned above and experiences gains in efficiency methods are compared through a numerical study and an application to a study of life events and neurotic illness

merit functions for semi definite complementarity problems merit functions such as the gap function the regularized gap function the implicit lagrangian and the norm squared of the fischer burmeister function have played an important role in the solution of complementarity problems defined over the cone of nonnegative real vectors we study the extension of these merit functions to complementarity problems defined over the cone of block diagonal symmetric positive semi definite real matrices the extension suggests new solution methods for the latter problems

wavelet based segmentation on the sphere abstract segmentation a useful powerful technique in pattern recognition is the process of identifying object outlines within images there are a number of efficient algorithms for segmentation in euclidean space that depend on the variational approach and partial differential equation modelling wavelets have been used successfully in various problems in image processing including segmentation inpainting noise removal super resolution image restoration and many others wavelets on the sphere have been developed to solve such problems for data defined on the sphere which arise in numerous fields such as cosmology and geophysics in this work we propose a wavelet based method to segment images on the sphere accounting for the underlying geometry of spherical data our method is a direct extension of the tight frame based segmentation method used to automatically identify tube like structures such as blood vessels in medical imaging it is compatible with any arbitrary type of wavelet frame defined on the sphere such as axisymmetric wavelets directional wavelets curvelets and hybrid wavelet constructions such an approach allows the desirable properties of wavelets to be naturally inherited in the segmentation process in particular directional wavelets and curvelets which were designed to efficiently capture directional signal content provide additional advantages in segmenting images containing prominent directional and curvilinear features we present several numerical experiments applying our wavelet based segmentation method as well as the common k means method on real world spherical images including an earth topographic map a light probe image solar data sets and spherical retina images these experiments demonstrate the superiority of our method and show that it is capable of segmenting different kinds of spherical images including those with prominent directional features moreover our algorithm is efficient with convergence usually within a few iterations

a spectral element basin model for the shallow water equations abstract a spectral element model is built for the shallow water equations in complex geometry it is proved to be an efficient computational model in solving oceanic problems in particular the equatorial rossby modon s reflection process is simulated

spin weighted spherical wavelets derived from approximate identities abstract spin weighted functions introduced in 1966 by newman and penrose are used primarily for description of the cosmic microwave background radiation in the present paper an analysis tool for spin weighted functions is proposed namely spin weighted spherical wavelets based on approximate identities in the spin 0 case there exist two different definitions of continuous wavelet transforms the group theoretical one introduced by antoine et al and that based on approximate identities pioneered by freeden et al the first one has been recently extended to the case of spin weighted functions by mcewen et al and the present research is the approximate identities counterpart of their work wavelets presented here can be constructed for and the wavelet transform can be applied to functions of each integer spin weight further the set of parameters scale and position is continuous a big advantage of the construction is that the wavelet transform is invertible directly by an integral last but not least wavelets can reveal directional features such that the directional intensity of a signal can be probed

solvability of semidefinite complementarity problems abstract the concept of exceptional family has been introduced to study the existence theorem for nonlinear complementarity problems and variational inequality problems we describe extensions of such concepts to complementarity problems defined over the cone of block diagonal symmetric positive semidefinite real matrices using the concept of exceptional family we propose a very general existence theorem for the semidefinite complementarity problem extensions of isac carbone s condition karamardian s condition properness and coercivity are also introduced several applications of the main results are presented and we prove that without exceptional family is a sufficient and necessary condition for the solvability of pseudomonotone semidefinite complementarity problems

zero inflated poisson regression with an application to defects in manufacturing zero inflated poisson zip regression is a model for count data with excess zeros it assumes that with probability p the only possible observation is 0 and with probability 1 p a poisson random variable is observed for example when manufacturing equipment is properly aligned defects may be nearly impossible but when it is misaligned defects may occur according to a poisson distribution both the probability p of the perfect zero defect state and the mean number of defects in the imperfect state may depend on covariates sometimes p and are unrelated other times p is a simple function of such as p l 1 t for an unknown constant t in either case zip regression models are easy to fit the maximum likelihood estimates mle s are approximately normal in large samples and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the mle s simulations suggest that the confidence intervals based on likelihood ratio test

fast polynomial multiplication and convolutions related to the discrete cosine transform abstract a classical scheme for multiplying polynomials is given by the cauchy product formula faster methods for computing this product have been developed using circular convolution and fast fourier transform algorithms from the numerical point of view the chebyshev expansion of polynomials is preferred to the monomial form we develop a direct scheme for multiplication of polynomials in chebyshev form as well as a fast algorithm using discrete cosine transforms this approach leads to a new convolution operation and a new type of circulant matrices both related to the discrete cosine transform extensions to bivariate polynomial products are also discussed

a test of a modified algorithm for computing spherical harmonic coefficients using an fft this note describes the results of testing a modified method based on an algorithm by dilts 1 for computing the spherical harmonic expansion coefficients for a function on a sphere using a two dimensional fft the new version of the dilts program eliminates problems of overflow and large storage requirements encountered when harmonic degree values of l 16 are computed thus allowing the determination of coefficients for high l values l 300 however results from timing tests indicate that the new version of the dilts program is not practical for computing spherical harmonic expansion coefficients for large l due to the very long cpu times required for execution of the program the most effective technique remains the one pioneered by brown 2

a solution condition for complementarity problems with an application to spatial price equilibrium a sufficient condition is developed for the existence of solutions to complementarity problems which is applicable to all continuous functions in addition it is shown to imply a number of simpler conditions including the well known coerciveness condition finally this condition is applied to an existence problem in spatial price equilibrium where it is shown to yield not only a more general result but also a simpler method of proof

sampling sparse signals on the sphere algorithms and applications we propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass filtered observations central to our algorithm is a generalization of the annihilating filter method a tool widely used in array signal processing and finite rate of innovation fri sampling the proposed algorithm can reconstruct k spikes from k sqrt k 2 spatial samples for large k this sampling requirement improves over previously known fri sampling schemes on the sphere by a factor of four we showcase the versatility of the proposed algorithm by applying it to three problems 1 sampling diffusion processes induced by localized sources on the sphere 2 shot noise removal and 3 sound source localization ssl by a spherical microphone array in particular we show how ssl can be reformulated as a spherical sparse sampling problem

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

on linear and quadratic estimating functions summary in some cases maximum quasi likelihood estimation which is at the core of glim can fail to give reasonable results a more general class of estimating functions is investigated which avoids such failure and also is not restricted to the particular forms of mean and variance function of glim

a phase sensitive approach to filtering on the sphere this paper examines filtering on a sphere by first examining the roles of spherical harmonic magnitude and phase we show that phase is more important than magnitude in determining the structure of a spherical function we examine the properties of linear phase shifts in the spherical harmonic domain which suggest a mechanism for constructing finite impulse response fir filters we show that those filters have desirable properties such as being associative mapping spherical functions to spherical functions allowing directional filtering and being defined by relatively simple equations we provide examples of the filters for both spherical and manifold data

sampling signals with a finite rate of innovation on the sphere the state of the art in sampling theory now contains several theorems for signals that are non bandlimited for signals on the sphere however most theorems still require the assumptions of bandlimitedness in this work we show that a particular class of non bandlimited signals which have a finite rate of innovation can be exactly recovered using a finite number of samples we consider a sampling scheme where k weighted diracs are convolved with a kernel on the rotation group we prove that if the sampling kernel has a bandlimit l 2k then 2k 1 4k 1 1 equiangular samples are sufficient for exact reconstruction if the samples are uniformly distributed on the sphere we argue that the signal can be accurately reconstructed using 4k2 samples and validate our claim through numerical simulations to further reduce the number of samples required we design an optimal sampling kernel that achieves accurate reconstruction of the signal using only 3k samples the number of parameters of the weighted diracs in addition to weighted diracs we show that our results can be extended to sample diracs integrated along the azimuth finally we consider kernels with antipodal symmetry which are common in applications such as diffusion magnetic resonance imaging

estimating equations for parameters in means and covariances of multivariate discrete and continuous responses generalized estimating equations are introduced in an ad hoc fashion for the covariance matrix of a multivariate response these equations are to be solved jointly with score equations from a generalized linear model for mean parameters a class of quadratic exponential models is used to develop joint estimating equations for mean and covariance parameters in a more systematic fashion and proposals for the use of such equations are developed comments on the relative merits of the ad hoc and model based approaches to estimation are given and a regression illustration with a bivariate response is provided

fast algorithms for discrete polynomial transforms consider the vandermonde like matrix p p k cos j n j k 0 n where the polynomials p k satisfy a three term recurrence relation if p k are the chebyshev polynomials t k then p coincides with c n 1 cos jk n j k 0 n this paper presents a new fast algorithm for the computation of the matrix vector product pa in o n log 2 n arithmetical operations the algorithm divides into a fast transform which replaces pa with c n 1 and a subsequent fast cosine transform the first and central part of the algorithm is realized by a straightforward cascade summation based on properties of associated polynomials and by fast polynomial multiplications numerical tests demonstrate that our fast polynomial transform realizes pa with almost the same precision as the clenshaw algorithm but is much faster for n 128

a fourier spectral element algorithm for thermal convection in rotating axisymmetric containers we present a fourier spectral element approach for modeling thermal convection in a rotating axisymmetric container following the theory detailed in bernardi et al c bernardi m dauge y maday spectral methods for axisymmetric domains gauthier villars paris 1999 a fourier expansion of the field variables is performed in the periodic direction and the resulting collection of meridional problems is discretized by means of a parallel spectral element method a gauss lobatto jacobi 0 1 quadrature which incorporates the cylindrical radius in its weight is introduced to avoid a potential degeneracy of the discrete set of equations due to those nodes located on the axis of symmetry a second order timestepping scheme is presented which treats the coriolis and viscous forces implicitly numerical comparisons with analytical and published numerical solutions in spherical and cylindrical geometries are presented which highlight the accuracy of the model and demonstrate its spectral convergence properties

generalized sampling expansion for functions on the sphere functions on the sphere appear in several applications including geodesics imaging and acoustics sampling of these functions may result in aliasing if the sampling condition is not met the generalized sampling expansion introduced by papoulis enables the reconstruction of a band limited function sampled at a frequency lower than the nyquist frequency using the outputs of several linear time invariant systems this paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition facilitating sub nyquit sampling without aliasing error an analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented examples demonstrating the performance of the method and its limitations are studied

sparse image reconstruction on the sphere implications of a new sampling theorem we study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere we discuss how a reduction in the number of samples required to represent all information content of a band limited signal acts to improve the fidelity of sparse image reconstruction through both the dimensionality and sparsity of signals to demonstrate this result we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient we develop a framework for total variation inpainting on the sphere including fast methods to render the inpainting problem computationally feasible at high resolution recently a new sampling theorem on the sphere was developed reducing the required number of samples by a factor of two for equiangular sampling schemes through numerical simulations we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem

generalized discrete spherical harmonic transforms two generalizations of the spherical harmonic transforms are provided first they are generalized to an arbitrary distribution of latitudinal points i this unifies transforms for gaussian and equally spaced distributions and provides transforms for other distributions commonly used to model geophysical phenomena the discrete associated legendre functions pnm i are shown to be orthogonal to within roundoff error with respect to a weighted inner product thus providing the forward transform to spectral space second the representation of the transforms is also generalized to rotations of the discrete basis set pnm i a discrete function basis is defined that provides an alternative to pnm i on a grid with n latitudes the new basis requires o n2 memory compared to the usual o n3 the resulting transforms differ in spectral space but provide identical results for certain applications for example a forward transform followed immediately by a backward transform projects the original discrete function in a manner identical to the existing transforms namely they both project the original function onto the same smooth least squares approximation without the high frequencies induced by the closeness of the points in the neighborhood of the poles finally a faster projection is developed based on the new transforms

a stable algorithm for flat radial basis functions on a sphere when radial basis functions rbfs are made increasingly flat the interpolation error typically decreases steadily until some point when runge type oscillations either halt or reverse this trend because the most obvious method to calculate an rbf interpolant becomes a numerically unstable algorithm for a stable problem in the case of near flat basis functions there will typically also be a separate point at which disastrous ill conditioning enters we introduce here a new method rbf qr which entirely eliminates such ill conditioning and we apply it in the special case when the data points are distributed over the surface of a sphere this algorithm works even for thousands of node points and it allows the rbf shape parameter to be optimized without the limitations imposed by stability concerns since interpolation in the flat rbf limit on a sphere is found to coincide with spherical harmonics interpolation new insights are gained as to why the rbf approach with nonflat basis functions often is the more accurate of the two methods

fast and stable algorithms for discrete spherical fourier transforms abstract in this paper we propose an algorithm for the stable and efficient computation of fourier expansions of square integrable functions on the unit sphere s r 3 as well as for the evaluation of these fourier expansions at special knots the heart of the algorithm is an efficient realization of discrete legendre function transforms based on a modified and stabilized version of the driscoll healy algorithm

symmetry stabilization for fast discrete monomial transforms and polynomial evaluation abstract we discuss and explain the issues present in implementing a fast algorithm for discrete monomial transforms dmts in the context of certain applications in mri and data analysis the dmt of a sequence f 0 m with respect to sample points z0 zm c m 1 is the sequence of sums f 0 f m where f j mk 0 k zjk for different sets of sample points the dmt is an important component of many applications driscoll healy and rockmore described a fast o m log2m operations algorithm via matrix factorization for computing the dmt while the asymptotic complexity of the algorithm is guaranteed for any choice of the sample points the numerical stability is not in this paper we present a heuristic for stabilizing the fast dmt which makes its implementation feasible numerically for certain sets of sample points while retaining its computational advantages even for moderate problem sizes where it is shown to be more efficient than implementations using horner s rule

associated legendre functions on the cut abstract algorithms and a code are described for the computation of the associated legendre functions pvu cos pv u cos qvu cos and the normalized legendre polynomial p v u cos in the ranges 0 1 2 0 1 2 1 2 v the algorithms are based on power series expansions and recurrence relations they are executed in extended range arithmetic thereby admitting very extensive ranges of and v without causing overflow or underflow

on the robust variance estimator in generalised estimating equations summary the variance matrix of the estimated regression coefficient in the liang zeger generalised estimating equation approach can be consistently estimated by the so called sandwich or robust estimator in this note we propose a modification to the liang zeger prescription for implementing the robust variance estimator analytical and numerical evidence shows the superior performance of our proposal

interior point methods for the monotone semidefinite linear complementarity problem in symmetric matrices the sdlcp semidefinite linear complementarity problem in symmetric matrices introduced in this paper provides a unified mathematical model for various problems arising from systems and control theory and combinatorial optimization it is defined as the problem of finding a pair x y of n times n symmetric positive semidefinite matrices which lies in a given n n 1 2 dimensional affine subspace fc of sc 2 and satisfies the complementarity condition x bullet y 0 where sc denotes the n n 1 2 dimensional linear space of symmetric matrices and x bullet y the inner product of x and y the problem enjoys a close analogy with the lcp in the euclidean space in particular the central trajectory leading to a solution of the problem exists under the nonemptiness of the interior of the feasible region and a monotonicity assumption on the affine subspace fc the aim of this paper is to establish a theoretical basis of interior point methods with the use of newton directions toward the central trajectory for the monotone sdlcp

spatially varying spectral filtering of signals on the unit sphere this paper presents a general framework for spatially varying spectral filtering of signals defined on the unit sphere as an analogy to joint time frequency filtering for this purpose we first map spherical signals from spatial domain into joint spatio spectral domain where a spatio spectral signal transformation or modification is introduced for mapping spatial signals into joint spatio spectral domain we use the spatially localized spherical harmonic transform slsht from the literature we then propose a suitable scheme to transform the modified signal from the spatio spectral domain back to an admissible signal in the spatial domain using the least squares approach we also show that the overall action of the slsht and spatio spectral signal modification can be described through a single transformation matrix which is useful in practice finally we discuss two specific and useful instances of spatially varying spectral filtering defined through multiplicative and convolutive modification of the slsht distribution and show through numerical examples their effectiveness in selective spectral filtering of different spatial regions of the signal

zero inflated poisson and binomial regression with random effects a case study summary in a 1992 technometrics paper lambert 1992 34 1 14 described zero inflated poisson zip regression a class of models for count data with excess zeros in a zip model a count response variable is assumed to be distributed as a mixture of a poisson distribution and a distribution with point mass of one at zero with mixing probability p both p and are allowed to depend on covariates through canonical link generalized linear models in this paper we adapt lambert s methodology to an upper bounded count situation thereby obtaining a zero inflated binomial zip model in addition we add to the flexibility of these fixed effects models by incorporating random effects so that e g the within subject correlation and between subject heterogeneity typical of repeated measures data can be accommodated we motivate develop and illustrate the methods described here with an example from horticulture where both upper bounded count binomial type and unbounded count poisson type data with excess zeros were collected in a repeated measures designed experiment

variable selection for distribution free models for longitudinal zero inflated count responses zero inflated count outcomes arise quite often in research and practice parametric models such as the zero inflated poisson and zero inflated negative binomial are widely used to model such responses like most parametric models they are quite sensitive to departures from assumed distributions recently new approaches have been proposed to provide distribution free or semi parametric alternatives these methods extend the generalized estimating equations to provide robust inference for population mixtures defined by zero inflated count outcomes in this paper we propose methods to extend smoothly clipped absolute deviation scad based variable selection methods to these new models variable selection has been gaining popularity in modern clinical research studies as determining differential treatment effects of interventions for different subgroups has become the norm rather the exception in the era of patent centered outcome research such moderation analysis in general creates many explanatory variables in regression analysis and the advantages of scad based methods over their traditional counterparts render them a great choice for addressing this important and timely issues in clinical research we illustrate the proposed approach with both simulated and real study data copyright 2016 john wiley sons ltd

on performance of parametric and distribution free models for zero inflated and over dispersed count responses zero inflated poisson zip and negative binomial zinb models are widely used to model zero inflated count responses these models extend the poisson and negative binomial nb to address excessive zeros in the count response by adding a degenerate distribution centered at 0 and interpreting it as describing a non risk group in the population the zip zinb models a two component population mixture as in applications of poisson and nb the key difference between zip and zinb is the allowance for overdispersion by the zinb in its nb component in modeling the count response for the at risk group overdispersion arising in practice too often does not follow the nb and applications of zinb to such data yield invalid inference if sources of overdispersion are known other parametric models may be used to directly model the overdispersion such models too are subject to assumed distributions further this approach may not be applicable if information about the sources of overdispersion is unavailable in this paper we propose a distribution free alternative and compare its performance with these popular parametric models as well as a moment based approach proposed by yu et al statistics in medicine 2013 32 2390 2405 like the generalized estimating equations the proposed approach requires no elaborate distribution assumptions compared with the approach of yu et al it is more robust to overdispersed zero inflated responses we illustrate our approach with both simulated and real study data

fast spherical fourier algorithms spherical fourier series play an important role in many applications a numerically stable fast transform analogous to the fast fourier transform is of great interest for a standard grid of o n2 points on the sphere a direct calculation has computational complexity of o n4 but a simple separation of variables reduces the complexity to o n3 here we improve well known fast algorithms for the discrete spherical fourier transform with a computational complexity of o n2 log2 n furthermore we present for the first time a fast algorithm for scattered data on the sphere for arbitrary o n2 points on the sphere a direct calculation has a computational complexity of o n4 but we present an approximate algorithm with a computational complexity of o n2 log2 n

fast directional spatially localized spherical harmonic transform we propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio spectral domain when used in conjunction with an asymmetric window function we call this transform the directional spatially localized spherical harmonic transform directional slsht which extends the slsht from the literature whose usefulness is limited to symmetric windows we present an inversion relation to synthesize the original signal from its directional slsht distribution for an arbitrary window function as an example of an asymmetric window the most concentrated band limited eigenfunction in an elliptical region on the sphere is proposed for directional spatio spectral analysis and its effectiveness is illustrated on the synthetic and mars topographic data sets finally since such typical data sets on the sphere are of considerable size and the directional slsht is intrinsically computationally demanding depending on the band limits of the signal and window a fast algorithm for the efficient computation of the transform is developed the floating point precision numerical accuracy of the fast algorithm is demonstrated and a full numerical complexity analysis is presented

exceptional family and solvability of the second order cone complementarity problems abstract in this paper we introduce a concept of exceptional family for second order cone complementarity problems denoted by soccp which is the particular case of the concept of exceptional family of elements introduced by isac and carbone 1999 25 for the nonlinear complementarity problems and the exceptional family for second order cone complementarity problems has some pretty unique properties furthermore we propose a new sufficient existence condition of a solution to soccp and give a particular example to show that the new condition is not stronger than known isac carbone s condition

on the associated orthogonal polynomials abstract by using the second order recurrence relation this paper gives some new results on associated orthogonal polynomials without referring to the continued fractions tool some results are very useful for obtaining the second order differential equation satisfied by the semi classical orthogonal polynomials hendriksen and van rossum 1985 maroni 1987 cf section 3 also the main formula derives from proposition 2 6 by which the fourth order differential equation satisfied by some laguerre hahn polynomials magnus 1984 is obtained cf belmehdi and ronveaux 1989 dini 1989 ronveaux 1990

on the efficient parallel computation of legendre transforms 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

fast evaluation of quadrature formulae on the sphere recently a fast approximate algorithm for the evaluation of expansions in terms of standard l 2 s 2 orthonormal spherical harmonics at arbitrary nodes on the sphere s 2 has been proposed in s kunis and d potts fast spherical fourier algorithms j comput appl math 161 75 98 2003 the aim of this paper is to develop a new fast algorithm for the adjoint problem which can be used to compute expansion coefficients from sampled data by means of quadrature rules we give a formulation in matrix vector notation and an explicit factorisation of the spherical fourier matrix based on the former algorithm starting from this we obtain the corresponding factorisation of the adjoint spherical fourier matrix and are able to describe the associated algorithm for the adjoint transformation which can be employed to evaluate quadrature rules for arbitrary weights and nodes on the sphere we provide results of numerical tests showing the stability of the obtained algorithm using as examples classical gaus legendre and clenshaw curtis quadrature rules as well as the healpix pixelation scheme and an equidistribution

a pseudospectral matrix method for time dependent tensor fields on a spherical shell we construct a pseudospectral method for the solution of time dependent non linear partial differential equations on a three dimensional spherical shell the problem we address is the treatment of tensor fields on the sphere as a test case we consider the evolution of a single black hole in numerical general relativity a natural strategy would be the expansion in tensor spherical harmonics in spherical coordinates instead we consider the simpler and potentially more efficient possibility of a double fourier expansion on the sphere for tensors in cartesian coordinates as usual for the double fourier method we employ a filter to address time step limitations and certain stability issues we find that a tensor filter based on spin weighted spherical harmonics is successful while two simplified non spin weighted filters do not lead to stable evolutions the derivatives and the filter are implemented by matrix multiplication for efficiency a key technical point is the construction of a matrix multiplication method for the spin weighted spherical harmonic filter as example for the efficient parallelization of the double fourier spin weighted filter method we discuss an implementation on a gpu which achieves a speed up of up to a factor of 20 compared to a single core cpu implementation

fast global optimization on the torus the sphere and the rotation group detecting all local extrema or the global extremum of a polynomial on the torus the sphere or the rotation group is a tough yet often requested numerical problem we present a heuristic approach that applies common descent methods like nonlinear conjugated gradients or newtons methods simultaneously to a large number of starting points the cornerstone of our approach is fft like algorithms i e algorithms that scale almost linearly with respect to the sum of the dimension of the polynomial space and the number of evaluation points these fft like algorithms allow us to compute one step of a descent method simultaneously for all starting points at almost the same cost as for one single starting point the effectiveness of the proposed algorithms is demonstrated in various applications in particular we apply it to the radon transform of a spherical function which allows us to detect lines in spherical patterns

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

computation of spherical harmonic expansion coefficients via fft s abstract a method for numerically expanding an arbitrary function on the sphere in a series of spherical harmonics which makes use of the speed of a fast fourier transform is described discussions of the operation count storage requirements accuracy and an algebraic and a numerical example are included a comparison with straightforward integration is made throughout also a new method for evaluating the spherical harmonics is discussed

an optimal dimensionality sampling scheme on the sphere with fast spherical harmonic transforms we develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band limited at l using only l 2 samples we obtain the optimal number of samples given by the degrees of freedom of the signal in harmonic space the number of samples required in our scheme is a factor of two or four fewer than existing techniques which require either 2l 2 or 4l 2 samples we note however that we do not recover a sampling theorem on the sphere where spherical harmonic transforms are theoretically exact nevertheless we achieve high accuracy even for very large band limits for our optimal dimensionality sampling scheme we develop a fast and accurate algorithm to compute the spherical harmonic transform and inverse with computational complexity comparable with existing schemes in practice we conduct numerical experiments to study in detail the stability accuracy and computational complexity of the proposed transforms we also highlight the advantages of the proposed sampling scheme and associated transforms in the context of potential applications

computational harmonic analysis for tensor fields on the two sphere in this paper we describe algorithms for the numerical computation of fourier transforms of tensor fields on the two sphere s2 these algorithms reduce the computation of an expansion on tensor spherical harmonics to expansions in scalar spherical harmonics and hence can take advantage of recent improvements in the efficiency of computation of scalar spherical harmonic transforms

a novel sampling theorem on the sphere we develop a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension the fundamental property of any sampling theorem is the number of samples required to represent a band limited signal to represent exactly a signal on the sphere band limited at l all sampling theorems on the sphere require o l2 samples however our sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere and an asymptotically identical but smaller number of samples than the gauss legendre sampling theorem the complexity of our algorithms scale as o l3 however the continual use of fast fourier transforms reduces the constant prefactor associated with the asymptotic scaling considerably resulting in algorithms that are fast furthermore we do not require any precomputation and our algorithms apply to both scalar and spin functions on the sphere without any change in computational complexity or computation time we make our implementation of these algorithms available publicly and perform numerical experiments demonstrating their speed and accuracy up to very high band limits finally we highlight the advantages of our sampling theorem in the context of potential applications notably in the field of compressive sampling

research and development competition and innovation pseudo maximum likelihood and simulated maximum likelihood methods applied to count data models with heterogeneity abstract this paper focuses on the relationship between the research and development r d expenditures undertaken by firms and the number of patents claimed by them the econometric methods we use incorporate two important features of the data first we introduce a heterogeneity term accounting for the unobservable factors affecting the production of innovations second we allow for a large proportion of the sample not to apply for a patent depending on the specification estimation proceeds by maximum likelihood pseudo maximum likelihood or simulated maximum likelihood methods our main findings are the following i the returns to scale in the innovation technology may be constant on average and ii competitors r d may have a negative impact on own innovation thus revealing a rivalry effect of intellectual property

second generation curvelets on the sphere curvelets are efficient to represent highly anisotropic signal content such as a local linear and curvilinear structure first generation curvelets on the sphere however suffered from blocking artefacts we present a new second generation curvelet transform where scale discretized curvelets are constructed directly on the sphere scale discretized curvelets exhibit a parabolic scaling relation are well localized in both spatial and harmonic domains support the exact analysis and synthesis of both scalar and spin signals and are free of blocking artefacts we present fast algorithms to compute the exact curvelet transform reducing computational complexity from mathcal o l 5 to mathcal o l 3 log 2 l for signals band limited at l the implementation of these algorithms is made publicly available finally we present an illustrative application demonstrating the effectiveness of curvelets for representing directional curve like features in natural spherical images

zero inflated models for regression analysis of count data a study of growth and development poisson regression is widely used in medical studies and can be extended to negative binomial regression to allow for heterogeneity when there is an excess number of zero counts a useful approach is to used a mixture model with a proportion p of subjects not at risk and a proportion of 1 p at risk subjects who take on outcome values following a poisson or negative binomial distribution covariate effects can be incorporated into both components of the models in child assessment fine motor development is often measured by test items that involve a process of imitation and a process of fine motor exercise one such developmental milestone is building a tower of cubes this study analyses the impact of foetal growth and postnatal somatic growth on this milestone operationalized as the number of cubes and measured around the age of 22 months it is shown that the two aspects of early growth may have different implications for imitation and fine motor dexterity the usual approach of recording and analysing the milestone as a binary outcome such as whether the child can build a tower of three cubes may leave out important information copyright 2002 john wiley sons ltd

exceptional family and solvability of copositive complementarity problems abstract in this paper by extending the concept of exceptional family to complementarity problems over the cone of symmetric copositive real matrices we propose an existence theorem of a solution to the copositive complementarity problem extensions of isac carbone s condition karamardian s condition weakly properness and coercivity are also introduced several applications of these results are presented and we prove that without exceptional family is a sufficient and necessary condition for the solvability of pseudomonotone copositive complementarity problems

convergence acceleration of fourier series by analytical and numerical application of poisson s formula a form of the poisson summation formula appropriate for the transformation of infinite fourier series is derived and shown to be applicable to slowly converging series arising in the solution of laplace s equation in a rectangular electrochemical cell the result is a rapidly convergent fourier series which is particularly useful in giving the potential close to the electrode surface results obtained from the analytical expression are found to be in close agreement with those resulting from numerical evaluation of the fourier integrals using simpson s rule and the euler transformation and direct summation by using goertzel s 1958 algorithm

a fast spherical harmonics transform algorithm the spectral method with discrete spherical harmonics transform plays an important role in many applications in spite of its advantages the spherical harmonics transform has a drawback of high computational complexity which is determined by that of the associated legendre transform and the direct computation requires time of o n3 for cut off frequency n in this paper we propose a fast approximate algorithm for the associated legendre transform our algorithm evaluates the transform by means of polynomial interpolation accelerated by the fast multipole method fmm the divide and conquer approach with split legendre functions gives computational complexity o n2 log n experimental results show that our algorithm is stable and is faster than the direct computation for n 511

distribution free models for longitudinal count responses with overdispersion and structural zeros overdispersion and structural zeros are two major manifestations of departure from the poisson assumption when modeling count responses using poisson loglinear regression as noted in a large body of literature ignoring such departures could yield bias and lead to wrong conclusions different approaches have been developed to tackle these two major problems in this paper we review available methods for dealing with overdispersion and structural zeros within a longitudinal data setting and propose a distribution free modeling approach to address the limitations of these methods by utilizing a new class of functional response models frm we illustrate our approach with both simulated and real study data

efficient computation of slepian functions for arbitrary regions on the sphere in this paper we develop a new method for the fast and memory efficient computation of slepian functions on the sphere slepian functions which arise as the solution of the slepian concentration problem on the sphere have desirable properties for applications where measurements are only available within a spatially limited region on the sphere and or a function is required to be analyzed over the spatially limited region slepian functions are currently not easily computed for large band limits for an arbitrary spatial region due to high computational and large memory storage requirements for the special case of a polar cap the symmetry of the region enables the decomposition of the slepian concentration problem into smaller subproblems and consequently the efficient computation of slepian functions for large band limits by exploiting the efficient computation of slepian functions for the polar cap region on the sphere we develop a formulation supported by a fast algorithm for the approximate computation of slepian functions for an arbitrary spatial region to enable the analysis of modern datasets that support large band limits for the proposed algorithm we carry out accuracy analysis of the approximation computational complexity analysis and review of memory storage requirements we illustrate through numerical experiments that the proposed method enables faster computation and has smaller storage requirements while allowing for sufficiently accurate computation of the slepian functions

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

a predictor corrector interior point algorithm for the semidefinite linear complementarity problem using the alizadeh haeberly overton search direction this paper proposes a globally convergent predictor corrector infeasible interior point algorithm for the monotone semidefinite linear complementarity problem using the alizadeh haeberly overton search direction and shows its quadratic local convergence under the strict complementarity condition

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research