tridiagonal realization of the antisymmetric gaussian β ensemble the householder reduction of a member of the antisymmetric gaussian unitary ensemble gives an antisymmetric tridiagonal matrix with all independent elements the random variables permit the introduction of a positive parameter and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly as can the distribution of qi the first components of the eigenvectors three proofs are given one involves an inductive construction based on bordering of a family of random matrices which are shown to have the same distributions as the antisymmetric tridiagonal matrices this proof uses the dixon anderson integral from selberg integral theory a second proof involves the explicit computation of the jacobian for the change of variables between real antisymmetric tridiagonal matrices its eigenvalues and qi the third proof maps matrices from the antisymmetric gaussian ensemble to those realizing particular examples of the laguerre ensemble in addition to t

application of gee procedures for sample size calculations in repeated measures experiments derivation of the minimum sample size is an important consideration in an applied research effort when the outcome is measured at a single time point sample size procedures are well known and widely applied the corresponding situation for longitudinal designs however is less well developed in this paper we adapt the generalized estimating equation gee approach of liang and zeger to sample size calculations for discrete and continuous outcome variables the non central version of the wald 2 test is considered we use the damped exponential family of correlation structures described in munoz et al for the working correlation matrix among the repeated measures we present a table of minimum sample sizes for binary outcomes and discuss extensions that account for unequal allocation staggered entry and loss to follow up 1998 john wiley sons ltd

exemplary data set sample size calculation for wilcoxon mann whitney tests zhao rahardja and qu consider sample size calculation for wilcoxon mann whitney wmw tests for data with ties and present a straightforward formula we observe that the exemplary data set approach usually applied in more complex situations has a close relationship to the zhao rahardja qu method for wmw sample size estimation and they are asymptotically equivalent therefore the exemplary data set approach can be used to easily obtain estimates similar to those that the closed formula gives we illustrate application of both methods for a wmw sample size estimation example and also extend the simulation study presented by zhao et al we find that the zhao rahardja qu formula and by extension the exemplary data set method can give estimates just as accurate as those obtained using either the kolassa approach via nquery advisor or the o brien castelloe approach via sas 9 2 proc power for 1 1 and 1 2 allocation ratios however the latter two methods can be more accurate for a ratio of 1 4 or 1 19 finally we note the general utility of the exemplary data set approach for sample size estimation even in other situations where closed form sample size formulae exist

dynamical localization for the random dimer schrodinger operator we study the one dimensional random dimer model with hamiltonian h v where for all x mathbb z v 2x v 2x 1 and where the v 2x are i i d bernoulli random variables taking the values v v 0 we show that for all values of vand with probability one in the spectrum of his pure point if v 1 and v 1 sqrt 2 the lyapunov exponent vanishes only at the two critical energies given by e v for the particular value v 1 sqrt 2 respectively v sqrt 2 we show the existence of new additional critical energies at e 3 sqrt 2 respectively e 0 on any compact interval inot containing the critical energies the eigenfunctions are then shown to be semi uniformly exponentially localized and this implies dynamical localization for all q 0 and for all ell 2 mathbb z with sufficiently rapid decrease mathop sup limits t r psi i left q right kern 1pt left t right mathop sup limits t left langle p i left h omega right psi t left x right q p i left h omega right psi t right rangle infty here psi t e ih omega t psi and pi h is the spectral projector of h onto the interval i in particular if v 1 and v sqrt 2 these results hold on the entire spectrum so that one can take i h

on power and sample size calculations for likelihood ratio tests in generalized linear models summary a direct extension of the approach described in self mauritsen and ohara 1992 biometrics 48 31 39 for power and sample size calculations in generalized linear models is presented the major feature of the proposed approach is that the modification accommodates both a finite and an infinite number of covariate configurations furthermore for the approximation of the noncentrality of the noncentral chi square distribution for the likelihood ratio statistic a simplification is provided that not only reduces substantial computation but also maintains the accuracy simulation studies are conducted to assess the accuracy for various model configurations and covariate distributions

sample size calculation for comparing two negative binomial rates negative binomial model has been increasingly used to model the count data in recent clinical trials it is frequently chosen over poisson model in cases of overdispersed count data that are commonly seen in clinical trials one of the challenges of applying negative binomial model in clinical trial design is the sample size estimation in practice simulation methods have been frequently used for sample size estimation in this paper an explicit formula is developed to calculate sample size based on the negative binomial model depending on different approaches to estimate the variance under null hypothesis three variations of the sample size formula are proposed and discussed important characteristics of the formula include its accuracy and its ability to explicitly incorporate dispersion parameter and exposure time the performance of the formula with each variation is assessed using simulations

absence of ballistic motion for large classes of schrodinger operators and jacobi matrices we prove that if h has only one point spectrum then for 0 of compact support lim t t 2 xe ith 0 2 0

a combined finite element stiffness equation transfer method for steady state vibration response analysis of structures an extended finite element transfer matrix method in combination with stiffness equation transfer is applied to dynamic response analysis of the structures under periodic excitations in the present method the transfer of state vectors from left to right in a combined finite element transfer matrix fe tm method is changed into the transfer of general stiffness equations of every section from left to right this method has the advantages of reducing the order of standard transfer equation systems and minimizing the propagation of round off errors occurring in recursive multiplication of transfer and point matrices furthermore the drawback that in the ordinary fe tm method the number of degrees of freedom on the left boundary be the same on the right boundary is now avoided a feset program based on this method using microcomputers is developed finally numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for steady state vibration response analysis of structures

a characterization of the anderson metal insulator transport transition we investigate the anderson metal insulator transition for random schrodinger operators we define the strong insulator region to be the part of the spectrum where the random operator exhibits strong dynamical localization in the hilbert schmidt norm we introduce a local transport exponent e and set the weak metallic transport region to be the part of the spectrum with nontrivial transport i e e 0 we prove that these insulator and metallic regions are complementary sets in the spectrum of the random operator and that the local transport exponent e provides a characterization of the metal insulator transport transition moreover we show that if there is such a transition then e has to be discontinuous at a transport mobility edge more precisely we show that if the transport is nontrivial then e 1 2d where d is the space dimension these results follow from a proof that slow transport of quantum waves in random media implies the starting hypothesis for the authors bootstrap multiscale analysis we also conclude that the strong insulator region coincides with the part of the spectrum where we can perform a bootstrap multiscale analysis proving that the multiscale analysis is valid all the way up to a transport mobility edge

singular behaviour of certain infinite products of random 2 2 matrices the authors consider an infinite product of random matrices which appears in several physical problems in particular the ising chain in a random field the random matrices depend analytically on a parameter epsilon in such a way that for 0 they all commute under certain conditions they find that the lyapunov index of this product behaves approximately as c 2 for to 0 their approach is based on the decomposition of an exact integral equation for this problem into two reduced equations they give an expression for the exponent alpha in terms of the probability distribution of the matrices and for the proportionality constant c in terms of the solutions of the reduced integral equations in cases where exact results are available agreement is obtained the physical consequences for disordered one dimensional systems are pointed out

a simple approach to power and sample size calculations in logistic regression and cox regression models for a given regression problem it is possible to identify a suitably defined equivalent two sample problem such that the power or sample size obtained for the two sample problem also applies to the regression problem for a standard linear regression model the equivalent two sample problem is easily identified but for generalized linear models and for cox regression models the situation is more complicated an approximately equivalent two sample problem may however also be identified here in particular we show that for logistic regression and cox regression models the equivalent two sample problem is obtained by selecting two equally sized samples for which the parameters differ by a value equal to the slope times twice the standard deviation of the independent variable and further requiring that the overall expected number of events is unchanged in a simulation study we examine the validity of this approach to power calculations in logistic regression and cox regression models several different covariate distributions are considered for selected values of the overall response probability and a range of alternatives for the cox regression model we consider both constant and non constant hazard rates the results show that in general the approach is remarkably accurate even in relatively small samples some discrepancies are however found in small samples with few events and a highly skewed covariate distribution comparison with results based on alternative methods for logistic regression models with a single continuous covariate indicates that the proposed method is at least as good as its competitors the method is easy to implement and therefore provides a simple way to extend the range of problems that can be covered by the usual formulas for power and sample size determination

perturbation theory for the random dimer model the authors study a one dimensional tight binding model with a random potential taking two values or nu with the restriction that on pairs of two neighbouring sites the potentials take the same value this random dimer model proposed by dunlap phillips and wu 1990 has a vanishing lyapunov exponent for the energy e or nu they compute the lyapunov exponent and the density of states perturbatively in the vicinity of this energy using the invariant measure formalism

positive lyapunov exponents for a class of deterministic potentials letv be a smooth non constant function on the torus and lett be a hyperbolic toral automorphism consider a discrete one dimensional schrodinger operatorh whose potential at sitej is given bygv j gv t j we prove that wheng 0 is small andg 1 2 e 2 g 1 2 the lyapunov exponent for the cocycle generated byh e is proportional tog 2 the proof relies on a formula of pastur and figotin and on symbolic dynamics

sample size planning of two arm superiority and noninferiority survival studies with discrete follow up in clinical trials using lifetime as primary outcome variable it is more the rule than the exception that even for patients who are failing in the course of the study survival time does not become known exactly since follow up takes place according to a restricted schedule with fixed possibly long intervals between successive visits in practice the discreteness of the data obtained under such circumstances is plainly ignored both in data analysis and in sample size planning of survival time studies as a framework for analyzing the impact of making no difference between continuous and discrete recording of failure times we use a scenario in which the partially observed times are assigned to the points of the grid of inspection times in the natural way evaluating the treatment effect in a two arm trial fitting into this framework by means of ordinary methods based on cox s relative risk model is shown to produce biased estimates and or confidence bounds whose actual coverage exhibits marked discrepancies from the nominal confidence level not surprisingly the amount of these distorting effects turns out to be the larger the coarser the grid of inspection times has been chosen as a promising approach to correctly analyzing and planning studies generating discretely recorded failure times we use large sample likelihood theory for parametric models accommodating the key features of the scenario under consideration the main result is an easily implementable representation of the expected information and hence of the asymptotic covariance matrix of the maximum likelihood estimators of all parameters contained in such a model in two real examples of large scale clinical trials sample size calculation based on this result is contrasted with the traditional approach which consists of applying the usual methods for exactly observed failure times copyright 2017 john wiley sons ltd

random dirac operators with time reversal symmetry quasi one dimensional stochastic dirac operators with an odd number of channels time reversal symmetry but otherwise efficiently coupled randomness are shown to have one conducting channel and absolutely continuous spectrum of multiplicity two this follows by adapting the criteria of guivarch raugi and goldsheid margulis to the analysis of random products of matrices in the group so 2l and then a version of kotani theory for these operators absence of singular spectrum can be shown by adapting an argument of jaksic last if the potential contains random dirac peaks with absolutely continuous distribution

adjusting power for a baseline covariate in linear models the analysis of covariance provides a common approach to adjusting for a baseline covariate in medical research with gaussian errors adding random covariates does not change either the theory or the computations of general linear model data analysis however adding random covariates does change the theory and computation of power analysis many data analysts fail to fully account for this complication in planning a study we present our results in five parts i a review of published results helps document the importance of the problem and the limitations of available methods ii a taxonomy for general linear multivariate models and hypotheses allows identifying a particular problem iii we describe how random covariates introduce the need to consider quantiles and conditional values of power iv we provide new exact and approximate methods for power analysis of a range of multivariate models with a gaussian baseline covariate for both small and large samples the new results apply to the hotelling lawley test and the four tests in the univariate approach to repeated measures unadjusted huynh feldt geisser greenhouse box the techniques allow rapid calculation and an interactive graphical approach to sample size choice v calculating power for a clinical trial of a treatment for increasing bone density illustrates the new methods we particularly recommend using quantile power with a new satterthwaite style approximation

delocalization in random polymer models a random polymer model is a one dimensional jacobi matrix randomly composed of two finite building blocks if the two associated transfer matrices commute the corresponding energy is called critical such critical energies appear in physical models an example being the widely studied random dimer model it is proven that the lyapunov exponent vanishes quadratically at a generic critical energy and that the density of states is positive there large deviation estimates around these asymptotics allow to prove optimal lower bounds on quantum transport showing that it is almost surely overdiffusive even though the models are known to have pure point spectrum with exponentially localized eigenstates for almost every configuration of the polymers furthermore the level spacing is shown to be regular at the critical energy

sample size calculations for comparative clinical trials with over dispersed poisson process data this paper develops a new formula for sample size calculations for comparative clinical trials with poisson or over dispersed poisson process data the criteria for sample size calculations is developed on the basis of asymptotic approximations for a two sample non parametric test to compare the empirical event rate function between treatment groups this formula can accommodate time heterogeneity inter patient heterogeneity in event rate and also time varying treatment effects an application of the formula to a trial for chronic granulomatous disease is provided

sensitivity analysis for free vibration of rectangular plate abstract this paper presents an effective sensitivity analysis algorithm for free vibration of a rectangular plate structure by using the finite element transfer stiffness coefficient method fe tscm the basic concept of fe tscm combines both the modeling technique of the finite element method fem and the transfer technique of the transfer stiffness coefficient method tscm in order to benefit from the merits of both fem and tscm in the dynamic analysis of a structure from the results computing the sensitivities of eigenvalues and eigenvectors for a simply supported rectangular plate structure by fe tscm and fox s method we can confirm that fe tscm has merits from the viewpoint of computational time and memory in sensitivity analysis for free vibration of the rectangular plate structure with a large number of degrees of freedom in addition when the design variables are the thicknesses of the plate elements the results computing the sensitivities of the first eigenvalues for the rectangular plate structures with clamped edges are illustrated in detail by using the computation program introducing the concept of fe tscm

anderson localization for bernoulli and other singular potentials we prove exponential localization in the anderson model under very weak assumptions on the potential distribution in one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment in particular this solves the longstanding problem of localization for bernoulli potentials i e potentials that take only two values in dimensions greater than one we prove localization at high disorder for potentials with holder continuous distributions and for bounded potentials whose distribution is a convex combination of a holder continuous distribution with high disorder and an arbitrary distribution these include potentials with singular distributions we also show that for certain bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component

large deviations for products of random two dimensional matrices we establish large deviation type estimates for i i d products of two dimensional random matrices with finitely supported probability distribution the estimates are stable under perturbations and require no irreducibility assumptions in consequence we obtain a uniform local modulus of continuity for the corresponding lyapunov exponent regarded as a function of the support of the distribution this in turn has consequences on the modulus of continuity of the integrated density of states and on the localization properties of random jacobi operators

fine structure of the zeros of orthogonal polynomials iv a priori bounds and clock behavior we prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions jacobi parameters approach the free ones and are of bounded variation we prove that for ergodic discrete schrodinger operators poisson behavior implies a positive lyapunov exponent both results depend on a priori bounds on eigenvalue spacings for which we provide several proofs

upper bounds in quantum dynamics of course the case of main interest is where h is given by l2 rd or 2 zd h is a schr dinger operator of the form a v and ip 0 is a localized wavepacket under the time evolution 1 the wavepacket i t will in general spread out with time finding quantitative bounds for this spreading in concrete cases and developing methods for proving such bounds has been the objective of a great number of papers in recent years one is often interested in the growth behavior of the moments of the position operator that is the function 11 x p 2 i 2 these questions are particularly complicated and interesting in situations where singular continuous spectra occur the discovery of the occurrence of such spectra for many models of physical relevance has triggered some activity on the quantum dynamical side for models with absolutely continuous spectra on the other hand quantum dynamical questions have been investigated much earlier in the context of scattering theory and have been answered to a great degree of satisfaction models with point spectrum or more restrictively models exhibiting anderson localization have also been investigated from a quantum dynamical point of view while it is not true in general that spectral localization implies dynamical localization 26 73 it has been shown that the three main approaches to spectral localization the fractional moment method 3 4 5 multi scale analysis 28 27 75 and the bourgain goldstein schlag method 12 37 yield dynamical localization as a by product 2 13 22 31 34 quantum dynamics for schr dinger operators with singular continuous spectra is much less understood the two primary examples motivated by physics are the harper model also known as the almost mathieu operator at critical cou pling which describes a bloch electron in a constant magnetic field with irrational flux through a unit cell and the fibonacci model which describes a standard one dimensional quasicrystal both models have been studied heavily in both the physics and mathematics communities

a stiffness equation transfer method for transient dynamic response analysis of structures a stiffness equation transfer method is proposed for transient dynamic response analysis of structures under various excitations this method is a development and refinement of the combined finite element transfer matrix fe tm method in the present method the transfer of state vectors from left to right in the fe tm method is changed into the transfer of general stiffness equations of every section from left to right this method has the advantages of reducing the order of the ordinary transfer equation systems and minimizing the propagation of round off errors occurring in recursive multiplication of transfer and point matrices furthermore the drawback that the number of degrees of freedom on the left boundary must be the same as that on the right boundary in the ordinary fe tm method has now been avoided the newmark generalized acceleration formulation for time discretization is employed for a solution of the time problem at the end numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for transient dynamic response analysis of structures

lower transport bounds for one dimensional continuum schrodinger operators we prove quantum dynamical lower bounds for one dimensional continuum schrodinger operators that possess critical energies for which there is slow growth of transfer matrix norms and a large class of compactly supported initial states this general result is applied to a number of models including the bernoulli anderson model with a constant single site potential

a simple method of sample size calculation for linear and logistic regression a sample size calculation for logistic regression involves complicated formulae this paper suggests use of sample size formulae for comparing means or for comparing proportions in order to calculate the required sample size for a simple logistic regression model one can then adjust the required sample size for a multiple logistic regression model by a variance inflation factor this method requires no assumption of low response probability in the logistic model as in a previous publication one can similarly calculate the sample size for linear regression models this paper also compares the accuracy of some existing sample size software for logistic regression with computer power simulations an example illustrates the methods

universal lower bounds for quantum diffusion abstract we study the connections between dynamical properties of schrodinger operators h on separable hilbert space h and the properties of corresponding spectral measures our main result establishes a relation for the moment of order p of the form x p t t t 1 t 0 x p 2 e ith 2 h dt l p d t 1 here l p d t is a function connected to the behavior of the fourier transform of measures in the subclass of measures absolutely continuous with respect to the spectral measure beyond the intrinsic interest of the general formulation 1 this result allows us to derive necessary conditions for dynamical localization in the presence of a pure point spectrum on the other hand if we focus on subsequences of time t k we can exhibit lower bounds which are in certain cases strictly larger than the well known power law lower bound for all t expressed in terms of the hausdorff dimension of spectral measures

localization for discrete one dimensional random word models we consider schrodinger operators in l2 z whose potentials are obtained by randomly concatenating words from an underlying set w according to some probability measure on w our assumptions allow us to consider models with local correlations such as the random dimer model or more generally random polymer models we prove spectral localization and away from a finite set of exceptional energies dynamical localization for such models these results are obtained by employing scattering theoretic methods together with furstenberg s theorem to verify the necessary input to perform a multiscale analysis

sample size calculations for ordered categorical data many clinical trials yield data on an ordered categorical scale such as very good good moderate poor under the assumption of proportional odds such data can be analysed using techniques of logistic regression in simple comparisons of two treatments this approach becomes equivalent to the mann whitney test in this paper sample size formulae consistent with an eventual logistic regression analysis are derived the influence on efficiency of the number and breadth of categories will be examined effects of misclassification and of stratification are discussed and examples of the calculations are given

power law bounds on transfer matrices and quantum dynamics in one dimension we present an approach to quantum dynamical lower bounds for discrete one dimensional schrodinger operators which is based on power law bounds on transfer matrices it suffices to have such bounds for a nonempty set of energies we apply this result to various models including the fibonacci hamiltonian

power sample size calculations for generalized linear models an approach for estimating power sample size is described within the framework of generalized linear models this approach is based on an asymptotic approximation to the power of the score test under contiguous alternatives and is applicable to tests of composite null hypotheses an implementation is described for the special case of logistic regression models simulation studies are presented which indicate that the asymptotic approximation to the finite sample situation is good over a range of parameter configurations

sample size calculations for logistic and poisson regression models summary a method is proposed for improving sample size calculations for logistic and poisson regression models by incorporating the limiting value of the maximum likelihood estimates of nuisance parameters under the composite null hypothesis the method modifies existing approaches of whittemnore 1981 and signorini 1991 and provides explicit formulae for determining the sample size needed to test hypotheses about a single parameter at a specified significance level and power simulation studies assess its accuracy for various model configurations and covariate distributions the results show that the proposed method is more accurate than the previous approaches over the range of conditions considered here

quantum harmonic oscillator systems with disorder we study many body properties of quantum harmonic oscillator lattices with disorder a sufficient condition for dynamical localization expressed as a zero velocity lieb robinson bound is formulated in terms of the decay of the eigenfunction correlators for an effective one particle hamiltonian we show how state of the art techniques for proving anderson localization can be used to prove that these properties hold in a number of standard models we also derive bounds on the static and dynamic correlation functions at both zero and positive temperature in terms of one particle eigenfunction correlators in particular we show that static correlations decay exponentially fast if the corresponding effective one particle hamiltonian exhibits localization at low energies regardless of whether there is a gap in the spectrum above the ground state or not our results apply to finite as well as to infinite oscillator systems the eigenfunction correlators that appear are more general than those previously studied in the literature in particular we must allow for functions of the hamiltonian that have a singularity at the bottom of the spectrum we prove exponential bounds for such correlators for some of the standard models

bootstrap multiscale analysis and localization in random media we introduce an enhanced multiscale analysis that yields subexponentially decaying probabilities for bad events for quantum and classical waves in random media we obtain exponential decay for the resolvent of the corresponding random operators in boxes of side l with probability higher than 1 e l for any 0 1 the starting hypothesis for the enhanced multiscale analysis only requires the verification of polynomial decay of the finite volume resolvent at some sufficiently large scale with probability bigger than 1 d is the dimension note that from the same starting hypothesis we get conclusions that are valid for any 0 1 this is achieved by the repeated use of a bootstrap argument as an application we use a generalized eigenfunction expansion to obtain strong dynamical localization of any order in the hilbert schmidt norm and better estimates on the behavior of the eigenfunctions

disordered quantum walks in one lattice dimension we study a spin 12 particle moving on a one dimensional lattice subject to disorder induced by a random space dependent quantum coin the discrete time evolution is given by a family of random unitary quantum walk operators where the shift operation is assumed to be deterministic each coin is an independent identically distributed random variable with values in the group of two dimensional unitary matrices we derive sufficient conditions on the probability distribution of the coins such that the system exhibits dynamical localization put differently the tunneling probability between two lattice sites decays rapidly for almost all choices of random coins and after arbitrary many time steps with increasing distance our findings imply that this effect takes place if the coin is chosen at random from the haar measure or some measure continuous with respect to it but also for a class of discrete probability measures which support consists of two coins one of them being the hadamard coin

power law bounds on transfer matrices and quantum dynamics in one dimension ii abstract we establish quantum dynamical lower bounds for a number of discrete one dimensional schrodinger operators these dynamical bounds are derived from power law upper bounds on the norms of transfer matrices we develop further the approach from part i and study many examples particular focus is put on models with finitely or at most countably many exceptional energies for which one can prove power law bounds on transfer matrices the models discussed in this paper include substitution models sturmian models a hierarchical model the prime model and a class of moderately sparse potentials

power calculations for likelihood ratio tests in generalized linear models summary recently self and mauritsen 1988 biometrics 44 79 86 described an approach for sample size power calculations within the framework of generalized linear models that is based on a noncentral chi square approximation to the distribution of score statistics in this work we present another approach to this same problem that is based on a noncentral chi square approximation to the distribution of the likelihood ratio statistic this approach is easier to implement than the previous one and simulation studies indicate that it is accurate over a much wider range of parameter values and data configurations than the earlier method the new method is also applied to the problem of power calculations for 1 k matched case control studies which is related to but formally outside of the generalized linear model framework

a stiffness equation transfer method for natural frequencies of structures abstract a stiffness equation transfer method is proposed for obtaining vibration frequencies of structures this method is an extension of the finite element transfer matrix fe tm method in the present method the transfer of state vectors from left to right in the ordinary fe tm method is changed into the transfer of stiffness equations of every section from left to right this method reduces the propagation of round off errors produced in the ordinary transfer matrix method furthermore the drawback that the number of degrees of freedom on the left boundary must be the same as that on the right boundary in the ordinary fe tm method is now avoided besides this method finds out the values of the frequency by newton raphson iteration method so no plotting of the value of the determinant versus assumed frequency is necessary an ifetm w program based on this method for use on an ibm pc586 microcomputer is developed finally numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for free vibration analysis of structures

anomalies in the one dimensional anderson model at weak disorder we show that at the special energiese 2cos p q the invariant measure the lyapunov exponent and the density of states can be extended to zero disorder as c functions in the disorder parameter in particular we obtain asymptotic series in the disorder parameter this gives a rigorous proof of the existence of the anomalies originally discovered by kappus and wegner and studied by derrida and gardner and by bovier and klein

global bounds for the lyapunov exponent and the integrated density of states of random schrodinger operators in one dimension in this paper we prove an upper bound for the lyapunov exponent e and a two sided bound for the integrated density of states n e at an arbitrary energy e 0 of random schrodinger operators in one dimension these schrodinger operators are given by potentials of identical shape centred at every lattice site but with non overlapping supports and with randomly varying coupling constants both types of bounds only involve scattering data for the single site potential they show in particular that both e and n e e 1 2 decay at infinity at least like 1 e 1 2 as an example we consider the random kronig penney model

sample size calculations for evaluating mediation this paper presents sample size calculations for testing the mediation of the effect of a primary predictor by an intermediate variable this problem is related to validating surrogate markers and to testing the effect of a primary predictor in the presence of confounders for those problems proposals for sample size calculation exist in the literature and can be adapted to the problem of mediation methods based on the variance inflation factor in linear regression provide exact sample size calculations for the linear model and approximations for the logistic poisson and cox models we propose another procedure based on simulation of the underlying data structure with applications to the logistic and cox models for the poisson model a new analytic method is also proposed the behavior of the different proposals is investigated by means of simulation studies copyright 2008 john wiley sons ltd

a practical approach to computing power for generalized linear models with nominal count or ordinal responses data analysts facing study design questions on a regular basis could derive substantial benefit from a straightforward and unified approach to power calculations for generalized linear models many current proposals for dealing with binary ordinal or count outcomes are conceptually or computationally demanding limited in terms of accommodating covariates and or have not been extensively assessed for accuracy assuming moderate sample sizes here we present a simple method for estimating conditional power that requires only standard software for fitting the desired generalized linear model for a non continuous outcome the model is fit to an appropriate expanded data set using easily calculated weights that represent response probabilities given the assumed values of the parameters the variance covariance matrix resulting from this fit is then used in conjunction with an established non central chi square approximation to the distribution of the wald statistic alternatively the model can be re fit under the null hypothesis to approximate power based on the likelihood ratio statistic we provide guidelines for constructing a representative expanded data set to allow close approximation of unconditional power based on the assumed joint distribution of the covariates relative to prior proposals the approach proves particularly flexible for handling one or more continuous covariates without any need for discretizing we illustrate the method for a variety of outcome types and covariate patterns using simulations to demonstrate its accuracy for realistic sample sizes

sample size for logistic regression with small response probability abstract the fisher information matrix for the estimated parameters in a multiple logistic regression can be approximated by the augmented hessian matrix of the moment generating function for the covariates the approximation is valid when the probability of response is small with its use one can obtain a simple closed form estimate of the asymptotic covariance matrix of the maximum likelihood parameter estimates and thus approximate sample sizes needed to test hypotheses about the parameters the method is developed for selected distributions of a single covariate and for a class of exponential type distributions of several covariates it is illustrated with an example concerning risk factors for coronary heart disease