between and within cluster covariate effects in the analysis of clustered data standard methods for the regression analysis of clustered data postulate models relating covariates to the response without regard to between and within cluster covariate effects implicit in these analyses is the assumption that these effects are identical example data show that this is frequently not the case and that analyses that ignore differential between and within cluster covariate effects can be misleading consideration of between and within cluster effects also helps to explain observed and theoretical differences between mixture model analyses and those based on conditional likelihood methods in particular we show that conditional likelihood methods estimate purely within cluster covariate effects whereas mixture model approaches estimate a weighted average of between and within cluster covariate effects

eigenvalues of cartan matrices of principal 3 blocks of finite groups with abelian sylow 3 subgroups abstract let a be the principal 3 block of a finite group g with an abelian sylow 3 subgroup p let c a be the cartan matrix of a and we denote by c a the unique largest eigenvalue of c a the value c a is called the frobenius perron eigenvalue of c a we shall prove that c a is a rational number if and only if a and the principal 3 block of n g p are morita equivalent this generalizes earlier wada s theorem in 2007 where he proves it only for the case that the order of p is nine while we prove it for the case that p is an arbitrary finite abelian 3 group the result presented here uses the classification of finite simple groups

semiparametric estimation of random effects using the cox model based on the em algorithm consider a survival experiment where individuals within a certain subset of the population share a common unobservable random frailty such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households suppose that if the frailty omega is known the cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate assuming tht the random frailties follow a gamma distribution estimates of the fixed and random effects are obtained by using an em algorithm based on a profile likelihood construction the method developed is applied to the framingham heart study to examine the risks of smoking and cholesterol levels adjusting for potential random effects

broue s conjecture holds for principal 3 blocks with elementary abelian defect group of order 9 abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a finite group g has an abelian sylow p subgroup p then the derived categories of the principal p blocks of g and of the normalizer ng p of p in g are equivalent we prove in this paper that broue inage kus conjecture holds for the principal 3 block of an arbitrary finite group g with an elementary abelian sylow 3 subgroup p of order 9 by using initiated works for the case where g is simple which are due to puig okuyama waki miyachi and the authors the result depends on the classification of finite simple groups

conditional generalized estimating equations for the analysis of clustered and longitudinal data a common and important problem in clustered sampling designs is that the effect of within cluster exposures i e exposures that vary within clusters on outcome may be confounded by both measured and unmeasured cluster level factors i e measurements that do not vary within clusters when some of these are ill not accounted for estimation of this effect through population averaged models or random effects models may introduce bias we accommodate this by developing a general theory for the analysis of clustered data which enables consistent and asymptotically normal estimation of the effects of within cluster exposures in the presence of cluster level confounders semiparametric efficient estimators are obtained by solving so called conditional generalized estimating equations we compare this approach with a popular proposal by neuhaus and kalbfleisch 1998 biometrics 54 638 645 who separate the exposure effect into a within and a between cluster component within a random intercept model we find that the latter approach yields consistent and efficient estimators when the model is linear but is less flexible in terms of model specification under nonlinear models this approach may yield inconsistent and inefficient estimators though with little bias in most practical settings

cellular algebras and cartan matrices abstract let a be a finite dimensional algebra over a field k and let c be the cartan matrix of a usually the eigenvalues of c being integers do not imply the semisimplicity of a however we prove that a cellular algebra a is semisimple if and only if det c 1 and all eigenvalues of c are integers moreover we use cartan matrices to classify the cellular algebras with the property that the determinant of the cartan matrix equals a given prime p and all eigenvalues are integers we also give a classification of cellular nakayama algebras with integral eigenvalues of their cartan matrices finally we show that if a is a cellular algebra then its trivial extension t a is also a cellular algebra in particular if a non simple connected cellular algebra a is quasi hereditary then the cartan matrix of t a has at least one non integral eigenvalue the main tool used in this paper is the well known perron frobenius theory on non negative matrices

on equivalences between blocks of group algebras reduction to the simple components abstract a conjecture of michel broue states that if d is an abelian sylow p subgroup of a finite group g and h n g d then the principal blocks of g and h are rickard equivalent the structure of groups with abelian sylow p subgroups as determined by p fong and m e harris raises the following question assuming that broue s conjecture holds for the simple components of g under what conditions does it hold for g itself due to the structure of g this problem requires mainly the lifting of rickard complexes to p extensions of the simple components and the construction of complexes over wreath products we give here these reduction steps which may be regarded as a clifford theory of tilting complexes

eigenvalues of cartan matrices of principal 2 blocks with abelian defect groups abstract let g be a finite group with an abelian sylow 2 subgroup p let c b be the cartan matrix of the principal 2 block b of g we show that the frobenius perron eigenvalue b of c b is a rational integer if and only if b and its brauer correspondent block b of n g p are morita equivalent by using a classification of finite simple groups with an abelian sylow 2 subgroup in this case we can take the brauer character table b of b as a unimodular eigenvector matrix u b of c b over a complete discrete valuation ring r

phase lag in epidemics on a network of cities of cities between which individuals commute the frequency and amplitude of these oscillations is known to be very well captured by the van kampen system size expansion and we use this approximation to compute the complex coherence function that describes their correlation we find that if the infection rate differs from city to city and the coupling between them is not too strong these oscillations are synchronized with a well defined phase lag between cities the analytic description of the effect is shown to be in good agreement with the results of stochastic simulations for realistic population sizes

stochastic oscillations in models of epidemics on a network of cities we carry out an analytic investigation of stochastic oscillations in a susceptible infected recovered model of disease spread on a network of n cities in the model a fraction f jk of individuals from city k commute to city j where they may infect or be infected by others starting from a continuous time markov description of the model the deterministic equations which are valid in the limit when the population of each city is infinite are recovered the stochastic fluctuations about the fixed point of these equations are derived by use of the van kampen system size expansion the fixed point structure of the deterministic equations is remarkably simple a unique nontrivial fixed point always exists and has the feature that the fraction of susceptible infected and recovered individuals is the same for each city irrespective of its size we find that the stochastic fluctuations have an analogously simple dynamics all oscillations have a single frequency equal to that found in the one city case we interpret this phenomenon in terms of the properties of the spectrum of the matrix of the linear approximation of the deterministic equations at the fixed point

stochastic effects in a seasonally forced epidemic model the interplay of seasonality the system s nonlinearities and intrinsic stochasticity is studied for a seasonally forced susceptible exposed infective recovered stochastic model the model is explored in the parameter region that corresponds to childhood infectious diseases such as measles the power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes size effects are studied through additional simulations other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated the main conclusion is that stochastic amplification rather than these effects is the key ingredient to understand the observed incidence patterns

on robustness of marginal regression coefficient estimates and hazard functions in multivariate survival analysis of family data when the frailty distribution is mis specified the shared frailty model is an extension of the cox model to correlated failure times and essentially a random effects model for failure time outcomes in this model the latent frailty shared by individual members in a cluster acts multiplicatively as a factor on the hazard function and is typically modelled parametrically one commonly used distribution is gamma where both shape and scale parameters are set to be the same to allow for unique identification of baseline hazard function it is popular because it is a conjugate prior and the posterior distribution possesses the same form as gamma in addition the parameter can be interpreted as a time independent cross ratio function a natural extension of odds ratio to failure time outcomes in this paper we study the effect of frailty distribution mis specification on the marginal regression estimates and hazard functions under assumed gamma distribution with an application to family studies the simulation results show that the biases are generally 10 and lower even when the true frailty distribution deviates substantially from the assumed gamma distribution this suggests that the gamma frailty model can be a practical choice in real data analyses if the regression parameters and marginal hazard function are of primary interest and individual cluster members are exchangeable with respect to their dependencies

the principal 3 blocks of four and five dimensional projective special linear groups in non defining characteristic abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he has conjectured that for any prime p if a finite group g has an abelian sylow p subgroup p then the principal p blocks of g and the normalizer ng p of p in g are derived equivalent let q be a power of a prime such that q 2 or 5 mod 9 in this paper we show that broue s conjecture is true for p 3 and for g psl4 q and g psl5 q in these cases g has elementary abelian sylow 3 subgroups of order 9 what we prove here is the following in the case g psl4 q all the principal 3 blocks of g are morita even puig equivalent independently of infinitely many q in the case g psl5 q all the principal 3 blocks of g are morita even puig equivalent to the principal 3 block of ng p independently of infinitely many q

eigenvalues and elementary divisors of cartan matrices of cyclic blocks with l b 5 and tame blocks abstract we give a conjecture on relation between eigenvalues and elementary divisors of the cartan matrix of a p block b of a finite group then we prove the conjecture is true for cyclic blocks with l b 5 and for tame blocks

between within models for survival analysis a popular way to control for confounding in observational studies is to identify clusters of individuals e g twin pairs such that a large set of potential confounders are constant shared wit

analytical solution for post death transmission model of ebola epidemics abstract in this paper we shall introduce deceased human d transmission to the cycle phenomenon of disease modelling which has a direct relationship with the infective compartment of the stochastic susceptible infected recovered sir disease model due to this the noise covariance matrices of the standard stochastic sir model will be modified this will be done by using van kampen s expansion method to approximate the master equation and the stochastic fokker planck equation to analytically calculate a power spectral density psd expression a vector valued process is used and shows that the absolute value of the real part of the principal diagonal of the psd matrix solution is the spectral density of the system which is compared to the average psd of the stochastic simulations we aim to investigate the problem of identifiability when deceased humans act as an extended state of host infection using the sir d model during ebola epidemics using our analytical solution model we show that for an increasing degree of transmission parameter values the infected route cannot be identified whereas the deceased human transmission shows enhancement for the persistence of ebola virus disease using epidemiology data of the democratic republic of congo

proportional hazards tests and diagnostics based on weighted residuals summary nonproportional hazards can often be expressed by extending the cox model to include time varying coefficients e g for a single covariate the hazard function for subject i is modelled as exp fl t zi t a common example is a treatment effect that decreases with time we show that the function 3 t can be directly visualized by smoothing an appropriate residual plot also many tests of proportional hazards including those of cox 1972 gill schumacher 1987 harrell 1986 lin 1991 moreau o quigley mesbah 1985 nagelkerke oosting hart 1984 o quigley pessione 1989 schoenfeld 1980 and wei 1984 are related to time weighted score tests of the proportional hazards hypothesis and can be visualized as a weighted least squares line fitted to the residual plot

a counterexample to a conjecture of wada abstract wada conjectured in 2007 that the largest eigenvalue of the cartan matrix c of a block of a finite group is rational if and only if all eigenvalues of c are rational we provide a counterexample to this conjecture and discuss related questions

rationality of eigenvalues of cartan matrices in finite groups abstract we study the case in which eigenvalues and elementary divisors of a cartan matrix of a p block b of a finite group coincide in several cases we prove the coincidence occurs if and only if the perron frobenius eigenvalue of the cartan matrix is equal to the order of a defect group of b

permutation tests for centre effect on survival endpoints with application in an acute myeloid leukaemia multicentre study when analysing multicentre data it may be of interest to test whether the distribution of the endpoint varies among centres in a mixed effect model testing for such a centre effect consists in testing to zero a random centre effect variance component it has been shown that the usual asymptotic 2 distribution of the likelihood ratio and score statistics under the null does not necessarily hold in the case of censored data mixed effects cox models have been used to account for random effects but few works have concentrated on testing to zero the variance component of the random effects we propose a permutation test using random permutation of the cluster indices to test for a centre effect in multilevel censored data results from a simulation study indicate that the permutation tests have correct type i error rates contrary to standard likelihood ratio tests and are more powerful the proposed tests are illustrated using data of a multicentre clinical trial of induction therapy in acute myeloid leukaemia patients copyright 2014 john wiley sons ltd

eigenvector matrices of cartan matrices for finite groups abstract let c b be the cartan matrix of a p block b of a finite group g we show that there is a unimodular eigenvector matrix u b of c b over a discrete valuation ring r if all eigenvalues of c b are integers when b is a cyclic block a tame block a p block of a p solvable group or the principal 3 block with elementary abelian defect group of order 9

separating between and within cluster covariate effects by using conditional and partitioning methods summary we consider the situation where the random effects in a generalized linear mixed model may be correlated with one of the predictors which leads to inconsistent estimators we show that conditional maximum likelihood can eliminate this bias conditional likelihood leads naturally to the partitioning of the covariate into between and within cluster components and models that include separate terms for these components also eliminate the source of the bias another viewpoint that we develop is the idea that many violations of the assumptions including correlation between the random effects and a covariate in a generalized linear mixed model may be cast as misspecified mixing distributions we illustrate the results with two examples and simulations