nonadditive conditional entropy and its significance for local realism based on the form invariance of the structures given by khinchin s axiomatic foundations of information theory and the pseudoadditivity of the tsallis entropy indexed by q the concept of conditional entropy is generalized to the case of nonadditive nonextensive composite systems the proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum context indicating its utility for characterizing quantum entanglement a criterion deduced from it for separability of density matrices for validity of local realism is examined in detail by employing a bipartite spin 1 2 system it is found that the strongest criterion is obtained in the limit q

a class of blocks behaving like blocks of p solvable groups abstract we define a class of blocks having similar properties to blocks of p solvable groups and show that a version of the fong swan theorem holds for irreducible brauer characters in such blocks we also show that the height of an irreducible character in such block is bounded by the exponent of the central quotient of a defect group which in particular implies that if further the defect groups are abelian then every irreducible character in the block has height zero

nonadditive entropies and quantum entanglement abstract generalized quantum information theory is developed based on the nonadditive tsallis entropy indexed by q to see how this formalism is superior to the ordinary additive theory with the von neumann entropy realized in the limit q 1 the problem of quantum entanglement of mixed states is discussed it is shown that for the parameterized werner popescu type state of a general nn system i e an n partite n level system the present approach leads to the limitation on validity of local realism which is stronger than that derived from the additive theory

empirical bayes estimation of rates in longitudinal studies abstract the usually irregular follow up intervals in epidemiologic studies preclude the use of classical growth curve analysis for short follow up intervals it is suggested that individual rates of change are useful for exploratory analysis empirical bayes estimates of these rates of change are recommended and developed an example of bone loss with age in women is also given

zj controlled blocks of quasisimple groups for odd primes abstract we investigated the converses of glauberman s zj theorem and its block theoretic analogue proved by kessar linckelmann and robinson for a finite group g we proved that a block b of g with a defect group d is zj controlled that is n g z j d controls b fusion in g if and only if b is controlled provided that g is quasisimple and the characteristic p of the modular representation is odd this implies by a result of 5 that the converses of glauberman s zj theorem and its block theoretic analogue both hold in these cases as an application we obtain all q d p free quasisimple groups

nilpotent blocks of quasisimple groups for odd primes we investigate the nilpotent blocks of positive defect of the quasisimple groups for odd primes in particular it is shown that every nilpotent block of a quasisimple group has abelian defect groups a conjecture of puig concerning the recognition of nilpotent blocks is also shown for these groups

controlled 2 blocks of quasisimple groups abstract controlled p blocks introduced by alperin and broue in 1979 were classified for quasisimple groups g for odd primes in 10 we classify the controlled 2 blocks of quasisimple groups g the results imply that every nilpotent 2 block of g has abelian defect groups this agrees with one of the main results proved in 15 we also give an explicit characterization of non controlled 2 blocks of all quasisimple groups this implies that the p 2 version of the block theoretic analogue of glauberman s zj theorem proved by kessar linckelmann and robinson in 27 holds for quasisimple groups g

minimax robust designs and weights for approximately specified regression models with heteroscedastic errors abstract this article addresses the problem of constructing designs for regression models in the presence of both possible heteroscedasticity and an approximately and possibly incorrectly specified response function working with very general models for both types of departure from the classical assumptions i exhibit minimax designs and correspondingly optimal weights simulation studies and a case study accompanying the theoretical results lead to the conclusions that the robust designs yield substantial gains over some common competitors in the presence of realistic departures that are sufficiently mild so as to be generally undetectable by common test procedures specifically i exhibit solutions to the following problems p1 for ordinary least squares determine a design to minimize the maximum value of the integrated mean squared error imse of the fitted values with the maximum being evaluated over both types of departure p2 for weighted least squares determine both weights and a design to m

vertices for characters of p solvable groups suppose that g is a finite p solvable group we associate to every irreducible complex character x irr g of g a canonical pair q where q is a p subgroup of g and irr q uniquely determined by x up to g conjugacy this pair behaves as a green vertex and partitions irr g into families of characters using the pair q we give a canonical choice of a certain p radical subgroup r of g and a character irr r associated to x which was predicted by some conjecture of g r robinson

iterative weighted least squares estimation in heteroscedastic linear models this article addresses the problem of choosing weights for iterative weighted least squares estimation in heteroscedastic linear models an asymptotically optimal method for determining weights at each iteration is derived under a bayesian model for the variances the method uses a compromise between model based and model free variance estimates consider a heteroscedastic linear regression model in which responses are grouped so that the variance is constant within each group let denote the vector of regression parameters and let denote a vector of parameters determining a prior distribution for the variances iterative weighted least squares estimators are defined as follows given estimates and calculate a weight for the ith group as a function of the values in the ith group of the predictor variables and the average of the squared residuals from the estimated mean responses in the ith group given weights calculate the weighted least squares estimate and a new estimate continue until conv

the green correspondence and normal subgroups in a recent paper harris and knorr 6 have discovered a connection between the brauer correspondence and the covering relation between blocks of a finite group and blocks of its normal subgroups green s module point of view of blocks 4 suggests that this result has a moduletheoretic proof and that there is a more general result on indecomposable modules we shall show that this is the case by giving a short moduletheoretic proof of the harris kniirr theorem and then use the ideas of the proof to formulate and establish a result relating the green correspondence is with normal subgroups let us establish some notation let g be a finite group and h a normal subgroup let k be a field of prime characteristic p and b a block of h so b is an indecomposable algebra summand of kh we shall regard b as a k h x hi module in the usual way let d be a defect group of b k n d and b equal the block of k with bf b that is the brauer correspondent of b finally set l n d so k is a normal subgroup of l

vertices for irreducible characters of a class of blocks we observe that navarro s definition of a vertex for an irreducible character of a p solvable group may be extended to irreducible characters in p blocks with defect groups contained in a normal p solvable subgroup and show that this definition is independent of the choice of n we show that the fundamental properties of navarro s vertices generalize and as a corollary show that the vertices of the irreducible brauer characters in blocks of the above form are radical and are intersections of pairs of sylow p subgroups

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

anchors of irreducible characters given a prime number p every irreducible character of a finite group g determines a unique conjugacy class of p subgroups of g which we will call the anchors of this invariant has been considered by barker in the context of finite p solvable groups besides proving some basic properties of these anchors we investigate the relation to other p groups which can be attached to irreducible characters such as defect groups vertices in the sense of j a green and vertices in the sense of g navarro

controlled blocks of the finite quasisimple groups for odd primes abstract we classify controlled blocks introduced by alperin and broue in 1979 for all quasisimple groups g for odd primes the results imply that every nilpotent block of g has abelian defect groups which in turn is one of the main results proved in an and eaton 2011 6 we also give an explicit characterization of non controlled blocks of all quasisimple groups g for odd primes this implies the block theoretic analogue of glauberman s zj theorem for g proved by kessar linckelmann and robinson 2002 18

quantum q divergence the quantum q divergence is the nonadditive relative entropy associated with the tsallis entropy indexed by q here its basic properties including the q deformation and quantum group structure convexity and monotonicity are summarized then it is applied to measuring the degree of state purification it is shown that the quantum q divergence is always well defined if the entropic index q is in the range 0 1 whereas the ordinary quantum relative entropy is singular when the reference state is a pure state thus the additive limit q 1 0 does not exist in general

exact tests that recover interblock information in balanced incomplete blocks designs abstract consider a balanced incomplete blocks design in which treatment effects are fixed and blocks are random assume that the number of blocks is greater than i the number of treatments the objective is to test the null hypothesis that there are no differences in treatment effects other null hypotheses are that v treatment contrasts are 0 where v may be any number from 1 to i 1 the usual exact test for no treatment effects is the f test based entirely on intrablock estimates a long standing problem has been to find good exact tests that use both intrablock and interblock estimates e g see houtman and speed 1983 p 1078 scheffe 1959 p 175 in this study such exact tests are found furthermore they are easy to implement and perform much better than the usual f test

robust estimation in heteroscedastic linear models we consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter theta we propose robust estimates for the regression parameter beta and show that as long as a reasonable starting estimate of theta is available our estimates of beta are asymptotically equivalent to the natural estimate obtained with known variances a particular method for estimating theta is proposed and shown by monte carlo to work quite well especially in power and exponential models for the variances we also briefly discuss a feedback estimate of beta

an asymptotic theory for weighted least squares with weights estimated by replication summary we consider a heteroscedastic linear regression model with replication to estimate the variances one can use the sample variances or the sample average squared errors from a regression fit we study the large sample properties of these weighted least squares estimates with estimated weights when the number of replicates is small the estimates are generally inconsistent for asymmetrically distributed data if sample variances are used based on m replicates the weighted least squares estimates are inconsistent for m 2 replicates even when the data are normally distributed with between 3 and 5 replicates the rates of convergence are slower than the usual square root of n with m 6 replicates the effect of estimating the weights is to increase variances by m 5 m 3 relative to weighted least squares estimates with known weights

a generalized linear modeling approach to robust design this article presents an extension of the response surface approach to taguchi s parameter design by accommodating generalized linear modeling the approach of myers khuri and vining is taken as a starting point treating noise variables as fixed effects it is however assumed that process variability is caused not only by the presence of noise factors but also by residual variation therefore in addition to a model with a linear link function that relates the process mean to design and noise factors a second model with a log link function is proposed that relates the variance to a linear predictor in the design factors the conditional response model with noise factors taken as fixed is fitted by iteratively reweighted least squares unconditionally response surfaces for the process mean and process variance are produced through the use of a mean and variance operator on the conditional response model as an illustration data from an injection molding experiment are reanalyzed and residual disp

the effect of estimating weights in weighted least squares abstract in weighted least squares it is typical that the weights are unknown and must be estimated most packages provide standard errors assuming that the weights are known this is fine for sufficiently large sample sizes but what about for small to moderate sample sizes the investigation of this article into the effect of estimating weights proceeds under the assumption typical in practice that one has a parametric model for the variance function in this context generalized least squares consists of a an initial estimate of the regression parameter b a method for estimating the variance function and c the number of iterations in reweighted least squares by means of expansions for the covariance it is shown that each of a c can matter in problems of small to moderate size a few conclusions may be of practical interest first estimated standard errors assuming that the weights are known can be too small in practice the investigation indicates that a simple bootstrap operation resul

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators