adaptivity in space and time for reaction diffusion systems in electrocardiology the paper introduces and studies numerical methods that are fully adaptive in both three dimensional 3d space and time to challenging multiscale cardiac reaction diffusion models in these methods temporal adaptivity comes via stepsize control in function space oriented linearly implicit time integration while spatial adaptivity is realized within multilevel finite element methods controlled by a posteriori local error estimators in contrast to other recent adaptivity approaches to cardiac modeling that discretize first in space and then in time so called method of lines our method discretizes first in time and then in space so called rothe method an approach that has already proven to be highly efficient in a number of challenging multiscale problems in science and technology kardos code library with this method the evolution of a complete heartbeat from the excitation to the recovery phase is simulated both in the frame of the anisotropic monodomain models and in the more realistic anisotropic bidomain models coupled with either a variant of the simple fitzhugh nagumo model or the more complex phase i luo rudy ionic model the numerical results exhibit a rather satisfactory performance of our adaptive method for complex cardiac reaction diffusion models on 3d domains up to moderate sizes in particular the method accurately resolves the evolution of the intra and extracellular potentials gating variables and ion concentrations during the excitation plateau and recovery phases

score confidence intervals and sample sizes for stratified comparisons of binomial proportions in a series of articles gart and nam construct the efficient score tests and confidence intervals with or without skewness correction for stratified comparisons of binomial proportions on the risk difference relative risk and odds ratio effect metrics however the stratified score methods and their properties are not well understood we rederive the efficient score tests which reveals their theoretical relationship with the contrast based score tests and provides a basis for adapting the method by using other weighting schemes the inverse variance weight is optimal for a common treatment effect in large samples we explore the behavior of the score approach in the presence of extreme outcomes when either no or all subjects in some strata are responders and provide guidance on the choice of weights in the analysis of rare events the score method is recommended for studies with a small number of moderate or large sized strata a general framework is proposed to calculate the asymptotic power and sample size for the score test in superiority noninferiority and equivalence clinical trials or case control studies we also describe a nearly exact procedure that underestimates the exact power but the degree of underestimation can be controlled to a negligible level the proposed methods are illustrated by numerical examples

optimal allocation for the comparison of proportions optimal allocation strategies for the comparison of proportions p1 and p2 in two groups are discussed allocations which i maximize the precision in the estimation of the difference p1 p2 ii maximize the precision in the estimation of the ratio p1 p2 iii maximize the power to detect a group difference and iv minimize the total cost of a study are compared the recommended allocation varies markedly with the desired objective furthermore there is a wide range of allocation schemes which are effectively optimal with regard to each criterion considered a study of congenital malformations occurring in pregnancies of diabetic women is used to illustrate how these considerations apply to the planning of a study

strictly convex norms and topology we introduce a new topological property called and the corresponding class of topological spaces which includes spaces with g diagonals and gruenhage spaces using we characterize those banach spaces which admit equivalent strictly convex norms and give an internal topological characterization of those scattered compact spaces k for which the dual banach space c k admits an equivalent strictly convex dual norm we establish some relationships between and other topological concepts and the position of several well known examples in this context for instance we show that c k admits an equivalent strictly convex dual norm where k is kunen s compact s space also under additional axioms we provide examples of compact scattered non gruenhage spaces of cardinality 1 having

simultaneous confidence bounds for relative risks in multiple comparisons to control we discuss the construction of asymptotic simultaneous upper confidence limits that jointly bound relative risks formed by comparing several treatments to a control motivated by a vaccine study we investigate the performance of several methods under such settings inverting the minimum of score statistics together with estimating the correlation matrix of these statistics under the null gives simultaneous coverage rates closest to the nominal level in typical settings of vaccine studies this method proves to be the most powerful of the ones considered but computationally simpler alternatives are also worth exploring when the number of comparisons is large simultaneous lower and two sided confidence intervals are also considered all procedures can be implemented and evaluated using freely available and general r code

on tests of equivalence via non unity relative risk for matched pair design matched pair design is often used in clinical trials to increase the efficiency of treatment comparison we consider the problem of equivalence test with a relative risk endpoint in matched pair studies with binary outcomes and develop several score and wald type statistics for testing a hypothesis of non unity relative risk examples from an assessment of hiv screening test and a cross over clinical trial of soft contact lenses are used to illustrate the proposed methods through simulations we compare the empirical performance of these tests with the test proposed by lachenbruch and lynch we show that a score test based on a reparameterized multinomial model by tango performs best in the sense that the test satisfactorily controls the type i error rate and its empirical type i error rates are generally much closer to the prespecified nominal significance level than those of the other tests

minimization of sample size when comparing two small probabilities in a non inferiority safety trial in clinical trials success rates of two treatments to be compared often range from 10 to 90 per cent when the comparison probabilities are much smaller than 10 per cent standard methods for sample size and power calculations may provide invalid results this situation may occur when there is interest in safety rather than in efficacy in such trials no more patients should be included than strictly necessary we compared the results of maximum likelihood methods for the computation of sample sizes in a non inferiority trial including exact procedures and considered unequal sample sizes for experimental and reference treatment an exact unequal sample size maximum likelihood procedure is advocated when the specified non zero risk difference under the null hypothesis is not too large such a procedure is also indicated when the parameter of interest is the relative risk rather than the risk difference

blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions we describe and test an adaptive algorithm for evolution problems that employs a sequence of blocks consisting of fixed though nonuniform space meshes this approach offers the advantages of adaptive mesh refinement but with reduced overhead costs associated with load balancing remeshing matrix reassembly and the solution of adjoint problems used to estimate discretization error and the effects of mesh changes a major issue with a block adaptive approach is determining block discretizations from coarse scale solution information that achieve the desired accuracy we describe several strategies for achieving this goal using adjoint based a posteriori error estimates and we demonstrate the behavior of the proposed algorithms as well as several technical issues in a set of examples

test based exact confidence intervals for the difference of two binomial proportions summary confidence intervals are often provided to estimate a treatment difference when the sample size is small as is typical in early phases of clinical trials confidence intervals based on large sample approximations may not be reliable in this report we propose test based methods of constructing exact confidence intervals for the difference in two binomial proportions these exact confidence intervals are obtained from the unconditional distribution of two binomial responses and they guarantee the level of coverage we compare the performance of these confidence intervals to ones based on the observed difference alone we show that a large improvement can be achieved by using the standardized z test with a constrained maximum likelihood estimate of the variance

a new test of non inferiority for anti infective trials this paper describes a new statistical test of non inferiority in clinical trials of anti infective medications the test allows the inferiority limit delta to vary with the underlying success rates the test is a simple modification of the standard fixed delta test and its parameters can be adjusted to yield the fixed delta test a test similar to the fda s points to consider procedure or a test with nearly constant power values over a range of success rates the test satisfies the size and power criteria for a valid statistical test the effects on the test of lowering success rates through stringent criteria or through error are discussed

an a posteriori error estimator for anisotropic refinement besides an algorithm for local refinement an a posteriori error estimator is the basic tool of every adaptive finite element method using information generated by such an error estimator the refinement of the grid is controlled for 2nd order elliptic problems we present an error estimator for anisotropically refined grids like n d cuboidal and 3 d prismatic grids that gives correct information about the size of the error additionally it generates information about the direction into which some element has to be refined to reduce the error in a proper way numerical examples are presented for 2 d rectangular and 3 d prismatic grids

finite difference methods and spatial a posteriori error estimates for solving parabolic equations in three space dimensions on grids with irregular nodes adaptive methods for solving systems of partial differential equations have become widespread much of the effort has focused on finite element methods in this paper modified finite difference approximations are obtained for grids with irregular nodes the modifications are required to ensure consistency and stability asymptotically exact a posteriori error estimates of the spatial error are presented for the finite difference method these estimates are derived from interpolation estimates and are computed using central difference approximations of second derivatives of the solution at grid nodes the interpolation error estimates are shown to converge for irregular grids while the a posteriori error estimates are shown to converge for uniform grids computational results demonstrate the convergence of the finite difference method and a posteriori error estimates for cases not covered by the theory

a u statistics based approach to sample size planning of two arm trials with discrete outcome criterion aiming to establish either superiority or noninferiority in current practice the most frequently applied approach to the handling of ties in the mann whitney wilcoxon mww test is based on the conditional distribution of the sum of mid ranks given the observed pattern of ties starting from this conditional version of the testing procedure a sample size formula was derived and investigated by zhao et al stat med 2008 in contrast the approach we pursue here is a nonconditional one exploiting explicit representations for the variances of and the covariance between the two u statistics estimators involved in the mann whitney form of the test statistic the accuracy of both ways of approximating the sample sizes required for attaining a prespecified level of power in the mww test for superiority with arbitrarily tied data is comparatively evaluated by means of simulation the key qualitative conclusions to be drawn from these numerical comparisons are as follows with the sample sizes calculated by means of the respective formula both versions of the test maintain the level and the prespecified power with about the same degree of accuracy despite the equivalence in terms of accuracy the sample size estimates obtained by means of the new formula are in many cases markedly lower than that calculated for the conditional test perhaps a still more important advantage of the nonconditional approach based on u statistics is that it can be also adopted for noninferiority trials copyright 2016 john wiley sons ltd

on trees and dual rotund norms abstract we give a necessary and sufficient condition for the existence of an equivalent dual rotund norm on c 0 l 1 where is a tree the condition is expressed succinctly in terms of the embeddability of into a particular totally ordered set and compares very well with the analogous situation for local uniform rotundity this resolves an open problem from haydon s work in asplund spaces trees and renorming theory

a posteriori finite element error estimation for diffusion problems adjerid babuska and flaherty math models methods appl sci 9 1999 pp 261 286 and yu math numer sinica 13 1991 pp 89 101 and math numer sinica 13 1991 pp 307 314 show that a posteriori estimates of spatial discretization errors of piecewise bi p polynomial finite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is even we show that these simple error estimates are asymptotically correct for other finite element spaces the key requirement is that the trial space contain all monomial terms of degree p 1 except for x 1 p 1 and x 2 p 1 in a cartesian x1 x2 frame computational results show that the error estimates are accurate robust and efficient for a wide range of problems including some that are not supported by the present theory these involve quadrilateral element meshes problems with singularities and nonlinear problems

establishing equivalence of two treatments and sample size requirements in matched pairs design statistical methods for testing the null hypothesis of a nonzero difference between two treatments and the sample size determination for matched pairs studies are investigated a wald type test proposed by lu and bean 1995 statistics in medicine 14 1831 1839 is anticonservative i e its false positive error rate is greater than specified score method and normal deviate based on a restricted maximum likelihood estimation are presented these two test statistics are shown to be algebraically equal their actual type i error probabilities are satisfactorily close to a nominal level numerical examinations demonstrate that the sample size formulas using these alternative methods are reasonable while that by lu and bean is not the efficiency of matching in equivalence studies is positively related to intercorrelation or the kappa coefficient of agreements we recommend the score or ml methods to establish equivalence of two treatments for individually matched samples

mantel haenszel type tests for testing equivalence or more than equivalence in comparative clinical trials this paper proposes mantel haenszel type statistics for testing whether a new treatment is at least as effective as the standard treatment in comparative binomial trials the null hypotheses considered are of a specified nonzero difference and of a ratio not equal to unity it is shown that we may also use these tests for testing the equivalence of two treatments

an incomplete assembly with thresholding algorithm for systems of reaction diffusion equations in three space dimensions iat for reaction diffusion systems solving systems of reaction diffusion equations in three space dimensions can be prohibitively expensive both in terms of storage and cpu time herein i present a new incomplete assembly procedure that is designed to reduce storage requirements incomplete assembly is analogous to incomplete factorization in that only a fixed number of nonzero entries are stored per row and a drop tolerance is used to discard small values the algorithm is incorporated in a finite element method of lines code and tested on a set of reaction diffusion systems the effect of incomplete assembly on cpu time and storage and on the performance of the temporal integrator daspk algebraic solver gmres and preconditioner ilut is studied

weak locally uniformly rotund norms and descriptive compact spaces we prove that a dual banach space x has an equivalent w lur norm if and only if the weak topology has a isolated network we give sufficient conditions for the existence of equivalent norms with various kinds of differentiability

sample size and power for prospective analysis of relative risk in a placebo controlled vaccine efficacy trial or a trial of equivalence of vaccines one may wish to show that relative risk of disease is less than a specified value r0 not equal to one this paper compares three methods for estimating relative risk in the binomial setting based on a logarithmic transformation likelihood scores and a poisson approximation exact power and size of test are calculated by enumeration of possible binomial outcomes and power is approximated from asymptotic formulations although the score method is generally preferable for most studies of practical interest the log and score methods are comparable and the poisson method is also appropriate for small risks up to about 0 05 when true and null relative risks are less than one unequal allocation of study individuals can increase power and the asymptotic formula for the log method may substantially underestimate power in such a study the power approximation for the score method is more reliable even if the log method is used in analysis exact power calculations are helpful in planning studies the log and poisson methods but not the score method apply readily in the case of unequal follow up

confidence intervals based on some weighting functions for the difference of two binomial proportions in this paper we propose two new methods for computing confidence intervals for the difference of two independent binomial proportions in small sample cases several test based exact confidence intervals have been developed to guarantee the nominal coverage probability in small sample cases however these methods are sometimes unnecessarily too conservative because they use the exact p value for constructing confidence intervals by maximizing the tail probability to account for the worst configuration in order to reduce conservatism our new methods adopt the p value weighted by two types of functions instead of the maximum p value our proposed methods can be regarded as quasi exact methods the performance evaluation results showed that our methods are much less conservative than the exact method compared with other existing quasi exact methods generally our methods possess coverage probabilities closer to the nominal confidence level and shorter expected confidence widths in particular the beta weighing method provides the most reasonable balance between accurate coverage probability and short interval width in small sample cases

statistical approaches to establishing vaccine safety in a vaccine safety trial the primary interest is to demonstrate that the vaccine is sufficiently safe rejecting the null hypothesis that the relative risk of an adverse event attributable to the new vaccine is above a prespecified value greater than one we evaluate the exact probability of type i error of the likelihood score test with sample size determined by normal approximation by enumeration of the binomial outcomes in the rejection region and show that it exceeds the nominal level in the case of rare adverse events we recommend the poisson approximation as an alternative and develop the corresponding conditional and unconditional tests we give sample size and power calculations for these tests we also propose optimal randomization strategies which either i minimize the total number of adverse cases or ii minimize the expected number of subjects when the vaccine is unsafe we illustrate the proposed methods using a hypothetical vaccine safety study copyright 2002 john wiley sons ltd

comparative analysis of two rates in this paper we examine comparative analysis of rates with a view to each of the usual comparative parameters rate difference rd rate ratio rr and odds ratio or and with particular reference to first principles for rd and rr we show the prevailing statistical practices to be rather poor we stress the need for restricted estimation of variance in the chi square function underlying interval estimation and also point estimation and hypothesis testing for rr analysis we propose a chi square formulation analogous to that for rd and thus one which obviates the present practice of log transformation and its associated use of taylor series approximation of the variance as for or analysis we emphasize that the chi square function introduced by cornfield for unstratified data and extended by gart to the case of stratified analysis is based on the efficient score and thus embodies its optimality properties we provide simulation results to evince the better performance of the proposed parameter constrained procedures over the traditional ones

sample size requirements for stratified prospective studies with null hypothesis of non unity relative risk using the score test the standard test of the null hypothesis of unity of the relative risk seeks to determine if two treatments differ it does not apply when the requirement is either to establish the equivalence of two treatments or to determine whether the relative risk is less than a specified value other than one this paper presents the asymptotic power function of the score test for the null hypothesis of a specified value of a common relative risk for stratified prospective studies and proposes an approximate formula for the sample size required for a specific power of the test one can obtain a sample size formula for stratified studies with the standard null hypothesis of unity relative risk as a special case of this formula

noninferiority trial designs for odds ratios and risk differences this study presents constrained maximum likelihood derivations of the design parameters of noninferiority trials for binary outcomes with the margin defined on the odds ratio or risk difference scale the derivations show that for trials in which the group specific response rates are equal under the point alternative hypothesis the common response rate n is a fixed design parameter whose value lies between the control and experimental rates hypothesized at the point null c e we show that setting n equal to the value of c that holds under h 0 underestimates the overall sample size requirement given c or c and the type i and ii error rates or algorithm finds clinically meaningful design values of n and the corresponding minimum asymptotic sample size n n e n c and optimal allocation ratio n e n c we find that optimal allocations are increasingly imbalanced as increases with 2 5 trial results that are presented on both scales will differ in power with more power lost if the study is designed on the risk difference scale and reported on the odds ratio scale than vice versa

analysis of the ratio of marginal probabilities in a matched pair setting statistical methods for testing and interval estimation of the ratio of marginal probabilities in the matched pair setting are considered in this paper we are especially interested in the situation where the null value is not one as in one sided equivalence trials we propose a fieller type statistic based on constrained maximum likelihood cml estimation of nuisance parameters for a series of examples the significance level of the cml test is satisfactorily close to the nominal level while a wald type test is anticonservative for reasonable sample sizes we present formulae for approximate power and sample size for the cml and wald tests the matched design is seen to have a clear advantage over the unmatched design in terms of asymptotic efficiency when the two responses of the pair are highly positively correlated we recommend the cml method over the wald method especially for small or moderate sample sizes

adaptive finite element methods for parabolic problems iv nonlinear problems we extend our program on adaptive finite element methods for parabolic problems to a class of nonlinear scalar problems we prove a posteriori error estimates design corresponding adaptive algorithms and present some numerical results

deviance estimates of sample size for equivalence tests in vaccine trials this paper proposes a sample size procedure for both equivalence and conventional tests for the comparison of two binomial proportions based on the signed square root of the deviance when the comparison is based on the odds ratio i describe an alternate close conditional exact method that gives results that support those given by the deviance method i summarize the advantages of the deviance based method and also show that in general equivalence situations the sample size estimate depends upon the measure of comparison selected odds ratio risk ratio or risk difference

planning and analysis of three arm non inferiority trials with binary endpoints three arm trials including an experimental treatment an active control and a placebo group are frequently preferred for the assessment of non inferiority in contrast to two arm non inferiority studies these designs allow a direct proof of efficacy of a new treatment by comparison with placebo as a further advantage the test problem for establishing non inferiority can be formulated in such a way that rejection of the null hypothesis assures that a pre defined portion of the unknown effect the reference shows versus placebo is preserved by the treatment under investigation we present statistical methods for this study design and the situation of a binary outcome variable asymptotic test procedures are given and their actual type i error rates are calculated approximate sample size formulae are derived and their accuracy is discussed furthermore the question of optimal allocation of the total sample size is considered power properties of the testing strategy including a pre test for assay sensitivity are presented the derived methods are illustrated by application to a clinical trial in depression

using krylov methods in the solution of large scale differential algebraic systems in this paper a new algorithm for the solution of large scale systems of differential algebraic equations is described it is based on the integration methods in the solver dassl but instead of a direct method for the associated linear systems which arise at each time step we apply the preconditioned gmres iteration in combination with an inexact newton method the algorithm along with those in dassl is implemented in a new solver called daspk we outline the algorithms and strategies used and discuss the use of the solver we develop and analyze some preconditioners for a certain class of dae stems and finally demonstrate the application of daspk on two example problems

sample size determination in stratified trials to establish the equivalence of two treatments when designing a trial to establish that a new treatment is as effective as a standard one the conventional test procedure and sample size based on a null hypothesis of no difference between two treatments is inappropriate several authors have investigated test statistics and corresponding sample sizes based on the null hypothesis that the standard treatment is more effective than the new by at least some specific value for a single 2 x 2 table this paper considers a trial that involves several 2 x 2 tables and presents an approximate formula for the sample size required to obtain a given power of a one tailed score test for a null hypothesis of a specific common non zero difference between two treatments across strata i show that the sample size for a trial based on an unstratified test is always larger than that based on a stratified test when the design is balanced

sample size determination for establishing equivalence noninferiority via ratio of two proportions in matched pair design summary in this article we propose approximate sample size formulas for establishing equivalence or noninferiority of two treatments in match pairs design using the ratio of two proportions as the equivalence measure we derive sample size formulas based on a score statistic for two types of analyses hypothesis testing and confidence interval estimation depending on the purpose of a study these formulas can be used to provide a sample size estimate that guarantees a prespecified power of a hypothesis test at a certain significance level or controls the width of a confidence interval with a certain confidence level our empirical results confirm that these score methods are reliable in terms of true size coverage probability and skewness a liver scan detection study is used to illustrate the proposed methods

comparison of tests and sample size formulae for proving therapeutic equivalence based on the difference of binomial probabilities to prove the hypothesis that a new treatment is as effective as a standard one a possibility is to test the one sided null hypothesis of a clear inferiority of the new treatment against the alternative hypothesis that if at all it is only negligibly inferior such a problem is of clinical relevance if for instance a new treatment with an effectiveness which is comparable to that of the standard one would be preferred if it is less toxic if the difference between the two treatments is measured by the difference of failure rates approximate statistical tests and sample size formulae have to be used this paper reports the results of an extensive empirical investigation comparing the well known calculations proposed by blackwelder rodary comnougue and tournade which propose a sample size formula for the test of dunnett and gent and farrington and manning the investigation was conducted in order to allow more comprehensive conclusions than those which may be drawn from the limited examples given by the last authors for the usual settings in clinical trials the formulae of farrington and manning are recommended however there are combinations of statistical parameters for which they are not preferred

test statistics and sample size formulae for comparative binomial trials with null hypothesis of non zero risk difference or non unity relative risk when it is required to establish a materially significant difference between two treatments or alternatively to show that two treatments are equivalent standard test statistics and sample size formulae based on a null hypothesis of no difference no longer apply this paper reviews some of the test statistics and sample size formulae proposed for comparative binomial trials when the null hypothesis is of a specified non zero difference or non unity relative risk methods based on restricted maximum likelihood estimation are recommended and applied to studies of pertussis vaccine

approximate interval estimation of the ratio of binomial parameters a review and corrections for skewness various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically it is found that the method based on likelihood scores koopman 1984 biometrics 40 513 517 miettinen and nurminen 1985 statistics in medicine 4 213 226 performs best in achieving the nominal confidence coefficient but it may distribute the tail probabilities quite disparately using general theory of bartlett 1953 biometrika 40 306 317 1955 biometrika 42 201 203 we correct this method for asymptotic skewness following gart 1985 biometrika 72 673 677 we extend this correction to the case of estimating the common ratio in a series of two by two tables computing algorithms are given and applied to numerical examples parallel methods for the odds ratio and the ratio of poisson parameters are noted

confidence intervals for the ratio of two binomial proportions sometimes the ratio of two binomial proportions is the parameter of major interest for instance as the risk ratio in a two group cohort study fleiss 1973 or as the likelihood ratio for a diagnostic test procedure mcneill keeler and adelstein 1975 let x and y be independent binomial variates based on sample sizes m and n and parameters p and p2 respectively let 0 pm p2 we consider the construction of confidence intervals for 0 santner and snell 1980 have proposed a nonanalytical procedure which guarantees a lower bound on the confidence coefficient of the 1 a interval for 0 their algorithm is usable for small m and n but may produce conservative intervals in 2 an analytical method for obtaining approximate confidence intervals for 0 is proposed and compared to the one recommended by katz et al 1978

an adaptive finite element method for parabolic differential systems some algorithmic considerations in solving in three space dimensions an adaptive h refinement method is described for solving systems of parabolic partial differential equations in three space dimensions on hexahedral grids these grids typically have irregular hanging nodes solutions are calculated using galerkin s method with a piecewise trilinear basis in space and a backward difference formula bdf code in time new a posteriori error indicators based on interpolation error estimates for irregular grids are used to control refinement and coarsening a more efficient algorithm for assembling banded portions of the jacobian is introduced a simple strategy for dealing with storage limitations by limiting the level of refinement is developed computational results demonstrate the effectiveness of the adaptive method on linear and nonlinear problems

bootstrap and second order tests of risk difference clinical trials data often come in the form of low dimensional tables of small counts standard approximate tests such as score and likelihood ratio tests are imperfect in several respects first they can give quite different answers from the same data second the actual type 1 error can differ significantly from nominal even for quite large sample sizes third exact inferences based on these can be strongly nonmonotonic functions of the null parameter and lead to confidence sets that are discontiguous there are two modern approaches to small sample inference one is to use so called higher order asymptotics reid 2003 annal of statistics 31 1695 1731 to provide an explicit adjustment to the likelihood ratio statistic the theory for this is complex but the statistic is quick to compute the second approach is to perform an exact calculation of significance assuming the nuisance parameters equal their null estimate lee and young 2005 statistic and probability letters 71 143 153 which is a kind of parametric bootstrap the purpose of this article is to explain and evaluate these two methods for testing whether a difference in probabilities p 2 p 1 exceeds a prechosen noninferiority margin 0 on the basis of an extensive numerical study we recommend bootstrap p values as superior to all other alternatives first they produce practically identical answers regardless of the basic test statistic chosen second they have excellent size accuracy and higher power third they vary much less erratically with the null parameter value 0

adaptive space and time numerical simulation of reaction diffusion models for intracellular calcium dynamics abstract adaptivity in space and time for the numerical simulation of stochastic and deterministic equations for intracellular calcium dynamics is presented the modeling of diffusion reaction and membrane transport of calcium ions in cells leads to a system of reaction diffusion equations we describe the modulation of cytosolic and er calcium concentrations close to the membrane of the cell organelle a conforming piecewise linear finite element method is used for the spatial discretization linearly implicit methods of rosenbrock type are used for the time integration we adopt a hybrid algorithm to solve the stochastic part the space grid is adjusted to the strong localization of the calcium release following stochastic channel transitions by automatically adapting the spatial meshes and time steps to the proper scales during the transition of channel states the method accurately resolves the evolution of intracellular calcium concentrations as well as buffer concentrations this article emphasizes adaptive and efficient hybrid numerical simulations in two space dimensions the presented work establishes the basis for future simulations in a realistic 3d geometry

gruenhage compacta and strictly convex dual norms abstract we prove that if k is a gruenhage compact space then c k admits an equivalent strictly convex dual norm as a corollary we show that if x is a banach space and x span k where k is a gruenhage compact in the w topology and is equivalent to a coarser w lower semicontinuous norm on x then x admits an equivalent strictly convex dual norm we give a partial converse to the first result by showing that if is a tree then c 0 admits an equivalent strictly convex dual norm if and only if is a gruenhage space finally we present some stability properties satisfied by gruenhage spaces in particular gruenhage spaces are stable under perfect images