essential spectrum of a periodic waveguide with non periodic perturbation abstract we consider the spectral dirichlet laplacian problem on a domain which is formed from a periodic waveguide perturbed by non compact non periodic changes of geometry we show that the domain perturbation causes an addition to the essential spectrum which consists of isolated points belonging to the discrete spectrum of a model problem this model problem is posed on a domain which is just a compact perturbation of we discuss the position of the new spectral components in relation to the essential spectrum of the problem in

a quasi exact method for the confidence intervals of the difference of two independent binomial proportions in small sample cases in this paper we propose a quasi exact alternative to the exact unconditional method by chan and zhang 1999 estimating confidence intervals for the difference of two independent binomial proportions in small sample cases the quasi exact method is an approximation to a modified version of chan and zhang s method where the two sided p value of an observation is defined by adding to the one sided p value the sum of all probabilities of more extreme events in the unobserved tail we show that distinctively less conservative interval estimates can be derived following the modified definition of the two sided p value the approximations applied in the quasi exact method help to simplify the computations greatly while the resulting infringements to the nominal level are low compared with other approximate methods including the mid p quasi exact methods and the miettinen and nurminen m n asymptotic method our quasi exact method demonstrates much better reliability in small sample cases

gaps in the differential forms spectrum on cyclic coverings we are interested in the spectrum of the hodge de rham operator on a mathbb z covering x over a compact manifold m of dimension n 1 let be a hypersurface in m which does not disconnect m and such that m is a fundamental domain of the covering if the cohomology group hn 2 is trivial we can construct for each n in mathbb n a metric g gn on m such that the hodge de rham operator on the covering x g has at least n gaps in its essential spectrum if h n 2 sigma ne 0 the same statement holds true for the hodge de rham operators on p forms provided p notin n 2 n 2 1

spectral ordering of trees with small index abstract studying graphs by means of the largest eigenvalue of the adjacency matrix the index has been a problem largely investigated in spectral graph theory here we consider trees with index in the real interval 2 2 5 and their ordering with respect to the index for such graphs we prove three indices comparisons whose order has been conjectured in belardo et al 2008 2 by doing so we prove a conjectured ordering of trees with smallest indices open since 2002 and we obtain the first 8 trees of even order with largest index

large gaps in point coupled periodic systems of manifolds we study a free quantum motion on periodically structured manifolds composed of elementary two dimensional cells c onnected either by linear segments or through points where the two cells touch the general theory is illustrated with numerous examples in which the elementary components are spherical surfaces arranged into chains in a straight or zigzag way or two dimensional square lattice carpets we show that the spectra of such systems have an infinite number of gaps and that the latter dominate the spectrum at high energies

confidence interval construction for proportion difference in small sample paired studies paired dichotomous data may arise in clinical trials such as pre post test comparison studies and equivalence trials reporting parameter estimates e g odds ratio rate difference and rate ratio along with their associated confidence interval estimates becomes a necessity in many medical journals various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions nevertheless the performance of these asymptotic methods may have poor coverage properties in small samples in this article we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small sample paired data specifically we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test the exact unconditional confidence interval guarantees the coverage probability and it is recommended if strict control of coverage probability is required however the exact method tends to be overly conservative and computationally demanding our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small sample designs and yet they are relatively easy to implement computationally we illustrate the methods using real examples from a pain management study and a cancer study

spectra of open waveguides in periodic media abstract we study the essential spectra of formally self adjoint elliptic systems on doubly periodic planar domains perturbed by a semi infinite periodic row of foreign inclusions we show that the essential spectrum of the problem consists of the essential spectrum of the purely periodic problem and another component which is the union of the discrete spectra of model problems in the infinite perturbation strip these model problems arise by an application of the partial floquet bloch gelfand transform

neumann spectral problem in a domain with very corrugated boundary let rn be a bounded domain we perturb it to a domain e attaching a family of small protuberances with room and passage like geometry e 0 is a small parameter peculiar spectral properties of neumann problems in so perturbed domains were observed for the first time by r courant and d hilbert we study the case when the number of protuberances tends to infinity as e 0 and they are e periodically distributed along a part of our goal is to describe the behavior of the spectrum of the operator ae e 1 e where e is the neumann laplacian in e and the positive function e is equal to 1 in we prove that the spectrum of ae converges as e 0 to the spectrum of a certain boundary value problem for the neumann laplacian in with boundary conditions containing the spectral parameter in a nonlinear manner its eigenvalues may accumulate to a finite point

combining one sample confidence procedures for inference in the two sample case we present a simple general method for combining two one sample confidence procedures to obtain inferences in the two sample problem some applications give striking connections to established methods for example combining exact binomial confidence procedures gives new confidence intervals on the difference or ratio of proportions that match inferences using fisher s exact test and numeric studies show the associated confidence intervals bound the type i error rate combining exact one sample poisson confidence procedures recreates standard confidence intervals on the ratio and introduces new ones for the difference combining confidence procedures associated with one sample t tests recreates the behrens fisher intervals other applications provide new confidence intervals with fewer assumptions than previously needed for example the method creates new confidence intervals on the difference in medians that do not require shift and continuity assumptions we create a new confidence interval for the difference between two survival distributions at a fixed time point when there is independent censoring by combining the recently developed beta product confidence procedure for each single sample the resulting interval is designed to guarantee coverage regardless of sample size or censoring distribution and produces equivalent inferences to fisher s exact test when there is no censoring we show theoretically that when combining intervals asymptotically equivalent to normal intervals our method has asymptotically accurate coverage importantly all situations studied suggest guaranteed nominal coverage for our new interval whenever the original confidence procedures themselves guarantee coverage

exact properties of some exact test statistics for comparing two binomial proportions abstract using exact unconditional distributions we evaluated the size and power of four exact test procedures and three versions of the 2 statistic for the two sample binomial problem in small to moderate sample sizes the exact unconditional test suissa and shuster 1985 and fisher s 1935 exact test are the only tests whose size can be guaranteed never to exceed the nominal size though the former is distinctly more powerful it is also computationally difficult we propose an alternative that approximates the exact unconditional test by computing the exact distribution of the 2 statistic at a single point the maximum likelihood estimate of the common success probability this test is a modification of the test of liddell 1978 which considered the exact distribution of the difference in the sample proportions our test is generally more powerful than either the exact unconditional or liddell s test and its true size rarely exceeds the nominal size the uncorrected 2 statistic is frequently a

a comparative study of tests for homogeneity of variances with applications to the outer continental shelf bidding data many of the existing parametric and nonparametric tests for homogeneity of variances and some variations of these tests are examined in this paper comparisons are made under the null hypothesis for robustness and under the alternative for power monte carlo simulations of various symmetric and asymmetric distributions for various sample sizes reveal a few tests that are robust and have good power these tests are further compared using data from outer continental shelf bidding on oil and gas leases

a practical two step method for testing moment inequalities this paper considers the problem of testing a finite number of moment inequalities we propose a two step approach in the first step a confidence region for the moments is constructed in the second step this set is used to provide information about which moments are negative a bonferonni type correction is used to account for the fact that with some probability the moments may not lie in the confidence region it is shown that the test controls size uniformly over a large class of distributions for the observed data an important feature of the proposal is that it remains computationally feasible even when the number of moments is large the finite sample properties of the procedure are examined via a simulation study which demonstrates among other things that the proposal remains competitive with existing procedures while being computationally more attractive

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

a more powerful exact test of noninferiority from binary matched pairs data assessing the therapeutic noninferiority of one medical treatment compared with another is often based on the difference in response rates from a matched binary pairs design this paper develops a new exact unconditional test for noninferiority that is more powerful than available alternatives there are two new elements presented in this paper first we introduce the likelihood ratio statistic as an alternative to the previously proposed score statistic of nam biometrics 1997 53 1422 1430 second we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of berger and boos am stat assoc 1994 89 1012 1016 or traditional full maximization based on an extensive numerical study we recommend tests based on the score statistic the nuisance parameter being controlled by estimation followed by maximization

periodic manifolds with spectral gaps abstract we investigate spectral properties of the laplace operator on a class of non compact riemannian manifolds for a given number n we construct periodic manifolds such that the essential spectrum of the corresponding laplacian has at least n open gaps we use two different methods first we construct a periodic manifold starting from an infinite number of copies of a compact manifold connected by small cylinders in the second construction we begin with a periodic manifold which will be conformally deformed in both constructions a decoupling of the different period cells is responsible for the gaps

diffraction by a defect in an open waveguide a mathematical analysis based on a modal radiation condition we consider the scattering of a time harmonic acoustic wave by a defect in a twodimensional open waveguide the scattered wave satisfies the helmholtz equation in a perturbed layered half plane we introduce a modal radiation condition based on a generalized fourier transform which diagonalizes the transverse contribution of the helmholtz operator the uniqueness of the solution is proved by an original technique which combines a property of the energy flux with an argument of analyticity with respect to the generalized fourier variable the existence is then deduced classically from fredholm s alternative by reformulating the scattering problem as a lippmann schwinger equation by means of the green s function for the layered half plane 2009 society for industrial and applied mathematics

exact and approximate unconditional confidence intervals for proportion difference in the presence of incomplete data confidence interval ci construction with respect to proportion rate difference for paired binary data has become a standard procedure in many clinical trials and medical studies when the sample size is small and incomplete data are present asymptotic cis may be dubious and exact cis are not yet available in this article we propose exact and approximate unconditional test based methods for constructing ci for proportion rate difference in the presence of incomplete paired binary data approaches based on one and two sided wald s tests will be considered unlike asymptotic ci estimators exact unconditional ci estimators always guarantee their coverage probabilities at or above the pre specified confidence level our empirical studies further show that i approximate unconditional ci estimators usually yield shorter expected confidence width ecw with their coverage probabilities being well controlled around the pre specified confidence level and ii the ecws of the unconditional two sided test based ci estimators are generally narrower than those of the unconditional one sided test based ci estimators moreover ecws of asymptotic cis may not necessarily be narrower than those of two sided based exact unconditional cis two real examples will be used to illustrate our methodologies

p values maximized over a confidence set for the nuisance parameter abstract for testing problems of the form h 0 v v 0 with unknown nuisance parameter various methods are used to deal with the simplest approach is exemplified by the t test where the unknown variance is replaced by the sample variance and the t distribution accounts for estimation of the variance in other problems such as the 2 2 contingency table one conditions on a sufficient statistic for 0 and proceeds as in fisher s exact test because neither of these standard methods is appropriate for all situations this article suggests a new method for handling the unknown this new method is a simple modification of the formal definition of a p value that involves taking a maximum over the nuisance parameter space of a p value obtained for the case when is known the suggested modification is to restrict the maximization to a confidence set for the nuisance parameter after giving a brief justification we give various examples to show how this new method gives improved results for 2 2 tabl

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

recommended tests for association in 2 2 tables summary the asymptotic pearson s chi squared test and fisher s exact test have long been the most used for testing association in 2 2 tables unconditional tests preserve the significance level and generally are more powerful than fisher s exact test for moderate to small samples but previously were disadvantaged by being computationally demanding this disadvantage is now moot as software to facilitate unconditional tests has been available for years moreover fisher s exact test with mid p adjustment gives about the same results as an unconditional test consequently several better tests are available and the choice of a test should depend only on its merits for the application involved unconditional tests and the mid p approach ought to be used more than they now are the traditional fisher s exact test should practically never be used copyright q 2009 john wiley sons ltd

tests for the homogeneity of two binomial proportions in extremely unbalanced 2 2 contingency tables asymptotic tests such as the pearson chi square test are unreliable for testing the homogeneity of two binomial probabilities in extremely unbalanced cases two exact tests conditional and unconditional are available as alternatives and can be implemented easily in statxact 6 0 in equal sample cases it is well known that the unconditional exact test is more powerful than the conditional exact test however in this paper we show that the opposite result holds in extremely unbalanced cases the reason is that the peaks of the type i error occur at the extremes of the nuisance parameter when the imbalance among the sample sizes becomes severe after we show that the conditional exact test is more powerful than the unconditional exact test in extremely unbalanced cases whose sample ratio is greater than 20 we compare the conditional exact test with the berger and boos approach j amer stat assoc 1994 89 1012 1016 in which the supremum is taken over a confidence interval for the nuisance parameter the berger and boos approach turns out to be slightly more powerful than the conditional exact test in extremely unbalanced data a real example is provided

ramsey numbers graph eigenvalues and a conjecture of cao and yuan abstract let n be a positive integer and r n n denote the ramsey number see 15 or 11 such that any graph with at least r n n vertices contains a clique with n vertices or an independent set with n vertices we show that any graph g with order at least r n n must have its n th largest eigenvalue n g 1 and that any graph g with order at least r n 1 n 1 must have its n th smallest eigenvalue n g 0 where the bounds 1 and 0 are best possible this reveals some connection between graph spectra and ramsey numbers and enables us to give bounds of some eigenvalues for graphs with order greater than certain numbers moreover it leads to a disproof of a conjecture on limit points of graph eigenvalues posted by cao and yuan 3 in 1995 finally we post some problems for further research

exact confidence intervals for the relative risk and the odds ratio for comparison of proportions there are three commonly used measurements the difference the relative risk and the odds ratio significant effort has been spent on exact confidence intervals for the difference in this article we focus on the relative risk and the odds ratio when data are collected from a matched pairs design or a two arm independent binomial experiment exact one sided and two sided confidence intervals are proposed for each configuration of two measurements and two types of data the one sided intervals are constructed using an inductive order they are the smallest under the order and are admissible under the set inclusion criterion the two sided intervals are the intersection of two one sided intervals r codes are developed to implement the intervals supplementary materials for this article are available online

opening up and control of spectral gaps of the laplacian in periodic domains the main result of this work is as follows for arbitrary pairwise disjoint finite intervals j j 0 j 1 m and for arbitrary n 2 we construct a family of periodic non compact domains e n e 0 such that the spectrum of the neumann laplacian in e has at least m gaps when e is small enough moreover the first m gaps tend to the intervals j j as e 0 the constructed domain e is obtained by removing from n a system of periodically distributed trap like surfaces the parameter e characterizes the period of the domain e also it is involved in a geometry of the removed surfaces

on the spectral radius of a class of non odd bipartite even uniform hypergraphs abstract in order to investigate the non odd bipartiteness of even uniform hypergraphs starting from a simple graph g we construct a generalized power of g denoted by g k s which is obtained from g by blowing up each vertex into a s set and each edge into a k 2 s set where s k 2 when s k 2 g k s is always odd bipartite we show that g k k 2 is non odd bipartite if and only if g is non bipartite and find that g k k 2 has the same adjacency respectively signless laplacian spectral radius as g so the results involving the adjacency or signless laplacian spectral radius of a simple graph g hold for g k k 2 in particular we characterize the unique graph with minimum adjacency or signless laplacian spectral radius among all non odd bipartite hypergraphs g k k 2 of fixed order and prove that 2 5 is the smallest limit point of the non odd bipartite hypergraphs g k k 2 in addition we obtain some results for the spectral radii of the weakly irreducible nonnegative tensors

on the lowest eigenvalue of the laplacian with neumann boundary condition at a small obstacle we study the lowest eigenvalue 1 e of the laplacian in a bounded domain rd d 2 from which a small compact set ke be has been deleted imposing dirichlet boundary conditions along and neumann boundary conditions on ke we are mainly interested in results that require minimal regularity of ke expressed in terms of a poincare condition for the domains e 1ke we then show that 1 e converges to 1 the first dirichlet eigenvalue of as e 0 assuming some more regularity we also obtain asymptotic bounds on 1 e 1 for e small where we employ an idea of burenkov and davies j differential equations 186 2002 485 508

spectral asymptotics of periodic elliptic operators we demonstrate that the structure of complex second order strongly elliptic operators h on bf r d with coefficients invariant under translation by bf z d can be analyzed through decomposition in terms of versions h z z in bf t d of h with z periodic boundary conditions acting on l 2 bf i d where bf i 0 1 rangle if the s emigroup s generated by h has a holder continuous integral kernel satisfying gaussian bounds then the semigroups s z generated by the h z have kernels with similar properties and z mapsto s z extends to a function on bf c d backslash 0 which is analytic with respect to the trace norm the sequence of semigroups s m z obtained by rescaling the coefficients of h z by c x to c mx converges in trace norm to the semigroup widehat s z generated by the homogenization widehat h z of h z these convergence properties allow asymptotic analysis of the spectrum of h

growth rates of permutation grid classes tours on graphs and the spectral radius monotone grid classes of permutations have proven very effective in helping to determine structural and enumerative properties of classical permutation pattern classes associated with grid class grid m is a graph g m known as its row column graph we prove that the exponential growth rate of grid m is equal to the square of the spectral radius of g m consequently we utilize spectral graph theoretic results to characterise all slowly growing grid classes and to show that for every 2 5 there is a grid class with growth rate arbitrarily close to to prove our main result we establish bounds on the size of certain families of tours on graphs in the process we prove that the family of tours of even length on a connected graph grows at the same rate as the family of balanced tours on the graph in which the number of times an edge is traversed in one direction is the same as the number of times it is traversed in the other direction

unconditional exact tests for equivalence or noninferiority for paired binary endpoints problems of establishing equivalence or noninferiority between two medical diagnostic procedures involve comparisons of the response rates between correlated proportions when the sample size is small the asymptotic tests may not be reliable this article proposes an unconditional exact test procedure to assess equivalence or noninferiority two statistics a sample based test statistic and a restricted maximum likelihood estimation rmle based test statistic to define the rejection region of the exact test are considered we show the p value of the proposed unconditional exact tests can be attained at the boundary point of the null hypothesis assessment of equivalence is often based on a comparison of the confidence limits with the equivalence limits we also derive the unconditional exact confidence intervals on the difference of the two proportion means for the two test statistics a typical data set of comparing two diagnostic procedures is analyzed using the proposed unconditional exact and asymptotic methods the p value from the unconditional exact tests is generally larger than the p value from the asymptotic tests in other words an exact confidence interval is generally wider than the confidence interval obtained from an asymptotic test

on the spectrum of a finite volume negatively curved manifold we show that a noncompact manifold with bounded sectional curvature whose ends are sufficiently gromov hausdorff close to rays has a finite dimensional space of square integrable harmonic forms in the special case of a finite volume manifold with pinched negative sectional curvature we show that the essential spectrum of the p iorm laplacian is the union of the essential spectra of a collection of ordinary differential operators associated to the ends we give examples of such manifolds with curvature pinched arbitrarily close to 1 and with an infinite number of gaps in the spectrum of the function laplacian 1 introduction in this paper we consider riemannian manifolds of finite volume and pinched negative sectional curvature we give results about the kernel of the differential form laplacian and about its essential spectrum our first result is the finite dimensionality of the space of square integrable harmonic forms for a more general class of riemannian manifolds which can be roughly characterized as those with bounded sectional curvature and with ends that are sufficiently gromov hausdorff close to rays let m be a complete connected rc dimensional riemannian manifold with a basepoint m let br m denote the distance ball around m and let sr m dbr m be the distance sphere around m put

unbiased confidence intervals for the odds ratio of two independent binomial samples with application to case control data the problem of confidence interval construction for the odds ratio of two independent binomial samples is considered two methods of eliminating the nuisance parameter from the exact likelihood conditioning and maximization are described a conditionally exact tail method exists by putting together upper and lower bounds a shorter interval can be obtained by simultaneous consideration of both tails we present here new methods that extend the tail and simultaneous approaches to the maximized likelihood the methods are unbiased and applicable to case control data for which the odds ratio is important the confidence interval procedures are compared unconditionally for small sample sizes in terms of their expected length and coverage probability a bayesian confidence interval method and a large sample chi2 procedure are included in the comparisons

unconditional versions of several tests commonly used in the analysis of contingency tables summary by focusing on a confidence interval for a nuisance parameter berger and boos 1994 journal of the american statistical association89 1012 1016 proposed new unconditional tests in particular they showed that for a 2 2 table this procedure generally was more powerful than fisher s exact test this paper utilizes and extends their approach to obtain unconditional tests for combining several 2 2 tables and testing for trend and homogeneity in a 2 k table the unconditional procedures are compared to the conditional ones by reanalyzing some published biomedical data

on the distribution of the maximum eigenvalue of graphs abstract given a graph g let g denote the largest eigenvalue of the adjacency matrix of g we prove that for any 2 5 2 058 there exists a sequence of graphs g1 g2 such that limk gk thus answering a question posed by hoffman

a cautionary note on exact unconditional inference for a difference between two independent binomial proportions utilise pour la comparaison de proportions dans le cadre d essais randomises le test exact de ficher peut se reveler particulierement conservateur principalement lorsque les echantillons sont de petite taille ou lorsque les proportions observees sont proches de 0 ou de 1 cette propriete indesirable s explique surtout par une distribution de la statistique de test sous hypothese nulle trop discretisee notamment en raison d une inference effectuee conditionnellement au nombre total des repondeurs de ce fait les procedures exactes non conditionnelles ont conquis une popularite fondee sur l idee d une augmentation de la puissance entrainee par des distributions de statistiques de tests sous hypothese nulle necessairement moins discretisees toutefois nous mettons en garde les chercheurs contre le choix hasardeux d un test exact non conditionnel car dans certains cas leur utilisation peut s averer franchement moins puissante que le test de fisher a l appui de nos propos nous traitons d un exemple reel puis nous calculons les risques de type i et les puissances associees a differents tests lors de comparaisons portant sur des groupes de tailles egales ou inegales nos resultats montrent que le test exact de fisher fait generalement mieux que les tests exacts non conditionnels bases sur la difference des proportions mieux aussi dans le cas d echantillons de taille inegales que les tests exacts non conditionnels bases sur la difference des proportions divisee par son ecart type estime sous hypothese alternative a l inverse le test exact non conditionnel base sur la difference des proportions divisee par son ecart type estime sous hypothese nulle il s agit de la statistique du score fait mieux que le test de fisher ce test est recommande tout comme le test de boschloo test dans lequel le test de fisher est utilise comme une statistique de test dans un test exact non conditionnel ce dernier test s avere quant a lui uniformement plus puissant que le test de fisher

complete manifolds with bounded curvature and spectral gaps abstract we study the spectrum of complete noncompact manifolds with bounded curvature and positive injectivity radius we give general conditions which imply that their essential spectrum has an arbitrarily large finite number of gaps in particular for any noncompact covering of a compact manifold there is a metric on the base so that the lifted metric has an arbitrarily large finite number of gaps in its essential spectrum also for any complete noncompact manifold with bounded curvature and positive injectivity radius we construct a metric uniformly equivalent to the given one also of bounded curvature and positive injectivity radius with an arbitrarily large finite number of gaps in its essential spectrum

welch s approximate solution for the behrens fisher problem the wald likelihood ratio and score statistics have been calculated for the behrens fisher problem these statistics provide asymptotically equivalent and weakly optimal tests the test based on the wald statistic was found to be very similar to the v test discussed by welch 1937 hence the v test was compared with the likelihood ratio and score tests in a power study since the powers were very similar and the v test was more convenient to use from several points of view we recommend this test sizes of the v test as well as a power comparison with the usual pooled t test were also obtained

generalized p values in significance testing of hypotheses in the presence of nuisance parameters abstract this article examines some problems of significance testing for one sided hypotheses of the form h 0 0 versus h 1 0 where is the parameter of interest in the usual setting let x be the observed data and let t x be a test statistic such that the family of distributions of t x is stochastically increasing in define cx as x t x t x 0 the p value is p x sup 0 pr x cx in the presence of a nuisance parameter there may not exist a nontrivial cx with a p value independent of we consider tests based on generalized extreme regions of the form cx x t x x t x x and conditions on t x x are given such that the p value p x sup 0 pr x cx is free of the nuisance parameter where t is stochastically increasing in we provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions a problem for which the fixed level testing approach

using pilot data to size a two arm randomized trial to find a nearly optimal personalized treatment strategy a personalized treatment strategy formalizes evidence based treatment selection by mapping patient information to a recommended treatment personalized treatment strategies can produce better patient outcomes while reducing cost and treatment burden thus among clinical and intervention scientists there is a growing interest in conducting randomized clinical trials when one of the primary aims is estimation of a personalized treatment strategy however at present there are no appropriate sample size formulae to assist in the design of such a trial furthermore because the sampling distribution of the estimated outcome under an estimated optimal treatment strategy can be highly sensitive to small perturbations in the underlying generative model sample size calculations based on standard uncorrected asymptotic approximations or computer simulations may not be reliable we offer a simple and robust method for powering a single stage two armed randomized clinical trial when the primary aim is estimating the optimal single stage personalized treatment strategy the proposed method is based on inverting a plugin projection confidence interval and is thereby regular and robust to small perturbations of the underlying generative model the proposed method requires elicitation of two clinically meaningful parameters from clinical scientists and uses data from a small pilot study to estimate nuisance parameters which are not easily elicited the method performs well in simulated experiments and is illustrated using data from a pilot study of time to conception and fertility awareness

unconditional efficient one sided confidence limits for the odds ratio based on conditional likelihood we compare various one sided confidence limits for the odds ratio in a 2 x 2 table the first group of limits relies on first order asymptotic approximations and includes limits based on the signed likelihood ratio score and wald statistics the second group of limits is based on the conditional tilted hypergeometric distribution with and without mid p correction all these limits have poor unconditional coverage properties and so we apply the general transformation of buehler j am statist assoc 1957 52 482 493 to obtain limits which are unconditionally exact the performance of these competing exact limits is assessed across a range of sample sizes and parameter values by looking at their mean size the results indicate that buehler limits generated from the conditional likelihood have the best performance with a slight preference for the mid p version this confidence limit has not been proposed before and is recommended for general use especially when the underlying probabilities are not extreme

randomization based inference within principal strata in randomized studies treatment comparisons conditional on intermediate postrandomization outcomes using standard analytic methods do not have a causal interpretation an alternative approach entails treatment comparisons within principal strata defined by the potential outcomes for the intermediate outcome that would be observed under each treatment assignment in this article we develop methods for randomization based inference within principal strata we compare our proposed methods with existing large sample methods as well as traditional intent to treat approaches this research is motivated by hiv prevention studies where few infections are expected and inference is desired within the always infected principal stratum that is all individuals who would become infected regardless of randomization assignment

the limit points of laplacian spectra of graphs abstract let g be a graph on n vertices denote by l g the laplacian matrix of g it is easy to see that l g is positive semidefinite symmetric and that its second smallest eigenvalue g 0 if and only if g is connected this observation let fiedler to call g the algebraic connectivity of the graph g in this paper the limit points of laplacian spectra of graphs are investigated particular attention is given to the limit points of algebraic connectivity some new results and generalizations are included

more powerful exact noninferiority and equivalence tests based on binary matched pairs assessing the therapeutic noninferiority or equivalence of one medical treatment compared to another is often based on the difference of response rates from a matched binary pairs design this paper develops new exact unconditional tests for noninferiority and equivalence that are more powerful than available alternatives there are three new elements presented in this paper first we introduce the lr statistic as an alternative to the previously proposed score statistic of nam 1997 second we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of berger and boos 1994 or traditional full maximization third for testing equivalence it is standard to combine two one sided tests tost we point out that even if the one sided tests are exact and efficient the tost will be conservative and requires a further adjustment to remove this conservatism based on an extensive numerical study we recommend tests based on the score statistic the nuisance parameter being controlled by estimation followed by maximization

on small sample confidence intervals for parameters in discrete distributions summary the traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level in constructing such intervals for parameters in discrete distributions less conservative behavior results from inverting a single two sided test than inverting two separate one sided tests of half the nominal level each we illustrate for a variety of discrete problems including interval estimation of a binomial parameter the difference and the ratio of two binomial parameters for independent samples and the odds ratio

periodic riemannian manifold with preassigned gaps in spectrum of laplace beltrami operator it is known e l green 1997 o post 2003 that for an arbitrary m n one can construct a periodic non compact riemannian manifold m with at least m gaps in the spectrum of the corresponding laplace beltrami operator m in this work we want not only to produce a new type of periodic manifolds with spectral gaps but also to control the edges of these gaps the main result of the paper is as follows for arbitrary pairwise disjoint intervals j j 0 j 1 m m n for an arbitrarily small 0 and for an arbitrarily large l 0 we construct a periodic non compact riemannian manifold m with at least m gaps in the spectrum of the operator m moreover the edges of the first m gaps belong to neighbourhoods of the edges of the intervals j j while the remaining gaps if any are located outside the interval 0 l

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

collapsing of riemannian manifolds and eigenvalues of laplace operator on etudie la perturbation des valeurs propres de l operateur de laplace sous des deformations des varietes qui ne conservent pas les dimensions

exact one sided confidence limits for the difference between two correlated proportions we construct exact and optimal one sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well established optimality theory of buehler starting with five different approximate lower and upper limits we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use

an overview of periodic elliptic operators the article surveys the main techniques and results of the spectral theory of periodic operators arising in mathematical physics and other areas close attention is paid to studying analytic properties of bloch and fermi varieties which influence significantly most properties of such operators the approaches described are applicable not only to the standard model example of schrodinger operator with periodic electric potential v x but to a wide variety of elliptic periodic equations and systems equations on graphs operator and other operators on abelian coverings of compact bases many important applications are mentioned however due to the size restrictions they are not dealt with in details

connected hypergraphs with small spectral radius abstract in 1970 smith classified all connected graphs with spectral radius at most 2 here the spectral radius of a graph is the largest eigenvalue of its adjacency matrix recently the definition of spectral radius has been extended to r uniform hypergraphs in this paper we generalize smith s theorem to r uniform hypergraphs we show that the smallest limit point of the spectral radii of connected r uniform hypergraphs is r 4 r we discovered a novel method for computing the spectral radius of hypergraphs and classified all connected r uniform hypergraphs with spectral radius at most r

asymptotic analysis polarization matrices and topological derivatives for piezoelectric materials with small voids asymptotic formulae for the mechanical and electric fields in a piezoelectric body with a small void are derived and justified such results are new and useful for applications in the field of design of smart materials in this way the topological derivatives of shape functionals are obtained for piezoelectricity the asymptotic formulae are given in terms of the so called polarization tensors matrices which are determined by the integral characteristics of voids the distinguishing feature of the piezoelectricity boundary value problems under consideration is the absence of positive definiteness of a differential operator which is non self adjoint two specific gibbs functionals of the problem are defined by the energy and the electric enthalpy the topological derivatives are defined in different manners for each of the governing functionals actually the topological derivative of the enthalpy functional is local i e defined by the pointwise values of the mechanical and electric fields which is contrary to the energy functional and some other suitable shape functionals which admit nonlocal topological derivatives i e depending on the whole problem data an example with weak interaction between mechanical and electric fields provides the analytic asymptotic expansions and can be used in numerical procedures of optimal design for smart materials

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

the spectrum radiation conditions and the fredholm property for the dirichlet laplacian in a perforated plane with semi infinite inclusions abstract we consider the spectral dirichlet problem for the laplace operator in the plane with double periodic perforation but also in the domain with a semi infinite foreign inclusion so that the floquet bloch technique and the gelfand transform do not apply directly we describe waves which are localized near the inclusion and propagate along it we give a formulation of the problem with radiation conditions that provides a fredholm operator of index zero the main conclusion concerns the spectra and of the problems in and namely we present a concrete geometry which supports the relation due to a new non empty spectral band caused by the semi infinite inclusion called an open waveguide in the double periodic medium

spectral theory of laplace beltrami operators with periodic metrics abstract the spectra of laplace beltrami operators with periodic metrics has been less investigated than that of schrodinger operators with a periodic potentials and there are many differences between these two cases it has been established that the spectrum of a laplace beltrami operator with periodic metric is the union of closed intervals and that spectral gaps are possible but whether an infinite number of spectral gaps is possible is an open question utilizing special transformations it is shown that there are two dimensional laplace beltrami operators having an arbitrarily large number of spectral gaps by proving that a particular two dimensional operator has an infinite number of spectral gaps in the case of a periodic conformal metric relationships between the scalar curvature and the number of gaps are investigated

random hamiltonians ergodic in all but one direction letv 1 andv 2 be two ergodic random potentials on d we consider the schrodinger operatorh h0 v withh0 and forx x1 x2 v omega x left begin array 20 c v omega 1 x if x 1 over smash scriptstyle vphantom x 0 end array right we prove certain ergodic properties of the spectrum for this model and express the integrated density of states in terms of the density of states of the stationary potentialsv 1 andv 2 finally we prove the existence of the density of surface states forh

accurate confidence limits for stratified clinical trials for stratified 2 2 tables standard approximate confidence limits can perform poorly from a strict frequentist perspective even for moderate sized samples yet they are routinely used in this paper i show how to use importance sampling to compute highly accurate limits in reasonable time the methodology is very general and simple to implement and orders of magnitude are faster than existing alternatives copyright 2013 john wiley sons ltd

assessing equivalence or non inferiority in screening tests with paired and independent binomial endpoints through confidence intervals for the odds ratio the confidence interval ci on the population average pa odds ratio or is a useful measure of agreement among different diagnostic methods when no gold standard is available it can be calculated by the repeated measures logistic regression procedure genmod sas we compare the width of cis from paired and independent samples with an identical number of measurements and an identical probability of positive response among them for two and three diagnostic methods with binomial endpoints the best performing sampling strategy is analytically described the asymptotic formulae of the ratio of the ci widths for paired and independent samples are provided we numerically study the dependence of the width of the cis on the number of positive concordant outcomes the width of cis from independent samples is an increasing function of the sample size with a saturation asymptote and rather weak dependence on the argument the width of cis from paired samples is a decreasing function of the sample size with a saturation asymptote and significant dependence on the argument when the sample size is small if curves for paired and independent samples intersect a critical sample size exists at this point a small change in the sample size can reverse the choice of the best performing sampling policy we numerically validated the robustness of the critical point to variations of the conditional or

graph representations two distance sets and equiangular lines abstract using the new concepts of graph representations and heights it is shown among other results that all sufficiently large sets of equiangular lines with mutual angle arccos 1 5 are known

fully specified bootstrap confidence intervals for the difference of two independent binomial proportions based on the median unbiased estimator in studies in which a binary response for each subject is observed the success probability and functions of this quantity are of interest the use of confidence intervals has been increasingly encouraged as complementary to and indeed preferable to p values as the primary expression of the impact of sampling uncertainty on the findings the asymptotic confidence interval based on a normal approximation is often considered but this interval can have poor statistical properties when the sample size is small and or when the success probability is near 0 or 1 in this paper an estimate of the risk difference based on median unbiased estimates mues of the two group probabilities is proposed a corresponding confidence interval is derived using a fully specified bootstrap sample space the proposed method is compared with chen s quasi exact method wald intervals and agresti and caffo s method with regard to mean square error and coverage probability for a variety of settings the mue based estimate of risk difference has mean square error uniformly smaller than maximum likelihood estimate within a certain range of risk difference the fully specified bootstrap had better coverage probability in the tail area than chen s quasi exact method wald intervals and agresti and caffo s intervals

clique inserted graphs and spectral dynamics of clique inserting abstract motivated by studying the spectra of truncated polyhedra we consider the clique inserted graphs for a regular graph g of degree r 0 the graph obtained by replacing every vertex of g with a complete graph of order r is called the clique inserted graph of g denoted as c g we obtain a formula for the characteristic polynomial of c g in terms of the characteristic polynomial of g furthermore we analyze the spectral dynamics of iterations of clique inserting on a regular graph g for any r regular graph g with r 2 let s g denote the union of the eigenvalue sets of all iterated clique inserted graphs of g we discover that the set of limit points of s g is a fractal with the maximum r and the minimum 2 and that the fractal is independent of the structure of the concerned regular graph g as long as the degree r of g is fixed it follows that for any integer r 2 there exist infinitely many connected r regular graphs or non regular graphs with r as the maximum degree with arbitrarily many distinct eigenvalues in an arbitrarily small interval around any given point in the fractal we also present a formula on the number of spanning trees of any k th iterated clique inserted graph and other related results

the spectrum of the laplacian on forms over flat manifolds in this article we prove that the spectrum of the laplacian on k forms over a non compact flat manifold is always a connected closed interval of the non negative real line the proof is based on a detailed decomposition of the structure of flat manifolds

on graphs whose laplacian index does not exceed 4 5 abstract let a g and d g be the adjacency matrix and the vertex degree matrix of a graph g respectively the laplacian matrix of g is defined as l g d g a g the l index of g denoted by g is the largest root of the characteristic polynomial of l g the laplacian hoffman limit value h l is the limit of hn where the graph hn is obtained by attaching a pendant edge to the cycle c n 1 of length n 1 it is known that h l 2 where is the largest root of x 3 4 x 4 in this paper we characterize the structure of graphs whose l index does not exceed 4 5 and we completely describe those graphs whose l index does not exceed h l by doing so we complete the so called hoffman program w r t the laplacian theory of graph spectra

confidence intervals for an exposure adjusted incidence rate difference with applications to clinical trials to summarize safety data such as clinical adverse experiences in clinical trials with a moderate to long term follow up we may use a measurement which accounts for the potential differences in the follow up duration between treatment groups the incidence rate which uses the total person time follow up in a treatment group as the denominator is one of these measures when treatment comparisons are based on the difference of the incidence rates it is of interest to construct confidence intervals for the rate differences in this paper we first discuss the assumptions and scenarios in which the exposure adjusted incidence rate may be appropriate then we review several methods of calculating confidence intervals for the difference of two incidence rates assuming that the number of events come from a poisson distribution the methods considered include wald s method the two by two table method the miettinen and nurminen mn method and the conditional mn method for all but the mn method explicit confidence intervals can be obtained for the mn method some numerical iterations are required the properties of these methods are evaluated by simulations the results show that the mn method outperforms the other three in terms of the coverage of the confidence interval especially when the rates and therefore the number of events are small lastly data from a clinical study are used to demonstrate the application of the methods

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

mathematical analysis of the junction of two acoustic open waveguides the present paper concerns the scattering of a time harmonic acoustic wave by the junction of two open uniform waveguides where the junction is limited to a bounded region we consider a two dimensional problem for which wave propagation is described by the scalar helmholtz equation the main difficulty in the modeling of the scattering problem lies in the choice of conditions which characterize the outgoing behavior of a scattered wave we use here modal radiation conditions which extend the classical conditions used for closed waveguides they are based on the generalized fourier transforms which diagonalize the transverse contributions of the helmholtz operator on both sides of the junction we prove the existence and uniqueness of the solution which seems to be the first result in this context the originality lies in the proof of uniqueness which combines a natural property related to energy fluxes with an argument of analyticity with respect to the generalized fourier variable

exact tests of equivalence and efficacy with a non zero lower bound for comparative studies exact tests of equivalence and efficacy with a non zero lower bound based on two independent binomial proportions for comparative trials are proposed these exact tests are desirable for studies with small sample sizes they generalize classical methods to include testing of null hypotheses of prespecified differences and can be used to demonstrate a new treatment s efficacy or its equivalence to a standard treatment the proposed exact tests use unconditional distributions of the test statistics variances of test statistics are estimated via a constrained maximum likelihood method farrington and manning data from oncology and vaccine clinical trials are used to illustrate the exact tests

some notes on graphs whose index is close to 2 abstract we consider two classes of graphs i trees of order n and diameter d n 3 and ii unicyclic graphs of order n and girth g n 2 assuming that each graph within these classes has two vertices of degree 3 at distance k we order by the index i e spectral radius the graphs from i for any fixed k 1 k d 2 and the graphs from ii independently of k

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

δ interaction as a limit of a thin neumann waveguide with transversal window abstract we consider a waveguide like domain consisting of two thin straight tubular domains connected through a tiny window the perpendicular size of this waveguide is of order e under the assumption that the window is appropriately scaled we prove that the neumann laplacian on this domain converges in a kind of norm resolvent sense as e 0 to a one dimensional schrodinger operator corresponding to a interaction of a non negative strength we estimate the rate of this convergence also we prove the convergence of spectra

on graphs whose signless laplacian index does not exceed 4 5 abstract let a g and d g be respectively the adjacency matrix and the degree matrix of a graph g the signless laplacian matrix of g is defined as q g d g a g the q spectrum of g is the set of the eigenvalues together with their multiplicities of q g the q index of g is the maximum eigenvalue of q g the possibilities for developing a spectral theory of graphs based on the signless laplacian matrices were discussed by cvetkovic et al d cvetkovic p rowlinson s k simic signless laplacians of finite graphs linear algebra appl 423 2007 155 171 in the latter paper the authors determine the graphs whose q index is in the interval 0 4 in this paper we investigate some properties of q spectra of graphs especially for the limit points of the q index by using these results we characterize respectively the structures of graphs whose the q index lies in the intervals 4 2 5 2 5 2 and 2 4 5 where 1 3 54 6 33 1 3 54 6 33 1 3 2 382975767

the distribution of eigenvalues of graphs abstract we show that every limit point of the kth largest eigenvalues of graphs is a limit point of the k 1 th largest eigenvalues and we find out the smallest limit point of the kth largest eigenvalues and an upper bound of the limit points of the kth smallest eigenvalues for k 4 we prove that there exists a gap beyond the smallest limit point in which no point is the limit point of the kth largest eigenvalues for the third largest eigenvalues of a graph g with at least three vertices we obtain that 1 3 g 1 3 g 1 5 2 consequently if gc is not a complete bipartite graph plus isolated vertices 3 g 3 d n where d n is the complement of the double star s 1 n 3

conformally flat riemannian metrics schrodinger operators and semiclassical approximation abstract a relationship between laplace beltrami and schrodinger operators on euclidean domains is analyzed and exploited for several purposes we use the schrodinger equation to analyze the spectra of laplace beltrami operators with periodic metrics on r v and use geometric notions and nonlinear differential equations to bound spectra and green functions of schrodinger operators in various ways we also have a new more operator theoretic analysis of the semiclassical limit and the liouville green or jwkb approximation in one dimension

meta analysis framework for exact inferences with application to the analysis of rare events the usefulness of meta analysis has been recognized in the evaluation of drug safety as a single trial usually yields few adverse events and offers limited information for rare events conventional meta analysis methods may yield an invalid inference as they often rely on large sample theories and require empirical corrections for zero events these problems motivate research in developing exact methods including tian et al s method of combining confidence intervals 2009 biostatistics 10 275 281 and liu et al s method of combining p value functions 2014 jasa 109 1450 1465 this article shows that these two exact methods can be unified under the framework of combining confidence distributions cds furthermore we show that the cd method generalizes tian et al s method in several aspects given that the cd framework also subsumes the mantel haenszel and peto methods we conclude that the cd method offers a general framework for meta analysis of rare events we illustrate the cd framework using two real data sets collected for the safety analysis of diabetes drugs

planar waveguide with twisted boundary conditions discrete spectrum we consider a planar waveguide with combined dirichlet and neumann conditions imposed in a twisted way we study the discrete spectrum and describe it dependence on the configuration of the boundary conditions in particular we show that in certain cases the model can have discrete eigenvalues emerging from the threshold of the essential spectrum we give a criterium for their existence and construct them as convergent holomorphic series

bound states in curved quantum waveguides a free quantum particle living on a curved planar strip of a fixed width d with dirichlet boundary conditions is studied it can serve as a model for electrons in thin films on a cylinder type substrate or in a curved quantum wire assuming that the boundary of is infinitely smooth and its curvature decays fast enough at infinity it is proved that a bound state with energy below the first transversal mode exists for all sufficiently small d a lower bound on the critical width is obtained using the birman schwinger technique