survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

t equivariant k theory of generalized flag varieties let g be a kac moody group with borel subgroup b and compact maximal torus t analogous to kostant and kumar kostant b kumar s 1986 proc nati acad sci usa 83 1543 1545 we define a certain ring y purely in terms of the weyl group w associated to g and its action on t by dualizing y we get another ring 1 which we prove is canonically isomorphic with the t equivariant ktheory kt g b of gib now kt g b apart from being an algebra over kt pt a t also has a weyl group action and moreover kt g b admits certain operators dw w similar to the demazure operators defined on a t we prove that these structures on kt g b come naturally from the ring y by evaluating the a t module w at 1 we recover k g b together with the above mentioned structures we believe that many of the results of this paper are new in the finite case i e g is a finite dimensional semisimple group over c

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

on the conjecture o of ggi for g p abstract in this paper we show that general homogeneous manifolds g p satisfy conjecture o of galkin golyshev and iritani which underlies gamma conjectures i and ii of them our main tools are the quantum chevalley formula for g p and a theory on nonnegative matrices including perron frobenius theorem

deletion diagnostics for generalised estimating equations summary deletion diagnostics are proposed for generalised estimating equations the diagnostics consider leverage and residuals to measure the influence of a subset of observations on the estimated regression parameters and on the estimated values of the linear predictor computational formulae are provided which correspond to the influence of a single observation and of an entire cluster of correlated observations additionally diagnostics are given which approximate the effect of deletion of an arbitrary subset of observations under a model with general covariance structure and arbitrary link function extending proposition 3 of christensen pearson johnson 1992 the proposed measures are applied to medical data

influence measures for logistic regression another point of view summary several measures of influence for logistic regression have been suggested these measures have been developed for the purpose of identifying observations which are influential relative to the estimation of the regression coefficients vector and the deviance we propose measures for detecting influence relative to the determination of probabilities and the classification of future observations the relationships among measures are indicated

improved nonnegative estimation of variance components in some mixed models with unbalanced data mixed models involving two variance components are considered when the data are unbalanced one variance component corresponding to a random effect and a second variance component corresponding to experimental error for estimating the random effect variance component several nonnegative estimators are derived the estimators have explicit expressions and are easily computable the performances of the various estimators are studied by simulating their mean squared errors and biases using some one way models with unbalanced data and specific recommendations are made on the choice of the nonnegative estimator to be used in practical applications some generalizations are obtained for estimating a randomeffect variance component in a more general model with unbalanced data the analysis of variance anova estimator and the proposed estimators are computed using real data for two examples the anova estimator has a value that is substantially different from the other estimators in the two examples the sim

perturbation and scaled cook s distance cook s cook 1977 distance is one of the most important diagnostic tools for detecting influential individual or subsets of observations in linear regression for cross sectional data however for many complex data structures e g longitudinal data no rigorous approach has been developed to address a fundamental issue deleting subsets with different numbers of observations introduces different degrees of perturbation to the current model fitted to the data and the magnitude of cook s distance is associated with the degree of the perturbation the aim of this paper is to address this issue in general parametric models with complex data structures we propose a new quantity for measuring the degree of the perturbation introduced by deleting a subset we use stochastic ordering to quantify the stochastic relationship between the degree of the perturbation and the magnitude of cook s distance we develop several scaled cook s distances to resolve the comparison of cook s distance for different subset deletions theoretical and numerical examples are examined to highlight the broad spectrum of applications of these scaled cook s distances in a formal influence analysis

confidence intervals for a variance ratio or for heritability in an unbalanced mixed linear model a procedure is presented for constructing an exact confidence interval for the ratio of the two variance components in a possibly unbalanced mixed linear model that contains a single set of m random effects this procedure can be used in animal and plant breeding problems to obtain an exact confidence interval for a heritability the confidence interval can be defined in terms of the output of a least squares analysis it can be computed by a graphical or iterative technique requiring the diagonalization of an m x m matrix or alternatively the inversion of a number of m x m matrices confidence intervals that are approximate can be obtained with much less computational burden using either of two approaches the various confidence interval procedures can be extended to some problems in which the mixed linear model contains more than one set of random effects corresponding to each interval procedure is a significance test and one or more estimators

information content of cluster period cells in stepped wedge trials stepped wedge and other multiple period cluster randomized trials which collect data from multiple clusters across multiple time periods are being conducted with increasing frequency statistical research into these designs has not kept apace in particular some stepped wedge designs with missing cluster period cells have been proposed without any formal justification indeed there are no general guidelines regarding which cells of a stepped wedge design contribute the least information toward estimation of the treatment effect and correspondingly which may be preferentially omitted in this article we define a metric of the information content of cluster period cells entire treatment sequences and entire periods of the standard stepped wedge design as the increase in variance of the estimator of the treatment effect when that cell sequence or period is omitted we show that the most information rich cells are those that occur immediately before or after treatment switches but also that there are additional cells that contribute almost as much to the estimation of the treatment effect however the information content patterns depend on the assumed correlation structure for the repeated measurements within a cluster

case deletion diagnostics for linear mixed models based on the q function the conditional expectation of the logarithm of the joint likelihood between responses and random effects we propose a case deletion approach to identify influential subjects and influential observations in linear mixed models the models considered here are very broad in the sense that any covariance structures can be specified in the covariance matrices of the random effects and random errors analytically explicit forms of diagnostic measures for the fixed effects and variance components are provided comparisons with existing methods including likelihood based case deletion and local influence methods are made numerical results including real data analysis and simulation studies are presented for both illustration and comparison this article has supplementary material online

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

monte carlo comparison of anova mivque reml and ml estimators of variance components for the one way classification random model with unbalanced data we compare five estimators of 2 a and 2 e the among and within treatments variance components analysis of variance anova maximum likelihood ml restricted maximum likelihood reml and two minimum variance quadratic unbiased mivque estimators mivque 0 is mivque with a priori values 0 and 1 mivque a is mivque with the anova estimates used as a priori s we enforce nonnegativity for all estimators setting any negative estimate to zero in accord with usual practice the estimators are compared through their biases and mse s estimated by monte carlo simulation our results indicate that the anova estimators perform well except with seriously unbalanced data when 2 a 2 e 1 ml is excellent when 2 a 2 e 0 5 and mivque a is adequate further iteration to the reml estimates is unnecessary when 2 a 2 e 1 mivque 0 the default for sass procedure varcomp is poor for estimating 2 a and very poor for 2 e

pole placement via static output feedback is np hard this note proves that the problem of pole placement via static output feedback for linear time invariant systems is np hard

effects of residual smoothing on the posterior of the fixed effects in disease mapping models disease mapping models for areal data often have fixed effects to measure the effect of spatially varying covariates and random effects with a conditionally autoregressive car prior to account for spatial clustering in such spatial regressions the objective may be to estimate the fixed effects while accounting for the spatial correlation but adding the car random effects can cause large changes in the posterior mean and variance of fixed effects compared to the nonspatial regression model this article explores the impact of adding spatial random effects on fixed effect estimates and posterior variance diagnostics are proposed to measure posterior variance inflation from collinearity between the fixed effect covariates and the car random effects and to measure each region s influence on the change in the fixed effect s estimates by adding the car random effects a new model that alleviates the collinearity between the fixed effect covariates and the car random effects is developed and extensions of these methods to point referenced data models are discussed

odd symplectic groups on definit des groupes symplectiques sur des espaces vectoriels de dimension impaire ces groupes de lie ne sont ni simples ni reductifs on obtient une formule de caracteres pour certaines representations tensorielles de ces groupes

adaptive boundary control for unstable parabolic pdes part i lyapunov design we develop adaptive controllers for parabolic partial differential equations pdes controlled from a boundary and containing unknown destabilizing parameters affecting the interior of the domain these are the first adaptive controllers for unstable pdes without relative degree limitations open loop stability assumptions or domain wide actuation it is the first necessary step towards developing adaptive controllers for physical systems such as fluid thermal and chemical dynamics where actuation can be only applied non intrusively the dynamics are unstable and the parameters such as the reynolds rayleigh prandtl or peclet numbers are unknown because they vary with operating conditions our method builds upon our explicitly parametrized control formulae to avoid solving riccati or bezout equations at each time step most of the designs we present are state feedback but we present two benchmark designs with output feedback which have infinite relative degree

influence diagnostics and outlier tests for semiparametric mixed models summary semiparametric mixed models are useful in biometric and econometric applications especially for longitudinal data maximum penalized likelihood estimators mples have been shown to work well by zhang and co workers for both linear coefficients and nonparametric functions this paper considers the role of influence diagnostics in the mple by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric component we focus on influence measures for the fixed effects and provide formulae that are analogous to those for simpler models and readily computable with the mple algorithm we also establish an equivalence between the case or subject deletion model and a mean shift outlier model from which we derive tests for outliers the influence diagnostics proposed are illustrated through a longitudinal hormone study on progesterone and a simulated example

local influence to detect influential data structures for generalized linear mixed models biometrics 2001 dec 57 4 1166 72 related articles books linkout local influence to detect influential data structures for generalized linear mixed models ouwens mj tan fe berger mp department of methodology and statistics maastricht university the netherlands mario ouwens stat unimaas nl this article discusses the generalization of the local influence measures for normally distributed responses to local influence measures for generalized linear models with random effects for these models it is shown that the subject oriented influence measure is a special case of the proposed observation oriented influence measure a two step diagnostic procedure is proposed the first step is to search for influential subjects a search for influential observations is proposed as the second step an illustration of a two treatment multiple period crossover trial demonstrates the practical importance of the detection of influential observations in addition to the detection of influential subjects

application of delete replace to deletion diagnostics for variance component estimation in the linear mixed model summary delete replace is a powerful and intuitive modelling identity this paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model we present a new fast transparent and approximate computational procedure arising as a by product of the fitting process we illustrate the effect of the deletion of individual observations of subjects and of arbitrary subsets central to the identity and its application is the conditional residual

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

robust statistical analysis of interlaboratory studies summary a common procedure in testing analytical methods is to send a portion of each of a number of samples to each of several laboratories the results of such a study are submitted to statistical analysis to determine the two important variance components in the problem replication error and laboratory bias outliers are relatively common in these data both among laboratory effects and among the residuals this paper presents a method of analysis for interlaboratory studies that is robust to the existence of outliers and long tailed distributions of random effects theoretical considerations as well as a monte carlo study are adduced as support for this new technique

a simple derivation of deletion diagnostic results for the general linear model with correlated errors a general simple and intuitive derivation is provided for diagnostics associated with the deletion of arbitrary subsets for the linear model with general covariance structure these are seen to be most simply expressed even for the well studied case of independent and identically distributed data in terms of a residual known variously as the conditional residual the deletion prediction residual and the cross validation residual particularly simple specializations arise when the subsets are of size 1 and of size 2 but the method is easy to apply for all subsets and to conditional deletions

decomposition of prediction error abstract the problem considered is that of predicting the value of an unobservable random variable w from the value of an observable random vector y this problem is considered under each of four states of knowledge about the joint distribution of w and y ranging from complete knowledge to no knowledge a point predictor or predictors are presented for each case prediction error is decomposed so that each component reflects an absence of information under certain conditions these components are uncorrelated and have zero means an exact or approximate expression is given for the variance of each component

quantum cohomology of the odd symplectic grassmannian of lines abstract odd symplectic grassmannians are a generalization of symplectic grassmannians to odd dimensional spaces here we compute the classical and quantum cohomology of the odd symplectic grassmannian of lines although these varieties are not homogeneous we obtain pieri and giambelli formulas that are very similar to the symplectic case we notice that their quantum cohomology is semisimple which enables us to check dubrovin s conjecture for this case

a littlewood richardson rule for factorial schur functions we give a combinatorial rule for calculating the coefficients in the expansion of a product of two factorial schur functions it is a special case of a more general rule which also gives the coefficients in the expansion of a skew factorial schur function applications to capelli operators and quantum immanants are also given

galerkin proper orthogonal decomposition methods for parabolic problems in this work error estimates for galerkin proper orthogonal decomposition pod methods for linear and certain non linear parabolic systems are proved the resulting error bounds depend on the number of pod basis functions and on the time discretization numerical examples are included

globally convergent algorithms for robust pole assignment by state feedback it is observed that an algorithm proposed in 1985 by kautsky nichols and van dooren knv amounts to maximizing at each iteration the determinant of the candidate closed loop eigenvector matrix x with respect to one of its columns with unit length constraint subject to the constraint that it remains an achievable closed loop eigenvector matrix this interpretation is used to prove convergence of the knv algorithm it is then shown that a more efficient algorithm is obtained if det x is concurrently maximized with respect to two columns of x and such a scheme is easily extended to the case where the eigenvalues to be assigned include complex conjugate pairs variations exploiting the availability of multiple processors are suggested convergence properties of the proposed algorithms are established their superiority is demonstrated numerically

an lmi approach to stability analysis of coupled parabolic systems we analyze the exponential stability of a class of distributed parameter systems the system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients we approximate the coefficients by splitting space domains but take into account approximation errors during stability analysis using a quadratic lyapunov function we obtain sufficient conditions for exponential stability in terms of linear matrix inequalities

prediction diagnostics for spatial linear models case deletion diagnostics are developed for detecting observations that are influential for prediction in linear models with a general covariance matrix a primary application of such results is in universal kriging and the related methodologies of ordinary kriging and intrinsic random function kriging in these applications the linear model and the covariance matrix of the data are determined by the locations at which observations are taken computational formulae are given that make the procedures feasible the diagnostics are illustrated using an example

equivariant quantum schubert calculus abstract we study the t equivariant quantum cohomology of the grassmannian we prove the vanishing of a certain class of equivariant quantum littlewood richardson coefficients which implies an equivariant quantum pieri rule as in the equivariant case this implies an algorithm to compute the equivariant quantum littlewood richardson coefficients

brief paper an lmi approach to h boundary control of semilinear parabolic and hyperbolic systems exponential stability analysis and l 2 gain analysis are developed for scalar uncertain distributed parameter systems governed by semilinear partial differential equations of parabolic and hyperbolic types sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities lmis for both systems these conditions are then utilized to synthesize h static output feedback boundary controllers of the systems in question

stability of partial difference equations governing control gains in infinite dimensional backstepping abstract we examine the stability properties of a class of ltv difference equations on an infinite dimensional state space that arise in backstepping designs for parabolic pdes the nominal system matrix of the difference equation has a special structure all of its powers have entries that are 1 0 or 1 and all of the eigenvalues of the matrix are on the unit circle the difference equation is driven by initial conditions additive forcing and a system matrix perturbation all of which depend on problem data for example viscosity and reactivity in the case of a reaction diffusion equation and all of which go to zero as the discretization step in the backstepping design goes to zero all of these observations combined with the fact that the equation evolves only in a number of steps equal to the dimension of its state space combined with the discrete gronwall inequality establish that the difference equation has bounded solutions this in turn guarantees the existence of a state feedback gain kernel in the backstepping control law with this approach we greatly expand relative to our previous results the class of parabolic pdes to which backstepping is applicable

quadratic optimal control of stable well posed linear systems we consider the infinite horizon quadratic cost minimization problem for a stable time invariant well posed linear system in the sense of salamon and weiss and show that it can be reduced to a spectral factorization problem in the control space more precisely we show that the optimal solution of the quadratic cost minimization problem is of static state feedback type if and only if a certain spectral factorization problem has a solution if both the system and the spectral factor are regular then the feedback operator can be expressed in terms of the riccati operator and the riccati operator is a positive self adjoint solution of an algebraic riccati equation this riccati equation is similar to the usual algebraic riccati equation but one of its coefficients varies depending on the subspace in which the equation is posed similar results are true for unstable systems as we have proved elsewhere

a note on jorgensen s iteratively defined statistics summary the newton raphson and fisher scoring iteratively reweighted least squares methods are two fundamental tools for computing parameter estimators and deletion diagnostics jorgensen 1993 proposed a modified method to compute deletion diagnostics in this paper we study the relationship between jorgensen s newton raphson and fisher scoring one step deletion estimators by using the observed and expected fisher information matrices in addition we extend jorgensen s true leverage and approximate leverage from binary regression models to general model settings

quantum giambelli formulas for isotropic grassmannians let x be a symplectic or odd orthogonal grassmannian which parametrizes isotropic subspaces in a vector space equipped with a nondegenerate skew symmetric form we prove quantum giambelli formulas which express an arbitrary schubert class in the small quantum cohomology ring of x as a polynomial in certain special schubert classes extending the authors cohomological giambelli formulas

case deletion diagnostics for mixed models mixed linear models arise in many areas of application standard estimation methods for mixed models are sensitive to bizarre observations such influential observations can completely distort an analysis and lead to inappropriate actions and conclusions we develop case deletion diagnostics for detecting influential observations in mixed linear models diagnostics for both fixed effects and variance components are proposed computational formulas are given that make the procedures feasible the methods are illustrated using examples

positivity in equivariant quantum schubert calculus a conjecture of d peterson proved by w graham states that the structure constants of the t equivariant cohomology of a homogeneous space g p satisfy a certain positivity property in this paper we show that this positivity property holds in the more general situation of equivariant quantum cohomology 1 introduction it is well known that the integral cohomology of the homogeneous space x g p for g a connected semisimple complex lie group and p a parabolic subgroup satisfies a positivity property its structure constants are nonnegative integers equal to the number of intersection points of three schubert varieties in general position whose codimensions add up to the dimension of x recently graham gr has proved a conjecture of peterson p asserting that h x the t equivariant cohomology of x where t c r is a maximal torus in g enjoys a more general positivity property

quadratic optimal control of well posed linear systems we study the infinite horizon quadratic cost minimization problem for a well posed linear system in the sense of salamon and weiss the quadratic cost function that we seek to minimize need not be positive but it is convex and bounded from below we assume the system to be jointly stabilizable and detectable and give a feedback solution to the cost minimization problem moreover we connect this solution to the computation of either a j s inner or an s normalized coprime factorization of the transfer function depending on how the problem is formulated we apply the general theory to get factorization versions of the bounded and positive real lemmas in the case where the system is regular it is possible to show that the feedback operator can be expressed in terms of the riccati operator and that the riccati operator is a stabilizing self adjoint solution of an algebraic riccati equation this riccati equation is nonstandard in the sense that the weighting operator in the quadratic term differs from the expected one and the computation of the correct weighting operator is a nontrivial task

plane answers to complex questions the theory of linear models providing a wide ranging introduction to the use of linear models in analyzing data this text presents a vector space and projections approach to the subject the topics covered include anova estimation hypothesis testing multiple comparison regression analysis and experimental design also covered are testing for lack of fit models with singular covariance matrices variance component estimation best linear prediction colinearity and variable selection

robust estimation of variance components outliers may occur with respect to any of the random components in the mixed linear model a procedure for limiting the influence of these outliers on the estimates of the model parameters is described given the variances or estimates of them the model effects are estimated by augmenting the original observations with auxiliary observations that contain the prior information represented by the variances large residuals among either the original or the auxiliary observations are interpreted as outlying random errors or outlying random effects as appropriate and winsorized the robust estimation of the variances is obtained by modifying the defining equations for the restricted maximum likelihood estimates under normality along the lines of huber s proposal 2 a numerical example illustrates the use of the methodology both as a diagnostic and as an estimation tool

gamma classes and quantum cohomology of fano manifolds gamma conjectures we propose gamma conjectures for fano manifolds which can be thought of as a square root of the index theorem studying the exponential asymptotics of solutions to the quantum differential equation we associate a principal asymptotic class a f to a fano manifold f we say that f satisfies gamma conjecture i if a f equals the gamma class widehat gamma f when the quantum cohomology of f is semisimple we say that f satisfies gamma conjecture ii if the columns of the central connection matrix of the quantum cohomology are formed by widehat gamma f operatorname ch e i for an exceptional collection e i in the derived category of coherent sheaves mathcal d b mathrm coh f gamma conjecture ii refines a part of a conjecture by dubrovin we prove gamma conjectures for projective spaces and grassmannians

residuals for the linear model with general covariance structure a general theory is presented for residuals from the general linear model with correlated errors it is demonstrated that there are two fundamental types of residual associated with this model referred to here as the marginal and the conditional residual these measure respectively the distance to the global aspects of the model as represented by the expected value and the local aspects as represented by the conditional expected value these residuals may be multivariate some important dualities are developed which have simple implications for diagnostics the results are illustrated by reference to model diagnostics in time series and in classical multivariate analysis with independent cases

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

exponential stabilization of well posed systems by colocated feedback we consider well posed linear systems whose state trajectories satisfy dot x ax bu where u is the input and a is an essentially skew adjoint and dissipative operator on the hilbert space x this means that the domains of a and a are equal and a a q where q geq 0 is bounded on x the control operator b is possibly unbounded but admissible and the observation operator of the system is b such a description fits many wave and beam equations with colocated sensors and actuators and it has been shown for many particular cases that the feedback u ka y v with ka 0 stabilizes the system strongly or even exponentially here y is the output of the system and v is the new input we show by means of a counterexample that if b is sufficiently unbounded then such a feedback may be unsuitable the closed loop semigroup may even grow exponentially our counterexample is a simple regular system with feedthrough operator zero however we prove that if the original system is exactly controllable and observable and if ka is sufficiently small then the closed loop system is exponentially stable

influence analysis for linear mixed effects models in this paper we extend several regression diagnostic techniques commonly used in linear regression such as leverage infinitesimal influence case deletion diagnostics cook s distance and local influence to the linear mixed effects model in each case the proposed new measure has a direct interpretation in terms of the effects on a parameter of interest and collapses to the familiar linear regression measure when there are no random effects the new measures are explicitly defined functions and do not necessitate re estimation of the model especially for cluster deletion diagnostics the basis for both the cluster deletion diagnostics and cook s distance is a generalization of miller s simple update formula for case deletion for linear models pregibon s infinitesimal case deletion diagnostics is adapted to the linear mixed effects model a simple compact matrix formula is derived to assess the local influence of the fixed effects regression coefficients finally a link between the local influence approach and cook s distance is established these influence measures are applied to an analysis of 5 year medicare reimbursements to colon cancer patients to identify the most influential observations and their effects on the fixed effects coefficients

equivariant quantum cohomology of the odd symplectic grassmannian the odd symplectic grassmannian mathrm ig mathrm ig k 2n 1 parametrizes k dimensional subspaces of mathbb c 2n 1 which are isotropic with respect to a general necessarily degenerate symplectic form the odd symplectic group acts on mathrm ig with two orbits and mathrm ig is itself a smooth schubert variety in the submaximal isotropic grassmannian mathrm ig k 2n 2 we use the technique of curve neighborhoods to prove a chevalley formula in the equivariant quantum cohomology of mathrm ig i e a formula to multiply a schubert class by the schubert divisor class this generalizes a formula of pech in the case k 2 and it gives an algorithm to calculate any multiplication in the equivariant quantum cohomology ring

high dimensional influence measure influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations for high dimensional data it is particularly so as the increased dimensionality and complexity may amplify both the chance of an observation being influential and its potential impact on the analysis in this article we propose a novel high dimensional influence measure for regressions with the number of predictors far exceeding the sample size our proposal can be viewed as a high dimensional counterpart to the classical cook s distance however whereas the cook s distance quantifies the individual observation s influence on the least squares regression coefficient estimate our new diagnosis measure captures the influence on the marginal correlations which in turn exerts serious influence on downstream analysis including coefficient estimation variable selection and screening moreover we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure

assessing influence for pharmaceutical data in zero inflated generalized poisson mixed models for clustered count data with excess zeros where the observations are either over dispersed or under dispersed the zero inflated generalized poisson mixed zigpm regression model may be appropriate in which the baseline discrete distribution is a generalized poisson distribution which is a natural extension of standard poisson distribution motivated by one data set drawn from a pharmaceutical study influence diagnostics for zigpm models based on case deletion and local influence analysis are developed in this work the one step approximations of the estimates under case deletion model and some case deletion measures are given meanwhile local influence measures are obtained under various perturbations of the observed data or model assumptions results from a pharmaceutical study illustrate the usefulness of the diagnostic statistics

influence diagnostics for linear longitudinal models abstract influence diagnostics are important for analyzing cross sectional regression studies because they allow the analyst to understand the impact of individual observations on the estimated regression model in this article we consider the role of influence diagnostics in subject specific longitudinal models diagnostics are proposed under both fixed and random subject effects our approach is based on subject deletion which in this setting involves deleting a group of correlated observations we develop partial influence statistics to understand the combined impact of observations from a subject on population parameters simple computational formulas make the procedures feasible finally we illustrate the use of our new influence statistics by examining a dataset to model a taxpayer s charitable givings

quantum pieri rules for isotropic grassmannians we study the three point genus zero gromov witten invariants on the grassmannians which parametrize non maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew symmetric form we establish pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties which give a combinatorial formula for the product of any schubert class with certain special schubert classes we also give presentations of these rings with integer coefficients in terms of special schubert class generators and relations

giambelli formulae for the equivariant quantum cohomology of the grassmannian we find presentations by generators and relations for the equivariant quantum cohomology of the grassmannian for these presentations we also find determinantal formulae for the equivariant quantum schubert classes to prove this we use the theory of factorial schur functions and a characterization of the equivariant quantum cohomology ring

adaptive boundary control for unstable parabolic pdes part ii estimation based designs the certainty equivalence approach to adaptive control is commonly used with two types of identifiers passivity based identifiers and swapping identifiers the passive also known as observer based approach is the prevalent identification technique in existing results on adaptive control for pdes but has so far not been used in boundary control problems the swapping approach prevalent in finite dimensional adaptive control is employed here for the first time in adaptive control of pdes for a class of unstable parabolic pdes we prove a separation principle result for both the passive and swapping identifiers combined with the backstepping boundary controllers the result is applicable in any dimension for physical reasons we restrict our attention to dimensions no higher than three the results of the paper are illustrated by simulations

brief paper adaptive boundary control for unstable parabolic pdes part iii output feedback examples with swapping identifiers we develop output feedback adaptive controllers for two benchmark parabolic pdes motivated by a model of thermal instability in solid propellant rockets both benchmark plants are unstable have infinite relative degree and are controlled from the boundary one plant has an unknown parameter in the pde and the other in the boundary condition in both cases the unknown parameter multiplies the measured output of the system which is obtained with a boundary sensor located on the opposite side of the domain from the actuator in comparison with the lyapunov output feedback adaptive controllers in krstic and smyshlyaev 2005 adaptive boundary control for unstable parabolic pdes part i lyapunov design ieee transactions on automatic control submitted for publication the controllers presented here employ much simpler update laws and do not require a priori knowledge about the unknown parameters we show how our two benchmarks examples can be combined and illustrate the adaptive stabilization design by simulation

a sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems this paper presents a sum of squares sos approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems the proposed sos based framework provides a number of innovations and improvements over the existing linear matrix inequality lmi based approaches to takagi sugeno t s fuzzy modeling and control first we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well known t s fuzzy modeling and control secondly we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial lyapunov functions that contain quadratic lyapunov functions as a special case hence the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing lmi based approaches to t s fuzzy modeling and control moreover the derived stability and stabilizability conditions are represented in terms of sos and can be numerically partially symbolically solved via the recently developed sostools to illustrate the validity and applicability of the proposed approach a number of analysis and design examples are provided the first example shows that the sos approach renders more relaxed stability results than those of both the lmi based approaches and a polynomial system approach the second example presents an extensive application of the sos approach in comparison with a piecewise lyapunov function approach the last example is a design exercise that demonstrates the viability of the sos based approach to synthesizing a stabilizing controller

a convex sum of squares approach to analysis state feedback and output feedback control of parabolic pdes we present an optimization based framework for analysis and control of linear parabolic partial differential equations pdes with spatially varying coefficients without discretization or numerical approximation for controller synthesis we consider both full state feedback and point observation output feedback the input occurs at the boundary point actuation we use positive definite matrices to parameterize positive lyapunov functions and polynomials to parameterize controller and observer gains we use duality and an invertible state variable transformation to convexify the controller synthesis problem finally we combine our synthesis condition with the luenberger observer framework to express the output feedback controller synthesis problem as a set of lmi sdp constraints we perform an extensive set of numerical experiments to demonstrate the accuracy of the conditions and to prove the necessity of the lyapunov structures chosen we provide numerical and analytical comparisons with alternative approaches to control including sturm liouville theory and backstepping finally we use numerical tests to show that the method retains its accuracy for alternative boundary conditions