recovery of inter block information in cross over trials for cross over designs we show that one can recover information on direct and or residual treatment effects from an inter block patients as blocks analysis as is done in an incomplete block design 1 by combining the intra and inter block estimates we obtain the generalized least squares estimate in analysing cross over trials we recommended this approach provided the between patient variance component can be estimated efficiently

locally conformal finite difference time domain techniques for particle in cell plasma simulation the dey mittra s dey r mitra a locally conformal finite difference time domain fdtd algorithm for modeling three dimensional perfectly conducting objects ieee microwave guided wave lett 7 273 1997 finite difference time domain partial cell method enables the modeling of irregularly shaped conducting surfaces while retaining second order accuracy we present an algorithm to extend this method to include charged particle emission and absorption in particle in cell codes several examples are presented that illustrate the possible improvements that can be realized using the new algorithm for problems relevant to plasma simulation

small sample inference for fixed effects from restricted maximum likelihood restricted maximum likelihood reml is now well established as a method for estimating the parameters of the general gaussian linear model with a structured covariance matrix in particular for mixed linear models conventionally estimates of precision and inference for fixed effects are based on their asymptotic distribution which is known to be inadequate for some small sample problems in this paper we present a scaled wald statistic together with an f approximation to its sampling distribution that is shown to perform well in a range of small sample settings the statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias this approach has the advantage that it reproduces both the statistics and f distributions in those settings where the latter is exact namely for hotelling t2 type statistics and for analysis of variance f ratios the performance of the modified statistics is assessed through simulation studies of four different reml analyses and the methods are illustrated using three examples

a method for incorporating gauss lasw into electromagnetic pic codes abstract an algorithm is presented which solves a modified set of maxwell s equations none of them elliptic in an electromagnetic pic type code the algorithm prevents large violations of gauss law by diffusing away numerical errors arising from the particle to grid apportionment method there are no restrictions on the manner in which charge and current densities are determined from the particle distribution in particular point particles and simple linear interpolation are used

the t k diagnosability of the bc graphs processor fault diagnosis takes an important role in fault tolerant computing on multiprocessor systems there are two classical diagnosis strategies the precise strategy and the pessimistic strategy both of which are based on the well known pmc diagnostic model nevertheless the degree of diagnosability of the system is limited under these two strategies a better method called the t k diagnosis strategy is proposed by somani and peleg in which the identified fault set is allowed to contain at most k fault free processors using this diagnosis strategy the degree of diagnosability of the hypercube increases greatly as the number of the fault free processors in the fault set increases we study the t k diagnosability of so called bc graphs that include hypercubes crossed cubes mobius cubes and twisted cubes etc we show that any n dimensional bc graph is t n k k diagnosable when n spl ges 4 and 0 spl les k spl les n where t n k k 1 n 1 2 k 1 k 2 1 therefore the crossed cube the mobius cube and the twisted cube all have the same t k diagnosability as the hypercube as a result the algorithms developed for diagnosis on the hypercube may also be used to diagnose multiprocessor systems whose network topologies are based on bc graphs

fault tolerant edge bipancyclicity of faulty hypercubes under the conditional fault model it is well known that the n dimensional hypercube qn is one of the most versatile and efficient interconnection network architecture yet discovered for building massively parallel or distributed systems let f be the faulty set of qn and let fv fe be the numbers of faulty vertices and faulty edges in f respectively an edge e x y is said to be free if e x y are not in f and a cycle is said to be fault free if there is no faulty vertex or faulty edge on the cycle in this paper we prove that each free edge x y in qn 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 f e n 2 and both x and y are incident to at least two free edges this result confirms a conjecture reported in the literature

the embedded curved boundary method for orthogonal simulation meshes a method for incorporating piecewise linear approximations to curved boundaries is developed for codes using orthogonal meshes the resulting method retains much of the fidelity of adaptive triangle meshes in 2d while retaining essentially all of the speed of traditional methods relying on banded matrix solutions we find this technique useful for situations lying between the crude but fast stairstep approximation and the elegant but slower adaptive mesh techniques this method provides a practical approach to problems such as space charge emission while retaining the simplicity and run time advantage of orthogonal mesh based codes examples from space charge limited flow between curved electrodes are given

edge pancyclicity and path embeddability of bijective connection graphs an n dimensional bijective connection graph in brief bc graph is a regular graph with 2 n nodes and n2 n 1 edges the n dimensional hypercube crossed cube mobius cube etc are some examples of the n dimensional bc graphs in this paper we propose a general method to study the edge pancyclicity and path embeddability of the bc graphs first we prove that a path of length l with dist x n x y 2 y in x n where x n n 4 is a n dimensional bc graph satisfying the three specific conditions and v x n is the node set of x n furthermore by this result we can claim that x n is edge pancyclic lastly we show that these results can be applied to not only crossed cubes and mobius cubes but also other bc graphs except crossed cubes and mobius cubes so far the research on edge pancyclicity and path embeddability has been limited in some specific interconnection architectures such as crossed cubes mobius cubes

fault tolerant embedding of paths in crossed cubes the crossed cube cq n is an important variant of the hypercube q n and possesses many desirable properties for interconnection networks this paper shows that in cq n with f v faulty vertices and f e faulty edges there exists a fault free path of length between any two distinct fault free vertices for each satisfying 2 n email protected email protected email protected 2 n f v 1 provided that f v f email protected n 3 where the lower bound of and the upper bound of f v f e are tight for some n moreover this result improves the known result that cq n is n 3 hamiltonian connected

embedding meshes into crossed cubes crossed cubes are important variants of hypercubes in this paper we consider embeddings of meshes in crossed cubes the major research findings in this paper are 1 for any integer n 1 a 2x2 n 1 mesh can be embedded in the n dimensional crossed cube with dilation 1 and expansion 1 2 for any integer n 4 two node disjoint 4x2 n 3 meshes can be embedded in the n dimensional crossed cube with dilation 1 and expansion 2 the obtained results are optimal in the sense that the dilations of the embeddings are 1 the embedding of the 2x2 n 1 mesh is also optimal in terms of expansion because it has the smallest expansion 1

constructing the nearly shortest path in crossed cubes a graph g is panconnected if each pair of distinct vertices u v v g are joined by a path of length l for all d g u v

mean squared error of estimation or prediction under a general linear model abstract the problem considered is that of predicting a linear combination of the fixed and random effects of a mixed effects linear model more generally the problem considered is that of predicting an unobservable random variable from a set of observable random variables the best linear unbiased predictor depends on parameters which generally are unknown various exact or approximate expressions are given for the mean squared error mse of the predictor obtained by replacing the unknown parameters with estimates several estimators of the mse are investigated

distribution free estimation of some nonlinear panel data models this paper studies distribution free estimation of some multiplicative unobserved components panel data models one class of estimators requires only specification of the conditional mean in particular the multinomial quasi conditional maximum likelihood estimator is shown to be consistent when only the conditional mean in the unobserved effects model is correctly specified additional orthogonality conditions can be used in a method of moments framework a second class of problems specifies the conditional mean conditional variances and conditional covariances using the notion of a conditional linear predictor it is shown that specification of conditional second moments implies further orthogonality conditions in the observable data that can be exploited for efficiency gains this has applications to both count and gamma type panel data regression models

embedding hamiltonian paths in augmented cubes with a required vertex in a fixed position it is proved that there exists a path p l x y of length l if d a q n x y l 2 n 1 between any two distinct vertices x and y of aq n obviously we expect that such a path p l x y can be further extended by including the vertices not in p l x y into a hamiltonian path from x to a fixed vertex z or a hamiltonian cycle in this paper we prove that there exists a hamiltonian path r x y z l from x to z such that d r x y z l x y l for any three distinct vertices x y and z of aq n with n 2 and for any d a q n x y l 2 n 1 d a q n y z furthermore there exists a hamiltonian cycle s x y l such that d s x y l x y l for any two distinct vertices x and y and for any d a q n x y l 2 n 1

average information reml an efficient algorithm for variance parameter estimation in linear mixed models a strategy of using an average information matrix is shown to be computationally convenient and efficient for estimating variance components by restricted maximum likelihood reml in the mixed linear model three applications are described the motivation for the algorithm was the estimation of variance components in the analysis of wheat variety means from 1 071 experiments representing 10 years and 60 locations in new south wales we also apply the algorithm to the analysis of designed experiments by incomplete block analysis and spatial analysis of field experiments

multiple imputation approaches for the analysis of dichotomized responses in longitudinal studies with missing data often a binary variable is generated by dichotomizing an underlying continuous variable measured at a specific time point according to a prespecified threshold value in the event that the underlying continuous measurements are from a longitudinal study one can use the repeated measures model to impute missing data on responder status as a result of subject dropout and apply the logistic regression model on the observed or otherwise imputed responder status standard bayesian multiple imputation techniques rubin 1987 in multiple imputation for nonresponse in surveys that draw the parameters for the imputation model from the posterior distribution and construct the variance of parameter estimates for the analysis model as a combination of within and between imputation variances are found to be conservative the frequentist multiple imputation approach that fixes the parameters for the imputation model at the maximum likelihood estimates and construct the variance of parameter estimates for the analysis model using the results of robins and wang 2000 biometrika 87 113 124 is shown to be more efficient we propose to apply kenward and roger 1997 biometrics 53 983 997 degrees of freedom to account for the uncertainty associated with variance covariance parameter estimates for the repeated measures model

fault free hamiltonian cycles in crossed cubes with conditional link faults the crossed cube which is a variation of the hypercube possesses some properties superior to the hypercube in this paper assuming that each node is incident with at least two fault free links we show that an n dimensional crossed cube contains a fault free hamiltonian cycle even if there are up to 2n 5 link faults the result is optimal with respect to the number of link faults tolerated we also verify that the assumption is practically meaningful by evaluating its occurrence probability which is very close to 1

internal pilots for a class of linear mixed models with gaussian and compound symmetric data an internal pilot design uses interim sample size analysis without interim data analysis to adjust the final number of observations the approach helps to choose a sample size sufficiently large to achieve the statistical power desired but not too large which would waste money and time we report on recent research in cerebral vascular tortuosity curvature in three dimensions which would benefit greatly from internal pilots due to uncertainty in the parameters of the covariance matrix used for study planning unfortunately observations correlated across the four regions of the brain and small sample sizes preclude using existing methods however as in a wide range of medical imaging studies tortuosity data have no missing or mistimed data a factorial within subject design the same between subject design for all responses and a gaussian distribution with compound symmetry for such restricted models we extend exact small sample univariate methods for internal pilots to linear mixed models with any between subject design not just two groups planning a new tortuosity study illustrates how the new methods help to avoid sample sizes that are too small or too large while still controlling the type i error rate

hamiltonian paths and cycles with prescribed edges in the 3 ary n cube the k ary n cube has been one of the most popular interconnection networks for massively parallel systems given a set p of at most 2n 2 n 2 prescribed edges and two vertices u and v we show that the 3 ary n cube contains a hamiltonian path between u and v passing through all edges of p if and only if the subgraph induced by p consists of pairwise vertex disjoint paths none of them having u or v as internal vertices or both of them as end vertices as an immediate result the 3 ary n cube contains a hamiltonian cycle passing through a set p of at most 2n 1 prescribed edges if and only if the subgraph induced by p consists of pairwise vertex disjoint paths

fault hamiltonicity and fault hamiltonian connectivity of the arrangement graphs the arrangement graph a sub n k is a generalization of the star graph there are some results concerning fault hamiltonicity and fault hamiltonian connectivity of the arrangement graph however these results are restricted in some particular cases and thus are less completed we improve these results and obtain a stronger and simpler statement let n k spl ges 2 and f spl sube v a sub n k spl cup e a sub n k we prove that a sub n k f is hamiltonian if f spl les k n k 2 and a sub n k f is hamiltonian connected if f spl les k n k 3 these results are optimal

row column α designs in row column designs the experimental units are grouped in two directions i e two blocking factors are used with one factor representing the rows of the design and the other factor representing columns for instance in an agricultural experiment the rows and columns of a design might represent different times and method of application of fertilizers in a preference testing experiment the columns might represent different subjects and the rows the order in which different products are presented to the subjects in an insulin response experiment the rows columns and treatments may represent respectively individual animals date of injection and levels of insulin in all these experiments it is hoped that there will be a gain in the accuracy of estimating treatment comparisons resulting from eliminating the effects of the row and column factors

performance of analytical methods for overdispersed counts in cluster randomized trials sample size degree of clustering and imbalance many different methods have been proposed for the analysis of cluster randomized trials crts over the last 30 years however the evaluation of methods on overdispersed count data has been based mostly on the comparison of results using empiric data i e when the true model parameters are not known in this study we assess via simulation the performance of five methods for the analysis of counts in situations similar to real community intervention trials we used the negative binomial distribution to simulate overdispersed counts of crts with two study arms allowing the period of time under observation to vary among individuals we assessed different sample sizes degrees of clustering and degrees of cluster size imbalance the compared methods are i the two sample t test of cluster level rates ii generalized estimating equations gee with empirical covariance estimators iii gee with model based covariance estimators iv generalized linear mixed models glmm and v bayesian hierarchical models bayes hm variation in sample size and clustering led to differences between the methods in terms of coverage significance power and random effects estimation glmm and bayes hm performed better in general with bayes hm producing less dispersed results for random effects estimates although upward biased when clustering was low gee showed higher power but anticonservative coverage and elevated type i error rates imbalance affected the overall performance of the cluster level t test and the gee s coverage in small samples important effects arising from accounting for overdispersion are illustrated through the analysis of a community intervention trial on solar water disinfection in rural bolivia

geodesic pancyclicity of twisted cubes the hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement an n dimensional twisted cube tq n is an important variation of the hypercube q n and preserves many of its desirable properties the problem of embedding linear arrays and cycles into a host graph has attracted substantial attention in recent years the geodesic cycle embedding problem is for any two distinct vertices to find all the possible lengths of cycles that include a shortest path joining them in this paper we prove that tq n is geodesic 2 pancyclic for each odd integer n 3 this result implies that tq n is edge pancyclic for each odd integer n 3 moreover tq nxk 2 is also demonstrated to be geodesic 4 pancyclic

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

model selection in estimating equations summary model selection is a necessary step in many practical regression analyses but for methods based on estimating equations such as the quasi likelihood and generalized estimating equation gee approaches there seem to be few well studied model selection techniques in this article we propose a new model selection criterion that minimizes the expected predictive bias epb of estimating equations a bootstrap smoothed cross validation bcv estimate of epb is presented and its performance is assessed via simulation for overdispersed generalized linear models for illustration the method is applied to a real data set taken from a study of the development of ewe embryos

a general strategy for analyzing data from split plot and multistratum experimental designs increasingly industrial experiments use multistratum designs such as split plot and strip plot designs often these experiments span more than one processing stage the challenge is to identify an appropriate multistratum design along with an appropriate statistical model in this article we introduce hasse diagrams in the response surface context as a tool to visualize the unit structure of the experimental design the randomization and sampling approaches used the stratum in which each experimental factor is applied and the degrees of freedom available in each stratum to estimate main effects interactions and variance components we illustrate their use on several responses measured in a large study of the adhesion properties of coatings to polypropylene we discuss quantitative binary and ordered categorical responses for designs ranging from a simple split plot to a strip plot that involves repeated measurements of the response the datasets discussed in this article are available online a

multistratum response surface designs response surface designs are usually described as if the treatments have been completely randomized to the experimental units however in practice there is often a structure to the units implying the need for blocking if in addition some factors are more difficult to vary between units than others a multistratum structure arises naturally we present a general strategy for constructing response surface designs in multistratum unit structures designs are constructed stratum by stratum starting in the highest stratum in each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata allowing for all the effects that have to be estimated three examples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment set finally some practical considerations in randomization are discussed

embedding a hamiltonian cycle in the crossed cube with two required vertices in the fixed positions abstract a hamiltonian graph g is said to be panpositionably hamiltonian if for any two distinct vertices x and y of g there is a hamiltonian cycle c of g having dc x y l for any integer l satisfying d g x y l v g 2 where dg x y respectively dc x y denotes the distance between vertices x and y in g respectively c and v g denotes the total number of vertices of g as the importance of hamiltonian properties for data communication among units in an interconnected system the panpositionable hamiltonicity involves more flexible message transmission in this paper we study this property with respect to the class of crossed cubes which is a popular variant of the hypercube network

classical and bayesian prediction as applied to an unbalanced mixed linear model unbalanced mixed linear models that contain a single set of random effects are frequently employed in animal breeding applications in small area estimation and in the analysis of comparative experiments the problem considered is that of the point or interval prediction of the value of a linear combination of the fixed and random effects or the value of a future data point a common approach is empirical blup best linear unbiased prediction in which an estimate of the variance ratio is regarded as the true value empirical blup is satisfactory or can be made satisfactory by introducing appropriate modifications unless the estimate of the variance ratio is imprecise and is close to zero in which case more sensible point and interval predictions can be obtained by adopting a bayesian approach two animal breeding examples are used to illustrate the similarities and differences between the bayesian and empirical blup approaches

the application of reml in clinical trials residual maximum likelihood reml is a technique for estimating variance components in multi classified data in contrast to analysis of variance it can be routinely applied to unbalanced data and avoids some of the problems of biased variance estimates found with standard maximum likelihood estimation the full reml method is of particular value for the analysis of unbalanced clinical trials as it allows recovery of all the available information on treatment effects which can lead to significant improvements in their precision the use of reml has until recently been limited by heavy computational requirements and lack of readily available software this is no longer such a restriction however as reml procedures are now available in several widely used statistical packages including bmdp genstat and sas this paper describes the reml technique and discusses its application to three common types of clinical trial crossover repeated measures and multicentre

application of dey mittra conformal boundary algorithm to 3d electromagnetic modeling the dey mittra conformal boundary conditions have been implemented for the finite difference time domain fdtd electromagnetic solver of the vorpal plasma simulation framework and studied in the context of three dimensional large scale computations the maximum stable time step when using these boundary conditions can be arbitrarily small due to the presence of small fractional cells inside the vacuum region use of the gershgorin circle theorem allows the determination of a rigorous criterion for exclusion of small cells in order to have numerical stability for particular values of the ratio f d m dt dt c f l of the time step to the courant friedrichs lewy value for the infinite system application to a spherical cavity shows that these boundary conditions allow computation of frequencies with second order error for sufficiently small f d m however for sufficiently fine resolution dependent on f d m the error becomes first order just like the error for stair step boundary conditions nevertheless provided one does use a sufficiently small value of f d m one can obtain third order accuracy through richardson extrapolation computations for the tesla superconducting rf cavity design compare favorably with experimental measurements

embedding graphs onto the supercube in this paper we consider the supercube a new interconnection network derived from the hypercube the supercube introduced by a sen 1989 has the same diameter and connectivity as a hypercube but can be realized for any number of nodes not only powers of 2 we study the supercube s ability to execute parallel programs using graph embedding techniques we show that complete binary trees and bidimensional meshes with a side length power of 2 are spanning subgraphs of the supercube we then prove that the supercube is hamiltonian and when the number of nodes is not a power of 2 it contains all cycles of length greater than 3 as subgraphs

the influence of design on validity and efficiency of neighbour methods summary neighbour methods have often been shown to be apparently more efficient than analysis of variance for the analysis of field experiments this means that the precision of the analysis estimated by the statistical method itself is smaller for the neighbour method than for the classical one this comparison is meaningful only if the analysis is valid in the sense that it estimates its own precision without bias although precise validity properties are known for the analysis of variance of randomized designs no analogous properties are known for neighbour analyses in this paper we investigate the validity and efficiency of some neighbour methods and their relations with the design first we give precise definitions of the desirable properties of the combination of design including randomization and method of analysis then we report on a simulation study we show that neighbour methods are often valid or conservative with higher efficiency than classical ones to better ensure these properties we advocate the use of randomized neighbour designs and corrections to degrees of freedom finally we discuss how these results can be used to assess neighbour methods for routine trials

decomposition of prediction error abstract the problem considered is that of predicting the value of an unobservable random variable w from the value of an observable random vector y this problem is considered under each of four states of knowledge about the joint distribution of w and y ranging from complete knowledge to no knowledge a point predictor or predictors are presented for each case prediction error is decomposed so that each component reflects an absence of information under certain conditions these components are uncorrelated and have zero means an exact or approximate expression is given for the variance of each component

embedding a family of disjoint 3d meshes into a crossed cube crossed cubes are an important class of hypercube variants this paper addresses how to embed a family of disjoint 3d meshes into a crossed cube two major contributions of this paper are 1 for n 4 a family of two disjoint 3d meshes of size 2x2x2 n 3 can be embedded in an n d crossed cube with unit dilation and unit expansion and 2 for n 6 a family of four disjoint 3d meshes of size 4x2x2 n 5 can be embedded in an n d crossed cube with unit dilation and unit expansion these results mean that a family of two or four 3d mesh structured parallel algorithms can be executed on a same crossed cube efficiently and in parallel our work extends the results recently obtained by fan and jia j fan x jia embedding meshes into crossed cubes information sciences 177 15 2007 3151 3160

a powerful and robust test statistic for randomization inference in group randomized trials with matched pairs of groups summary for group randomized trials randomization inference based on rank statistics provides robust exact inference against nonnormal distributions however in a matched pair design the currently available rank based statistics lose significant power compared to normal linear mixed model lmm test statistics when the lmm is true in this article we investigate and develop an optimal test statistic over all statistics in the form of the weighted sum of signed mann whitney wilcoxon statistics under certain assumptions this test is almost as powerful as the lmm even when the lmm is true but it is much more powerful for heavy tailed distributions a simulation study is conducted to examine the power

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

hamiltonian laceability of bubble sort graphs with edge faults it is known that the n dimensional bubble sort graph b n is bipartite n 1 regular and has n vertices we first show that for any vertex v b n v has a hamiltonian path between any two vertices in the same partite set without v let f be a subset of edges of b n we next show that b n f has a hamiltonian path between any two vertices of different partite sets if f is at most n 3 then we also prove that b n f has a path of length n 2 between any pair of vertices in the same partite set

on efficiency of constrained longitudinal data analysis versus longitudinal analysis of covariance in randomized clinical trials measurements are often collected on each subject at a baseline visit and several post randomization time points the longitudinal analysis of covariance in which the postbaseline values form the response vector and the baseline value is treated as a covariate can be used to evaluate the treatment differences at the postbaseline time points liang and zeger 2000 sankhy the indian journal of statistics series b 62 134 148 propose a constrained longitudinal data analysis in which the baseline value is included in the response vector together with the postbaseline values and a constraint of a common baseline mean across treatment groups is imposed on the model as a result of randomization if the baseline value is subject to missingness the constrained longitudinal data analysis is shown to be more efficient for estimating the treatment differences at postbaseline time points than the longitudinal analysis of covariance the efficiency gain increases with the number of subjects missing baseline and the number of subjects missing all postbaseline values and for the pre post design decreases with the absolute correlation between baseline and postbaseline values

the analysis of very small samples of repeated measurements ii a modified box correction there is a need for appropriate methods for the analysis of very small samples of continuous repeated measurements a key feature of such analyses is the role played by the covariance matrix of the repeated observations when subjects are few it can be difficult to assess the fit of parsimonious structures for this matrix while the use of an unstructured form may lead to a serious lack of power the kenward roger adjustment is now widely adopted as a means of providing an appropriate inferences in small samples but does not perform adequately in very small samples adjusted tests based on the empirical sandwich estimator can be constructed that have good nominal properties but are seriously underpowered further when such data are incomplete or unbalanced or non saturated mean models are used exact distributional results do not exist that justify analyses with any sample size in this paper a modification of box s correction applied to a linear model based f statistic is developed for such small sample settings and is shown to have both the required nominal properties and acceptable power across a range of settings for repeated measurements

conditional akaike information for mixed effects models summary this paper focuses on the akaike information criterion aic for linear mixed effects models in the analysis of clustered data we make the distinction between questions regarding the population and questions regarding the particular clusters in the data we show that the aic in current use is not appropriate for the focus on clusters and we propose instead the conditional akaike information and its corresponding criterion the conditional aic caic the penalty term in caic is related to the effective degrees of freedom p for a linear mixed model proposed by hodges sargent 2001 p reflects an intermediate level of complexity between a fixed effects model with no cluster effect and a corresponding model with fixed cluster effects the caic is defined for both maximum likelihood and residual maximum likelihood estimation a pharmacokinetics data appli cation is used to illuminate the distinction between the two inference settings and to illustrate the use of the conditional aic in model selection

inverse probability weighted estimation for general missing data problems abstract i study inverse probability weighted m estimation under a general missing data scheme examples include m estimation with missing data due to a censored survival time propensity score estimation of the average treatment effect in the linear exponential family and variable probability sampling with observed retention frequencies i extend an important result known to hold in special cases estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation for the treatment effect case the setup allows a general characterization of a double robustness result due to scharfstein et al 1999 rejoinder journal of the american statistical association 94 1135 1146

fault tolerant edge pancyclicity of locally twisted cubes the n dimensional locally twisted cube ltq n is a new variant of the hypercube which possesses some properties superior to the hypercube this paper investigates the fault tolerant edge pancyclicity of ltq n and shows that if ltq n n 3 contains at most n 3 faulty vertices and or edges then for any fault free edge e and any integer with 6 2 n f v there is a fault free cycle of length containing the edge e where f v is the number of faulty vertices the result is optimal in some senses the proof is based on the recursive structure of ltq n

on embedding subclasses of height balanced trees in hypercubes a height balanced tree is a rooted binary tree t in which for every vertex v v t the heights of the subtrees rooted at the left and right child of v differ by at most one this difference is called the balance factor of v these trees are extensively used as data structures for sorting and searching we embed several subclasses of height balanced trees of height h in q h 1 under certain conditions in particular if a tree t is such that the balance factor of every vertex in the first three levels is arbitrary 0 or 1 and the balance factor of every other vertex is zero then we prove that t is embeddable in its optimal hypercube with dilation 1 or 2 according to whether it is balanced or not

edge disjoint hamiltonian cycles in k ary n cubes and hypercubes solutions for decomposing a higher dimensional torus to edge disjoint lower dimensional tori in particular edge disjoint hamiltonian cycles are obtained based on the coding theory approach first lee distance gray codes in z sub k sup n are presented and then it is shown how these codes can directly be used to generate edge disjoint hamiltonian cycles in k ary n cubes further some new classes of binary gray codes are designed from these lee distance gray codes and using these new classes of binary gray codes edge disjoint hamiltonian cycles in hypercubes are generated

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

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

complete path embeddings in crossed cubes crossed cubes are popular variants of hypercubes in this paper we study path embeddings between any two distinct nodes in crossed cubes we prove two important results in the n dimensional crossed cube a for any two nodes all paths whose lengths are greater than or equal to the distance between the two nodes plus 2 can be embedded between the two nodes with dilation 1 b for any two integers n 2 and l with 1

constructing vertex disjoint paths in n k star graphs this work describes a novel routing algorithm for constructing a container of width n 1 between a pair of vertices in an n k star graph with connectivity n 1 since lin et al t c lin d r duh h c cheng wide diameter of n k star networks in proceedings of the international conference on computing communications and control technologies vol 5 2004 pp 160 165 already calculated the wide diameters in n n 1 star and n 1 star graphs this study only considers an n k star with 2

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

fixed effects random effects and gee what are the differences for analyses of longitudinal repeated measures data statistical methods include the random effects model fixed effects model and the method of generalized estimating equations we examine the assumptions that underlie these approaches to assessing covariate effects on the mean of a continuous dichotomous or count outcome access to statistical software to implement these models has led to widespread application in numerous disciplines however careful consideration should be paid to their critical assumptions to ascertain which model might be appropriate in a given setting to illustrate similarities and differences that might exist in empirical results we use a study that assessed depressive symptoms in low income pregnant women using a structured instrument with up to five assessments that spanned the pre natal and post natal periods understanding the conceptual differences between the methods is important in their proper application even though empirically they might not differ substantively the choice of model in specific applications would depend on the relevant questions being addressed which in turn informs the type of design and data collection that would be relevant

some alternatives to asymptotic tests for the analysis of pharmacogenetic data using nonlinear mixed effects models nonlinear mixed effects models allow investigating individual differences in drug concentration profiles pharmacokinetics and responses pharmacogenetics focuses on the genetic component of this variability two tests often used to detect a gene effect on a pharmacokinetic parameter are 1 the wald test assessing whether estimates for the gene effect are significantly different from 0 and 2 the likelihood ratio test comparing models with and without the genetic effect because those asymptotic tests show inflated type i error on small sample size and or with unevenly distributed genotypes we develop two alternatives and evaluate them by means of a simulation study first we assess the performance of the permutation test using the wald and the likelihood ratio statistics second for the wald test we propose the use of the f distribution with four different values for the denominator degrees of freedom we also explore the influence of the estimation algorithm using both the first order conditional estimation with interaction linearization based algorithm and the stochastic approximation expectation maximization algorithm we apply these methods to the analysis of the pharmacogenetics of indinavir in hiv patients recruited in the cophar2 anrs 111 trial results of the simulation study show that the permutation test seems appropriate but at the cost of an additional computational burden one of the four f distribution based approaches provides a correct type i error estimate for the wald test and should be further investigated

embedding binary trees into crossed cubes the recently introduced interconnection network crossed cube has attracted much attention in the parallel processing area due to its many attractive features like the ordinary hypercube the n dimensional crossed cube is a regular graph with 2 sup n vertices and n2 sup n 1 edges the diameter of the crossed cube is approximately half that of the ordinary hypercube these advantages of the crossed cube motivated the study of how well it can simulate other networks such as the complete binary tree we show that the 2 sup n 1 node complete binary tree can be embedded into the n dimensional crossed cube with dilation 1

cross sectional versus longitudinal designs for function estimation with an application to cerebral cortex development motivated by studies of the development of the human cerebral cortex we consider the estimation of a mean growth trajectory and the relative merits of cross sectional and longitudinal data for that task we define a class of relative efficiencies that compare function estimates in terms of aggregate variance of a parametric function estimate these generalize the classical design effect for estimating a scalar with cross sectional versus longitudinal data and are shown to be bounded above by it in certain cases turning to nonparametric function estimation we find that longitudinal fits may tend to have higher aggregate variance than cross sectional ones but that this may occur because the former have higher effective degrees of freedom reflecting greater sensitivity to subtle features of the estimand these ideas are illustrated with cortical thickness data from a longitudinal neuroimaging study

some bayesian and non bayesian procedures for the analysis of comparative experiments and for small area estimation computational aspects frequentist properties and relationships abstract the estimation of a treatment contrast from experimental data and the estimation of a small area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two part mixed linear model in this article a bayesian approach to point and interval prediction is presented and its computational requirements are examined differences between the bayesian approach and the traditional classical approach are discussed in general terms and in addition in terms of two examples taken from the literature 1 the comparison of drug formulations in a bioavailability trial westlake and 2 the estimation of corn crop areas using satellite data battese harter and fuller some deficiencies in the classical approach are pointed out and the bayesian approach is considered from a frequentist perspective it is shown via a monte carlo study that for certain noninformative choices of the prior distribution the frequentist prop

topological properties of twisted cube twisted cube tq n is derived by changing some connections of hypercube q n according to specific rules recently many topological properties of this variation cube are studied in this paper we prove that its connectivity is n its wide diameter and fault diameter are n 2 2 furthermore we show that tq n is a pancyclic network that is cycles of an arbitrary length at least four

slanted conducting boundaries and field emission of particles in an electromagnetic particle simulation code abstract a method to handle slanted perfectly conducting boundaries in electromagnetic particle simulation codes is described modifications to standard algorithms for the electromagnetic field advance charge and current densities particle destruction and field averaging are discussed in addition a new model for field emission from conducting boundary surfaces is described particles can be emitted from conformal or slanted surfaces and also from certain types of corners results of the new models on several problems involving slanted surfaces are presented

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

two spanning disjoint paths with required length in generalized hypercubes given two pairs and of vertices of a graph g v e and two integers l 1 and l 2 with l 1 l 2 v g 2 g is said to be satisfying the 2rp property if there exist two disjoint paths p 1 and p 2 such that 1 p 1 is a path joining u to v with l p 1 l 1 2 p 2 is a path joining x to y with l p 2 l 2 and 3 p email protected p 2 spans g where l p denotes the length of path p in this paper we show that an r dimensional generalized hypercube denoted by g m r m r 1 m 1 satisfies the 2rp property except some special conditions where m i 4 for all 1

handling of baseline measurements in the analysis of crossover trials different analytic approaches for modeling baseline data in crossover trials were compared based on the efficiency in estimating treatment effects jointly modeling baseline and post baseline data is recommended to best utilize baseline data it results in the most significant gain in efficiency when data are strongly correlated within the same period but weakly correlated between different periods its performance remains comparable to the best of various other modeling methods under small within period correlation or large between period correlation we also examined the use of baseline data in modeling carryover effect we noted that to model carryover effect in crossover trial generally would lead to a much less efficient estimator and much more sensitive inference copyright 2012 john wiley sons ltd

maximum likelihood estimation of limited and discrete dependent variable models with nested random effects abstract gauss hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models unfortunately the estimates are biased for large cluster sizes and or intraclass correlations we show that adaptive quadrature largely overcomes these problems we then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables the models can include several nested random effects intercepts and coefficients representing unobserved heterogeneity at different levels of a hierarchical dataset the required multivariate integrals are evaluated efficiently using spherical quadrature rules simulations show that adaptive quadrature performs well in a wide range of situations