estimating the proportion of cured patients in a censored sample there has been a recurring interest in modelling survival data which hypothesize subpopulations of individuals highly susceptible to some types of adverse events while other individuals are assumed to be at much less risk like recurrence of breast cancer a binary random effect is assumed in this article to model the susceptibility of each individual we propose a simple multiple imputation algorithm for the analysis of censored data which combines a binary regression formulation for the probability of occurrence of an event say recurrence of the breast cancer tumour and a cox s proportional hazards regression model for the time to occurrence of the event if it does the model distinguishes the effects of the covariates on the probability of cure and on the time to recurrence of the disease a sas macro has been written to implement the proposed multiple imputation algorithm so that sophisticated programming effort can be rendered into a user friendly application simulation results show that the estimates are reasonably efficient the method is applied to analyse the breast cancer recurrence data the proposed method can be modified easily to accommodate more general random effects other than the binary random effects so that the random effects not only affect the probability of occurrence of the event but also the heterogeneity of the time to recurrence of the event among the uncured patients

semiparametric analysis of zero inflated count data medical and public health research often involve the analysis of count data that exhibit a substantially large proportion of zeros such as the number of heart attacks and the number of days of missed primary activities in a given period a zero inflated poisson regression model which hypothesizes a two point heterogeneity in the population characterized by a binary random effect is generally used to model such data subjects are broadly categorized into the low risk group leading to structural zero counts and high risk or normal group so that the counts can be modeled by a poisson regression model the main aim is to identify the explanatory variables that have significant effects on i the probability that the subject is from the low risk group by means of a logistic regression formulation and ii the magnitude of the counts given that the subject is from the high risk group by means of a poisson regression where the effects of the covariates are assumed to be linearly related to the natural logarithm of the mean of the counts in this article we consider a semiparametric zero inflated poisson regression model that postulates a possibly nonlinear relationship between the natural logarithm of the mean of the counts and a particular covariate a sieve maximum likelihood estimation method is proposed asymptotic properties of the proposed sieve maximum likelihood estimators are discussed under some mild conditions the estimators are shown to be asymptotically efficient and normally distributed simulation studies were carried out to investigate the performance of the proposed method for illustration purpose the method is applied to a data set from a public health survey conducted in indonesia where the variable of interest is the number of days of missed primary activities due to illness in a 4 week period

quantum symmetric kac moody pairs the present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable kac moody algebras the resulting quantum symmetric pairs are right coideal subalgebras of quantized enveloping algebras they give rise to triangular decompositions including a quantum analog of the iwasawa decomposition and they can be written explicitly in terms of generators and relations moreover their centers and their specializations are determined the constructions follow g letzter s theory of quantum symmetric pairs for semisimple lie algebras the main additional ingredient is the classification of involutive automorphisms of the second kind of symmetrizable kac moody algebras due to kac and wang the resulting theory comprises various classes of examples which have previously appeared in the literature such as q onsager algebras and the twisted q yangians introduced by molev ragoucy and sorba

a multiple imputation approach to cox regression with interval censored data we propose a general semiparametric method based on multiple imputation for cox regression with interval censored data the method consists of iterating the following two steps first from finite interval censored but not right censored data exact failure times are imputed using tanner and wei s poor man s or asymptotic normal data augmentation scheme based on the current estimates of the regression coefficient and the baseline survival curve second a standard statistical procedure for right censored data such as the cox partial likelihood method is applied to imputed data to update the estimates through simulation we demonstrate that the resulting estimate of the regression coefficient and its associated standard error provide a promising alternative to the nonparametric maximum likelihood estimate our proposal is easily implemented by taking advantage of existing computer programs for right censored data

nonexistence of the reversed flow solutions of the falkner skan equations abstract nonexistence of reversed flow solutions of the well known falkner skan equations arising in the boundary layer theory is considered analytically a new system of two singular integral equations are proposed and studied which plays a key role in the study of reversed flow solutions the properties of the velocity and the shear stress of the reversed flows are provided these properties describe the shapes and behaviors of the curves of the velocity and the shear stress functions a new lower bound of the skin friction which is useful in numerical analysis is given the results on the nonexistence of reversed flow solutions can be used to estimate the exact critical value which is of importance in aeronautics because separation occurs at this value

affine kac moody symmetric spaces related with a1 1 a2 1 a2 2 symmetric spaces associated with lie algebras and lie groups which are riemannian manifolds have recently got a lot of attention in various branches of physics for their role in classical quantum integrable systems transport phenomena etc their infinite dimensional counter parts have recently been discovered which are affine kac moody symmetric spaces in this paper we have algebraically explicitly computed the affine kac moody symmetric spaces associated with affine kac moody algebras a1 1 a2 1 a2 2 we hope these types of spaces will play similar roles as that of symmetric spaces in many physical systems

multiple imputation in mixture models for nonignorable nonresponse with follow ups abstract one approach to inference for means or linear regression parameters when the outcome is subject to nonignorable nonresponse is mixture modeling mixture models assume separate parameters for respondents and nonrespondents implementation by multiple imputation consists of repeatedly filling in missing values for nonrespondents estimating parameters using the filled in data and then adjusting for variability between imputations we evaluated the performance of this scheme using simulated data with a 25 sample of nonrespondents followed up we conclude that it provides a generally satisfactory and robust approach to inference for means and regression parameters in this case although a greater number of imputations may be required for good performance compared to the number required for estimation when nonresponse is ignorable

modelling count data with excessive zeros the need for class prediction in zero inflated models and the issue of data generation in choosing between zero inflated and generic mixture models for dental caries data count data may possess an excess of zeros relative to standard distributions zero inflated poisson zip or binomial zib and generic mixture models have been proposed to deal with such data we consider biomedical count data with an excess number of zeros and seek to address the following i do zero inflated models need covariates in the distribution part to predict class membership ii what model fit criteria have clinical relevance to predicted counts iii can very different model parameterizations have near identical fit and iv how could model selection and hence model interpretation be aided by considering data generation processes we show that covariates in the distribution part of zero inflated models are needed to predict class membership a range of model fit criteria should be considered as consensus is rarely achieved and considering predicted outcomes may be just as valuable as likelihood based criteria zero inflated and generic mixture models may be indistinguishable according to both likelihood based model fit criteria and predicted outcomes in which case model differentiation hence model selection and interpretation might be guided by the consideration of a priori data generation processes zero inflated models reflect whether or not there are or have been risk differences in disease onset and disease progression while generic mixture models identify sub types of individuals with similar risks of disease onset and progression one or both modelling strategies may be used though a priori knowledge or clinical impression of data generation might help to distinguish between two or more parameterizations that exhibit similar fit and yield near identical predicted counts

involutive automorphisms of the affine kac moody algebra a1 1 the matrix formulation of automorphisms of an affine kac moody algebra that was developed in a previous paper is here applied to the determination of all the conjugacy classes of involutive automorphisms of the affine kac moody algebra a1 1 where it is compared with the application of more traditional structural techniques

modelling heterogeneity in clustered count data with extra zeros using compound poisson random effect in medical and health studies heterogeneities in clustered count data have been traditionally modeled by positive random effects in poisson mixed models however excessive zeros often occur in clustered medical and health count data in this paper we consider a three level random effects zero inflated poisson model for health care utilization data where data are clustered by both subjects and families to accommodate zero and positive components in the count response compatibly we model the subject level random effects by a compound poisson distribution our model displays a variance components decomposition which clearly reflects the hierarchical structure of clustered data a quasi likelihood approach has been developed in the estimation of our model we illustrate the method with analysis of the health care utilization data the performance of our method is also evaluated through simulation studies

zero inflated poisson regression with an application to defects in manufacturing zero inflated poisson zip regression is a model for count data with excess zeros it assumes that with probability p the only possible observation is 0 and with probability 1 p a poisson random variable is observed for example when manufacturing equipment is properly aligned defects may be nearly impossible but when it is misaligned defects may occur according to a poisson distribution both the probability p of the perfect zero defect state and the mean number of defects in the imperfect state may depend on covariates sometimes p and are unrelated other times p is a simple function of such as p l 1 t for an unknown constant t in either case zip regression models are easy to fit the maximum likelihood estimates mle s are approximately normal in large samples and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the mle s simulations suggest that the confidence intervals based on likelihood ratio test

a classification of involutive automorphisms of an affine kac moody lie algebra abstract in this thesis we classify the conjugacy classes of involutions in aut g where g is an affine kac moody lie algebra we distinguish between two kinds of involutions those which preserve the conjugacy class of a borel subalgebra and those which don t we give a complete and non redundant list of representatives of involutions of the first kind and we compute their fixed points sets we prove that any involution of the first kind has a conjugate which leaves invariant the components of the gauss decomposition g n h n we also give a complete list of representatives of the conjugacy classes of involutions of the second kind

existence and nonuniqueness of solutions of a singular nonlinear boundary layer problem abstract sufficient conditions for existence and nonuniqueness of positive solutions of the singular boundary value problem g x g x h x 0 k x k 0 g k c g 1 0 are obtained also it is proved that the solutions with g k ck for c and g k k 2 2h k for c 0 are unique furthermore it is shown numerically that for h x x there are exactly two solutions for the problem

on solutions of some singular non linear differential equations arising in boundary layer theory abstract solutions for a class of singular non linear second order differential equations arising in boundary layer theory with suction injection when crocco variables are employed are obtained existence uniqueness and analyticity results are established for boundary conditions corresponding to flow of a uniform stream past a semi infinite flat plate classical problem of blasius and for the flow behind weak expansion since the standardization technique in refs 8 9 11 does not work a new technique is developed and used in proving existence and uniqueness theorems furthermore the analytical solutions are compared with the numerical ones

the matrix theory of automorphisms for twisted affine kac moody algebras for and for 1 the application to the two series of classical twisted affine kac moody algebras for and for of the matrix formulation of automorphisms developed earlier for untwisted affine kac moody algebras is investigated the conjugacy classes of involutive automorphisms and the corresponding real forms are deduced explicitly for the special case of

involutive automorphisms of the class of affine kac moody algebras bl 1 all the conjugacy classes of involutive automorphisms of the affine kac moody algebras bl 1 for l or 1 are determined using the matrix formulation of automorphisms of an affine kac moody algebra

specification and testing of some modified count data models abstract this paper explores the specification and testing of some modified count data models these alternatives permit more flexible specification of the data generating process dgp than do familiar count data models e g the poisson and provide a natural means for modeling data that are over or underdispersed by the standards of the basic models in the cases considered the familiar forms of the distributions result as parameter restricted versions of the proposed modified distributions accordingly score tests of the restrictions that use only the easily computed ml estimates of the standard models are proposed the tests proposed by hausman 1978 and white 1982 are also considered the tests are then applied to count data models estimated using survey microdata on beverage consumption

general theory of the matrix formulation of the automorphisms of affine kac moody algebras the determination of conjugacy classes within the group of all automorphisms of an affine kac moody algebra is discussed in detail and the limited role of cartan preserving automorphisms is emphasized a comprehensive method of dealing with all the automorphisms of an untwisted affine kac moody algebra is developed this is based on a matrix formulation of the untwisted affine kac moody algebras four different types of automorphism called type 1a type 1b type 2a and type 2b are identified and analysed within this matrix formulation the development of the detailed properties of automorphisms in the matrix formulation includes formulae for the products and inverses of automorphisms together with the conjugacy and involutive conditions

modeling heaping in self reported cigarette counts in studies of smoking behavior some subjects report exact cigarette counts whereas others report rounded off counts particularly multiples of 20 10 or 5 this form of data reporting error known as heaping can bias the estimation of parameters of interest such as mean cigarette consumption we present a model to describe heaped count data from a randomized trial of bupropion treatment for smoking cessation the model posits that the reported cigarette count is a deterministic function of an underlying precise cigarette count variable and a heaping behavior variable both of which are at best partially observed to account for an excess of zeros as would likely occur in a smoking cessation study where some subjects successfully quit we model the underlying count variable with zero inflated count distributions we study the sensitivity of the inference on smoking cessation by fitting various models that either do or do not account for heaping and zero inflation comparing the models by means of bayes factors our results suggest that sufficiently rich models for both the underlying distribution and the heaping behavior are indispensable to obtaining a good fit with heaped smoking data the analyses moreover reveal that bupropion has a significant effect on the fraction abstinent but not on mean cigarette consumption among the non abstinent

new results of falkner skan equation arising in boundary layer theory abstract this paper presents a new nonexistence result and upper and lower bounds of the shear stress f 0 to the well known falkner skan equation arising from the boundary layer problems f f f 1 f 2 0 0 subject to the boundary condition f 0 f 0 0 f 1 and the side condition 0 f 1 for 0

numerical solution of the falkner skan equation using piecewise linear functions we present a finite element method for the solution of the falkner skan equation the method uses a coordinate transformation to map the semi infinite domain of the problem to the unit interval 0 1 by means of a suitable change of variables the transformed third order boundary value problem is further rewritten as a system of differential equations consisting of a second order equation and a first order equation the second order equation is approximated using a galerkin formulation with piecewise linear elements and the first order equation is approximated using a centered difference approximation in the process of the initial transformation a finite computational boundary is introduced this boundary is obtained as part of the computational solution by imposing an additional asymptotic boundary condition the solutions obtained thus are in excellent agreement with those obtained by previous authors

applications of multiple imputation to the analysis of censored regression data the first part of the article reviews the data augmentation algorithm and presents two approximations to the data augmentation algorithm for the analysis of missing data problems the poor man s data augmentation algorithm and the asymptotic data augmentation algorithm these two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology the performances of the censored regression algorithms are examined in a simulation study it is found up to the precision of the study that the bias of both the poor man s and asymptotic data augmentation estimators as well as the buckley james estimator does not appear to differ from zero however with regard to mean squared error over a wide range of settings examined in this simulation study the two data augmentation estimators have a smaller mean squared error than does the buckley james estimator in addition associated with the two data augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters it is shown how this device can be used to estimate the standard error of either data augmentation estimate of any parameter e g the correlation coefficient associated with the model in the simulation study the estimated standard error of the asymptotic data augmentation estimate of the regression parameter is found to be congruent with the monte carlo standard deviation of the corresponding parameter estimate the algorithms are illustrated using the updated stanford heart transplant data set

on the solution of falkner skan equations abstract new existence and uniqueness proofs are given for the solutions of the equations governing the self similar compressible boundary layer falkner skan equations the properties of the solutions are studied and some bounds on important quantities are concluded the paper is restricted to favourable pressure gradients and to wall cooling

real forms and conjugacy classes of involutive automorphisms of the d 1 affine kac moody algebras the real forms of the complex affine kac moody algebras d 1 for 4 are found by determining all the conjugacy classes of the involutive automorphisms of d 1 using the matrix formulation of automorphisms of an affine kac moody algebra

existence of solutions of laminar boundary layer equations with decelerating external flows abstract new results on the existence and nonexistence of solutions of laminar boundary layer equations with decelerating external flows are obtained some previous results treated these equations with accelerating or constant external flows our approach is to establish a system of two integral equations with singularities which will be proved to be equivalent to the laminar boundary layer equations and prove that the system has solutions by using the leray schauder fixed point theorem and the helly selection principle

involutive automorphisms and iwasawa decomposition of affine kac moody superalgebras the involutive automorphisms of affine kac moody superalgebras are computed from satake superdiagrams corresponding to these algebras these are then used to furnish a general treatment of the iwasawa decomposition of these algebras in particular we consider a 1 0 1 and b 1 1 1 as representative examples for the purpose of illustration

involutive automorphisms of the affine kac moody algebras al 1 for l or 3 by the matrix method the determination of all the conjugacy classes of involutive automorphisms of the affine kac moody algebras al 1 for l or 3 is presented using the matrix formulation of automorphisms of an affine kac moody algebra that was developed in a previous paper ibid vol 25 p 3955 1992

fixed sign solutions for a system of singular focal boundary value problems we consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments using schauder fixed point theorem we establish criteria such that the system of boundary value problems has at least one fixed sign solution

the conjugacy classes of the involutive automorphisms of affine kac moody algebra a2 1 all the conjugacy classes of involutive automorphisms of the affine kac moody algebra a2 1 are obtained using the matrix formulation of automorphisms of an affine kac moody algebra that was developed in a previous paper

singular nonlinear boundary value problems arising in boundary layer theory abstract the singular nonlinear boundary value problem equation arises in the boundary layer theory we prove in this paper that the problem has a unique positive solution for each fixed 0 and there is no positive solution for 1 2

multiple solutions of the falkner skan equation for flow past a stretching boundary similarity solutions for pressure gradient driven flow over a stretching boundary may be obtained when the external velocity and the boundary velocity are each proportional to the same power law of the downstream coordinate the problem is governed by a two parameter falkner skan equation with beta measuring the stretch rate of the moving boundary and lambda equal to the ratio of free stream velocity to boundary velocity numerical calculations for beta leqq 1 over a range of positive and negative lambda display rich solution behavior for 1 leqq beta leqq 0 dual solutions no solution are found below above a critical value lambda m beta when lambda 0 one observes triple solutions for 0 beta lesssim 0 14 unique solutions for 0 14 lesssim beta leqq 0 5 and dual solutions for 0 5 beta leqq 1 an exact solution is given for beta 1 and asymptotic analysis is employed to elucidate the solution behavior for beta 0 as lambda to 0 and for

invariants of real forms of affine kac moody lie algebras abstract the theory of vogan diagrams which are dynkin diagrams with an overlay of certain additional information allows one to give a rapid classification of finite dimensional real semisimple lie algebras and to make use of this classification in practice this paper develops a corresponding theory of vogan diagrams for almost compact real forms of indecomposable nontwisted affine kac moody lie algebras in this case also the equivalence classes of vogan diagrams correspond to the isomorphism classes of almost compact real forms although the real forms of such algebras had already been classified the theory of vogan diagrams introduces invariants for such algebras and makes it possible to locate a given real form within the classification

nontrivial solution of third order nonlinear eigenvalue problems ii abstract in this paper we firstly make some corrections for typos errors on our paper nontrivial solution of third order nonlinear eigenvalue problems appl math comput 176 2006 714 721 and then we supplement some cases which have not been studied in the above paper

infinite flag varieties and conjugacy theorems abstract we study the orbit of a highest weight vector in an integrable highest weight module of the group g associated to a kac moody algebra unk a we obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of unk a in particular we prove conjugacy theorems for cartan and borel subalgebras of unk a so that the cartan matrix a is an invariant of unk a

the velocity and shear stress functions of the falkner skan equation arising in boundary layer theory abstract new compactness results on the velocity functions and shear stress functions of the well known falkner skan equation are obtained the methodology is to utilize the equivalence between the falkner skan equation and a singular integral equation established recently by lan and yang

modeling zero inflated count data using a covariate dependent random effect model in various medical related researches excessive zeros which make the standard poisson regression model inadequate often exist in count data we proposed a covariate dependent random effect model to accommodate the excess zeros and the heterogeneity in the population simultaneously this work is motivated by a data set from a survey on the dental health status of hong kong preschool children where the response variable is the number of decayed missing or filled teeth the random effect has a sound biological interpretation as the overall oral health status or other personal qualities of an individual child that is unobserved and unable to be quantified easily the overall measure of oral health status responsible for accommodating the excessive zeros and also the heterogeneity among the children is covariate dependent this covariate dependent random effect model allows one to distinguish whether a potential covariate has an effect on the conceived overall oral health condition of the children that is the random effect or has a direct effect on the magnitude of the counts or both we proposed a multiple imputation approach for estimation of the parameters we discussed the choice of the imputation size we evaluated the performance of the proposed estimation method through simulation studies and we applied the model and method to the dental data copyright 2012 john wiley sons ltd

satake diagrams of affine kac moody algebras satake diagrams of affine kac moody algebras untwisted and twisted are obtained from their dynkin diagrams these diagrams give a classification of restricted root systems associated with these algebras in the case of simple lie algebras these root systems and satake diagrams correspond to symmetric spaces which have recently found many physical applications in quantum integrable systems quantum transport problems random matrix theories etc we hope these types of root systems may have similar applications in theoretical physics in future and may correspond to symmetric spaces analogue of affine kac moody algebras if they exist

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea