a nonparametric mixture model for cure rate estimation summary nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis in this paper we study a general nonparametric mixture model the proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured the em algorithm the marginal likelihood approach and multiple amputations are employed to estimate parameters of interest in the model this model extends models and improves estimation methods proposed by other researchers it also extends cox s proportional hazards regression model by allowing a proportion of event free patients and investigating covariate effects on that proportion the model and its estimation method are investigated by simulations an application to breast cancer data including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers confirms the conclusions from the parametric model but not those from the existing nonparametric model

hermitian completions of band matrices and applications linear fractional descriptions are given for hermitian completions of partial banded matrices with prescribed cholesky signatures an inertia related notion the results are applied to obtain a linear fractional description for completions of partial triangular matrices with prescribed numbers of singular values 1

minimal quasi separable realizations for the inverse of a quasi separable operator we derive minimal quasi separable i e state space representations for the upper and lower parts of the inverse of an invertible but otherwise general operator t which itself is given by its upper and lower minimal quasi separable representations we show that if the original representation is given in an adequate normal form then the computation of the representation of the inverse can be done in a single downward or upward pass involving only small local computations so called intrinsic factors play an essential role in the derivation we define them and show how they can be extracted the results are given in closed form provided one accepts the computation of a basis for a space and its orthogonal complement as numerically closed qr type factorizations common in array computations the central workhorse is the classical square root algorithm utilized here in a generalized form

a higher order beam finite element for bending and vibration problems abstract the finite element equations for a variationally consistent higher order beam theory are presented for the static and dynamic behavior of rectangular beams the higher order theory correctly accounts for the stress free conditions on the upper and lower surfaces of the beam while retaining the parabolic shear strain distribution the need for a shear correction coefficient is therefore eliminated full integration of the shear stiffness terms is shown to result in the recovery of the kirchhoff constraint for thin beams without introducing spurious locking constraints the accuracy of this formulation is demonstrated by using several numerical examples for the cases of small and large displacements for a hinged hinged beam the linear thickness shear mode frequency can be matched with the timoshenko frequency to yield a shear coefficient of 0 824 matching the bending frequencies between the two theories indicates a shear coefficient for the timoshenko theory that changes with mode number and slenderness ratio the influence of in plane inertia and slenderness ratio on the non linear frequency is examined for beams with a number of different support conditions

invertible completions of band matrices abstract starting with a hermitian band matrix r we fill it in as we try to complete it to an invertible hermitian matrix f often we can make f invertible even though all but one of the maximal hermitian submatrices in the band may be not invertible this paper is a continuation of the author s recent paper on bordered matrices

lossless inverse scattering digital filters and estimation theory methods to construct rational solutions of the lossless inverse scattering lis problem for one port passive digital systems are described the first method is recursive and can be viewed as a generalization of the celebrated schur algorithm the second method is global and leads to a parametrization of what we call fundamental solutions from which all lis solutions may be constructed quite a few classical problems in estimation theory and network theory may be viewed as special cases of the lis problem with each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process

on low complexity approximation of matrices the operation multiplication of a vector by a matrix can be represented by a computational scheme or model that acts on the entries of the vector sequentially the number of intermediate quantities states that are needed in the computations is a measure of the complexity of the model if that complexity is low then not only multiplication but also other operations such as inversion can be carried out efficiently using the model rather than the original matrix in the introductory sections we describe an algorithm to derive a computational model of minimal complexity that gives an exact representation of an arbitrary upper triangular matrix the main result of the paper is an algorithm for computing an approximating matrix with a model of much lower complexity than the original as low as possible for a given tolerance on the approximation error as measure for the tolerance we will use a strong norm which we will call the hankel norm it is a generalization of the hankel norm which is used in the classical model approximation theory for complex analytical functions

finding positive matrices subject to linear restrictions abstract we characterize the existence of a positive definite l l matrix x the entries of which satisfy n nonhomogeneous linear conditions by the existence of a minimum for an associated function v smooth and strictly convex on r n if there exist solutions x 0 then lim x v x and the critical point x 0 of v can be approximated by the conjugate gradients method knowing x 0 provides by a simple analytic formula the unique solution x maximizing the entropy tr x ln x j 1 l j ln j where 1 l are the eigenvalues of x subject to the given restrictions related results are obtained in the semipositive definite case too

robust inference for multivariate survival data multivariate survival data arise when an individual records multiple survival events or when individuals recording single survival events are grouped into clusters in this paper we propose a new method for the analysis of multivariate survival data the technique is a synthesis of the poisson regression formulation for univariate censored survival analysis and the generalized estimating equation approach for obtaining valid variance estimates for generalized linear models in the presence of clustering when the survival data are clustered combining the methods provides not only valid estimates for the variances of regression parameters but also estimates of the dependence between survival times the approach entails specifying parametric models for the marginal hazards and a dependence structure but does not require specification of the joint multivariate survival distribution properties of the methodology are investigated by simulation and through an illustrative example

positive definite hankel matrix completions and hamburger moment completions abstract in this paper we give solutions to hamburger moment problems with missing entries the problem of completing partial positive sequences is considered the main result is a characterization of positive definite completable patterns namely patterns that guarantee the existence of hamburger moment completion of a partial positive definite sequence moreover several patterns which are not positive definite completable are given

shift invariant subspaces factorization and interpolation for matrices i the canonical case abstract this article begins a program of classifying subspaces of block matrices that are invariant under multiplication on the right by the algebra of block upper or lower triangular matrices this gives a unifying point of view to several general kinds of factorization problems including lu qr and cholesky factorization a second application is to some matrix completion problems such as that of filling in the upper triangular entries of a partially defined matrix to make the result of norm less than or equal to 1 included is a linear fractional parametrization of the set of all solutions of this problem

positive semidefinite completions of partial hermitian matrices abstract we classify the ranks of positive semidefinite completions of hermitian band matrices and other partially specified hermitian matrices with chordal graphs and specified main diagonals completing a partially specified matrix means filling in the unspecified entries

the spectral connection matrix for classical orthogonal polynomials of a single parameter abstract in this paper we study the so called connection problem of given a polynomial expressed in the basis of one set of orthogonal polynomials computing the coefficients with respect to a different set of orthogonal polynomials we restrict our current study to the classical real orthogonal polynomials of the hermite laguerre and gegenbauer including legendre families the computational tool for this work is the class of quasiseparable matrices while the relationships between orthogonal polynomials and rank structured matrices such as quasiseparable matrices are very well known in this paper we investigate a more recently considered relationship we prove that while the matrix that implements the desired connection is not itself quasiseparable it is an eigenvector matrix of one that is quasiseparable we suggest to refer to this structured matrix as the spectral connection matrix finally we present a simple algorithm exploiting the computationally favorable properties of quasiseparable matrices to implement the desired change of basis by exploiting the quasiseparable structure this algorithm enjoys an order of magnitude reduction of complexity as compared to the simple method of inverting the connection matrix directly while not the focus of the paper some very preliminary numerical experimentation shows some positive indications that even with this reduction in complexity the accuracy of the resulting change of basis algorithm is comparable to that of inverting the connection matrix directly

a modification of the dewilde van der veen method for inversion of finite structured matrices abstract we study a class of block structured matrices r r ij i j 1 n with a property that the solution of the corresponding system rx y of linear algebraic equations may be performed for o n arithmetic operations in this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms these algorithms are related to those suggested by p m dewilde and a j van der veen time varying systems and computations kluwer academic publishers new york 1998 for a class of finite and infinite matrices with a small hankel rank the algorithms presented here are more transparent and are a modification of the algorithms from the above reference the approach and the proofs are essentially different from those in the above mentioned reference the paper contains also analysis of complexity and results of numerical experiments

spanning tree extensions of the hadamard fischer inequalities abstract all possible graph theoretic generalizations of a certain sort for the hadamard fischer determinantal inequalities are determined these involve ratios of products of principal minors which dominate the determinant furthermore the cases of equality in these inequalities are characterized and equality is possible for every set of values which can occur for the relevant minors this relates recent work of the authors on positive definite completions and determinantal identities when applied to the same collections of principal minors earlier generalizations give poorer more difficult to compute bounds than the present inequalities thus this work extends and in a certain sense completes a series of generalizations of hadamard fischer begun in the 1960s

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

constructive solutions to spectral and inner outer factorizations with respect to the disk we use state space realizations to solve the spectral and inner outer factorization problems with respect to the unit disk formulated for a completely general rational matrix the algorithm is based on orthogonal transformations and standard reliable procedures for solving stein and riccati equations the formulas apply in particular to general descriptor systems or polynomial matrices the main novelty is that we allow for arbitrary rank poles and zeros on the unit circle or at infinity

model validation of multirate systems from time domain experimental data the model validation problem using time domain experimental data is studied for multirate linear fractional uncertain models in this note as a technical tool the caratheodory fejer cf interpolation problem with a nest operator constraint is first investigated this problem is itself of interest mathematically and has potential applications in addressing other problems in control signal processing and circuit theory a necessary and sufficient solvability condition for this interpolation problem is given the validation tests are then presented based on this condition and the lifting technique tractable convex optimization methods can be used to solve the validation problems

the circulant rational covariance extension problem the complete solution the rational covariance extension problem to determine a rational spectral density given a finite number of covariance lags can be seen as a matrix completion problem to construct an infinite dimensional positive definite toeplitz matrix the northwest corner of which is given the circulant rational covariance extension problem considered in this paper is a modification of this problem to partial stochastic realization of periodic stationary process which are better represented on the discrete unit circle rather than on the discrete real line the corresponding matrix completion problem then amounts to completing a finite dimensional toeplitz matrix that is circulant another important motivation for this problem is that it provides a natural approximation involving only computations based on the fast fourier transform for the ordinary rational covariance extension problem potentially leading to an efficient numerical procedure for the latter the circulant rational covariance extension problem is an inverse problem with infinitely many solutions in general each corresponding to a bilateral arma representation of the underlying periodic process in this paper we present a complete smooth parameterization of all solutions and convex optimization procedures for determining them a procedure to determine which solution that best matches additional data in the form of logarithmic moments is also presented

inheritance principles for chordal graphs abstract we prove two results concerning positive completions of partial positive matrices first we give a parametrization of all positive invertible completions of a partial positive matrix having as support a chordal graph along a fixed increasing chordal sequence then a formula for the determinant of each completion is obtained in terms of the associated parameters as an application we obtained a proof of a conjecture of w w barrett c r johnson and l rodman regarding an inheritance principle for chordal graphs

positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming let g v e be a graph in matrix completion theory it is known that the following two conditions are equivalent i g is a chordal graph ii every g partial positive semidefinite matrix has a positive semidefinite matrix completion in this paper we relate these two conditions to constraint nondegeneracy condition in semidefinite programming and prove that they are each equivalent to iii for any g partial positive definite matrix that has a positive semidefinite completion constraint nondegeneracy is satisfied at each of its positive semidefinite matrix completions

direct approach to the band completion problem we study the problem of completion of a matrix with a specified band in such a way that the inverse be a band matrix with the same width for the general block matrix case a new approach to solve this and related problems is proposed the relations with the class of quasiseparable matrices play an important role

two dimensional multivariate parametric models for radar applications part ii maximum entropy extensions for hermitian block matrices in a series of two papers a new class of parametric models for two dimensional multivariate matrix valued space time adaptive processing is introduced this class is based on the maximum entropy extension and or completion of partially specified matrix valued hermitian covariance matrices in both the space and time dimensions this first paper considers the more restricted class of toeplitz hermitian covariance matrices that model stationary clutter if the clutter is stationary only in time then we deal with a toeplitz block matrix whereas clutter that is stationary in time and space is described by a toeplitz block toeplitz matrix we first derive exact expressions for this new class of 2 d models that act as approximations for the unknown true covariance matrix second we propose suboptimal but computationally simpler relaxed 2 d time varying autoregressive models ldquorelaxationsrdquo that directly use the non toeplitz hermitian sample covariance matrix the high efficiency of these parametric models is illustrated by simulation results using true ground clutter covariance matrices provided by the darpa kassper dataset 1 which is a trusted phenomenological airborne radar model and a complementary afrl dataset

numerical solution of the discrete time periodic riccati equation in this paper we present a method for the computation of the periodic nonnegative definite stabilizing solution of the periodic riccati equation this method simultaneously triangularizes by orthogonal equivalences a sequence of matrices associated with a cyclic pencil formulation related to the euler lagrange difference equations in doing so it is possible to extract a basis for the stable deflating subspace of the extended pencil from which the riccati solution is obtained this algorithm is an extension of the standard qz algorithm and retains its attractive features such as quadratic convergence and small relative backward error a method to compute the optimal feedback controller gains for linear discrete time periodic systems is dealt with

blind separation of gaussian sources with general covariance structures bounds and optimal estimation we consider the separation of gaussian sources exhibiting general arbitrary not necessarily stationary covariance structures first assuming a semi blind scenario in which the sources covariance structures are known we derive the maximum likelihood estimate of the separation matrix as well as the induced cramer rao lower bound icrlb on the attainable interference to source ratio isr we then extend our results to the fully blind scenario in which the covariance structures are unknown we show that under a scaling convention the fisher information matrix in this case is block diagonal implying that the same icrlb as in the semi blind scenario applies in this case as well subsequently we demonstrate that the same semi blind optimal performance can be approached asymptotically in the fully blind scenario if the sources are sufficiently ergodic or if multiple snapshots are available

a new rectangular beam theory abstract a new theory for beams of rectangular cross section which includes warping of the cross sections is presented in the present work by satisfying the shear free conditions on the lateral surfaces of the beam a pair of coupled equations of motion are obtained such that no arbitrary shear coefficient is required it is shown that the uncoupled equation for the transverse displacement is the same as the corresponding equation in timoshenko beam theory provided that for the timoshenko equation the shear coefficient is taken to be 5 6 this value lies within the range of values 0 822 0 870 appearing in the literature for the beam of rectangular cross section results for two typical static examples are given for both the new theory and timoshenko beam theory these results are compared with the solutions of the comparable problems in the linear theory of elasticity for the end loaded cantilever beam the new theory predicts the same result for the neutral surface deflection as does the linear theory of elasticity while timoshenko beam theory underestimates the shear correction term by 20 for the uniformly loaded and simply supported case both beam theories provide the same overestimate of the central deflection when compared with the theory of elasticity solution

inner outer factorization and the inversion of locally finite systems of equations abstract we consider the problem of computing the inverse of a large class of infinite systems of linear equations which are described by a finite set of data the class consists of equations in which the linear operator is represented by a discrete time varying dynamical system whose local state space is of finite dimension at each time point k and which reduces to time invariant systems for time points k in this generalization of classical matrix inversion theory inner outer factorizations of operators play the role that qr factorization plays in classical linear algebra numerically they lead to so called square root implementations for which attractive algorithms can be derived which do not require the determination of spurious multiple eigenvalues as would be the case if the problem was converted to a discrete time riccati equation by squaring we give an overview of the theory and the derivation of the main algorithms the theory contains both the standard lti case and the case of a finite set of linear equations as special instances a particularly instance of which is called matrices of low hankel rank recently sometimes called quasi separable matrices however in the general case considered here new phenomena occur which are not observed in these classical cases namely the occurrence of defect spaces we describe these and give an algorithm to compute them as well in all cases the algorithms given are linear in the amount of data

a maximum entropy solution of the covariance extension problem for reciprocal processes stationary reciprocal processes defined on a finite interval of the integer line can be seen as a special class of markov random fields restricted to one dimension nonstationary reciprocal processes have been extensively studied in the past especially by jamison et al the specialization of the nonstationary theory to the stationary case however does not seem to have been pursued in sufficient depth in the literature stationary reciprocal processes and reciprocal stochastic models are potentially useful for describing signals which naturally live in a finite region of the time or space line estimation or identification of these models starting from observed data seems still to be an open problem which can lead to many interesting applications in signal and image processing in this paper we discuss a class of reciprocal processes which is the acausal analog of auto regressive ar processes familiar in control and signal processing we show that maximum likelihood identification of these processes leads to a covariance extension problem for block circulant covariance matrices this generalizes the famous covariance band extension problem for stationary processes on the integer line as in the usual stationary setting on the integer line the covariance extension problem turns out to be a basic conceptual and practical step in solving the identification problem we show that the maximum entropy principle leads to a complete solution of the problem

vibration and buckling of multilayered composite beams according to higher order deformation theories natural frequencies and buckling stresses of laminated composite beams are analyzed by taking into account the complete effects of transverse shear and normal stresses and rotatory inertia by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimensional higher order theory for laminated composite beams subjected to axial stress is derived through hamilton s principle several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported laminated composite beam in order to ensure the accuracy of the present theory convergence properties of the first seven natural frequencies are examined in detail numerical results are compared with those of the published existing theories and fem solutions the modal displacement and stress distributions in the depth direction are obtained and plotted in figures the present global higher order approximate theories can predict the natural frequencies buckling stresses and interlaminar stresses of multilayered composite beams as accurately as three dimensional elasticity solutions

factorization of block matrices abstract an lu type factorization theorem due to elsner and to gohberg and goldberg is generalized to block matrices one form of the general factorization takes the form lmu where l is block lower triangular u is block upper triangular and m is a subpermutation matrix each of whose blocks is diagonal a factorization is also given where the middle term is a block diagonal subpermutation matrix and the factorization is applied to wiener hopf equations the nonuniqueness of the middle term in the factorization is analyzed a special factorization for self adjoint block matrices is also obtained

mihaly matrix completions moments and sums of hermitian squares by mihaly bakonyi and hugo j woerdeman princeton series in applied mathematics princeton university press 2011 xii 518 pp hardback isbn 978 0 691 12889 4

dualistic differential geometry of positive definite matrices and its applications to related problems abstract analysis on the set of positive definite matrices is involved in many engineering problems we develop a differential geometric theory of the set of positive definite matrices by means of a specific class of connections introduced into it consequently various dualistic aspects of the set are elucidated next using the theory we derive new results and interesting geometrical interpretations for matrix approximation positive definite matrix completion and linear matrix inequality problems

a maximum entropy principle in the general framework of the band method abstract a maximum entropy principle is developed in the general framework of the band method known maximum entropy principles appear as corollaries and new ones are derived

mixtures of marginal models summary in this paper we adapt a mixture model originally developed for regression models with independent data for the more general case of correlated outcome data which includes longitudinal data as a special case the estimation is performed by a generalisation of the em algorithm which we call the expectation solution es algorithm in this es algorithm the m step of the em algorithm is replaced by a step requiring the solution of a series of generalised estimating equations the es algorithm a general algorithm for solving generalised estimating equations with incomplete data is then applied to the present problem of mixtures of marginal models in addition to allowing for correlation inherent in correlated outcome data the systematic component of this mixture of marginal models is more flexible than the conventional linear function the methodology is applied in the contexts of normal and poisson response data some theory regarding the es algorithm is presented

order estimation and discrimination between stationary and time varying tvar autoregressive models for a set of t independent observations of the same n variate correlated gaussian process we derive a method of estimating the order of an autoregressive ar model of this process regardless of its stationary or time varying nature we also derive a test to discriminate between stationary ar models of order m ar m and time varying autoregressive models of order m tvar m we demonstrate that within this technique the number t of independent identically distributed data samples required for order estimation and discrimination just exceeds the maximum possible order mmax which in many cases is significantly fewer than the dimension of the problem n

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

a note on extensions of band matrices with maximal and submaximal invertible blocks abstract completions or extensions of band matrices with invertible maximal and submaximal blocks are considered linear fractional descriptions for invertible minimal rank and lu ul decomposable extensions are derived self adjoint and toeplitz cases are included

the negative signature of some hermitian matrices abstract it is proved that the range of the negative signature of the hermitian completions of the partial matrix a b b c d d e is an interval and explicit formulae for the bounds of this interval are obtained as an application the solvability of the problem of lifting with prescribed negative signature of defect is settled

extensions of band matrices with band inverses abstract let r ij be a given set of i j matrices for i j 1 n and i j m where 0 m n 1 necessary and sufficient conditions are established for the existence and uniqueness of an invertible block matrix f ij i j 1 n such that f ij r ij for i j m f admits either a left or right block triangular factorization and f 1 ij 0 for i j m the well known conditions for an invertible block matrix to admit a block triangular factorization emerge for the particular choice m n 1 the special case in which the given r ij are positive definite in an appropriate sense is explored in detail and an inequality which corresponds to burg s maximal entropy inequality in the theory of covariance extension is deduced the block toeplitz case is also studied

on the covariance completion problem under a circulant structure covariance matrices with a circulant structure arise in the context of discrete time periodic processes and their significance stems also partly from the fact that they can be diagonalized via a fourier transformation this note deals with the problem of completion of partially specified circulant covariance matrices the particular completion that has maximal determinant i e the so called maximum entropy completion was considered in carli where it was shown that if a single band is unspecified and to be completed the algebraic restriction that enforces the circulant structure is automatically satisfied and that the inverse of the maximizer has a band of zero values that corresponds to the unspecified band in the data i e it has the dempster property the purpose of the present note is to develop an independent proof of this result which in fact extends naturally to any number of missing bands as well as arbitrary missing elements more specifically we show that this general fact is a direct consequence of the invariance of the determinant under the group of transformations that leave circulant matrices invariant a description of the complete set of all positive extensions of partially specified circulant matrices is also given and certain connections between such sets and the factorization of certain polynomials in many variables facilitated by the circulant structure is highlighted

linearly constrained positive definite completions abstract a partial matrix is a rectangular array consisting of specified entries which are fixed elements of the complex numbers c and unspecified entries which are free variables over c given a partial hermitian matrix a z in which z is the vector of unspecified entries of a a fixed matrix b and a fixed vector c the optimal solution of the problem maximize det a z subject to a z positive definite bz c is unique provided the problem is feasible and has a simple characterization this class of problems includes the case in which a z is constrained to be toeplitz

unitary rank structured matrices in this paper we describe how one can represent a unitary rank structured matrix in an efficient way as a product of elementary unitary or givens transformations we also provide some basic operations for manipulating the representation such as the transition to zero creating form the transition to a unitary givens weight representation as well as an internal pull through process of the two branches of the representation finally we characterize how to determine the shift correction term to the rank structure and we provide some applications to this result

strictly contractive and positive completions for block matrices abstract this paper deals with the following two problems of completion of block matrices 1 let a ij i j q be given matrices find additional matrices a ij such that the block matrix a a ij n i 1 m j 1 has norm less than one 2 let b ij j i q be given matrices find additional b ij such that the completion b b ij n i j 1 is positive definite the analysis is based on a study of certain linear fractional maps this approach leads to an explicit description of all solutions by linear fractional maps of which the coefficients are given directly in terms of the given data the maximum entropy principle appears as a corollary of a general formula for the determinant of a completion special attention is paid to the toeplitz case

a semiparametric marginal mixture cure model for clustered survival data we consider a marginal model for the regression analysis of clustered failure time data with a cure fraction we propose to use novel generalized estimating equations in an expectation maximization algorithm to estimate regression parameters in a semiparametric proportional hazards mixture cure model the dependence among the cure statuses and among the survival times of uncured patients within clusters are modeled by working correlation matrices in the estimating equations we use a bootstrap method to obtain the variances of the estimates we report a simulation study to demonstrate a substantial efficiency gain of the proposed method over an existing marginal method finally we apply the model and the proposed method to a set of data from a multi institutional study of tonsil cancer patients treated with a radiation therapy

vibration and buckling of deep beam columns on two parameter elastic foundations natural frequencies and buckling stresses of a deep beam column on two parameter elastic foundations are analyzed by taking into account the effect of shear deformation depth change the transverse displacement w can vary in the depth direction of beam columns and rotatory inertia by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimensional higher order theory for thin rectangular beam columns subjected to axial stress is derived through hamilton s principle several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported deep elastic beam column in order to assure the accuracy of the present theory convergence properties of the minimum natural frequency and the buckling stress are examined in detail it is noted that the present approximate theories can predict the natural frequencies and buckling stress of deep beam columns on elastic foundations accurately compared with the timoshenko beam theory and the classical beam theory

maximum entropy kernels for system identification bayesian nonparametric approaches have been recently introduced in system identification scenario where the impulse response is modeled as the realization of a zero mean gaussian process whose covariance kernel has to be estimated from data in this scheme quality of the estimates crucially depends on the parametrization of the covariance of the gaussian process a family of kernels that have been shown to be particularly effective in the system identification framework is the family of diagonal correlated dc kernels maximum entropy properties of a related family of kernels the tuned correlated tc kernels have been recently pointed out in the literature in this technical note we show that maximum entropy properties indeed extend to the whole family of dc kernels the maximum entropy interpretation can be exploited in conjunction with results on matrix completion problems in the graphical models literature to shed light on the structure of the dc kernel in particular we prove that the dc kernel admits a closed form factorization inverse and determinant these results can be exploited both to improve the numerical stability and to reduce the computational complexity associated with the computation of the dc estimator

thermo mechanical vibration of fgm sandwich beam under variable elastic foundations using differential quadrature method thermo mechanical vibration analysis of functionally graded fg beams and functionally graded sandwich fgsw beams are presented the functionally graded material fgm beams are considered to be resting on variable i winkler foundation and ii two parameter elastic foundation the material properties of these beams are assumed to be varying in the thickness direction the governing differential equations for beam vibration are being solved using the modified differential quadrature method mdqm the applied kinematic boundary conditions are implemented using the modified weighting coefficient matrix mwcm the weighting coefficients are generated from the chebyshev basis function present results for the vibration of isotropic beam with variable winkler foundation are in good agreement with those reported in the literature parametric study on the vibration response of fg beams and fgsw beams are being investigated these parameters include i temperature distributions ii power law index iii variable winkler foundation modulus iv two parameter elastic foundation modulus and v normalized core thickness of fgsw beams

schur analysis of some completion problems abstract the complete schur analysis for contractive block matrices is given together with its connections with positiveness these are used for reobtaining some results on completion problems sometimes in a more general setting these completion problems include positive completions contractive and isometric completions and the realizability of upper triangular contractions

a bivariate cure mixture approach for modeling familial association in diseases summary for modeling correlation in familial diseases with variable ages at onset we propose a bivariate model that incorporates two types of pairwise association one between the lifetime risk or the overall susceptibility of two individuals and one between the ages at onset between two susceptible individuals for estimation we consider a two stage estimation procedure similar to that of shih 1998 biometrics 54 1115 1128 we evaluate the properties of the estimators through simulations and compare the performance with that from a bivariate survival model that allows correlation between ages at onset only we apply the methodology to breast cancer using the kinship data from the washington ashkenazi study we also discuss potential applications of the proposed method in the area of cure modeling

the intertwining lifting theorem for ordered groups abstract sz nagy s dilation theorem for a contraction on a hilbert space has been extended by mlak to the case of a contraction semigroup whose indices are the positive elements of a totally ordered discrete group we generalize to this case the intertwining lifting theorem of sz nagy and foias some previous interpolation results on ordered groups are obtained as consequences

free vibration and stability of thin elastic beams subjected to axial forces abstract natural frequencies and buckling loads of a simply supported beam with small length to depth ratio and sufficiently thin rectangular cross sections subjected to initial axial tensile and or compressive forces are analyzed by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimentional higher order beam theory for thin rectangular beams is derived through hamilton s principle several sets of truncated approximate theories which can take into account the effects of both shear deformations with depth changes and rotary inertia are applied to solve the eigenvalue problem of a thin elastic beam the navier solution procedure is used to satisfy the boundary conditions of a simply supported thin rectangular beam in order to assure the accuracy of the present theory convergence properties of the minimum natural frequency and the buckling load for the axial and bending problems of thin beams are examined in detail it is noticed that the present approximate theories can predict the natural frequencies and buckling loads of thin beams with small length to depth ratio more accurately than other refined higher order theories and the classical beam theory

spn completable graphs abstract an spn matrix is a matrix which is the sum of a real positive semidefinite matrix and a symmetric nonnegative one we solve the spn completion problem we show that the spn completable graphs are the graphs in which every odd cycle induces a complete subgraph

computation of general inner outer and spectral factorizations in this paper we solve two problems in linear systems theory the computation of the inner outer and spectral factorizations of a continuous time system considered in the most general setting we show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic riccati equation of order usually much smaller than the mcmillan degree of the transfer function matrix of the system the proposed procedures are completely general being applicable for a polynomial proper improper system whose transfer function matrix could be rank deficient and could have poles zeros on the imaginary axis or at infinity as an application we discuss the extension to the case of rational matrices of the complete orthogonal decomposition of a constant matrix numerical refinements and examples illustrating the proposed approach are discussed in detail

block matrices with l block banded inverse inversion algorithms block banded matrices generalize banded matrices we study the properties of positive definite full matrices p whose inverses a are l block banded we show that for such matrices the blocks in the l block band of p completely determine p namely all blocks of p outside its l block band are computed from the blocks in the l block band of p we derive fast inversion algorithms for p and its inverse a that when compared to direct inversion are faster by two orders of magnitude of the linear dimension of the constituent blocks we apply these inversion algorithms to successfully develop fast approximations to kalman bucy filters in applications with high dimensional states where the direct inversion of the covariance matrix is computationally unfeasible

the maximum distance problem and band sequences abstract we solve the following problem for 1 j k n and j k m let a jk be a given complex number with a kj jk we wish to find linearly independent vectors x 1 x n such that x k x j a jk for j k m and such that the distance from x k to the linear span of x 1 x k 1 is maximal for 2 k n we construct and characterize all such sequences of vectors our solution leads naturally to the class of m band sequences of vectors in an inner product space we study these sequences and characterize their equivalence classes under unitary transformations