an rns discrete fourier transform implementation a novel discrete fourier transform dft implementation is described it is based on the union of number theoretic transforms modular arithmetic and distributed arithmetic in order to achieve megahertz class transform rates with a limited amount of hardware several new technologies are integrated to accelerate complex arithmetic speed a new body of knowledge called the quadratic residue number system qrns is employed to overcome the overflow management problem introduced by the qrns a finite impulse response form of the dft known as the prime factor transform pft is used in order to implement the pft and the required qrns overflow scaling units a fast and compact distributed arithmetic filter daf and number system converter is designed the integrated system is developed and analyzed in the context of existing semiconductor technology the resulting machine is shown to potentially possess megahertz class performance over a 16 to 24 bit data dynamic range in a limited amount of hardware

frequentist validity of posterior quantiles in the presence of a nuisance parameter higher order asymptotics given a random sample from a distribution with density function that depends on an unknown parameter 1 2 we are concerned with frequentist validity up to o n 1 of posterior quantiles of 1 treating 2 as a nuisance parameter we propose to make the best choice of the prior on by matching as far as practicable the posterior and frequentist coverage probabilities up to o n 1

further experiments on supersonic turbulent flow development in a square duct the mean flow structure of supersonic turbulent adiabatic wall flow in a square duct is investigated experimentally over a development length x d 0 50 for a uniform flow mach 3 9 condition at the duct inlet the results show that a secondary flow cell structure develops which is similar to that for the incompressible case development of the primary flow is influenced by the combined effects of the secondary flow and the streamwise adverse pressure gradient total pressure axial mean velocity and mach number profiles are presented which show that the outer flow is sensitive primarily to the streamwise pressure gradient while flow in the near wall region is dominated by the secondary flow axial mean velocity profiles plotted in terms of van driest scaled variables show that a well defined log law region exists in the near wall layer this region exists in the presence of a secondary flow which continuously modifies spanwise wall shear stress behavior along the length of the duct

on the coefficient quantization of the fourier basis a family of function bases is devised from a superposition of unit characteristic functions it is shown that these simple bases can be used to perform a quantized fourier transform furthermore the transform can be implemented in an iterative scheme such that system resources are balanced in accordance with performance

new square wave transform for digital signal processing a novel transform for spectral decomposition that uses regular square waves as the basis functions is presented the digital transform requires order n operations the transform possesses unusually symmetry properties which may prove useful in many applications in particular it can act as a generalized frequency filter that only depends on the periodicity of the data

experimental and numerical investigation of supersonic turbulent flow through a square duct les resultats experimentaux montrent que deux cellules d ecoulement secondaire se developpent autour des coins de maniere semblable a celle observee dans le cas incompressible les resultats numeriques sont bases sur le modele de baldwin lomay

wall normal free reynolds stress closure for three dimensional compressible separated flows a near wall reynolds stress closure that is independent of the distance from the wall and of the normal to the walldirection isdevelopedandvalidated particularattention wasgiven intheapplicabilityofthemodeltocomplex three dimensional e ows with shock waves and boundary layer separation in the separated e ow region measurements andmodelcomputations indicatethatthe e atnessparameter aoftheanisotropy tensor aij approaches unity therefore controlofseparation isachieved in themodel through theparticularfunctional dependenceoftherapid pressure strain isotropization of production model coefe cienton a echo termsaretreated by replacing geometric normalsanddistancesbyfunctionsofthegradientsofturbulencelengthscaleandanisotropytensorinvariants the modelisinitiallycomparedwithmeasurementsforcompressiblee at plateboundary layere ows itisthenvalidated by comparison with experimental data in a two dimensional compression corner oblique shock wave boundarylayer interaction at mach 3 finally the model is applied to the computation of the three dimensional interaction of a mach 1 5 1 8 strong shock wave with the boundary layers of a rectangular channel e tted with a swept bump on the lower wall and results are compared with measurements one important advantage of the proposed model is its robustness in complex three dimensional e ows a detailed discussion of therange of validity of the model and possible improvements is presented

conditions for ignoring the missing data mechanism in likelihood inferences for parameter subsets abstractfor likelihood based inferences from data with missing values models are generally needed for both the data and the missing data mechanism however modeling the mechanism can be challenging and parameters are often poorly identified rubin in 1976 showed that for likelihood and bayesian inference sufficient conditions for ignoring the missing data mechanism are a the missing data are missing at random mar in the sense that missingness does not depend on the missing values after conditioning on the observed data and b the parameters of the data model and the missingness mechanism are distinct that is there are no a priori ties via parameter space restrictions or prior distributions between these two sets of parameters these conditions are sufficient but not always necessary and they relate to the full vector of parameters of the data model we propose definitions of partially mar and ignorability for a subvector of the parameters of particular substantive interest for direct likel

elimination of nuisance parameters with reference priors summary the problem of eliminating nuisance parameters is tackled from different points of view standard likelihood techniques such as profile likelihood and its modifications are compared with a bayesian analysis based on reference priors berger bernardo 1992a examples are considered to illustrate what happens in multiparameter problems in particular the frequentist coverage probabilities of the credible sets derived from the reference priors are shown to be better than those computed from a likelihood approach advantages and disadvantages of bayesian and likelihood analyses are discussed

dirichlet multiplication and easily generated function analysis abstract following sine cosine functions sawtooth wave square wave triangular wave and trapezoidal wave become new easily generated periodic functions can a signal be considered to be a superposition of easily generated functions with different frequencies in order to answer this question we generalize fourier analysis to easily generated function analysis including easily generated functions series easily generated function transformation and discrete transformation for easily generated functions the results in this paper make it possible to represent a signal by use of easily generated functions a lot of techniques based on sine cosine functions can be translated into techniques based on easily generated functions because dirichlet multiplication in number theory plays a basic role in easily generated function analysis we briefly introduce this concept and present a related formula the main contents of this paper include dirichlet multiplication and a related formula relations between basic waveforms in electronics easily generated function series easily generated function transformation discrete transformation for easily generated functions and techniques of easily generated function analysis

integrated likelihood functions for non bayesian inference consider a model with parameter 0 where is the parameter of interest and let l denote the likelihood function one approach to likelihood inference for is to use an integrated likelihood function in which is eliminated from l by integrating with respect to a density function the goal of this paper is to consider the problem of selecting so that the resulting integrated likelihood function is useful for non bayesian likelihood inference the desirable properties of an integrated likelihood function are analyzed and these suggest that should be chosen by finding a nuisance parameter that is unrelated to and then taking the prior density for to be independent of such an unrelated parameter is constructed and the resulting integrated likelihood is shown to be closely related to the modified profile likelihood

a bayesian justification of cox s partial likelihood summary in this paper we establish both naive and formal bayesian justifications of cox s 1975 partial likelihood and its various modifications we extend the original work of kalbfieisch 1978 who showed that the partial likelihood is a limiting marginal posterior under noninformative priors for baseline hazards we extend the result to scenarios with timedependent covariates and time varying regression parameters we establish results for continuous time as well as grouped survival data in addition we present a bayesian justification of a modified partial likelihood for handling ties we also present tools for simplification of the gibbs sampling algorithm for implementing partial likelihood based bayesian inference in various practical applications

bayes and likelihood calculations from confidence intervals recently there has been considerable progress on setting good approximate confidence intervals for a single parameter in a multi parameter family here we use these frequentist results as a convenient device for making bayes empirical bayes and likelihood inferences about a simple formula is given that produces an approximate likelihood function l x for with all nuisance parameters eliminated based on any system of approximate confidence intervals the statistician can then modify l x with bayes or empirical bayes information for without worrying about nuisance parameters

supersonic corner flow predictions using the quadratic constitutive relation a series of reynolds averaged navier stokes simulations is performed for a supersonic wall bounded turbulent corner flow these simulations are compared to a high order implicit large eddy simulation for the same geometry and flow conditions inclusion of the quadratic constitutive relation in the reynolds averaged navier stokes simulation results in significant improvement in qualitative agreement with the large eddy simulation specifically the presence of secondary flow a counter rotating vortex pair the range of valid values for the constant in the quadratic constitutive relation formulation is explored additionally the effects on this range from different turbulence models and momentum thickness reynolds numbers for the corner are also examined these effects of the quadratic constitutive relation are explored using both the finite difference fluid solver overflow and the finite volume fluid solver us3d the results indicate that the quadratic constitutive relation term directly affects the str

improvement of corner flow prediction using the quadratic constitutive relation this paper presents results of the implementation of spalart s quadratic constitutive relation into the reynolds averaged navier stokes equations on two applications encountered in applied aerodynamics these applications one in external flow and one in internal flow are intended to be representative of the problem of corner flow simulation with the corner separation size being generally overestimated by classical turbulence models the first application is the dlr f6 wing body configuration used in the drag prediction workshop where a separation occurs at the wing body junction in the case without fairing the second application is the shock induced separation in a rectangular duct it is shown that the quadratic constitutive relation greatly improves the accuracy of the junction flow simulation without worsening the quality of the solution elsewhere

comparison of explicit and traditional algebraic stress models of turbulence a critical comparison of explicit vs traditional algebraic stress models of turbulence is made in an effort to clear up the confusion that appears to have been generated by the recently published literature on the subject in which disparate approaches are adopted the only way that general second order closures can formally lead to fully explicit algebraic stress models in a global sense is in the limit of equilibrium homogeneous turbulence when these fully explicit models are then applled to turbulent flows that are far from equilibrium a singularity can arise which can be removed by a systematic regularization when solved explicitly either analytically or numerically the traditional implicit algebraic stress models have either multiple solutions or singularities which tends to explain why they have had problems in applications to complex flows thus it is argued that traditional algebraic stress models are intrinsically ill behaved and should be abandoned in future applications in favor of regularized explicit algebraic stress models it is furthermore argued that these should be based on the homogeneous equilibrium hypothesis which allows for more general second order closures to be used to obtain single valued models

fourier analysis and signal processing by use of the mobius inversion formula a novel fourier technique for digital signal processing is developed this approach to fourier analysis is based on the number theoretic method of the mobius inversion of series the fourier transform method developed is shown also to yield the convolution of two signals a computer simulation shows that this method for finding fourier coefficients is quite suitable for digital signal processing it competes with the classical fft fast fourier transform approach in terms of accuracy complexity and speed

linear programming algorithms for sparse filter design in designing discrete time filters the length of the impulse response is often used as an indication of computational cost in systems where the complexity is dominated by arithmetic operations the number of nonzero coefficients in the impulse response may be a more appropriate metric to consider instead and computational savings are realized by omitting arithmetic operations associated with zero valued coefficients this metric is particularly relevant to the design of sensor arrays where a set of array weights with many zero valued entries allows for the elimination of physical array elements resulting in a reduction of data acquisition and communication costs however designing a filter with the fewest number of nonzero coefficients subject to a set of frequency domain constraints is a computationally difficult optimization problem this paper describes several approximate polynomial time algorithms that use linear programming to design filters having a small number of nonzero coefficients i e filters that are sparse specifically we present two approaches that have different computational complexities in terms of the number of required linear programs the first technique iteratively thins the impulse response of a non sparse filter until frequency domain constraints are violated the second minimizes the 1 norm of the impulse response of the filter using the resulting design to determine the coefficients that are constrained to zero in a subsequent re optimization stage the algorithms are evaluated within the contexts of array design and acoustic equalization

experiments on supersonic turbulent flow development in a square duct les experiences sont concues de telle sorte qu on minimise les effets d onde et de distorsions induites par la tuyere dans l ecoulement determination des contours de pression totale et des distributions du coefficient de frottement superficiel local comparaison avec le cas incompressible

bayesian exponentially tilted empirical likelihood summary while empirical likelihood has been shown to exhibit many of the properties of conven tional parametric likelihoods a formal probabilistic interpretation has so far been lacking we show that a likelihood function very closely related to empirical likelihood naturally arises from a nonparametric bayesian procedure which places a type of noninformative prior on the space of distributions this prior gives preference to distributions having a small support and among those sharing the same support it favours entropy maximising distributions the resulting nonparametric bayesian procedure admits a computationally convenient representation as an empirical likelihood type likelihood where the probability weights are obtained via exponential tilting the proposed methodology provides an attractive alternative to the bayesian bootstrap as a nonparametric limit of a bayesian procedure for moment condition models

algorithms meeting the lower bounds on the multiplicative complexity of length 2 sup n dfts and their connection with practical algorithms in a previous work see electron lett vol 20 no 17 p 690 1984 the author described an algorithm that computes a length 2 sup n discrete fourier transform using 2 sup 2 1 2n sup 2 4n 8 nontrivial i e not or j or square root 1 complex multiplications in the present work it is first shown that this algorithm actually provides the attainable lower bound on the number of complex multiplications a slight modification of the last step of this algorithm is also shown to provide the attainable lower bound on the number of real multiplications a connection with the split radix fft algorithm srfft is then explained showing that srfft is another variation of these optimal algorithms where the last step is computed recursively from shorter ffts in a suboptimal manner finally once the connection between the minimal complexity and srfft which is the best known practical algorithm is understood it provides useful information on the possibility of further improvements of the srfft

on a property of probability matching priors matching the alternative coverage probabilities summary in frequentist inference based on confidence sets both the true coverage and the probability for a confidence set to include an alternative value of the parameter of interest are important thus if probability matching priors also match such alternative coverage probabilites there is perhaps a stronger justification for calling them noninformative considering contiguous alternatives we obtain the relevant necessary and sufficient conditions in particular with n denoting the sample size it is seen that probability matching priors up to o n 2 also match the alternative coverage probabilities up to that order while this is not necessarily the case with probability matching priors up to o n

bayesian empirical likelihood summary research has shown that empirical likelihood tests have many of the same asymptotic properties as those derived from parametric likelihoods this leads naturally to the possibility of using empirical likelihood as the basis for bayesian inference different ways in which this goal might be accomplished are considered the validity of the resultant posterior inferences is examined as are frequentist properties of the bayesian empirical likelihood intervals

the poorman s transform approximating the fourier transform without multiplication a time domain to frequency domain transformation for sampled signals which is computed with only additions and trivial complex multiplications is described this poorman s transform is an approximation to the usual fourier transform obtained by quantizing the fourier coefficients to the four values or 1 or j and is especially useful when multiplication is expensive for the general case of an n point quantization an analytic formula is given for the error in the approximation which involves only contributions from aliased harmonics continuous time signals are considered in this case the approximation is exact for bandlimited signals

noninformative priors for one parameter of many summary we consider the problem of constructing a prior that is noninformative for a single parameter in the presence of nuisance parameters our approach is to require that the resulting marginal posterior intervals have accurate frequentist coverage stein 1985 derived nonrigorously a sufficient condition for such a prior through the use of orthogonal parameters we give a general form for the class of priors satisfying stein s condition the priors are proportional to the square root of the information element for the parameter of interest times an arbitrary function of the nuisance parameters this is in contrast to jeffreys 1946 invariant prior for the overall parameter which is proportional to the square root of the determinant of the information matrix several examples are given and comparisons are made to the reference priors of bernardo 1979

on the equivalence between a minimal codomain cardinality riesz basis construction a system of hadamard sylvester operators and a class of sparse binary optimization problems piecewise low order polynomial riesz basis families are constructed such that they share the same coefficient functionals of smoother orthonormal bases in a localized indexing subset it is shown that a minimal cardinality basis codomain can be realized by inducing sparsity via l1 regularization in the distributional derivatives of the basis functions and that the optimal construction can be found numerically by constrained binary optimization over a suitably large dictionary furthermore it is shown that a subset of these solutions are equivalent to a specific constrained analytical solution derived via sylvester type hadamard operators

pattern mixture models for multivariate incomplete data consider a random sample on variables x1 xv with some values of xv missing selection models specify the distribution of x1 xv over respondents and nonrespondents to xv and the conditional distribution that xv is missing given x1 xv in contrast pattern mixture models specify the conditional distribution of x 1 xv given that xv is observed or missing respectively and the marginal distribution of the binary indicator for whether or not xv is missing for multivariate data with a general pattern of missing values the literature has tended to adopt the selection modeling approach see for example little and rubin here pattern mixture models are proposed for this more general problem pattern mixture models are chronically underidentified in particular for the case of univariate nonresponse mentioned above there are no data on the distribution of xv given x1 xv 1 in the stratum with xv missing thus the models require restrictions or prior information to identify the paramet

on the implementation of local probability matching priors for interest parameters probability matching priors are priors for which the posterior probabilities of certain specified sets are exactly or approximately equal to their coverage probabilities these priors arise as solutions of partial differential equations that may be difficult to solve either analytically or numerically recently levine casella 2003 presented an algorithm for the implementation of probability matching priors for an interest parameter in the presence of a single nuisance parameter in this paper we develop a local implementation that is very much more easily computed a local probability matching prior is a data dependent approximation to a probability matching prior and is such that the asymptotic order of approximation of the frequentist coverage probability is not degraded we illustrate the theory with a number of examples including three discussed in levine casella 2003

improvements to the quadratic constitutive relation based on nasa juncture flow data modifications to the quadratic constitutive relations qcrs of spalart strategies for turbulence modelling and simulation international journal of heat and fluid flow vol 21 2000 pp 252 2

likelihood functions for inference in the presence of a nuisance parameter consider inference about a scalar parameter of interest in the presence of a vector nuisance parameter inference about is often based on a pseudolikelihood function in this paper the general problem of constructing a pseudo loglikelihood function h is considered conditions are given under which h has the same properties as a genuine loglikelihood function for a model without a nuisance parameter when these conditions are satisfied to a given order of approximation h is said to be a jth order local loglikelihood function the theory of local loglikelihood functions is developed and it is shown that second order versions of these have a number of desirable properties several commonly used pseudolikelihood functions are studied from this point of view one commonly used pseudolikelihood function is profile likelihood in which parameters other than 0 are replaced by their maximum likelihood estimates a second aspect of the paper is to consider the use of other estimates in this context examples are given which suggest that inference about may be improved if a method other than maximum likelihood is used particularly when the number of other parameters is large relative to the sample size

a hybrid explicit implicit numerical algorithm for the three dimensional compressible navier stokes equations a hybrid explicit implicit numerical algorithm has been developed for the three dimensional mean compressible navier stokes equations the algorithm combines the explicit finite difference algorithm of maccormack and an implicit algorithm for the viscous sublayer and transition wall regions of the turbulent boundary layers the algebraic turbulent eddy viscosity model of baldwin and lomax is employed a bodyoriented coordinate transformation is utilized to facilitate treatment of arbitrary flow regions the hybrid algorithm has been vectorized on the cdc cyber 203 computer using the sl 1 vector programming language developed at nasa langley the accuracy of the numerical algorithm established previously for twodimensional flows with strong viscous inviscid interaction including flow separation is validated for threedimensional flows the algorithm is applied to the interaction of an oblique shock wave with a turbulent boundary layer in three dimensions the computed results generally are found to be in close agreement with the experimental data the hybrid algorithm is shown to provide a substantial improvement in computational efficiency compared to a vectorized maccormack explicit algorithm alone

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

investigation of a nonlinear reynolds averaged navier stokes closure for corner flows this study gives an insight into the corner flow around a wing mounted on a flat plate reynolds averaged navier stokes simulations and experimental data are compared for a reynolds number based on the wing chord rec equal to 3 105 and an angle of attack of 12 deg the flat plate and wing boundary layers are fully turbulent and the reynolds number based on the momentum thickness of the incoming boundary layer is equal to re 2200 it is shown that the reynolds averaged navier stokes simulation using the spalart allmaras model with the boussinesq closure predicts a massive corner flow separation whereas on the experimental side the separation is confined to a small area better predictions are obtained when resorting to the spalart allmaras model with the quadratic constitutive relation closure a comprehensive investigation of the numerical results using the experimental data is performed to get a better understanding of the behavior of the spalart allmaras quadratic constitutive relation model for t

turbulence modeling in rotating and curved channels assessing the spalart shur correction aunie edapproachtosystem rotationandstreamline curvatureeffectsintheframeworkofsimpleeddy viscosity turbulence models is exercised in a range of rotating and curved channel e ows the spalart allmaras sa oneequation turbulence model spalart p r and allmaras s r a one equation turbulence model for aerodynamic flows aiaapaper 92 0439 1992 modie ed in thismanner is shown to bequitecompetitivewith advanced nonlinear and reynolds stress models and to be much more accurate than the original sa model and other eddyviscosity models that are widely used for industrial e ow computations the new term adds about 20 to the computing cost but does not degrade convergence

clarifying missing at random and related definitions and implications when coupled with exchangeability we clarify the key concept of missingness at random in incomplete data analysis we first distinguish between data being missing at random and the missingness mechanism being a missing at random one which we call missing always at random and which is more restrictive we further discuss how in general neither of these conditions is a statement about conditional independence we then consider the implication of the more restrictive missing always at random assumption when coupled with full unit exchangeability for the matrix of the variables of interest and the missingness indicators the conditional distribution of the missingness indicators for any variable that can have a missing value can depend only on variables that are always fully observed we discuss implications of this for modelling missingness mechanisms

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

implementing matching priors for frequentist inference summary nuisance parameters do not pose any problems in bayesian inference as marginalisation allows for study of the posterior distribution solely in terms of the parameter of interest however no general solution is available for removing nuisance parameters under the frequentist paradigm in this paper we merge the two approaches to construct a general procedure for frequentist elimination of nuisance parameters through the use of matching priors in particular we perform bayesian marginalisation with respect to a prior distribution under which posterior inferences have approximate frequentist validity matching priors are constructed as solutions to a partial differential equation unfortunately except in simple cases these partial differential equations do not yield to analytical nor even standard numerical methods of solution we present a numerical monte carlo algorithm for obtaining the matching prior in general as a solution to the appropriate partial differential equation and draw posterior inferences to be specific we develop an automated routine through an implementation of the metropolis hastings algorithm for deriving frequentist valid inferences via the matching prior we illustrate our results in the contexts of fitting random effects models fitting logistic regression models and fitting teratological data by beta binomial models

prior distributions from pseudo likelihoods in the presence of nuisance parameters consider a model parameterized by where is the parameter of interest the problem of eliminating the nuisance parameter can be tackled by resorting to a pseudo likelihood function l for namely a function of only and the data y with properties similar to those of a likelihood function if one treats l as a true likelihood the posterior distribution y l for can be considered where is a prior distribution on the goal of this article is to construct probability matching priors for a scalar parameter of interest only i e priors for which bayesian and frequentist inference agree to some order of approximation to be used in y when l is a marginal a conditional or a modification of the profile likelihood we show that is simply proportional to the square root of the inverse of the asymptotic variance of the pseudo maximum likelihood estimator the proposed priors are compared with the reference or jeffreys priors in four

proper likelihoods for bayesian analysis summary the validity of posterior probability statements follows from probability calculus when the likelihood is the density of the observations to investigate other cases a second more intuitive definition of validity is introduced based on coverage of posterior sets this notion of validity suggests that the likelihood must be the density of a statistic not necessarily sufficient for posterior probability statements to be valid a convenient numerical method is proposed to invalidate the use of certain likelihoods for bayesian analysis integrated marginal and conditional likelihoods derived to avoid nuisance parameters are also discussed

bayesian intervals with good frequentist behaviour in the presence of nuisance parameters given a random sample from a distribution with density function that depends on an unknown parameter 1 p we are concerned with the problem of setting confidence intervals for a particular component of it say 1 treating the remaining components as a nuisance parameter adopting an objective bayesian approach we show that the bayes intervals with a certain conditional prior density on the parameter of interest 1 are confidence intervals as well having nearly the correct frequency of coverage the frequentist performance of the proposed intervals is tested in a simulation study for gamma mean and shape parameters

a polynomial time algorithm for designing fir filters with power of two coefficients this paper presents a polynomial time algorithm for designing digital filters with coefficients expressible as sums of signed power of two spt terms our proposal is based on an observation that under certain circumstances the realization cost of a filter with spt coefficients depends only on the total number of spt terms regardless of how the terms distribute among the coefficients therefore the number of spt terms for each coefficient is not necessarily limited to a fixed number instead they should be allowed to vary subject to a given number of total spt terms for the filter this provides the possibility of finding a better set of coefficients our algorithm starts with initializing all the quantized coefficient values to zero it chooses one spt term at a time and allocates it to the currently most deserving coefficient to minimize the l sup spl infin distance between the spt coefficients and their corresponding infinite wordlength values this process of allocating the spt terms is repeated until the total number of spt terms for the filter is equal to a prescribed number for each filter gain the time complexity is a second order polynomial in the number of coefficients to be optimized and is a first order polynomial in the filter wordlength

data parallel line relaxation method for the navier stokes equations the gauss seidel line relaxation method is modie ed for the simulation of viscous e ows on massively parallel computers the resulting data parallel line relaxation method is shown to have good convergence properties for a seriesoftestcases thenewmethodrequiressignie cantlymorememorythanthepreviouslydevelopeddata parallel relaxation methods but it reaches a steady state solution in much less time for all cases tested to date in addition the data parallel line relaxation method shows good convergence properties even on the high cell aspect ratio grids required to simulate high reynolds number e ows the new method is implemented using message passing on the cray t3e and the parallel performance of the method on this machine is discussed the data parallel line relaxation method combines the fast convergence of the gauss seidel line relaxation method with a high parallel efe ciency and thus shows promise for large scale simulation of viscous e ows

on priors providing frequentist validity for bayesian inference summary we derive the differential equation that a prior must satisfy if the posterior probability of a one sided credibility interval for a parametric function and its frequentist probability agree up to o n 1 this equation turns out to be identical with stein s equation for a slightly different problem for which also our method provides a rigorous justification our method is different in details from stein s but similar in spirit to dawid 1991 and bickel ghosh 1990 some examples are provided