analytic formulas for the regulator of a number field letr rk andw wk be the regulator and the number of roots of unity in the number fieldk we determine allk for whichr w 1 8 there are nine such fields sincew 2 we have allk withr 1 4 in particular we find the first three minima ofr over allk there are three main ingredients to the proof i a new analytic formula theorem a below ii a refinement of remak s geometric approach iii a refinement of zimmert s analytic method

lattice coding and decoding achieve the optimal diversity multiplexing tradeoff of mimo channels this paper considers communication over coherent multiple input multiple output mimo flat fading channels where the channel is only known at the receiver for this setting we introduce the class of lattice space time last codes we show that these codes achieve the optimal diversity multiplexing tradeoff defined by zheng and tse under generalized minimum euclidean distance lattice decoding our scheme is based on a generalization of erez and zamir mod lambda scheme to the mimo case in our construction the scalar scaling of erez zamir and costa gaussian dirty paper schemes is replaced by the minimum mean square error generalized decision feedback equalizer mmse gdfe this result settles the open problem posed by zheng and tse on the construction of explicit coding and decoding schemes that achieve the optimal diversity multiplexing tradeoff moreover our results shed more light on the structure of optimal coding decoding techniques in delay limited mimo channels and hence open the door for novel approaches for space time code constructions in particular 1 we show that mmse gdfe plays a fundamental role in approaching the limits of delay limited mimo channels in the high signal to noise ratio snr regime unlike the additive white gaussian noise awgn channel case and 2 our random coding arguments represent a major departure from traditional space time code designs based on the rank and or mutual information design criteria

capacity of compound mimo gaussian channels with additive uncertainty this paper considers reliable communications over a multiple input multiple output mimo gaussian channel where the channel matrix is within a bounded channel uncertainty region around a nominal channel matrix i e an instance of the compound mimo gaussian channel we study the optimal transmit covariance matrix design to achieve the capacity of compound mimo gaussian channels where the channel uncertainty region is characterized by the spectral norm this design problem is a challenging nonconvex optimization problem however in this paper we reveal that this problem has a hidden convexity property which can be exploited to map the problem into a convex optimization problem we first prove that the optimal transmit design is to diagonalize the nominal channel and then show that the duality gap between the capacity of the compound mimo gaussian channel and the min max channel capacity is zero which proves and generalizes a conjecture of loyka and charalambous the key tools for showing these results are a new matrix determinant inequality and some unitarily invariant properties

working correlation structure misspecification estimation and covariate design implications for generalised estimating equations performance the method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations we investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods the asymptotic relative efficiency depends on three features of the analysis namely i the discrepancy between the working correlation structure and the unobservable true correlation structure ii the method by which the correlation parameters are estimated and iii the design by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes analytical and numerical studies of realistic data analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a gaussian estimation pseudolikelihood procedure is used with an ar 1 structure

improving power in small sample longitudinal studies when using generalized estimating equations generalized estimating equations gee are often used for the marginal analysis of longitudinal data although much work has been performed to improve the validity of gee for the analysis of data arising from small sample studies little attention has been given to power in such settings therefore we propose a valid gee approach to improve power in small sample longitudinal study settings in which the temporal spacing of outcomes is the same for each subject specifically we use a modified empirical sandwich covariance matrix estimator within correlation structure selection criteria and test statistics use of this estimator can improve the accuracy of selection criteria and increase the degrees of freedom to be used for inference the resulting impacts on power are demonstrated via a simulation study and application example copyright 2016 john wiley sons ltd

bivariate categorical data analysis using normal linear conditional multinomial probability model bivariate multinomial data such as the left and right eyes retinopathy status data are analyzed either by using a joint bivariate probability model or by exploiting certain odds ratio based association models however the joint bivariate probability model yields marginal probabilities which are complicated functions of marginal and association parameters for both variables and the odds ratio based association model treats the odds ratios involved in the joint probabilities as working parameters which are consequently estimated through certain arbitrary working regression models also this later odds ratio based model does not provide any easy interpretations of the correlations between two categorical variables on the basis of pre specified marginal probabilities in this paper we develop a bivariate normal type linear conditional multinomial probability model to understand the correlations between two categorical variables the parameters involved in the model are consistently estimated using the optimal likelihood and generalized quasi likelihood approaches the proposed model and the inferences are illustrated through an intensive simulation study as well as an analysis of the well known wisconsin diabetic retinopathy status data copyright 2014 john wiley sons ltd

accurate approximation of green s functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves a robust and computationally expedient methodology is presented for accurate closed form approximation of the green s functions used in the mixed potential integral equation statement of the electromagnetic boundary value problem in planar stratified media the proposed methodology is based on the fitting of the spectrum of the green s function after the extraction of the quasistatic part making use of rational functions the effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit the resulting closed form approximation is in terms of both spherical and cylindrical waves thus high accuracy is obtained in the approximation of the green s function irrespective of the distance of the observation point from the source the methodology is validated through its application to the approximation of the green s function for a multi layered planar dielectric stack

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

achieving awgn channel capacity with lattice gaussian coding we propose a new coding scheme using only one lattice that achieves the 1 2 log 1 snr capacity of the additive white gaussian noise awgn channel with lattice decoding which is provable for signal to noise ratio snr e at present the scheme applies a discrete gaussian distribution over an awgn good lattice but otherwise does not require a shaping lattice or dither thus it significantly simplifies the default lattice coding scheme of erez and zamir which involves a quantization good lattice as well as an awgn good lattice using the flatness factor we show that the error probability of the proposed scheme under minimum mean square error lattice decoding is almost the same as that of erez and zamir for any rate up to the awgn channel capacity we introduce the notion of good constellations which carry almost the same mutual information as that of continuous gaussian inputs we also address the implementation of gaussian shaping for the proposed lattice gaussian coding scheme

an improved discrete complex image method based on a special sampling path a special sampling path is proposed to improve the accuracy of the discrete complex image method dcim in evaluating the lateral wave different from all the previous dcim implementations the proposed sampling path goes through the branch point directly which helps to evaluate its contribution to the lateral wave more accurately in this communication different sampling paths of dcim have been implemented and compared it is found that in the situations where the lateral wave dominates the far field region dcim with the new path gives more accurate and stable results

awgn goodness is enough capacity achieving lattice codes based on dithered probabilistic shaping in this paper we show that any sequence of infinite lattice constellations which is good for the unconstrained gaussian channel can be shaped into a capacity achieving sequence of codes for the power constrained gaussian channel under lattice decoding and non uniform signaling unlike previous results in the literature our scheme holds with no extra condition on the lattices e g quantization goodness or vanishing flatness factor thus establishing a direct implication between awgn goodness in the sense of poltyrev and capacity achieving codes our analysis uses properties of the discrete gaussian distribution in order to obtain precise bounds on the probability of error and achievable rates in particular we obtain a simple characterization of the finite blocklength behavior of the scheme showing that it approaches the optimal dispersion coefficient for high signal to noise ratio we further show that for low signal to noise ratio the discrete gaussian over centered lattice constellations cannot achieve capacity and thus a shift or dither is essentially necessary

estimated estimating equations semiparametric inference for clustered and longitudinal data summary we introduce a flexible marginal modelling approach for statistical inference for clustered and longitudinal data under minimal assumptions this estimated estimating equations approach is semiparametric and the proposed models are fitted by quasi likelihood regression where the unknown marginal means are a function of the fixed effects linear predictor with unknown smooth link and variance covariance is an unknown smooth function of the marginal means we propose to estimate the nonparametric link and variance covariance functions via smoothing methods whereas the regression parameters are obtained via the estimated estimating equations these are score equations that contain nonparametric function estimates the proposed estimated estimating equations approach is motivated by its flexibility and easy implementation moreover if data follow a generalized linear mixed model with either a specified or an unspecified distribution of random effects and link function the model proposed emerges as the corresponding marginal population average version and can be used to obtain inference for the fixed effects in the underlying generalized linear mixed model without the need to specify any other components of this generalized linear mixed model among marginal models the estimated estimating equations approach provides a flexible alternative to modelling with generalized estimating equations applications of estimated estimating equations include diagnostics and link selection the asymptotic distribution of the proposed estimators for the model parameters is derived enabling statistical inference practical illustrations include poisson modelling of repeated epileptic seizure counts and simulations for clustered binomial responses

a comparison of bias corrected empirical covariance estimators with generalized estimating equations in small sample longitudinal study settings data arising from longitudinal studies are commonly analyzed with generalized estimating equations previous literature has shown that liberal inference may result from the use of the empirical sandwich covariance matrix estimator when the number of subjects is small therefore two different approaches have been used to improve the validity of inference first many different small sample corrections to the empirical estimator have been offered in order to reduce bias in resulting standard error estimates second critical values can be obtained from a t distribution or an f distribution with approximated degrees of freedom although limited studies on the comparison of these small sample corrections and degrees of freedom have been published there is a need for a comprehensive study of currently existing methods in a wider range of scenarios therefore in this manuscript we conduct such a simulation study finding two methods to attain nominal type i error rates more consistently than other methods in a variety of settings first a recently proposed method by westgate and burchett 2016 statistics in medicine 35 3733 3744 that specifies both a covariance estimator and degrees of freedom and second an average of two popular corrections developed by mancl and derouen 2001 biometrics 57 126 134 and kauermann and carroll 2001 journal of the american statistical association 96 1387 1396 with degrees of freedom equaling the number of subjects minus the number of parameters in the marginal model

on the densest mimo lattices from cyclic division algebras it is shown why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed nonvanishing minimum determinant using results from class field theory a lower bound to the minimum discriminant of a maximal order with a given center and index the number of tx rx antennas is derived also numerous examples of division algebras achieving the bound are given for example a matrix lattice with quadrature amplitude modulation qam coefficients that has 2 5 times as many codewords as the celebrated golden code of the same minimum determinant is constructed also a general algorithm due to ivanyos and ronyai for finding maximal orders within a cyclic division algebra is described and enhancements to this algorithm are discussed also some general methods for finding cyclic division algebras of a prescribed index achieving the lower bound are proposed

on the use of cavity modes as basis functions in the full wave analysis of printed antennas magnetic wall cavity mwc modes are often employed as basis functions in the method of moments mom full wave analysis of printed antennas especially in its spectral domain version where the use of entire domain basis functions is particularly convenient but in some cases the te solenoidal modes are not included here we investigate on the effect of this exclusion explaining the nature of the te tm coupling presenting criteria to determine the necessary number of modes and giving numerical results for annular patches especially relevant in this context

green s functions in lossy layered media integration along the imaginary axis and asymptotic behavior this paper presents an efficient technique for evaluating green s functions associated to layered media when formulated as sommerfeld integrals in the space domain the key step in the formulation is that sommerfeld integrals are computed choosing a suitable integration path which is closed through the imaginary axis of the complex spectral plane it is shown that with this original choice of the integration contour the numerical effort usually involved in the evaluation of sommerfeld integrals can be greatly reduced specially when large source observer distances are involved one asset of this technique is that it can be easily incorporated into integral equation based cad packages for the efficient analysis of complex printed microwave circuit and antennas in addition the theoretical developments needed to set up the numerical algorithm throw a new light on the asymptotic behavior of the layered media green s functions for large source observer distances

inference for clustered data using the independence loglikelihood we use the properties of independence estimating equations to adjust the independence loglikelihood function in the presence of clustering the proposed adjustment relies on the robust sandwich estimator of the parameter covariance matrix which is easily calculated the methodology competes favourably with established techniques based on independence estimating equations we provide some insight as to why this is so the adjustment is applied to examples relating to the modelling of wind speed in europe and annual maximum temperatures in the u k

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

a note on implementation of decaying product correlation structures for quasi least squares this note implements an unstructured decaying product matrix via the quasi least squares approach for estimation of the correlation parameters in the framework of generalized estimating equations the structure we consider is fairly general without requiring the large number of parameters that are involved in a fully unstructured matrix it is straightforward to show that the quasi least squares estimators of the correlation parameters yield feasible values for the unstructured decaying product structure furthermore subject to conditions that are easily checked the quasi least squares estimators are valid for longitudinal bernoulli data we demonstrate implementation of the structure in a longitudinal clinical trial with both a continuous and binary outcome variable

a novel approach for the efficient computation of 1 d and 2 d summations a novel computational method is proposed to evaluate 1 d and 2 d summations and integrals which are relatively difficult to compute numerically the method is based on applying a subspace algorithm to the samples of partial sums and approximating them in terms of complex exponentials for a convergent summation the residue of the exponential term with zero complex pole of this approximation corresponds to the result of the summation since the procedure requires the evaluation of relatively small number of terms the computation time for the evaluation of the summation is reduced significantly in addition by using the proposed method very accurate and convergent results are obtained for the summations which are not even absolutely convergent the efficiency and accuracy of the method are verified by evaluating some challenging 1 d and 2 d summations and integrals

almost universal codes for mimo wiretap channels despite several works on secrecy coding for fading and mimo wiretap channels from an error probability perspective the construction of information theoretically secure codes over such channels remains an open problem in this paper we consider a fading wiretap channel model where the transmitter has only partial statistical channel state information our channel model includes static channels i i d block fading channels and ergodic stationary fading with fast decay of large deviations for the eavesdropper s channel we extend the flatness factor criterion from the gaussian wiretap channel to fading and mimo wiretap channels and establish a simple design criterion where the normalized product distance minimum determinant of the lattice and its dual should be maximized simultaneously moreover we propose concrete lattice codes satisfying this design criterion which are built from algebraic number fields with constant root discriminant in the single antenna case and from division algebras centered at such number fields in the multiple antenna case the proposed lattice codes achieve strong secrecy and semantic security for all rates r where c b and c e are bob and eve s channel capacities respectively and kappa is an explicit constant gap furthermore these codes are almost universal in the sense that a fixed code is good for secrecy for a wide range of fading models finally we consider a compound wiretap model with a more restricted uncertainty set and show that rates r are achievable where bar c b is a lower bound for bob s capacity and bar c e is an upper bound for eve s capacity for all the channels in the set

marginal analysis of incomplete longitudinal binary data a cautionary note on locf imputation in recent years there has been considerable research devoted to the development of methods for the analysis of incomplete data in longitudinal studies despite these advances the methods used in practice have changed relatively little particularly in the reporting of pharmaceutical trials in this setting perhaps the most widely adopted strategy for dealing with incomplete longitudinal data is imputation by the last observation carried forward locf approach in which values for missing responses are imputed using observations from the most recently completed assessment we examine the asymptotic and empirical bias the empirical type i error rate and the empirical coverage probability associated with estimators and tests of treatment effect based on the locf imputation strategy we consider a setting involving longitudinal binary data with longitudinal analyses based on generalized estimating equations and an analysis based simply on the response at the end of the scheduled follow up we find that for both of these approaches imputation by locf can lead to substantial biases in estimators of treatment effects the type i error rates of associated tests can be greatly inflated and the coverage probability can be far from the nominal level alternative analyses based on all available data lead to estimators with comparatively small bias and inverse probability weighted analyses yield consistent estimators subject to correct specification of the missing data process we illustrate the differences between various methods of dealing with drop outs using data from a study of smoking behavior

on the accuracy of efficiency of estimating equation approach summary liang and zeger 1986 biometrika73 13 22 introduced a generalized estimating equation gee approach based on a working correlation matrix to obtain efficient estimators of regression parameters in the class of generalized linear models for repeated measures data as demonstrated by crowder 1995 biometrika82 407 410 because of uncertainty of the definition of the working correlation matrix the liang zeger approach may in some cases lead to a complete breakdown of the estimation of the regression parameters after taking this comment of crowder into account recently sutradhar and das 1999 biometrika86 459 465 examined the loss of efficiency of the regression estimators due to misspecification of the correlation structures but their study was confined to the regression estimation with cluster level covariates as in the original paper of liang and zeger in this paper we study this efficiency loss problem for the generalized regression models with within cluster covariates by utilizing the approach of sutsadhar and das 1999

closed form green s function representations in cylindrically stratified media for method of moments applications closed form green s function cfgf representations for cylindrically stratified media which can be used as the kernel of an electric field integral equation are developed the developed cfgf representations can safely be used in a method of moments solution procedure as they are valid for almost all possible source and field points that lie on the same radial distance from the axis of the cylinder such as the air dielectric and dielectric dielectric interfaces including the axial line rho rho and phi phi which has not been available before in the course of obtaining these expressions the conventional spectral domain green s function representations are rewritten in a different form so that i we can attack the axial line problem and ii the method can handle electrically large cylinders available acceleration techniques that exist in the literature are implemented to perform the summation over the cylindrical eigenmodes efficiently lastly the resulting expressions are transformed to the spatial domain using the discrete complex image method with the help of the generalized pencil of function method where a modified two level approach is used numerical results are presented in the form of mutual coupling between two current modes to assess the accuracy of the final spatial domain cfgf representations

a hybrid time domain technique that combines the finite element finite difference and method of moment techniques to solve complex electromagnetic problems this paper describes a hybrid technique directly operating in time domain that combines the finite element time domain fetd the finite difference time domain fdtd and the integral equation based method of moments in the time domain momtd techniques to analyze complex electromagnetic problems involving thin wire antennas radiating in the presence of inhomogeneous dielectric bodies whose shape can be arbitrary the method brings together the ability of the fdtd scheme to deal with arbitrary material properties the versatility of the fetd to accurately model curved geometries and that of the mom to analyze thin wire structures working in the time domain provides wide band information from a single execution of the marching on in time procedure and simplifies the interfacing of the fe and mom methods with the fdtd an approach specifically designed for time domain analysis numerical results that validate the hybrid method and show its capabilities are presented in the paper

miscellanea on the efficiency of regression estimators in generalised linear models for longitudinal data summary liang zeger 1986 introduced a generalised estimating equations approach based on a working correlation matrix to obtain consistent and efficient estimators of regression parameters in the class of generalised linear models for repeated measures data as demonstrated by crowder 1995 because of the uncertainty of definition of the working correlation matrix the liang zeger approach may in some cases lead to a complete breakdown of the estimation of the regression parameters in this paper we show that even though the liang zeger approach in many situations yields consistent estimators for the regression parameters these estimators are usually inefficient as compared to the regression estimators obtained by using the independence estimating equations approach

efficiency of generalized estimating equations for binary responses summary using standard correlation bounds we show that in generalized estimation equations gees the so called working correlation matrix r for analysing binary data cannot in general be the true correlation matrix of the data methods for estimating the correlation param eter in current gee software for binary responses disregard these bounds to show that the gee applied on binary data has high efficiency we use a multivariate binary model so that the covariance matrix from estimating equation theory can be compared with the inverse fisher information matrix but r should be viewed as the weight matrix and it should not be confused with the correlation matrix of the binary responses we also do a comparison with more general weighted estimating equations by using a matrix cauchy schwarz inequality our analysis leads to simple rules for the choice of in an exchangeable or autoregressive ar 1 weight matrix r based on the strength of dependence between the binary variables an example is given to illustrate the assessment of dependence and choice of

a study on universal codes with finite block lengths based on random codes and typical set decoding an alternative proof of root and varaiya s compound channel coding theorem for linear gaussian channels is presented the performance limit of codes with finite block length under a compound channel is studied through error bounds and simulation although the theorem promises uniform convergence of the probability of error as the block length approaches infinity with short block lengths the performance can differ considerably for individual channels simulation results show that universal performance can be a practical goal as the block lengths become large

utilization of a unitary transform for efficient computation in the matrix pencil method to find the direction of arrival in this study we use the matrix pencil mp method to compute the direction of arrival doa of the signals using a very efficient computational procedure in which the complexity of the computation can be reduced significantly by using a unitary matrix transformation this method applies the technique directly to the data without forming a covariance matrix simulation results show that the variance of the estimate approaches to the cramer rao lower bound using real computations through the unitary transformation for the mp method leads to a very efficient computational methodology for real time implementation on a digital signal processor chip a unitary transform can convert the complex matrix to a real matrix along with their eigenvectors and thereby reducing the computational cost at least by a factor of four without sacrificing accuracy this reduction in the number of computations is achieved by using a transformation which maps centro hermitian matrices to real matrices this transformation is based on lee s work on centro hermitian matrices

construction a of lattices over number fields and block fading wiretap coding we propose a lattice construction from totally real and complex multiplication fields which naturally generalizes construction a of lattices from p ary codes obtained from the cyclotomic field mathbb q zeta p p a prime which in turn contains the so called construction a of lattices from binary codes as a particular case we focus on the maximal totally real subfield mathbb q zeta p r zeta p r of the cyclotomic field mathbb q zeta p r r geq 1 our construction has applications to coset encoding of algebraic lattice codes for block fading channels and in particular for block fading wiretap channels

an enhanced gap source model an enhanced gap source model is introduced by combination with rao wilton glisson rwg basis functions for decades the stability of the delta gap source model remains a big problem the rwg basis with triangulation and the feeding edge model have been widely used in numerical analysis of antennas since the feeding edge model uses a single rwg edge as the driving source and neglects the gap width effect the resulting current undergoes sharp transition across the gap and thus the model is highly sensitive to the choice of the feeding edge consequently the feeding edge model suffers instability in calculations of current and input impedance to circumvent these pitfalls this enhanced gap source model uses multiple rwg edges and impulsive function to formulate the feeding behavior this new gap source model exhibits significant improvements on both accuracy and stability numerical results are included to illustrate improved accuracy and stability of this new model by virtue of several typical antennas

rational modeling by pencil of functions method pole zero modeling of signals such as an electromagnetic scatterer response is considered in this paper it is shown by use of the pencil of functions theorem that a the true parameters can be recovered in the ideal case where the signal is the impulse reponse of a rational function h z and b the parameters are optimal in the functional dependence sense when the observed data are corrupted by additive noise or by systematic error although the computations are more involved than in all pole modeling they are considerably less than those required in iterative schemes of pole zero modeling the advantages of the method are demonstrated by a simulation example and through application to the electromagnetic response of a scatterer the paper also includes very recent and promising results on a new approach to noise correction in contradistinction with spectral subtraction techniques where only amplitude information is emphasized and phase is ignored we propose a method that a estimates the noise spectral density for the data frame and then b performs the subtraction of the noise correlation matrix from the gram matrix of the signal

good lattice constellations for both rayleigh fading and gaussian channels recent work on lattices matched to the rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency we present a new family of lattice constellations based on complex algebraic number fields which have good performance on rayleigh fading channels some of these lattices also present a reasonable packing density and thus may be used at the same time over a gaussian channel conversely we show that particular versions of the best lattice packings d sub 4 e sub 6 e sub 8 k sub 12 spl lambda sub 16 spl lambda sub 24 constructed from totally complex algebraic cyclotomic fields present better performance over the rayleigh fading channel the practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links some further results in algebraic number theory related to ideals and their factorization are presented and the decoding algorithm used with these lattice constellations are illustrated together with practical results

clarification of issues on the closed form green s functions in stratified media the closed form green s functions cfgf derived for the vector and scalar potentials in planar multilayer media have been revisited to clarify some issues and misunderstandings on the derivation of these green s functions in addition the range of validity of these green s functions is assessed with and without explicit evaluation of the surface wave contributions as it is well known the derivation of the cfgf begins with the approximation of the spectral domain green s functions by complex exponentials and continues with applying the sommerfeld identity to cast these approximated spectral domain green s functions into the space domain in closed forms questions and misunderstandings of this derivation which have mainly originated from the approximation process of the spectral domain green s functions in terms of complex exponentials can be categorized and discussed under the topics of 1 branch point contributions 2 surface wave pole contributions and 3 the accuracy of the obtained cfgf when these issues are clarified the region of validity of the cfgf so obtained may be defined better therefore in this paper these issues will be addressed first and then their origins and possible remedies will be provided with solid analysis and numerical demonstrations

taylor expansion based fast multipole method for 3 d helmholtz equations in layered media abstract in this paper we develop a taylor expansion te based fast multipole method fmm for low frequency 3d helmholtz green s function in layered media two forms of taylor expansions with either non symmetric or symmetric derivatives of layered media green s functions are used for the implementations of the proposed te fmm in the implementation with non symmetric derivatives an algorithm based on discrete complex image approximations and recurrence formulas is shown to be very efficient and accurate in computing the high order derivatives meanwhile the implementation based on symmetric derivatives is more robust and pre computed tables for the high order derivatives in translation operators are used numerical tests in layered media have validated the accuracy and o n complexity of the proposed algorithms

analysing longitudinal count data with overdispersion summary in many biomedical studies longitudinal count data comprise repeated responses and a set of multidimensional covariates for a large number of individuals when the response variable in such models is subject to overdispersion the overdispersion parameter influences the marginal variance in such cases the overdispersion parameter plays a significant role in efficient estimation of the regression parameters this raises the need for joint estimation of the regression parameters and the overdispersion parameter the longitudinal correlations being nuisance parameters in this paper we develop a generalised estimating equations approach based on a general autocorrelation structure for the repeated overdispersed data the asymptotic properties of the estimators of the main parameters are discussed and the estimation methodology is illustrated by analysing data on epileptic seizure counts

universal lattice codes for mimo channels we propose a coding scheme that achieves the capacity of the compound mimo channel with algebraic lattices our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill conditioned channel realizations to shape the constellation a discrete gaussian distribution over the lattice points is applied these techniques along with algebraic properties of the proposed lattices are then used to construct a sub optimal de coupled coding scheme that achieves a constant gap to compound capacity by decoding in a lattice that does not dependent on the channel realization the gap is characterized in terms of algebraic invariants of the code and is shown to be significantly smaller than previous schemes in the literature we also exhibit alternative algebraic constructions that achieve the capacity of ergodic siso fading channels

fast and accurate mom analysis of periodic arrays of multilayered stacked rectangular patches with application to the design of reflectarray antennas the scattering of plane waves by periodic arrays of stacked rectangular patches in multilayered substrates is a problem that has to be solved many times when designing reflectarray antennas made of those patches under the local periodicity assumption the solution to the periodic multilayered problem has been traditionally carried out by means of the galerkin s version of the method of moments mom in the spectral domain this approach involves the computation of double infinite summations and whereas some of these summations converge very fast some other converge very slowly in this paper the slowly convergent summations are computed by making use of an enhanced mixed potential integral equation mpie formulation of the mom in the spatial domain this enhanced formulation is based on the interpolation of the multilayered periodic green s functions and on the efficient computation of the four dimensional 4 d integrals leading to the mom matrix entries both the novel hybrid spectral spatial mom code and the standard spectral domain mom code have been used for the design of a contoured beam reflectarray antenna it has been verified that the spectral spatial mom code requires cpu times that are typically 30 times smaller than those required by the pure spectral domain mom code

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

an improved pencil of functions method and comparisons with traditional methods of pole extraction prony s method is usually used for the determination of poles from experimental data in the singularity expansion method sem literature it is the aim here to show that this is not the best method and that jain s pencil of functions pof method can be generalized to provide a better method an example of such a method is given

correlate measurements at different test sites a new method for systematic correlation of measurements in semi anechoic and anechoic chambers is presented a signal measured in a semi anechoic chamber is first processed using the matrix pencil method which is applied sequentially on small frequency intervals on each interval the measured signal is decomposed into its propagating wave components the component corresponding to the wave reflected from the ground is identified and removed to fully retrieve the signal measured in an anechoic chamber three examples using log periodic and vivaldi antennas in different anechoic and semi anechoic chambers for varying frequency ranges illustrate the method the proposed decomposition algorithm can be utilized to characterize measurement test site imperfections

perturbation analysis of tk method for harmonic retrieval problems the authors present a first order perturbation analysis of the tufts kumaresan tk 1980 method used to estimate frequencies of complex sinusoids in small additive noise several fundamental properties are presented and proved further illustrations are provided through numerical examples

rigorous analysis of a circular patch antenna excited by a microstrip transmission line boundary conditions are enforced on a portion of the microstrip feed line as well as the patch antenna the integral equation for the unknown currents on the antenna and feed is solved by applying the galerkin method of moments in the fourier transform domain the validity of the solution is tested by comparison of computed results with experimental data the theoretical treatment proves to be applicable to the most common feeding arrangements namely the direct edge feed and proximity coupling excitation in the latter case two layer substrates having distinct dielectric constants are studied the purpose of the study is to deduce for a given overall substrate thickness the smallest line ground plane separation for which a match of the radiator to the feed line is still possible the advantages of such a configuration are discussed

effects of variance function misspecification in analysis of longitudinal data the approach of generalized estimating equations gee is based on the framework of generalized linear models but allows for specification of a working matrix for modeling within subject correlations the variance is often assumed to be a known function of the mean this article investigates the impacts of misspecifying the variance function on estimators of the mean parameters for quantitative responses our numerical studies indicate that 1 correct specification of the variance function can improve the estimation efficiency even if the correlation structure is misspecified 2 misspecification of the variance function impacts much more on estimators for within cluster covariates than for cluster level covariates and 3 if the variance function is misspecified correct choice of the correlation structure may not necessarily improve estimation efficiency we illustrate impacts of different variance functions using a real data set from cow growth

synthetic functions analysis of large aperture coupled antennas the application is described the synthetic function expansion sfx approach to large arrays of aperture coupled antennas the problem is formulated in terms of coupled magnetic field continuity integral equations mfcie and electric field integral equations efie and discretized via the method of moments mom the sfx is a domain decomposition technique on each block of the broken down structure functions are generated with domain over the entire block these ldquosynthetic functionsrdquo sf are obtained from the solution of the electromagnetic problem for the isolated block upon specification of appropriate sources on the block bounding box and from a further singular value decomposition svd based procedure to select the relevant terms the complete problem is solved using the sfs as basis functions for the mom this results in a strong reduction of the mom matrix size applications are presented to configurations of open and cavity backed radiators

analysing ordinal longitudinal survey data generalised estimating equations approach summary longitudinal survey data may comprise ordinal polytomous repeated observations and a set of multidimensional covariates for a large number of individuals one of the main goals of the longitudinal survey is then to describe the marginal expectation of the ordinal polytomous outcome variable as a function of the covariates while accounting for the structural as well as longitudinal correlations the structural correlations come from the polytomous nature of the response variable and the longitudinal correlations from the repetition of the polytomous responses over time in this paper we develop a generalised estimating equations approach based on autocorrelation structure to deal with multivariate polytomous longitudinal survey data the univariate and bivariate analyses being special cases the regression estimators are shown to be consistent for the corresponding regression parameters the methods are illustrated by using the survey of labour and income dynamics data from statistics canada

ring compute and forward over block fading channels the compute and forward c f protocol in quasi static channels normally employs lattice codes based on the rational integers mathbb z the gaussian integers mathbb z i or the eisenstein integers mathbb z omega while its extension to more general channels often assumes channel state information at transmitters csit in this paper we propose a novel scheme for c f in block fading channels without csit which is referred to as ring c f because the fading coefficients are quantized to the canonical embedding of a ring of algebraic integers owing to the multiplicative closure of the algebraic lattices employed a relay is able to decode an algebraic integer linear combination of lattice codewords we analyze its achievable computation rates and show it outperforms conventional c f based on the mathbb z lattices by investigating the effect of the diophantine approximation by algebraic conjugates we prove that the degrees of freedom dofs of the optimized computation rate are n l where n is the number of blocks and l is the number of users

a novel analysis of microstrip structures using the gaussian green s function method a novel closed form expression is derived for spatial green s functions of microstrip structures by expanding the spectral green s function into a gaussian series this innovative method is called the gaussian green s function ggf method due to the gaussian form in the closed form green s function representation the main advantage of the ggf method lies in its precision as well as rapid convergence to demonstrate the versatility of this method the current distribution of a microstrip antenna is achieved via the combination of the method of moments mom and ggf method it is shown that this method can be computationally very efficient with less than 1 error compared to the numerical integration of the spectral integral also the results of the ggf method have been compared to the results of the commercial full wave software of agilent ads

analysis of conformal microstrip antennas with the discrete mode matching method an extension of the discrete mode matching dmm method is used to analyze microstrip antennas conformed to cylinders the structure needs to be discretized only along the azimuthal and the axial directions by sampling the fields and current densities in the interfaces between dielectric layers the solution in the radial direction is obtained analytically with the dyadic green s function which is calculated using the full wave equivalent circuit fwec in the spectral domain the structure is truncated in the axial direction by employing absorbing boundary conditions abcs the mathematical formulation is given in this paper followed by its application to compute the main properties of conformal microstrip antennas such as resonant frequency radiation patterns and input impedance validation with the commercial software hfss has been done and good agreement between the results has been observed

robust analysis of generalized linear mixed models the method of maximum likelihood ml is widely used for analyzing generalized linear mixed models glmm s a full maximum likelihood analysis requires numerical integration techniques for calculation of the log likelihood and to avoid the computational problems involving irreducibly high dimensional integrals several maximum likelihood algorithms have been proposed in the literature to estimate the model parameters by approximating the log likelihood function although these likelihood algorithms are useful for fitting the glmm s efficiently under strict model assumptions they can be highly influenced by the presence of unusual data points in this article the author develops a technique for finding robust maximum likelihood rml estimates of the model parameters in glmm s which appears to be useful in downweighting the influential data points when estimating the parameters the asymptotic properties of the robust estimators are investigated under some regularity conditions small simulations are

estimating and interpolating a markov chain from aggregate data given aggregated longitudinal data generated by a markov chain which may be nonhomogeneous the problem considered is that of modelling estimating and interpolating the logarithms of partial odds and hence the transition probabilities by partial odds is meant the probability of a transition to another state divided by the probability of no transition a result establishing asymptotic normality leads to vector weighted least squares estimation of parameterised partial odds using standard regression methods it is shown how to obtain estimates of one step transition probabilities from widely or irregularly spaced data the methods are illustrated on an example concerning competing causes of death

on the application of parametric models to the transient analysis of resonant and multiband antennas the transient responses of a resonant antenna and a fractal multiband antenna both formed by conducting surfaces are calculated the surfaces are modeled by planar triangular patches and the study is carried out by solving the time domain electric field integral equation td efie linear parametric modeling techniques are applied to considerably reduce the computation time numerical results are compared with experimental measurements

combining an extrapolation technique with the method of moments for solving large scattering problems involving bodies of revolution the purpose of this work is to combine an extrapolation technique with the method of moments mom to solve scattering problems involving large bodies it has been shown in a previous work that the current induced on the smooth parts of large scatterers may be represented as a series of complex exponential functions with a few terms based on this concept a hybrid set of basis functions is constructed using entire domain functions of complex exponential type on the smooth portion of the scatterer complemented by subdomain basis functions near edges and discontinuities an extrapolation procedure is developed in which the scattering problem is first solved for a portion of the scatterer using the conventional mom next a set of entire domain basis functions whose behaviour could be extrapolated with an increase in the size of the scatterer is extracted from this original solution the procedure outlined has the very desirable feature that the total number of basis functions remains unchanged even as the scatterer size is increased allowing for large scatterers to be handled with a relatively small number of unknowns the extrapolation technique is applied to scattering problems from bodies of revolution bors and numerical results for an open cylinder and a barrel shaped bor are presented

improving the correlation structure selection approach for generalized estimating equations and balanced longitudinal data generalized estimating equations are commonly used to analyze correlated data choosing an appropriate working correlation structure for the data is important as the efficiency of generalized estimating equations depends on how closely this structure approximates the true structure therefore most studies have proposed multiple criteria to select the working correlation structure although some of these criteria have neither been compared nor extensively studied to ease the correlation selection process we propose a criterion that utilizes the trace of the empirical covariance matrix furthermore use of the unstructured working correlation can potentially improve estimation precision and therefore should be considered when data arise from a balanced longitudinal study however most previous studies have not allowed the unstructured working correlation to be selected as it estimates more nuisance correlation parameters than other structures such as ar 1 or exchangeable therefore we propose appropriate penalties for the selection criteria that can be imposed upon the unstructured working correlation via simulation in multiple scenarios and in application to a longitudinal study we show that the trace of the empirical covariance matrix works very well relative to existing criteria we further show that allowing criteria to select the unstructured working correlation when utilizing the penalties can substantially improve parameter estimation copyright 2014 john wiley sons ltd

evaluation of efficient closed form green s function in a cylindrically stratified medium an efficient technique is proposed for the removal of the spatial singularity for a z directed current source in a cylindrically layered structure by decomposing the spectral domain green s function into the particular and homogeneous parts the particular part with the singularity is converted into the spatial domain using sommerfeld s identity while the dcim with general pencil of function technique is applied on the spectral domain homogeneous part the use of the ratio form of the reflection transmission matrices the debye approximation and the subsequent envelope extraction for the treatment of the spatial domain singularity is thus avoided in addition a very significant reduction in the number of modes required for convergence is also achieved the technique is applied for evaluating the input impedance of several antennas in the cylindrical multilayer structure together with a coupling configuration for the excitation of the multilayer structure

on the use of a working correlation matrix in using generalised linear models for repeated measures summary in a seminal paper liang zeger 1986 extended the use of generalised linear models to repeated measures data they based the analysis on specifications for the means and variances of the observations as usual for generalised linear models but showed how specifications for the correlations between measurements made on the same unit could be avoided by using a working correlation matrix in some cases the parameters involved in this matrix are subject to an uncertainty of definition which can lead to a breakdown of the asymptotic properties of the estimators

modelling and generating correlated binary variables summary many applications use simple parametric models for the correlation structure of binary responses which are observed in clusters the usual approach to use correlation models appropriate for normally distributed responses suffers from two drawbacks when the marginal probabilities within the clusters differ first as it does not explicitly take into account constraints on the second moments which must be satisfied for binary responses it may fail to model realistically the range of correlations present in the data secondly computer simulation of observations from these models is very difficult we present an alternative class of correlation models which reflect the binary nature of the responses and allow for simple simulation some key wor ds binary variable computer simulation correlation structure generalised estimating equation

exponential convergence under mixing we show that for a mixing stationary sequence of bounded random variables the average of the firstn variables converges exponentially fast withn to the mean value of these random variables

the analysis of arbitrarily shaped aperture coupled patch antennas via a mixed potential integral equation a mixed potential integral equation mpie is formulated for the electric and magnetic currents on a multilayered aperture coupled patch antenna the integral equation is solved via the method of moments mom using subsectional basis functions that allow the analysis of nonrectangular aperture and patch shapes the input impedance and radiation efficiency of various aperture coupled elements are calculated using the proposed technique and compared to measured results the advantages and disadvantages of several aperture and patch configurations are discussed and six methods of numerically de embedding the element s input impedance are compared

locating all the modes of green s function for a three layered medium based on the path tracking algorithm through a mathematical analysis on the relationship between the characteristic equations of the microstrip geometry and a configuration with a three layered medium a method based on the path tracking algorithm is proposed for precisely locating all the modes for a three layered medium with moderate thickness including surface wave modes leaky wave modes and improper real modes with this method the difficulty caused by branch points and cuts in the contour integral method could be avoided this method can be applied not only in the discrete complex image method dcim but also in the steepest descent path sdp method the proposed method can be extended to more complicated configurations

precoded integer forcing universally achieves the mimo capacity to within a constant gap an open loop single user multiple input multiple output mimo communication scheme is considered where a transmitter equipped with multiple antennas encodes the data into independent streams all taken from the same linear code the coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space time code at the receiver side integer forcing equalization is applied followed by standard single stream decoding it is shown that this communication architecture achieves the capacity of any gaussian mimo channel up to a gap that depends only on the number of transmit antennas

full wave analysis of layered aperture arrays the rigorous numerical analytical approach has been developed and used for study of the periodic aperture arrays containing multiple dissimilar apertures of complex shapes in stratified medium the analysis method is based on the solution of the system of integro differential equations by galerkin method with the entire domain basis functions explicitly accounting for the field singularities at the edges of the whole aperture except corners an analytical treatment of the green s function convolutions with the basis and test functions provides an efficient regularization and rapid uniform convergence of the solutions thickness of conducting screen has been taken into account with the aid of the approximation for effective aperture dimensions the characteristics of the quasioptical slot arrays simulated by the developed method are in excellent agreement with the results of measurements and alternative simulations an extensive parametric study of several aperture array configurations has been performed to explore properties of the single layer array arrangements with multiple apertures of complex shapes in a unit cell and stacked layered arrays effect of the aperture shape on the array performance and the physical mechanisms underlying the transverse magnetic wave resonances and luebbers anomaly in the two layer arrays are discussed in detail

on the compound capacity of a class of mimo channels subject to normed uncertainty the compound capacity of uncertain multiple input multiple output channels is considered when the channel is modeled by a class described by a known nominal channel and a constrained norm unknown uncertainty within this framework two types of classes are investigated with additive and multiplicative uncertainties subject to a spectral norm constraint using the singular value decomposition and related singular value inequalities as the main tools the compound capacity is a maxmin mutual information representing the capacity of the class in which the minimization is done over the class of channels while the maximization is done over the transmit covariance closed form solutions for the compound capacity of the classes are obtained and several properties related to transmit and receive eigenvectors are presented it is shown that under certain conditions the compound capacity of the class is equal to the worst case channel capacity thus establishing a saddle point property explicit closed form solutions are given for the worst case channel uncertainty and the capacity achieving transmit covariance matrix the best transmission strategy achieving the compound capacity is a multiple beamforming on the nominal known channel eigenmodes with the beam power distribution via the water filling at a degraded snr as the uncertainty increases fewer eigenmodes are used until only the strongest one remains active so that transmit beamforming is an optimal robust transmission strategy in this large uncertainty regime for which explicit conditions are given using these results upper and lower bounds of the compound capacity are constructed for other bounded uncertainties and some generic properties are pointed out the results are extended to compound multiple access and broadcast channels in all considered cases the price to pay for channel uncertainty is an snr loss or equivalently the nominal channel degradation commensurate with the uncertainty set radius measured by the spectral norm and the optimal signaling strategy is the transmission on the degraded nominal channel

generalized least squares taylor series linearization and fisher s scoring in multivariate nonlinear regression in this article we consider a general multivariate nonlinear regression setting in which the marginal mean and variance covariance structure share a common set of regression parameters estimation is carried out via iteratively reweighted generalized least squares irgls that entails repeated application of taylor series linearization and estimated generalized least squares egls under normality this irgls procedure is equivalent to fisher s method of scoring and hence maximum likelihood estimation mle however estimates from this procedure are also shown to minimize a bias corrected generalized least squares objective function that does not require the assumption of normality under fairly mild regularity conditions the resulting estimates are consistent asymptotically normal and under normality assumptions asymptotically efficient the estimates are compared against those obtained as solutions to the usual generalized estimating equations gee using both simulation and numerical examples

application of the matrix pencil method for estimating the sem singularity expansion method poles of source free transient responses from multiple look directions the matrix pencil method has been utilized for estimating the natural resonances from different transient responses recorded along multiple look directions as a function of time after the incident field has passed the structure the novelty of this article is that a single estimate for all the poles are done utilizing multiple transient waveforms emanating from the structure along multiple look directions the sem poles are independent of the angle at which the transient response is recorded the only difference between the various waveforms are that the residues at the various poles are of different magnitudes some of the residues may even be zero for some of the poles indicating that the contribution from certain sem poles may not be significant along that look direction here all the waveforms are utilized providing a single estimate for the poles without performing an arithmetic mean of the various waveforms

unbiased estimating equations from working correlation models for irregularly timed repeated measures the method of generalized estimating equations gees has been criticized recently for a failure to protect against misspecification of working correlation models which in some cases leads to loss of efficiency or infeasibility of solutions however the feasibility and efficiency of gee methods can be enhanced considerably by using flexible families of working correlation models we propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance gee the supplementary estimating equations are obtained by differentiation of the cholesky decomposition of the working correlation or as score equations for decoupled gaussian pseudolikelihood the estimating equations are solved with computational effort equivalent to that required for a first order gee full details and analytic expressions are developed for a generalized markovian model that was evaluated through simulation large sample sandwich standard errors for working correlation parameter estimates are derived and shown to have good performance the proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children

wave oriented signal processing of dispersive time domain scattering data phase space data processing is receiving increased attention because or its potential for furnishing new discriminants relating to classification and identification of targets and other scattering environments primary emphasis has been on time frequency processing because of its impact on transient especially wideband short pulse excitations here we investigate the windowed fourier transform the wavelet transform and model based superresolution algorithms within the context of a fully quantified and calibrated test problem investigated by us previously two dimensional 2 d short pulse plane wave scattering by a finite periodic array of perfectly conducting coplanar flat strips because the forward problem has been fully calibrated and parametrized some quantitative measures can be assigned with respect to the tradeoffs of these time frequency algorithms yielding tentative performance assessments of the tested processing algorithms

application of dcim on marine controlled source electromagnetic survey the discrete complex image method dcim is used to calculate the mixed potential electric field integral equation the dcim has been used broadly in high frequency domain and now is successfully introduced to the extremely low frequency situation of marine controlled source electromagnetic mcsem survey the integral path in high frequency situation does not hold valid for extremely low frequency situation the reason can be ascribed to the change of wave number formulas a new integral path suitable for the extremely low frequency situation is proposed the appropriate ranges of the parameters used in dcim are given the computation is stable at these considerably large ranges the results of a five layer model calculated with dcim are compared with those with the filter method and the direct integral method the computation time with dcim is comparable to the time with filter method the effects of water depth upper sediment thickness and oil layer thickness are studied with dcim the results show that electric field varies with the change of thickness the effects accord to the physical meanings of mcsem survey it is safe to conclude that the dcim with the new path is valid in mcsem survey

almost universal codes achieving ergodic mimo capacity within a constant gap this paper addresses the question of achieving capacity with lattice codes in multi antenna block fading channels when the number of fading blocks tends to infinity a design criterion based on the normalized minimum determinant is proposed for division algebra multi block space time codes over fading channels this plays a similar role to the hermite invariant for gaussian channels under maximum likelihood decoding it is shown that this criterion is sufficient to guarantee transmission rates within a constant gap from capacity both for deterministic channels and ergodic fading channels moreover if the number of receive antennas is greater than or equal to the number of transmit antennas the same constant gap is achieved under naive lattice decoding as well in the case of independent identically distributed rayleigh fading the error probability vanishes exponentially fast in contrast to the standard approach in the literature which employs random lattice ensembles the existence results in this paper are derived from the number theory first the gap to capacity is shown to depend on the discriminant of the chosen division algebra then class field theory is applied to build families of algebras with small discriminants the key element in the construction is the choice of a sequence of division algebras whose centers are number fields with small root discriminants

averaging bounds for lattices and linear codes general random coding theorems for lattices are derived from the minkowski hlawka theorem and their close relation to standard averaging arguments for linear codes over finite fields is pointed out a new version of the minkowski hlawka theorem itself is obtained as the limit for p spl rarr spl infin of a simple lemma for linear codes over gf p used with p level amplitude modulation the relation between the combinatorial packing of solid bodies and the information theoretic soft packing with arbitrarily small but positive overlap is illuminated the soft packing results are new when specialized to the additive white gaussian noise channel they reduce to a version of the de buda poltyrev result that spherically shaped lattice codes and a decoder that is unaware of the shaping can achieve the rate 1 2 log sub 2 p n

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

comparative evaluation of absorbing boundary conditions using green s functions for layered media absorbing boundary conditions are comparatively studied using the green s functions of the vector and scalar potentials for multilayer geometries and general sources since the absorbing boundaries are introduced as additional layers with predefined reflection coefficients into the calculation of the green s functions this approach provides an absolute measure of the effectiveness of different absorbing boundaries the green s functions are calculated using different reflection coefficients corresponding to different absorbing boundaries and compared to those obtained with no absorbing boundary it is observed that the perfectly matched layer pml is by far the best among the other absorbing boundary conditions whose reflection coefficients are available

fundamental limits of infinite constellations in mimo fading channels the fundamental and natural connection between the infinite constellation ic dimension and the best diversity order it can achieve is investigated in this paper in the first part of this paper we develop an upper bound on the diversity order of ics for any dimension and any number of transmit and receive antennas by choosing the right dimensions we prove in the second part of this paper that ics in general and lattices in particular can achieve the optimal diversity multiplexing tradeoff of finite constellations this paper gives a framework for designing lattices for multiple antenna channels using lattice decoding