scalability of 2 d wavelet transform algorithms analytical and experimental results on mpps this paper studies the scalability of two dimensional 2 d discrete wavelet transform dwt algorithms on massively parallel processors mpps the principal operation in the 2 d dwt is the filtering operation used to implement the filter banks of the 2 d subband decomposition this filtering operation can be implemented as a convolution in the time domain or as a multiplication in the frequency domain we demonstrate that there exist combinations of machine size image size and wavelet kernel size for which the time domain algorithms outperform the frequency domain algorithms and vice versa we therefore demonstrate that a hybrid approach that combines time and frequency domain approaches can yield linear scalability for a broad range of problem and machine sizes furthermore we show the effect of processor speed versus communication overhead and the use of separable versus nonseparable wavelets on the crossover points between the algorithm approaches

a hybrid method using wavelets for the numerical solution of boundary value problems on the interval abstract in this work various aspects of wavelet based methods for second order boundary value problems under galerkin framework are investigated based on the b spline multiresolution analysis mra on the line we propose a hybrid method on the interval which combines different treatments for interior and boundary splines by using this procedure the mra structure was conserved and hierarchical representations of the solution at different scales were obtained without much computational effort numerical examples are given to verify the effectiveness of the proposed method and the comparison with other techniques is presented

vibration analysis of harmonically excited non linear system using the method of multiple scales an analytical method is presented for evaluation of the steady state periodic behavior of non linear systems this method is based on the substructure synthesis formulation and a multiple scales procedure which is applied to the analysis of non linear responses a complex non linear system is divided into substructures of which equations are approximately transformed to modal co ordinates including non linear term under the reasonable procedure then the equations are synthesized into the overall system and the solution of the non linear system can be obtained based on the method of multiple scales the proposed procedure reduces the size of large degree of freedom problem in solving the non linear equations feasibility and advantages of the proposed method are illustrated by the application of the analytic procedure to the non linear rotating machine system as a large mechanical structure system results obtained are reported to be an efficient approach with respect to non linear response prediction when compared with other conventional methods

on the representation of operators in bases of compactly supported wavelets this paper describes exact and explicit representations of the differential operators d n dx n n 1 2 cdots in orthonormal bases of compactly supported wavelets as well as the representations of the hilbert transform and fractional derivatives the method of computing these representations is directly applicable to multidimensional convolution operators also sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring o n log n operations for computing the wavelet coefficients of all n circulant shifts of a vector of the length n 2 n is constructed as an example of an application of this algorithm it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector see g beylkin r r coifman and v rokhlin comm pure appl math 44 1991 pp 141 183 may be reduced from o n to o log 2 n significant entries

solution of atomic orbitals in an interpolating wavelet basis the schrodinger equation of hydrogenic atoms and the hartree fock equations of some many electron atoms are solved using interpolating wavelets as basis functions the nonstandard operator form is used to compute operators in basis sets including multiple resolution levels we introduce an algorithm for converting matrices from nonstandard operator form to standard operator form we also consider the different components of the hamiltonian and fock operators separately and derive analytic formulas for their evaluation extension to many electron atoms is done within the hartree fock formalism convergence of atomic parameters such as orbital eigenvalues with respect to the number of resolution levels is inspected numerically for hydrogenlike atoms ions and some light many electron atoms helium lithium beryllium neon sodium magnesium and argon

hat interpolation wavelet based multi scale galerkin method for thin walled box beam analysis the objective of the present work is to propose a new adaptive wavelet galerkin method based on the lowest order hat interpolation wavelets the specific application of the present method is made on the one dimensional analysis of thin walled box beam problems exhibiting rapidly varying local end effects higher order interpolation wavelets have been used in the wavelet collocation setting but the lowest order hat interpolation is applied here first and a hat interpolation wavelet based galerkin method is newly formulated unlike existing orthogonal or biorthogonal wavelet based galerkin methods the present method does not require special treatment in dealing with general boundary conditions furthermore the present method directly works with nodal values and does not require special formula for the evaluation of system matrices though interpolation wavelets do not have any vanishing moment an adaptive scheme based on multi resolution approximations is possible and a preconditioned conjugate gradient method can be used to enhance numerical efficiency copyright 2001 john wiley sons ltd

numerical study of time splitting and space time adaptive wavelet scheme for schrodinger equations in this paper we present a time splitting and space time adaptive wavelet scheme for solving schrodinger equations with a small planck constant the scheme is stable and it can overcome high frequency pseudo oscillation of the solution the concrete steps and numerical experiments are also given

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

patch ordering based wavelet frame and its use in inverse problems in our previous work 1 we have introduced a redundant tree based wavelet transform rtbwt originally designed to represent functions defined on high dimensional data clouds and graphs we have further shown that rtbwt can be used as a highly effective image adaptive redundant transform that operates on an image using orderings of its overlapped patches the resulting transform is robust to corruptions in the image and thus able to efficiently represent the unknown target image even when it is calculated from its corrupted version in this paper we utilize this redundant transform as a powerful sparsity promoting regularizer in inverse problems in image processing we show that the image representation obtained with this transform is a frame expansion and derive the analysis and synthesis operators associated with it we explore the use of this frame operators to image denoising and deblurring and demonstrate in both these cases state of the art results

on the use of biorthogonal interpolating wavelets for large eddy simulation of turbulence recent work in the field of turbulence modelling has demonstrated the benefits of the wavelet based multiresolution analysis technique as a tool for the formulation of the large eddy simulation les equations in this formalism the les equations are obtained by projecting the navier stokes equations onto a hierarchy of wavelet spaces this paper investigates the use of biorthogonal interpolating wavelets as a basis for this projection placing special emphasis on the wavelet based differential operators that define this mapping a detailed analysis of their convergence properties is presented and compared to those of their orthogonal counterpart the daubechies wavelets based on this study we highlight the weaknesses of the unlifted interpolating wavelet representation for les sub grid modelling finally we establish a link between the unlifted framework and the sampling based les approach recently proposed in the literature

on the efficacy of the wavelet decomposition for high frequency vibration analyses abstract this paper reports the extraordinary ability of the wavelet decomposition for vibration analyses under the framework of rayleigh ritz method using a beam as an example daubechies wavelet scale functions are used as admissible functions for decomposing the flexural displacement of the structure along with the artificial springs at the boundary to predict vibration of an euler bernoulli beam in an extremely large frequency range it is shown that the use of wavelet basis allows reaching very high frequencies typically covering more than 1000 modes using conventional computational facility within the available numerical dynamics of the computers with no particular care needed for round off errors as a side benefit the use of spring boundary also allows handling any elastic boundary conditions through a dynamic contribution in the hamiltonian of the beam the wavelet decomposed approach combines the flexibility of the global methods and the accuracy of local methods by inheriting the versatility of the rayleigh ritz approach and the superior fitting ability of the wavelets numerical results on both free and forced vibrations are given in excellent agreement with predictions of classical methods

a copula based mixed poisson model for bivariate recurrent events under event dependent censoring in many chronic disease processes subjects are at risk of two or more types of events we describe a bivariate mixed poisson model in which a copula function is used to model the association between two gamma distributed random effects the resulting model is a bivariate negative binomial process in which each type of event arises from a negative binomial process methods for parameter estimation are described for parametric and semiparametric models based on an em algorithm we also consider the issue of event dependent censoring based on one type of event which arises when one event is sufficiently serious that its occurence may influence the decision of whether to withdraw a patient from a study the asymptotic biases of estimators of rate and mean functions from naive marginal analyses are discussed as well as associated treatment effects because the joint model is fit based on a likelihood consistent estimates are obtained simulation studies are carried out to evaluate the empirical performance of the proposed estimators with independent and event dependent censoring and applications to a trial of breast cancer patients with skeletal metastases and a study of patients with chronic obstructive pulmonary disease illustrate the approach

the shift invariant discrete wavelet transform and application to speech waveform analysis the discrete wavelet transform may be used as a signal processing tool for visualization and analysis of nonstationary time sampled waveforms the highly desirable property of shift invariance can be obtained at the cost of a moderate increase in computational complexity and accepting a least squares inverse pseudoinverse in place of a true inverse a new algorithm for the pseudoinverse of the shift invariant transform that is easier to implement in array oriented scripting languages than existing algorithms is presented together with self contained proofs representing only one of the many and varied potential applications a recorded speech waveform illustrates the benefits of shift invariance with pseudoinvertibility visualization shows the glottal modulation of vowel formants and frication noise revealing secondary glottal pulses and other waveform irregularities additionally performing sound waveform editing operations i e cutting and pasting sections on the shift invariant wavelet representation automatically produces quiet click free section boundaries in the resulting sound the capabilities of this wavelet domain editing technique are demonstrated by changing the rate of a recorded spoken word individual pitch periods are repeated to obtain a half speed result and alternate individual pitch periods are removed to obtain a double speed result the original pitch and formant frequencies are preserved in informal listening tests the results are clear and understandable

image coding using translation invariant wavelet transforms with symmetric extensions in this correspondence we address the problem of translation sensitivity of conventional wavelet transforms for two dimensional 2 d signals we propose wavelet transform algorithms that achieve the following desirable properties simultaneously i translation invariance ii reduced edge effects and iii size limitedness we apply this translation invariant biorthogonal wavelet transform with symmetric extensions to image coding applications with good results

wavelet based schemes for linear advection dispersion equation abstract in this paper two wavelet based adaptive solvers are developed for linear advection dispersion equation the localization properties and multilevel structure of the wavelets in the physical space are used for adaptive computational methods for solution of equation which exhibit both smooth and shock like behaviour the first framework is based on wavelet galerkin and the second is based on multiscale decomposition of finite element method coiflet wavelet filter is incorporated in both the methods the main advantage of both the adaptive methods is the elimination of spurious oscillations at very high peclet number

a wavelet based multiresolution approach to large eddy simulation of turbulence the wavelet based multiresolution analysis mra technique is used to develop a modelling approach to large eddy simulation les and its associated subgrid closure problem the les equations are derived by projecting the navier stokes n s equations onto a hierarchy of wavelet spaces a numerical framework is then developed for the solution of the large and the small scale equations this is done in one dimension for the burgers equation and in three dimensions for the n s problem the proposed methodology is assessed in a priori tests on an atmospheric turbulent time series and on data from direct numerical simulation a posteriori dynamic tests are also carried out for decaying and force driven burgers turbulence

improved transient signal detection using a wavepacket based detector with an extended translation invariant wavelet transform this paper presents the theory of m band extended translation invariant eti wavelet transforms the eti generalizes the translation invariant wavelet transform of weiss 1933 it is shown that iteration of the eti in a tree structure provides a signal decomposition into an orthonormal wavepacket basis other properties such as translation invariance and invertibility of the transform are proven the theory is then applied to transient signal detection through development of a family of translation invariant wavepacket based detectors this family of detectors provides improved the performance over previously defined wavepacket based detectors a performance analysis is conducted roc curves generated by monte carlo simulation are presented indicating the detector performance the detector performance is demonstrated to be independent of the signal translation

a dynamic multiscale lifting computation method using daubechies wavelet an important property of wavelet multiresolution analysis is the capability to represent functions in a dynamic multiscale manner so the solution in the wavelet domain enables a hierarchical approximation to the exact solution the typical problem that arises when using daubechies wavelets in numerical analysis especially in finite element analysis is how to calculate the connection coefficients an integral of products of wavelet scaling functions or derivative operators associated with these the method to calculate multiscale connection coefficients for stiffness matrices and load vectors is presented for the first time and the algorithm of multiscale lifting computation is developed the numerical examples are given to verify the effectiveness of such a method

interpolating wavelet collocation method of time dependent maxwell s equations characterization of electrically large optical waveguide discontinuities biorthogonal interpolating wavelets have been applied to electromagnetic field modeling through the wavelet collocation method in time domain yielding a versatile first principle algorithm for the solution of time dependent maxwell s equations with inhomogeneous media the resulting scheme maintains high accuracy while by virtue of its sub gridding capability significant reduction of the computational expenditure has been obtained the proposed method has been applied to the analysis of two dimensional dielectric waveguide discontinuities particularly for the modeling of electrically large optical waveguides where the dimension of the analyzed structure is much larger than the wavelength of the highest frequency content of the transmitted signal the proposed method has been proven to be highly efficient compared to the standard finite difference method

on the dependence structure of bivariate recurrent event processes inference and estimation bivariate or multivariate recurrent event processes are often encountered in longitudinal studies in which more than one type of event is of interest there has been much research on regression analysis for such data but little has been done to measure the dependence between recurrent event processes we propose a time dependent measure termed the rate ratio to assess the local dependence between two types of recurrent event processes we model the rate ratio as a parametric function of time and leave unspecified all other aspects of the distribution we develop a composite likelihood procedure for model fitting and parameter estimation we show that the proposed estimator is consistent and asymptotically normal its finite sample performance is evaluated by simulation and illustrated by an application to a soft tissue sarcoma study

a new framework for complex wavelet transforms although the discrete wavelet transform dwt is a powerful tool for signal and image processing it has three serious disadvantages shift sensitivity poor directionality and lack of phase information to overcome these disadvantages we introduce two stage mapping based complex wavelet transforms that consist of a mapping onto a complex function space followed by a dwt of the complex mapping unlike other popular transforms that also mitigate dwt shortcomings the decoupled implementation of our transforms has two important advantages first the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy this allows us to create a directional non redundant complex wavelet transform with potential benefits for image coding systems to the best of our knowledge no other complex wavelet transform is simultaneously directional and non redundant the second advantage of our approach is the flexibility to use any dwt in the transform implementation as an example we can exploit this flexibility to create the complex double density dwt cddwt a shift insensitive directional complex wavelet transform with a low redundancy of 3 sup m 1 2 sup m 1 in m dimensions to the best of our knowledge no other transform achieves all these properties at a lower redundancy

numerical methods for the generalized zakharov system we present two numerical methods for the approximation of the generalized zakharov system zs the first one is the time splitting spectral tssp method which is explicit time reversible and time transverse in variant if the generalized zs is keeps the same decay rate of the wave energy as that in the generalized zs gives exact results for the plane wave solution and is of spectral order accuracy in space and second order accuracy in time the second one is to use a local spectral method the discrete singular convolution dsc for spatial derivatives and the fourth order runge kutta rk4 for time integration which is of high the same as spectral order accuracy in space and can be applied to deal with general boundary conditions in order to test accuracy and stability we compare these two methods with other existing methods fourier pseudospectral method fps and wavelet galerkin method wg for spatial derivatives combining with the rk4 for time integration as well as the standard finite difference method fd for solving the zs with a solitary wave solution furthermore extensive numerical tests are presented for plane waves solitary wave collisions in 1d as well as a 2d problem of the generalized zs numerical results show that tssp and dsc are spectralorder accuracy in space and much more accurate than fd and for stability tssp requires k o h dsc rk4 requires k o h2 for fixed acoustic speed where k is the time step and h is the spatial mesh size

connection coefficients on an interval and wavelet solutions of burgers equation a definition of connection coefficients is introduced and techniques of computation are presented we use semi implicit time difference scheme to solve burgers equation by applying the evaluations of connection coefficients in calculating the integrals of the variational form comparisons of accuracy and robustness of numerical solutions are mentioned in the examples

simultaneous space time adaptive wavelet solution of nonlinear parabolic differential equations dynamically adaptive numerical methods have been developed to efficiently solve differential equations whose solutions are intermittent in both space and time these methods combine an adjustable time step with a spatial grid that adapts to spatial intermittency at a fixed time the same time step is used for all spatial locations and all scales this approach clearly does not fully exploit space time intermittency we propose an adaptive wavelet collocation method for solving highly intermittent problems e g turbulence on a simultaneous space time computational domain which naturally adapts both the space and time resolution to match the solution besides generating a near optimal grid for the full space time solution this approach also allows the global time integration error to be controlled the efficiency and accuracy of the method is demonstrated by applying it to several highly intermittent 1d t dimensional and 2d t dimensional test problems in particular we found that the space time method uses roughly 18 times fewer space time grid points and is roughly 4 times faster than a dynamically adaptive explicit time marching method while achieving similar global accuracy

a new image flux conduction model and its application to selective image smoothing a discrete image flux conduction equation which is completely new in this field is proposed the new approach starts with formulating a discrete image flux conduction equation based on the concept of heat conduction theory based on this discrete equation the status change at a time point can be directly computed from its spatial neighborhood to more accurately estimate an image flux we have used an orthogonal wavelet basis to approximate the gradient of the intensity at each point since the proposed approach is discrete by nature it is not necessary to formulate a continuous pde to fit the discrete image data set furthermore introduction of different numerical methods to solve the pde can also be avoided since the proposed approach does not require that a pde be solved it is therefore more efficient and accurate than the conventional methods experimental results obtained using both synthetic signals and real images have demonstrated that the proposed model could effectively handle the selective image smoothing problem

analysis of multi type recurrent events in longitudinal studies application to a skin cancer prevention trial we consider the statistical modeling and analysis of replicated multi type point process data with covariates such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types the underlying processes are modeled as nonhomogeneous mixed poisson processes with random subject and fixed covariate effects the method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients score tests and likelihood ratio statistics are used for covariate selection a graphical test of goodness of fit of the selected model is based on generalized residuals measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed an application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer

use of transformations with the higher order method of multiple scales to determine the steady state periodic response of harmonically excited non linear oscillators part i transformation of derivative abstract use of the higher order method of multiple scales with reconstitution to determine the periodic steady state response of harmonically excited non linear oscillators is considered in this method frequency detuning can be introduced in several different ways the main objective of this work is to compare the second order results determined by introducing detuning in the square of the excitation frequency against the second order results determined by introducing detuning in the excitation frequency itself a modified reconstitution procedure is used to uncover the relative approximations used in these second order solutions the well known primary resonance in the duffing oscillator is used as a prototype example and it is shown that the combined effects of using transformed time and introducing a detuning parameter in the square of the excitation frequency can lead to a non uniform expansion within the excitation frequency band in which large amplitude primary response is excited

a spline wavelet finite element method in structural mechanics the wavelet based methods are powerful to analyse the field problems with changes in gradients and singularities due to the excellent multi resolution properties of wavelet functions wavelet based finite elements are often constructed in the wavelet space where field displacements are expressed as a product of wavelet functions and wavelet coefficients when a complex structural problem is analysed the interface between different elements and boundary conditions cannot be easily treated as in the case of conventional finite element methods fems a new wavelet based fem in structural mechanics is proposed in the paper by using the spline wavelets in which the formulation is developed in a similar way of conventional displacement based fem the spline wavelet functions are used as the element displacement interpolation functions and the shape functions are expressed by wavelets the detailed formulations of typical spline wavelet elements such as plane beam element in plane triangular element in plane rectangular element tetrahedral solid element and hexahedral solid element are derived the numerical examples have illustrated that the proposed spline wavelet finite element formulation achieves a high numerical accuracy and fast convergence rate copyright 2005 john wiley sons ltd

necessary and sufficient conditions for constructing orthonormal wavelet bases this paper proves a previous conjecture of the author characterizing sequences h l2 z that yield orthonormal wavelet bases of l2 r in terms of the multiplicity of the eigenvalue 1 of an operator associated to h the proof utilizes a result of cohen characterizing these sequences in terms of the real zeros of their fourier transforms the mapping from sequences to wavelets is shown to define a continuous mapping from a subset of l2 z into l2 r related conjectures are discussed

non linear structural vibrations under combined parametric and external excitations abstract a set of second order equations with weak quadratic and cubic non linearities is considered simultaneous parametric and external forcing excitations are included the frequency of the parametric excitation is near a natural frequency of the system and three cases are analyzed i the external excitation is absent ii the external excitation is present but is not involved in a resonance and iii the external frequency is the same as the parametric frequency results are obtained by the method of multiple scales frequency response curves are presented for various combinations of excitation amplitudes damping coefficients and phase shift between the excitations it is found that stable multi modal responses may exist in the first order asymptotic solution even though only one mode is involved in the resonance and no internal resonance condition is present

on the design of highly accurate and efficient iir and fir filters we describe a systematic method for designing highly accurate and efficient infinite impulse response iir and finite impulse response fir filters given their specifications in our approach we first meet the specifications by constructing an iir filter with possibly a large number of poles we then construct for any given accuracy an optimal iir version of such filter with a minimal number of poles finally also for any given accuracy we convert the iir filter to an efficient fir filter cascade either serial or parallel since in this fir approximation the non causal part of the iir filter only introduces an additional delay as a function of the desired accuracy our iir construction does not have to enforce causality thus we obtain a simple method for constructing linear phase filters if the specifications so require all of these procedures are accomplished via robust fast algorithms we provide several illustrative examples of our method

convergence of cascade algorithms in sobolev spaces and integrals of wavelets the cascade algorithm with mask a and dilation m generates a sequence phi n n 1 2 ldots by the iterative process

wave extrapolation in the spatial wavelet domain with application to poststack reverse time migration a wavelet transformation is performed over each of the spatial coordinates of the scalar wave equation this transformed equation is solved directly with a finite difference scheme for both homogeneous and smooth inhomogeneous media wavefield extrapolation is performed completely in the spatial wavelet domain without transforming back into the space domain at each time step the wavelet coefficients are extrapolated rather than the wavefield itself the numerical solution of the scalar wave equation in the spatial wavelet domain is closely related to the finite difference method because of the compact support of the wavelet bases poststack reverse time migration is implemented as an application the resolution spaces of the wavelet transform provide a natural framework for multigrid analysis migrated images are constructed from various resolution spaces

wavelet and fourier methods for solving the sideways heat equation we consider an inverse heat conduction problem the sideways heat equation which is a model of a problem where one wants to determine the temperature on both sides of a thick wall but where one side is inaccessible to measurements mathematically it is formulated as a cauchy problem for the heat equation in a quarter plane with data given along the line x 1 where the solution is wanted for 0 leq x 1 the problem is ill posed in the sense that the solution if it exists does not depend continuously on the data we consider stabilizations based on replacing the time derivative in the heat equation by wavelet based approximations or a fourier based approximation the resulting problem is an initial value problem for an ordinary differential equation which can be solved by standard numerical methods e g a runge kutta method we discuss the numerical implementation of fourier and wavelet methods for solving the sideways heat equation theory predicts that the fourier method and a method based on meyer wavelets will give equally good results our numerical experiments indicate that also a method based on daubechies wavelets gives comparable accuracy as test problems we take model equations with constant and variable coefficients we also solve a problem from an industrial application with actual measured data

testing for homogeneity of variance in time series long memory wavelets and the nile river 1 we consider the problem of testing for homogeneity of variance in a time series with long memorystructure wedemonstratethat atest whose nullhypothesis isdesigned tobewhite noisecan in fact be applied on a scale by scale basis to the discrete wavelet transform of long memory processes in particular we show that evaluating a normalized cumulative sum of squares test statistic using critical levels for the null hypothesis of white noise yields approximately the same null hypothesis rejection rates when applied to the discrete wavelet transform of samples from a fractionally differenced process the point at which the test statistic using a nondecimated version of the discrete wavelet transform achieves its maximum value can be used to estimate the time of the unknown variance change we apply our proposed test statistic on five time series derived from the historical record of nile river yearly minimum water levels covering 622 1922 a d each series exhibiting various degrees of serial correlation including long memory in the longest subseries spanning 622 1284 a d the test confirms an inhomogeneity of variance at short time scales and identifies the change point around 720 a d which coincides closely with the construction of a new device around 715 a d for measuring the nile river the test also detects a change in variance for a record of only 36 years index terms 1829 hydrology groundwater hydrology 1869 hydrology stochastic processes 3299 mathematical geophysics general or miscellaneous

wavelet calculus and finite difference operators this paper shows that the naturally induced discrete differentiation operators induced from a wavelet galerkin finite dimensional approximation to a standard function space approximates differentiation with an error of order 0 h2d 2 where d is the degree of the wavelet system the degree of a wavelet system is defined as one less than the degree of the lowest order nonvanishing moment of the fundamental wavelet we consider in this paper compactly supported wavelets of the type introduced by daubechies in 1988 the induced differentiation operators are described in terms of connection coefficients which are intrinsically defined functional invariants of the wavelet system defined as l2 inner products of derivatives of wavelet basis functions with the basis functions themselves these connection coefficients can be explicitly computed without quadrature and they themselves have key moment vanishing properties proved in this paper which are dependent upon the degree of the wavelet system this is the basis for the proof of the principal results concerning the degree of approximation of the differentiation operator by the wavelet galerkin discrete differentiation operator

coiflet systems and zero moments the coifman wavelets created by daubechies 1992 have more zero moments than imposed by specifications this results in systems with approximately equal numbers of zero scaling function and wavelet moments and gives a partitioning of the systems into three well defined classes the nonunique solutions are more complex than for daubechies wavelets

multiscale adjoint waveform tomography for surface and body waves abstractwe have developed a wavelet multiscale adjoint scheme for the elastic full waveform inversion of seismic data including body waves bws and surface waves sws we start the inversion on the sw portion of the seismograms to avoid cycle skipping and reduce the dependence on the initial model of these dispersive waves we commence by minimizing an envelope based misfit function subsequently we proceed to the minimization of a waveform difference wd metric applied to the sws only after that we fit bws and sws indiscriminately using a wd misfit metric in each of these three steps we guide the iterative inversion through a sequence of nested subspace projections in a wavelet basis sw analysis preserves a wealth of near surface features that would be lost in conventional bw tomography we used a toy model to illustrate the dispersive and cycle skipping behavior of the sws and to introduce the two ways by which we combat the nonlinearity of waveform inversions involving sws the first is the

semiparametric inference in a model for association in bivanate survival data summary clayton s 1978 model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem that is a problem where inference about a parameter is required in the presence of nuisance functions we derive the asymptotic variance of clayton s estimator obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random censorship some comparisons are made with results derived by oakes 1982 for other estimators within this model in the absence of censoring the exact null variance of the score statistic corresponding to clayton s estimator is derived and compared with that of the locally most powerful rank test given by cuzick 1982

solution of inverse problems in image processing by wavelet expansion we describe a wavelet based approach to linear inverse problems in image processing in this approach both the images and the linear operator to be inverted are represented by wavelet expansions leading to a multiresolution sparse matrix representation of the inverse problem the constraints for a regularized solution are enforced through wavelet expansion coefficients a unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions an important problem in multigrid multiresolution processing this and the sparseness of the representation induce a multigrid algorithm the proposed approach was tested on image restoration problems and produced good results

nonlinear transverse free vibrations of piles the nonlinear partial differential equation governing the nonlinear transverse vibration of pile was derived under the assumption of that both the materials of pile and soil obey nonlinear elastic and linear viscoelastic constitutive relations the approximate expressions of the nth order main frequency and the response of the nonlinear vibration of pile with ends hinged have been obtained by the complex mode method and multiple time scales method results point out that the main frequency of the nonlinear system is related to not only the natural frequency of linear vibration system but also the amplitude damping and nonlinearity of materials there are high order harmonic waves with twice the main frequency and the main frequency of three times as well as the sum and or difference of 2 or 3 main frequencies besides the harmonic wave with the main frequency in the response of the nonlinear system numerical examples were given and the effect of parameters was considered in detail

trigonometric wavelet method for some elliptic boundary value problems abstract in this paper we apply trigonometric wavelet method to investigate the numerical solution of elliptic boundary value problem in an exterior unit disk the simple computation formulae of the entries in the stiffness matrix are obtained it shows that we only need to compute 2 2 j 1 elements of one 2 j 2 2 j 2 stiffness matrix moreover the error estimates of the approximation solutions are given and some test examples are presented

log polar wavelet energy signatures for rotation and scale invariant texture classification classification of texture images is important in image analysis and classification this paper proposes an effective scheme for rotation and scale invariant texture classification using log polar wavelet signatures the rotation and scale invariant feature extraction for a given image involves applying a log polar transform to eliminate the rotation and scale effects but at same time produce a row shifted log polar image which is then passed to an adaptive row shift invariant wavelet packet transform to eliminate the row shift effects so the output wavelet coefficients are rotation and scale invariant the adaptive row shift invariant wavelet packet transform is quite efficient with only o n spl middot log n complexity a feature vector of the most dominant log polar wavelet energy signatures extracted from each subband of wavelet coefficients is constructed for rotation and scale invariant texture classification in the experiments we employed a mahalanobis classifier to classify a set of 25 distinct natural textures selected from the brodatz album the experimental results based on different testing data sets for images with different orientations and scales show that the proposed classification scheme using log polar wavelet signatures outperforms two other texture classification methods its overall accuracy rate for joint rotation and scale invariance being 90 8 percent demonstrating that the extracted energy signatures are effective rotation and scale invariant features concerning its robustness to noise the classification scheme also performs better than the other methods

some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates abstract recurrent event time data are common in medical research examples include infections in aids patients and seizures in epilepsy patients in this context as well as in the more usual context of a single failure time variable time dependent covariates are frequently of interest we suggest some rate functions that might be displayed when analyzing recurrent failure time data or when the effect of a categorical time dependent covariate is of interest estimators of these functions are provided along with two sample test statistics a new approach to regression modeling of these data is suggested and contrasted with existing methods our methods do not require that an explicit model be formulated for the probabilistic association between failure times within an individual this is in line with the currently popular generalized estimating equation approach to longitudinal data if the nature of such associations is known or is of particular interest then alternative methods may be appropriate

wavelet methods for pdes some recent developments abstract this paper is concerned with recent developments of wavelet schemes for the numerical treatment of operator equations with special emphasis on two issues adaptive solution concepts and nontrivial domain geometries after describing a general multiresolution framework the key features of wavelet bases are highlighted namely locality norm equivalences and cancellation properties assuming first that wavelet bases with these properties are available on the relevant problem domains the relevance of these features for a wide class of stationary problems is explained in subsequent sections the main issues are preconditioning and the efficient adaptive application of wavelet representations of the involved operators we indicate then how these ingredients combined with concepts from nonlinear or best n term approximation culminate in an adaptive wavelet scheme for elliptic selfadjoint problems covering boundary value problems as well as boundary integral equations these schemes can be shown to exhibit convergence rates that are in a certain sense asymptotically optimal we conclude this section with some brief remarks on data structures and implementation interrelations with regularity in a certain scale of besov spaces and strategies of extending such schemes to unsymmetric or indefinite problems we address then the adaptive evaluation of nonlinear functionals of wavelet expansions as a central task arising in connection with nonlinear problems wavelet bases on nontrivial domains are discussed next the main issues are the development of fourier free construction principles and criteria for the validity of norm equivalences finally we indicate possible combinations of wavelet concepts with conventional discretizations such as finite element or finite volume schemes in connection with convection dominated and hyperbolic problems

the applications of partial integro differential equations related to adaptive wavelet collocation methods for viscosity solutions to jump diffusion models this paper presents adaptive wavelet collocation methods for the numerical solutions to partial integro differential equations pides arising from option pricing in a market driven by jump diffusion process the first contribution of this paper lies in the formulation of the wavelet collocation schemes the integral and differential operators are formulated in the collocation setting exactly and efficiently in both adaptive and non adaptive wavelet settings the wavelet compression technique is employed to replace the full matrix corresponding to the nonlocal integral term by a sparse matrix an adaptive algorithm is developed which automatically obtains the solution on a near optimal grid the second contribution of this paper is the theoretical analysis of the wavelet collocation schemes due to the possible degeneracy of the parabolic operators classical solutions of the jump diffusion models may not exist in this paper we first prove the convergence and stability of the proposed numerical schemes under the framework of viscosity solution theory and then the numerical experiments demonstrate the accuracy and computational efficiency of the methods we developed

adaptive multiscale wavelet galerkin analysis for plane elasticity problems and its applications to multiscale topology design optimization the multiscale galerkin formulation of two dimensional elasticity problems is presented for easy interpolation and boundary handlings as well as efficient adaptive analysis two dimensional interpolation wavelets are used as the multiscale trial functions in the galerkin formulation after the validity of the present multiscale adaptive method is verified with some benchmark problems the present wavelet based method is applied to the multiscale topology optimization that progresses design resolution levels dyadically from low to high levels by this application we show the potential of the multiscale method and the possibility of developing a fully integrated analysis and topology design optimization in the multiscale multiresolution setting

alternating wavelet time finite element method modeling and analysis of nonlinear wave propagation in one and two dimensional waveguides abstract in this paper a novel method named the alternating wavelet time finite element method awt fem is proposed for studying elastic wave propagation in nonlinear structures an alternating iterative procedure between the time domain and a wavelet domain combined with the spectral finite element method sfem is employed to solve wave equations with general nonlinearities the advantages of the proposed method are 1 the potential to provide high fidelity results for impacts with high frequency content through the use of the spectral finite element method 2 nonlinear structures with physically realistic boundary conditions can easily be studied by circumventing wrap around issues associated with fourier based methods 3 the parallel computing compatible framework and the semi analytical nature of sfem make it more computationally efficient for nonlinear systems modeled with structural components simulations using the proposed method are conducted to demonstrate its applicability to study nonlinear wave propagation in one dimensional and two dimensional systems

new wavelet based approach for time domain simulations a new numerical method for the time domain solution of maxwell s equations in linear media is proposed in this paper the field quantities derived from the spatial discretization of maxwell s equations are expanded in the time domain by wavelets on the interval this choice yields a new arrangement of the unknowns into a matrix instead of the usual vector and transforms the differential equations in time in a sylvester 1983 matrix equation the memory requirements are proportional to the number of spatial unknowns and the time evolution of the space quantities is obtained with better accuracy than in conventional marching on time techniques

translation invariant data visualization with orthogonal discrete wavelets orthogonal discrete wavelet transforms can be made translation invariant by adding redundant wavelet coefficients through repeated shifting operations orthogonality is lost but isometry and compact time support can be preserved the practical application to data visualization of scalograms based on such transforms is discussed and illustrated with measured transient signals

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

power and sample size calculation for paired recurrent events data based on robust nonparametric tests the purpose of this paper is to develop a formula for calculating the required sample size for paired recurrent events data the developed formula is based on robust non parametric tests for comparing the marginal mean function of events between paired samples this calculation can accommodate the associations among a sequence of paired recurrent event times with a specification of correlated gamma frailty variables for a proportional intensity model we evaluate the performance of the proposed method with comprehensive simulations including the impacts of paired correlations homogeneous or nonhomogeneous processes marginal hazard rates censoring rate accrual and follow up times as well as the sensitivity analysis for the assumption of the frailty distribution the use of the formula is also demonstrated using a premature infant study from the neonatal intensive care unit of a tertiary center in southern taiwan copyright 2017 john wiley sons ltd

divergence free wavelets and high order regularization expanding on a wavelet basis the solution of an inverse problem provides several advantages first of all wavelet bases yield a natural and efficient multiresolution analysis which allows defining clear optimization strategies on nested subspaces of the solution space besides the continuous representation of the solution with wavelets enables analytical calculation of regularization integrals over the spatial domain by choosing differentiable wavelets accurate high order derivative regularizers can be efficiently designed via the basis s mass and stiffness matrices more importantly differential constraints on vector solutions such as the divergence free constraint in physics can be nicely handled with biorthogonal wavelet bases this paper illustrates these advantages in the particular case of fluid flow motion estimation numerical results on synthetic and real images of incompressible turbulence show that divergence free wavelets and high order regularizers are particularly relevant in this context

meshfree methods and boundary conditions summary we perform here some meshfree methods to inhomogeneous laplace equations we prove the efficiency of those methods compared with classical ones for one or two dimensional case for numerics and for one dimensional for theoretical results copyright 2006 john wiley sons ltd

galerkin trigonometric wavelet methods for the natural boundary integral equations a simply supported boundary value problem of biharmonic equations in the unit disk is reduced into an equivalent second kind natural boundary integral equation nbie with hypersingular kernel in the sense of hadamard finite part trigonometric hermite interpolatory wavelets introduced by quak math comput 65 1996 683 722 as trial functions are used to its galerkin discretization with 2 j 1 degrees of freedom on the boundary it is proved that the stiffness matrix is a block diagonal matrix and its diagonal elements are some symmetric and block circulant submatrices the simple computational formulae of the entries in stiffness matrix are obtained these show that we only need to compute 2 2 j j 1 elements of a 2 j 2x2 j 2 stiffness matrix the error estimates for the approximation solutions are established finally numerical examples are given

solution of cartesian and curvilinear quantum equations via multiwavelets on the interval abstract it is shown how orthogonal compact support multiwavelets may be used for the solution of quantum mechanical eigenvalue problems subject to specific boundary conditions special scaling functions and wavelets with convenient limiting behaviors at the edges of an interval are constructed in analogy to earlier work on single wavelet families all of the integrals required for hamiltonian matrix elements involving both regular and edge functions are calculated efficiently through use of recursion and quadrature methods it is demonstrated through accurate eigenvalue determination that both cartesian and curvilinear degrees of freedom are readily accommodated with such a basis using as examples the particle in a box and the hydrogen atom in spherical polar coordinates

translation invariant contourlet transform and its application to image denoising most subsampled filter banks lack the feature of translation invariance which is an important characteristic in denoising applications in this paper we study and develop new methods to convert a general multichannel multidimensional filter bank to a corresponding translation invariant ti framework in particular we propose a generalized algorithme agrave trous which is an extension of the algorithme agrave trous introduced for 1 d wavelet transforms using the proposed algorithm as well as incorporating modified versions of directional filter banks we construct the ti contourlet transform tict to reduce the high redundancy and complexity of the tict we also introduce semi translation invariant contourlet transform stict then we employ an adapted bivariate shrinkage scheme to the stict to achieve an efficient image denoising approach our experimental results demonstrate the benefits and potential of the proposed denoising approach complexity analysis and efficient realization of the proposed ti schemes are also presented

solution of time dependent diffusion equations with variable coefficients using multiwavelets a new numerical algorithm is developed for the solution of time dependent differential equations of diffusion type it allows for an accurate and efficient treatment of multidimensional problems with variable coefficients nonlinearities and general boundary conditions for space discretization we use the multiwavelet bases introduced by alpert 1993 siam j math anal 24 246 262 and then applied to the representation of differential operators and functions of operators presented by alpert beylkin and vozovoi representation of operators in the multiwavelet basis in preparation an important advantage of multiwavelet basis functions is the fact that they are supported only on non overlapping subdomains thus multiwavelet bases are attractive for solving problems in finite non periodic domains boundary conditions are imposed with a penalty technique of hesthaven and gottlieb 1996 siam j sci comput 579 612 which can be used to impose rather general boundary conditions the penalty approach was extended to a procedure for ensuring the continuity of the solution and its first derivative across interior boundaries between neighboring subdomains while time stepping the solution of a time dependent problem this penalty procedure on the interfaces allows for a simplification and sparsification of the representation of differential operators by discarding the elements responsible for interactions between neighboring subdomains consequently the matrices representing the differential operators on the finest scale have block diagonal structure for a fixed order of multiwavelets i e a fixed number of vanishing moments the computational complexity of the present algorithm is proportional to the number of subdomains the time discretization method of beylkin keiser and vozovoi 1998 pam report 347 is used in view of its favorable stability properties numerical results are presented for evolution equations with variable coefficients in one and two dimensions

imposing boundary and interface conditions in multi resolution wavelet galerkin method for numerical solution of helmholtz problems abstract in this paper we propose a new formulation for numerical solution of boundary value problems using mesh free multi resolution wavelet galerkin wg method a difficulty with the wg method is imposing boundary condition constraints single scale wavelet basis functions together with a jump function approach using cubic polynomial functions have been used in solving some boundary problems in the literature ramp and cubic polynomial functions have been also used in the jump function approach described in element free galerkin context and it is proven ramp functions exactly satisfy the desirable property for the derivative of jump but the cubic polynomial functions do not in this paper a multi resolution wg method is employed and both ramp and cubic polynomial jump functions are applied obtained results in one dimension are compared with analytical solutions results obtained with ramp jump functions in two dimensions are also reported the results obtained with the wg method manifest boundary and interface conditions are accurately imposed when the ramp jump functions are applied numerical results are in good agreement with accurate solutions

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

wavelet solutions for the dirichlet problem a modified classical penalty method for solving a dirichlet boundary value problem is presented this new fictitious domain penalty method eliminates the traditional need of generating a complex computation grid in the case of irregular domains it is based on the fact that one can expand the boundary measure under the chosen basis which leads to a fast approximate calculation of boundary integral the compact support and orthonormality of the basis are essential for representing the boundary measure numerically and therefore for implementing this methodology

on higher order methods of multiple scales in non linear oscillations periodic steady state response abstract the application of the method of multiple scales mms to determine higher order steady state responses of weakly non linear harmonically forced oscillators is considered two fundamentally different versions of mms are currently in use in the study of such non linear resonance phenomena our purpose is to describe the way in which these two versions lead to different results and to discuss each version from the standpoint of the basic ideas underlying the perturbation approach the work is considered relevant because of the relative ease in making higher order calculations by using symbolic manipulation which will probably render such higher order analyses routine in the future

symmetric daubechies wavelets and numerical solution of nls equations recent work has shown that wavelet based numerical schemes are at least as effective and accurate as standard methods and may allow an easy implementation of a spacetime adaptive grid up to now wavelets which have been used for such studies are the classical ones real daubechies wavelets splines shannon and meyer wavelets etc and were applied to diffusion type equations the present work differs in two points firstly for the first time we use a new set of complex symmetric wavelets which have been found recently the advantage of this set is that unlike classical wavelets they are simultaneously orthogonal compactly supported and symmetric secondly we apply these wavelets to the physically meaningful cubic and quintic nonlinear schrodinger equations the most common method to simulate these models numerically is the symmetrized split step fourier method for the first time we propose and study a new way of implementing a global spacetime adaptive discretization in this numerical scheme based on the interpolation properties of complex symmetric scaling functions second we propose a locally adaptive split step wavelet method

an efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the daubechies wavelet basis an efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with daubechies wavelet and scaling function basis sets our quadrature is also applicable in the case of adaptive spatial resolution our theoretical error estimates are confirmed by numerical test calculations of the ground state energy and wavefunction of the harmonic oscillator in one dimension with and without adaptive resolution as a byproduct we derive a filter which upon application on the scaling function coefficients of a smooth function renders the approximate grid values of this function this also allows for a fast calculation of the charge density from the wavefunction

a new class of time discretization schemes for the solution of nonlinear pdes we consider issues of stability of time discretization schemes withexacttreatment of thelinear part elp schemes for solving nonlinear pdes a distinctive feature of elp schemes is the exact evaluation of the contribution of the linear term that is if the nonlinear term of the equation is zero then the scheme reduces to the evaluation of the exponential function of the operator representing the linear term computing and applying the exponential or other functions of operators with variable coefficients in the usual manner requires evaluating dense matrices and is highly inefficient it turns out that computing the exponential of strictly elliptic operators in the wavelet system of coordinates yields sparse matrices for a finite but arbitrary accuracy this observation makes our approach practical in a number of applications in particular we consider applications of elp schemes to advection diffusion equations we study the stability of these schemes and show that both explicit and implicit elp schemes have distinctly different stability properties if compared with known implicit explicit schemes for example we describe explicit schemes with stability regions similar to those of typical implicit schemes used for solving advection diffusion equations

multiscale adjoint waveform difference tomography using wavelets abstractfull waveform seismic inversions based on minimizing the distance between observed and predicted seismograms are in principle able to yield better resolved earth models than those minimizing misfits derived from traveltimes alone adjoint based methods provide an efficient way of calculating the gradient of the misfit function via a sequence of forward modeling steps which using spectral element codes can be carried out in realistically complex media convergence and stability of full waveform difference adjoint schemes are greatly improved when data and synthetics are progressively presented to the algorithms in a constructive multiscale approximation using a bi orthogonal wavelet transform wavelets provide the nonredundant spectral decomposition that paves the way for the inversion to proceed successively from long wavelength fitting to detailed exploration of the phases in the seismogram the choice of wavelet class and type the initial depth of the multiscale decomposition and the min

on the adaptive numerical solution of nonlinear partial differential equations in wavelet bases this work develops fast and adaptive algorithms for numerically solving nonlinear partial differential equations of the formut lu nf u where l and n are linear differential operators andf u is a nonlinear function these equations are adaptively solved by projecting the solutionuand the operators l and n into a wavelet basis vanishing moments of the basis functions permit a sparse representation of the solution and operators using these sparse representations fast and adaptive algorithms that apply operators to functions and evaluate nonlinear functions are developed for solving evolution equations for a wavelet representation of the solutionuthat containsnssignificant coefficients the algorithms update the solution usingo ns operations the approach is applied to a number of examples and numerical results are given

a fast adaptive wavelet collocation algorithm for multidimensional pdes a fast multilevel wavelet collocation method for the solution of partial differential equations in multiple dimensions is developed the computational cost of the algorithm is independent of the dimensionality of the problem and is o n where n is the total number of collocation points the method can handle general boundary conditions the multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution high resolution computations are performed only in regions where singularities or sharp transitions occur numerical results demonstrate the ability of the method to resolve localized structures such as shocks which change their location and steepness in space and time the present results indicate that the method has clear advantages in comparison with well established numerical algorithms

symplectic wavelet collocation method for hamiltonian wave equations this paper introduces a novel symplectic wavelet collocation method for solving nonlinear hamiltonian wave equations based on the autocorrelation functions of daubechies compactly supported scaling functions collocation method is conducted for the spatial discretization which leads to a finite dimensional hamiltonian system then appropriate symplectic scheme is employed for the integration of the hamiltonian system under the hypothesis of periodicity the properties of the resulted space differentiation matrix are analyzed in detail conservation of energy and momentum is also investigated various numerical experiments show the effectiveness of the proposed method

semiparametric modelling and estimation of covariate adjusted dependence between bivariate recurrent events a time dependent measure termed the rate ratio was proposed to assess the local dependence between two types of recurrent event processes in one sample settings however the one sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received the focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events we propose the covariate adjusted rate ratio a measure of covariate adjusted dependence we propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure we develop a pseudo partial likelihood to estimate the parameters in the proportional rate ratio model we establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies we illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence

time dependent association measures for bivariate survival distributions abstract we propose time dependent association measures for application to bivariate survival analysis such association measures provide informative summaries for data on twins ophthalmic and auditory studies and for other matched pair designs we develop several desirable properties of time dependent association measures and study three measures motivated by these properties we examine the measures from a general bivariate survival perspective and for the proportional hazards frailty model we use monozygotic mz and dizygotic dz twin data from the danish twin registry to illustrate how these measures depend on the specification of the proportional hazards frailty model this model consists of two components a baseline hazard function and a frailty distribution we produce gamma and nonparametric maximum likelihood estimates of the frailty distribution and estimate a gompertz baseline hazard function for two of the measures a nonparametric estimate provides a comparison to the model based estim

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

the fuzzy rule base solution of differential equations abstract the equivalence between differential equation models and fuzzy logic models is demonstrated for a certain family of fuzzy systems those which use fuzzy spline wavelets as membership functions the universal approximation property of fuzzy systems built with spline wavelets is exploited for replacing operational representations of differential equations with sparse matrix equations the solution of the matrix equations has a direct interpretation as a set of fuzzy rules the fuzzy rule base thus generated provides an approximate solution to the original differential equation while retaining the explanatory power of fuzzy systems the proposed method enjoys the excellent numerical and computational characteristics of the fast wavelet transform

computation of shift operators in orthonormal compactly supported wavelet bases in this paper some algorithms to translate signals using orthonormal compactly supported wavelet bases are introduced the approximation to the shift operator in these bases is obtained and the performance of the different wavelets is studied through examples

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided