a density corrected quantum boltzmann equation binary correlations are a recognized part of the pair density operator but the influence of binary correlations on the singlet density operator is usually not emphasized here free motion and binary correlations are taken as independent building blocks for the structure of the nonequilibrium singlet and pair density operators binary correlations are assumed to arise from the collision of twofree particles together with the first bbgky equation and a retention of all terms that are second order in gas density a generalization of the boltzmann equation is obtained this is an equation for thefree particle density operator rather than for the full singlet density operator the form for the pressure tensor calculated from this equation reduces at equilibrium to give the correct beth uhlenbeck second virial coefficient in contrast to a previous quantum boltzmann equation which gave only part of the quantum second virial coefficient generalizations to include higher order correlations and collision types are indicated

subdiffusive quantum transport for 3d hamiltonians with absolutely continuous spectra we exhibit a class of hamiltonians in dimension d 3 describing a quantum particle in an aperiodic medium with absolutely continuous spectrum and subdiffusive behavior the diffusion exponent which characterizes the time growth of the mean square displacement can be chosen slightly bigger than guarneri s lower bound these models are built out of 1d hamiltonians with well understood spectral and transport properties

log linear non uniform association models for agreement between two ratings on an ordinal scale in agreement studies when objects are rated independently by two raters or twice by the same rater an association between their ratings on two categories arises reflecting the distinguishability of these two categories for these raters when ratings are performed on an ordinal scale this association between ratings on two categories increases when the distance between these categories increases on the ordinal scale goodman s log linear models derived for the analysis of agreement between two raters on an ordinal scale assume that distinguishabilities between adjacent categories are either constant or a priori fixed log non linear models that allow variations of the distinguishabilities between adjacent categories along the scale may lead to difficulties in parameter estimation this paper describes a new class of log linear non uniform association models these models extend the log linear uniform association model by allowing variations of distinguishability between adjacent categories along the scale these new models are used to analyse ordinal agreement between dermatologists when assessing the severity of different cutaneous signs of ageing on women faces

upper bounds on wavepacket spreading for random jacobi matrices a method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random possibly correlated jacobi matrix as an application one obtains sharp upper bounds on the diffusion exponents for random polymer models coinciding with the lower bounds obtained in a prior work the second application is an elementary argument not using multiscale analysis or the aizenman molchanov method showing that under the condition of uniformly positive lyapunov exponents the moments of the position operator grow at most logarithmically in time

association models and the bivariate normal for contingency tables with ordered categories summary association models considered by goodman 1979 for contingency tables with ordered categories are presented here in a somewhat different form to facilitate comparison with the bivariate normal association models can be applied when an underlying bivariate normal is assumed and also under more general conditions and they provide alternatives to tetrachoric and polychoric correlation these models agree more closely with the bivariate normal than does plackett s model 1965 when the row and column classifications arise from underlying univariate normal distributions the general utility of the association models is illustrated here

dynamical analysis of schrodinger operators with growing sparse potentials we consider discrete half line schrodinger operators h with potentials of the form v n s n q n here q is any compactly supported real function open image in new window if n l n and s n 0 otherwise where 0 1 and l n is a very fast growing sequence we study in a rather detailed manner the time averaged dynamics exp ith for various initial states in particular for some we calculate explicitly the intermittency function p which turns out to be nonconstant the dynamical results obtained imply that the spectral measure of h has exact hausdorff dimension for all boundary conditions improving the result of jitomirskaya and last

dynamical localization for the random dimer schrodinger operator we study the one dimensional random dimer model with hamiltonian h v where for all x mathbb z v 2x v 2x 1 and where the v 2x are i i d bernoulli random variables taking the values v v 0 we show that for all values of vand with probability one in the spectrum of his pure point if v 1 and v 1 sqrt 2 the lyapunov exponent vanishes only at the two critical energies given by e v for the particular value v 1 sqrt 2 respectively v sqrt 2 we show the existence of new additional critical energies at e 3 sqrt 2 respectively e 0 on any compact interval inot containing the critical energies the eigenfunctions are then shown to be semi uniformly exponentially localized and this implies dynamical localization for all q 0 and for all ell 2 mathbb z with sufficiently rapid decrease mathop sup limits t r psi i left q right kern 1pt left t right mathop sup limits t left langle p i left h omega right psi t left x right q p i left h omega right psi t right rangle infty here psi t e ih omega t psi and pi h is the spectral projector of h onto the interval i in particular if v 1 and v sqrt 2 these results hold on the entire spectrum so that one can take i h

on the snider equation we study the physical content of the snider quantum transport equation and the origin of a puzzling feature of this equation which implies contradictory values for the one particle density operator we discuss in detail why the two values are in fact not very different provided that the studied particles have sufficiently large wave packets and only a small interaction probability a condition which puts a limit on the validity of the snider equation in order to improve its range of application we propose a reinterpretation of the equation as a mixed equation relating the real one particle distribution function on the left hand side of the equation to the free distribution on the right hand side which we have introduced in a recent contribution in its original form the snider equation is valid only when used to generate boltzmann type equations where collisions are treated as point processes in space and time no range no duration in this approximation virial corrections are not included so that the real and free distributions coincide if the equation is used beyond this approximation to generate nonlocal and density corrections we conclude that the results are not necessarily correct

quasisymmetric models for the analysis of square contingency tables summary a parametric model is presented for the analysis of square contingency tables where there is a one to one correspondence between the categories of the row variable and the categories of the column variable the model is applicable to cross classifications where the categories are unordered partially ordered or completely ordered but the interpretation of the model and associated parameters is most straightforward when the categories are at least partially ordered connections with the mover stayer model and the usual model of quasisymmetry are described two data sets are used to illustrate the utility of the model

power law subordinacy and singular spectra i half line operators we study hausdorff dimensional spectral properties of certain whole line quasiperiodic discrete schrodinger operators by using the extension of the gilbert pearson subordinacy theory that we previously developed in 19

eigenvalue spacings and dynamical upper bounds for discrete one dimensional schrodinger operators we prove dynamical upper bounds for discrete one dimensional schrodinger operators in terms of various spacing properties of the eigenvalues of finite volume approximations we demonstrate the applicability of our approach by a study of the fibonacci hamiltonian

solutions spectrum and dynamics for schrodinger operators on infinite domains 1 introduction and main results in this paper we investigate the relations between the rate of decay of solutions of schrodinger equations continuity properties of spectral measures of the corresponding operators and dynamical properties of the corresponding quantum systems the first main result of this paper shows that in great generality certain upper bounds on the rate of growth of l 2 norms of generalized eigenfunctions over expanding balls imply certain minimal singularity of the spectral measures consider an operator h v defined by the differential expression h v v x

general observer agreement measures on individual subjects and groups of subjects general chance corrected measures of agreement on individual subjects for several observers using nominal or ordinal categories are developed the subject specific measures can be used to identify subjects whom the observers find difficult to rate the relationship of the subject specific measures to a general chance corrected measure of agreement for a group of subjects is demonstrated by suitable choices of disagreement functions the measure of agreement for a group of subjects is shown to include as special cases many of the kappa like statistics also it is asymptotically equivalent to various intraclass correlation coefficients the measures do not require that the observers all use the classification scale in the same way the asymptotic null and non null variances obtained by taylorseries approximations for the statistics are presented the application of the measures is illustrated by data obtained when seven pathologists classified slides on a five point ordinal scale for the diagnosis of carcinoma in situ of the uterine cervix

perturbation theory for the random dimer model the authors study a one dimensional tight binding model with a random potential taking two values or nu with the restriction that on pairs of two neighbouring sites the potentials take the same value this random dimer model proposed by dunlap phillips and wu 1990 has a vanishing lyapunov exponent for the energy e or nu they compute the lyapunov exponent and the density of states perturbatively in the vicinity of this energy using the invariant measure formalism

assessing rater agreement using marginal association models new models that are useful in the assessment of rater agreement particularly when the rating scale is ordered or partially ordered are presented the models are parameterized to address two important aspects of rater agreement i agreement in terms of the overall frequency in which raters assign categories and ii the extent to which raters agree on the category assigned to individual subjects or items we present methodology for the simultaneous modelling of univariate marginal responses and bivariate marginal associations in the k way contingency table representing the joint distribution of k rater responses the univariate marginal responses provide information for evaluating agreement in terms of the overall frequency of responses and the bivariate marginal associations provide information on category wise agreement among pairs of raters in addition estimated scores within a generalized log non linear model for bivariate associations facilitate the assessment of category distinguishability

optimum experimental designs for multinomial logistic models multinomial responses frequently occur in dose level experiments for example in a study of the influence of gamma radiation on the emergence of house flies musca domestica l 1758 three disjoint outcomes occurred death before the pupae opened death during emergence and life after emergence although the flies are easy to breed this sort of bioassay is in general very expensive since it requires the use of a gamma radiation source experiments therefore need to be designed to involve the minimum number of different doses here the theory of optimum experimental design is applied to provide efficient experiments to estimate the parameters of those multinomial logistic models that are a special case of the multivariate logistic models of glonek and mccullagh 1995 journal of the royal statistical society series b 57 533 546 the purpose is to reduce the overall experimental cost the general equivalence theorem fedorov 1972 theory of optimal experiments is adapted to this class of models providing an effective method of generating and checking the optimality of designs one example on flies demonstrates the method which can be easily implemented

analysis of sets of two way contingency tables using association models abstract a class of models is introduced for the analysis of group differences in the association between two discrete variables the rc m association model for two way tables is reviewed and alternative weighting systems for identifying interaction parameters are presented this model is generalized for the setting where a two way contingency table is available for two or more groups various restricted models can be used to examine possible sources of intergroup heterogeneity in the association these sources pertain to heterogeneity in the intrinsic association and or in the scores for the row and column variables the importance of weights used to identify the row and column scores is emphasized a classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here

dynamical upper bounds on wavepacket spreading we derive a general upper bound on the spreading rate of wavepackets in the framework of schrodinger time evolution our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically in time where the rate of this growth is determined by properties of the spectral measure and by spatial properties of solutions of an associated time independent schrodinger equation we also derive a new lower bound on the spreading rate which is strongly connected with our upper bound we apply these new bounds to the fibonacci hamiltonian the most studied one dimensional model of quasicrystals as a result we obtain for this model upper and lower dynamical bounds establishing wavepacket spreading rates which are intermediate between ballistic transport and localization the bounds have the same qualitative behavior in the limit of large coupling

a latent trait finite mixture model for the analysis of rating agreement this article presents a latent distribution model for the analysis of agreement on dichotomous or ordered category ratings the model includes parameters that characterize bias category definitions and measurement error for each rater or test parameter estimates can be used to evaluate rater performance and to improve classification or measurement with use of multiple ratings a simple maximum likelihood estimation procedure is described two examples illustrate the approach although considered in the context of analyzing rater agreement the model provides a general approach for mixture analysis using two or more ordered caregory measures

delocalization in random polymer models a random polymer model is a one dimensional jacobi matrix randomly composed of two finite building blocks if the two associated transfer matrices commute the corresponding energy is called critical such critical energies appear in physical models an example being the widely studied random dimer model it is proven that the lyapunov exponent vanishes quadratically at a generic critical energy and that the density of states is positive there large deviation estimates around these asymptotics allow to prove optimal lower bounds on quantum transport showing that it is almost surely overdiffusive even though the models are known to have pure point spectrum with exponentially localized eigenstates for almost every configuration of the polymers furthermore the level spacing is shown to be regular at the critical energy

anderson localization for bernoulli and other singular potentials we prove exponential localization in the anderson model under very weak assumptions on the potential distribution in one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment in particular this solves the longstanding problem of localization for bernoulli potentials i e potentials that take only two values in dimensions greater than one we prove localization at high disorder for potentials with holder continuous distributions and for bounded potentials whose distribution is a convex combination of a holder continuous distribution with high disorder and an arbitrary distribution these include potentials with singular distributions we also show that for certain bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component

pure point spectrum under 1 parameter perturbations and instability of anderson localization we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic fora we study the set of all eigenvalues of the operatora t a tp t that belong to its essential spectrum which does not depend on the parametert we prove that this set is empty for a dense set of values oft then we apply this result or its idea to questions of anderson localization for 1 dimensional schrodinger operators discrete and continuous

upper bounds in quantum dynamics of course the case of main interest is where h is given by l2 rd or 2 zd h is a schr dinger operator of the form a v and ip 0 is a localized wavepacket under the time evolution 1 the wavepacket i t will in general spread out with time finding quantitative bounds for this spreading in concrete cases and developing methods for proving such bounds has been the objective of a great number of papers in recent years one is often interested in the growth behavior of the moments of the position operator that is the function 11 x p 2 i 2 these questions are particularly complicated and interesting in situations where singular continuous spectra occur the discovery of the occurrence of such spectra for many models of physical relevance has triggered some activity on the quantum dynamical side for models with absolutely continuous spectra on the other hand quantum dynamical questions have been investigated much earlier in the context of scattering theory and have been answered to a great degree of satisfaction models with point spectrum or more restrictively models exhibiting anderson localization have also been investigated from a quantum dynamical point of view while it is not true in general that spectral localization implies dynamical localization 26 73 it has been shown that the three main approaches to spectral localization the fractional moment method 3 4 5 multi scale analysis 28 27 75 and the bourgain goldstein schlag method 12 37 yield dynamical localization as a by product 2 13 22 31 34 quantum dynamics for schr dinger operators with singular continuous spectra is much less understood the two primary examples motivated by physics are the harper model also known as the almost mathieu operator at critical cou pling which describes a bloch electron in a constant magnetic field with irrational flux through a unit cell and the fibonacci model which describes a standard one dimensional quasicrystal both models have been studied heavily in both the physics and mathematics communities

ordinal association in contingency tables some interpretive aspects abstract two families of models for ordered contingency tables goodman s association models and canonical correlation models are investigated and compared with respect to the interpretation of their parameters we show that the two families of models actually refer to different kinds of ordinal association stochastic order extremity for correlation models and stochastic order entropy for association models this difference is related to the way the two models scale interaction the scale difference is proven to be of substantial consequence especially under strong association

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

localization at large disorder and at extreme energies an elementary derivation the work presents a short proof of localization under the conditions of either strong disorder 0 or extreme energies for a wide class of self adjoint operators with random matrix elements acting inl 2 spaces a prototypical example is the discrete schrodinger operatorh u 0 x v x onz d d 1 withu 0 x a specified background potential and v x generated as random variables the general results apply to operators with replaced by a non local self adjoint operatort whose matrix elements satisfy y t x y s const uniformly inx for somes 1 localization means here that within a specified energy range the spectrum ofh is of the pure point type or equivalently the wave functions do not spread indefinitely under the unitary time evolution generated byh the effect is produced by strong disorder in either the potential or in the off diagonal matrix elementst x y under rapid decay oft x y the corresponding eigenfunctions are also proven to decay exponentially the method is based on resolvent techniques the central technical ideas include the use of low moments of the resolvent kernel i e g e x y s withs small enough 1 to avoid the divergence caused by the distribution s cauchy tails and an effective use of the simple form of the dependence ofg e x y on the individual matrix elements ofh in elucidating the implications of the fundamental equation h e g e x x 0 x x0 this approach simplifies previous derivations of localization results avoiding the small denominator difficulties which have been hitherto encountered in the subject it also yields some new results which include localization under the following sets of conditions i potentials with an inhomogeneous non random partu 0 x ii the bethe lattice iii operators with very slow decay in the off diagonal terms t x y 1 x y d e and iv localization produced by disordered boundary conditions

localization for discrete one dimensional random word models we consider schrodinger operators in l2 z whose potentials are obtained by randomly concatenating words from an underlying set w according to some probability measure on w our assumptions allow us to consider models with local correlations such as the random dimer model or more generally random polymer models we prove spectral localization and away from a finite set of exceptional energies dynamical localization for such models these results are obtained by employing scattering theoretic methods together with furstenberg s theorem to verify the necessary input to perform a multiscale analysis

on the comparison of multinomial and poisson log linear models summary we introduce a method for comparing multinomial and poisson log linear models which affords an explicit description of their equivalences and differences the method involves specifying the model in terms of constraint equations rather than the more common freedom equations the poisson and multinomial large sample distributions of log linear model parameter estimators are derived and compared within this constraint equation context reparameterizations are thereby avoided as a by product the method provides the practitioner with the adjustment that is necessary to make valid inferences about all multinomial log linear parameters when as a matter of convenience the poisson log linear model is fitted this implies that valid large sample inferences about the multinomial cell probabilities can be made directly by using the poisson log linear model to illustrate the utility of this approach several examples are considered

the fisher information matrix for log linear models arguing conditionally on observed explanatory variable summary for poisson or multinomial contingency table data the conditional distribution is product multinomial when conditioning on observed values of explanatory variables birch 1963 showed that under the restriction formed by keeping the marginal totals of one margin fixed at their observed values the poisson multinomial and product multinomial likelihoods are proportional and give the same estimates for common parameters in the log linear model here the inverses of the fisher information matrices are shown to be identical over common parameters so that the asymptotic covariance matrices of the estimates correspond

operators with singular continuous spectrum ii rank one operators for an operator a with cyclic vector we studya p wherep is the rank one projection onto multiples of if spec a anda has no a c spectrum we prove thata p has purely singular continuous spectrum on for a denseg of s

maximum likelihood estimation in log linear models we study maximum likelihood estimation in log linear models under conditional poisson sampling schemes we derive necessary and sufficient conditions for existence of the maximum likelihood estimator mle of the model parameters and investigate estimability of the natural and mean value parameters under a nonexistent mle our conditions focus on the role of sampling zeros in the observed table we situate our results within the framework of extended exponential families and we exploit the geometric properties of log linear models we propose algorithms for extended maximum likelihood estimation that improve and correct the existing algorithms for log linear model analysis

maximum likelihood methods for a generalized class of log linear models we discuss maximum likelihood methods for fitting a broad class of multivariate categorical response data models in particular we derive the large sample distributions for maximum likelihood estimators of parameters of product multinomial generalized log linear models the large sample behavior of other relevant likelihood based statistics such as goodness of fit statistics and adjusted residuals is also described the asymptotic results are derived within the framework of the constraint specification rather than the more common freedom specification of the model we also outline an improved fitting algorithm for computing parameter maximum likelihood estimates and other relevant statistics the broad class of multivariate categorical response data models which are referred to as generalized log linear models can imply structure on several response configuration distributions e g joint and marginal distributions these models which include as special cases log linear logit and cumulative logit models enjoy a wide breadth of application including longitudinal rater agreement and crossover data analyses

generalized bilinear models generalized bilinear models are presented for the statistical analysis of two way arrays these models combine bilinear models and generalized linear modeling and yield a family of models that includes many existing models as well as suggest other potentially useful ones this approach both unifies and extends models for two way arrays including the ability to treat response and explanatory variables differently in the models and the incorporation of external information about the variables directly into the analysis a unifying framework for the generalized bilinear models is provided by considering four particular cases which have been proposed and used in the existing statistical literature a three step procedure is proposed to analyze data sets by generalized bilinear models two data sets of different nature are analyzed

simultaneously modeling joint and marginal distributions of multivariate categorical responses abstract we discuss model fitting methods for analyzing simultaneously the joint and marginal distributions of multivariate categorical responses the models are members of a broad class of generalized logit and loglinear models we fit them by improving a maximum likelihood algorithm that uses lagrange s method of undetermined multipliers and a newton raphson iterative scheme we also discuss goodness of fit tests and adjusted residuals and give asymptotic distributions of model parameter estimators for this class of models inferences are equivalent for poisson and multinomial sampling assumptions simultaneous models for joint and marginal distributions may be useful in a variety of applications including studies dealing with longitudinal data multiple indicators in opinion research cross over designs social mobility and inter rater agreement the models are illustrated for one such application using data from a recent general social survey regarding opinions about various types of government s

quasi symmetric latent class models with application to rater agreement suppose we observe responses on several categorical variables having the same scale we consider latent class models for the joint classification that satisfy quasi symmetry the models apply when subject specific response distributions are such that i for a given subject responses on different variables are independent and ii odds ratios comparing marginal distributions of the variables are identical for each subject these assumptions are often reasonable in modeling multirater agreement when a sample of subjects is rated independently by different observers in this application the model parameters describe two components of agreement strength of association between classifications by pairs of observers and degree of heterogeneity among the observers marginal distributions we illustrate the models by analyzing a data set in which seven pathologists classified 118 subjects in terms of presence or absence of carcinoma yielding seven categorical classifications with the same binary scale a good fitting model has a latent classification that differentiates between subjects on whom there is agreement and subjects on whom there is disagreement

a reinterpretation of dense gas kinetic theory in dense gas kinetic theory it is standard to express all reduced distribution functions as functionals of the singlet distribution function since the singlet distribution function includes aspects of correlated particles as well as describing the properties of freely moving particles it is here argued that these aspects should more clearly be distinguished and that it is the distribution function for free particles that is the prime object in terms of which dense gas kinetic theory should be expressed the standard equations of dense gas kinetic theory are rewritten from this point of view and the advantages of doing so are discussed

invariance and factorial models summary two factors having the same set of levels are said to be homologous this paper aims to extend the domain of factorial models to designs that include homologous factors in doing so it is necessary first to identify the characteristic property of those vector spaces that constitute the standard factorial models we argue here that essentially every interesting statistical model specified by a vector space is necessarily a representation of some algebraic category logical consistency of the sort associated with the standard marginality conditions is guaranteed by category representations but not by group representations marginality is thus interpreted as invariance under selection of factor levels z representations and invariance under replication of levels s representations for designs in which each factor occurs once the representations of the product category coincide with the standard factorial models for designs that include homologous factors the set of srepresentations is a subset of the z representations it is shown that symmetry and quasi symmetry are representations in both senses but that not all representations include the constant functions intercept the beginnings of an extended algebra for constructing general z representations is described and illustrated by a diallel cross design

on the equivalence of prospective and retrospective likelihood methods in case control studies summary we present new approaches to analyzing case control studies using prospective likelihood methods in the classical framework we extend the equality of the profile likelihoods to the barndorff nielsen modified profile likelihoods for prospective and retrospective models this enables simple and accurate approximate conditional inference for stratified case control studies of moderate stratum size in the bayesian framework we provide sufficient conditions on priors for the prospective model parameters to yield a prospective marginal posterior density equal to its retrospective counterpart our results extend the prospective retrospective equivalence in the bayesian paradigm with a more general class of priors than has previously been investigated

using association models to analyse agreement data two examples two examples demonstrate how one can use association models to analyse agreement data the first example concerns intra rater variability in the classification of sputum cytology slides and the second deals with variability associated with the reporting of passive smoking histories the paper emphasizes models in which one estimates category scores from the data that is models that are not in the log linear family of models such models have use in assessment of category distinguishability and provide insights not easily obtained with log linear models

extended rc association models allowing for order restrictions and marginal modeling in the context of two way contingency tables the rc model may be seen as a way of modeling the set of log odds ratios for adjacent 2 2 subtables through row and column scores this article presents an extended class of rc models that allows simultaneous modeling of the marginal distributions and the association between two categorical variables these components are parameterized with logits and log odds ratios that may be of different types e g global or continuation to suit the nature of the data and the type of dependence of interest an algorithm for maximum likelihood estimation under equality and inequality constraints is presented the asymptotic distribution of the likelihood ratio statistic to test some interesting hypotheses is derived and extensions to multiway tables are outlined three examples are presented to highlight the features of the new approach

log linear modelling of pairwise interobserver agreement on a categorical scale this article uses log linear models to describe pairwise agreement among several raters who classify a sample on a subjective categorical scale the models describe agreement structure simultaneously for second order marginal tables of a multidimensional cross classification of ratings practical difficulties arise in fitting the models because models refer to pairwise marginal tables of a very large and sparse table a standard analysis that treats the marginal tables as independent yields consistent estimates of model parameters but not of the covariance matrix of the estimates we estimate the covariance matrix using the jackknife we apply the models to describe agreement between evaluations made by seven pathologists of carcinoma in situ of the uterine cervix using a five level ordinal scale previous analyses showed differences among the pathologists in their pairwise levels of agreement but we observe near homogeneity in the dependence structure of their ratings

fractal dimensions and the phenomenon of intermittency in quantum dynamics we exhibit an intermittency phenomenon in quantum dynamics more precisely we derive new lower bounds for the moments of order p associated to the state t e it h and averaged in time between zero and t these lower bounds are expressed in terms of generalized fractal dimensions d 1 1 p d of the measure where d is the space dimension this improves previous results obtained in terms of hausdorff and packing dimension

canonical analysis of contingency tables by maximum likelihood abstract canonical analysis has often been employed instead of log linear models to analyze the relationship of two polytomous random variables however until the last few years analysis has been informal in this article models are examined that place nontrivial restrictions on the values of the canonical parameters so that a parsimonious description of association is obtained maximum likelihood is used to obtain parameter estimates for these restricted models approximate confidence intervals are derived for parameters and chi squared tests are used to check adequacy of models the resulting models may be used to determine the appropriateness of latent class analysis or to determine whether a set of canonical scores has specified patterns results are illustrated through analysis of two tables previously analyzed in the statistical literature comparisons are made with alternate methods of analysis based on a log linear parameterization of cell probabilities it is shown that canonical analysis wh