symplectic geometry of suq h 0 2 and suq h 2 algebras the authors give a complete description of q deformation of su 2 algebra in terms of symplectic geometry the geometric meanings of such a deformation are manifestly shown at classical as well as at quantum level as a model they study the classical and quantum dynamics of a particle with q spin moving in electromagnetic fields in detail

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

bayesian semiparametric median regression modeling median regression models become an attractive alternative to mean regression models when employing flexible families of distributions for the errors classical approaches are typically algorithmic with desirable properties emerging asymptotically however nonparametric error models may be most attractive in the case of smaller sample sizes where parametric specifications are difficult to justify hence a bayesian approach enabling exact inference given the observed data may be appealing in this context there is little bayesian work we develop two fully bayesian modeling approaches employing mixture models for the errors in a median regression model the associated families of error distributions allow for increased variability skewness and flexible tail behavior the first family is semiparametric with extra variability captured nonparametrically through mixing and skewness handled parametrically the second family a fully nonparametric one includes all unimodal densities on the real line with

solving the two dimensional constant quantum yang baxter equation a detailed analysis of the constant quantum yang baxter equation rk1k2j1j2 rl1k3k1j3rl2l3k2k3 rk2k3j2j3 rk1l3j1k3rl1l2k1k2 in two dimensions is presented leading to an exhaustive list of its solutions the set of 64 equations for 16 unknowns was first reduced by hand to several subcases which were then solved by computer using the grobner basis methods each solution was then transformed into a canonical form based on the various trace matrices of r for final elimination of duplicates and subcases if we use homogeneous parametrization the solutions can be combined into 23 distinct cases modulo the well known c p and t reflections and rotations and scalings r q q r q q 1

multiparameter solutions of the yang baxter equation the multiparameter solutions 4 4 r matrices of the quantum yang baxter equation have been systematically investigated and more than thirty selected solutions are presented by using wu elimination the free parameters and non zero eigenvalues of these r matrices vary from one to five and zero to four respectively they are classified according to the corresponding algebraic structures

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

analysis of covariance structures under elliptical distributions abstract this article examines the adjustment of normal theory methods for the analysis of covariance structures to make them applicable under the class of elliptical distributions it is shown that if the model satisfies a mild scale invariance condition and the data have an elliptical distribution the asymptotic covariance matrix of sample covariances has a structure that results in the retention of many of the asymptotic properties of normal theory methods if a scale adjustment is applied the likelihood ratio tests of fit have the usual asymptotic chi squared distributions difference tests retain their property of asymptotic independence and maximum likelihood estimators retain their relative asymptotic efficiency within the class of estimators based on the sample covariance matrix an adjustment to the asymptotic covariance matrix of normal theory maximum likelihood estimators for elliptical distributions is provided this adjustment is particularly simple in models for patterned covariance or co

on the new algebra related to the non standard r matrix the authors demonstrate that the new algebra associated to the non standard r matrix investigated previously by fei and yue 1993 is related to the su 2 q algebra by a simple transformation criteria which identify equivalent quantum algebra are given

embedding long cycles in faulty k ary 2 cubes abstract the class of k ary n cubes represents the most commonly used interconnection topology for distributed memory parallel systems given an even k 4 let v 1 v 2 be the bipartition of the k ary 2 cube f v 1 f v 2 be the numbers of faulty vertices in v 1 and v 2 respectively and f e be the number of faulty edges in this paper we prove that there exists a cycle of length k 2 2max f v 1 f v 2 in the k ary 2 cube with 0 f v 1 f v 2 f e 2 this result is optimal with respect to the number of faults tolerated

fault tolerant cycle embedding in alternating group graphs abstract cycle embedding is an important issue in evaluating the efficiency of interconnection networks and is also an extension of the theoretical research on hamiltonicity in this paper we study the fault tolerant hamiltonicity of alternating group graphs which were recently proposed as interconnection topologies for parallel and distributed systems a cycle of length l is said to be an l cycle let f be a set of faulty vertices in an n dimensional alternating group graph ag n and let m be the number of vertices in ag n f a previous result in j m chang j s yang y l wang y cheng panconnectivity fault tolerant hamiltonicity and hamiltonian connectivity in alternating group graphs networks 44 2004 302 310 showed that for n 4 ag n f is hamiltonian i e ag n f possesses a hamiltonian cycle if f n 2 and ag n f is hamiltonian connected i e every two vertices of ag n f are connected by a hamiltonian path if f n 3 in this paper we show the following results i ag n f is pancyclic i e ag n f contains an l cycle for each l with 3 l m if f n 2 ii ag n f is vertex pancyclic i e every vertex of ag n f is contained in an l cycle for each l with 3 l m if f n 3 and iii ag n f is edge 4 pancyclic i e every edge of ag n f is contained in an l cycle for each l with 4 l m if f n 4 the first result is an improvement over the previous one and the last two results are new characterization of fault tolerant pancyclicity on ag n all the results we achieved are the best possible in the sense that the number of faulty vertices cannot be increased

bayesian semiparametric analysis of structural equation models with mixed continuous and unordered categorical variables recently structural equation models sems have been applied for analyzing interrelationships among observed and latent variables in biological and medical research latent variables in these models are typically assumed to have a normal distribution this article considers a bayesian semparametric sem with covariates and mixed continuous and unordered categorical variables in which the explanatory latent variables in the structural equation are modeled via an appropriate truncated dirichlet process with a stick breaking procedure results obtained from a simulation study and an analysis of a real medical data set are presented to illustrate the methodology

a predictive approach to the analysis of designed experiments abstract viewing the analysis of designed experiments as a model selection problem we introduce the use of a predictive bayesian criterion in this context based on the predictive density of a replicate experiment pdre a calibration of the criterion is provided to assist in the model choice the relationships of the proposed criterion to other prevalent criteria such as aic bic and mallows s c p are given an information theoretic criterion based on the pdre s of two competing models is also introduced and compared with the usual f statistic for two nested models examples are given to illustrate the proposed methodology

cycle embedding of augmented cubes a graph g v e is vertex pancyclic if for every vertex u and any integer l ranging from a positive constant l to v g contains a cycle c of length l such that u is in c in this paper we show that an n dimensional augmented cube where n 2 is vertex pancyclic with l 3

bayesian nonparametric estimation of the median part i computation of the estimates let x i i 1 ldots n be i i d sim f theta where f theta x f x theta for some f that has median equal to 0 f is assumed unknown or only partially known and the problem is to estimate theta priors are put on the pair f theta the priors on f concentrate all their mass on c d f s with median equal to 0 these priors include dirichlet type priors the marginal posterior distribution of theta given x 1 ldots x n is computed the mean of the posterior is taken as the estimate of theta

conditional fault tolerant edge bipancyclicity of hypercubes with faulty vertices and edges let f be a faulty set in an n dimensional hypercube q n such that in q n f each vertex is incident to at least two edges and let f v f e be the numbers of faulty vertices and faulty edges in f respectively in this paper we consider the fault tolerant edge bipancyclicity of hypercubes it is shown that each edge in q n f for n 3 lies on a fault free cycle of any even length from 6 to 2 n 2 f v if f v f e 2 n 5 this gives an answer for a problem proposed by yang et al 2016 33 consider hypercubes with mixed faulty edges and faulty vertices under conditional fault model improve the previous results about the fault tolerant edge bipancyclicity of hypercubes give an affirmative answer for a problem proposed by yang et al 2016

generalized multilevel structural equation modeling a unifying framework for generalized multilevel structural equation modeling is introduced the models in the framework called generalized linear latent and mixed models gllamm combine features of generalized linear mixed models glmm and structural equation models sem and consist of a response model and a structural model for the latent variables the response model generalizes glmms to incorporate factor structures in addition to random intercepts and coefficients as in glmms the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower level units in the higher level units and missing data a wide range of response processes can be modeled including ordered and unordered categorical responses counts and responses of mixed types the structural model is similar to the structural part of a sem except that it may include latent and observed variables varying at different levels for example unit level latent variables factors or random coefficients can be regressed on cluster level latent variables special cases of this framework are explored and data from the british social attitudes survey are used for illustration maximum likelihood estimation and empirical bayes latent score prediction within the gllamm framework can be performed using adaptive quadrature in gllamm a freely available program running in stata

new algebra related to nonstandard r matrix a new algebra that is different to the known algebras in both quantum r matrix and quantum enveloping algebras is presented its nontrivial hopf algebraic structures are also discussed

a two level structural equation model approach for analyzing multivariate longitudinal responses the analysis of longitudinal data to study changes in variables measured repeatedly over time has received considerable attention in many fields this paper proposes a two level structural equation model for analyzing multivariate longitudinal responses that are mixed continuous and ordered categorical variables the first level model is defined for measures taken at each time point nested within individuals for investigating their characteristics that are changed with time the second level is defined for individuals to assess their characteristics that are invariant with time the proposed model accommodates fixed covariates nonlinear terms of the latent variables and missing data a maximum likelihood ml approach is developed for the estimation of parameters and model comparison results of a simulation study indicate that the performance of the ml estimation is satisfactory the proposed methodology is applied to a longitudinal study concerning cocaine use

marginal likelihood and bayes factors for dirichlet process mixture models we present a method for comparing semiparametric bayesian models constructed under the dirichlet process mixture dpm framework with alternative semiparameteric or parameteric bayesian models a distinctive feature of the method is that it can be applied to semiparametric models containing covariates and hierarchical prior structures and is apparently the first method of its kind formally the method is based on the marginal likelihood estimation approach of chib 1995 and requires estimation of the likelihood and posterior ordinates of the dpm model at a single high density point an interesting computation is involved in the estimation of the likelihood ordinate which is devised via collapsed sequential importance sampling extensive experiments with synthetic and real data involving semiparametric binary data regression models and hierarchical longitudinal mixed effects models are used to illustrate the implementation performance and applicability of the method

statistical inference based on pseudo maximum likelihood estimators in elliptical populations in this article we develop statistical inference based on the maximum likelihood method in elliptical populations with an unknown density function the method assuming the multivariate normal distribution using the sample mean and the sample covariance matrix is basically correct even for elliptical populations under a certain kurtosis adjustment but is not statistically efficient especially when the kurtosis of the population distribution has higher than moderate values on the other hand several methods of statistical inference assuming a particular family e g multivariate t distribution of elliptical distributions have been recommended as a robust procedure against outliers or distributions with heavy tails such inference also will be important to maintain a high efficiency of statistical inference in elliptical populations in practice however it is very difficult to choose an appropriate family of elliptical distributions and one may misspecify the family furthermore extra parameters

maximum likelihood analysis of a general latent variable model with hierarchically mixed data summary a general two level latent variable model is developed to provide a comprehensive framework for model comparison of various submodels nonlinear relationships among the latent variables in the structural equations at both levels as well as the effects of fixed covariates in the measurement and structural equations at both levels can be analyzed within the framework moreover the methodology can be applied to hierarchically mixed continuous dichotomous and polytomous data a monte carlo em algorithm is implemented to produce the maximum likelihood estimate the e step is completed by approximating the conditional expectations through observations that are simulated by markov chain monte carlo methods while the m step is completed by conditional maximization a procedure is proposed for computing the complicated observed data log likelihood and the bic for model comparison the methods are illustrated by using a real data set

the bipancycle connectivity of the hypercube paths and cycles are popular interconnection networks due to their simplicity and low degrees and therefore an efficient way of embedding them into an interconnection network is of particular importance many path embedding aspects and cycle embedding aspects such as hamiltonicity hamiltonian connectivity panconnectivity bipanconnectivity pancyclicity vertex pancyclicity and edge pancyclicity have been proposed and extensively studied in fact these discussions are meaningful for interconnection networks of resource allocated systems or heterogeneous computing systems in this paper we propose a new cycle embedding aspect called bipancycle connectivity that combines the concepts of vertex pancyclicity and bipanconnectivity a bipartite graph is bipancycle connected if an arbitrary pair of vertices x y is contained by common cycles called bipanconnected cycles that include a cycle of every even length ranging from minc x y to n where minc x y denotes the length of the minimum cycle that contains x and y and n is the number of vertices in this paper we introduce a new graph called the cycle of ladders we show that the hypercube is bipancycle connected by presenting algorithms to embed the cycle of ladders into the hypercube

a bayesian analysis of the multinomial probit model using marginal data augmentation we introduce a set of new markov chain monte carlo algorithms for bayesian analysis of the multinomial probit model our bayesian representation of the model places a new and possibly improper prior distribution directlyon the identi0able parameters and thus is relativelyeasyto interpret and use our algorithms which are based on the method of marginal data augmentation involve onlydraws from standard distributions and dominate other available bay esian methods in that theyare as quick to converge as the fastest methods but with a more attractive prior speci0cation c code along with an r interface for our algorithms is publiclyavailable 1

path embeddings in faulty 3 ary n cubes the class of k ary n cubes represents the most commonly used interconnection topology for distributed memory parallel systems in this paper we study the problem of embedding paths of various lengths into faulty 3 ary n cubes and prove that a faulty 3 ary n cube with f 2n 3 faulty vertices admits a path of every length from 2n 1 to 3 n f 1 connecting any two distinct healthy vertices this result is optimal with respect to the number of vertex faults tolerated

bayesian criterion based model assessment for categorical data we propose a general bayesian criterion for model assessment for categorical data called the weighted l measure which is constructed from the posterior predictive distribution of the data the measure is based on weighting the observations according to the sampling variance of their future response vector the weight component in the weighted l measure plays the role of a penalty term in the criterion in which a greater weight assigned to covariate values implies a greater penalty term on the dimension of the model a detailed justification is provided for such a weighting procedure and several theoretical properties of the weighted l measure are presented for a wide variety of discrete data models for these models we examine properties of the weighted l measure and show that it can perform better than the unweighted l measure in a variety of settings in addition we show that the weighted quadratic loss l measure is more attractive than the unweighted l measure and the deviance loss l measure for categorical data moreover a calibration for the weighted l measure is motivated and proposed which allows us to compare formally the l measure values of competing models a detailed simulation study is presented to examine the performance of the weighted l measure and it is compared to other established model selection methods finally the method is applied to a real dataset using a bivariate ordinal response model

suq h 0 2 and suq h 2 the classical and quantum q deformations of the su 2 algebra by means of classical harmonic oscillators and their canonical quantization we show that the q deformation of the su 2 lie algebra can be realized at a classical level in the sense of poisson brackets denoted by suq inf not 0 2 and that the canonical quantization of the system leads to the quantum q deformation of the su 2 algebra denoted by suq 2 this means that the q deformation and the h cross quantization are in general two different concepts

bayesian analysis of structural equation models with multinomial variables and an application to type 2 diabetic nephropathy there is now increasing evidence proving that many complex diseases can be significantly influenced by correlated phenotype and genotype variables as well as their interactions effective and rigorous assessment of such influence is difficult because the number of phenotype and genotype variables of interest may not be small and a genotype variable is an unordered categorical variable that follows a multinomial distribution to address the problem we establish a novel nonlinear structural equation model for analysing mixed continuous and multinomial data that can be missing at random a confirmatory factor analysis model with kronecker product is proposed for grouping the manifest continuous and multinomial variables into latent variables according to their functions and a nonlinear structural equation is formulated to assess the linear and interaction effects of the independent latent variables to the dependent latent variables bayesian methods for estimation and model comparison are developed through markov chain monte carlo techniques and path sampling the newly developed methodologies are applied to a case control cohort of type 2 diabetic patients with nephropathy

path embedding in faulty hypercubes abstract there are some interesting results concerning longest paths or even cycles embedding in faulty hypercubes this paper considers the embeddings of paths of all possible lengths between any two fault free vertices in faulty hypercubes let fv respectively fe denote the number of faulty vertices respectively edges in an n dimensional hypercube qn we prove that there exists a fault free path of length l between any two distinct fault free vertices u and v in qn with f v f e n 2 for each l satisfying d q n u v 2 l 2 n 2 f v 1 and 2 l d q n u v the bounds on path length l and faulty set size f v f e for a successful embedding are tight that is the result does not hold if l d q n u v 2 or l 2 n 2 f v 1 or f v f e n 2 moreover our result improves some known results

bayesian model selection in finite mixtures by marginal density decompositions we consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture model in which d is bounded by some fixed finite number n our approach relies on the use of a prior over the space of mixing distributions with at most n components by decomposing the resulting marginal density under this prior we discover a weighted bayes factor method for consistently estimating d that can be implemented by an iid generalized weighted chinese restaurant gwcr monte carlo algorithm we also discuss a gibbs sampling method the blocked gibbs sampler for estimating d and also the mixing distribution we show that our resulting posterior is consistent and achieves the frequentist optimal op n 1 4 rate of estimation we compare the performance of the new gwcr model selection procedure with that of the akaike information criterion and the bayes information criterion implemented through an em algorithm applications of our methods to five real datasets and simulation