stability analysis of lattice boltzmann methods the lattice boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered although the equation is a derivative of lattice gas automata it may be interpreted as a lagrangian finite difference method for the numerical simulation of the discrete velocity boltzmann equation that makes use of a bgk collision operator as a result it is not surprising that numerical instability of lattice boltzmann methods have been frequently encountered by researchers we present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant density uniform mean flow the linear stability depends on the following parameters the distribution of the mass at a site between the different discrete speeds the bgk relaxation time the mean velocity and the wavenumber of the perturbations this parameter space is too large to compute the complete stability characteristics we report some stability results for a subset of the parameter space for a 7 velocity hexagonal lattice a 9 velocity square lattice and a 15 velocity cubic lattice results common to all three lattices are 1 the bgk relaxation time must be greater than 12 corresponding to positive shear viscosity 2 there exists a maximum stable mean velocity for fixed values of the other parameters and 3 as is increased from 12 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger

a critical evaluation of the resolution properties of b spline and compact finite difference methods resolution properties of b spline and compact finite difference schemes are compared using fourier analysis in periodic domains and tests based on solution of the wave and heat equations in finite domains with uniform and nonuniform grids results show that compact finite difference schemes have a higher convergence rate and in some cases better resolution however b spline schemes have a more straightforward and robust formulation particularly near boundaries on nonuniform meshes

optimal low dispersion low dissipation lbm schemes for computational aeroacoustics lattice boltmzann methods lbm have been proved to be very effective methods for computational aeroacoustics caa which have been used to capture the dynamics of weak acoustic fluctuations in this paper we propose a strategy to reduce the dispersive and disspative errors of the two dimensional 2d multi relaxation time lattice boltzmann method mrt lbm by presenting an effective algorithm we obtain a uniform form of the linearized navier stokes equations corresponding to the mrt lbm in wave number space using the matrix perturbation theory and the equivalent modified equation approach for finite difference methods we propose a class of minimization problems to optimize the free parameters in the mrt lbm we obtain this way a dispersion relation preserving lbm drp lbm to circumvent the minimized dispersion error of the mrt lbm the dissipation relation precision is also improved and the stability of the mrt lbm with the small bulk viscosity is guaranteed von neuman analysis of the linearized mrt lbm is performed to validate the optimized dispersion dissipation relations considering monochromatic wave solutions meanwhile dispersion and dissipation errors of the optimized mrt lbm are quantitatively compared with the original mrt lbm finally some numerical simulations are carried out to assess the new optimized mrt lbm schemes

numerical analysis of the lattice boltzmann method for simulation of linear acoustic waves we analyze a linear lattice boltzmann lb formulation for simulation of linear acoustic wave propagation in heterogeneous media we employ the single relaxation time bhatnagar gross krook as well as the general multirelaxation time collision operators by calculating the dispersion relation for various 2d lattices we show that the d2q5 lattice is the most suitable model for the linear acoustic problem we also implement a grid refinement algorithm for the lb scheme to simulate waves propagating in a heterogeneous medium with velocity contrasts our results show that the lb scheme performance is comparable to the classical second order finite difference schemes given its efficiency for parallel computation the lb method can be a cost effective tool for the simulation of linear acoustic waves in complex geometries and multiphase media

regression analysis for a functional response functional responses are encountered when units are observed over time although the whole function itself is not observed a sufficiently large number of evaluations as is common with modern recording equipment are assumed to be available functional regression analysis relates the smooth functional response y t to known covariates x by a linear combination of parameter functions t which are to be estimated the model takes the standard form y t x t t t this approach provides an alternative to standard longitudinal data methods used in the biological sciences where less and noisier data necessitate parametric modeling the methodology is illustrated by an application in ergonomics

numerical comparisons of high order nonlinear solvers for the transient navier stokes equations based on homotopy and perturbation techniques efficient solvers for the unsteady navier stokes equations are presented a classic time stepping scheme is combined with high order nonlinear solvers coupling homotopy and a perturbation technique polynomial and rational representations are used to approximate the unknowns of the problem a pseudo residual criterion is proposed to improve the efficiency of the solvers the numerical example considered in this paper is the time periodic two dimensional flow around a circular cylinder comparisons with the classical first order newton raphson solver are performed numerical results reveal that a lower number of matrix factorization is needed with the proposed methods decreasing the computational effort

lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

error dynamics the propagation of a signal in a continuous medium and the associated evolution of error is of prime importance in many applications of applied physics there have been many efforts in analyzing error dynamics using method attributed to von neumann 1 2 that is readily applied for linear equations and in quasilinearized form for non linear equations the main assumption for linear problems is that the error and the signal follow the same dynamics while this appears intuitively correct the main aim behind this work is to show that this is not correct for discrete computing due to dispersion or phase error or when the numerical method is not strictly neutrally stable we demonstrate the above with the help of the linear advection equation for the analysis of space time discretization schemes the linear advection equation as a model that represents many flows and wave phenomena is used

on the effect of numerical errors in large eddy simulations of turbulent flows aliased and dealiased numerical simulations of a turbulent channel flow are performed using spectral and finite difference methods analytical and numerical studies show that aliasing errors are more destructive for spectral and high order finite difference calculations than for low order finite difference simulations numerical errors have different effects for different forms of the nonlinear terms in the navier stokes equations for divergence and convective forms spectral methods are energy conserving only if dealiasing is performed for skew symmetric and rotational forms both spectral and finite difference methods are energy conserving even in the presence of aliasing errors it is shown that discrepancies between the results of dealiased spectral and standard nondialiased finite difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences the relative importance of aliasing and truncation errors as compared to subgrid scale model terms in large eddy simulations is analyzed and discussed for low order finite difference simulations truncation errors can exceed the magnitude of the subgrid scale term

on properties of functional principal components analysis summary functional data analysis is intrinsically infinite dimensional functional principal component analysis reduces dimension to a finite level and points to the most significant components of the data however although this technique is often discussed its properties are not as well understood as they might be we show how the properties of functional principal component analysis can be elucidated through stochastic expansions and related results our approach quantifies the errors that arise through statistical approximation in successive terms of orders n 1 2 n 1 n 3 2 where n denotes sample size the expansions show how spacings among eigenvalues impact on statistical performance the term of size n 1 2 illustrates first order properties and leads directly to limit theory which describes the dominant effect of spacings thus for example spacings are seen to have an immediate first order effect on properties of eigenfunction estimators but only a second order effect on eigenvalue estimators our results can be used to explore properties of existing methods and also to suggest new techniques in particular we suggest bootstrap methods for constructing simultaneous confidence regions for an infinite number of eigenvalues and also for individual eigenvalues and eigenvectors

a family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non square matrix based on a quadratical convergence method a family of iterative methods to compute the approximate inverse of square matrix are presented the theoretical proofs and numerical experiments show that these iterative methods are very effective and more importantly these methods can be used to compute the inner inverse and their convergence proofs are given by fundamental matrix tools

a statistical analysis of brain morphology using wild bootstrapping methods for the analysis of brain morphology including voxel based morphology and surface based morphometries have been used to detect associations between brain structure and covariates of interest such as diagnosis severity of disease age iq and genotype the statistical analysis of morphometric measures usually involves two statistical procedures 1 invoking a statistical model at each voxel or point on the surface of the brain or brain subregion followed by mapping test statistics e g t test or their associated p values at each of those voxels 2 correction for the multiple statistical tests conducted across all voxels on the surface of the brain region under investigation we propose the use of new statistical methods for each of these procedures we first use a heteroscedastic linear model to test the associations between the morphological measures at each voxel on the surface of the specified subregion e g cortical or subcortical surfaces and the covariates of interest moreover we develop a robust test procedure that is based on a resampling method called wild bootstrapping this procedure assesses the statistical significance of the associations between a measure of given brain structure and the covariates of interest the value of this robust test procedure lies in its computationally simplicity and in its applicability to a wide range of imaging data including data from both anatomical and functional magnetic resonance imaging fmri simulation studies demonstrate that this robust test procedure can accurately control the family wise error rate we demonstrate the application of this robust test procedure to the detection of statistically significant differences in the morphology of the hippocampus over time across gender groups in a large sample of healthy subjects

cook s distance measures for varying coefficient models with functional responses the aim of this article is to develop cook s distance measures for assessing the influence of both atypical curves and observations under varying coefficient model with functional responses our cook s distance measures include cook s distances for deleting multiple curves and for deleting multiple grid points and their scaled cook s distances we systematically investigate some theoretical properties of these diagnostic measures simulation studies are conducted to evaluate the finite sample properties of these cook s distances under different scenarios a real diffusion tensor tract dataset is analyzed to illustrate the use of our diagnostic measures

high order low dispersive and low dissipative explicit schemes for multiple scale and boundary problems explicit high order numerical schemes are proposed for the accurate computation of multiple scale problems and for the implementation of boundary conditions specific high order node centered finite differences and selective filters removing grid to grid oscillations are first designed for the discretization of the buffer region between a x grid domain and 2 x grid domain the coefficients of these matching schemes are chosen so that the maximum order of accuracy is reached non centered finite differences and selective filters are then developed with the aim of accurately computing boundary conditions they are constructed by minimizing the dispersion and the dissipation errors in the wave number space for waves down to four points per wavelength the dispersion and dissipation properties of the matching and the boundary schemes are described in detail and their accuracy limits are determined to show that these schemes calculate accurately waves with at least five points per wavelength test problems including linear convection wall reflection and acoustic scattering around a cylinder are finally solved to illustrate the accuracy of the schemes

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

homotopy perturbation method for solving hyperbolic partial differential equations this paper applies the homotopy perturbation method proposed by ji huan he to obtain approximate analytic solutions of hyperbolic partial differential equations the procedure of the method is systematically illustrated to give an extensive account of the method some examples are provided the results derived by this method will be compared with the results of characteristics method the results of homotopy perturbation method are of high accuracy verifying that the method is very effective and promising

uniform convergence rates for nonparametric regression and principal component analysis in functional longitudinal data we consider nonparametric estimation of the mean and covariance functions for functional longitudinal data strong uniform convergence rates are developed for estimators that are local linear smoothers our results are obtained in a unified framework in which the number of observations within each curve cluster can be of any rate relative to the sample size we show that the convergence rates for the procedures depend on both the number of sample curves and the number of observations on each curve for sparse functional data these rates are equivalent to the optimal rates in nonparametric regression for dense functional data root n rates of convergence can be achieved with proper choices of bandwidths we further derive almost sure rates of convergence for principal component analysis using the estimated covariance function the results are illustrated with simulation studies

lattice boltzmann method with selective viscosity filter for high reynolds number flows the lattice boltzmann method suffers from numerical instabilities that can induce local blowup of the computation the von neumann stability analysis applied to the lbe bgk and lbe mrt models shows that numerical instabilities occur in the high wavenumber range and are due to the interplay between acoustic modes and some other modes as it is done in the lbe mrt model an increase of the bulk viscosity is an efficient way of damping spurious oscillations however this stabilization method induces an over damping of acoustic waves some selective spatial filters can be used in order to eliminate the spurious small spatial scales without affecting the large scale physical modes three different lattice boltzmann algorithms based on filtering step are proposed the fully filtered lbe the lbe with filtered macroscopic quantities and the lbe with filtered collision operator the behavior of several explicit filter stencils is studied in the fourier space for a given filter stencil the filtered collision operator approach leads to the highest cut off wavenumber in this case the theoretical wavenumber dependent viscosity is n k c s 2 t email protected k 1 2 where f k is the filter shape and s the filter strength under resolved simulations high reynolds number are performed on the case of the doubly periodic shear layers the performance of the three filtered lbe is found to be the same as the mrt model for stability control propagation of acoustic plane waves is also simulated with the three filtering algorithms the measured dissipation of acoustic wave compares well with the theoretical results

convergence analysis of an iterative scheme for solving initial value problem for multidimensional partial differential equations existence and uniqueness of solutions of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations are proved using banach fixed point theorem an iterative scheme is derived and rigorous convergence analysis of this scheme and an error estimate are included as well several numerical examples for high dimensional initial value problem for heat and wave type partial differential equations are presented to demonstrate reliability and performance of proposed iterative scheme

comparison between lattice boltzmann method and navier stokes high order schemes for computational aeroacoustics computational aeroacoustic caa simulation requires accurate schemes to capture the dynamics of acoustic fluctuations which are weak compared with aerodynamic ones in this paper two kinds of schemes are studied and compared the classical approach based on high order schemes for navier stokes like equations and the lattice boltzmann method the reference macroscopic equations are the 3d isothermal and compressible navier stokes equations a von neumann analysis of these linearized equations is carried out to obtain exact plane wave solutions three physical modes are recovered and the corresponding theoretical dispersion relations are obtained then the same analysis is made on the space and time discretization of the navier stokes equations with the classical high order schemes to quantify the influence of both space and time discretization on the exact solutions different orders of discretization are considered with and without a uniform mean flow three different lattice boltzmann models are then presented and studied with the von neumann analysis the theoretical dispersion relations of these models are obtained and the error terms of the model are identified and studied it is shown that the dispersion error in the lattice boltzmann models is only due to the space and time discretization and that the continuous discrete velocity boltzmann equation yield the same exact dispersion as the navier stokes equations finally dispersion and dissipation errors of the different kind of schemes are quantitatively compared it is found that the lattice boltzmann method is less dissipative than high order schemes and less dispersive than a second order scheme in space with a 3 step runge kutta scheme in time the number of floating point operations at a given error level associated with these two kinds of schemes are then compared

variational iteration method new development and applications variational iteration method has been favourably applied to various kinds of nonlinear problems the main property of the method is in its flexibility and ability to solve nonlinear equations accurately and conveniently in this paper recent trends and developments in the use of the method are reviewed major applications to nonlinear wave equation nonlinear fractional differential equations nonlinear oscillations and nonlinear problems arising in various engineering applications are surveyed the confluence of modern mathematics and symbol computation has posed a challenge to developing technologies capable of handling strongly nonlinear equations which cannot be successfully dealt with by classical methods variational iteration method is uniquely qualified to address this challenge the flexibility and adaptation provided by the method have made the method a strong candidate for approximate analytical solutions this paper outlines the basic conceptual framework of variational iteration technique with application to nonlinear problems both achievements and limitations are discussed with direct reference to approximate solutions for nonlinear equations a new iteration formulation is suggested to overcome the shortcoming a very useful formulation for determining approximately the period of a nonlinear oscillator is suggested examples are given to illustrate the solution procedure

numerical solutions of two dimensional burgers equations by discrete adomian decomposition method in this paper the discrete adomian decomposition method adm is proposed to numerically solve the two dimensional burgers nonlinear difference equations two test problems are considered to illustrate the accuracy of the proposed discrete decomposition method it is shown that the numerical results are in good agreement with the exact solutions for each problem

variable selection in nonparametric varying coefficient models for analysis of repeated measurements nonparametric varying coefficient models are commonly used for analyzing data measured repeatedly over time including longitudinal and functional response data although many procedures have been developed for estimating varying coefficients the problem of variable selection for such models has not been addressed to date in this article we present a regularized estimation procedure for variable selection that combines basis function approximations and the smoothly clipped absolute deviation penalty the proposed procedure simultaneously selects significant variables with time varying effects and estimates the nonzero smooth coefficient functions under suitable conditions we establish the theoretical properties of our procedure including consistency in variable selection and the oracle property in estimation here the oracle property means that the asymptotic distribution of an estimated coefficient function is the same as that when it is known a priori which variables are in the model the method is

group analysis of dti fiber tract statistics with application to neurodevelopment abstract diffusion tensor imaging dti provides a unique source of information about the underlying tissue structure of brain white matter in vivo including both the geometry of major fiber bundles as well as quantitative information about tissue properties represented by derived tensor measures this paper presents a method for statistical comparison of fiber bundle diffusion properties between populations of diffusion tensor images unbiased diffeomorphic atlas building is used to compute a normalized coordinate system for populations of diffusion images the diffeomorphic transformations between each subject and the atlas provide spatial normalization for the comparison of tract statistics diffusion properties such as fractional anisotropy fa and tensor norm along fiber tracts are modeled as multivariate functions of arc length hypothesis testing is performed non parametrically using permutation testing based on the hotelling t 2 statistic the linear discriminant embedded in the t 2 metric provides an intuitive localized interpretation of detected differences the proposed methodology was tested on two clinical studies of neurodevelopment in a study of 1 and 2 year old subjects a significant increase in fa and a correlated decrease in frobenius norm was found in several tracts significant differences in neonates were found in the splenium tract between controls and subjects with isolated mild ventriculomegaly mvm demonstrating the potential of this method for clinical studies

higher entropy conservation and numerical stability of compressible turbulence simulations we present a numerical formulation for the treatment of nonlinear instabilities in shock free compressible turbulence simulations the formulation is high order and contains no artificial dissipation numerical stability is enhanced through semi discrete satisfaction of global conservation properties stemming from the second law of thermodynamics and the entropy equation the numerical implementation is achieved using a conservative skew symmetric splitting of the nonlinear terms the robustness of the method is demonstrated by performing unresolved numerical simulations and large eddy simulations of compressible isotropic turbulence at a very high reynolds number results show the scheme is capable of capturing the statistical equilibrium of low mach number compressible turbulent fluctuations at infinite reynolds number comparisons with the entropy splitting technique j comput phys 162 2000 33 j comput phys 178 2002 307 staggered method j comput phys 191 2 2003 392 and skew symmetric like schemes j comput phys 161 2000 114 confirm the superiority of the current approach we also discuss a flaw in the skew symmetric splitting implemented in the literature very good results are obtained based on the proper splitting

single index varying coefficient model for functional responses recently massive functional data have been widely collected over space across a set of grid points in various imaging studies it is interesting to correlate functional data with various clinical variables such as age and gender in order to address scientific questions of interest the aim of this article is to develop a single index varying coefficient sivc model for establishing a varying association between functional responses e g image and a set of covariates it enjoys several unique features of both varying coefficient and single index models an estimation procedure is developed to estimate varying coefficient functions the index function and the covariance function of individual functions the optimal integration of information across different grid points is systematically delineated and the asymptotic properties e g consistency and convergence rate of all estimators are examined simulation studies are conducted to assess the finite sample performance of the proposed estimation procedure furthermore our real data analysis of a white matter tract dataset obtained from the alzheimer s disease neuroimaging initiative adni study confirms the advantage and accuracy of sivc model over the popular varying coefficient model

a functional varying coefficient single index model for functional response data abstractmotivated by the analysis of imaging data we propose a novel functional varying coefficient single index model fvcsim to carry out the regression analysis of functional response data on a set of covariates of interest fvcsim represents a new extension of varying coefficient single index models for scalar responses collected from cross sectional and longitudinal studies an efficient estimation procedure is developed to iteratively estimate varying coefficient functions link functions index parameter vectors and the covariance function of individual functions we systematically examine the asymptotic properties of all estimators including the weak convergence of the estimated varying coefficient functions the asymptotic distribution of the estimated index parameter vectors and the uniform convergence rate of the estimated covariance function and their spectrum simulation studies are carried out to assess the finite sample performance of the proposed procedure we apply fvcsim to investiga

generalized conservative approximations of split convective derivative operators we propose a strategy to design locally conservative finite difference approximations of convective derivatives for shock free compressible flows with arbitrary order of accuracy that generalizes the approach of ducros et al 2000 1 and that can be applied as a building block of low dissipative hybrid shock capturing methods the approximations stem from application of standard central difference formulas to split forms of the convective terms in the compressible euler equations which guarantee strong numerical stability and near energy preservation in the inviscid limit a convenient implementation of the high order fluxes is suggested which guarantees improved computational efficiency over existing methods numerical tests performed for isotropic turbulence at zero viscosity show stability of schemes with order of accuracy up to ten and effectiveness of convective splitting of kennedy and gruber 2008 2 in providing extra stability in the presence of strong density variations numerical simulations of compressible turbulent boundary layer flow indicate suitability of the method for non uniform grids and overall support superior computational efficiency of high order schemes

properties of principal component methods for functional and longitudinal data analysis the use of principal component methods to analyze functional data is appropriate in a wide range of different settings in studies of functional data analysis it has often been assumed that a sample of random functions is observed precisely in the continuum and without noise while this has been the traditional setting for functional data analysis in the context of longitudinal data analysis a random function typically represents a patient or subject who is observed at only a small number of randomly distributed points with nonnegligible measurement error nevertheless essentially the same methods can be used in both these cases as well as in the vast number of settings that lie between them how is performance affected by the sampling plan in this paper we answer that question we show that if there is a sample of n functions or subjects then estimation of eigenvalues is a semiparametric problem with root n consistent estimators even if only a few observations are made of each function and if each observation is encumbered by noise however estimation of eigenfunctions becomes a nonparametric problem when observations are sparse the optimal convergence rates in this case are those which pertain to more familiar function estimation settings we also describe the effects of sampling at regularly spaced points as opposed to random points in particular it is shown that there are often advantages in sampling randomly however even in the case of noisy data there is a threshold sampling rate depending on the number of functions treated above which the rate of sampling either randomly or regularly has negligible impact on estimator performance no matter whether eigenfunctions or eigenvectors are being estimated

two dimensional mesh embedding for b spline methods many factors motivate consideration of b splines as basis functions for solving partial differential equations these are arbitrary orders of accuracy and high resolving powers similar to those of compact schemes furthermore if one uses a galerkin scheme one gets in addition to conservation of the discretized quantities conservation of quadratic invariants such as energy this work develops another property namely the ability to treat semi structured embedded or zonal meshes for two dimensional geometries this can drastically reduce the number of grid points in many applications an algorithm is presented for constructing a global spline basis that automatically hasd 1 continuous derivatives at mesh block boundaries as everywhere else heredis the polynomial degree the basis functions are simply suitable products of one dimensional b splines both integer and noninteger refinement ratios are allowed across mesh blocks finally test cases for linear scalar equations such as the poisson and advection equation are presented

modelling sparse generalized longitudinal observations with latent gaussian processes summary in longitudinal data analysis one frequently encounters non gaussian data that are repeatedly collected for a sample of individuals over time the repeated observations could be binomial poisson or of another discrete type or could be continuous the timings of the repeated measurements are often sparse and irregular we introduce a latent gaussian process model for such data establishing a connection to functional data analysis the functional methods proposed are non parametric and computationally straightforward as they do not involve a likelihood we develop functional principal components analysis for this situation and demonstrate the prediction of individual trajectories from sparse observations this method can handle missing data and leads to predictions of the functional principal component scores which serve as random effects in this model these scores can then be used for further statistical analysis such as inference regression discriminant analysis or clustering we illustrate these non parametric methods with longitudinal data on primary biliary cirrhosis and show in simulations that they are competitive in comparisons with generalized estimating equations and generalized linear mixed models

statistical analysis of diffusion tensors in diffusion weighted magnetic resonance imaging data diffusion tensor imaging has been widely used to reconstruct the structure and orientation of fibers in biological tissues particularly in the white matter of the brain because it can track the effective diffusion of water along those fibers the raw diffusion weighted images from which diffusion tensors are estimated however inherently contain noise noise in the images produces uncertainty in the estimation of the tensors which are 3 3 positive definite matrices and of their derived quantities including eigenvalues eigenvectors and the fiber pathways that are reconstructed based on those tensor elements the aim of this article is to provide a comprehensive theoretical framework of statistical inference for quantifying the effects of noise on diffusion tensors on their eigenvalues and eigenvectors and on their morphological classification we propose a semiparametric model to account for noise in diffusion weighted images we then develop a one step weighted least squares estimate of the t

boundary consistent b spline filtering schemes and application to high fidelity simulations of turbulence abstract a filtering operation based on b spline discretizations is introduced to target weakly growing mesh scale oscillations that can arise in high fidelity turbulence simulations this is a spectral regularization that can be described using the singular values of a banded matrix operator with the filtering strength set by a scalar or vector valued penalty parameter the penalty parameter can be specified though it can also be advantageously selected to minimize the generalized cross validation gcv measure of distance between the pre and post filtered solutions efficient algorithms are developed to compute both the scalar and vector penalty parameters the b spline filter has a sharper localization to high wavenumber than compact or explicit filters of the same stencil width and is demonstrated for solutions of the burgers equation decaying burgers turbulence and compressible navier stokes turbulent channel flow these simulations confirm the scheme s numerical stability and ability to narrowly target the high wavenumber components of numerical solutions an advantage over finite difference filters is that these are stable on bounded domains and even preserve formal order of accuracy

exact solutions for heat like and wave like equations with variable coefficients in this paper adomian decomposition method is presented for solving heat like and wave like models with variable coefficients the method is demonstrated for a variety of problems in one and higher dimensional spaces where exact solutions are obtained the results obtained in all cases show the reliability and the efficiency of this method

penalized spline models for functional principal component analysis summary we propose an iterative estimation procedure for performing functional principal component analysis the procedure aims at functional or longitudinal data where the repeated measurements from the same subject are correlated an increasingly popular smoothing approach penalized spline regression is used to represent the mean function this allows straightforward incorporation of covariates and simple implementation of approximate inference procedures for coefficients for the handling of the within subject correlation we develop an iterative procedure which reduces the dependence between the repeated measurements that are made for the same subject the resulting data after iteration are theoretically shown to be asymptotically equivalent in probability to a set of independent data this suggests that the general theory of penalized spline regression that has been developed for independent data can also be applied to functional data the effectiveness of the proposed procedure is demonstrated via a simulation study and an application to yeast cell cycle gene expression data

frats functional regression analysis of dti tract statistics diffusion tensor imaging dti provides important information on the structure of white matter fiber bundles as well as detailed tissue properties along these fiber bundles in vivo this paper presents a functional regression framework called frats for the analysis of multiple diffusion properties along fiber bundle as functions in an infinite dimensional space and their association with a set of covariates of interest such as age diagnostic status and gender in real applications the functional regression framework consists of four integrated components the local polynomial kernel method for smoothing multiple diffusion properties along individual fiber bundles a functional linear model for characterizing the association between fiber bundle diffusion properties and a set of covariates a global test statistic for testing hypotheses of interest and a resampling method for approximating the p value of the global test statistic the proposed methodology is applied to characterizing the development of five diffusion properties including fractional anisotropy mean diffusivity and the three eigenvalues of diffusion tensor along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment significant age and gestational age effects on the five diffusion properties were found in both tracts the resulting analysis pipeline can be used for understanding normal brain development the neural bases of neuropsychiatric disorders and the joint effects of environmental and genetic factors on white matter fiber bundles

b spline method and zonal grids for simulations of complex turbulent flows a numerical technique for computations of turbulent flows is described the technique is based on b splines and allows grid embedding in physically significant flow regions numerical tests which include solutions of nonlinear advection diffusion equations and computations of flow over a circular cylinder at reynolds numbers up to 300 indicate that the method is accurate and efficient in computations of flow over a cylinder the lift drag and base suction coefficients agree well with existing experimental data and previous numerical simulations

multivariate varying coefficient model for functional responses motivated by recent work studying massive imaging data in the neuroimaging literature we propose multivariate varying coefficient models mvcm for modeling the relation between multiple functional responses and a set of covariates we develop several statistical inference procedures for mvcm and systematically study their theoretical properties we first establish the weak convergence of the local linear estimate of coefficient functions as well as its asymptotic bias and variance and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate we establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions we propose a global test for linear hypotheses of varying coefficient functions and derive its asymptotic distribution under the null hypothesis we also propose a simultaneous confidence band for each individual effect curve we conduct monte carlo simulation to examine the finite sample performance of the proposed procedures we apply mvcm to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment

fgwas functional genome wide association analysis functional phenotypes e g subcortical surface representation which commonly arise in imaging genetic studies have been used to detect putative genes for complexly inherited neuropsychiatric and neurodegenerative disorders however existing statistical methods largely ignore the functional features e g functional smoothness and correlation the aim of this paper is to develop a functional genome wide association analysis fgwas framework to efficiently carry out whole genome analyses of functional phenotypes fgwas consists of three components a multivariate varying coefficient model a global sure independence screening procedure and a test procedure compared with the standard multivariate regression model the multivariate varying coefficient model explicitly models the functional features of functional phenotypes through the integration of smooth coefficient functions and functional principal component analysis statistically compared with existing methods for genome wide association studies gwas fgwas can substantially boost the detection power for discovering important genetic variants influencing brain structure and function simulation studies show that fgwas outperforms existing gwas methods for searching sparse signals in an extremely large search space while controlling for the family wise error rate we have successfully applied fgwas to large scale analysis of data from the alzheimer s disease neuroimaging initiative for 708 subjects 30 000 vertices on the left and right hippocampal surfaces and 501 584 snps

statistical inferences for functional data with modem technology development functional data are being observed frequently in many scientific fields a popular method for analyzing such functional data is smoothing first then estimation that is statistical inference such as estimation and hypothesis testing about functional data is conducted based on the substitution of the underlying individual functions by their reconstructions obtained by one smoothing technique or another however little is known about this substitution effect on functional data analysis in this paper this problem is investigated when the local polynomial kernel lpk smoothing technique is used for individual function reconstructions we find that under some mild conditions the substitution effect can be ignored asymptotically based on this we construct lpk reconstruction based estimators for the mean covariance and noise variance functions of a functional data set and derive their asymptotics we also propose a gcv rule for selecting good bandwidths for the lpk reconstructions when the mean function also depends on some time independent covariates we consider a functional linear model where the mean function is linearly related to the covariates but the covariate effects are functions of time the lpk reconstruction based estimators for the covariate effects and the covariance function are also constructed and their asymptotics are derived moreover we propose a l 2 norm based global test statistic for a general hypothesis testing problem about the covariate effects and derive its asymptotic random expression the effect of the bandwidths selected by the proposed gcv rule on the accuracy of the lpk reconstructions and the mean function estimator is investigated via a simulation study the proposed methodologies are illustrated via an application to a real functional data set collected in climatology

on the homotopy analysis method for nonlinear problems a powerful easy to use analytic tool for nonlinear problems in general namely the homotopy analysis method is further improved and systematically described through a typical nonlinear problem i e the algebraically decaying viscous boundary layer flow due to a moving sheet two rules the rule of solution expression and the rule of coefficient ergodicity are proposed which play important roles in the frame of the homotopy analysis method and simplify its applications in science and engineering an explicit analytic solution is given for the first time with recursive formulas for coefficients this analytic solution agrees well with numerical results and can be regarded as a definition of the solution of the considered nonlinear problem

fsem functional structural equation models for twin functional data the aim of this article is to develop a novel class of functional structural equation models fsems for dissecting functional genetic and environmental effects on twin functional data while chara

derivation and analysis of lattice boltzmann schemes for the linearized euler equations we derive lattice boltzmann lbm schemes to solve the linearized euler equations in 1d 2d and 3d with the future goal of coupling them to an lbm scheme for navier stokes equations and a finite volume scheme for linearized euler equations the derivation uses the analytical maxwellian in a bgk model in this way we are able to obtain second order schemes in addition we perform an l 2 stability analysis numerical results validate the approach

linear stability and isotropy properties of athermal regularized lattice boltzmann methods the present work proposes a general methodology to study stability and isotropy properties of lattice boltzmann lb schemes as a first investigation such a methodology is applied to better understand these properties in the context of regularized approaches to this extent linear stability analyses of two dimensional models are proposed the standard bhatnagar gross krook collision model the original precollision regularization and the recursive regularized model where off equilibrium distributions are partially computed thanks to a recursive formula a systematic identification of the physical content carried by each lb mode is done by analyzing the eigenvectors of the linear systems stability results are then numerically confirmed by performing simulations of shear and acoustic waves this work allows drawing fair conclusions on the stability properties of each model in particular among the aforementioned models recursive regularization turns out to be the most stable one for the d2q9 lattice especially in the zero viscosity limit two major properties shared by every regularized model are highlighted 1 a mode filtering property and 2 an incorrect and broadly anisotropic dissipation rate of the modes carrying physical waves in under resolved conditions the first property is the main source of increased stability especially for the recursive regularization it is a direct consequence of the reconstruction of off equilibrium populations before each collision process decreasing the rank of the system of discrete equations the second property seems to be related to numerical errors directly induced by the equilibration of high order moments in such a case this property is likely to occur with any collision model that follows such a stabilization methodology

numerical method for the wave and nonlinear diffusion equations with the homotopy perturbation method in this paper the homotopy perturbation method and a modified homotopy perturbation method are used for analytical treatment of the wave equation and some nonlinear diffusion equations respectively some examples are given to illustrate that a suitable choice of an initial solution can lead to the exact solution this revealing the reliability and effectiveness of the method

wall model for large eddy simulation based on the lattice boltzmann method an original wall model for lattice boltzmann based large eddy simulation is presented it relies on either an analytical profile for the velocity profile within the first off wall cell or the solution of turbulent boundary layer equations the latter are solved thanks to a meshless approach to obtain a user friendly method the proposed method is observed to be both robust and accurate yielding very satisfactory results in plane channel flow up to re email protected 000 on uniform grids with dx email protected email protected 1000 the computed maximum error on skin friction is about 4 in most investigated cases on the coarsest grids 10 grid points across the half channel height it lies within 1 2 on finer grids with 20 60 uniformly distributed grid points in the channel half height

an arbitrary lagrangian eulerian approach for the simulation of immersed moving solids with lattice boltzmann method the flow structure interactions streaming from the motion of an immersed solid body are investigated through an arbitrary lagrangian eulerian ale approach applied to the lattice boltzmann method lbm the method is based on the use of a moving grid to describe the flow around the solid body while the physical domain is resolved by the use of an eulerian frame fixed grid the moving grid displacements follows the same moving law of the body and its shape does not change during the simulation the communication between the moving grid and the fixed grid is performed at the beginning of each time step through interpolation the ale lbm approach has been derived from the discretized boltzmann equation by a chapman enskog expansion procedure the equivalence of the proposed method with the navier stokes equations for a weakly compressible athermal flow being recovered numerical simulations of academical test cases have been performed in order to assess the method and to investigate the sensitivity of the error to the simulation parameters three different test cases have been considered in order to perform a robust assessment of the ale lbm approach more specifically the uniform flow the poiseuille flow and the plane wave test cases have been studied and the limits of application of the approach have been defined and discussed finally the case of a rotating two dimensional square cylinder immersed in a poiseuille flow re 80 has been numerically investigated the results confirm that the ale lbm approach is able to correctly represent the physical flow features and in particular the transition zone between the two grids used is smooth and continuous a sign that the error due to the interpolation process is bounded and does not diverge in time

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized

kernel meets sieve post regularization confidence bands for sparse additive model we develop a novel procedure for constructing confidence bands for components of a sparse additive model our procedure is based on a new kernel sieve hybrid estimator that combines two most popula

unified univariate and multivariate random field theory we report new random field theory p values for peaks of canonical correlation spms for detecting multiple contrasts in a linear model for multivariate image data this completes results for all types of univariate and multivariate image data analysis all other known univariate and multivariate random field theory results are now special cases so these new results present a true unification of all currently known results as an illustration we use these results in a deformation based morphometry dbm analysis to look for regions of the brain where vector deformations of nonmissile trauma patients are related to several verbal memory scores to detect regions of changes in anatomical effective connectivity between the trauma patients and a group of age and sex matched controls and to look for anatomical connectivity in cortical thickness

adaptive filtering for the lattice boltzmann method in this study a new selective filtering technique is proposed for the lattice boltzmann method this technique is based on an adaptive implementation of the selective filter coefficient the proposed model makes the latter coefficient dependent on the shear stress in order to restrict the use of the spatial filtering technique in sheared stress region where numerical instabilities may occur different parameters are tested on 2d test cases sensitive to numerical stability and on a 3d decaying taylorgreen vortex the results are compared to the classical static filtering technique and to the use of a standard subgrid scale model and give significant improvements in particular for low order filter consistent with the lbm stencil