testing by verifying walsh coefficients testing of logic networks by verifying the walsh coefricients of the outputs is explored measurement of one of these can detect arbitrarily many input leads stuck and just two measurements requiring little hardware can detect any single stuck at fault in appropriately designed networks

reference bayesian methods for generalized linear mixed models abstract bayesian methods furnish an attractive approach to inference in generalized linear mixed models in the absence of subjective prior information for the random effect variance components these analyses are typically conducted using either the standard invariant prior for normal responses or diffuse conjugate priors previous work has pointed out serious difficulties with both strategies and we show here that as in normal mixed models the standard invariant prior leads to an improper posterior distribution for generalized linear mixed models this article proposes and investigates two alternative reference i e objective or noninformative priors an approximate uniform shrinkage prior and an approximate jeffreys s prior we give conditions for the existence of the posterior distribution under any prior for the variance components in conjunction with a uniform prior for the fixed effects the approximate uniform shrinkage prior is shown to satisfy these conditions for several families of d

distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution summary a fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry and to generate a whole set of non symmetric densities the approach is sufficiently general to encompass some recent proposals in the literature variously related to the skew normal distribution the special case of skew elliptical densities is examined in detail establishing connections with existing similar work the final part of the paper specializes further to a form of multivariate skew t density likelihood inference for this distribution is examined and it is illustrated with numerical examples

linear mixed models for skew normal independent bivariate responses with an application to periodontal disease bivariate clustered correlated data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed model framework with underlying normality assumptions of the random effects and within subject errors however such normality assumptions might be questionable if the data set particularly exhibit skewness and heavy tails using a bayesian paradigm we use the skew normal independent sni distribution as a tool for modeling clustered data with bivariate non normal responses in a linear mixed model framework the sni distribution is an attractive class of asymmetric thick tailed parametric structure which includes the skew normal distribution as a special case we assume that the random effects follows multivariate skew normal independent distributions and the random errors follow symmetric normal independent distributions which provides substantial robustness over the symmetric normal process in a linear mixed model framework specific distributions obtained as special cases viz the skew t the skew slash and the skew contaminated normal distributions are compared along with the default skew normal density the methodology is illustrated through an application to a real data which records the periodontal health status of an interesting population using periodontal pocket depth ppd and clinical attachment level cal

accumulator compression testing a new test data reduction technique called accumulator compression testng act is proposed act is an extension of syndrome testing it is shown that the enumeration of errors missed by act for a unit under test is equivalent to the number of restricted partitions of a number asymptotic results are obtained for independent and dependent error modes comparison is made between signature analysis sa and act theoretical results indicate that with act a better control over fault coverage can be obtained than with sa experimental results are supportive of this indication built in self test for processor environments may be feasible with act however for general vlsi circuits the complexity of act may be a problem as an adder is necessary

test pattern generation based on reed muller coefficients reed muller coefficients are used to generate a test pattern selection procedure for detecting single stuck at faults this procedure is based on the heuristics deduced from the way in which the spectral coefficients are affected by such faults the changes that the spectral coefficients undergo are also compared with the fault models used most frequently to model defects in combinational circuits the proposed pattern generating procedure does not need a simulation of the circuit for each of the possible stuck at faults and its complexity is proportional to the number of gates in the circuit the proportionality constant increases exponentially as the number of inputs in the circuit increases to evaluate the performance of the proposed method its application to some benchmark circuits including the alu 74181 is presented

on conformal deformations of metrics onsn abstract on s n there is a naturally metric defined n th order conformal invariant operator p n associated with this operator is a so called q curvature quantity when two metrics are pointwise conformally related their associated operators together with their q curvatures satisfy the natural differential equations this paper is devoted to the question of which function can be a q curvature candidate this is the so called prescribing q curvature problem our main result is that if q is positive nondegenerate and the naturally defined mapping associated with q has nonzero degree then our problem has a solution this is the natural generalization of prescribing gaussian curvature on s 2 into s n

q curvature flow on 4 manifolds with boundary given a compact four dimensional smooth riemannian manifold m g with smooth boundary we consider the evolution equation by q curvature in the interior keeping the t curvature and the mean curvature to be zero using integral methods we prove global existence and convergence for the q curvature flow to a smooth metric conformal to g of prescribed q curvature zero t curvature and vanishing mean curvature under conformally invariant assumptions

q curvature flow on the standard sphere of even dimension using a gradient flow approach initiated by s brendle we generalize the existence theorem for the prescribing q curvature equation on s2 gauss curvature by m struwe 2005 14 and on s4 by malchiodi and struwe 2006 12 to sn for all even n with the similar assumption on the prescribed curvature candidate f

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

a bayesian population model with hierarchical mixture priors applied to blood count data abstract population pharmacokinetic and pharmacodynamic studies require analyzing nonlinear growth curves fit to multiple measurements from study subjects we propose a class of nonlinear population models with nonparametric second stage priors for analyzing such data the proposed models apply a flexible class of mixtures to implement the nonparametric second stage the discussion is based on a pharmacodynamic study involving longitudinal data consisting of hematologic profiles i e blood counts measured over time of cancer patients undergoing chemotherapy we describe a full posterior analysis in a bayesian framework this includes prediction of future observations profiles and end points for new patients estimation of the mean response function for observed individuals and inference on population characteristics the mixture model is specified and given a hyperprior distribution by means of a dirichlet processes prior on the mixing measure estimation is implemented by a combination of various m

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

the profile of bubbling solutions of a class of fourth order geometric equations on 4 manifolds abstract we study a class of fourth order geometric equations defined on a 4 dimensional compact riemannian manifold which includes the q curvature equation we obtain sharp estimates on the difference near the blow up points between a bubbling sequence of solutions and the standard bubble

bayesian semiparametric variable selection with applications to periodontal data a normality assumption is typically adopted for the random effects in a clustered or longitudinal data analysis using a linear mixed model however such an assumption is not always realistic and it may lead to potential biases of the estimates especially when variable selection is taken into account furthermore flexibility of nonparametric assumptions e g dirichlet process on these random effects may potentially cause centering problems leading to difficulty of interpretation of fixed effects and variable selection motivated by these problems we proposed a bayesian method for fixed and random effects selection in nonparametric random effects models we modeled the regression coefficients via centered latent variables which are distributed as probit stick breaking scale mixtures by using the mixture priors for centered latent variables along with covariance decomposition we could avoid the aforementioned problems and allow efficient selection of fixed and random effects from the model we demonstrated the advantages of our proposed approach over other competing alternatives through a simulated example and also via an illustrative application to a data set from a periodontal disease study copyright 2017 john wiley sons ltd

global existence and convergence for a higher order flow in conformal geometry an important problem in conformal geometry is the construction of conformal metrics for which a certain curvature quantity equals a prescribed function e g a constant in two dimensions the uniformization theorem assures the existence of a conformal metric with constant gauss curvature moreover j moser 20 proved that for every positive function f on s2 satisfying f x f x for all x e s2 there exists a conformal metric on s2 whose gauss curvature is equal to f a natural conformal invariant in dimension four is 1 2 q ar r2 3 irici2 where r denotes the scalar curvature and ric the ricci tensor this formula can also be written in the form

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

the effect of improper priors on gibbs sampling in hierarchical linear mixed models abstract often either from a lack of prior information or simply for convenience variance components are modeled with improper priors in hierarchical linear mixed models although the posterior distributions for these models are rarely available in closed form the usual conjugate structure of the prior specification allows for painless calculation of the gibbs conditionals thus the gibbs sampler may be used to explore the posterior distribution without ever having established propriety of the posterior an example is given showing that the output from a gibbs chain corresponding to an improper posterior may appear perfectly reasonable thus one cannot expect the gibbs output to provide a red flag informing the user that the posterior is improper the user must demonstrate propriety before a markov chain monte carlo technique is used a theorem is given that classifies improper priors according to the propriety of the resulting posteriors applications concerning bayesian analysis of animal breeding

mixed models for bivariate response repeated measures data using gibbs sampling repeated measures data are frequently incomplete unbalanced and correlated there has been a great deal of recent interest in mixed effects models for analysing such data in this paper we develop bivariate response mixed effects models that are a generalization of linear mixed effects models for a single response variable we describe their estimation procedures using a markov chain monte carlo method the gibbs sampler we illustrate the methods with analyses of intravenous vitamin d3 administration for secondary hyperparathyroidism in hemodialysis patients in these data there were two response variables on each individual pth and calcium level this study also suffered from attrition like many longitudinal studies while considering the study design it was reasonable to assume the drop out mechanism for the calcium ca level to be missing at random the drop out mechanism for the pth level was likely to be non ignorable we found that the posterior treatment effects for the pth level by the single response model were underestimated compared with those obtained by the bivariate response model while there were little differences in the posterior features for the ca level under both models

a mixed effect model for positive responses augmented by zeros in this research article we propose a class of models for positive and zero responses by means of a zero augmented mixed regression model under this class we are particularly interested in studying positive responses whose distribution accommodates skewness at the same time responses can be zero and therefore we justify the use of a zero augmented mixture model we model the mean of the positive response in a logarithmic scale and the mixture probability in a logit scale both as a function of fixed and random effects moreover the random effects link the two random components through their joint distribution and incorporate within subject correlation because of the repeated measurements and between subject heterogeneity a markov chain monte carlo algorithm is tailored to obtain bayesian posterior distributions of the unknown quantities of interest and bayesian case deletion influence diagnostics based on the q divergence measure is performed we apply the proposed method to a dataset from a 24 hour dietary recall study conducted in the city of sao paulo and present a simulation study to evaluate the performance of the proposed methods

a semiparametric approach to simultaneous covariance estimation for bivariate sparse longitudinal data estimation of the covariance structure for irregular sparse longitudinal data has been studied by many authors in recent years but typically using fully parametric specifications in addition when data are collected from several groups over time it is known that assuming the same or completely different covariance matrices over groups can lead to loss of efficiency and or bias nonparametric approaches have been proposed for estimating the covariance matrix for regular univariate longitudinal data by sharing information across the groups under study for the irregular case with longitudinal measurements that are bivariate or multivariate modeling becomes more difficult in this article to model bivariate sparse longitudinal data from several groups we propose a flexible covariance structure via a novel matrix stick breaking process for the residual covariance structure and a dirichlet process mixture of normals for the random effects simulation studies are performed to investigate the effectiveness of the proposed approach over more traditional approaches we also analyze a subset of framingham heart study data to examine how the blood pressure trajectories and covariance structures differ for the patients from different bmi groups high medium and low at baseline

estimates and extremals for zeta function determinants on four manifolds leta be a positive integral power of a natural conformally covariant differential operator on tensor spinors in a riemannian manifold suppose thata is formally self adjoint and has positive definite leading symbol for example a could be the conformal laplacian yamabe operator l or the square of the dirac operator open image in new window within the conformal class left g e 2w g 0 w in c infty m right of an einstein locally symmetric background metricgo on a compact four manifoldm we use an exponential sobolev inequality of adams to show that bounds on the functional determinant ofa and the volume ofg imply bounds on thew2 2 norm of the conformal factorw provided that a certain conformally invariant geometric constantk k m g o a is strictly less than 32 2 we show for the operatorsl and open image in new window that indeedk 32 2 except when m g o is the standard sphere or a hyperbolic space form on the sphere a centering argument allows us to obtain a bound of the same type despite the fact thatk is exactly equal to 32 2 in this case finally we use an inequality of beckner to show that in the conformal class of the standard four sphere the determinant ofl or of open image in new window is extremized exactly at the standard metric and its images under the conformal transformation groupo 5 1

an analysis of the use of rademacher walsh spectrum in compact testing earlier approaches to random compact testing use a random pattern generator which depends on the combinational function under test and a circuit signature which remains the same independent of the circuit in this correspondence we analyze the performance of a new scheme in which the pattern generator is simple and independent of the function being tested but the circuit signature is chosen to be a coefficient from the rademacher walsh rw spectrum of the function under test the analysis provides guidelines for choosing an rw coefficient a test length and an error tolerance so as to minimize the probabilities of rejecting a good unit or accepting a faulty one

the scalar curvature flow on s n perturbation theorem revisited for the problem of finding a geometry on s n for n 3 with a prescribed scalar curvature there is a well known result which is called the perturbation theorem it is due to chang and yang duke math j 64 27 69 1991 their key assumption is that the candidate f for the prescribed scalar curvature is sufficiently near the scalar curvature of the standard metric in the sup norm it is important to know how large that difference in sup norm can possibly be here we consider prescribing scalar curvature problem using the scalar curvature flow

the q curvature on a 4 dimensional riemannian manifold m g with mqdvg 8π2 abstract we deal with the q curvature problem on a 4 dimensional compact riemannian manifold m g with m q g d v g 8 2 and positive paneitz operator p g let q be a positive smooth function the question we consider is when can we find a metric g which is conformal to g such that q is just the q curvature of g a sufficient condition to this question is given in this paper

linear mixed models with flexible distributions of random effects for longitudinal data normality of random effects is a routine assumption for the linear mixed model but it may be unrealistic obscuring important features of among individual variation we relax this assumption by approximating the random effects density by the seminonparameteric snp representation of gallant and nychka 1987 econometrics 55 363 390 which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior controlled by a user chosen tuning parameter an advantage is that the marginal likelihood may be expressed in closed form so inference may be carried out using standard optimization techniques we demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality and we illustrate the approach via simulation and using longitudinal data from the framingham study

semiparametric bayesian latent variable regression for skewed multivariate data for many real life studies with skewed multivariate responses the level of skewness and association structure assumptions are essential for evaluating the covariate effects on the response and its predictive distribution we present a novel semiparametric multivariate model and associated bayesian analysis for multivariate skewed responses similar to multivariate gaussian densities this multivariate model is closed under marginalization allows a wide class of multivariate associations and has meaningful physical interpretations of skewness levels and covariate effects on the marginal density other desirable properties of our model include the markov chain monte carlo computation through available statistical software and the assurance of consistent bayesian estimates of the parameters and the nonparametric error density under a set of plausible prior assumptions we illustrate the practical advantages of our methods over existing alternatives via simulation studies and the analysis of a clinical study on periodontal disease

statistical applications of the multivariate skew normal distribution azzalini and dalla valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter the first part of the present paper examines further probabilistic properties of the distribution with special emphasis on aspects of statistical relevance inferential and other statistical issues are discussed in the following part with applications to some multivariate statistics problems illustrated by numerical examples finally a further extension is described which introduces a skewing factor of an elliptical density

a fast algorithm for optimum syndrome space compression a procedure for multiple output combinational circuits is presented that yields the optimum space compressor while using counting for time compression the procedure is intended for the built in selftest environment where output response data compression is appropriate optimum is defined as the minimum number of error patterns missed by the combination of space and time compression the procedure uses the fast walsh transform to determine the number of errors missed by each linear combination for all possible space compression combinations a illustrative example is included to show the effectiveness of the algorithm a comparison between cases with and without space compression is included

a linear mixed effects model with heterogeneity in the random effects population abstract this article investigates the impact of the normality assumption for random effects on their estimates in the linear mixed effects model it shows that if the distribution of random effects is a finite mixture of normal distributions then the random effects may be badly estimated if normality is assumed and the current methods for inspecting the appropriateness of the model assumptions are not sound further it is argued that a better way to detect the components of the mixture is to build this assumption in the model and then compare the fitted model with the gaussian model all of this is illustrated on two practical examples

a unified view of test compression methods a unified treatment of the various techniques to reduce the output data from a unit under test is given the characteristics of time compression schemes with respect to errors detected are developed the use of two or more of these methods together is considered methods to design efficient test compression structures for built in tests are proposed the feasibility of the proposed approach is demonstrated by simulation results

on the impossible class of faulty functions in logic networks under short circuit faults the important problem of recognizing a priori the class of boolean functions which are never obtainable from a given combinational network under short circuit faults is almost unexplored primarily due to lack of understanding of the functional and structural factors that influence the fault behavior in the network in view of this a new concept of impossible class of faulty functions icff is introduced in this correspondence several intriguing properties of icff are uncovered namely the undetectability of input bridging faults the impossibility of the transformation of a fault free function fo to a subset or superset of fo and to other functions belonging to the same p and n equivalence classes of fo etc the closure amongst the fan out free and unate functions under bridging faults is investigated the impact of icff on the testability of the network is also discussed

spectral analysis of boolean functions as a graph eigenvalue problem several problems in digital logic can be conveniently approached in the spectral domain in this paper we show that the walsh spectrum of boolean functions can be analyzed by looking at algebraic properties of a class of cayley graphs associated with boolean functions we use this idea to investigate the walsh spectrum of certain special functions

spectral signature testing of multiple stuck at faults in irredundant combinational networks earlier spectral signature testing methods are extended to the multiple stuck at fault model the testability condition for multiple input faults is established and a minimal spanning signature mss is defined to cover all these faults it is then shown that an mss which in most cases contains a single spectral coefficient will detect over 99 percent of all input and internal multiple faults an approach is described to obtain a complete signature for all multiple faults in any irredundant combinational network with comparatively small numbers of fan outs tree networks that include xor xnor gates are shown to be easily tested internally fan out free and general irredundant networks are also considered a design approach is proposed to enable a network to be tested for all single and most multiple faults using a single coefficient with the possible overhead being an extra control input

smooth random effects distribution in a linear mixed model a linear mixed model with a smooth random effects density is proposed a similar approach to p spline smoothing of eilers and marx 1996 statistical science 11 89 121 is applied to yield a more flexible estimate of the random effects density our approach differs from theirs in that the b spline basis functions are replaced by approximating gaussian densities fitting the model involves maximizing a penalized marginal likelihood the best penalty parameters minimize akaike s information criterion employing gray s 1992 journal of the american statistical association 87 942 951 results although our method is applicable to any dimensions of the random effects structure in this article the two dimensional case is explored our methodology is conceptually simple and it is relatively easy to fit in practice and is applied to the cholesterol data first analyzed by zhang and davidian 2001 biometrics 57 795 802 a simulation study shows that our approach yields almost unbiased estimates of the regression and the smoothing parameters in small sample settings consistency of the estimates is shown in a particular case

spatial analyses of periodontal data using conditionally autoregressive priors having two classes of neighbor relations attachment loss the extent of a tooth s root in millimeters that is no longer attached to surrounding bone by periodontal ligament is often used to measure the current state of a patient s periodontal disease and monitor disease progression attachment loss data can be analyzed using a conditionally autoregressive car prior distribution that smooths fitted values toward neighboring values however it may be desirable to have more than one class of neighbor relation in the spatial structure so the different classes of neighbor relations can induce different degrees of smoothing for example we may wish to allow smoothing of neighbor pairs bridging the gap between teeth to differ from smoothing of pairs that do not bridge such gaps adequately modeling the spatial structure may improve the monitoring of periodontal disease progression this article develops a two neighbor relation car model to handle this situation and presents associated theory to help explain the sometimes unusual posterior distr

decision diagram method for calculation of pruned walsh transform discrete walsh transform is an orthogonal transform often used in spectral methods for different applications in signal processing and logic design fft like algorithms make it possible to efficiently calculate the discrete walsh spectrum however for their exponential complexity these algorithms are practically unsuitable for large functions for this reason a binary decision diagram bdd based recursive method for walsh spectrum calculation has been introduced in clarke et al 1993 a disadvantage of this algorithm is that the resulting multi terminal binary decision diagram mtbdd representing the walsh spectrum for f can be large for some functions another disadvantage turns out if particular walsh coefficients are to be computed separately the algorithm always calculates the entire spectrum and therefore it is rather inefficient for applications where a subset of walsh spectral coefficients i e the pruned walsh spectrum is required in this paper we propose another bdd based method for walsh spectrum calculation adapted for application where the pruned walsh spectrum is needed the method takes advantage of the property that for most switching functions the size of a bdd for f is usually quite a bit smaller than the size of the mtbdd for the walsh spectrum in our method a mtbdd representing the walsh spectrum is not constructed instead two additional fields are assigned to each node in the bdd for the processed function f these fields are used to store the results of intermediate calculations pairs of spectral coefficients are calculated and stored in the fields assigned to the root node therefore the calculation complexity of the proposed algorithm is proportional to the size of the bdd for f whose spectrum is calculated experimental results demonstrate the efficiency of the approach

uniqueness of stable capillary hypersurfaces in a ball in this paper we prove that any immersed stable capillary hypersurfaces in a ball in space forms are totally umbilical our result also provides a proof of a conjecture proposed by sternberg and zumbrun j reine angew math 503 63 85 1998 we also prove a heintze karcher ros type inequality for hypersurfaces with free boundary in a ball which together with the new minkowski formula yields a new proof of alexandrov s theorem for embedded cmc hypersurfaces in a ball with free boundary

model choice a minimum posterior predictive loss approach summary model choice is a fundamental and much discussed activity in the analysis of datasets nonnested hierarchical models introducing random effects may not be handled by classical methods bayesian approaches using predictive distributions can be used though the formal solution which includes bayes factors as a special case can be criticised we propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values we obtain this criterion by minimising posterior loss for a given model and then for models under consideration selecting the one which minimises this criterion for a broad range of losses the criterion emerges as a form partitioned into a goodness of fit term and a penalty term we illustrate its performance with an application to a large dataset involving residential property transactions

extremal metrics of zeta function determinants on 4 manifolds in conformal geometry the sobolev inequality at a critical exponent has received much attention in particular the determination of the best constants has played a crucial role in the yamabe problem in dimension two the analogous problem deals with the moser trudinger inequality on a compact riemann surface m2 there exists a constant c c m so that f e47w2 c m if f ivw12 1 and f w 0 the connection of this inequality with geometry comes through the zeta functional determinant of the laplacian as defined by ray singer for a riemannian metric g let 0 a1 a2 be the spectrum

the ricci flow on the 2 sphere the classical uniformization theorem interpreted differential geomet rically states that any riemannian metric on a 2 dimensional surface ispointwise conformal to a constant curvature metric thus one can con sider the question of whether there is a natural evolution equation whichconformally deforms any metric on a surface to a constant curvature met ric the primary interest in this question is not so much to give a newproof of the uniformization theorem but rather to understand nonlinearparabolic equations better especially those arising in differential geome try a sufficiently deep understanding of parabolic equations should yieldimportant new results in riemannian geometry the question in the preceding paragraph has been studied by richardhamilton 3 and brad osgood ralph phillips and peter sarnak 6 in 3 hamilton studied the following equation which we refer to as

convergence of the q curvature flow on s4 in this paper we study the q curvature flow on the standard sphere s4 we show that the flow converges exponentially for all initial data

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

spectral fault signatures for single stuck at faults in combinational networks a method is described for the derivation of fault signatures for the detection of stuck at faults in single output combinational networks these signatures consist of a set of values derived from the network any single stuck at fault causes at least one value to change the fault signatures developed are a generalization of syndrome testing the technique is developed in the rademacher walsh spectral domain but is easily implemented using conters and basic gates

spectral fault signatures for internally unate combinational networks a method is described for the derivation of fault signatures for certain classes or irredundant combinational networks these signatures consist of a set of values derived from the network any stuck at fault causes at least one of the values to change the signatures provide complete fault detection for all single stuck at faults they are usually short and never contain more than n 1 values for an n input network