types and unitary representations of reductive p adic groups we prove that for every bushnell kutzko type that satisfies a certain rigidity assumption the equivalence of categories between the corresponding bernstein component and the category of modules for the hecke algebra of the type induces a bijection between irreducible unitary representations in the two categories moreover we show that every irreducible smooth g representation contains a rigid type this is a generalization of the unitarity criterion of barbasch and moy for representations with iwahori fixed vectors

modelling multivariate binary data with alternating logistic regressions marginal models for multivariate binary data permit separate modelling of the relationship of the response with explanatory variables and the association between pairs of responses when the former is the scientific focus a first order generalized estimating equation method liang zeger 1986 is easy to implement and gives efficient estimates of regression coefficients although estimates of the association among the binary outcomes can be inefficient when the association model is a focus simultaneous modelling of the responses and all pairwise products prentice 1988 using second order estimating equations gives more efficient estimates of association parameters as well however this procedure can become computationally infeasible as the cluster size gets large this paper proposes an alternative approach alternating logistic regressions for simultaneously regressing the response on explanatory variables as well as modelling the association among responses in terms of pairwise odds ratios this algorithm iterates between a logistic regression using first order generalized estimating equations to estimate regression coefficients and a logistic regression of each response on others from the same cluster using an appropriate offset to update the odds ratio parameters for clusters of size n alternating logistic regression involves evaluation and inversion of matrices of order n2 rather than n4 as required for second order generalized estimating equations the alternating logistic regression estimates are shown to be reasonably efficient relative to solutions of second order equations in a few problems the new method is illustrated with an analysis of neuropsychological tests on patients with epileptic seizures

discrete series representations for the orbit spaces arising from two involutions of real reductive lie groups leth gbe real reductive lie groups a discrete series representation for a homogeneous spaceg his an irreducible representation ofgrealized as a closedg invariant subspace ofl2 g h the condition for the existence of discrete series representations forg hwas not known in general except for reductive symmetric spaces this paper offers a sufficient condition for the existence of discrete series representations forg hin the setting thatg his a homogeneous submanifold of a symmetric space g hwhereg g h we prove that discrete series representations are non empty for a number of non symmetric homogeneous spaces such assp 2n r sp n0 c gl n1 c gl nk c nj n ando 4m n u 2m j 0 2j n

working covariance model selection for generalized estimating equations we investigate methods for data based selection of working covariance models in the analysis of correlated data with generalized estimating equations we study two selection criteria gaussian pseudolikelihood and a geodesic distance based on discrepancy between model sensitive and model robust regression parameter covariance estimators the gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean variance relations for longitudinal data application is also made to a clinical dataset assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications and we describe open source software supporting this practice

coadjoint orbits and reductive dual pairs let g g be a reductive dual pair of subgroups of the metaplectic group s 2m r where g is compact then the restriction of the oscillator representation o of sp 2m r to g decomposes as x 5 t t where the correspondence zj r is a bijection 7 the modules t are unitary highest weight modules and all such representations are obtained this way 5 on the other hand the unitary highest weight modules of g have been constructed in 3 via derived functors in particular each such representation is associated to is the quantization of a coadjoint orbit for g the purpose of this paper is to establish the connection between these two realizations via the orbit structure of the symplectic manifold r co these results have been known in principle for some time the main problem being an understanding of how to quantize nilpotent and degenerate elliptic coadjoint orbits let 8 lie g 0 lie c let respectively ic be projection from gp 2m r to s respectively a here hom r then and i restriced to the minimal coadjoint orbit i of gp 2m r define the graph of a correspondence between coadjoint gand orbits note that 0 in z r o via the moment map for the action of sp 2m r on r 0 generically this is a bijection nilpotent orbits for c do arise suppose a c orbit 0 corresponds to a orbit c in 111 it was observed that in some cases if we associate representations x o and x p to 0 and 0 via geometric quantization then x o x 0 occurs in wjgg i e x 6 corresponds to x 0 in 2 the derived functor construction was used to quantize some elliptic orbits and this was done in greater generality that is for 0 g i elliptic 8 is cohomologically induced from a one dimensional representation of l stab i and similarly for g if 0 and n 0 have regular infinitesimal character then n o corresponds to 6 at the time 2 was written the modules n o with singular infinitesimal character were not understood furthermore it was not known how 138 oool 8708 87 7 50

entropy analysis of stochastic processes at finite resolution abstract the time evolution of complex systems usually can be described through stochastic processes these processes are measured at finite resolution which necessarily reduces them to finite sequences of real numbers in order to relate these data sets to realizations of the original stochastic processes to any functions indeed it is obligatory to choose an interpolation space for example the space of band limited functions clearly this choice is crucial if the intent is to approximate optimally the original processes inside the interval of measurement here we argue that discrete wavelets are suitable to this end the wavelet approximations of stochastic processes allow us to define an entropy measure for the order disorder balance of evolution regimes of complex systems where order is understood as confinement of energy in simple local modes we calculate exact results for the fractional brownian motion fbm with application to kolmogorov k41 theory for fully developed turbulence

discrete decomposability of the restriction of a_q λ with respect to reductive subgroups ii micro local analysis and asymptotic k support let g c g be real reductive lie groups this paper offers a criterion on the triplet g g ir that the irreducible unitary representation ir of g splits into a discrete sum of irreducible unitary representations of a subgroup g when restricted to g each of finite multiplicity furthermore we shall give an upper estimate of the multiplicity of an irreducible unitary representation of g occurring in wrig

models for correlated multifractal hypersurfaces we discuss and implement computer approximations of fractal and multifractal hypersurfaces these hypersurfaces consist of reconstructions of a stochastic process in the real space from randomly distributed variables in the discrete wavelet domain the synthetic surfaces have the usual fractional brownian motion as a particular case and inherit the correlation structure of these fractals we first introduce the one dimensional version of these surfaces that obey a weak self affine symmetry this symmetry appears in the wavelet domain as a condition on the second moments of the probability distributions of the wavelet coefficients then we use these relations to define the fractals and multifractals in d dimensions finally we concentrate on the generation of samples of these hypersurfaces

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

one dimensional representations of u p q and the howe correspondence abstract we explicitly determine the theta lifts of all one dimensional representations of u p q in terms of langlands parameters and determine exactly which lifts are unitary moreover we show that such a lift is unitary if and only if it is a weakly fair derived functor module of the form a q finally we show that the correspondence of unitary representations behaves well with respect to associated cycles

unitary representations induced from maximal parabolic subgroups abstract it is known that the problem of classifying the irreducible unitary representations of a linear connected semisimple lie group g comes down to deciding which langlands quotients j man v are infinitesimally unitary here man is any cuspidal parabolic subgroup is any discrete series or nondegenerate limit of discrete series representation of m and v is any complex valued linear functional on the lie algebra of a satisfying certain positivity and symmetry properties the authors determine which langlands quotients are infinitesimally unitary under the conditions that g is simple that dim a 1 and that g is neither split f 4 nor split g 2

a modified pseudolikelihood approach for analysis of longitudinal data we consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters in general inconsistent estimators of the covariance variance correlation parameters will be produced when the working correlation matrix is misspecified which may result in great loss of efficiency of the mean parameter estimators albeit the consistency is preserved we consider using different working correlation models for the variance and the mean parameters in particular we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified the designated working correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters simulation studies indicate that the proposed algorithm performs very well we also applied different estimation procedures to a data set from a clinical trial for illustration

on the geometry and quantization of symplectic howe pairs we study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold if the pair of actions fulfils a symplectic howe condition we show that there is a canonical correspondence between the orbit spaces of the respective moment images furthermore we show that reduced spaces with respect to the action of one group are symplectomorphic to coadjoint orbits of the other group in the kahler case we show that the linear representation of a pair of compact connected lie groups on the geometric quantization of the manifold is then equipped with a representation theoretic howe duality

generalized estimating equations for correlated binary data using the odds ratio as a measure of association summary moment methods for analyzing repeated binary responses have been proposed by liang zeger 1986 and extended by prentice 1988 in their generalized estimating equations both liang zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses because the odds ratio has many desirable properties and some investigators may find the odds ratio is easier to interpret we discuss modelling the association between binary responses at pairs of times with the odds ratio we then modify the estimating equations of prentice to estimate the odds ratios in simulations the parameter estimates for the logistic regression model for the marginal probabilities appear slightly more efficient when using the odds ratio parameterization

dirac series for some real exceptional lie groups abstract up to equivalence this paper classifies all the irreducible unitary representations with non zero dirac cohomology for the following simple real exceptional lie groups ei e 6 6 eiv e 6 26 fi f 4 4 fii f 4 20 along the way we find an irreducible unitary representation of f 4 4 whose dirac index vanishes while its dirac cohomology is non zero this disproves a conjecture raised in 2015 asserting that there should be no cancellation between the even part and the odd part of the dirac cohomology

what can go wrong when ignoring correlation bounds in the use of generalized estimating equations the analysis of repeated measure or clustered data is often complicated by the presence of correlation further complications arise for discrete responses where the marginal probability dependent frechet bounds impose feasibility limits on the correlation that are often more restrictive than the positive definite range some popular statistical methods such as generalized estimating equations gee ignore these bounds and as such can generate erroneous estimates and lead to incorrect inferential results in this paper we discuss two alternative strategies i using qic to select a data driven correlation value within the frechet bounds and ii the use of likelihood based latent variable modeling such as multivariate probit to get around the problem all together we provide two examples of the repercussions of incorrectly using existing gee software in the presence of correlated binary responses

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

spectral multiplicity of derived functor modules abstract let be a discrete torsion free subgroup of a semisimple lie group g such that the volume of g is finite we obtain a cohomological interpretation in the sense of langlands of the multiplicity in the discrete spectrum of l 2 g of an irreducible unitarizable derived functor module r sqc after zuckerman with non singular infinitesimal character

signatures of invariant hermitian forms on irreducible highest weight modules perhaps the most important problem in representation theory in the 1970s and early 1980s was the determination of the multiplicity of com position factors in a verma module this problem was settled by the proof of the kazhdan lusztig conjecture which states that the multiplicities may be computed via kazhdan lusztig polynomials in this paper we introduce signed kazhdan lusztig polynomials a variation of kazhdan lusztig polyno mials which encodes signature information in addition to composition factor multiplicities and jantzen filtration level careful consideration of gabber and joseph s proof of kazhdan and lusztig s recursive formula for computing kazhdan lusztig polynomials and an application of jantzen s determinant for mula lead to a recursive formula for the signed kazhdan lusztig polynomials we use these polynomials to compute the signature of an invariant hermitian form on an irreducible highest weight module such a formula has applications to unitarity testing 1 1 the unitary dual problem in the 1930s i m gelfand introduced a broad programme in abstract harmonic analysis which would permit the transfer of dif ficult problems in areas as distinct from analysis as topology to more tractable problems in algebra fourier analysis is just one incarnation of this programme an unresolved component in gelfand s programme is the classification of the irre ducible unitary representations of a group known as the unitary dual problem in the case of a real reductive lie group the problem is equivalent to identifying all irreducible harish chandra modules which admit a positive definite invariant hermitian form as harish chandra modules may be constructed via an algebraic method introduced by zuckerman in 1978 known as cohomological induction it is of interest to study signatures of invariant hermitian forms on cohomologically induced modules and to understand how positivity can fail cohomological induction is a two step process in which we compose an induction functor with a zuckerman functor i the intermediate module in cohomological induction is a generalized verma module which admits an invariant hermitian form if the module to which induction was applied admits an invariant hermitian form formulas for the signatures of invariant hermitian forms on these intermediate modules may be used to compute signatures of forms on corresponding cohomo logically induced modules eg wal84 this motivates the study of invariant hermitian forms on verma modules see wal84 yee05 and irreducible highest weight modules

a serially correlated gamma frailty model for longitudinal count data a poisson gamma model is introduced to account for between subjects heterogeneity and within subjects serial correlation occurring in longitudinal count data the model extends the usual time constant shared frailty approach to allow time varying serially correlated gamma frailty whilst retaining standard marginal assumptions a composite likelihood approach to estimation and testing for serial correlation is proposed the work is motivated by a clinical trial on patient controlled analgesia where the number of analgesic doses taken by hospital patients in successive time intervals following abdominal surgery is recorded

goodness of fit tests for gee modeling with binary responses analysis of data with repeated measures is often accomplished through the use of generalized estimating equations gee methodology although methods exist for assessing the adequacy of the fitted models for uncorrelated data with likelihood methods it is not appropriate to use these methods for models fitted with gee methodology we propose model based and robust empirically corrected goodness of fit tests for gee modeling with binary responses based on partitioning the space of covariates into distinct regions and forming score statistics that are asymptotically distributed as chi square random variables with the appropriate degrees of freedom the null distribution and the statistical power of the proposed goodness of fit tests were assessed using simulated data the proposed goodness of fit tests are illustrated by two examples using data from clinical studies

the holomorphic discrete series of an affine symmetric space and representations with reproducing kernels consider a semisimple connected lie group g with an aisine symmetric space x we study abstractly the intertwining operators from the discrete series of x into representations with reproducing kernel and in particular into the discrete series of g each such is given by a convolution with an analytic function for x of hermitian type we consider the holomorphic discrete series of x and here derive very explicit formulas for the intertwining operators as a corollary we get a multiplicity one result for the series in question 0 introduction the purpose of this work is twofold the first is to study abstractly the intertwining operators between discrete series representations of an affine symmetric space x and discrete series of the corresponding semisimple group the second is to obtain very explicit formulas for certain discrete representations on x in effect giving the analogue of harish chandra s original construction of the holomorphic discrete series in the group case not surprisingly these two problems are highly connected thus theorem 5 4 below gives the formula for the lowest k type the flensted jensen function on x whereas in theorem 7 3 essentially the same function gives the intertwining operator much of our analysis builds on the framework in 14 but otherwise we have tried to make the paper reasonably self contained this is in particular the case in 1 2 and 4 where we abstract the properties of our intertwining operators with an eye towards later applications we shall always let g be a connected noncompact semisimple lie group such that the associated riemannian symmetric space is a bounded symmetric domain d c cn the best known and most interesting discrete series representations of g are the holomorphic discrete series representations as explained above one of our aims in this paper is to generalize this construction to affine symmetric spaces of hermitian type and relate those with other well known representations received by the editors september 23 1988 and in revised form june 27 1989 1980 mathematics subject classiffcation 1985 rerision primary 22e46 secondary 43a85 d 1991 american mathematical society 0002 9947 91 1 00 25 per page

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

the homomorphisms between scalar generalized verma modules associated to maximal parabolic subalgebras let g be a finite dimensional simple lie algebra over c we classify the homomorphisms between g modules induced from one dimensional modules of maximal parabolic subalgebras 1

the langlands parameters of subquotients of certain derived functor modules letgbe a noncompact simple lie group with finite center letkbe a maximal compact subgroup and let g0 k0 p0be the corresponding decomposition of the lie algebra suppose rank g rank k and let t0be a compact cartan subalgebra and b be a borel subalgebra letab be a derived functor module with infinitesimal character which is nondominant with respect to a noncompact simple root suppose that 2 p iskdominant so that thektype with highest weight occurs with multiplicity one inab we develop conditions on the roots of g under which a functor of cohomological induction maps a certain module of parabolic induction to another module of parabolic induction extending a result due to vogan this allows us in many cases to determine the langlands parameters of the subquotient ofab containing via a conjectured method of knapp

a series of unitary irreducible representations induced from a symmetric subgroup of a semisimple lie group letg h be a semisimple symmetric space generalizing results of flensted jensen we give a sufficient condition for the existence of irreducible closed invariant subspaces of the unitary representations ofg induced from unitary finite dimensional representations ofh this provides a method of constructing unitary irreducible representations ofg and we show by examples that for some irreducible admissible representations ofg this method exhibits not previously known unitarity

invariant syzygies and semisimple groups the purpose of this paper is to explore some intriguing connections between lie theory relative homological algebra invariant theory and representations of finite dimensional algebras in the process some results of hilbert 20 cartan and eilenberg 7 hochschild 21 gelfand 171 and others are generalized and a question of zl is partly answered in theorem 1 5 duflo seems to have stronger unpublished results on this problem sections 1 to 3 take place in a fairly general setting whereas section 4 focuses on semisimple lie groups the problem considered here goes back in some sense to hilbert 20 this paper was published 102 years ago to explain this let me start by singling out two out of many fundamental contributions of the great mathematician the first one is invariant theory namely the study of the algebra sv n consisting of those polynomial functions on a finite dimensional vector space v which are invariant under the action of a group h of linear transformations the second one is the so called syzygy theorem which asserts in today s language that the global dimension of the full symmetric algebra sv is dim v this prompts the question is there an algebra d attached to v as naturally as sv is on which h acts by automorphisms such that the global dimension of the algebra b dh of invariants is dim v the most natural candidate is

analysing longitudinal count data with overdispersion summary in many biomedical studies longitudinal count data comprise repeated responses and a set of multidimensional covariates for a large number of individuals when the response variable in such models is subject to overdispersion the overdispersion parameter influences the marginal variance in such cases the overdispersion parameter plays a significant role in efficient estimation of the regression parameters this raises the need for joint estimation of the regression parameters and the overdispersion parameter the longitudinal correlations being nuisance parameters in this paper we develop a generalised estimating equations approach based on a general autocorrelation structure for the repeated overdispersed data the asymptotic properties of the estimators of the main parameters are discussed and the estimation methodology is illustrated by analysing data on epileptic seizure counts

hilbert series howe duality and branching rules abstract let be a partition with l parts and let f be the irreducible finite dimensional representation of gl m associated to when l m the littlewood restriction rule describes how f decomposes when restricted to the orthogonal group o m or to the symplectic group sp m 2 under the condition that l m 2 in this paper this result is extended to all partitions our method combines resolutions of unitary highest weight modules by generalized verma modules with reciprocity laws from the theory of dual pairs in classical invariant theory corollaries include determination of the gelfand kirillov dimension of any unitary highest weight representation occurring in a dual pair setting and the determination of their hilbert series as a graded module for p let l be a unitary highest weight representation of sp n r so 2n or u p q when the highest weight of l plus satisfies a partial dominance condition called quasi dominance we associate to l a reductive lie algebra gl and a graded finite dimensional representation bl of gl the representation bl will have a hilbert series p q that is a polynomial in q with positive integer coefficients let l be the gelfand kirillov dimension of l and set cl equal to the ratio of the dimensions of the zeroth levels in the gradings of l and bl then the hilbert series of l may be expressed in the form in the easiest example of the correspondence l bl the two components of the weil representation of the symplectic group correspond to the two spin representations of an orthogonal group

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

the langlands parameters of flensted jensen s discrete series for semisimple symmetric spaces abstract let g be a semisimple lie group flensted jensen has for certain symmetric homogeneous spaces g h given a construction of a series of irreducible unitary representations of g realized on l 2 g h in this paper the langlands parameters of most of these representations are found for some sets of langlands parameters this leads to the fact not previously known that the corresponding representations of g are actually unitary

on repeated measures analysis with misspecified covariance structure in recent years various sophisticated methods have been developed for the analysis of repeated measures or longitudinal data the more traditional approach based on a normal likelihood function has been shown to be unsatisfactory in the sense of yielding asymptotically biased estimates when the covariance structure is misspecified more recent methodology based on generalized linear models and quasi likelihood estimation has gained widespread acceptance as generalized estimating equations however this also has theoretical problems in this paper a suggestion is made for improving the asymptotic behaviour of estimators by using the older approach implemented via gaussian estimation the resulting estimating equations include the quasi score function as one component so the methodology proposed can be viewed as a combination of gaussian estimation and generalized estimating equations which has a firmer asymptotic basis than either alone has

effects of variance function misspecification in analysis of longitudinal data the approach of generalized estimating equations gee is based on the framework of generalized linear models but allows for specification of a working matrix for modeling within subject correlations the variance is often assumed to be a known function of the mean this article investigates the impacts of misspecifying the variance function on estimators of the mean parameters for quantitative responses our numerical studies indicate that 1 correct specification of the variance function can improve the estimation efficiency even if the correlation structure is misspecified 2 misspecification of the variance function impacts much more on estimators for within cluster covariates than for cluster level covariates and 3 if the variance function is misspecified correct choice of the correlation structure may not necessarily improve estimation efficiency we illustrate impacts of different variance functions using a real data set from cow growth

econophysics financial time series from a statistical physics point of view in recent years physicists have started applying concepts and methods of statistical physics to study economic problems the word econophysics is sometimes used to refer to this work much recent work is focused on understanding the statistical properties of nancial time series one reason for this interest is that nancial markets are examples of complex interacting systems for which a huge amount of data exist and it is possible that nancial time series viewed from a dierent perspective might yield new results this article reviews the results of three recent phenomenological studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as eight orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by three orders of magnitude from 1 min up to approximately 10 d ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law and persist for several months iii correlations among dierent companies the third result bears on the application of random matrix theory to understand the correlations among price uctuations of any two dierent stocks from a study of the eigenvalue statistics of the cross correlation matrix constructed from price uctuations of the leading 1000 stocks we nd that the largest 1 of the eigenvalues and the corresponding eigenvectors show systematic deviations from the predictions for a random matrix whereas the rest of the eigenvalues conform to random matrix behavior suggesting that these 1 of the eigenvalues contain system specic information about correlated time evolution of dierent companies c 2000 published by elsevier science b v all rights reserved

singular unitary representations and indefinite harmonic theory abstract square integrable harmonic spaces are defined and studied in a homogeneous indefinite metric setting in the process dolbeault cohomologies are unitarized and singlar unitary representations are obtained and studied

variances are not always nuisance parameters summary in classical problems e g comparing two populations fitting a regression surface etc variability is a nuisance parameter the term nuisance parameter is meant here in both the technical and the practical sense however there are many instances where understanding the structure of variability is just as central as understanding the mean structure the purpose of this article is to review a few of these problems i focus in particular on two issues a the determination of the validity of an assay and b the issue of the power for detecting health effects from nutrient intakes when the latter are measured by food frequency questionnaires i will also briefly mention the problems of variance structure in generalized linear mixed models robust parameter design in quality technology and the signal in microarrays in these and other problems treating variance structure as a nuisance instead of a central part of the modeling effort not only leads to inefficient estimation of means but also to misleading conclusions

hermitian symmetric spaces and their unitary highest weight modules abstract the purpose of this article is to determine the set of unitarizable highest weight modules corresponding to hermitian symmetric spaces of the noncompact type the major step is that of proving unitarity at the last possible place with this established the description of the full set of unitarizable highest weight modules follows by a straightforward tensor product argument combined with the main ingredients of the proof of the key theorem bernstein gelfand gelfand and a diagramatic representation of the set of positive noncompact roots

improving the analysis of well logs by wavelet cross correlation abstract the concept of wavelet cross correlation is used to provide a new approach to identify similar patterns in related data sets which largely improves the confidence of the results the method amounts to decompose the data sets in the wavelet space so that correlations between wavelet coefficients can be analyzed in every scale besides the identification of the scales in which two independent measures are correlated the method makes it possible to find patches of data sets where correlations exist simultaneously in all scales this allows to extend the information of a small number of spots to larger regions well log data sets from two neighboring oil wells are used we compare similar measures at different probe sites and also measurements of different physical quantities taken on the same place although this is a typical scenario for the application of classical geostatistical methods it is well known that such methods erase out local differences in favor of smoother variability in contraposition this wavelet cross correlation takes advantage of the fluctuations to give information about the continuity of the geological structures in space it works even better if no filtering procedure has been applied to the original raw data

scaling multifractality and long range correlations in well log data of large scale porous media abstract three distinct methods namely the spectral density the multifractal random walk approach and the multifractal detrended fluctuation analysis are utilized to study the properties of four distinct types of well logs from three oil and gas fields namely the natural gamma ray emission neutron porosity bulk density and the sonic transient time logs such well logs have never been analyzed by the methods that we utilize in the present study the results indicate that the well logs exhibit multifractal characteristics and the estimated hurst exponents by the three methods are close to each other using multifractal detrended fluctuation analysis and the shuffled and surrogated data we find that the source of multifractality is due to both broad probability density functions of the data and long range correlations in them the correlations are persistent and are characterized by a hurst exponent h 0 5 despite very significant differences in the geology of the three reservoirs ranging from shaly sands to fractured carbonate reservoirs there is a rough universality in the log data in that the hurst exponents for all the logs vary in a very narrow range

unitary highest weight modules the unitary highest weight modules of a semisimple lie group g have been classified s 93 unfortunately this classification does not fit well with a more general picture of the unitary dual of g we give such a classification for g a classical group using derived functors and the philosophy of unipotent representations in particular these representations are associated to coadjoint orbits of g let 8 lie g 0 a cartan involution of 6 8 c a derived functor module is defined by the data q i u a o stable parabolic subalgebra of 0 and 17 an irreducible unitary representation of l the stabilizer of l in g considering z7 as a representation of i write z7 a rc where a e c c center of i denotes dual and rt z7l r we define a rc i rc cf definition 6 1 now fix n and vary 1 under certain restrictions on i which amount to a positivity condition on the corresponding bundle over g l a i rr is known to be irreducible and unitary as ii varies within this range the langlands parameters of a a rr vary smoothly however one cannot obtain all unitary highest weight modules under these restrictions the orbit method suggests how to obtain the remaining unitary highest weight modules the modules a rr are associated to coadjoint orbits as follows if rc is trivial we say a rr is associated to the elliptic orbit 0 g ii not all unitary highest weight modules may be obtained with rc trivial an example of which is the oscillator representation of 2n r the metapletic group we define 2n irreducible unitary highest weight modules rc 1 2 n k r is 113 oool 8708 87 7 50

improving the correlation structure selection approach for generalized estimating equations and balanced longitudinal data generalized estimating equations are commonly used to analyze correlated data choosing an appropriate working correlation structure for the data is important as the efficiency of generalized estimating equations depends on how closely this structure approximates the true structure therefore most studies have proposed multiple criteria to select the working correlation structure although some of these criteria have neither been compared nor extensively studied to ease the correlation selection process we propose a criterion that utilizes the trace of the empirical covariance matrix furthermore use of the unstructured working correlation can potentially improve estimation precision and therefore should be considered when data arise from a balanced longitudinal study however most previous studies have not allowed the unstructured working correlation to be selected as it estimates more nuisance correlation parameters than other structures such as ar 1 or exchangeable therefore we propose appropriate penalties for the selection criteria that can be imposed upon the unstructured working correlation via simulation in multiple scenarios and in application to a longitudinal study we show that the trace of the empirical covariance matrix works very well relative to existing criteria we further show that allowing criteria to select the unstructured working correlation when utilizing the penalties can substantially improve parameter estimation copyright 2014 john wiley sons ltd

on the use of a working correlation matrix in using generalised linear models for repeated measures summary in a seminal paper liang zeger 1986 extended the use of generalised linear models to repeated measures data they based the analysis on specifications for the means and variances of the observations as usual for generalised linear models but showed how specifications for the correlations between measurements made on the same unit could be avoided by using a working correlation matrix in some cases the parameters involved in this matrix are subject to an uncertainty of definition which can lead to a breakdown of the asymptotic properties of the estimators

a generalized linear model with nested strata of extra poisson variation on etend la definition de quasivraisemblance pour tenir compte de plusieurs strates de variation emboitees dans un modele lineaire generalise

an cohomology construction of unitary highest weight modules for in this paper a geometric construction is given of all unitary highest weight modules of g u p q the construction is based on the unitary model of the kth tensor power of the metaplectic representation in a bargmannsegal fock space of square integrable differential forms the representations are constructed as holomorphic sections of certain vector bundles over g k and the construction is implemented via an integral transform analogous to the penrose transform of mathematical physics 0 introduction a major area of research in the representation theory of lie groups is the explicit analysis of naturally occurring unitary representations one aspect of this problem is that of producing geometric constructions of the unitary representations of a semisimple lie group g here we consider unitary highest weight representations of g u p q these representations have been classified algebraically in various ways see ehw j1 a and have been constructed as spaces of vector valued functions on the generalized unit disk d ds most singular highest weight representations appear in the l 2 cohomology construction of rsw z our approach starts with the kth tensor power of the metaplectic representation of u p q in the l cohomology space zo k cnxk as defined by blattner and rawnsley br the reductive dual pair u p q u k acts on this space results of kashiwara and vergne kv decompose this space into a sum of irreducible representations ua indexed by a set a c u k of representations of u k all unitary highest weight modules of u p q appear in this way for some k j2 ep each irreducible g u p q module corresponds to a vector bundle over g k as follows corresponding to a particular representation a of g each element c of g k determines a subspace vs c received by the editors october 31 1989 results presented in the special session on geometric methods in representation theory at the american mathematical society meeting in los angeles califormia november 1987 1980 mathematics subject classification 1985 revision primary 22e45

discrete decomposability of the restriction of aq λ with respect to reductive subgroupsiii restriction of harish chandra modules and associated varieties let h g be real reductive lie groups and an irreducible unitary representation of g we introduce an algebraic formulation discretely decomposable restriction to single out the nice class of the branching problem breaking symmetry in physics in the sense that there is no continuous spectrum in the irreducible decomposition of the restriction h this paper offers basic algebraic properties of discretely decomposable restrictions especially for a reductive symmetric pair g h and for the zuckerman vogan derived functor module and proves that the sufficient condition invent math 94 is in fact necessary a finite multiplicity theorem is established for discretely decomposable modules which is in sharp contrast to known examples of the continuous spectrum an application to the restriction h of discrete series for a symmetric space g h is also given

discrete decomposability of the restriction of a q λ with respect to reductive subgroups and its applications letg g be real reductive lie groups and q a stable parabolic subalgebra of lie g this paper offers a sufficient condition on g g q that the irreducible unitary representation mathop a q limits ofg with non zero continuous cohomology splits into a discrete sum of irreducible unitary representations of a subgroupg each of finite multiplicity as an application to purely analytic problems new results on discrete series are also obtained for some pseudo riemannian non symmetric spherical homogeneous spaces which fit nicely into this framework some explicit examples of a decomposition formula are also found in the cases wherea q is not necessarily a highest weight module

wavelet analysis and synthesis of fractional brownian motion fractional brownian motion fbm offers a convenient modeling for nonstationary stochastic processes with long term dependencies and 1 f type spectral behavior over wide ranges of frequencies statistical self similarity is an essential feature of fbm and makes natural the use of wavelets for both its analysis and its synthesis a detailed second order analysis is carried out for wavelet coefficients of fbm it reveals a stationary structure at each scale and a power law behavior of the coefficients variance from which the fractal dimension of fbm can be estimated conditions for using orthonormal wavelet decompositions as approximate whitening filters are discussed consequences of discretization are considered and some connections between the wavelet point of view and previous approaches based on length measurements analysis or dyadic interpolation synthesis are briefly pointed out

signature characters of invariant hermitian forms on irreducible verma modules and hall littlewood polynomials the unitary dual problem is one of mathematics most important open problems classify the irreducible unitary representations of a group the general approach has been to classify all representations admitting non degenerate invariant hermitian forms compute the signatures of those forms and then determine which forms are positive definite signature character algorithms and formulas arising from deforming representations and analysing changes at reducibility points as in adams et al unitary representations of real reductive groups arxiv e prints 2012 and yee represent theory 9 638 677 2005 produce very complicated formulas or algorithms from the resulting recursion this paper shows that in the case of irreducible verma modules all of the complexity can be encapsulated by the affine hecke algebra for compact real forms and for alcoves corresponding to translations of the fundamental alcove by a regular weight signature characters of irreducible verma modules are in fact negatives of hall littlewood polynomial summands evaluated at q 1 times a version of the weyl denominator establishing a simple signature character formula and drawing an important connection between signature characters and the affine hecke algebra signature characters of irreducible highest weight modules are shown to be related to kazhdan lusztig basis elements this paper also handles noncompact real forms the current state of the art for the unitary dual is a computer algorithm for determining if a given representation is unitary these results suggest the potential to move the state of the art to a closed form classification for the entire unitary dual

hilbert series howe duality and branching for classical groups an extension of the littlewood restriction rule is given that covers all pertinent parameters and simplifies to the original under littlewood s hypotheses two formulas are derived for the gelfand kirillov dimension of any unitary highest weight representation occurring in a dual pair setting one in terms of the dual pair index and the other in terms of the highest weight for a fixed dual pair setting all the irreducible highest weight representations which occur have the same gelfand kirillov dimension we define a class of unitary highest weight representations and show that each of these representations l has a hilbert series hl q of the form

unbiased estimating equations from working correlation models for irregularly timed repeated measures the method of generalized estimating equations gees has been criticized recently for a failure to protect against misspecification of working correlation models which in some cases leads to loss of efficiency or infeasibility of solutions however the feasibility and efficiency of gee methods can be enhanced considerably by using flexible families of working correlation models we propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance gee the supplementary estimating equations are obtained by differentiation of the cholesky decomposition of the working correlation or as score equations for decoupled gaussian pseudolikelihood the estimating equations are solved with computational effort equivalent to that required for a first order gee full details and analytic expressions are developed for a generalized markovian model that was evaluated through simulation large sample sandwich standard errors for working correlation parameter estimates are derived and shown to have good performance the proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children

brst cohomology and highest weight vectors i we initiate a program to study certain recent problems in non compact coset cft by the brst approach we derive a reduction formula for the brst cohomology by making use of a twisting by highest weight modules as illustrations we apply the formula to the bosonic string model and a rank one non compact coset model dpl our formula provides a completely new approach to non compact coset construction

an l2 cohomology construction of negative spin mass zero equations for u p q abstract in this paper a geometric construction is given of the ladder representations of g u p q which correspond to negative spin solutions of the massless field equations the construction is based on the unitary model of the ladder representations in a bargmann segal fock space of square integrable 0 q forms the representations are constructed as holomorphic sections of certain vector bundles over g k and the construction is implemented via an integral transform analogous to the penrose transform of mathematical physics finally the resulting differential equations are exhibited explicitly over g k

the holomorphic discrete series for affine symmetric spaces i abstract let x g h be an affine symmetric space we study part of the discrete spectrum of l2 x for x of hermitian type a notion we define in analogy with the group case in particular we find intertwining operators from the scalar holomorphic discrete series of g which is automatically of hermitian type into l2 x the multiplicity of this series is then shown to be one by a uniqueness result for the intertwining operators finally we investigate the complexification x c of x and show that the discrete series in question admits holomorphic continuation into a certain domain in x c

eigenspaces of the laplacian on hyperbolic spaces composition series and integral transforms abstract let x be a projective real complex or quaternion hyperbolic space realized as the pseudo riemannian symmetric space x g h with g o p q u p q or sp p q these are the classical isotropic symmetric spaces let be the g invariant laplace beltrami operator on x a complete description by k types for each c of all closed g invariant subspaces of the eigenspace f c x f f is given the eigenspace representations are compared with principal series representations using poisson transformations similar results are obtained also for the exceptional isotropic symmetric space the langlands parameters of the spherical discrete series representations are determined