a multilevel mixed effects varying coefficient model with multilevel predictors and random effects for modeling hospitalization risk in patients on dialysis for patients on dialysis hospitalizations remain a major risk factor for mortality and morbidity we use data from a large national database united states renal data system to model time varying effects of hospitalization risk factors as functions of time since initiation of dialysis to account for the three level hierarchical structure in the data where hospitalizations are nested in patients and patients are nested in dialysis facilities we propose a multilevel mixed effects varying coefficient model mme vcm where multilevel patient and facility level random effects are used to model the dependence structure of the data the proposed mme vcm also includes multilevel covariates where baseline demographics and comorbidities are among the patient level factors and staffing composition and facility size are among the facility level risk factors to address the challenge of high dimensional integrals due to the hierarchical structure of the random effects we propose a novel two step approximate em algorithm based on the fully exponential laplace approximation inference for the varying coefficient functions and variance components is achieved via derivation of the standard errors using score contributions the finite sample performance of the proposed estimation procedure is studied through simulations

input output stabilization of linear systems on spl zopf a formal framework is set up for the discussion of generalized autoregressive with external input models of the form ay bu where a and b are linear operators with the main emphasis being on signal spaces consisting of bounded sequences parametrized by the integers different notions of stability are explored and topological notions such as the idea of a closed system are linked with questions of stabilizability in this very general context various problems inherent in using spl zopf as the time axis are analyzed in this operatorial framework

from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

strong detectability and observers conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state the concepts of strong detectability and strong observability introduced before in the literature for discrete time systems only are defined and studied for continuous time systems it is shown that there are two different concepts of strong detectability which coincide for discrete time systems algebraic conditions for either concept are given it is shown that these concepts are intimately related to the existence of strong observers i e observers that only use the output of the plant

functional t observers abstract this article is a contribution to behavioral observer theory which was started by valcher and willems in 1999 and which was recently exposed by fuhrmann in a comprehensive survey article it is also a further development of the article on t observers by oberst and the author for a given continuous or discrete time linear time invariant behavior we assume that a linear function of a trajectory e g some components can be measured we are interested in estimating another linear function of this trajectory we generalize the notions of t observability and t observers introduced by oberst and the author t denotes a multiplicatively closed subset of the ring of operators for different choices of t t observability coincides with observability reconstructibility trackability or detectability a t observer is an exact dead beat tracking or asymptotic observer we show the equivalence of t observability and the existence of t observers and give a constructive parametrization of all t observers corresponding results for proper t observers are also presented partial observation of the state of a kalman state space system compare e g fuhrmann s work is a special case of our setting and so are the observers of certain unknown components of a behavior studied by bisiacco valcher and willems the first result on functional observers in context with rosenbrock equations or polynomial matrix descriptions is due to wolovich 1974

worst case input output identification we consider worst case l1 identification of causal linear shift invariant systems from time series many results are given on general aspects of identification algorithm performance existence of optimal algorithms robust convergence and input experiment design the identification methodology studied here is compatible with the modelling requirements of modern robust control design

structural identification of muitivariabie systems by the eigenvector method abstract the structural identification of linear muitivariabie systems can be performed on the basis of the predicted percentage of reconstruction errors ppcre associated to a sequence of increasing complexity models this paper extends some previous results describing the properties of the ppcre for canonical models whose parameters are estimated by means of the eigenvector method

varying coefficient model with unknown within subject covariance for analysis of tumor growth curves in this article we develop a nonparametric estimation procedure for the varying coefficient model when the within subject covariance is unknown extending the idea of iterative reweighted least squares to the functional setting we iterate between estimating the coefficients conditional on the covariance and estimating the functional covariance conditional on the coefficients smoothing splines for correlated errors are used to estimate the functional coefficients with smoothing parameters selected via the generalized maximum likelihood the covariance is nonparametrically estimated using a penalized estimator with smoothing parameters chosen via a kullback leibler criterion empirical properties of the proposed method are demonstrated in simulations and the method is applied to the data collected from an ovarian tumor study in mice to analyze the effects of different chemotherapy treatments on the volumes of two classes of tumors

from time series to linear system part iii approximate modelling abstract in the third part of this paper the problem of finding a linear time invariant complete system which models an observed time series will be continued however in this part it will be assumed that the model is required to explain the observations only approximately this raises the question of what is meant by an approximate model and how one should judge a model against data which in a strict sense falsify the model the initial sections of this paper introduce the methodology either the maximal admissible complexity is fixed and the best fitting model in the model class is sought or the maximally tolerated misfit is fixed and the least complex model in the model class is sought this is illustrated by means of finite dimensional models where natural complexity and misfit functions suggest themselves subsequently what is meant by the complexity of a linear time invariant complete system is discussed a concrete complexity function is proposed which is defined in terms of the richness of the behaviour on finite time intervals and is in one to one correspondence with the number of inputs the number of states and the observability indices of the underlying minimal i s o system the next definition is that of the misfit between an observed time series and a system a concrete misfit function is proposed which takes into consideration the lag structure of the system and in how far the observations fail to corroborate the ar equations which define the system s behaviour how the misfit may be computed by means of the correlation function of the data is then shown these concepts are subsequently used in order to set up two algorithms for approximate modelling of an observed q dimensional time series the first algorithm fixes the maximal complexity in a sense this comes down to fixing the number and the lags of the required ar equations the second algorithm fixes the tolerated misfit it is adaptive in nature in the sense that the number and the structure of the resulting ar equations will depend on the observations these ideas and algorithms are illustrated by means of two simulated examples

observer synthesis in the behavioral approach analyzes the observer design problem in the behavioral context observability and detectability notions are first introduced and fully characterized necessary and sufficient conditions for the existence of an observer possibly an asymptotic or an exact one are introduced and a complete parameterization of all admissible observers is given the problem of obtaining observers endowed with a strictly proper transfer matrix and the design of observer based controllers are later addressed and solved finally the above issues are particularized to the case of state space systems thus showing they naturally generalize well known theorems of traditional system theory

covariance matrix selection and estimation via penalised normal likelihood summary we propose a nonparametric method for identifying parsimony and for producing a statistically efficient estimator of a large covariance matrix we reparameterise a covariance matrix through the modified cholesky decomposition of its inverse or the one step ahead predictive representation of the vector of responses and reduce the nonintuitive task of modelling covariance matrices to the familiar task of model selection and estimation for a sequence of regression models the cholesky factor containing these regression coefficients is likely to have many off diagonal elements that are zero or close to zero penalised normal likelihoods in this situation with l1 and l2 penalities are shown to be closely related to tibshirani s 1996 lasso approach and to ridge regression adding either penalty to the likelihood helps to produce more stable estimators by introducing shrinkage to the elements in the cholesky factor while because of its singularity the l1 penalty will set some elements to zero and produce interpretable models an algorithm is developed for computing the estimator and selecting the tuning parameter the proposed maximum penalised likelihood estimator is illustrated using simulation and a real dataset involving estimation of a 102 x 102 covariance matrix

brief a minimal polynomial basis solution to residual generation for fault diagnosis in linear systems a fundamental part of a fault diagnosis system is the residual generator here a new method the minimal polynomial basis approach for design of residual generators for linear systems is presented the residual generation problem is transformed into a problem of finding polynomial bases for null spaces of polynomial matrices this is a standard problem in established linear systems theory which means that numerically efficient computational tools are generally available it is shown that the minimal polynomial basis approach can find all possible residual generators and explicitly those of minimal order

continuous varying linear systems abstract we discuss implicit systems of ordinary linear differential equations with time variable coefficients their solutions in the signal space of hyperfunctions according to sato and their solution spaces called time varying linear systems or behaviours from the system theoretic point of view the basic result inspired by an analogous one for multidimensional constant linear systems is a duality theorem which establishes a categorical one one correspondence between time varying linear systems or behaviours and finitely generated modules over a suitable skew polynomial ring of differential operators this theorem is false for the signal spaces of infinitely often differentiable functions or of meromorphic hyper functions or of distributions on r it is used to obtain various results on key notions of linear system theory several new algorithms for modules over rings of differential operators and in particular new grobner basis algorithms due to insa and pauer make the system theoretic results effective

derivative estimation for longitudinal data analysis examining features of blood pressure measured repeatedly during pregnancy estimating velocity and acceleration trajectories allows novel inferences in the field of longitudinal data analysis such as estimating change regions rather than change points and testing group effects on nonlinear change in an outcome ie a nonlinear interaction in this article we develop derivative estimation for 2 standard approaches polynomial mixed models and spline mixed models we compare their performance with an established method principal component analysis through conditional expectation through a simulation study we then apply the methods to repeated blood pressure bp measurements in a uk cohort of pregnant women where the goals of analysis are to i identify and estimate regions of bp change for each individual and ii investigate the association between parity and bp change at the population level the penalized spline mixed model had the lowest bias in our simulation study and we identified evidence for bp change regions in over 75 of pregnant women using mean velocity difference revealed differences in bp change between women in their first pregnancy compared with those who had at least 1 previous pregnancy we recommend the use of penalized spline mixed models for derivative estimation in longitudinal data analysis

a novel approach to the design of unknown input observers a novel state estimator design scheme for linear dynamical systems driven by partially unknown inputs is presented it is assumed that there is no information available about the unknown inputs and thus no prior assumption is made about the nature of these inputs a simple approach for designing a reduced order unknown input observer uio with pole placement capability is proposed by carefully examining the dynamic system involved and simple algebraic manipulations it is possible to rewrite equations eliminating the unknown inputs from part of the system and to put them into a form where it could be partitioned into two interconnected subsystems one of which is directly driven by known inputs only this makes it possible to use a conventional luenberger observer with a slight modification for the purpose of estimating the state of the system as a result it is also possible to state similar necessary and sufficient conditions to those of a conventional observer for the existence of a stable estimator and also arbitrary placement of the eigenvalues of the observer the design and computational complexities involved in designing uios are greatly reduced in the proposed approach

zero time controllability and dead beat control of two dimensional behaviors in this paper two dimensional 2d discrete behaviors defined on the grid mathbb z times mathbb z and having the time as first independent variable are investigated for these behaviors by emphasizing the causality notion that is naturally associated with the time variable we introduce two new concepts of controllability algebraic characterizations of time controllability and of zero time controllability are provided and it is shown that behaviors endowed with these properties admit special decompositions next the dead beat control dbc problem and the concept of admissible dbc are introduced and related to the zero time controllability property differently from what happens with one dimensional behaviors zero time controllability does not ensure the existence of regular dbcs and stronger algebraic properties need to be imposed on the behavior finally necessary and sufficient conditions for the existence of a dbc that makes the resulting behavior both strongly autonomous and nilpot

on observability subspaces the paper presents an in depth study of topics in geometric control pertaining to observer theory from a functional point of view we give characterizations of several classes of subspaces including observability almost observability and reconstructibility subspaces we solve completely the problem of spectral assignability for observer dynamics by generalizing rosenbrock s pole placement theorem these results are then applied to observer theory

notes on the definition of behavioural controllability we take another look at the behavioural definition of controllability for discrete 1d systems and its extension to multidimensional nd systems defined on z n or n n we suggest that the current definition for nd systems is inappropriate for systems defined on the domain n n and that care has to be taken even with the 1d definition we propose a new definition which applies to all standard classes of discrete nd systems

functional mixed effects models in this article a new class of functional models in which smoothing splines are used to model fixed effects as well as random effects is introduced the linear mixed effects models are extended to nonparametric mixed effects models by introducing functional random effects which are modeled as realizations of zero mean stochastic processes the fixed functional effects and the random functional effects are modeled in the same functional space which guarantee the population average and subject specific curves have the same smoothness property these models inherit the flexibility of the linear mixed effects models in handling complex designs and correlation structures can include continuous covariates as well as dummy factors in both the fixed or random design matrices and include the nested curves models as special cases two estimation procedures are proposed the first estimation procedure exploits the connection between linear mixed effects models and smoothing splines and can be fitted using existing software the second procedure is a sequential estimation procedure using kalman filtering this algorithm avoids inversion of large dimensional matrices and therefore can be applied to large data sets a generalized maximum likelihood gml ratio test is proposed for inference and model selection an application to comparison of cortisol profiles is used as an illustration

a penalized spline approach to functional mixed effects model analysis summary in this work we propose penalized spline based methods for functional mixed effects models with varying coefficients we decompose longitudinal outcomes as a sum of several terms a population mean function covariates with time varying coefficients functional subject specific random effects and residual measurement error processes using penalized splines we propose nonparametric estimation of the population mean function varying coefficient random subject specific curves and the associated covariance function which represents between subject variation and the variance function of the residual measurement errors which represents within subject variation proposed methods offer flexible estimation of both the population level and subject level curves in addition decomposing variability of the outcomes as a between subject and a within subject source is useful in identifying the dominant variance component therefore optimally model a covariance function we use a likelihood based method to select multiple smoothing parameters furthermore we study the asymptotics of the baseline p spline estimator with longitudinal data we conduct simulation studies to investigate performance of the proposed methods the benefit of the between and within subject covariance decomposition is illustrated through an analysis of berkeley growth data where we identified clearly distinct patterns of the between and within subject covariance functions of children s heights we also apply the proposed methods to estimate the effect of anti hypertensive treatment from the framingham heart study data

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

a behavioral approach to estimation and dead beat observer design with applications to state space models the observer design problem is investigated in the context of linear left shift invariant discrete behaviors whose trajectories have supports on z necessary and sufficient conditions for the existence of a dead beat observer of some relevant variables from some measured ones in the presence of some unmeasured and irrelevant variables are introduced and a complete parametrization of all dead beat observers is given equivalent conditions for the existence of causal dead beat observers are then derived finally several classical problems addressed for state space models like state estimation the design of unknown input observers or the design of fault detectors and identifiers possibly in the presence of disturbances are cast in this general framework and the aforementioned equivalent conditions and parametrizations are specialized to these cases

on the asymptotics of marginal regression splines with longitudinal data summary there have been studies on how the asymptotic efficiency of a nonparametric function estimator depends on the handling of the within cluster correlation when nonparametric regression models are used on longitudinal or cluster data in particular methods based on smoothing splines and local polynomial kernels exhibit different behaviour we show that the generalized estimation equations based on weighted least squares regression splines for the nonparametric function have an interesting property the asymptotic bias of the estimator does not depend on the working correlation matrix but the asymptotic variance and therefore the mean squared error is minimized when the true correlation structure is specified this property of the asymptotic bias distinguishes regression splines from smoothing splines

dead beat control in the behavioral approach in this paper the concepts of controllability and zero controllability of a variable w appearing either in a standard or in a latent variable description as manifest variable are introduced and characterized by assuming this perspective the dead beat control dbc problem is posed as the problem of designing a controller involving both w and the latent variable c such that for the resulting controlled behavior the variable w goes to zero in a finite number of steps in every trajectory zero controllability of w turns out to be a necessary and sufficient condition for the existence of admissible dbcs as well as for the existence of regular dbcs the class of minimal dbcs namely dbcs with the least possible number of rows is singled out and a parametrization of such controllers is provided finally a necessary and sufficient condition for the existence of dbcs that can be implemented via a feedback law for which w is the input and the latent variable c the corresponding output is provided

analysis of longitudinal data with semiparametric estimation of covariance function improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data both involve estimation of the covariance function yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points a class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed a kernel estimator for estimating the nonparametric variance function is developed two methods for estimating parameters in the correlation structure a quasi likelihood approach and a minimum generalized variance method are proposed a semiparametric varying coefficient partially linear model for longitudinal data is introduced and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed sampling properties of the proposed estimation procedures are studied and asy

observer based fault detection and isolation for structured systems fault detection and isolation fdi problems are here consid ered for linear systems with faults and disturbances we design a set of ob server based residuals in such a way that the transfer from the disturbances to the residuals is zero and the transfer from the faults to the residuals al lows fault isolation we are interested in obtaining a transfer function from faults to residuals with either a diagonal structure i e a dedicated struc tured residuals set or a triangular one we deal with this problem when the system under consideration is structured that is the entries of the system matrices are either fixed zeros or free parameters to a structured system one can associate in a natural way a directed graph we can then provide necessary and sufficient conditions under which the fdi problems have a solution for almost any value of the free parameters these conditions are simply expressed in terms of input output paths in the associated graph index terms fault detection and isolation graph theory model based approach structured residuals structured systems

a new parametrization of linear observers the estimation of unknown variables of a system the plant based on a set of known or measured variables is a fundamental and widely studied problem of system theory we investigate observers that solve this task in the behavioral setting our framework includes the discrete and the continuous linear time invariant cases and various notions of when a signal is considered to be small we characterize the observers that guarantee a small estimation error as those containing the essential part of the plant behavior a constructive one to one parametrization of all such observers follows naturally from this result

a general hankel norm approximation scheme for linear recursive filtering let x t and y t be stochastic processes which are weakly stationary and stationarily correlated we consider the problem of finding an approximate recursive low dimensional filter of x t based on the observation of the past of y t using hankel norm techniques several estimation problems have been investigated in the past using these techniques we present here a general framework which includes many of these approaches as special cases we also discuss some new applications the approximate filter so constructed allows for an a priori bound on the estimation error

disturbance decoupled observer design a unified viewpoint this paper is concerned with the observer design for linear systems with unknown inputs an equivalent system which is free of unknown inputs is derived for the purpose of the observer design based on the equivalent system description one can design an observer full order reduced order minimal order or functional for linear systems with unknown inputs using well known techniques it is shown that the equivalent system exists as long as there exists a disturbance decoupled observer two sets of the known existence conditions of disturbance decoupled observers are proved to be equivalent

on behavior homomorphisms and system equivalence in this paper we introduce the concept of a behavior homomorphisms and isomorphisms and use it to present a uni ed approach to the study of equivalence of di erent behavior representations concentrating on a special representation we call normalized arma narma representation c 2001 elsevier science b v all rights reserved

bayesian mixture of splines for spatially adaptive nonparametric regression summary a bayesian approach is presented for spatially adaptive nonparametric regression where the regression function is modelled as a mixture of splines each component spline in the mixture has associated with it a smoothing parameter which is defined over a local region of the covariate space these local regions overlap such that individual data points may lie simultaneously in multiple regions consequently each component spline has attached to it a weight at each point of the covariate space and by allowing the weight of each component spline to vary across the covariate space a spatially adaptive estimate of the regression function is obtained the number of mixing components is chosen using a modification of the bayesian information criteria we study the procedure analytically and show by simulation that it compares favourably to three competing techniques these techniques are the bayesian regression splines estimator of smith kohn 1996 the hybrid adaptive spline estimator of luo wahba 1997 and the automatic bayesian curve fitting estimator of denison et al 1998 the methodology is illustrated by modelling global air temperature anomalies all the computations are carried out efficiently using markov chain monte carlo

asymptotic properties of penalized spline estimators we study the class of penalized spline estimators which enjoy similarities to both regression splines without penalty and with fewer knots than data points and smoothing splines with knots equal to the data points and a penalty controlling the roughness of the fit depending on the number of knots sample size and penalty we show that the theoretical properties of penalized regression spline estimators are either similar to those of regression splines or to those of smoothing splines with a clear breakpoint distinguishing the cases we prove that using fewer knots results in better asymptotic rates than when using a large number of knots we obtain expressions for bias and variance and asymptotic rates for the number of knots and penalty parameter

on some special features which are peculiar to discrete time behaviors with trajectories on z abstract in this paper discrete time systems defined on z are analyzed within the behavioral approach once the main internal properties of such behaviors have been defined and characterized our attention is focused on those aspects that make behaviors defined on z dramatically different from behaviors defined on z specifically the general lack of permanence and the role of finite support trajectories several consequences of these two facts are analyzed in particular it is shown that while controllable behaviors with trajectories on z can always be identified by means of a finite set of finite support trajectories for controllable behaviors with trajectories on z this is no more possible

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

enhancement of robustness in observer based fault detection a prerequisite for the feasibility of the technique of observer based fault detection and isolation fdi in dynamic systems is a satisfactory robustness with respect to modelling uncertainties this paper surveys the most relevant methods to increase the robustness in both the stage of residual generation and residual evaluation among these methods are the generalized observer scheme the robust parity space check the unknown input and h observer scheme the decorrelation filter and the concept of adaptive threshold selection it is pointed out that the unknown input observer concept which provides perfect decoupling from the modelling errors or its optimal approximation with the aid of h techniques constitutes a general framework of robust residual generation that generalizes and unifies numerous other approaches among them the parity space and detection filter approach it is further shown that this fdi method can even be applied to a certain class of nonlinear systems

system theory for system identification abstract prediction and control problems require for their solution mathematical models in the form of dynamic systems in system theory the approach to this problem is to investigate realization problems for system identification novel in this paper is the emphasis on the realization problem for observation based realizations and on the realization problem for control a major aspect of these realization problems is computation and complexity algebraic approaches to realization problems may lead to the distinction of subclasses of systems with required finiteness properties to decompositions and to abstractions for hierarchical systems

flexible estimation of covariance function by penalized spline with application to longitudinal family data longitudinal data are routinely collected in biomedical research studies a natural model describing longitudinal data decomposes an individual s outcome as the sum of a population mean function and random subject specific deviations when parametric assumptions are too restrictive methods modeling the population mean function and the random subject specific functions nonparametrically are in demand in some applications it is desirable to estimate a covariance function of random subject specific deviations in this work flexible yet computationally efficient methods are developed for a general class of semiparametric mixed effects models where the functional forms of the population mean and the subject specific curves are unspecified we estimate nonparametric components of the model by penalized spline p spline biometrics 2001 57 253 259 and reparameterize the random curve covariance function by a modified cholesky decomposition biometrics 2002 58 121 128 which allows for unconstrained estimation of a positive semidefinite matrix to provide smooth estimates we penalize roughness of fitted curves and derive closed form solutions in the maximization step of an em algorithm in addition we present models and methods for longitudinal family data where subjects in a family are correlated and we decompose the covariance function into a subject level source and observation level source we apply these methods to the multi level framingham heart study data to estimate age specific heritability of systolic blood pressure nonparametrically copyright 2011 john wiley sons ltd

penalized spline models for functional principal component analysis summary we propose an iterative estimation procedure for performing functional principal component analysis the procedure aims at functional or longitudinal data where the repeated measurements from the same subject are correlated an increasingly popular smoothing approach penalized spline regression is used to represent the mean function this allows straightforward incorporation of covariates and simple implementation of approximate inference procedures for coefficients for the handling of the within subject correlation we develop an iterative procedure which reduces the dependence between the repeated measurements that are made for the same subject the resulting data after iteration are theoretically shown to be asymptotically equivalent in probability to a set of independent data this suggests that the general theory of penalized spline regression that has been developed for independent data can also be applied to functional data the effectiveness of the proposed procedure is demonstrated via a simulation study and an application to yeast cell cycle gene expression data

state observers for discrete time linear systems with unknown inputs in the paper the problem of designing a full order state observer for a general discrete time linear system with unknown inputs is analyzed necessary and sufficient conditions for the existence either of an asymptotic or of a deadbeat observer are provided and a constructive design procedure together with some examples are discussed finally the equivalence of these conditions for problem solvability with those derived in previous contributions by means of different approaches is explicitly proved

on the asymptotics of penalized splines summavry we study the asymptotic behaviour of penalized spline estimators in the univariate case we use b splines and a penalty is placed on mth order differences of the coefficients the number of knots is assumed to converge to infinity as the sample size increases we show that penalized splines behave similarly to nadaraya watson kernel estimators with equivalent kernels depending upon m the equivalent kernels we obtain for penalized splines are the same as those found by silverman for smoothing splines the asymptotic distribution of the penalized spline estimator is gaussian and we give simple expressions for the asymptotic mean and variance provided that it is fast enough the rate at which the number of knots converges to infinity does not affect the asymptotic distribution the optimal rate of convergence of the penalty parameter is given penalized splines are not design adaptive

a new design approach to unknown input observers this paper proposes a fundamentally new unknown input observer uio which has uniquely r decoupled modes provides r linearly independent combinations of plant system states and has zero gain to all p unknown inputs the parameter r is adjustable if the plant system satisfies the conditions of the existing uio then r n plant system order and there is no difference between our uio and the existing regular uio however if the plant system satisfies either of the following two significantly more general conditions m p m is the number of plant output measurements and at least one stable transmission zero then 1 n and our uio can still generate some constrained state feedback control signals hence this new uio can completely unify the regular uio r n and the static output feedback r m the two basic feedback structures of modern control theory far from being unified before

observers for linear systems with unknown inputs a direct design procedure of a full order observer for a linear system with unknown inputs is presented using straightforward matrix calculations some examples are given in these examples a reduced order observer is also derived it is shown that this may restrict the rate of convergence of some state estimates

when is a storage function a state function in discrete time the purpose of this paper is to investigate when a storage function is a state function in discrete time as shown by trentelman and willems systems control lett 32 1997 pp 249 259 siam j control optim 36 1998 pp 1703 1749 every storage function is a state function in continuous time at first glance the same claim seems to hold also in discrete time contrary to this expectation this is not true in general in fact the discrete time counterpart involves not only some different but also some more difficult issues compared with the continuous time case this paper addresses these issues exactly and shows that every nonnegative storage function is a state function of a supply rate with a linear time invariant dynamical system in discrete time

dead beat observer synthesis in the paper the observer design problem is investigated in the context of linear left shift invariant discrete behaviors whose trajectories have support on the positive axis observability and reconstructibility properties of certain manifest variables from certain others in the presence of latent variables are defined and fully characterized necessary and sufficient conditions for the existence of either a dead beat or an exact observer are introduced and a complete parametrization of all dead beat observers is given

simple fitting of subject specific curves for longitudinal data we present a simple semiparametric model for fitting subject specific curves for longitudinal data individual curves are modelled as penalized splines with random coefficients this model has a mixed model representation and it is easily implemented in standard statistical software we conduct an analysis of the long term effect of radiation therapy on the height of children suffering from acute lymphoblastic leukaemia using penalized splines in the framework of semiparametric mixed effects models the analysis revealed significant differences between therapies and showed that the growth rate of girls in the study cannot be fully explained by the group average curve and that individual curves are necessary to reflect the individual response to treatment we also show how to implement these models in s plus and r in the appendix

on behaviors and convolutional codes it is well known that a convolutional code is essentially a linear system defined over a finite field in this paper we elaborate on this connection we define a convolutional code as the dual of a complete linear behavior in the sense of willems 1979 using ideas from systems theory we describe a set of generalized first order descriptions for convolutional codes as an application of these ideas we present a new algebraic construction for convolutional codes

nonparametric estimation of covariance structure in longitudinal data summary in longitudinal studies the effect of various treatments over time is usually of prime interest however observations on the same subject are usually correlated and any analysis should account for the underlying covariance structure a nonparametric estimate of the covariance structure is useful either as a guide to the formulation of a parametric model or as the basis for formal inference without imposing parametric assumptions the sample covariance matrix provides such an estimate when the data consist of a short sequence of measurements at a common set of time points on each of many subjects but is impractical when the data are severely unbalanced or when the sequences of measurements on individual subjects are long relative to the number of subjects the variogram of residuals from a saturated model for the mean response has previously been suggested as a nonparametric estimator for covariance structure assuming stationarity in this paper we consider kernel weighted local linear regression smoothing of sample variogram ordinates and of squared residuals to provide a nonparametric estimator for the covariance structure without assuming stationarity the value of the estimator as a diagnostic tool is demonstrated in two applications one to a set of data concerning the blood pressure of newborn babies in an intensive care unit and the other to data on the time evolution of cd4 cell numbers in hiv seroconverters

varying coefficient models and basis function approximations for the analysis of repeated measurements summary a global smoothing procedure is developed using basis function approximations for estimating the parameters of a varying coefficient model with repeated measurements inference procedures based on a resampling subject bootstrap are proposed to construct confidence regions and to perform hypothesis testing conditional biases and variances of our estimators and their asymptotic consistency are developed explicitly finite sample properties of our procedures are investigated through a simulation study application of the proposed approach is demonstrated through an example in epidemiology in contrast to the existing methods this approach applies whether or not the covariates are timeinvariant and does not require binning of the data when observations are sparse at distinct observation times

deciding first order properties of locally tree decomposable structures we introduce the concept of a class of graphs or more generally relational structures being locally tree decomposable there are numerous examples of locally tree decomposable classes among them the class of planar graphs and all classes of bounded valence or of bounded tree width we also consider a slightly more general concept of a class of structures having bounded local tree width we show that for each property of structures that is definable in first order logic and for each locally tree decomposable class c of structures there is a linear time algorithm deciding whether a given structure a c has property for classes c of bounded local tree width we show that for every k 1 there is an algorithm solving the same problem in time o n1 1 k where n is the cardinality of the input structure

a marginal approach to reduced rank penalized spline smoothing with application to multilevel functional data multilevel functional data are collected in many biomedical studies for example in a study of the effect of nimodipine on patients with subarachnoid hemorrhage sah patients underwent multiple 4 hr treatment cycles within each treatment cycle subjects vital signs were reported every 10 min these data have a natural multilevel structure with treatment cycles nested within subjects and measurements nested within cycles most literature on nonparametric analysis of such multilevel functional data focuses on conditional approaches using functional mixed effects models however parameters obtained from the conditional models do not have direct interpretations as population average effects when population effects are of interest we may employ marginal regression models in this work we propose marginal approaches to fit multilevel functional data through penalized spline generalized estimating equation penalized spline gee the procedure is effective for modeling multilevel correlated generalized

optimal hankel norm identification of dynamical systems abstract the problem of optimal approximate system identification is addressed with a newly defined measure of misfit between observed time series and linear time invariant models the behavioral framework is used as a suitable axiomatic setting for a non parametric introduction of system complexity and allows for a notion of misfit of dynamical systems that is independent of system representations the misfit function introduced here is characterized in terms of the induced norm of a hankel operator associated with the data and a co inner kernel representation of a model sets of pareto optimal models are defined as feasible trade offs between complexity and misfit of models and it is shown how all pareto optimal models are characterized as exact models of compressed data sets obtained from hankel norm approximations of data matrices this leads to new conceptual algorithms for optimal approximate identification of time series 1997 elsevier science ltd

survey paper structured low rank approximation and its applications fitting data by a bounded complexity linear model is equivalent to low rank approximation of a matrix constructed from the data the data matrix being hankel structured is equivalent to the existence of a linear time invariant system that fits the data and the rank constraint is related to a bound on the model complexity in the special case of fitting by a static model the data matrix and its low rank approximation are unstructured we outline applications in system theory approximate realization model reduction output error and errors in variables identification signal processing harmonic retrieval sum of damped exponentials and finite impulse response modeling and computer algebra approximate common divisor algorithms based on heuristics and local optimization methods are presented generalizations of the low rank approximation problem result from different approximation criteria e g weighted norm and constraints on the data matrix e g nonnegativity related problems are rank minimization and structured pseudospectra

fault detection via factorization approach abstract problems of designing fault detection and identification filters in the frequency domain are formulated and solved using the factorization approach a characterization of all fault detection filters is derived this enables the derivation of necessary and sufficient conditions for the existence of fault identification as well as detection and isolation filters it is shown that these conditions are a generalization of existing results the formulas of constructing the filters are also derived in comparison with the algorithms given in previous work they are computationally straightforward and simple finally the proposed method for designing fault identification filters is extended so that more practical cases can be handled

fault detection and isolation observers a design of reduced order observers is proposed for linear time invariant systems with unknown inputs including unknown measurement disturbances based on the unknown input observer design a systematic treatment of designing fault detection and isolation fdi observers is provided the core of the fdi observer design is to find an observable subsystem where the faults of interest show up and the rest of the faults disappear the fdi observer design procedure has a clear physical meaning robust fdi observers for uncertain systems can also be obtained using the fdi observer design provided the uncertainties of the system can be formulated as unknown inputs it is shown that the parity equations of another important fdi method can be generated in an elegant way using a dead beat fdi observer scheme directly in the time domain examples are included to show some concepts and to illustrate the fdi observer design method

some asymptotic results on generalized penalized spline smoothing the paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size the proof is provided in a generalized smoothing model allowing for non normal responses the results are extended in two ways first assuming the spline coefficients to be a priori normally distributed links the smoothing framework to generalized linear mixed models we consider the asymptotic rates such that the laplace approximation is justified and the resulting fits in the mixed model correspond to penalized spline estimates secondly we make use of a fully bayesian viewpoint by imposing an a priori distribution on all parameters and coefficients we argue that with the postulated rates at which the spline basis dimension increases with the sample size the posterior distribution of the spline coefficients is approximately normal the validity of this result is investigated in finite samples by comparing markov chain monte carlo results with their asymptotic approximation in a simulation study

on the parametrization of conditioned invariant subspaces and observer theory the present paper is an in depth analysis of the set of conditioned invariant subspaces of a given observable pair c a we do this analysis in two different ways one based on polynomial models starting with a characterization obtained in p a fuhrmann linear operators and systems in hilbert space 1981 ieee trans automat control ac 26 1981 284 the other being a state space approach toeplitz operators projections in polynomial and rational models wiener hopf factorizations and factorization indices all appear and are tools in the characterizations we single out an important subclass of conditioned invariant subspaces namely the tight ones which already made an appearance in p a fuhrmann u helmke systems control lett 30 1997 217 a precursor of the present paper of particular importance for the study of the parametrization of the set of conditioned invariant subspaces of an observable pair c a is the structural map that associates with any reachable pair with only the input dimension constrained a uniquely determined conditioned invariant subspace the construction of this map uses polynomial models and the shift realization new objects the partial observability and reachability matrices are introduced which are needed for the state space characterizations kernel and image representations for conditioned invariant subspaces are derived uniqueness of a kernel representation of a conditioned invariant subspace is shown to be equivalent to tightness we pass on to an analysis and derivation of the kronecker hermite canonical form for full column rank rectangular polynomial matrices this extends the work of a e eckberg a characterization of linear systems via polynomial matrices and module theory ph d thesis mit cambridge ma 1974 g d forney siam j control optim 13 1973 493 and d hinrichsen h f munzner and d pratzel wolters systems

nonparametric estimation of large covariance matrices of longitudinal data summary estimation of an unstructured covariance matrix is difficult because of its positivedefiniteness constraint this obstacle is removed by regressing each variable on its predecessors so that estimation of a covariance matrix is shown to be equivalent to that of estimating a sequence of varying coefficient and varying order regression models our framework is similar to the use of increasing order autoregressive models in approximating the covariance matrix or the spectrum of a stationary time series as an illustration we adopt fan zhang s 2000 two step estimation of functional linear models and propose nonparametric estimators of covariance matrices which are guaranteed to be positive definite for parsimony a suitable order for the sequence of auto regression models is found using penalised likelihood criteria like aic and bic some asymptotic results for the local polynomial estimators of components of a covariance matrix are established two longitudinal datasets are analysed to illustrate the methodology a simulation study reveals the advantage of the nonparametric covariance estimator over the sample covariance matrix for large covariance matrices

fixed parameter tractability and completeness ii on completeness for w 1 abstract for many fixed parameter problems that are trivially solvable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is solvable in time bounded by a polynomial of degree c where c is a constant independent of k in a previous paper the w hierarchy of parameterized problems was defined and complete problems were identified for the classes w t for t 2 our main result shows that independent set is complete for w 1

the rank of reduced dispersion matrices psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements psychometricians concentrate on cases in which low rank can be attained preferably rank one the spearman case econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one the frisch case in this paper we give an extensive historial discussion of both fields we prove the two key results in a more satisfactory and uniform way we point out various small errors and misunderstandings and we present a methodological comparison of factor analysis and regression on the basis of our results

controllability of 2 d systems the concept of controllability of 2 d systems is introduced in a behavioral framework this property is defined as a systems concept and is characterized in terms of system representations state space realizations for controllable 2 d systems are presented the structure of state space systems is analyzed and the notions of trimness reachability and observability are introduced and characterized these realizations do not depend on any assumptions concerning causality

testing first order properties for subclasses of sparse graphs we present a linear time algorithm for deciding first order fo properties in classes of graphs with bounded expansion a notion recently introduced by neset il and ossona de mendez this generalizes several results from the literature because many natural classes of graphs have bounded expansion graphs of bounded tree width all proper minor closed classes of graphs graphs of bounded degree graphs with no subgraph isomorphic to a subdivision of a fixed graph and graphs that can be drawn in a fixed surface in such a way that each edge crosses at most a constant number of other edges we deduce that there is an almost linear time algorithm for deciding fo properties in classes of graphs with locally bounded expansion more generally we design a dynamic data structure for graphs belonging to a fixed class of graphs of bounded expansion after a linear time initialization the data structure allows us to test an fo property in constant time and the data structure can be updated in constant time after addition deletion of an edge provided the list of possible edges to be added is known in advance and their simultaneous addition results in a graph in the class all our results also hold for relational structures and are based on the seminal result of neset il and ossona de mendez on the existence of low tree depth colorings

internal model principles for observers this paper deals with the observer problem for dynamical systems in a behavioral context we are given a dynamical system together with a partition of the system variables into a set of known or measured variables and a set of unknown to be estimated variables the observer problem is to find a system that produces an estimate of the unknown variables on the basis of the known or measured variables for a given plant and partition we establish a characterization of all error behaviors that can be achieved by interconnecting the plant with some observer the main result of this paper is a very general behavioral formulation of an internal model principle for observers we will show that a nonintrusive observer achieves a stable error behavior if and only if in addition to a detectability condition on the observer the observer behavior contains the anti stabilizable part of the plant behavior

nonparametric mixed effects models for unequally sampled noisy curves we propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients the method is applicable when the individual curves are sampled at variable and irregularly spaced points this produces a low rank low frequency approximation to the covariance structure which can be estimated naturally by the em algorithm smooth curves for individual trajectories are constructed as best linear unbiased predictor blup estimates combining data from that individual and the entire collection this framework leads naturally to methods for examining the effects of covariates on the shapes of the curves we use model selection techniques akaike information criterion aic bayesian information criterion bic and cross validation to select the number of breakpoints for the spline approximation we believe that the methodology we propose provides a simple flexible and computationally efficient means of functional data analysis