fully supersymmetric hierarchies from an energy dependent super hill operator a super hill operator with energy dependent potentials is proposed and the associated integrable hierarchy is explicitly constructed explicitly it is shown that in the general case the resultant hierarchy is a multi hamiltonian system the miura type transformations and modified hierarchies are also presented

abundance based similarity indices and their estimation when there are unseen species in samples a wide variety of similarity indices for comparing two assemblages based on species incidence i e presence absence data have been proposed in the literature these indices are generally based on three simple incidence counts the number of species shared by two assemblages and the number of species unique to each of them we provide a new probabilistic derivation for any incidence based index that is symmetric i e the index is not affected by the identity ordering of the two assemblages and homogeneous i e the index is unchanged if all counts are multiplied by a constant the probabilistic approach is further extended to formulate abundance based indices thus any symmetric and homogeneous incidence index can be easily modified to an abundance type version applying the laplace approximation formulas we propose estimators that adjust for the effect of unseen shared species on our abundance based indices simulation results show that the adjusted estimators significantly reduce the biases of the corresponding unadjusted ones when a substantial fraction of species is missing from samples data on successional vegetation in six tropical forests are used for illustration advantages and disadvantages of some commonly applied indices are briefly discussed

an r matrix interpretation of modified systems abstract the r matrix formalism is applied to the loop algebra based on the central extension of l i v we recover by means of this single construction the modified systems of antonowicz and fordy associated with factorisations of the linear operator of the spectral problem ni 0 i ei d2 dx2 ui 0 together with a modification of ito s equation which was excluded by antonowicz and fordy we also reproduce several results of kupershmidt

free vibration analysis of cylindrical helical springs by the pseudospectral method abstract the pseudospectral method is applied to the free vibration analysis of cylindrical helical springs the displacements and the rotations are approximated by the series expansions of chebyshev polynomials and the governing equations are collocated the number of collocation points is chosen to be less than the number of the expansion terms to handle the boundary condition numerical examples are provided for fixed fixed free free fixed free and hinged hinged boundary conditions the results show good agreement with those of the transfer matrix method and the dynamic stiffness method the formulation of the pseudospectral method is straightforward and shows an exponential rate of convergence with mesh refinement

chebyshev polynomials moment matching and optimal estimation of the unseen we consider the problem of estimating the support size of a discrete distribution whose minimum non zero mass is at least 1 k using independent samples we show that the minimax sample complexity to achieve an additive error of k with probability at least 0 5 is within universal constant factors of k log k log 2 1 which improves the state of the art result k 2 log k due to valiant and valiant the optimal procedure is a linear estimator based on the chebyshev polynomial and its approximation theoretic properties we also study the closely related species problem where the goal is to estimate the number of distinct colors in an urn containing k balls from repeated draws while achieving an additive error proportional to k still requires k log k samples we show that with k samples one can strictly outperform a general support size estimator using interpolating polynomials

a martingale estimating equation for a capture recapture experiment in discrete time we use martingale theory and a method of moments technique to derive a class of estimators for the size of a closed population in a capture recapture experiment in discrete time where the capture probabilities on the successive capture occasions are allowed to be different the same capture probability is assumed to apply to all animals in the population on the same occasion explicit expressions are given for these estimators and their associated standard errors which involve only simple computation an optimal estimator for the population size is found asymptotic results are readily obtained by an application of a martingale central limit theorem two examples are given to compare the results

parameter orthogonality for a family of discrete distributions abstract the standard contagious distributions see douglas 1980 have been used in such varied fields as biology and automobile insurance often to model various physical phenomena as well as provide a good fit to count data when other models are inadequate unfortunately the parameterizations often used when working with these distributions normally lead to extremely high correlations of the maximum likelihood estimators mle s this tends to lead to mathematical complexities and causes difficulty or even errors in their interpretation furthermore numerical difficulties may arise when using numerical procedures to locate the estimates some of these difficulties were discussed by douglas 1980 pp 171 204 205 who suggested that a reparameterization to reduce or even eliminate such correlation is desirable if the mle s are asymptotically uncorrelated the parameterization is orthogonal philpot 1964 derived an orthogonal parameterization for the neyman type a distribution stein zucchini an

theoretical and experimental analysis of the stop band behavior of elastic springs with periodically discontinuous of curvature the advanced design of springs with tailored transmission characteristics is proposed the existence of frequency stop bands in the transmission characteristics is theoretically predicted and experimentally validated the underlying mechanism of generating stop band behavior is the periodic discontinuity of the curvature the theoretical analysis is performed in the framework of the floquet theory for an infinitely long spring experimental results are obtained for the springs consisting of a small number of repeated periodicity cells

parameter estimation for the sichel distribution and its multivariate extension abstract the sichel distribution is a three parameter compound poisson distribution it is a versatile model for highly skewed frequency distributions of observed counts and has proved useful in fields as diverse as mining engineering linguistics ecology industrial psychology and market research we propose a reparameterization of the sichel distribution and give an algorithm which can be implemented on a typical desktop microcomputer for computing the maximum likelihood estimates of the new parameters the reparameterization has a number of advantages over the old in the important two parameter special case of the sichel distribution known as the inverse gaussian poisson the new parameters are the population mean and a shape parameter and their maximum likelihood estimators are asymptotically uncorrelated the reparameterization also lends itself to the convenient multivariate extension presented here this distribution is well suited for modeling correlated count data whose marginal distribution

coupled tension torsion vibration of repetitive beam like structures equivalent continuum stiffness properties derived from the eigenanalysis of a single cell of a planar beam like repetitive structure have previously been employed within well known dynamic theories such as euler bernoulli and timoshenko for flexural vibration suitably modified to predict natural frequencies of vibration here the approach is applied to two structure types that exhibit tension torsion coupling the first is modelled on a nasa deployable structure with a cross section of equilateral triangular form but with asymmetric triangulation on the faces the second is a related more symmetric structure but with pre twist the simplest tension torsion dynamic theory due to di prima is employed and this is extended to more general end conditions this combined periodic structure substitute continuum approach provides excellent agreement with predictions from the finite element method especially for the lower modes of vibration typically agreement is within 1 for the lowest 8 10 natural frequencies for the longer 30 cell structures considered here the majority of these being torsional modes and within 1 for the lowest 4 5 modes for the shorter ten cell structures this level of accuracy is attainable so long as a single wavelength spans 2 3 cells of the repetitive structure

free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements this paper presents a formulation of an approximate spectral element for uniform and tapered rotating euler bernoulli beams the formulation takes into account the varying centrifugal force mass and bending stiffness the dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain where two different interpolating functions for the transverse displacement are used for the element formulation both free vibration and wave propagation analysis is performed using the formulated elements the studies show that the formulated element predicts results that compare well with the solution available in the literature at a fraction of the computational effort in addition for wave propagation analysis the element shows superior convergence

a statistical estimate of the structure of multi extremal problems the solution of ak extremal problem is defined as the set of pairs xi i i 1 k where xt isith local minimum and i is the volume of the set of attraction of this minimum a bayesian estimate ofk and 1 k is constructed

bayesian estimation of the number of species summary this paper is concerned with a method of estimating the number of species present in a population by considering the number of species obtained in a sample a bayesian approach is used and results are based on a zero truncated negative binomial prior distribution for the number of species in the population results for the posterior model are compared with the prior information and guidelines are suggested in the choice of values for the parameters the estimation of the number of species in a population or the number of species unrepresented by a sample is an inferential problem that occurs frequently in the biological sciences much previous work has stemmed from a parametric model due to fisher corbet and williams 1943 where fisher fitted a theoretical distribution to williams data on macrolepidoptera also good 1953 and later good and toulmin 1956 derived a model based on a set of statistical hypotheses concerning the population frequencies of the individual species however the estimation of the total number of species in the population was not the prime concern of any of the work described above when such estimation has been the main aim it has usually been assumed that the species have equal relative abundances as in for example the maximum likelihood approach of driml and ullrich 1967 clearly this assumption will not be appropriate in many practical situations more recently nonequiprobable models have been derived by efron and thisted 1976 and hill 1979 efron and thisted obtained a method of estimating the number of unseen species by an euler transformation and a linear programming approach they took the number of unseen species to be the number of words shakespeare knew but did not use in print hill provided a model that enables an estimate of the number of species in the population to be made by imposing a zero truncated negative binomial prior distribution for the number of species however hill s final analysis is limited to a uniform prior distribution for the number of species it is stated that this gives a sufficiently close approximation in the present paper it is proposed both to derive and to analyse a model based on the zero truncated negative binomial prior distribution for the number of species a similar generalization of hill s model for zipf s law was given by chen 1980 the form of joint prior density for the unknown species relative abundances given by equation 2 1 is derived under the assumptions used by kempton and wedderburn 1978 they explained that when the frequency distribution of the species abundances can be approximated by a continuous distribution then in practice the gamma distribution provides a reasonable fit hence the abundances of species in the population constitute independent observations from a gamma distribution the relative abundances are then beta variates and their joint density function is as shown in 2 1

estimating the population size for capture recapture data with unequal catchability a point estimator and its associated confidence interval for the size of a closed population are proposed under models that incorporate heterogeneity of capture probability real data sets provided in edwards and eberhardt 1967 journal of wildlife management 31 87 96 and carothers 1973 journal of animal ecology 42 125 146 are used to illustrate this method and to compare it with other estimates the performance of the proposed procedure is also investigated by means of monte carlo experiments the method is especially useful when most of the captured individuals are caught once or twice in the sample for which case the jackknife estimator usually does not work well numerical results also show that the proposed confidence interval performs satisfactorily in maintaining the nominal levels

distributions on partitions on obtient une famille de distributions a deux parametres sur des partitions par melange d une variable multinomiale avec une distribution de dirichlet symetrique

dynamic stiffness formulation free vibration and wave motion of helical springs a coil spring can only be treated as a simple massless force element at low frequencies the effects of internal resonances leading to significant dynamic stiffening for an automotive suspension spring this occurs at frequencies as low as about 40 hz this paper presents an efficient method for calculating the dynamic stiffness of a helical coil spring the partial differential equations of motion are used to derive the relation between wavenumber and frequency along with the associated wave shapes by expressing the response in terms of these waves the dynamic stiffness matrix is assembled natural frequencies are obtained from the reduced stiffness matrix allowing for different boundary conditions making use of the wittrick williams algorithm the results of the dynamic stiffness method are compared with those of the transfer matrix method and the finite element method the nature of the wave propagation is also investigated although at low frequencies four wave types propagate above a particular frequency only two propagating waves remain these are composite waves which are excited by both axial and transverse motion for lower values of helix angle an intermediate frequency range exists where six propagating waves can occur

computer assisted analysis of mixtures c a man statistical algorithms summary this paper presents various algorithmic approaches for computing the maximum likelihood estimator of the mixing distribution of a one parameter family of densities and provides a unifying computeroriented concept for the statistical analysis of unobserved heterogeneity i e observations stemming from different subpopulations in a univariate sample the case with unknown number of population subgroups as well as the case with known number of population subgroups with emphasis on the first is considered in the computer package c a man computer assisted mixture analysis it includes an algorithmic menu with choices of the em algorithm the vertex exchange algorithm a combination of both as well as the vertex direction method to ensure reliable convergence a steplength menu is provided for the three latter methods each achieving monotonicity for the direction of choice c a man has the option to work with restricted support size that is the case when the number of components is known a priori in the latter case the em algorithm is used applications of mixture modelling in medical problems are discussed

repetitive beam like structures distributed loading and intermediate support theory is developed for the elastostatic transfer matrix analysis of a repetitive beam like structure subject to point wise distributed loading with and without an intermediate support this complements previous work in which loading is applied at one end only and reacted at the other state vectors are expressed in terms of participation coefficients of the eigen and principal vectors leading to the simplest description of the evolution of nodal displacement and force components as one moves along the structure in terms of powers of the jordan canonical form inaccuracy due to ill conditioning is explained in terms of powers of greater than unity eigenvalues

transfer matrix analysis of the elastostatics of one dimensional repetitive structures transfer matrices are used widely for the dynamic analysis of engineering structures increasingly so for static analysis and are particularly useful in the treatment of repetitive structures for which in general the behaviour of a complete structure can be determined through the analysis of a single repeating cell together with boundary conditions if the structure is not of infinite extent for elastostatic analyses non unity eigenvalues of the transfer matrix of a repeating cell are the rates of decay of selfequilibrated loading as anticipated by saint venant s principle multiple unity eigenvalues pertain to the transmission of load e g tension or bending moment and equivalent homogenized continuum properties such as cross sectional area second moment of area and poisson s ratio can be determined from the associated eigen and principal vectors various disparate results the majority new others drawn from diverse sources are presented these include calculation of principal vectors using the moore penrose inverse bi and symplectic orthogonality and relationship with the reciprocal theorem restrictions on complex unity eigenvalues effect of cell left to right symmetry on both the stiffness and transfer matrices eigenvalue veering in the absence of translational symmetry and limitations on possible jordan canonical forms it is shown that only a repeating unity eigenvalue can lead to a non trivial jordan block form so degenerate decay modes cannot exist the present elastostatic analysis complements langley s langley 1996 proc r soc a 452 1631 1648 transfer matrix analysis of wave motion energetics

a poisson model for the coverage problem with a genomic application summary suppose a population has infinitely many individuals and is partitioned into unknown n disjoint classes the sample coverage of a random sample from the population is the total proportion of the classes observed in the sample this paper uses a nonparametric poisson mixture model to give new understanding and results for inference on the sample coverage the poisson mixture model provides a simplified framework for inferring any general abundance f coverage the sum of the proportions of those classes that contribute exactly k individuals in the sample for some k in with being a set of nonnegative integers a new moment based derivation of the well known turing estimators is presented as an application a gene categorisation problem in genomic research is addressed since turing s approach is a moment based method maximum likelihood estimation and minimum distance estimation are indicated as alternatives for the coverage problem finally it will be shown that any turing estimator is asymptotically fully efficient

wave propagation in continuous periodic structures research contributions from southampton 1964 1995 abstract after brief reference to some early studies by other investigators this paper focuses mainly on methods developed at the university of southampton since 1964 to analyze and predict the free and forced wave motion in continuous periodic engineering structures beginning with receptance methods which have been applied to periodic beams and rib skin structures it continues with a method of direct solution of the wave equation this uses floquet s principle and has been applied to beams and quasi one dimensional periodic plates and cylindrical shells sample curves of the propagation and attenuation constants pertaining to these structures are presented a limited discussion of the transfer matrix then follows after which the method of space harmonics is introduced as the method best suited to the prediction of sound radiated from a vibrating periodic structure reviewed next are some theorems and variational principles relating to periodic structures which have been developed at southampton and which form a basis for finding natural frequencies of finite structures or for computing free and forced wave notion by energy methods this has led to the finite element method in its standard and hierarchical forms being used to study wave motion in genuine two dimensional and three dimensional structures examples of this work are shown the method of phased array receptance functions is then introduced as possibly the easiest way of setting up exact equations for the propagation constants of uniform quasi one dimensional periodic structures a summary is finally presented of the limited and early work performed at southampton on simple disordered periodic structures

a generalization of chao s estimator for covariate information this note generalizes chao s estimator of population size for closed capture recapture studies if covariates are available chao s estimator was developed under unobserved heterogeneity in which case it represents a lower bound of the population size if observed heterogeneity is available in form of covariates we show how this information can be used to reduce the bias of chao s estimator the key element in this development is the understanding and placement of chao s estimator in a truncated poisson likelihood it is shown that a truncated poisson likelihood with log link with all counts truncated besides ones and twos is equivalent to a binomial likelihood with logit link this enables the development of a generalized chao estimator as the estimated expected value of the frequency of zero counts under a truncated all counts truncated except ones and twos poisson regression model if the regression model accounts for the heterogeneity entirely the generalized chao estimator is asymptotically unbiased a simulation study illustrates the potential in gain of bias reduction comparisons of the generalized chao estimator with the homogeneous zero truncated poisson regression approach are supplied as well the method is applied to a surveillance study on the completeness of farm submissions in great britain

small sample estimation of species richness applied to forest communities summary many well known methods are available for estimating the number of species in a forest community however most existing methods result in considerable negative bias in applications where field surveys typically represent only a small fraction of sampled communities this article develops a new method based on sampling with replacement to estimate species richness via the generalized jackknife procedure the proposed estimator yields small bias and reasonably accurate interval estimation even with small samples the performance of the proposed estimator is compared with several typical estimators via simulation study using two complete census datasets from panama and malaysia

free vibration analysis of non cylindrical helices with variable cross section by using mixed fem the objective of the study is to present a mixed finite element fe formulation for the free vibration analysis of non cylindrical helices with variable cross section non cylindrical helix geometry was well approximated through the variable arc lengths and linear variations in curvatures via shape functions the mixed fe model for non cylindrical helices was developed by using the exact cylindrical helix geometry and corresponding field equations the element and consistent mass matrices are attained under these assumptions the element matrix is derived based on the timoshenko beam theory and the effects of rotary inertia are involved into the mass matrix although the formulation is quite simple the generated element is capable to provide highly accurate solutions for the conical barrel and hyperboloidal geometries of non cylindrical helices the results of presented fe model based on an approximated geometry approach are in a good agreement with the other studies in the actual literature some original examples were generated and solved for the literature as well

eigenanalysis and continuum modelling of pre twisted repetitive beam like structures a repetitive pin jointed pre twisted structure is analysed using a state variable transfer matrix technique within a global coordinate system the transfer matrix is periodic but introduction of a local coordinate system rotating with nodal cross sections results in an autonomous transfer matrix for this floquet system eigenanalysis reveals four real unity eigenvalues indicating tension torsion coupling and equivalent continuum properties such as poisson s ratio cross sectional area torsion constant and the tension torsion coupling coefficient are determined a variety of real and complex near diagonal jordan decompositions are possible for the multiple eight complex unity eigenvalues and these are discussed in some detail analysis of the associated principal vectors shows that a bending moment produces curvature in the plane of the moment together with shear deformation in the perpendicular plane but no bending bending coupling the choice of a structure having an equilateral triangular cross section is thought responsible for this unexpected behaviour as the equivalent continuum second moments of area are equal about all cross sectional axes in addition an asymmetric stiffness matrix is obtained for bending moment and shearing force coupling and possible causes are discussed

nonparametric estimation of the probability of discovering a new species abstract a random sample is taken from a population consisting of an unknown number of distinct species a quantity of interest is the probability of discovering a new species when an additional draw from the population is made an estimator of this quantity was introduced by starr 1979 we prove a conjecture of starr s that the estimator is uniformly minimum variance unbiased and give various asymptotic properties of the estimator a nonparametric maximum likelihood estimator that has similar asymptotic properties is introduced a monte carlo study that suggests guidelines for choosing an estimator under various circumstances is given to amplify suppose that if we take a sample of size 1 from a population then the probability of drawing a representative of the ith species is p 1 if n draws are made with replacement the unconditional probability that species i will be observed for the first time on the n 1st draw is given simply as the term p i q n i q i 1 p i from a geometric distributio

an estimator of species overlap using a modified beta binomial model a new species overlap measure is defined as the probability that given a randomly selected species is present in at least one of the two communities it is present in both communities this measure can be thought of as a community analog of the jaccard index for species overlap between two samples standard maximum likelihood methods are used to estimate the parameters of a modified beta binomial distribution this leads directly to estimates of the community overlap measure in an example from decapod communities on coral reefs it is shown that this new estimate of community species overlap is 50 larger than the commonly used jaccard measure of species overlap

estimating the number of classes estimating the unknown number of classes in a population has numerous important applications in a poisson mixture model the problem is reduced to estimating the odds that a class is undetected in a sample the discontinuity of the odds prevents the existence of locally unbiased and informative estimators and restricts confidence intervals to be one sided confidence intervals for the number of classes are also necessarily one sided a sequence of lower bounds to the odds is developed and used to define pseudo maximum likelihood estimators for the number of classes

analytical formulation and evaluation for free vibration of naturally curved and twisted beams abstract an analytical study for free vibration of naturally curved and twisted beams with uniform cross sectional shapes is carried out using spatial curved beam theory based on the washizu s static model in the governing equations of motion of the beams all displacement functions and the generalized warping coordinate are defined at the centroid axis and also the effects of rotary inertia transverse shear deformations and torsion related warping are included in the proposed model explicit analytical expressions are derived for the vibrating mode shapes of a curved bending torsional shearing coupled beam under clamped clamped boundary condition with the help of symbolic computing package mathematica and a process of searching is used to determine the natural frequencies comparisons of the present results with the fem results using beam elements in ansys code show good accuracy in computation and validity of the model further the present model is used for cylindrical helical springs with circular cross section fixed at both ends and the results indicate that the natural frequencies agree well with the theoretical and experimental results available

did shakespeare write a newly discovered poem summary the consistency of the word usage in a previously unknown nine stanza poem attributed to shakespeare with that of the shakespearean canon is examined using a nonparametric empirical bayes model we consider also poems by jonson marlowe and donne as well as four poems definitely attributed to shakespeare on balance the poem is found to fit previous shakespearean usage reasonably well

estimating the number of classes via sample coverage abstract assume that a random sample is drawn from a population with unknown number of classes and possibly unequal class probabilities a nonparametric estimation technique is proposed to estimate the number of classes using the idea of sample coverage which is defined as the sum of the cell probabilities of the observed classes since expected sample coverage can be well estimated we were motivated to find its role in the estimation of the number of classes this work generalizes the result of esty to a nonparametric approach and extends darroch and ratcliff to incorporate the heterogeneity of the class probabilities the coefficient of variation of the class sizes is shown to play an important role in the recommended estimation procedures the performance of the proposed estimators is investigated by means of monte carlo simulations

nonexistence of informative unbiased estimators in singular problems in many nonparametric problems such as density estimation nonparametric regression and so on all the existing informative estimators are biased asymptotic or finite sample there has long been a suspicion that either informative unbiased estimators do not exist for such problems or they must be quite complicated in this paper we clarify the nonexistence of informative unbiased estimators in all singular problems both for fixed sample size and asymptotically this includes most problems with optimal rate of convergence slower than n1 2 we also discuss situations in regular problems where such nonexistences can occur

predicting the conditional probability of discovering a new class consider a population comprising disjoint classes an important problem arising from various fields is prediction of the random conditional probability of discovering a new class the asymptotic normality of the discovery probability is established in a poisson model where the number of individuals from each class is a poisson process with a class specific rate a new derivation is presented for the well known good toulmin predictor as a moment based estimator for the asymptotic limit of the discovery probability the good toulmin predictor is also shown to be a nonparametric empirical bayes estimator for the expectation of the discovery probability given the rates of the poisson processes and an approximation to an unbiased estimator only for the identifiable part of the expectation of the discovery probability in a multinomial model the properties of the moment based estimator are investigated so that confidence and prediction intervals can be constructed the good toulmin predictor and the discovery

a normal limit law for a nonparametric estimator of the coverage of a random sample the coverage of a multinomial random sample is the sum of the probabilities of the observed classes a normal limit law is rigorously proved for good s 1953 coverage estimator the result is valid under very general conditions and all terms except the coverage itself are observable nevertheless the implied confidence intervals are not much wider than those developed under restrictive assumptions such as in the classical occupancy problem the asymptotic variance is somewhat unexpected the proof utilizes a method of holst 1979

free vibration analysis of cylindrical helical springs with noncircular cross sections abstract the free vibration analysis of cylindrical helical springs with noncircular cross sections is carried out by means of an analytical study in the governing equations of motion of a spring all displacement functions and a generalized warping coordinate are defined at the centroidal principal axis the effects of the rotational inertia axial and shear deformations including torsion related warping deformations are also considered in the formulations explicit analytical expressions that give the vibrating mode shapes are derived by rigorous application of the symbolic computing package mathematica and the muller root search method is used to determine the natural frequencies numerical examples are provided for springs with elliptic rectangular and equilateral triangular cross sections and subjected to clamped clamped and clamped free boundary conditions the natural frequencies are presented for a range of geometric parameters in the case of elliptical wires results are presented for the aspect ratio a b ranging from 3 5 to 5 3 the helix pitch angle from 5 to 12 5 the number of active turns n from 6 to 12 and the ratio of cylinder radius to minor axis r 2a ranging from 20 3 to 50 3 validation of the proposed model has been achieved through comparison with a finite element model using three dimensional solid elements and the results available in published literature which in these cases indicates a good correlation

a nonparametric estimator of species overlap summary for two communities species overlap has been defined by smith solow and preston 1996 biometrics52 1472 1477 as the probability that a randomly selected species is present in both communities given that it is present in at least one community species overlap can thus be used to describe the similarity of two communities in contrast with the parametric estimator of smith et al we propose a nonparametric maximum likelihood estimator npmle we prove that the npmle is consistent and asymptotically normally distributed and show that computation of the npmle and its standard error is straightforward we also compare the npmle and the estimator of smith et al for a variety of situations

mathematics of dispersive water waves a commuting hierarchy of dispersive water wave equations makes a three hamiltonian system which belongs to a general class of nonstandard integrable systems whose theory is developed the modified water wave hierarchy is a bi hamiltonian system its modification bifurcates the water wave hierarchy and the hierarchies of the korteweg de vries and the modified korteweg de vries equations as well as the classical miura map are given new representations through various specializations of nonstandard systems

a lie algebraic setting for miura maps related to an energy dependent linear problem we study the affine semi direct product vect s 1 s 1 1 and show how the coadjoint action on its extended dual leads immediately to a generalisation of the miura map and also to the existence of several compatible hamiltonian structures

dynamics of complex truss type space structures a laboratory test was conducted to validate experimentally and to help establish the limits of the mbct approach the results show that the mbct method is a vital alternate technique for ground testing large flexible structures a three dimensional mast type truss structure has been successfully simulated

resampling inference with complex survey data abstract methods for standard errors and confidence intervals for nonlinear statistics such as ratios regression and correlation coefficients have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement in particular the important special case of two sampled clusters per stratum these methods include the customary linearization or taylor method and resampling methods based on the jackknife and balanced repeated replication brr unlike the jackknife or the brr the linearization method is applicable to general sampling designs but it involves a separate variance formula for each nonlinear statistic thereby requiring additional programming efforts both the jackknife and the brr use a single variance formula for all nonlinear statistics but they are more computing intensive the resampling methods developed here retain these features of the jackknife and the brr yet permit extension to more complex designs involving sampling without replace

diversity as a concept and its measurement abstract this paper puts forth the view that diversity is an average property of a community and identifies that property as species rarity an intrinsic diversity ordering of communities is defined and is shown to be equivalent to stochastic ordering also the sensitivity of an index to rare species is developed culminating in a crossing point theorem and a response theory to perturbations diversity decompositions analogous to the analysis of variance are discussed for two way classifications and mixtures the paper concludes with a brief survey of genetic diversity linguistic diversity industrial concentration and income inequality

on saint venant s principle in pin jointed frameworks numerical experiments performed by hoff 50 years ago on the application of saint venant s principle to frameworks are extended and his conclusions qualified guided by these results a general treatment is formulated employing a state variable approach this leads directly to an eigenvalue problem in which the decay rates are the eigenvalues of the cell transfer matrix unity eigenvalues correspond to the transmitting modes of rigid body displacement and the stress resultants of tension bending moment shearing force and twisting moment consideration of the associated eigenvectors and principal vectors gives exact values for the equivalent continuum beam properties of the framework such as equivalent cross sectional area poisson s ratio second moment of area shear coefficient and torsion constant

the torsion extension coupling in pretwisted elastic beams abstract an explicit asymptotic formula is derived for the untwist of a pretwisted elastic beam subjected to homogeneous extension or equivalently for the longitudinal contraction produced by a torsional moment it is based on an asymptotic expansion of the three dimensional equations of linear elasticity the general result consists of two terms one due to lengthwise variation of the warping of the cross sections and another due to local rotations from bending when the elastic center is not on the axis of pretwist the result supports some recent approximate theories for pretwisted elastic beams

a multinomial bayesian approach to the estimation of population and vocabulary size we approach estimation of the size of a population or a vocabulary through a bayesian analysis of the multinomial distribution we view the sample as being generated from such a distribution with an unknown number of cells and unknown cell probabilities and develop a bayesian procedure to estimate the number of cells and the coverage of the sample the prior distribution of the number of cells is arbitrary given that number the cell probabilities are assumed to follow a symmetric dirichlet prior a two stage approach is developed for use when the flattening constant of the latter prior cannot be specified in advance our procedures are applied to samples of butterflies insect species and alleles to the works of shakespeare and joyce and to eldridge s sample of english words

natural frequencies of axial torsional coupled motion in springs and composite bars the natural frequencies corresponding to axial torsional extension twist coupled motion of a helical spring or the corresponding motion induced through material coupling in a composite bar are considered using an equivalent continuum approach closed form solution of the governing differential equations leads either to an exact dynamic stiffness matrix or to a number of exact relationships between the natural frequencies corresponding to coupled and uncoupled motion the latter relationships both guarantee that the wittrick williams root finding algorithm can still be used to converge on any required natural frequency despite any lack of reciprocity arising from differential coupling and for the case of symmetric material coupling coefficients enable their value to be determined precisely from experimental results a number of examples are then given to confirm the accuracy of the proposed theory and to indicate its range of application

vibrations of beams and helices with arbitrarily large uniform curvature an analytical numerical and experimental study of the vibrational modes of beams with constant curvature ranging from small values up to helices with large numbers of turns is presented it is shown that after an initial stage at low curvature in which extensional symmetrical modes hybridize so as to become inextensional all modes show a decrease in frequency with increasing beam curvature the frequency reaches a minimum at a value of the curvature which is a function of mode number and successive minima are separated by steps of in the opening angle of the beam for large values of curvature it is shown that for both symmetric and antisymmetric modes there are two types of vibrational modes with comparable frequencies modes develop into one or the other of these types in a way that is precisely defined but that has the appearance of being random physical descriptions of the processes involved are given and the modes of the two types are described

a two stage probabilistic approach to multiple community similarity indices a traditional approach for assessing similarity among n n 2 communities is to use multiple pairwise comparisons however pairwise similarity indices do not completely characterize multiple community similarity because the information shared by at least three communities is ignored we propose a new and intuitive two stage probabilistic approach which leads to a general framework to simultaneously compare multiple communities based on abundance data the approach is specifically used to extend the commonly used morisita index and ness normalized expected species shared index to the case of n communities for comparing n communities a profile of n 1 indices is proposed to characterize similarity of species composition across communities based on sample abundance data nearly unbiased estimators of the proposed indices and their variances are obtained these generalized ness and morisita indices are applied to comparison of three size classes of plant data seedling saplings and trees within old growth and secondary rain forest plots in costa rica 2008 the international biometric society

on the analysis of accumulation curves summary identifying and counting the total number of biological species observed when plotted against a measure of the effort used to record them gives rise to a species accumulation curve we investigate estimation of the total number of species and other relevant properties of accumulation by elaborating on the multinomial model nakamura and peraza 1998 journal of agricultural biological and environmental statistics 3 17 36 that includes specification of a beta density for recording probabilities we consider a unified description including complete and incomplete aggregated curves a more general scheme for recording and a bayesian framework to allow for inclusion of the biologist s knowledge with regard to typical recording probabilities and the total number of species the beta distribution is used as a prior but recording probabilities are not restrained to be beta distributed the methods yield either closed analytical expressions for inference or relatively simple numerical procedures predictive distributions of future recordings that would eventually lead to an optimal decision theoretical rule for stopping collection effort may be easily calculated a case study regarding species of bats is considered including some guidelines for elicitation of an informative prior

on the number of observed classes from a multinomial distribution calcul du nombre de classes observees afin de determiner le nombre de loci sur les chromosomes de drosophila

bayesian nonparametric estimation of the probability of discovering new species summary we consider the problem of evaluating the probability of discovering a certain number of new species in a new sample of population units conditional on the number of species recorded in a basic sample we use a bayesian nonparametric approach the different species proportions are assumed to be random and the observations from the population exchangeable we provide a bayesian estimator under quadratic loss for the probability of discovering new species which can be compared with well known frequentist estimators the results we obtain are illustrated through a numerical example and an application to a genomic dataset concerning the discovery of new genes by sequencing additional single read sequences of cdna fragments

balanced repeated replications based on mixed orthogonal arrays summary for stratified samples with arbitrary numbers of primary sampling units per stratum one can divide the units in the stratum into two groups and then apply the balanced half samples method to the two groups thus formed the efficiency loss of the grouped balanced half samples variance estimator can be substantial use of a mixed orthogonal array whose numbers of symbols correspond to the numbers of units per stratum gives a set of balanced subsamples unlike that of gupta nigam 1987 the proposed method of analysis gives a consistent variance estimator and bias reduction for nonlinear statistics to further reduce the number of replicates use of nearly orthogonal arrays is considered the balanced half samples method mccarthy 1966 1969 is commonly used for estimating the variance of nonlinear statistics from stratified samples with two primary sampling units per stratum these samples arise naturally if deep stratification is desired as in some large scale surveys the method is extended gurney jewett 1975 to the case of p primary sampling units per stratum for prime p this extension for p 2 is not adopted in common practice since it requires a much larger number of replicates also in many survey designs the numbers of primary sampling units are unequal a common practice is to divide the units in the stratum into two groups and then to apply the balanced half samples method to the two groups thus formed this has gained popularity because the software for obtaining balanced half samples is readily available and the number of replicates required is more economical as shown in 2 the resulting variance estimators can be quite inefficient and their bias based on a conditional analysis can be considerable the conditional analysis also suggests a method of grouping to reduce the bias the degree of grouping depends on the tradeoff between computational economy and statistical efficiency if the efficiency loss from grouping is not justifiable one may draw replicates by using mixed orthogonal arrays with variable numbers of symbols to accommodate the different numbers of units or groups of units in the strata as long as an orthogonal array is used for drawing replicates we call the method balanced repeated replications in 3 we show that the analysis method of gupta nigam 1987 based on mixed orthogonal arrays leads to an inconsistent variance estimator for nonlinear statistics and propose a method that is valid for variance estimation and bias reduction

on the direct solution of wave propagation for repetitive structures abstract the direct method of solving the wave constants for a repetitive structure with given frequency is developed in this paper the analogy between structural mechanics and optimal control theory is applied the dynamic stiffness matrix approach is used to solve for the eigensolutions of wave propagation the weighted adjoint symplectic orthonormality relationship and the eigenvector expansion theorem are also established for this approach the symplectic eigenproblem is derived for skew symmetric matrices a cell triangular decomposition for skew symmetric matrices is introduced to reduce the generalized eigenproblem and the symplectic householder transformation is introduced to cell tri diagonalize the skew symmetric matrix to solve the eigenequation the problem of a wave impinging on the boundary is considered by the eigenvector expansion method which could also be applied to a wave scattering when passing over an abnormal part numerical examples show that resonance will occur for the localized vibration case

propagation of decaying waves in periodic and piecewise periodic structures of finite length abstract a new method is described for the analysis of long and complicated structures which are composed of spatially periodic units or sections of spatially periodic units the response of such a structure to external excitations is treated as a superposition of wave motions with account taken of the effects of wave reflection due to change in the construction pattern along the structure and boundary conditions since damping usually exists in a real structure a wave motion always decays as it propagates along the structure however this can cause numerical difficulties if the structure is rather long because a decaying wave appears as a growing wave in the opposite direction and since propagations in both directions must be accounted for in the analysis computational errors associated with the apparent growing waves also grow and the numerical results become meaningless in the proposed new scheme use is made of wave reflection and transmission matrices making it possible for all computations to proceed in the direction of wave propagation so that the results are always stable numerically furthermore the required computing time is greatly reduced in comparison with that of an all encompassing finite element analysis for the entire structure application of the new method is illustrated by examples

a bayesian analysis of multiple recapture sampling for a closed population summary this paper considers from a bayesian viewpoint inferences about the size of a closed animal population from data obtained by a multiple recapture sampling scheme the method developed enables prior information about the population size and the catch probabilities to be utilized to produce considerable improvements in certain cases on ordinary maximum likelihood methods several ways of expressing such prior information are explored and a practical example of the uses of these ways is given the main result of the paper is an approximation to the posterior distribution of sample size that exhibits the contributions made by the likelihood and the prior ideas the multiple recapture sampling scheme involves taking samples from a population of animals at each stage counting the number of marked animals in the sample marking the previously unmarked animals and returning the sample to the population the literature is reviewed by cormack 1968 and the papers most relevant to our problem are those of chapman 1952 and darroch 1958 in these papers maximum likelihood estimates for the population parameters and variances for these estimates are given our approach differs from previous ones by introducing prior information about the population size and about the propensities of the animals to be captured called catch probabilities by some previous authors the incorporation of these propensities is a feature not shared by many previous approaches darroch 1958 found their introduction into his model does not change the maximum likelihood estimates of the population size our approach will show that strong prior knowledge about the catch probabilities can greatly affect inference about the population size and it is in this respect that the greatest difference from previous approaches lies although it is recognized that models of an open population incorporating death and immigration such as those of jolly 1965 and seber 1965 are more practically realistic we feel that our method which deals only with a closed population is worth investigating as a step towards providing a bayesian treatment of the open population problem

linear dynamics of elastic helical springs asymptotic analysis of wave propagation helical springs serve as vibration isolators in virtually any suspension system a variety of theories to describe the dynamic behaviour of these structural elements which involves interaction of flexural torsion and longitudinal waves can be found in the literature alongside this various approximate methods are employed to determine the eigenfrequencies of vibrations of springs in this paper the validity ranges of alternative theories are assessed by comparison of the location of the dispersion curves this paper also contains a rigorous asymptotic analysis of the exact dispersion equation with two small parameters being employed it allows for the identification of significant regimes of linear wave motion in a helical spring in each of these regimes simple formulae for wavenumbers are obtained by the dominant balance method and their validity ranges are checked against direct numerical solution mode shapes associated with each wavenumber are also analysed

estimating the number of species a review how many kinds are there suppose that a population is partitioned into c classes in many situations interest focuses not on estimation of the relative sizes of the classes but on estimation of c itself for example biologists and ecologists may be interested in estimating the number of species in a population of plants or animals numismatists may be concemed with estimating the number of dies used to produce an ancient coin issue and linguists may be interested in estimating the size of an author s vocabulary in this article we review the problem of statistical estimation of c many approaches have been proposed some purely data analytic and others based in sampling theory in the latter case numerous variations have been considered the population may be finite or infinite if finite samples may be taken with replacement multinomial sampling or without replacement hypergeometric sampling or by bernoulli sampling if infinite sampling may be multinomial or bernoulli or the sample may be th

the efficiency of good s nonparametric coverage estimator the asymptotic efficiency of good s nonparametric coverage estimator is obtained relative to the best estimator derived under the assumption that all classes are equally likely even when that assumption is true good s estimator is quite efficient with an asymptotic relative efficiency of greater than 85 in all cases and greater than 95 if the expected coverage is less than one half

general type token distribution the problem of estimating the number of unique types or dis tinct species in a group occurs in many fields but is not a straightforward one given an arbitrary probabilistic distribution of entries to be sam pled this study shows in exact and approximated forms the conditional probabilistic distribution of unique entries sampled independently given the number of samples the numerical evaluation validates the proposed ap proximation finally we discuss a theory that unifies the related approaches regarding estimation of the number of classes ams 2000 subject classifications primary 60c05 62p99 secondary 62f10

inference for sichel s compound poisson distribution abstract in a long tailed compound poisson distribution introduced by sichel the probabilities can only readily be calculated if one of the parameters has half integer values that is m 1 2 m integer the maximum likelihood estimation of this parameter is compared with an approximate method derived from a grid of half integer values it is found that the approximate method which avoids excessive special computation yields inferences indistinguishable from those based on maximum likelihood and on the score statistic for testing values of thus a major numerical impediment to use of sichel s distribution is removed

an inference procedure for a capture and recapture experiment with time dependent capture probabilities summary estimates for the size of a closed population are given for multiple recapture studies in discrete time the estimates are derived by a method of moments for martingales an estimate and associated standard error of the population size are derived for a homogeneous population when the capture probabilities are permitted to be time dependent in the discrete case corresponding results are obtained for the continuous case as well explicit expressions are given for these estimates and their standard errors only simple computation is involved

work conjugacy between rotation dependent moments and finite rotations in this paper we investigate the work conjugacy between rotation dependent moments and finite rotation measures the methodology adopted consists of writing all the relevant quantities in terms of the rotation vector using expressions that remain exact in the finite rotation range through this procedure we show how i to identify work conjugate rotation dependent moments and rotation measures ii to derive a necessary condition for moment conservativeness and iii to obtain the general form of an isotropic conservative rotation dependent moment several moment and finite rotation definitions that have been used in the past are investigated and in particular it is shown that the various existing definitions for the so called semi tangential moments are distinct in the finite rotation range and that not all of them are conservative the tangent operator symmetry is discussed in the context of finite element analysis of conservative systems with rotational degrees of freedom adopting either an additive or a multiplicative update

factorisation of energy dependent schrodinger operators miura maps and modified systems we consider the energy dependent schrodinger operator mathbb l sum limits i 0 n lambda i varepsilon i partial 2 u i which we have previously shown to be associated with multi hamiltonian structures 2 in this paper we use an unusual form of the lax approach to derive by asingle construction the time evolutions of the eigenfunctions of mathbb l the associated hamiltonian operators and the hamiltonian functionals we then generalise the well known factorisation of standard lax operators to the case of energy dependent operators the simple product of linear factors is replaced by a dependent quadratic form we thus generalise the resulting construction of miura maps and modified equations we show that for some of our systems there exists a sequence ofn such modifications therth modification possessing n r 1 hamiltonian structures