limiting the effects of single member families in the estimation of the intraclass correlation summary because the maximum likelihood estimator for the intraclass correlation p does not exist in closed form for the unbalanced one way random effects model several noniterative estimators have been proposed for p in normal populations estimators that exclude all families of only one member have been recommended in the literature of familial correlations however these estimators lose efficiency appreciably for certain ranges of values of p indeed no single estimator can have the highest efficiency along the full range of the intraclass correlation coefficient three proposed estimators each formed by combining a pair of noniterative estimators of which one constituent estimator excludes families having only one member are shown by simulation to be nearly fully efficient for the full range of values of p a mathematical expression is given that can be used to calculate the large sample standard errors of all known noniterative estimators of the intraclass correlation

model order reduction for nonlinear dynamical systems based on trajectory piecewise linear approximations in this paper we analyze and expand a recently developed approach to model order reduction mor for nonlinear dynamical systems based on trajectory piecewise linear tpwl approximations error estimates are given for solutions computed with tpwl reduced order models and problems of preserving stability and passivity are examined since the tpwl method has limited a priori guarantees on global accuracy its effectiveness is demonstrated on a range of examples including a micromachined switch two nonlinear electronic circuits and shock propagation modeled by burgers equation

exponential improvements for superball packing upper bounds abstract we prove that for all fixed p 2 the translative packing density of unit l p balls in r n is at most 2 p o 1 n with p 1 p this is the first exponential improvement in high dimensions since van der corput and schaake 1936

finite element analysis of post buckling dynamics in plates part i an asymptotic approach abstract various static and dynamic aspects of post buckled thin plates including the transition of buckled patterns post buckling dynamics secondary bifurcation and dynamic snapping mode jumping phenomenon are investigated systematically using asymptotical and non stationary finite element methods in part i the secondary dynamic instability and the local post secondary buckling behavior of thin rectangular plates under generalized mechanical and thermal loading is investigated using an asymptotic numerical method which combines koiter s nonlinear instability theory with the finite element technique a dynamic multi mode reduction method similar to its static single mode counterpart liapunov schmidt reduction is developed in this perturbation approach post secondary buckling equilibrium branches are obtained by solving the reduced low dimensional parametric equations and their stability properties are determined directly by checking the eigenvalues of the resulting jacobian matrix typical post secondary buckling forms transcritical supercritical and subcritical bifurcations are observed according to different combinations of boundary conditions and load types geometric imperfection analysis shows that not only the secondary bifurcation load but also changes in the fundamental post secondary buckling behavior are affected the post buckling dynamics and the global analysis of mode jumping of the plates are addressed in part ii

galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics error estimates for galerkin proper orthogonal decomposition pod methods for nonlinear parabolic systems arising in fluid dynamics are proved for the time integration the backward euler scheme is considered the asymptotic estimates involve the singular values of the pod snapshot set and the grid structure of the time discretization as well as the snapshot locations

optimality and uniqueness of the leech lattice among lattices we prove that the leech lattice is the unique densest lattice in r24 the proof combines human reasoning with computer verification of the properties of certain explicit polynomials we furthermore prove that no sphere packing in r24 can exceed the leech lattice s density by a factor of more than 1 1 65 10 30 and we give a new proof that es is the unique densest lattice in r8

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

random ensembles of lattices from generalized reductions we propose a general framework to study constructions of euclidean lattices from linear codes over finite fields in particular we prove general conditions for an ensemble constructed using linear codes to contain dense lattices i e with packing density comparable to the minkowski hlawka lower bound specializing to number field lattices we obtain a number of interesting corollaries for instance the best known packing density of ideal lattices and an elementary coding theoretic construction of asymptotically dense hurwitz lattices all results are algorithmically effective in the sense that for any dimension a finite family containing dense lattices is exhibited for suitable constructions based on craig s lattices this family is smaller in terms of alphabet size than previous ensembles in the literature

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

the asymptotic variance of the interclass correlation coefficient summary in genetics the term interclass correlation has been used to refer to the parent offspring and son daughter correlations within families under the assumption of variable family sizes and normality we derive the asymptotic variance of the maximum likelihood estimator of the sondaughter interclass correlation

dimensional model reduction in non linear finite element dynamics of solids and structures a general approach to the dimensional reduction of non linear finite element models of solid dynamics is presented for the newmark implicit time discretization the computationally most expensive phase is the repeated solution of the system of linear equations for displacement increments to deal with this it is shown how the problem can be formulated in an approximation ritz basis of much smaller dimension similarly the explicit newmark algorithm can be also written in a reduced dimension basis and the computation time savings in that case follow from an increase in the stable time step length in addition the empirical eigenvectors are proposed as the basis in which to expand the incremental problem this basis achieves approximation optimality by using computational data for the response of the full model in time to construct a reduced basis which reproduces the full system in a statistical sense because of this global time viewpoint the basis need not be updated as with reduced bases computed from a linearization of the full finite element model if the dynamics of a finite element model is expressed in terms of a small number of basis vectors the asymptotic cost of the solution with the reduced model is lowered and optimal scalability of the computational algorithm with the size of the model is achieved at the same time numerical experiments indicate that by using reduced models substantial savings can be achieved even in the pre asymptotic range furthermore the algorithm parallelizes very efficiently the method we present is expected to become a useful tool in applications requiring a large number of repeated non linear solid dynamics simulations such as convergence studies design optimization and design of controllers of mechanical systems

sphere packing bounds via spherical codes the sphere packing problem asks for the greatest density of a packing of congruent balls in euclidean space the current best upper bound in all suciently high dimensions is due to kabatiansky and levenshtein in 1978 we revisit their argument and improve their bound by a constant factor using a simple geometric argument and we extend the argument to packings in hyperbolic space for which it gives an exponential improvement over the previously known bounds additionally we show that the cohn elkies linear programming bound is always at least as strong as the kabatiansky levenshtein bound this result is analogous to rodemich s theorem in coding theory finally we develop hyperbolic linear programming bounds and prove the analogue of rodemich s theorem there as well

reduction method for finite element nonlinear dynamic analysis of shells doi 10 2514 1 j051003theprojectionoftheequationsofmotiononasuitablemodalbasiscandrasticallyreducethenumberofdegreesoffreedom of a nonlinear dynamic nite element analysis a reduction method based on enriching a set of vibrationmodeswithsecond ordermodescalculatedviaaperturbationtechniqueispresented thesesecond ordermodesarereadily calculated via the solution of corresponding linear problems the results indicate that the second ordermodes are displacement elds that are essential for an appropriate representation of the nonlinear behavior of thestructure problems exhibiting strong geometrical nonlinearities under relatively high dynamic loads aresuccessfully handled by forming the reduction basis with vibration modes and their corresponding second ordermodes calculated at two different static equilibrium con gurations

robust asymptotic sampling theory for correlations in pedigrees methods to unravel the genetic determinants of non mendelian diseases lie at the next frontier of statistical approaches for human genetics it is generally agreed that before proceeding with segregation or linkage analysis the trait under study ought to be shown to exhibit familial correlation by coding dichotomous traits as binary variables a single robust approach in the estimation of pedigree correlations rather than two distinct approaches can be used to assess the potential heritability of a trait and latterly to examine the mode of inheritance the asymptotic theory to conduct hypothesis tests and confidence intervals for correlations among different members of nuclear families is well established but is applicable only if the nuclear families are independent as a further contribution to the literature we derive the asymptotic sampling distribution of correlations between random variables among arbitrary pairs of members in extended families for the pearson product moment estimator with generalized weights this derivation is done without assuming normality of the traits the sampling distribution is shown to be asymptotically normal to first order and hence large sample hypothesis tests and confidence intervals with estimates of the variances and correlation coefficients are proposed discussion concludes with an example and a suggestion for future research

projection based reduction of fluid structure interaction systems using monolithic space time modes abstract the focus of this work is the development of reduced models for engineering applications in complex bidirectional fluid structure interaction in the simultaneous solution procedure velocity variables are used for both fluid and solid and the whole set of model equations is discretized by a stabilized time discontinuous space time finite element method flexible structures are modeled using a three dimensional continuum approach in a total lagrangian setting considering large displacements and rotations in the flow domain the incompressible navier stokes equations describe the newtonian fluid a continuous finite element mesh is applied to the entire spatial domain and the discretized model equations are assembled in a single set of algebraic equations considering the two field problem as a whole the continuous fluid structure mesh with identical orders of approximation for both solid and fluid in space and time automatically yields conservation of mass momentum and energy at the fluid structure interface a mesh moving scheme is used to adapt the nodal coordinates of the fluid space time finite element mesh to the structural deformation the computational approach for strongly coupled fluid structure interaction is used to create suitable reduced models of generic nonlinear problems reduction is performed with monolithic projection based space time modes ensuring strong coupling of fluid and structure in the reduced model the contribution discusses results using proper orthogonal decomposition pod for determination of monolithic space time modes in the reduction of fluid structure systems

an optimal uncertainty principle in twelve dimensions via modular forms we prove an optimal bound in twelve dimensions for the uncertainty principle of bourgain clozel and kahane suppose f mathbb r 12 rightarrow mathbb r is an integrable function that is not identically zero normalize its fourier transform widehat f by widehat f xi int mathbb r d f x e 2 pi i langle x xi rangle dx and suppose widehat f is real valued and integrable we show that if f 0 le 0 widehat f 0 le 0 f x ge 0 for x ge r 1 and widehat f xi ge 0 for xi ge r 2 then r 1r 2 ge 2 and this bound is sharp the construction of a function attaining the bound is based on viazovska s modular form techniques and its optimality follows from the existence of the eisenstein series e 6 no sharp bound is known or even conjectured in any other dimension we also develop a connection with the linear programming bound of cohn and elkies which lets us generalize the sign pattern of f and widehat f to develop a complementary uncertainty principle this generalization unites the uncertainty principle with the linear programming bound as aspects of a broader theory

evaluation of geometrically nonlinear reduced order models with nonlinear normal modes several reduced order modeling strategies have been developed to create low order models of geometrically nonlinear structures from detailed finite element models allowing one to compute the dynamic response of the structure at a dramatically reduced cost however the parameters of these reduced order models are estimated by applying a series of static loads to the finite element model and the quality of the reduced order model can be highly sensitive to the amplitudes of the static load cases used and to the type number of modes used in the basis this paper proposes to combine reduced order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced order model can be assessed hence the second contribution of this

on the properties of maximum likelihood estimators of familial correlations under variable sibship size selected distributional properties of the maximum likelihood estimator and its z transformation of three familial correlations parental parent offspring filial were investigated numerically for the case of nuclear families with variable sibship size this investigation was based on six different sets of the three correlations and four different sample sizes defining 24 sampling conditions which were replicated 1 000 times each it was found that the distributional properties of the correlation estimator are affected by the magnitude of the correlations even in large samples although approximate normality is achieved locally fisher s z transformation here used only in its interclass form achieves reduction of skewness stabilization of variance and approach to normality already in small samples except for the filial correlation where it may be deemed inappropriate in smaller samples for both the correlation estimator and its z transformation the estimated relative efficiency was shown to be high better than 90 in most sampling conditions suggesting that the estimated minimum variance bound is a satisfactory estimator of the sampling variance it is concluded that the maximum likelihood estimation of familial correlations under variable sibship size is feasible and when prudently applied especially in the form of their z transformations provides an appropriate method in analyses of family studies

system identification guided basis selection for reduced order nonlinear response analysis reduced order nonlinear simulation is often times the only computationally efficient means of calculating the extended time response of large and complex structures under severe dynamic loading this is because the structure may respond in a geometrically nonlinear manner making the computational expense of direct numerical integration in physical degrees of freedom prohibitive as for any type of modal reduction scheme the quality of the reduced order solution is dictated by the modal basis selection the techniques for modal basis selection currently employed for nonlinear simulation are ad hoc and are strongly influenced by the analyst s subjective judgment this work develops a reliable and rigorous procedure through which an efficient modal basis can be chosen the method employs proper orthogonal decomposition to identify nonlinear system dynamics and the modal assurance criterion to relate proper orthogonal modes to the normal modes that are eventually used as the basis functions the method is successfully applied to the analysis of a planar beam and a shallow arch over a wide range of nonlinear dynamic response regimes the error associated with the reduced order simulation is quantified and related to the computational cost

estimation of interclass and intraclass correlations in multivariate familial data asymptotically normal estimators of interclass and intraclass correlations are derived for more than two quantitative characteristics of parent and siblings in a simple random sampling of families that have different numbers of offspring these estimators are proposed as an alternative to the maximum likelihood estimators which can be found only by iterative methods requiring prohibitively large amounts of computation the asymptotic variances of the proposed estimators are also given in an illustrative example these easily computable estimators are seen to be comparable to the corresponding maximum likelihood estimators

differential harnack inequalities on riemannian manifolds i linear heat equation abstract in the first part of this paper we get new li yau type gradient estimates for positive solutions of heat equation on riemannian manifolds with ricci m k k r as applications several parabolic harnack inequalities are obtained and they lead to new estimates on heat kernels of manifolds with ricci curvature bounded from below in the second part we establish a perelman type li yau hamilton differential harnack inequality for heat kernels on manifolds with ricci m k which generalizes a result of l ni 2004 2006 20 21 as applications we obtain new harnack inequalities and heat kernel estimates on general manifolds we also obtain various entropy monotonicity formulas for all compact riemannian manifolds

spherical cap packing asymptotics and rank extreme detection we study the spherical cap packing problem with a probabilistic approach such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a stochastically independent uniformly distributed unit vector when the set of unit vectors are themselves independently uniformly distributed we further develop the extreme value distribution limit of the maximal inner product which characterizes its uncertainty around the bound as applications of the above mentioned asymptotic results we derive 1 an asymptotic sharp universal uniform bound on the maximal spurious correlation as well as its uniform convergence in distribution when the explanatory variables are independently gaussian distributed and 2 an asymptotic sharp universal bound on the maximum norm of a low rank elliptically distributed vector as well as related limiting distributions with these results we develop a fast detection method for a low rank structure in high dimensional gaussian data without using the spectrum information

wiener s problem for positive definite functions we study the sharp constant w n d in wiener s inequality for positive definite functions begin aligned int mathbb t n f 2 dx le w n d d 1 int d f 2 dx quad d subset mathbb t n end aligned wiener proved that w 1 delta delta infty delta in 0 1 2 hlawka showed that w n d le 2 n where d is an origin symmetric convex body we sharpen hlawka s estimates for d being the ball delta b n and the cube delta i n in particular we prove that w n delta b n le 2 0 401 cdots o 1 n we also obtain a lower bound of w n d moreover for a cube d frac 1 q i n with q 3 4 ldots we obtain that w n d 2 n our proofs are based on the interrelation between wiener s problem and the problems of turan and delsarte

estimation of the interclass correlation coefficient summary a noniterative method for estimating the interclass correlation coefficient is derived from the technique of weighted sums of squares the asymptotic variance of this estimator is derived under the assumption of normality through extensive monte carlo simulations the sample variance of this estimator is found not to differ greatly from that of the maximum likelihood estimator an important problem in genetics is the estimation of the degree of resemblance between a mother and her children as measured by the interclass correlation coefficient because parents produce differing numbers of offspring during their reproductive period the maximum likelihood estimation of the interclass correlation presents computational difficulties requiring an iterative solution therefore a number of noniterative estimators have been proposed in the literature these estimators will be shown to be associated with special cases of the generalized estimator derived from the weighted sums of squares of measurements on parents and offspring because our purpose is to provide a comprehensive approach to the noniterative point and interval estimation problems for the interclass correlation coefficient the asymptotic variance of the proposed estimator is derived under the assumption of normality moreover the sample variances of two special cases of the proposed estimator are compared to that of the maximum likelihood estimator through monte carlo simulations by a theoretical argument it is shown that the estimator proposed by srivastava 1984 has a uniformly smaller asymptotic variance than the ensemble estimator proposed by rosner donner hennekens 1977 smith 1957 used the weighted sums of squares approach for the estimation problem concerning the intraclass correlation coefficient which measures the degree to which siblings resemble one another our results together with those of smith 1957 provide a unified approach to estimation problems concerning familial correlations among a parent and offspring

improved sphere packing lower bounds from hurwitz lattices abstract in this paper we prove an asymptotic lower bound for the sphere packing density in dimensions divisible by four this asymptotic lower bound improves on previous asymptotic bounds by a constant factor and improves not just lower bounds for the sphere packing density but also for the lattice sphere packing density and in fact the hurwitz lattice sphere packing density

sibling and parent offspring correlation estimation with variable family size abstract a method for estimating intrafamilial correlations under variable family sizes involving weightings of paired data points is introduced classical methods of intrafamilial correlation estimation and those in current use are outlined and critically analyzed extensions of the proposed estimation method to more general data structures are delineated

sensitivity analysis for dynamic mechanical systems with finite rotations this paper presents a sensitivity analysis for dynamic systems with large rotations using a semi analytical direct differentiation technique the choice of a suitable time integration strategy for the rotation group appears to be critical for the development of an efficient sensitivity analysis three versions of the generalized time integration scheme are considered a residual form a linear form and a geometric form their consistency is discussed and we show that the residual form which is the most direct extension of the generalized algorithm defined in structural dynamics should not be used for problems with large rotations the sensitivity analysis is performed and close connections are highlighted between the structure of the sensitivity equations and of the linearized dynamic equations hence algorithms developed for the original problem can be directly reused for the sensitivities finally a numerical example is analysed in detail copyright 2007 john wiley sons ltd

spherical codes maximal local packing density and the golden ratio the densest local packing dlp problem in d dimensional euclidean space rd involves the placement of n nonoverlapping spheres of unit diameter near an additional fixed unit diameter sphere such that the greatest distance from the center of the fixed sphere to the centers of any of the n surrounding spheres is minimized solutions to the dlp problem are relevant to the realizability of pair correlation functions for packings of nonoverlapping spheres and might prove useful in improving upon the best known upper bounds on the maximum packing fraction of sphere packings in dimensions greater than 3 the optimal spherical code problem in rd involves the placement of the centers of n nonoverlapping spheres of unit diameter onto the surface of a sphere of radius r such that r is minimized it is proved that in any dimension all solutions between unity and the golden ratio to the optimal spherical code problem for n spheres are also solutions to the corresponding dlp problem it follows that for any packing

noneuclidean harmonic analysis analysis on lie groups and their homogeneous spaces has seen a recent flowering thanks to the work of harish chandra helgason selberg and many others the purpose of this paper is to give an elementary discussion of fourier analysis on the noneuclidean upper half plane h that is the spectral resolution of the noneuclidean laplace operator delta this leads to a study of the elementary eigenfunctions of delta such eigenfunctions can be viewed as analogues of the trigonometric functions in euclidean fourier analysis the elementary eigenfunctions of delta on h are legendre conical or spherical functions k bessel functions and eisenstein series the invariance of delta under the special linear group g sl 2 mathbb r of 2 times 2 real matrices of determinant l gives a way of recognizing the spectral measure in the noneuclidean fourier inversion formula once one knows the asymptotics and functional equations of the elementary eigenfunctions of delta in fact this metho

a reduction method for nonlinear structural dynamic analysis abstract a computational algorithm for predicting the nonlinear dynamic response of a structure is presented the nonlinear system of ordinary differential equations resulting from the finite element discretization is highly reduced by means of a rayleigh ritz analysis the basis vectors are chosen to be the current tangent eigenmodes together with some modal derivatives that indicate the way in which the spectrum is changing only a few basis updatings are required during the whole time integration the truncation error introduced at every change of basis is pointed out as the cause for a divergence type behaviour and some means for eliminating it are discussed results for examples involving large displacements are shown and compared to the results obtained by integrating the complete system of equations

new upper bounds on sphere packings i we continue the study of the linear programming bounds for sphere packing introduced by cohn and elkies we use theta series to give another proof of the principal theorem and present some related results and conjectures this article is in the arxiv as arxiv math mg 0110010

a mordell inequality for lattices over maximal orders in this paper we prove an analogue of mordell s inequality for lattices in finite dimensional complex or quaternionic hermitian space that are modules over a maximal order in an imaginary quadratic number field or a totally definite rational quaternion algebra this inequality implies that the 16 dimensional barnes wall lattice has optimal density among all 16 dimensional lattices with hurwitz structures

vibration of geometrically imperfect beam and shell structures abstract the purpose of this paper is to present a general theory for analysis of the effect of initial geometrical imperfections on vibration frequencies of undamped conservatively loaded linear elastic beam and shell structures the theory will be restricted to single mode vibrations with imperfections in the same shape as the vibration modes the mathematical tool is a perturbational procedure developed with the aid of the principle of virtual work the approach is illustrated by applications to beams plates and axisymmetric shell structures the examples show that the vibration frequency of these structures may be significantly raised or lowered due to imperfections

on kissing numbers and spherical codes in high dimensions abstract we prove a lower bound of d 3 2 2 3 d on the kissing number in dimension d this improves the classical lower bound of chabauty shannon and wyner by a linear factor in the dimension we obtain a similar linear factor improvement to the best known lower bound on the maximal size of a spherical code of acute angle in high dimensions

a perturbation method for nonlinear vibrations of imperfect structures application to cylindrical shell vibrations abstract a perturbation method is used to analyse the nonlinear vibration behaviour of imperfect general structures under static preloading the method is based on a perturbation expansion for both the frequency parameter and the dependent variables the effects on the linearized and nonlinear vibrations caused by geometric imperfections a static fundamental state and a nontrivial static state are included in the perturbation procedure the theory is applied in the nonlinear vibration analysis of anisotropic cylindrical shells in the analysis the specified boundary conditions at the shell edges can be satisfied accurately the characteristics of the analysis capability are shown through examples of the vibration behaviour of specific shells results for single mode and coupled mode nonlinear vibrations of shells are presented parametric studies have been performed for a composite shell