scaling behavior of explosive percolation on the square lattice clusters generated by the product rule growth model of achlioptas d souza and spencer on a two dimensional square lattice are shown to obey qualitatively different scaling behavior than standard random growth percolation the threshold with unrestricted bond placement allowing loops is found precisely using several different criteria based on both moments and wrapping probabilities yielding p c 0 526 text 565 ifmmode pm else textpm fi 0 000 text 005 consistent with the recent result of radicchi and fortunato the correlation length exponent ensuremath nu is found to be close to 1 the qualitative difference from regular percolation is shown dramatically in the behavior of the percolation probability p ensuremath infty size of largest cluster of the susceptibility and of the second moment of finite clusters where discontinuities appear at the threshold the critical cluster size distribution does not follow a consistent power law for the range of system sizes we study l ensuremath le 8192 but may approach a power law with ensuremath tau g2 for larger l

multivariate continuation ratio models connections and caveats summary we develop semiparametric estimation methods for a pair of regressions that characterize the first and second moments of clustered discrete survival times in the first regression we represent discrete survival times through univariate continuation indicators whose expectations are modeled using a generalized linear model in the second regression we model the marginal pairwise association of survival times using the clayton oakes cross product ratio clayton 1978 biometrika65 141 151 oakes 1989 journal of the american statistical association84 487 493 these models have recently been proposed by shih 1998 biometrics54 1115 1128 we relate the discrete survival models to multivariate multinomial models presented in heagerty and zeger 1996 journal of the american statistical society91 1024 1036 and derive a paired estimating equations procedure that is computationally feasible for moderate and large clusters we extend the work of guo and lin 1994 biometrics50 632 639 and shih 1998 to allow covariance weighted estimating equations and investigate the impact of weighting in terms of asymptotic relative efficiency we demonstrate that the multinomial structure must be acknowledged when adopting weighted estimating equations and show that a naive use of gee methods can lead to inconsistent parameter estimates finally we illustrate the proposed methodology by analyzing psychological testing data previously summarized by tenhave and uttal 1994 applied statistics43 371 384 and guo and lin 1994

factors affecting power of tests for multiple binary outcomes frequently in clinical studies a primary outcome is formulated from a vector of binary events several methods exist to assess treatment effects on multiple correlated binary outcomes including comparing groups on the occurrence of at least one among the outcomes collapsed composite on the count of outcomes observed per subject on individual outcomes adjusting for multiplicity or with multivariate tests postulating either common or distinct effects across outcomes we focus on a 1 df distinct effects test in which the estimated outcome specific treatment effects from a gee model are simply averaged and compare it with other methods on clinical and statistical grounds using a flexible method to simulate multivariate binary data we show that the relative efficiencies of the assessed tests depend in a complex way on the magnitudes and variabilities of component incidences and treatment effects as well as correlations among component events while other tests are easily driven by high frequency components the average effect gee test is not since it averages the log odds ratios unweighted by the component frequencies thus the average effect test is relatively more powerful than other tests when lower frequency components have stronger associations with a treatment or other predictor but less powerful when higher frequency components are more strongly associated in studies when relative effects are at least as important as absolute effects or when lower frequency components are clinically most important this test may be preferred two clinical trials are discussed and analyzed and recommendations for practice are made sons ltd

a modified pseudolikelihood approach for analysis of longitudinal data we consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters in general inconsistent estimators of the covariance variance correlation parameters will be produced when the working correlation matrix is misspecified which may result in great loss of efficiency of the mean parameter estimators albeit the consistency is preserved we consider using different working correlation models for the variance and the mean parameters in particular we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified the designated working correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters simulation studies indicate that the proposed algorithm performs very well we also applied different estimation procedures to a data set from a clinical trial for illustration

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

generalized linear models a new program for depression is instituted in the hopes of reducing the number of visits each patient makes to the emergency room in the year following treatment predictors include among many others treatment yes no race and drug and alcohol usage indices a common and minimally invasive treatment for jaundice in newborns is exposure to light yet the cost of this is high mainly because of longer hospital stays which are expensive predictors of the cost include race gestational age and birthweight

cluster aggregation model for discontinuous percolation transitions the evolution of the erd ifmmode mbox h o else h o fi s r enyi er network by adding edges is a basis model for irreversible kinetic aggregation phenomena such er processes can be described by a rate equation for the evolution of the cluster size distribution with the connection kernel k ij ensuremath sim ij where ij is the product of the sizes of two merging clusters here we study that when the giant cluster is discouraged to develop by a sublinear kernel k ij ensuremath sim ij ensuremath omega with 0 ensuremath le ensuremath omega l1 2 the percolation transition pt is discontinuous such discontinuous pt can occur even when the er dynamics evolves from proper initial conditions the obtained evolutionary properties of the simple model sheds light on the origin of the discontinuous pt in other nonequilibrium kinetic systems

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

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

nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation abstractthis paper presents a fast constrained optimization approach which is tailored for nonlinear model predictive control of wave energy converters wec the advantage of this approach relies on its exploitation of the differential flatness of the wec model this can reduce the dimension of the resulting nonlinear programming problem nlp derived from the continuous constrained optimal control of wec using pseudospectral method the alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for wec control problems the method is applicable to nonlinear wec models nonconvex objective functions and nonlinear constraints which are commonly encountered in wec control problems numerical simulations demonstrate the efficacy of this approach

efficiency of regression estimates for clustered data statistical methods for clustered data such as generalized estimating equations gee and generalized least squares gls require selecting a correlation or convariance structure to specify the dependence between observations within a cluster valid regression estimates can be obtained that do not depend on correct specification of the true correlation but inappropriate specifications can result in a loss of efficiency we derive general expressions for the asymptotic relative efficiency of gee and gls estimators under nested correlation structures efficiency is shown to depend on the covariate distribution the cluster sizes the response variable correlation and the regression parameters the results demonstrate that efficiency is quite sensitive to the between and within cluster variation of the covariates and provide useful characterizations of models for which upper and lower efficiency bounds are attained efficiency losses for simple working correlation matrices such as independence can be large even for small to moderate correlations and cluster sizes

random sequential adsorption line segments on the square lattice we study kinetics of the rmgle layer random sequenrisl adsorption of lint segments of ked kn5h on the square iatijcc by a monte carlo srmulatton the area covered b the line segments grows with time and finally reacher a jamming limit when no more adsorption is possible the jamming coverage depends on the segment length and 11s vanation is studted at the late stage approach of the coverage to the jamming limit is arymptotieally exponential with a rate found to be independent of the segment length based on our monte carlo data an act expression for the late stage deposition kinettcs 15 conjectured random sequential adsorption rsa has been the subject of much recent experimental and theoretical investigation objects of figte size are randomly deposited adsorbed on an initially empty substrate so that no two objects overlap the quantity of interest is the fraction of the total area b f in time i covered by the depositing particles due to the blocking of the area by the already randomly adsorbed particles the limiting 3amming coverage co is less than the close packing the emergence of this jammed state is iduenced by the infiuite memory effects consequently its formation cannot he described by mean field theory except for very early times when 6 t af experimental studies 11 41 include e g adhesion of colloidal particles 131 and proteins 2 on homogeneous substrates with relaxation times much longer than the formation time of deposits theoretical studies s 171 of rsa include series expansions is l j numerical monte carlo mc simulations 9 14 16 and some analytical results 1171 mostly for one dimensional systems in such studies it was shown that the precise form of the long time behaviour of b r depends on the shape and orientational freedom of the adsorbing particles earlier studies have focused on continuum deposition models for which a power law behaviour of the late stage deposition 1171

analysis of serially correlated data using quasi least squares summary quasi least squares qls a marginal statistical approach via generalized estimating equations that is described in the balanced data setting by chaganty 1997 journal of statistical planning and inference 63 39 54 allows for application of a wide range of working correlation structures when analyzing serially correlated data we extend the application of qls to serially correlated unequally spaced and unbalanced data using three useful working correlation models the firstorder autoregressive ar 1 the markov and the generalized markov structure described by nuniez anton and woodworth 1994 biometrics 50 445 456 we compare qls and the original formulation of the generalized estimating equation approach gee for these structures demonstrating that i infeasibility of the gee correlation parameter estimates can be a problem ii it is difficult to obtain consistent moment estimates of the correlation parameters for the generalized markov structure and iii the use of qls can lead to reduced mean square error of the estimate of the regression parameter for small samples of moderately correlated data to choose between alternative correlation models we propose a criterion that is based on the principle of generalized least squares finally data for which the generalized markov structure is appropriate are analyzed to demonstrate the use of qls in selecting a suitable working correlation structure and identifying in this paper we apply a statistical method based on the generalized estimating equation approach of liang and zeger 1986 to the analysis of longitudinal data that may be difficult to analyze using other established methods we consider repeated measures data collected by taking measurements of an outcome variable and associated covariates on each of a group of independent subjects our primary data analysis goal is to identify important covariates and to explain their effect on the marginal mean of the outcome variable while also accounting for the correlation among observations on each subject accomplishing this research objective may be difficult due to certain conditions that are typical in longitudinal studies the timing and total number of measurements taken may vary from subject to subject so that the data may be unbalanced and unequally spaced the outcome variable may not be normally distributed the intrasubject correlation may be described using a time dependent pattern for example the correlation between two measurements may decrease as they become more

flatness of heavy chain systems in this paper the flatness m fliess j levine p martin and p rouchon internat j control 61 1995 pp 1327 1361 m fliess j levine p martin and p rouchon ieee trans automat control 44 1999 pp 922 937 of heavy chain systems i e trolleys carrying a fixed length heavy chain that may carry a load is addressed in the partial derivatives equations framework we parameterize the system trajectories by the trajectories of its free end and solve the motion planning problem namely steering from one state to another state when considered as a finite set of small pendulums these systems were shown to be flat r m murray in proceedings of the ifac world congress san francisco ca 1996 pp 395 400 our study is an extension to the infinite dimensional case under small angle approximations these heavy chain systems are described by a one dimensional 1d partial differential wave equation dealing with this infinite dimensional description we show how to get the explicit parameterization of the chain trajectory using distributed and punctual advances and delays of its free end this parameterization results from symbolic computations replacing the time derivative by the laplace variable s yields a second order differential equation in the spatial variable where s is a parameter its fundamental solution is for each point considered along the chain an entire function of s of exponential type moreover for each we show that thanks to the liouville transformation this solution satisfies modulo explicitly computable exponentials of s the assumptions of the paley wiener theorem this solution is in fact the transfer function from the flat output the position of the free end of the system to the whole state of the system using an inverse laplace transform we end up with an explicit motion planning formula involving both distributed and punctual advances and delays operators

use of quasi least squares to adjust for two levels of correlation this article considers data with two levels of association our motivating example is an international intervention trial with repeated observations on subjects who reside within geographically defined clusters to account for the potential correlation within clusters and within the repeated measurements that pertain to each subject we apply a method based on generalized estimating equations for a correlation structure proposed by lefkopoulou moore and ryan 1989 journal of the american statistical association 84 810 815

marginal regression analysis of longitudinal data with time dependent covariates a generalized method of moments approach summary we develop a new approach to using estimating equations to estimate marginal regression models for longitudinal data with time dependent covariates our approach classifies time dependent covariates into three types types i ii and iii the type of covariate determines what estimating equations can be used involving the covariate we use the generalized method of moments to make optimal use of the estimating equations that are made available by the covariates previous literature has suggested the use of generalized estimating equations with the independent working correlation when there are time dependent covariates we conduct a simulation study that shows that our approach can provide substantial gains in efficiency over generalized estimating equations with the independent working correlation when a time dependent covariate is of types i or ii and our approach remains consistent and comparable in efficiency with generalized estimating equations with the independent working correlation when a time dependent covariate is of type iii we apply our approach to analyse the relationship between the body mass index and future morbidity among children in the philippines

optimal combination of estimating equations in the analysis of multilevel nested correlated data multilevel nested correlated data often arise in biomedical research examples include teeth nested within quadrants in a mouth or students nested within classrooms in schools in some settings cluster sizes may be large relative to the number of independent clusters and the degree of correlation may vary across clusters when cluster sizes are large fitting marginal regression models using generalized estimating equations with flexible correlation structures that reflect the nested structure may fail to converge and result in unstable covariance estimates also the use of patterned nested working correlation structures may not be efficient when correlation varies across clusters this paper describes a flexible marginal regression modeling approach based on an optimal combination of estimating equations particular within cluster and between cluster data contrasts are used without specification of the working covariance structure and without estimation of covariance parameters the method involves estimation of the covariance matrix only for the vector of component estimating equations which is typically of small dimension rather than the covariance matrix of the observations within a cluster which may be of large dimension in settings where the number of clusters is large relative to the cluster size the method is stable and is highly efficient while maintaining appropriate coverage levels performance of the method is investigated with simulation studies and an application to a periodontal study

analysis of pregnancy and other factors on detection of human papilloma virus hpv infection using weighted estimating equations for follow up data generalized estimating equations have been well established to draw inference for the marginal mean from follow up data many studies suffer from missing data that may result in biased parameter estimates if the data are not missing completely at random robins and co workers proposed using weighted estimating equations wee in estimating the mean structure if drop out occurs missing at random we illustrate the differences between the wee and the commonly applied available case analysis in a simulation study we apply the wee and reanalyse data of a longitudinal study of pregnancy and human papilloma virus hpv infection we estimate the response probabilities and demonstrate that the data are not missing completely at random upon use of the wee we are able to show that pregnant women have an increased odds for an hpv infection compared with non pregnant women after delivery p 0 027 we conclude that the wee are useful for dealing with monotone missing data due to drop outs in follow up data

flatness of semilinear parabolic pdes a generalized cauchy kowalevski approach a generalized cauchy kowalevski approach is proposed for flatness based trajectory planning for boundary controlled semilinear systems of partial differential equations pdes in a one dimensional spatial domain for this the ansatz presented in trajectory planning for boundary controlled parabolic pdes with varying parameters on higher dimensional spatial domains t meurer and a kugi ieee trans autom control vol 54 no 8 pp 1854 1868 aug 2009 using formal integration is generalized towards a unified design framework which covers linear and semilinear pdes including rather broad classes of nonlinearities arising in applications in addition an efficient semi numerical solution of the implicit state and input parametrizations is developed and evaluated in different scenarios simulation results for various types of nonlinearities and a tubular reactor model described by a system of semilinear reaction diffusion convection equations illustrate the applicability of the proposed method

null controllability of the heat equation using flatness we derive in a direct and rather straightforward way the null controllability of the n dimensional heat equation in a bounded cylinder with boundary control at one end of the cylinder we use the so called flatness approach which consists in parameterizing the solution and the control by the derivatives of a flat output this yields an explicit control law achieving the exact steering to zero replacing the involved series by partial sums we obtain a simple numerical scheme for which we give explicit error bounds numerical experiments demonstrate the relevance of the approach

gee analysis of clustered binary data with diverging number of covariates clustered binary data with a large number of covariates have become increasingly common in many scientific disciplines this paper develops an asymptotic theory for generalized estimating equations gee analysis of clustered binary data when the number of covariates grows to infinity with the number of clusters in this large n diverging p framework we provide appropriate regularity conditions and establish the existence consistency and asymptotic normality of the gee estimator furthermore we prove that the sandwich variance formula remains valid even when the working correlation matrix is misspecified the use of the sandwich variance formula leads to an asymptotically valid confidence interval and wald test for an estimable linear combination of the unknown parameters the accuracy of the asymptotic approximation is examined via numerical simulations we also discuss the diverging p asymptotic theory for general gee the results in this paper extend the recent elegant work of xie and yang ann statist 31 2003 310 347 and balan and schiopu kratina ann statist 32 2005 522 541 in the fixed p setting

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

on the analysis of very small samples of gaussian repeated measurements an alternative approach the analysis of very small samples of gaussian repeated measurements can be challenging first due to a very small number of independent subjects contributing outcomes over time statistical power can be quite small second nuisance covariance parameters must be appropriately accounted for in the analysis in order to maintain the nominal test size however available statistical strategies that ensure valid statistical inference may lack power whereas more powerful methods may have the potential for inflated test sizes therefore we explore an alternative approach to the analysis of very small samples of gaussian repeated measurements with the goal of maintaining valid inference while also improving statistical power relative to other valid methods this approach uses generalized estimating equations with a bias corrected empirical covariance matrix that accounts for all small sample aspects of nuisance correlation parameter estimation in order to maintain valid inference furthermore the approach utilizes correlation selection strategies with the goal of choosing the working structure that will result in the greatest power in our study we show that when accurate modeling of the nuisance correlation structure impacts the efficiency of regression parameter estimation this method can improve power relative to existing methods that yield valid inference copyright 2017 john wiley sons ltd

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

gmm logistic regression models for longitudinal data with time dependent covariates and extended classifications when analyzing longitudinal data it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times as such one can analyze these data using generalized estimating equation with the independent working correlation however because it is essential to include all the appropriate moment conditions as you solve for the regression coefficients we explore an alternative approach using a generalized method of moments for estimating the coefficients in such data we develop an approach that makes use of all the valid moment conditions necessary with each time dependent and time independent covariate this approach does not assume that feedback is always present over time or if present occur at the same degree further we make use of continuously updating generalized method of moments in obtaining estimates we fit the generalized method of moments logistic regression model with time dependent covariates using sas proc iml and also in r we used p values adjusted for multiple correlated tests to determine the appropriate moment conditions for determining the regression coefficients we examined two datasets for illustrative purposes we looked at re hospitalization taken from a medicare database we also revisited data regarding the relationship between the body mass index and future morbidity among children in the philippines we conducted a simulated study to compare the performances of extended classifications copyright 2014 john wiley sons ltd

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

a caveat concerning independence estimating equations with multivariate binary data clustered binary data occur commonly in both the biomedical and health sciences in this paper we consider logistic regression models for multivariate binary responses where the association between the responses is largely regarded as a nuisance characteristic of the data in particular we consider the estimator based on independence estimating equations iee which assumes that the responses are independent this estimator has been shown to be nearly efficient when compared with maximum likelihood ml and generalized estimating equations gee in a variety of settings the purpose of this paper is to highlight a circumstance where assuming independence can lead to quite substantial losses of efficiency in particular when the covariate design includes within cluster covariates assuming independence can lead to a considerable loss of efficiency in estimating the regression parameters associated with those covariates

a new route to explosive percolation abstract the biased link occupation rule in the achlioptas process ap discourages the large clusters from growing much ahead of others and encourages faster growth of clusters which lag behind in this paper we propose a model where this tendency is sharply reflected in the gamma distribution of the cluster sizes unlike the power law distribution in ap in this model single edges between pairs of clusters of sizes s i and s j are occupied with a probability s i s j the parameter is continuously tunable over the entire real axis numerical studies indicate that for c the transition is first order c 0 for a square lattice and c 1 2 for random graphs in the limits of this model coincides with models well established in the literature

analysis of clustered data a combined estimating equations approach summary examples of clustered data include data from longitudinal studies and data sampled within groups this paper proposes a regression analysis method for clustered data that optimally weights and combines contrasts of the data through a combination of estimating equations examples of combining between cluster within cluster and longitudinal data contrasts are presented the method results in increased estimation efficiency relative to generalised estimating equations with standard working correlation structures the proposed method also simplifies modelling decisions regarding the true correlation structure of the data and avoids correlation parameter estimation

semiparametric efficient estimation for incomplete longitudinal binary data with application to smoking trends incomplete longitudinal data often are analyzed with estimating equations for inference on a parameter from a marginal mean regression model generalized estimating equations although commonly used for incomplete longitudinal data are invalid for data that are not missing completely at random there exists a class of inverse probability weighted estimating equations that are valid under dropouts missing at random including an easy to implement but inefficient member a relatively computationally complex semiparametric efficient estimator in this class has been applied to continuous data a specific form of this estimator is developed for binary data and used as a benchmark for assessing the efficiency of the simpler estimator in a simulation study both are applied in the estimation of 15 year cigarette smoking trends in the united states from a cohort of 5077 young adults the results suggest that declines in smoking from previous reports have been exaggerated

controllability and observability of grid graphs via reduction and symmetries in this paper we investigate the controllability and observability properties of a family of linear dynamical systems whose structure is induced by the laplacian of a grid graph this analysis is motivated by several applications in network control and estimation quantum computation and discretization of partial differential equations specifically we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph for each eigenvalue based on its multiplicity and on suitable symmetries of the corresponding eigenvectors we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable observable we discuss the proposed criteria and show through suitable examples how such criteria reduce the complexity of the controllability respectively observability analysis of the grid

flatness based trajectory planning for diffusion reaction systems in a parallelepipedon a spectral approach spectral analysis is considered for the flatness based solution of the trajectory planning problem for a boundary controlled diffusion reaction system defined on a 1 r dimensional parallelepipedon by exploiting the riesz spectral properties of the system operator it is shown that a suitable reformulation of the resolvent operator allows a systematic introduction of a basic output which yields a parametrization of both the system state and the boundary input in terms of differential operators of infinite order their convergence is verified for both infinite dimensional and finite dimensional actuator configurations by restricting the basic output to certain gevrey classes involving non analytic functions with this a systematic approach is introduced for basic output trajectory assignment and feedforward tracking control towards the realization of finite time transitions between stationary profiles

flatness based boundary control of a class of quasilinear parabolic distributed parameter systems motion planning and control of a boundary controlled quasilinear parabolic partial differential equation in one spatial variable is considered the approach relies on a flatness property of the system namely that the system solution can be differentially parameterized in terms of a flat output which in the case considered is a boundary value such a parameterization allows straightforward motion planning and computation of a control law the approach is based on power series in the spatial variable and the convergence of these series is ensured by choosing the flat output to be a nonanalytic smooth function of appropriate gevrey class

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

maximum likelihood algorithms for generalized linear mixed models abstract maximum likelihood algorithms are described for generalized linear mixed models i show how to construct a monte carlo version of the em algorithm propose a monte carlo newton raphson algorithm and evaluate and improve the use of importance sampling ideas calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously i also use the newton raphson algorithm as a framework to compare maximum likelihood to the joint maximization or penalized quasi likelihood methods and explain why the latter can perform poorly

using modified approaches on marginal regression analysis of longitudinal data with time dependent covariates quadratic inference functions qifs and estimating equations using the conjugate gradient method cgm for fitting marginal models to longitudinal data show appealing features in improving the efficiency without making assumptions on the correlation structure however our simulation study shows that both methods produce biased and inefficient estimates of regression parameters when time dependent covariates are present in this paper we extend both the qif and cgm methods for fitting marginal models to longitudinal data with time dependent covariates the idea is to restrict the moment conditions to the ones that are only valid to certain types of time dependent covariates our simulations show that efficiency on estimating regression parameters is achieved using modified approaches furthermore we apply the modified approach to anthropometric screening data to evaluate the association between body mass index and morbidity in children in the philippines

explosive percolation a numerical analysis percolation is one of the most studied processes in statistical physics a recent paper by achlioptas et al science 323 1453 2009 showed that the percolation transition which is usually continuous becomes discontinuous explosive if links are added to the system according to special cooperative rules achlioptas processes in this paper we present a detailed numerical analysis of achlioptas processes with product rule on various systems including lattices random networks a la erdos renyi and scale free networks in all cases we recover the explosive transition by achlioptas et al however the explosive percolation transition is kind of hybrid as despite the discontinuity of the order parameter at the threshold one observes traces of analytical behavior such as power law distributions of cluster sizes in particular for scale free networks with degree exponent 3 all relevant percolation variables display power law scaling just as in continuous second order phase transitions

trajectory planning for boundary controlled parabolic pdes with varying parameters on higher dimensional spatial domains the flatness based design of a feedforward tracking control is considered for the solution of the trajectory planning problem for a boundary controlled diffusion convection reaction system with spatially and temporally varying parameters defined on a 1 les m dimensional parallelepipedon with the nonlinear input being restricted to a m 1 dimensional hyperplane for this an implicit state and input parametrization in terms of a basic output is determined via a volterra type integral equation with operator kernel by recursively computing successive series coefficients a series solution of the integral equation is obtained whose absolute and uniform convergence is verified by restricting the system parameters and the basic output to a certain but broad gevrey class hence prescribing an admissible desired trajectory for the basic output directly yields the feedforward control by evaluating the input parametrization this results in a systematic procedure for trajectory planning and feedforward control design for boundary controlled parabolic distributed parameter systems defined on higher dimensional domains

hamiltonian approach for explosive percolation we present a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by d achlioptas et al science 323 1453 2009 we show that the following two ingredients are sufficient for obtaining an abrupt first order transition in the fraction of the system occupied by the largest cluster i the size of all growing clusters should be kept approximately the same and ii the inclusion of merging bonds i e bonds connecting vertices in different clusters should dominate with respect to the redundant bonds i e bonds connecting vertices in the same cluster moreover in the extreme limit where only merging bonds are present a complete enumeration scheme based on treelike graphs can be used to obtain an exact solution of our model that displays a first order transition finally the presented mechanism can be viewed as a generalization of standard percolation that discloses a family of models with potential application in growth and fragmentation processes of real network systems

shrinkage empirical likelihood estimator in longitudinal analysis with time dependent covariates application to modeling the health of filipino children the method of generalized estimating equations gee is a popular tool for analysing longitudinal panel data often the covariates collected are time dependent in nature for example age relapse status monthly income when using gee to analyse longitudinal data with time dependent covariates crucial assumptions about the covariates are necessary for valid inferences to be drawn when those assumptions do not hold or cannot be verified pepe and anderson 1994 communications in statistics simulations and computation 23 939 951 advocated using an independence working correlation assumption in the gee model as a robust approach however using gee with the independence correlation assumption may lead to significant efficiency loss fitzmaurice 1995 biometrics 51 309 317 in this article we propose a method that extracts additional information from the estimating equations that are excluded by the independence assumption the method always includes the estimating equations under the independence assumption and the contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries we apply the method to a longitudinal study of the health of a group of filipino children

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

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

about the fastest growth of the order parameter in models of percolation abstract the growth of the average size s max of the largest component at the percolation threshold p c n on a graph of size n has been defined as s max p c n n n here we argue that the precise value of the growth exponent indicates the nature of percolation transition 1 or 1 determines if the transition is continuous or discontinuous we show that a related exponent 1 which describes how the average maximal jump sizes in the order parameter decays on increasing the system size is the single exponent that describes the finite size scaling of a number of distributions related to the fastest growth of the order parameter in these problems excellent quality scaling analysis are presented for the two single peak distributions corresponding to the order parameters at the two ends of the maximal jump the bimodal distribution constructed by the weighted average of these distributions and for the distribution of the maximal jump in the order parameter

akaike s information criterion in generalized estimating equations correlated response data are common in biomedical studies regression analysis based on the generalized estimating equations gee is an increasingly important method for such data however there seem to be few model selection criteria available in gee the well known akaike information criterion aic cannot be directly applied since aic is based on maximum likelihood estimation while gee is nonlikelihood based we propose a modification to aic where the likelihood is replaced by the quasi likelihood and a proper adjustment is made for the penalty term its performance is investigated through simulation studies for illustration the method is applied to a real data set

multivariate mean parameter estimation by using a partly exponential model summary a class of partly exponential models is proposed for the regression analysis of multivariate response data the class is parameterized in terms of the response mean and a general shape parameter it includes the generalized linear error model and exponential dispersion models as special cases maximum likelihood equations for mean parameters are shown to be of the same form as certain generalized estimating equations and maximum likelihood estimates of mean and shape parameters are asymptotically independent some results are given on the efficiency of the estimating equation procedure under misspecification of the response covariance matrix

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

the analysis of binary longitudinal data with time dependent covariates we consider longitudinal studies with binary outcomes that are measured repeatedly on subjects over time the goal of our analysis was to fit a logistic model that relates the expected value of the outcomes with explanatory variables that are measured on each subject however additional care must be taken to adjust for the association between the repeated measurements on each subject we propose a new maximum likelihood method for covariates that may be fixed or time varying we also implement and make comparisons with two other approaches generalized estimating equations which may be more robust to misspecification of the true correlation structure and alternating logistic regression which models association via odds ratios that are subject to less restrictive constraints than are correlations the proposed estimation procedure will yield consistent and asymptotically normal estimates of the regression and correlation parameters if the correlation on consecutive measurements on a subject is correctly specified simulations demonstrate that our approach can yield improved efficiency in estimation of the regression parameter for equally spaced and complete data the gains in efficiency were greatest for the parameter associated with a time by group interaction term and for stronger values of the correlation for unequally spaced data and with dropout according to a missing at random mechanism mark1ml with correctly specified consecutive correlations yielded substantial improvements in terms of both bias and efficiency we present an analysis to demonstrate application of the methods we consider we also offer an r function for easy implementation of our approach copyright 2012 john wiley sons ltd

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

estimating logistic regression parameters for bivariate binary data summary consider bivariate binary data with possibly different covariates for each marginal binary observation suppose that the correlation between paired observations is a nuisance and the interest lies in estimating logistic regression parameters associated with the covariates we consider the estimator obtained by using the independence estimating equation with corrected variance this estimator can be very efficient and robust compared with maximum likelihood or the estimator of liang and zeger some comments are made concerning higher dimensional multivariate data

marginalized models for moderate to long series of longitudinal binary response data marginalized models heagerty 1999 biometrics 55 688 698 permit likelihood based inference when interest lies in marginal regression models for longitudinal binary response data two such models are the marginalized transition and marginalized latent variable models the former captures within subject serial dependence among repeated measurements with transition model terms while the latter assumes exchangeable or nondiminishing response dependence using random intercepts in this article we extend the class of marginalized models by proposing a single unifying model that describes both serial and long range dependence this model will be particularly useful in longitudinal analyses with a moderate to large number of repeated measurements per subject where both serial and exchangeable forms of response correlation can be identified we describe maximum likelihood and bayesian approaches toward parameter estimation and inference and we study the large sample operating characteristics under two types of dependence model misspecification data from the madras longitudinal schizophrenia study thara et al 1994 acta psychiatrica scandinavica 90 329 336 are analyzed

an appraisal of methods for the analysis of longitudinal categorical data with mar drop outs a number of methods for analysing longitudinal ordinal categorical data with missing at random drop outs are considered two are maximum likelihood methods maxlik which employ marginal global odds ratios to model associations the remainder use weighted or unweighted generalized estimating equations gee two of the gee use cholesky decomposed standardized residuals to model the association structure while another three extend methods developed for longitudinal binary data in which the association structures are modelled using either gaussian estimation multivariate normal estimating equations or conditional residuals simulated data sets were used to discover differences among the methods in terms of biases variances and convergence rates when the association structure is misspecified the methods were also applied to a real medical data set two of the gee methods referred to as cond and ml norm in this paper and by their originators were found to have relatively good convergence rates and mean squared errors for all sample sizes 80 120 300 considered and one more referred to as mgee in this paper and by its originators worked fairly well for all but the smallest sample size 80

mittag leffler convergent backstepping observers for coupled semilinear subdiffusion systems with spatially varying parameters abstract the purpose of this paper is to investigate the observer based boundary output feedback control for subdiffusion processes governed by coupled semilinear time fractional diffusion systems tfdss with spatially varying parameters for this backstepping technique is used to mittag leffler stabilize the coupled semilinear observer error dynamic systems we then design an observer based output feedback controller at the right boundary to realize the mittag leffler stability of the closed loop systems at hand a numerical example is finally included to test our methods

spectral assignability for distributed parameter systems with unbounded scalar control this article studies a class of control systems in a hilbert space h given dot x t ax t bu t where a generates a holomorphic semigroup on h u t is a scalar control and the control input b is possibly unbounded many systems with boundary or point control can be represented in this form the author considers the question of what eigenvalues alpha k k in i the closed loop system can have when u t is a feedback control shun hua sun s condition on alpha k k in i siam j control optim 19 1981 pp 730 743 is generalized to the case where b is unbounded but satisfies an admissibility criterion this condition is generalized further when unbounded feedback elements are allowed these results are applied to a structurally damped elastic beam with a single point actuator similar techniques also prove a spectral assignability result for a damped elastic beam with a moment control force at one end even though the associated input element is not admissible in

improved methods for the marginal analysis of longitudinal data in the presence of time dependent covariates generalized estimating equations gees are commonly used for the marginal analysis of longitudinal data in order to obtain consistent regression parameter estimates these estimating equations must be unbiased however in the presence of certain types of time dependent covariates these equations can be biased unless they incorporate the independence working correlation structure moreover in this case regression parameter estimation can be very inefficient because not all valid moment conditions are incorporated within the corresponding estimating equations therefore approaches based on the generalized method of moments or quadratic inference functions have been proposed in order to utilize all valid moment conditions however we have found in previous studies as well as the current study that such methods will not always provide valid inference and can also be improved upon in terms of finite sample regression parameter estimation therefore we propose both a modified gee approach and a method selection strategy in order to ensure valid inference with the goal of improving regression parameter estimation in a simulation study and application example we compare existing and proposed methods and demonstrate that our modified gee approach performs well and the correlation information criterion has good accuracy with respect to selecting the best approach in terms of regression parameter estimation copyright 2017 john wiley sons ltd

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

unstable supercritical discontinuous percolation transitions percolation is a pervasive concept 1 which has applications in a wide variety of natural technological and social systems 2 3 4 5 ranging from conductivity of composite materials 6 7 and polymerization 8 to epidemic spreading 9 10 11 and information diffusion 12 13

variable selection for distribution free models for longitudinal zero inflated count responses zero inflated count outcomes arise quite often in research and practice parametric models such as the zero inflated poisson and zero inflated negative binomial are widely used to model such responses like most parametric models they are quite sensitive to departures from assumed distributions recently new approaches have been proposed to provide distribution free or semi parametric alternatives these methods extend the generalized estimating equations to provide robust inference for population mixtures defined by zero inflated count outcomes in this paper we propose methods to extend smoothly clipped absolute deviation scad based variable selection methods to these new models variable selection has been gaining popularity in modern clinical research studies as determining differential treatment effects of interventions for different subgroups has become the norm rather the exception in the era of patent centered outcome research such moderation analysis in general creates many explanatory variables in regression analysis and the advantages of scad based methods over their traditional counterparts render them a great choice for addressing this important and timely issues in clinical research we illustrate the proposed approach with both simulated and real study data copyright 2016 john wiley sons ltd

classical diffusion on eden trees we study an aggregation process which gives rise to compact clusters with no loops a generalization of the node counting theorem applicable to such branched graphs trees is proved this is used to determine the spectral dimension of these clusters on square and cubic embedding lattices by monte carlo simulations the results are explained in terms of the geometric structure of these trees

violations of the independent increment assumption when using generalized estimating equation in longitudinal group sequential trials in phase 3 clinical trials ethical and financial concerns motivate sequential analyses in which the data are analyzed prior to completion of the entire planned study existing group sequential software accounts for the effects of these interim analyses on the sampling density by assuming that the contribution of subsequent increments is independent of the contribution from previous data this independent increment assumption is satisfied in many common circumstances including when using the efficient estimator however certain circumstances may dictate using an inefficient estimator and the independent increment assumption may then be violated consequences of assuming independent increments in a setting where the assumption does not hold have not been previously explored one important setting in which independent increments may not hold is the setting of longitudinal clinical trials this paper considers dependent increments that arise because of heteroscedastic and correlated data in the context of longitudinal clinical trials that use a generalized estimating equation gee approach both heteroscedasticity over time and correlation of observations within subjects may lead to departures from the independent increment assumption when using gee we characterize situations leading to greater departures in this paper despite violations of the independent increment assumption simulation results suggest that operating characteristics of sequential designs are largely maintained for typically observed patterns of accrual correlation and heteroscedasticity even when using analyses that use standard software that depends on an independent increment structure more extreme scenarios may require greater care to avoid departures from the nominal type i error rate and power copyright 2014 john wiley sons ltd

method for estimating critical exponents in percolation processes with low sampling in phase transition phenomena the estimation of the critical point is crucial for the calculation of the various critical exponents and the determination of the universality class they belong to however this is not an easy task since a large amount of realizations is needed to eliminate the noise in the data in this paper we introduce a novel method for the simultaneous estimation of the critical point p c and the critical exponent applied for the case of explosive bond percolation on two dimensional square lattices and erdos renyi networks the results show that with only a few hundred realizations it is possible to acquire accurate values for these quantities guidelines are given at the end for the applicability of the method to other cases as well

correlated percolation and tricriticality the recent proliferation of correlated percolation models models where the addition of edges and or vertices is no longer independent of other edges and or vertices has been motivated by the quest to find discontinuous percolation transitions the leader in this proliferation is what is known as explosive percolation a recent proof demonstrates that a large class of explosive percolation type models does not in fact exhibit a discontinuous transition riordan and warnke science 333 322 2011 here we discuss two lesser known correlated percolation models the k 3 core model on random graphs and the counter balance model in two dimensions both exhibiting discontinuous transitions to search for tricriticality we construct mixtures of these models with other percolation models exhibiting the more typical continuous transition using a powerful rate equation approach we demonstrate that a mixture of k 2 core and k 3 core vertices on the random graph exhibits a tricritical point however for a mixture of k core and counter balance vertices in two dimensions as the fraction of counter balance vertices is increased numerics and heuristic arguments suggest that there is a line of continuous transitions with the line ending at a discontinuous transition i e when all vertices are counter balanced interestingly these heuristic arguments may help identify the ingredients needed for a discontinuous transition in low dimensions in addition our results may have potential implications for glassy and jamming systems

estimation efficiency and tests of covariate effects with clustered binary data several approaches have been proposed to analyze clustered binary data which arise in fields such as teratology and ophthalmology these methods include mixed effects and quasi likelihood approaches as well as models that use cluster responses as covariates the three approaches measure different effects of covariates on binary responses but simple approximations relate the magnitudes of their parameters in this article we present approximations to relate the standard errors of model parameters and wald tests for covariate effects obtained from the different approaches these approximations show that wald tests involving cluster level covariates will be approximately equivalent using the different approaches however approaches that model intracluster correlation such as the mixed effects model provide more powerful tests of within cluster covariates than those that do not model the correlation simulations and example data illustrate these findings

finite size scaling theory for explosive percolation transitions the finite size scaling fss theory for continuous phase transitions has been useful in determining the critical behavior from the size dependent behaviors of thermodynamic quantities when the phase transition is discontinuous however fss approach has not been well established yet here we develop a fss theory for the explosive percolation transition arising in the erd s and renyi model under the achlioptas process a scaling function is derived based on the observed fact that the derivative of the curve of the order parameter at the critical point t c diverges with system size in a power law manner which is different from the conventional one based on the divergence of the correlation length at t c we show that the susceptibility is also described in the same scaling form numerical simulation data for different system sizes are well collapsed on the respective scaling functions

performance of generalized estimating equations in practical situations moment methods for analyzing repeated binary responses have been proposed by liang and zeger 1986 biometrika 73 13 22 and extended by prentice 1988 biometrics 44 1033 1048 in their generalized estimating equations gee both liang and zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses in this paper we discuss one step estimators i e estimators obtained from one step of the generalized estimating equations and compare their performance to that of the fully iterated estimators in small samples in simulations we find the performance of the one step estimator to be qualitatively similar to that of the fully iterated estimator when the sample size is small and the association between binary responses is high we recommend using the one step estimator to circumvent convergence problems associated with the fully iterated gee algorithm furthermore we find the gee methods to be more efficient than ordinary logistic regression with variance correction for estimating the effect of a time varying covariate

longitudinal studies of binary response data following case control and stratified case control sampling design and analysis we discuss design and analysis of longitudinal studies after case control sampling wherein interest is in the relationship between a longitudinal binary response that is related to the sampling case control variable and a set of covariates we propose a semiparametric modeling framework based on a marginal longitudinal binary response model and an ancillary model for subjects case control status in this approach the analyst must posit the population prevalence of being a case which is then used to compute an offset term in the ancillary model parameter estimates from this model are used to compute offsets for the longitudinal response model examining the impact of population prevalence and ancillary model misspecification we show that time invariant covariate parameter estimates other than the intercept are reasonably robust but intercept and time varying covariate parameter estimates can be sensitive to such misspecification we study design and analysis issues impacting study efficiency namely choice of sampling variable and the strength of its relationship to the response sample stratification choice of working covariance weighting and degree of flexibility of the ancillary model the research is motivated by a longitudinal study following case control sampling of the time course of attention deficit hyperactivity disorder adhd symptoms

analysis of repeated bouts of measurements in the framework of generalized estimating equations we consider a longitudinal study of interstitial cystitis ic in women in which the time between bouts of repeated measurements is large relative to the within bout separation in time our outcome of interest is the number of nocturnal voids that we model via quasi least squares qls in the framework of generalized estimating equations gee to account for potential intra subject correlation we directly apply a banded toeplitz correlation structure that previously was only implemented in an ad hoc approach using gee we describe this structure its appropriateness for data from the ic study and the results of our analysis we then demonstrate that correct specification of the underlying correlation structure versus incorrectly applying a simpler structure can prevent substantial losses in efficiency in estimation of the regression parameter these comparisons involve the limiting values of the estimates of the correlation parameters which are not consistent for the misspecification scenarios considered here we therefore obtain the limiting values of the qls estimates when the structure is incorrectly specified

using second order generalized estimating equations to model heterogeneous intraclass correlation in cluster randomized trials in cluster randomized trials it is commonly assumed that the magnitude of the correlation among subjects within a cluster is constant across clusters however the correlation may in fact be heterogeneous and depend on cluster characteristics accurate modeling of the correlation has the potential to improve inference we use second order generalized estimating equations to model heterogeneous correlation in cluster randomized trials using simulation studies we show that accurate modeling of heterogeneous correlation can improve inference when the correlation is high or varies by cluster size we apply the methods to a cluster randomized trial of an intervention to promote breast cancer screening

estimating the stenosis probabilities in arteriosclerosis obliterans using generalized estimating equations for each of 211 arteriosclerosis obliterans patients the degree of stenosis of arteries at four sites were examined at hiroshima university hospital to analyse the relationship between the degree of stenosis and age sex and site the generalized estimating equations using a proportional odds model for the stenosis probability with exchangeable correlation was applied to this clustered ordered polytomous data since the correlations between the responses were quite small we could apply the independence estimating equations the best mean model selected by akaike information criterion suggested that age dependency of the stenosis probability was not observed in the central sites but was observed in the peripheral sites and symmetry of the risk of stenosis was seen in the left and right sites details of the analysis will be described

recent progress in the theory of formal solutions for ode and pde in this article we describe the theory of multisummability of formal power series and discuss its application to power series solutions of ordinary and partial differential equations in particular we give some new application to a singular perturbation of a regular singular point

stabilization and structural assignment of dirichlet boundary feedback parabolic equations a parabolic equation defined on a bounded domain is considered with input acting on the boundary through the dirichlet b c expressed as a specified finite dimensional feedback of the solution the free system zero b c is assumed throughout to be unstable two main results are established first we provide in 2 a novel proof that fully solves the corresponding boundary feedback stabilization problem thereby removing an annoying assumption required by the technique of appl math optim 6 1980 pp 201 220 under certain natural algebraic conditions based on the finitely many unstable eigenvalues we establish the existence of general boundary vectors for which the corresponding feedback semigroup decays exponentially to zero in the l 2 omega operator norm or more generally in the h s omega operator norm 0 leqq s frac 1 2 however most of the paper is devoted to the second problem structural or spectral assignment which is a natural question relevant to the selfadj

maximum likelihood regression methods for paired binary data we discuss maximum likelihood methods for analysing binary responses measured at two times such as in a cross over design we construct a 2 2 table for each individual with cell probabilities corresponding to the cross classification of the responses at the two times the underlying likelihood for each individual is multinomial with four cells the three dimensional parameter space of the multinomial distribution is completely specified by the two marginal probabilities of success of the 2 2 table and an association parameter between the binary responses at the two times we examine a logistic model for the marginal probabilities of the 2 2 table for individual i the association parameters we consider are either the correlation coefficient the odds ratio or the relative risk simulations show that the parameter estimates for the logistic regression model for the marginal probabilities are not very sensitive to the parameters used to describe the association between the binary responses at the two times thus we suggest choosing the measure of association for ease of interpretation

consistent model selection and data driven smooth tests for longitudinal data in the estimating equations approach summary model selection for marginal regression analysis of longitudinal data is challenging owing to the presence of correlation and the difficulty of specifying the full likelihood particularly for correlated categorical data the paper introduces a novel bayesian information criterion type model selection procedure based on the quadratic inference function which does not require the full likelihood or quasi likelihood with probability approaching 1 the criterion selects the most parsimonious correct model although a working correlation matrix is assumed there is no need to estimate the nuisance parameters in the working correlation matrix moreover the model selection procedure is robust against the misspecification of the working correlation matrix the criterion proposed can also be used to construct a data driven neyman smooth test for checking the goodness of fit of a postulated model this test is especially useful and often yields much higher power in situations where the classical directional test behaves poorly the finite sample performance of the model selection and model checking procedures is demonstrated through monte carlo studies and analysis of a clinical trial data set

continuous percolation phase transitions of random networks under a generalized achlioptas process using finite size scaling we have investigated the percolation phase transitions of evolving random networks under a generalized achlioptas process gap during this gap the edge with a minimum product of two connecting cluster sizes is taken with a probability p from two randomly chosen edges this model becomes the erdos renyi network at p 0 5 and the random network under the achlioptas process at p 1 using both the fixed point of the size ratio s 2 s 1 and the straight line of ln s 1 where s 1 and s 2 are the reduced sizes of the largest and the second largest cluster we demonstrate that the phase transitions of this model are continuous for 0 5 0 9 beta upsilon and s 2 s 1 at critical point vary with p and the universality class of phase transitions depends on p

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

sample size calculations for randomised trials including both independent and paired data randomised trials including a mixture of independent and paired data arise in many areas of health research yet methods for determining the sample size for such trials are lacking we derive design effects algebraically assuming clustering because of paired data will be taken into account in the analysis using generalised estimating equations with either an independence or exchangeable working correlation structure continuous and binary outcomes are considered along with three different methods of randomisation cluster randomisation individual randomisation and randomisation to opposite treatment groups the design effect is shown to depend on the intracluster correlation coefficient proportion of observations belonging to a pair working correlation structure type of outcome and method of randomisation the derived design effects are validated through simulation and example calculations are presented to illustrate their use in sample size planning these design effects will enable appropriate sample size calculations to be performed for future randomised trials including both independent and paired data copyright 2017 john wiley sons ltd

percolation transitions with nonlocal constraint we investigate percolation transitions in a nonlocal network model numerically in this model each node has an exclusive partner and a link is forbidden between two nodes whose r neighbors share any exclusive pair the r neighbor of a node x is defined as a set of at most n r neighbors of x where n is the total number of nodes the parameter r controls the strength of a nonlocal effect the system is found to undergo a percolation transition belonging to the mean field universality class for r 1 2 the system undergoes a peculiar phase transition from a nonpercolating phase to a quasicritical phase where the largest cluster size g scales as g n with 0 74 1 in the marginal case with r 1 2 the model displays a percolation transition that does not belong to the mean field universality class

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