a comparative study of the dynamic critical behavior of the four state potts like models abstract we investigate the short time critical dynamics of the baxter wu bw and n 3 turban 3tu models to estimate their global persistence exponent g we conclude that this new dynamical exponent can be useful in detecting differences between the critical behavior of these models which are very difficult to obtain in usual simulations in addition we estimate again the dynamical exponents of the four state potts fsp model in order to compare them with results previously obtained for the bw and 3tu models and to decide between two sets of estimates presented in the current literature we also revisit the short time dynamics of the 3tu model in order to check if as already found for the fsp model the anomalous dimension of the initial magnetization x 0 could be equal to zero

on the 2 adic complexity and the k error 2 adic complexity of periodic binary sequences a significant difference between the linear complexity and the 2 adic complexity of periodic binary sequences is pointed out in this correspondence based on this observation we present the concept of the symmetric 2 adic complexity of periodic binary sequences the expected value of the 2 adic complexity is determined and a lower bound on the expected value of the symmetric 2 adic complexity of periodic binary sequences is derived we study the variance of the 2 adic complexity of periodic binary sequences and the exact value for it is given because the k adic complexity of periodic binary sequences is unstable we present the concepts of the kappa error 2 adic complexity and the k error symmetric 2 adic complexity and lower bounds on them are also derived in particular we give tighter upper and lower bounds for the minimum k adic complexity of l sequences by substituting two symbols within one period

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

the 3 state potts model in 2 1 dimensions the 3 state potts model in 2 1 dimensions is studied using series and monte carlo methods high temperature series for the vacuum energy mass gap and susceptibility are computed on the square and triangular lattices using linked cluster expansions monte carlo estimates are obtained by the stochastic truncation method the model is found to undergo a weak first order transition as in the euclidean version of the model

critical properties of an s 1 multispin coupling ising model strong and weak coupling series expansions are used to investigate the critical properties of the s 1 multispin coupling ising chain in the presence of a transverse field the order of the transition goes from second order to first order when more than three spins are coupled according to the numerical results the two spin and three spin coupling models belong to the ising and the four state potts universality classes respectively thus the critical properties of the model do not depend on the value of the spin even when three spins are coupled

the critical behaviour of a quantum spin problem with thee spin coupling the critical behaviour of an ising like model with three spin coupling is studied in a transverse field a self dual renormalisation group transformation can be applied which gives well converging results for the critical exponents when large enough cells are taken finite size scaling on the same model give comparable results

an algorithm for computing minimal bidirectional linear recurrence relations we consider the problem of computing a linear recurrence relation or equivalently a linear feedback shift register of minimum order for a finite sequence over a field with the additional requirement that not only the highest but also the lowest coefficient of the recurrence is nonzero such a recurrence relation can then be used to generate the sequence in both directions increasing or decreasing order of indices so we call it bidirectional if the field is finite a sequence is periodic if and only if it admits a bidirectional linear recurrence relation for solving the above problem we propose an algorithm similar to the berlekamp massey algorithm and prove its correctness we describe the set of all solutions to this problem and show that if a sequence admits more than one linear recurrence relation then it admits a bidirectional one we also prove some properties regarding the bidirectionality of the recurrences of the prefixes of the sequence

operator content of the three state potts quantum chain the authors compute the lowest excitations of the spectra of the three state potts quantum chain with periodic and twisted boundary conditions these spectra can be understood in terms of eighteen irreducible representations of the virasoro algebra with c 4 5

methods for conducting sensitivity analysis of trials with potentially nonignorable competing causes of censoring we consider inference for the treatment arm mean difference of an outcome that would have been measured at the end of a randomized follow up study if during the course of the study patients had not initiated a nonrandomized therapy or dropped out we argue that the treatment arm mean difference is not identified unless unverifiable assumptions are made we describe identifying assumptions that are tantamount to postulating relationships between the components of a pattern mixture model but that can also be interpreted as imposing restrictions on the cause specific censoring probabilities of a selection model we then argue that although sufficient for identification these assumptions are insufficient for inference due to the curse of dimensionality we propose reducing dimensionality by specifying semiparametric cause specific selection models these models are useful for conducting a sensitivity analysis to examine how inference for the treatment arm mean difference changes as one varies the magnitude of the cause specific selection bias over a plausible range we provide methodology for conducting such sensitivity analysis and illustrate our methods with an analysis of data from the aids clinical trial group actg study 002

the evaluation of integrals of the form f t exp t 2 dt application to logistic normal models abstract logistic normal distributions and related functions arise in a variety of statistical applications of current interest including binary measurement error models and the analysis of teratogenicity experiments analytic intractability has led to the development of numerous approximations to the desired forms often with consequences that have not been well studied a method is developed to compute these forms to arbitrary accuracy and comparative calculations are made that show when the common numerical alternative 20 point gaussian quadrature begins to fail by using a simple matrix transformation this method can be used with multiple covariate regression models of the logistic normal form we conducted a simulation study that compares the ability of 20 point gaussian quadrature and our new method to obtain the maximum likelihood estimator of relative risk in the logistic normal measurement error model using standard subroutines to maximize the likelihood equations 27 of 50 trials failed to

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

conformal invariance and the critical behaviour of a quantum spin hamiltonian with three spin coupling a quantum spin model with three spin coupling is studied by finite lattice methods the critical indices nu and alpha are obtained by standard finite size scaling analysis conformal invariance is used to estimate the exponents nu and eta the central charge or conformal anomaly c and the anomalous dimension of a spin 1 4 parafermion the authors conclude that the model belongs to the same universality class as the four state potts and baxter wu models although the convergence of the various finite lattice estimators is extremely slow

publication bias and meta analysis for 2x2 tables an average markov chain monte carlo em algorithm summary a major difficulty in meta analysis is publication bias studies with positive outcomes are more likely to be published than studies reporting negative or inconclusive results correcting for this bias is not possible without making untestable assumptions in this paper a sensitivity analysis is discussed for the meta analysis of 2 2 tables using exact conditional distributions a markov chain monte carlo em algorithm is used to calculate maximum likelihood estimates a rule for increasing the accuracy of estimation and automating the choice of the number of iterations is suggested

sensitivity analysis of longitudinal normal data with drop outs we propose to perform a sensitivity analysis to evaluate the extent to which results from a longitudinal study can be affected by informative drop outs the method is based on a selection model where the parameter relating the dropout probability to the current observation is not estimated but fixed to a set of values this allows to evaluate several hypotheses for the degree of informativeness of the drop out process expectation and variance of missing data conditional on the drop out time are computed and a stochastic em algorithm is used to obtain maximum likelihood estimates simulations show that when the drop out parameter is correctly specified unbiased estimates of the other parameters are obtained and coverage percentages of their confidence intervals are close to their theoretical value more interestingly misspecification of the drop out parameter does not considerably alter these results this method was applied to a randomized clinical trial designed to demonstrate non inferiority of an inhaled corticosteroid in terms of bone density compared with a reference treatment sensitivity analysis showed that the conclusion of non inferiority was robust against different hypotheses for the drop out process

the critical behaviour of self dual z n spin systems finite size scaling and conformal invariance this paper is concerned with the critical properties of a family of self dual two dimensional z n models whose bulk free energy is exactly known at the self dual point the author s analysis is performed by studying the finite size behaviour of the corresponding one dimensional quantum hamiltonians which also possess an exact solution at their self dual point by exploring finite size scaling ideas and the conformal invariance of the critical infinite system the author calculates for n up to 8 the critical temperature and critical exponents as well as the central charge associated with the underlying conformal algebra the results strongly suggest that the z n quantum field theory of zamolodchikov and fateev is the underlying field theory associated with these statistical mechanical systems the author also tests for the z 5 case the conjecture that these models correspond to the bifurcation points in the phase diagram of the general z n spin model where a massless phase originates

a class of pattern mixture models for normal incomplete data summary likelihood based methods are developed for analyzing a random sample on two continuous variables when values of one of the variables are missing normal maximum likelihood estimates when values are missing completely at random were derived by anderson 1957 they are also maximum likelihood providing the missing data mechanism is ignorable in rubin s 1976 sense that the mechanism depends only on observed data a new class of pattern mixture models little 1993 is described for the situation where missingness is assumed to depend on an arbitrary unspecified function of a linear combination of the two variables maximum likelihood for models in this class is straightforward and yields the estimates of anderson 1957 when missingness depends solely on the completely observed variable and the estimates of brown 1990 when missingness depends solely on the incompletely observed variable another choice of linear combination yields estimates from complete case analysis large sample and bayesian methods are described for this model the data do not supply information about the ratio of the coefficients of the linear combination that controls missingness if this ratio is not welldetermined based on prior knowledge a prior distribution can be specified and bayesian inference is then readily accomplished alternatively sensitivity of inferences can be displayed for a variety of choices of the ratio

q state potts models in hamiltonian field theory for q 4 in 1 1 dimensions finite lattice sequence extrapolation methods are applied to the q state potts models in 1 1 d hamiltonian field theory thermal exponents nu 0 71 or 0 02 alpha 0 53 or 0 02 are obtained for the four state model methods are discussed for treating the first order transitions for q 4 and a sequence extrapolation is used to estimate the latent heat exact analytic formulae are derived for the ground state energy the mass gap and the latent heat at the transition point these are compared with the numerical results

exact results for quantum chains with multisite interactions generalised spin 1 2 and potts quantum chains with m n site interactions for the z x component of the site variables are shown to be self dual through duality with m arbitrary n 2 versions of the models are transformed into m independent ising or potts chains in a transverse field allowing one to get the exact values of the critical exponents for any m

sensitivity analysis for nonrandom dropout a local influence approach diggle and kenward 1994 applied statistics 43 49 93 proposed a selection model for continuous longitudinal data subject to nonrandom dropout it has provoked a large debate about the role for such models the original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests since then the view has emerged that these models should ideally be made part of a sensitivity analysis this paper presents a formal and flexible approach to such a sensitivity assessment based on local influence cook 1986 journal of the royal statistical society series b 48 133 169 the influence of perturbing a missing at random dropout model in the direction of nonrandom dropout is explored the method is applied to data from a randomized experiment on the inhibition of testosterone production in rats

latent heats from finite size scaling a method of obtaining the latent heat at a first order transition from finite lattice matrix elements is discussed and demonstrated for the case of the 1 1 d potts model the method is shown to provide smoothly convergent finite lattice sequences the structure of the finite lattice hamiltonian eigenvalues is exhibited and a characteristic signal of the first order transition is proposed the finite size scaling behaviour at the transition is also discussed

selection models for repeated measurements with non random dropout an illustration of sensitivity the outcome based selection model of diggle and kenward for repeated measurements with non random dropout is applied to a very simple example concerning the occurrence of mastitis in dairy cows in which the occurrence of mastitis can be modelled as a dropout process it is shown through sensitivity analysis how the conclusions concerning the dropout mechanism depend crucially on untestable distributional assumptions this example is exceptional in that from a simple plot of the data two outlying observations can be identified that are the source of the apparent evidence for non random dropout and also provide an explanation of the behaviour of the sensitivity analysis it is concluded that a plausible model for the data does not require the assumption of non random dropout

multiple phase coexistence and the scaling transformation it is shown that a simple extension of the finite size scaling method in the theory of critical phenomena can yield a sequence of approximants to any point subset of the interaction parameter space where multiple phase coexistence is possible the method is illustrated by an application to the three four and five state potts models and even in its lowest order of approximation is able to distinguish the difference in the zero field critical behaviour between the five state and the three and four state models

conformal invariance studies of the baxter wu model and a related site colouring problem the partition function of the baxter wu model is exactly related to the generating function of a site colouring problem on a hexagonal lattice we extend the original bethe ansatz solution of these models in order to obtain the eigenspectra of their transfer matrices in finite geometries and general toroidal boundary conditions the operator content of these models is studied by solving numerically the bethe ansatz equations and by exploring conformal invariance since the eigenspectra are calculated for large lattices the corrections to finite size scaling are also calculated

critical behaviour and logarithmic corrections of a quantum model with three spin interaction extended finite size scaling and series expansion methods are used to determine the critical properties of the one dimensional quantum ising model with three spin interaction by supposing the presence of logarithmic corrections the universality class of the model is investigated the results obtained by different methods support the conjecture that the model belongs to the same universality class as the four state potts model

pattern mixture and selection models for analysing longitudinal data with monotone missing patterns summary we examine three pattern mixture models for making inference about parameters of the distribution of an outcome of interest y that is to be measured at the end of a longitudinal study when this outcome is missing in some subjects we show that these pattern mixture models also have an interpretation as selection models because these models make unverifiable assumptions we recommend that inference about the distribution of y be repeated under a range of plausible assumptions we argue that of the three models considered only one admits a parameterization that facilitates the examination of departures from the assumption of sequential ignorability the three models are nonparametric in the sense that they do not impose restrictions on the class of observed data distributions owing to the curse of dimensionality the assumptions that are encoded in these models are sufficient for identification but not for inference we describe additional flexible and easily interpretable assumptions under which it is possible to construct estimators that are well behaved with moderate sample sizes these assumptions define semiparametric models for the distribution of the observed data we describe a class of estimators which up to asymptotic equivalence comprise all the consistent and asymptotically normal estimators of the parameters of interest under the postulated semiparametric models we illustrate our methods with the analysis of data from a randomized clinical trial of contracepting women

conformal invariance and surface critical behaviour of a quantum chain with three spin interaction an ising model with three spin interaction is investigated by finite size scaling applying free boundary conditions the surface critical properties of the model were determined by conformal invariance taking into account logarithmic corrections the surface critical exponents obtained are in accordance with the four state potts values

minimal polynomial algorithms for finite sequences in this paper we show that a straightforward rewrite of a known minimal polynomial algorithm yields a simpler version of an algorithm in a recent paper of a salagean

reparameterizing the pattern mixture model for sensitivity analyses under informative dropout summary pattern mixture models are frequently used to analyze longitudinal data where missingness is induced by dropout for measured responses it is typical to model the complete data as a mixture of multivariate normal distributions where mixing is done over the dropout distribution fully parameterized pattern mixture models are not identified by incomplete data little 1993 journal of the american statistical association88 125 134 has characterized several identifying restrictions that can be used for model fitting we propose a reparameterization of the pattern mixture model that allows investigation of sensitivity to assumptions about nonidentified parameters in both the mean and variance allows consideration of a wide range of nonignorable missing data mechanisms and has intuitive appeal for eliciting plausible missing data mechanisms the parameterization makes clear an advantage of pattern mixture models over parametric selection models namely that the missing data mechanism can be varied without affecting the marginal distribution of the observed data to illustrate the utility of the new parameterization we analyze data from a recent clinical trial of growth hormone for maintaining muscle strength in the elderly dropout occurs at a high rate and is potentially informative we undertake a detailed sensitivity analysis to understand the impact of missing data assumptions on the inference about the effects of growth hormone on muscle strength