convergence and stability of distributed stochastic iterative processes a mathematical framework is proposed for convergence analysis of stochastic iterative processes arising in applications of pseudogradient optimization algorithms the framework is based upon the concepts of stochastic difference inequalities and vector lyapunov functions which are ideally suited for reducing the dimensionality problem arising in testing convergence of distributed parallel schemes by applying the m matrix conditions to a test matrix having a dimension equal to the number of the processor in the scheme one can use the framework to select suitable scaling factors for each individual processor producing a satisfactory convergence rate of the overall iterative process the results provide new convergence tests for distributed iterative processes arising in decentralized extremal regulation adaptation and parameter estimation schemes

the asymptotic properties of nonparametric tests for comparing survival distributions the asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary and possibly unequal right censoring the test statistics include equivalents to the log rank statistic the modified wilcoxon statistic and the class of rank invariant test procedures introduced by peto peto when there are equal censoring distributions and the hazard functions are proportional the sample size formula for the f test used to compare exponential samples is shown to be valid for the log rank test in certain situations the power of the log rank test falls as the amount of censoring decreases

score tests in generalized linear measurement error models summary hypothesis tests in generalized linear models are studied under the condition that a surrogate w is observed in place of the true predictor x the efficient score test for the hypothesis of no association depends on the conditional expectation e xi w which is generally unknown the usual test substitutes w for e xi w and is asymptotically valid but not efficient we investigate two new test statistics appropriate when w x z where z is an independent measurement error the first is a wald test based on estimators corrected for measurement error despite the correction for attenuation in the estimator this test has the same local power as the usual test the second test employs an estimator of e x i w and is both asymptotically efficient for normal errors and approximately efficient when the measurement error variance is small

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

tests for no treatment effect in randomized clinical trials summary we propose a test of the null hypothesis of no treatment effect in a randomized clinical trial that is based on the randomization distribution of residuals these residuals result from regressing the response on covariates but not treatment in contrast to model based score tests this procedure maintains nominal size when the model is misspecified and in particular when relevant covariates are omitted from the regression the efficiency of the procedure is evaluated for regressions with some but not all required covariates for many generalized linear models and survival models conventional model based score tests are shown to have supranominal size when relevant covariates are omitted but logistic regression and the proportional hazards model are robust

stabilization and gevrey regularity of a schrodinger equation in boundary feedback with a heat equation we study stability of a schrodinger equation with a collocated boundary feedback compensator in the form of a heat equation with a collocated input output pair remarkably exponential stability is achieved for both positive and negative gains namely as long as the gain is non zero we show that the spectrum of the closed loop system consists only of two branches along two parabolas which are asymptotically symmetric relative to the line re im the 135 line in the second quadrant the asymptotic expressions of both eigenvalues and eigenfunctions are obtained the riesz basis property and exponential stability of the system are then proved finally we show that the semigroup generated by the system operator is of gevrey class 2 a numerical computation is presented for the distributions of the spectrum of the closed loop system

aggregation of a class of interconnected linear dynamical systems abstract in this paper we introduce the notion of a meaningful average of a collection of dynamical systems as distinct from an ensemble average such a notion is useful for the study of a variety of dynamical systems such as traffic flow power systems and econometric systems we also address the associated issue of the existence and computation of such an average for a class of interconnected linear time invariant dynamical systems such an average dynamical system is not only attractive from a computational perspective but also represents the average behavior of the interconnected dynamical systems the problem of analysis and control of heirarchical large scale control systems can be simplified by approximating the lower level dynamics of such systems with such an average dynamical system

two equivalence theorems of different kinds of optimal control problems for schrodinger equations this paper builds up two equivalence theorems for different kinds of optimal control problems of internally controlled schrodinger equations the first one is an equivalence of the minimal norm and the minimal time control problems where the target sets are the origin of the state space the minimal time control problems are also called the first type of optimal time control problems the second one is an equivalence of three optimal control problems optimal target control problems optimal norm control problems and the second type of optimal time control problems

effects of mismodeling on tests of association based on logistic regression models we consider the effects of misspecifying the covariate vector on tests of association between a particular covariate and the response variable in logistic regression models misspecification can include random measurement error discretizing a continuous explanatory variable and mismodeling the functional form of an explanatory variable the effects of misspecification are examined by deriving the asymptotic distribution of the test statistic under a sequence of models applications of this result are discussed

comparing the effects of continuous and discrete covariate mismeasurement with emphasis on the dichotomization of mismeasured predictors it is well known that imprecision in the measurement of predictor variables typically leads to bias in estimated regression coefficients we compare the bias induced by measurement error in a continuous predictor with that induced by misclassification of a binary predictor in the contexts of linear and logistic regression to make the comparison fair we consider misclassification probabilities for a binary predictor that correspond to dichotomizing an imprecise continuous predictor in lieu of its precise counterpart on this basis nondifferential binary misclassification is seen to yield more bias than nondifferential continuous measurement error however it is known that differential misclassification results if a binary predictor is actually formed by dichotomizing a continuous predictor subject to nondifferential measurement error when the postulated model linking the response and precise continuous predictor is correct this differential misclassification is found to yield less bias than continuous measurement error in contrast with nondifferential misclassification i e dichotomization reduces the bias due to mismeasurement this finding however is sensitive to the form of the underlying relationship between the response and the continuous predictor in particular we give a scenario where dichotomization involves a trade off between model fit and misclassification bias we also examine how the bias depends on the choice of threshold in the dichotomization process and on the correlation between the imprecise predictor and a second precise predictor

stabilisation of schrodinger equation in dynamic boundary feedback with a memory typed heat equation abstractin this work we study the dynamic behaviour for a heat equation with exponential polynomial kernel memory to be a controller for a schrodinger system by introducing some new variables th

schrodinger operators with boundary singularities hardy inequality pohozaev identity and controllability results abstract the aim of this paper is two folded firstly we study the validity of a pohozaev type identity for the schrodinger operator a x 2 r in the situation where the origin is located on the boundary of a smooth domain r n n 1 showing some applications to semi linear elliptic equations the problem we address is very much related to optimal hardy poincare inequalities with boundary singularities which have been investigated in the recent past in various papers in view of that the proper functional framework is described and explained secondly we use the pohozaev identity to derive the method of multipliers and we apply it to study the exact boundary controllability for the wave and schrodinger equations corresponding to the singular operator a in particular this complements and extends well known results by vancostenoble and zuazua 2009 38 who discussed the same issue in the case of interior singularity

controllability observability of expanded composite systems abstract the relation between original and expanded systems within the inclusion principle from the point of view of controllability observability of both subsystems and composite systems is studied it is proved that complementary matrices always exist ensuring that the subsystems and the overall expanded system are simultaneously controllable observable two practically important large classes of complementary matrices are identified to offer results computationally attractive first the existence of complementary matrices ensuring controllability observability of decoupled subsystems is proved then using this result the same property is proved for the composite expanded system

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

sliding mode control of schrodinger equation ode in the presence of unmatched disturbances abstract in this paper we consider boundary stabilization for a cascade of schrodinger equation ode system with both matched and unmatched disturbances the backstepping method is first applied to transform the system into an equivalent target system where the target system is input to state stable to reject the matched disturbance the sliding mode control smc law is designed for the target system the well posedness of the closed loop system is proved and the reachability of the sliding manifold in finite time is justified by infinite dimensional system theory it is shown that the resulting closed loop system is input to state stable a numerical example illustrates the efficiency of the sliding mode design that reduces the ultimate bound of the closed loop system by rejecting the matched disturbance

exact controllability of the schrodinger equation in this paper we study the controllability of the linear schrodinger equation on bounded domains in r n first we state and prove a simple functional analytic characterization of the exact controllability of abstract schrodinger type equations which does not use the hilbert uniqueness method in a second part we discuss generalizations of results of machtyngier siam j control optim 32 1994 24 on the exact internal and boundary controllability of schrodinger equation by allowing lower order terms in the schrodinger equation this may be a first step to prove results on the exact controllability of semilinear nonlinear schrodinger equations which is a big problem

properties of proportional hazards score tests under misspecified regression models the effects are investigated of misspecifying a proportional hazards regression model on the associated partial likelihood score test for comparing two randomized treatments in the presence of covariates the asymptotic efficiency of the proportional hazards score test relative to the optimal partial likelihood test declines slowly as the hazard functions for the two treatments deviate from proportionality the efficiency can be very low when the hazard functions cross or differ only at large survival times misspecification of the functional form of the regression portion of a proportional hazards model introduces a quantitative treatment covariate interaction in the situations that we examine based on a binary covariate this misspecification usually results in only a minor drop in efficiency the omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test but can substantially reduce power when the covariate effect is strong the loss of power from mismodeling a balanced covariate is usually small

how violent are fast controls for schrodinger and plate vibrations given a time t 0 and a region on a compact riemannian manifold m we consider the best constant denoted ct in the observation inequality for the schrodinger evolution group of the laplacian with dirichlet boundary condition open image in new window we investigate the influence of the geometry of on the growth of ct as t tends to 0

exact boundary controllability for the linear korteweg de vries equation on the half line this paper is concerned with the controllability of the linear korteweg de vries equation on the domain o 0 infty the control being applied at the left endpoint x 0 it is shown that the em exact boundary controllability holds true in l 2 0 infty provided that the solutions are not required to be in l infty 0 t l 2 0 infty the proof rests on a carleman s estimate and an approximation theorem a similar result is obtained for the heat equation and for the schrodinger equation

observability and stabilization of magnetic schrodinger equations abstract we are mainly interested in extending the known results on observability inequalities and stabilization for the schrodinger equation to the magnetic schrodinger equation that is in presence of a magnetic potential we establish observability inequalities and exponential stabilization by extending the usual multiplier method under the same geometric condition that needed for the schrodinger equation we also prove with the help of elliptic carleman inequalities logarithmic stabilization results through a resolvent estimate although the approach is classical these results on logarithmic stabilization seem to be new even for the schrodinger equation

dual inclusion principle for overlapping interconnected systems restriction and aggregation are two dual inclusion conditions which are revealed in the research field of inclusion principle for state space descriptions of overlapping interconnected systems an input state output dual inclusion principle is proposed for linear time invariant systems and their dual systems with the focus on restriction and aggregation in duality for direct contraction of control laws and state observers in these two special inclusion cases dual relationships of restriction and aggregation inclusion conditions are formulated between an original system and its dual system overlapping decentralized controller design problems are considered within the framework of the dual inclusion principle it is shown that if dual inclusion is satisfied in the same type of expansions restriction or aggregation for both original system and its dual system direct contraction can be applied to designed control laws or state observers from the expansion to the original space while dual informatio

decentralized estimation and control with overlapping information sets the objective of this note is to present a solution to the decentralized estimation and control problem for linear discrete time varying systems composed of overlapping subsystems the solution is based on the expansion contraction framework of the inclusion principle it is shown how decentralized estimation and control laws can be independently computed for the expanded system and then contracted for implementation in the original system to satisfy the overlapping information structure constraint

overlapping decompositions expansions contractions and stability of hybrid systems inclusion and extension principles are defined and studied for hybrid systems the controller design problem for hybrid systems is then considered within the framework of the extension principle it is shown that if the extension principle is used then any controller designed in the expanded spaces is contractible to the original spaces for implementation the stability of hybrid systems is also considered a number of definitions of stability for hybrid systems are given and it is shown that if a system which includes another system is stable then the included system is also stable furthermore it is shown that if a controller designed for the expanded system achieves stability then the contracted controller also achieves stability for the original system decentralized controller design with overlapping decompositions is also discussed within the framework of extension an example is provided to illustrate the proposed approach

generalized selection of complementary matrices in the inclusion principle this paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state lq optimal control of lti systems it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control design

contractibility of dynamic lti controllers using complementary matrices a generalized structure of complementary matrices involved in the input state output inclusion principle for linear time invariant systems including contractibility conditions for static state feedback controllers is well known in this note it is shown how to further extend this structure when considering contractibility of dynamic controllers necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion contraction transformation matrices explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion contraction transformation matrices moreover these conditions are further specialized for a particular class of transformation matrices

general decentralized stabilization of large scale linear continuous and discrete time delay systems we consider the general stabilization problem of linear time invariant large scale multivariable decentralized systems with delays we have established sufficient stabilization conditions for a general class of decentralized systems namely in the continuous case the requirement is that the matrix measure of the closed loop subsystem matrices can be made sufficiently negative by appropriate local feedback control whereas in the discrete case the requirement is that the norm of the closed loop subsystem matrices can be made arbitrarily small by feedback control

decentralized estimation and control with overlapping input state and output decomposition abstract the extension principle which was introduced recently is generalized to the case of input state and output expansion estimator and controller design problems are considered within the framework of the extension principle decentralized estimator and controller design with overlapping decompositions is also discussed within the same framework it is shown that if the extension principle is used then any estimator or controller designed in the expanded spaces is contractible to the original spaces for implementation furthermore it is shown that if an estimator designed for the expanded system achieves good estimation and or asymptotic estimation then the contracted estimator also achieves good estimation and or asymptotic estimation for the original system similarly it is also shown that if a controller designed for the expanded system achieves stability and or good performance then the contracted controller achieves stability and or good performance for the original system

decentralized control using quasi block diagonal dominance of transfer function matrices the purpose of this paper is to present a generalization of the nyquist array method to blockwise decompositions which is based upon a new version of block diagonal dominance an additional flexibility of the proposed method is in partitioning of the system matrices into disjoint as well as overlapping submatrices which increases considerably the class of control systems which can be designed via block diagonal dominance within this framework the controllers for individual subsystems can be designed independently of each other so that their union represents a decentralized controller for the overall system

finite wordlength controller realisations using the specialised implicit form a specialised implicit state space representation is introduced to deal with finite wordlength effects in controller implementations this specialised implicit form provides a macroscopic description of the algorithm to be implemented so it constitutes a unifying framework allowing to encompass various implementation forms such as the operator the direct form ii transposed observer based and many other realisations usually considered separately in the literature different measures quantifying the finite wordlength effects on the overall closed loop behaviour are defined in this new context they concern both stability and performance the gap with the infinite precision case is evaluated classically through the coefficient sensitivity and roundoff noise analysis the problem of determining a realisation with minimum finite wordlength effects can subsequently be solved using appropriate numerical methods the approach is illustrated with an example

brief paper controllability and observability of expanded systems with overlapping decompositions the expanded system concept of siljak and his coworkers enables the design of robust overlapping controllers and observers for large scale systems to be carried out in a purely decentralised way in this paper we study the stability and detectability properties of expanded systems and show that it is only in certain special cases that these properties are preserved when the system is expanded these special cases define the classes of systems where the expanded system concept can be used for controller or observer design

effects of treatment induced mortality and tumor induced mortality on tests for carcinogenicity in small samples statistical tests of carcinogenicity are shown to have varying degrees of robustness to the effects of mortality mortality induced by two different mechanisms is studied mortality due to the tumor of interest and mortality due to treatment independent of the tumor the two most commonly used tests the life table test and the cochran armitage linear trend test are seen to be highly sensitive to increases in treatment lethality using small sample simulations increases in tumor lethality are seen to affect the performance of commonly used prevalence tests such as logistic regression a simple survival adjusted quantal response test appears to be the most robust of all the procedures considered

stochastic link activation for distributed filtering under sensor power constraint we consider the problem of link activation for distributed estimation with power constraint to satisfy the requirement of power consumption we propose a stochastic link activation scheme where each sensor equipped with a distributed estimator sends data to its neighboring sensors according to different probabilities first we design the optimal estimator gain of each sensor to minimize the state estimation error covariance then we find an upper bound of the expected state estimation error covariance and provide a sufficient condition to guarantee the stability of the proposed estimator finally we formulate the link activation problem as an optimization problem and convert it to a convex optimization

overlapping block diagonal dominance and existence of liapunov functions the main objective of this paper is to formulate a generalization of block diagonal dominance which can be used to establish nonsingularity of matrices via overlapping diagonal blocks a number of stability results are derived in the new setting by exploiting the well known m matrix properties as well as extensions of the normalization scaling and alternative norm utilization a link between generalized block diagonal dominance and vector liapunov functions is established which can be applied in the stability analysis of interconnected dynamic systems

brief paper on the v stability of complex dynamical networks this paper introduces the concept of lyapunov v stability for complex dynamical networks under the new framework each dynamical node is associated with a passivity degree which indicates to what extent an effort is required for stabilizing the node from this approach the network stability problem is converted to measuring the negative definiteness of one simple matrix that characterizes the topology of the network pinning control is then suggested and investigated based on the new v stability formulation as an illustrative example a network with different node dynamics and non uniform coupling strengths is simulated to verify the analytic results moreover a comparison study for three different kinds of networks is provided to further illustrate the novelty and efficacy of the proposed v stability criterion and stabilization scheme

an inclusion principle for dynamic systems the purpose of this paper is to present a detailed study of the inclusion concept in dynamic systems which is a suitable mathematical framework for comparing systems with different dimensions the framework offers immediate results in reduced order modeling and the overlapping decentralized control of complex systems the presentation which is limited to linear constant systems relies on both the matrix algebra computations and the geometric elements structure to provide a balanced view of the issues involved in the concept of inclusion the framework is quite broad and has been used to consider nonlinear and time varying systems as well as systems with hereditary and stochastic effects

inclusion principle for descriptor systems the purpose of this paper is to propose an expansion contraction framework for linear constant descriptor systems within the inclusion principle for dynamic systems our primary objective is to provide an explicit characterization of the expansion process whereby a given descriptor system is expanded into the larger space where all its solutions are reproducible by the expanded descriptor system if appropriate initial conditions are selected when a control law is formulated in the expanded space the proposed characterizations provide contractibility conditions for implementation of the control law in the original system a full freedom is provided for selecting appropriate matrices in the proposed expansion contraction control scheme in particular the derived theoretical framework serves as a flexible environment for expansion contraction control design of descriptor systems under overlapping information structure constraints

controllability of the 1d schrodinger equation using flatness we derive in a direct way the exact controllability of the 1d schrodinger equation with dirichlet boundary control we use the so called flatness approach which consists in parametrizing the solution and the control by the derivatives of a flat output this provides an explicit and very regular control achieving the exact controllability in the energy space

contractibility of overlapping decentralized control abstract the purpose of this paper is to generalize the concept of contractibility of decentralized control laws in the inclusion principle after a system with overlapping subsystems is expanded into a larger space and decentralized control laws are formulated for the disjoint subsystems the laws need to be contracted for implementation in the original space we propose broader definitions of restriction and aggregation in the framework of inclusion which provide more flexibility in the contraction phase of the expansion contraction process in particular we discuss contractibility conditions for dynamic output controllers including state observers which have been of special interest in applications

stability estimate for an inverse problem for the magnetic schrodinger equation from the dirichlet to neumann map abstract we consider the problem of stability estimate of the inverse problem of determining the magnetic field entering the magnetic schrodinger equation in a bounded smooth domain of r n with input dirichlet data from measured neumann boundary observations this information is enclosed in the dynamical dirichlet to neumann map associated to the solutions of the magnetic schrodinger equation we prove in dimension n 2 that the knowledge of the dirichlet to neumann map for the magnetic schrodinger equation measured on the boundary determines uniquely the magnetic field and we prove a holder type stability in determining the magnetic field induced by the magnetic potential

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

numerical null controllability of the 1d linear schrodinger equation abstract this paper deals with the numerical approximation to boundary controls that drive the solution to the 1 d linear schrodinger equation to a prescribed state at a final time using ideas from fursikov and imanuvilov we consider the control that minimizes over the class of admissible controls a functional that involves weighted integrals with weights that blow up at t we will see that this extremal problem is equivalent to a differential problem that is fourth order in space and second order in time adapting some numerical techniques applied by the first author and munch to the heat equation we approximate the variational formulation by introducing appropriate space time finite elements that are c 1 in space and c 0 in time we present two approaches the second one relies on a change of variable which leads to a lower condition number for the stiffness matrix the results of some experiments show the efficiency of these methods

stabilization of an ode schrodinger cascade abstract we consider the problem of stabilization of a linear ode with input dynamics governed by the linearized schrodinger equation the interconnection between the ode and schrodinger equation is bi directional at a single point we construct an explicit feedback law that compensates the schrodinger dynamics at the inputs of the ode and stabilizes the overall system our design is based on a two step backstepping transformation by introducing an intermediate system and an intermediate control by adopting the riesz basis approach the exponential stability of the closed loop system is built with the pre designed decay rate and the spectrum determined growth condition is obtained a numerical simulation is provided to illustrate the effectiveness of the proposed design

generalized decompositions of dynamic systems and vector lyapunov functions the notion of decomposition is generalized to provide more freedom in constructing vector lyapunov functions for stability analysis of nonlinear dynamic systems a generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state space of a given system an inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system so that stabliity of the expansion implies stability of the original system stability of the expansion can then be established by standard disjoint decompositions and vector lyapunov functions the applicability of the new approach is demonstrated using the lotka voiterra equations

model abstraction and inclusion principle a comparison this paper discusses connections between the inclusion principle and model abstraction in large scale hierarchical control systems it also provides conditions for implementation of controllability and observability in linear continuous time dynamic systems satisfying either aggregation or restriction conditions as well as for observability implementation in linear continuous time dynamic systems satisfying conditions for abstraction

partial exponential stability of semi state systems the general class of non linear non autonomous semi state systems is considered from the viewpoint of stability of system motions a theorem is proved giving necessary and sufficient conditions for partial exponential stability of arbitrary motion of these systems over finite or infinite time intervals the results are illustrated by the analysis of a non linear electrical circuit

optimal bilinear control of nonlinear schrodinger equations with singular potentials abstract we consider an optimal bilinear control problem for the nonlinear schrodinger equations with singular potentials we show the well posedness of the problem and the existence of an optimal control in addition the first order optimality system is rigorously derived our results give an improvement for some recent results

optimal bilinear control of gross pitaevskii equations with coulombian potentials in this paper we consider an optimal bilinear control problem for the gross pitaevskii equations with coulombian potentials we show the well posedness of the problem and the existence of an optimal control in addition the first order optimality system is rigorously derived in particular we prove the frechet differentiability of the unconstrained functional we extend the study of hintermuller et al 2013 15 to more general power nonlinearities and unbounded potentials c 2015 elsevier inc all rights reserved

the asymptotic relative efficiency of score tests in a generalized linear model with surrogate covariates summary in many epidemiological studies the exposure variable of interest cannot be measured directly the classical approaches to errors in variables in regression do not extend easily to the nonlinear models commonly used in epidemiologic al research furthermore the traditional additive measurement error model cannot adequately represent many surrogate relationships by considering the effect of using surrogate independent variables on the efficient score statistic some of the difficulties inherent in the estimation problem may be avoided for the null hypothesis of no association a simple and flexible procedure can be used to calculate the optimal score test the asymptotic relative efficiency of this test to the test based upon the true exposures is derived the optimal test is also compared to the naive procedure of substituting the surrogate into the score test for the true exposure

pair wise decomposition and coordinated control of complex systems pair wise decomposition and coordinated control for complex interconnected systems with any information structure constraints are proposed in this paper based on the inclusion principle a permuted inclusion principle is presented to expand the system into an expanded space from which a recurrent reverse order of pair wise subsystems is extracted by a standard lq control pair wise controllers can be designed to stabilize and coordinate the pair wise subsystems according to these controllers a coordinated compensator of subsystem interconnections is introduced in order to obtain a coordination based controller for the expanded system therefore a coordinated controller of the system can be contracted from the expanded space under the conditions of the inclusion principle moreover a sufficient condition of connective stability for the system is also proved by the lyapunov function and m matrix a main advantage of the proposed decomposition and control is that it allows any variation of information structure constraints of the system especially the increase and decrease of subsystem numbers finally the effectiveness of the proposed methodology is demonstrated by an application of automatic generation control to a four area electric power system

the effect of pooling across strata in perfectly balanced studies pair matching frequency matching and stratification are used to obtain perfect exposure balance within strata defined by levels of confounders we consider the consequences of pooling such balanced data across strata in the analysis we examine model based inference for a variety of response variables and generalized linear regressions as well as for the cox 1972 journal of the royal statistical society series b 34 187 220 model if the data are pooled so that stratum effects are omitted from the regression certain models retain nominal size including all poisson models and all normal models with known variance the model based tests have supranominal size for all exponential models and subnominal size for all bernoulli models and for the cox model these results contrast with a previous analysis of simple randomization which only ensures exposure balance on average with simple randomization omission of stratum effects from these models leads to model based significance tests with supranominal size except for the cox and bernoulli models which retain nominal size just as for simple randomization however it is wise to include stratum effects in the analysis of perfectly balanced data to avoid biased estimation of exposure effects and to increase the efficiency of the comparison though motivated by cohort data these results also apply to balanced case control data under the logistic model

robust estimation of causal effects of binary treatments in unconfounded studies with dichotomous outcomes the estimation of causal effects has been the subject of extensive research in unconfounded studies with a dichotomous outcome y cangul chretien gutman and rubin 2009 demonstrated that logistic regression for a scalar continuous covariate x is generally statistically invalid for testing null treatment effects when the distributions of x in the treated and control populations differ and the logistic model for y given x is misspecified in addition they showed that an approximately valid statistical test can be generally obtained by discretizing x followed by regression adjustment within each interval defined by the discretized x this paper extends the work of cangul et al 2009 in three major directions first we consider additional estimation procedures including a new one that is based on two independent splines and multiple imputation second we consider additional distributional factors and third we examine the performance of the procedures when the treatment effect is non null of all the methods considered and in most of the experimental conditions that were examined our proposed new methodology appears to work best in terms of point and interval estimation copyright 2012 john wiley sons ltd

contractible controller design and optimal control with state and input inclusion abstract a new inclusion concept which involves both state and input expansion is introduced it is shown that with the approach undertaken here any control law designed in the expanded spaces is always contractible to the original spaces the inclusion of the cost functions is also discussed and necessary and sufficient conditions are derived it is shown that unlike the case when the two input spaces are identical the inclusion conditions must in general depend on the control laws however certain sufficient conditions which do not involve final control laws can be found if the inclusion is taken with respect to the optimal control finally controller design with overlapping decompositions is discussed within the framework of the new inclusion concept and optimal control

deconvolution based score tests in measurement error models consider a generalized linear model with response y and scalar predictor x instead of observing x a surrogate w x z is observed where z represents measurement error and is independent of x and y the efficient score test for the absence of association depends on m w e x mid w w which is generally unknown assuming that the distribution of z is known asymptotically efficient tests are constructed using nonparametric estimators of m w rates of convergence for the estimator of m w are established in the course of proving efficiency of the proposed test

a decomposition technique for nonlinear dynamical system analysis a method for analyzing large scale nonlinear dynamical systems by decomposing them into coupled lower order subsystems that are sufficiently simple for computational analysis is presented it is shown that the decomposition approach can be used to scale the sum of squares programming framework for nonlinear systems analysis the method constructs subsystem lyapunov functions which are used to form a composite lyapunov function for the whole system further computational savings are achieved if a method based on sparsity maximization is used to obtain the subsystem lyapunov functions

the loss in efficiency from misspecifying covariates in proportional hazards regression models summary this note considers partial likelihood score tests for association between a covariate process and survival time based on a proportional hazards regression model we derive the asymptotic efficiency of the test based on a misspecified form of the covariate process relative to the test based on the correct form the results can be used to assess the consequences of various types of misspecification

exact boundary controllability of a microbeam model abstract in this paper we study the exact controllability property of a microbeam model by means of a single boundary control we use the multiplier method together with the controllability observability duality to obtain a time t 0 such that the corresponding linear equation is exactly controllable provided that the control time is greater than t 0 our exact controllability result improves the one obtained in vatankhah et al 2014 20 which uses six boundary controls instead of a single one

testing for gene environment interaction under exposure misspecification complex interplay between genetic and environmental factors characterizes the etiology of many diseases modeling gene environment gxe interactions is often challenged by the unknown functional form of the environment term in the true data generating mechanism we study the impact of misspecification of the environmental exposure effect on inference for the gxe interaction term in linear and logistic regression models we first examine the asymptotic bias of the gxe interaction regression coefficient allowing for confounders as well as arbitrary misspecification of the exposure and confounder effects for linear regression we show that under gene environment independence and some confounder dependent conditions when the environment effect is misspecified the regression coefficient of the gxe interaction can be unbiased however inference on the gxe interaction is still often incorrect in logistic regression we show that the regression coefficient is generally biased if the genetic factor is associated with the outcome directly or indirectly further we show that the standard robust sandwich variance estimator for the gxe interaction does not perform well in practical gxe studies and we provide an alternative testing procedure that has better finite sample properties

exact controllability for the schrodinger equation the exact controllability of schrodinger equation in bounded domains with dirichlet boundary condition is studied both the boundary controllability and the internal controllability problems are considered concerning the boundary controllability the paper proves the exact controllability in h 1 omega with l 2 boundary control on the other hand the exact controllability in l 2 omega is proved with l 2 controls supported in a neighborhood of the boundary both results hold for an arbitrarily small time the method of proof combines both the hum hilbert uniqueness method and multiplier techniques

exact boundary controllability of the nonlinear schrodinger equation abstract this paper studies the exact boundary controllability of the semi linear schrodinger equation posed on a bounded domain r n with either the dirichlet boundary conditions or the neumann boundary conditions it is shown that if s n 2 or 0 s n 2 with 1 n 2 2 s or s 0 1 with n 2 then the systems are locally exactly controllable in the classical sobolev space h s around any smooth solution of the cubic schrodinger equation

uniform decay rate estimates for schrodinger and plate equations with nonlinear locally distributed damping on a compact n dimensional riemannian manifold m g we establish uniform decay rate estimates for the linear schrodinger and plate equations subject to an internal nonlinear damping locally distributed on the manifold our approach can be also employed for other equations provided that inverse inequality for the linear model occurs in the particular case of the wave equation where the well known geometric control condition gcc is equivalent to the observability inequality our method generalizes the results due to cavalcanti et al 2010 2009 9 10 regarding the optimal choice of dissipative regions

loss in efficiency caused by omitting covariates and misspecifying exposure in logistic regression models we examine the effects of omitting covariates and misspecifying the explanatory variable of interest on tests of association between the explanatory variable and response based on logistic regression models we assume throughout that the covariates are statistically independent of the explanatory variable as under simple randomization a general expression for the asymptotic loss in efficiency from omitting covariates and misspecifying the explanatory variable is derived the expression for the asymptotic efficiency of the misspecified test statistic relative to the correctly specified test can be factored into two parts each of which is less than or equal to 1 the first part reflects the consequences of misspecifying exposure whereas the other part captures the effect of omitting needed covariates this result permits numerical evaluation of the approximate loss in efficiency and can be useful in developing guidelines for study design and model fitting procedures we discuss applications of the resul

boundary controllers and observers for the linearized schrodinger equation we consider a problem of stabilization of the linearized schrodinger equation using boundary actuation and measurements we propose two different control designs first a simple proportional collocated boundary controller is shown to exponentially stabilize the system how ever the decay rate of the closed loop system cannot be prescribed the second full state feedback boundary control design achieves an arbitrary decay rate we formally view the schrodinger equa tion as a heat equation in complex variables and apply the backstepping method recently developed for boundary control of reaction advection diffusion equations the resulting controller is then sup plied with the backstepping observer to obtain an output feedback compensator the designs are illustrated with simulations

observability and control of schrodinger equations we propose an exact controllability result for schrodinger equations in bounded domains under the bardos lebeau rauch geometric control condition with an estimate of the control which is explicit with respect to the time of controllability also we prove an explicit in time logarithmic observability estimate for the schrodinger equation where no geometrical conditions are supposed on the domain

the majorant lyapunov equation a nonnegative matrix equation for robust stability and performance of large scale systems a new robust stability and performance analysis technique is developed the approach involves replacing the state covariance by its block norm matrix i e the nonnegative matrix whose elements are the norms of subblocks of the covariance matrix partitioned according to subsystem dynamics a bound i e majorant for the block norm matrix is given by the majorant lyapunov equation a lyapunov type nonnegative matrix equation existence uniqueness and computational tractability of solutions to the majorant lyapunov equation are shown to be completely characterized in terms of m matrices two examples are considered for a damped simple harmonic oscillator with uncertain but constant natural frequency the majorant lyapunov equation predicts unconditional stability and for a pair of nominally uncoupled oscillators with uncertain coupling the majorant lyapunov equation shows that the range of nondestabilizing couplings is proportional to the frequency separation between the oscillators a result not predictable from quadratic or vector lyapunov functions

a canonical form for the inclusion principle of dynamic systems the inclusion principle provides a mathematical framework for comparing behavior of dynamic systems having different dimensions our main objective is to derive a canonical form for larger systems expansions that are obtained by expanding smaller systems contractions the form offers full freedom in selecting appropriate matrices for the expansion contraction process we will broaden the form to include feedback and propose an explicit characterization of contractible control laws subject to overlapping information structure constraints

an inclusion principle for hereditary systems abstract given two hereditary dynamic systems having different dimensions the conditions are provided under which a part of the motion of the larger system is reproduced by the smaller system that is the larger system includes the smaller one the conditions for inclusion are useful in applying the concept of vector liapunov functions to stability analysis of systems composed of overlapping subsystems by expanding the systems into a larger space the overlapping subsystems appear as disjoint and standard methods can be used to conclude stability of the expanded system under the inclusion conditions stability of the expansion implies stability of the original system an example is provided to show stability where the standard disjoint decompositions fail

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

on errors in variables in binary regression berkson case abstract in binary regression the predictor variables may be measured with error the berkson case of the errors in variables problem is considered under which the values of the predictor variables are set by the experimenter but not achieved exactly a particular model for this case is considered with probit regression and normally distributed errors of observation the regression parameters for intercept and slope are to be estimated two estimators are studied the maximum likelihood estimator mle and a modification of it in a simulation study the modified mle is shown to improve on the mle in a situation with substantial measurement error quantal bioassay is an important field of application of the berkson case of the binary regression model in quantal bioassay there is a stimulus perhaps a carcinogen or poison with doses x to be determined by the experimenter to address questions on carcinogenicity or toxicity of the stimulus each experimental animal is assigned a dose of the stimulus

nested e decompositions and clustering of complex systems abstract a graph theoretic method of extreme simplicity is proposed for decomposition and clustering of complex systems into interconnected subsystems with prescribed interaction strength the method is suitable for stability analysis via vector lyapunov functions and decentralized control and estimation of large scale systems the new decomposition scheme can be used in clustering aggregation of models in economics queuing networks and computer systems as well as decompositions in block iterative methods for solutions of linear algebraic equations

preservation of controllability observability in expanded systems the result contributed by the article is that controllability observability of an original continuous time lti dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices this new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases such as aggregations and restrictions which enable such preservation only in certain special cases a complete unrestricted transmission of these qualitative properties from the original controllable observable system to its expansion is a basic requirement on the expansion contraction process mainly when controllers observers are designed in expanded systems to be consequently contracted for implementation in initially given systems an original system composed of two overlapped subsystems is adopted as a general prototype ease a numerical example is supplied

hierarchical liapunov functions abstract a complex system is considered as a collection of dynamic components which may be combined in different ways to form stable subassemblies subsystems which may serve again as units to build still more complex stable configurations a hierarchical liapunov function is proposed which can be used to determine stability of the overall system obtained by the multilevel interconnection process stability when established in this way is hierarchically connective that is if at any instant in time the hierarchical evolution of the system is interrupted the system can fall apart in exactly the same way it was constructed and by re starting the process put together again without loss of stability this fact may be used to explain the evolution of stable forms in natural as well as man made systems

testing treatment effects in unconfounded studies under model misspecification logistic regression discretization and their combination logistic regression is commonly used to test for treatment effects in observational studies if the distribution of a continuous covariate differs between treated and control populations logistic regression yields an invalid hypothesis test even in an uncounfounded study if the link is not logistic this flaw is not corrected by the commonly used technique of discretizing the covariate into intervals a valid test can be obtained by discretization followed by regression adjustment within each interval

stabilization of fixed modes in expansions of lti systems the objective of this note is to propose a method for stabilization of structurally fixed modes in expansions of lti dynamic systems in the scope of overlapping decentralized control design based on the expansion contraction framework enabling successful design for a broader class of problems than considered so far the method is based on a judicious choice of complementary matrices in the expanded space numerical examples are provided to illustrate simplicity and efficiency of the proposed approach

exact controllability for stochastic schrodinger equations abstract this paper is addressed to studying the exact controllability of stochastic schrodinger equations by two controls one is a boundary control and the other is an internal control in the diffusion term by means of the duality argument the control problem is converted into an observability problem for backward stochastic schrodinger equations and the desired observability estimate is obtained by a global carleman estimate at last we give a result about the lack of exact controllability which shows that the action of two controls is necessary

internal null controllability of a linear schrodinger kdv system on a bounded interval abstract the control of a linear dispersive system coupling a schrodinger and a linear korteweg de vries equation is studied in this paper the system can be viewed as three coupled real valued equations by taking real and imaginary parts in the schrodinger equation the internal null controllability is proven by using either one complex valued control on the schrodinger equation or two real valued controls one on each equation notice that the single schrodinger equation is not known to be controllable with a real valued control the standard duality method is used to reduce the controllability property to an observability inequality which is obtained by means of a carleman estimates approach