adjustable robust solutions of uncertain linear programs we consider linear programs with uncertain parameters lying in some prescribed uncertainty set where part of the variables must be determined before the realization of the uncertain parameters non adjustable variables while the other part are variables that can be chosen after the realization adjustable variables we extend the robust optimization methodology 1 3 6 9 13 14 to this situation by introducing the adjustable robust counterpart arc associated with an lp of the above structure often the arc is significantly less conservative than the usual robust counterpart rc however in most cases the arc is computationally intractable np hard this difficulty is addressed by restricting the adjustable variables to be affine functions of the uncertain data the ensuing affinely adjustable robust counterpart aarc problem is then shown to be in certain important cases equivalent to a tractable optimization problem typically an lp or a semidefinite problem and in other cases having a tight approximation which is tractable the aarc approach is illustrated by applying it to a multi stage inventory management problem

ensemble control of bloch equations in this article we study a class of control problems which involves controlling a continuum of dynamical systems with different values of parameters characterizing the system dynamics by using the same control signal we call such problems control of ensembles the motivation for looking into these problems comes from the manipulation of an ensemble of nuclear spins in nuclear magnetic resonance nmr spectroscopy and imaging mri with dispersions in natural frequencies and the strengths of the applied radio frequency rf field from the standpoint of mathematical control theory the challenge is to simultaneously steer a continuum of systems between points of interest with the same control input this raises some new and unexplored questions about controllability of such systems we show that controllability of an ensemble can be understood by the study of the algebra of polynomials defined by the noncommuting vector fields that govern the system dynamics a systematic study of these systems has immediate applications to broad areas of control of ensembles of quantum systems as arising in coherent spectroscopy and quantum information processing the new mathematical structures appearing in such problems are excellent motivation for new developments in control theory

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

state distributions and minimum relative entropy noise sequences in uncertain stochastic systems the discrete time case this paper is concerned with dissipativity theory and robust performance analysis and design of discrete time stochastic systems driven by statistically uncertain random noise the uncertainty is quantified by the conditional relative entropy of the actual probability law of the noise with respect to a nominal product measure corresponding to a white noise sequence we discuss a balance equation dissipation inequality and superadditivity property for the corresponding conditional relative entropy supply as a function of time the problem of minimizing the supply required to drive the system between given state distributions over a specified time horizon is considered such variational problems involving entropy and probabilistic boundary conditions are known in the literature as schrodinger bridge problems in application to control systems the minimum required conditional relative entropy supply characterizes the robustness of the system with respect to a statistically uncertain random noise we o

the mutual independence hypothesis for categorical data in complex sampling schemes summary this paper is concerned with the analysis of contingency tables which are constructed using categorical data from a complex sampling scheme for the mutual independence hypothesis we extend tavare s 1983 results on two dimensional contingency tables to higher dimensions in particular with respect to pearson s statistic for testing the independence of two variables we strengthen the robustness result proven by tavare thus making it applicable more widely this paper is concerned with the analysis of contingency tables which are constructed using categorical data from a complex sampling scheme i e from data containing some form of between observation dependence which renders the multinomial sampling scheme invalid throughout we are interested in how departures from multinomial sampling affect pearson s statistic x2 which is appropriate for multinomial data in the literature to date two distinct approaches to the problem of categorical data from complex sampling schemes have been discussed first holt scott ewings 1980 demonstrate that for survey data analyses based on x2 can be extremely misleading and propose the one moment adjustment of x2 related references are rao scott 1981 1984 and bedrick 1983 secondly altham 1976 cohen 1976 and brier 1980 model inherent clustering in the sample they show that to avoid invalid analyses some adjustment of x2 is then necessary more recently tavare altham 1983 and tavare 1983 have considered two dimensional contingency tables which are constructed from data generated by markov chains analytic results for the null asymptotic distribution of x2 are obtained and once more it is shown that some adjustment of x2 will usually be necessary however tavare 1983 also obtains a very interesting robustness result let y1 and y2 be independent variables where y1 is an independent trials process and y2 is an arbitrary irreducible first order markov chain then the null asymptotic distribution of x2 for testing the independence of y1 and y2 is x2 on the appropriate degrees of freedom in other words no adjustment of x2 is necessary of the literature cited above the present

control and synchronization of neuron ensembles synchronization of oscillations is a phenomenon prevalent in natural social and engineering systems controlling synchronization of oscillating systems is motivated by a wide range of applications from surgical treatment of neurological diseases to the design of neurocomputers in this paper we study the control of an ensemble of uncoupled neuron oscillators described by phase models we examine controllability of such a neuron ensemble for various phase models and furthermore study the related optimal control problems in particular by employing pontryagin s maximum principle we analytically derive optimal controls for spiking single and two neuron systems and analyze the applicability of the latter to an ensemble system finally we present a robust computational method for optimal control of spiking neurons based on pseudospectral approximations the methodology developed here is universal to the control of general nonlinear phase oscillators

stochastic receding horizon control of constrained linear systems with state and control multiplicative noise we develop a receding horizon control approach to stochastic linear systems with control and state multiplicative noise that also contain constraints our receding horizon formulation is based upon an on line optimization that utilizes open loop plus linear feedback and is solved as a semi definite programming problem we also provide a characterization of stability performance and constraint satisfaction properties of the receding horizon controlled system under a specific choice of terminal weight and terminal constraint a simple numerical example is used to illustrate the approach

the analysis of categorical data from complex sample surveys chi squared tests for goodness of fit and independence in two way tables abstract the effect of stratification and clustering on the asymptotic distributions of standard pearson chi squared test statistics for goodness of fit simple hypothesis and independence in a two way contingency table denoted as x 2 and xi 2 respectively is investigated it is shown that both x 2 and xi 2 are asymptotically distributed as weighted sums of independent 1 2 random variables the weights are then related to the familiar design effects deffs used by survey samplers a simple correction to x 2 which requires only the knowledge of variance estimates or deffs for individual cells in the goodness of fit problem is proposed and empirical results on the performance of corrected x 2 provided empirical work on xi 2 indicated that the distortion of nominal significance level is substantially smaller with xi 2 than with x 2 some results under simple models for clustering are also given

on chi squared tests for multiway contingency tables with cell proportions estimated from survey data the impact of survey design on standard multinomial based methods for a multiway contingency table is studied under nested loglinear models the asymptotic null distribution of the pearson chi squared test statistic x 2 or the likelihood ratio test statistic g 2 is obtained as a weighted sum of independent chi 2 1 random variables and the weights are then related to the familiar design effects deffs used by survey samplers a simple correction to x 2 or g 2 is also obtained which requires the knowledge of only the cell deffs and the deffs for collapsed tables marginals whenever the model admits a direct solution of likelihood equations under multinomial sampling finally an example on the relative performance of x 2 and some corrected x 2 statistics in a three way table is given using some data from the canada health survey 1978 1979

design of affine controllers via convex optimization we consider a discrete time time varying linear dynamical system perturbed by process noise with linear noise corrupted measurements over a finite horizon we address the problem of designing a general affine causal controller in which the control input is an affine function of all previous measurements in order to minimize a convex objective in either a stochastic or worst case setting this controller design problem is not convex in its natural form but can be transformed to an equivalent convex optimization problem by a nonlinear change of variables which allows us to efficiently solve the problem our method is related to the classical design procedure for time invariant infinite horizon linear controller design and the more recent purified output control method we illustrate the method with applications to supply chain optimization and dynamic portfolio optimization and show the method can be combined with model predictive control techniques when perfect state information is available

extending scope of robust optimization comprehensive robust counterparts of uncertain problems in this paper we propose a new methodology for handling optimization problems with uncertain data with the usual robust optimization paradigm one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set whereas with the proposed approach we require also a controlled deterioration in performance when the data is outside the uncertainty set the extension of robust optimization methodology developed in this paper opens up new possibilities to solve efficiently multi stage finite horizon uncertain optimization problems in particular to analyze and to synthesize linear controllers for discrete time dynamical systems

on a separation theorem for generalized eigenvalues and a problem in the analysis of sample surveys abstract we obtain usable bounds for the asymptotic percentage points of chi squared tests of fit for log linear models fitted to contingency tables estimated from survey data by applying some new separation inequalities for the generalized eigenvalues of a matrix x ax with respect to a matrix x bx when both the matrices a and b are nonnegative definite we also present some historical remarks on the poincare separation theorem for eigenvalues from which our new inequalities are shown to follow

variation of mixed hodge structure i around 1970 griffiths introduced the notion of a variation of hodge structure on a complex manifold s see 17 w 2 it constitutes the axiomatization of the features possessed by the local systems of cohomology associated to a family of compact k ihler manifolds esp smooth projective varieties parametrized by s these are for a variation of hodge structure u of weight m 0 a locally constant sheaf u of q vector spaces or u of real vector spaces 1 hodge filtration horizontality a decreasing filtration o r of gs by holomorphic subbundles such that the evident connection v on takes o p into q 2 hodge decompositions if gs denotes the sheaf of functions on s and if

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

ensemble control of finite dimensional time varying linear systems in this article we investigate the problem of simultaneously steering an uncountable family of finite dimensional time varying linear systems with the same control signal this class of control problems motivates further research in the new subject of control theory called ensemble control a notion coming from the study of complex spin dynamics in nuclear magnetic resonance spectroscopy and imaging we derive the necessary and sufficient controllability conditions and an accompanying analytical optimal control law for an ensemble of finite dimensional time varying linear systems we show that ensemble controllability is in connection with singular values of the operator characterizing the system dynamics in addition the problem of optimal ensemble control of harmonic oscillators is studied to demonstrate the controllability results we show that the optimal solutions are pertinent to the study of time frequency limited signals and prolate spheroidal wave functions a systematic study of ensemble control systems has immediate applications to dynamical systems with parameter uncertainty as well as to wide ranging areas such as neuroscience and quantum control the work in ensemble control will foster further developments in mathematical control and systems theory

controllability issues for continuous spectrum systems and ensemble controllability of bloch equations we study the controllability of the bloch equation for an ensemble of non interactinghalf spins inastaticmagneticfield withdispersioninthelarmorfrequency this system may be seen as a prototype for infinite dimensional bilinear systems with continuous spectrum whose controllability is not well understood we provide several mathematical answers with discrimination between approximate and exact controlla bility and between finite time or infinite time controllability this system is not exactly controllable in finite time t with bounded controls in l 2 0 t but it is approximately controllable in l in finite time with unbounded controls in l 0 moreover we propose explicit controls realizing the asymptotic exact controllability to a uniform state of spin 1 2o r 1 2

a jackknifed chi squared test for complex samples abstract complex sample designs typically invalidate the direct application of the familiar pearson or likelihood ratio chi squared statistics for testing the fit of a model to a cross classified table of counts this article discusses the adjustment of these statistics through a jackknifing approach the technique may generally be applied whenever a standard replication method such as the jackknife bootstrap or repeated half samples provides a consistent estimate of the covariance matrix of the sample estimates properties of the limiting distribution of new test statistics xj and gj are described the new statistics may be used to test goodness of fit and to compare nested models

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

dynamic output feedback control of the liouville equation for discrete time siso linear systems in this paper we address the so called liouville control problem for discrete time siso linear systems in the class of gaussian distributions in particular we propose a systematic procedure for the characterization of a dynamic output feedback policy that will transfer the output of the system which is a known gaussian random variable to a goal gaussian distribution after a finite number of stages in the proposed approach the liouville control problem is reduced to two decoupled finite dimensional quadratic programs one of which is subject to a single affine constraint which is a convex program whereas the other one is subject to a single quadratic equality constraint despite the fact that the second optimization problem is not convex one can characterize its exact solution via a systematic procedure without resorting to convex relaxation techniques which may yield suboptimal or even infeasible solutions to the original nonconvex optimization problem finally we present numerical simulations that illustrate the key ideas of this paper

new statistics to test log linear modeling hypothesis with no distributional specifications and clusters with homogeneous correlation abstract traditionally the dirichlet multinomial distribution has been recognized as a key model for contingency tables generated by cluster sampling schemes there are however other possible distributions appropriate for these contingency tables this paper introduces new statistics capable of testing log linear modeling hypotheses with distributional unspecification when the individuals of the clusters are possibly homogeneously correlated an estimator for the intracluster correlation coefficient valid for different cluster sizes plays a crucial role in the construction of the goodness of fit test statistics

small sample comparisons of level and power for simple goodness of fit statistics under cluster sampling abstract monte carlo methods were used to examine the type i error performance of a number of goodness of fit statistics under cluster sampling the study has reduced the comparison to four procedures a x 2 s the rao scott satterthwaite adjusted x 2 b xj fay s jackknifed x 2 c fw a modified wald statistic referred to an f distribution and d fx 2 c an f based version of the rao scott adjusted x 2 depending only on the cell design effects de unlike the others the statistic fx 2 c performs well provided that the coefficient of variation a of the eigenvalues i of the design effects matrix is small in general both x 2 s and xj perform well even when a is not small fw behaves reasonably well for tests of uniform probability 0 1 k 1 k where k is the number of categories and 1 k 1 k 1 1 k 1 but it is sensitive to skewness in 0 the power performance of procedures a d was also examined attention was focused on 0 1 k 1 k

output feedback receding horizon control of constrained systems this paper considers output feedback control of linear discrete time systems with convex state and input constraints which are subject to bounded state disturbances and output measurement errors we show that the non convex problem of finding a constraint admissible affine output feedback policy over a finite horizon to be used in conjunction with a fixed linear state observer can be converted to an equivalent convex problem when used in the design of a time varying robust receding horizon control law we derive conditions under which the resulting closed loop system is guaranteed to satisfy the system constraints for all time given an initial state estimate and bound on the state estimation error when the state estimation error bound matches the minimal robust positively invariant mrpi set for the system error dynamics we show that this control law is time invariant but its calculation generally requires solution of an infinite dimensional optimization problem finally using an invariant outer

adjusted chi squared tests for cross classified tables of survey data summary holt scott ewings 1980 propose a modified pearson x2 statistic for testing independence in a two way table of survey data it is shown that the multiplier of x2 needed for this modification is a weighted sum of cell and marginal cell design effects a similar adjustment of the x2 and g2 statistics is possible whenever log linear models with closed form estimates are fitted to a cross classified table of survey data

a reduction factor in goodness of fit and independence tests for clustered and weighted observations situations often arise in a large scale household survey where a complex probability sample of clusters rather than of individuals is drawn from a large population typically the clusters of such complex samples include a number of correlated members the responses of these members are then weighted to obtain estimates for the population such weighted data are commonly published by the national center for health statistics and other u s federal agencies frequently problems arise when such data are tested by usual chi square test statistics for goodness of fit or independence researchers have discovered that the usual chi square tests provide spuriously inflated results when applied to cluster samples and that new methods are required to correct such problems this paper proposes a strategy for a goodness of fit or independence test based on correlated and weighted data arising in cluster samples and provides a factor that validly reduces the inflation of the usual chi square statistics this method is applied to the chronic condition data collected from the st paul minneapolis minnesota primary sampling unit psu during the 1975 national health interview survey nhis this analysis together with simulation studies presented elsewhere provides evidence that the usual chi square statistics from such data can be corrected for the impacts of clustering and weighting by use of the proposed reduction factor

testing mutual independence between two discrete valued spatial processes a correction to pearson chi squared a common feature of data collected in environmental and earth sciences is that they typically exhibit spatial autocorrelation violating the assumption of independent observations can have dramatic effects on inferences derived from standard statistical methods in this article we examine the consequences of spatial autocorrelation on pearson s chi squared test of mutual independence between two categorical responses with a general number of classes correspondingly we suggest a simple modification to the standard test statistic that allows for spatial autocorrelation our modified statistic is based on a first order correction factor and thus provides only an approximate test however we show by monte carlo simulation that this approximation results in satisfactory inferences in several situations of practical interest the usefulness of the method is displayed through an application to categorical data arising in the study of the relationship between the distribution pattern of plant species and woodland age in a forest in northern belgium

optimal ensemble control of stochastic time varying linear systems abstract we consider the optimal guidance of an ensemble of independent structurally identical finite dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by applying a common control function without the use of feedback our exploration of such ensemble control systems is motivated by practical control design problems in which variation in system parameters and stochastic effects must be compensated for when state feedback is unavailable such as in pulse design for nuclear magnetic resonance spectroscopy and imaging in this paper we extend the notion of ensemble control to stochastic linear systems with additive noise and jumps which we model using white gaussian noise and poisson counters respectively and investigate the optimal steering problem in our main result we prove that the minimum norm solution to a fredholm integral equation of the first kind provides the optimal control that simultaneously minimizes the mean square error mse and the error in the mean of the terminal state the optimal controls are generated numerically for several example ensemble control problems and monte carlo simulations are used to illustrate their performance this work has immediate applications to the control of dynamical systems with parameter dispersion or uncertainty that are subject to additive noise which are of interest in quantum control neuroscience and sensorless robotic manipulation

adjustments to the mantel haenszel test for data from stratified multistage surveys the usual form of the mantel haenszel test statistic assumes independent observations this is inappropriate for data from a stratified multistage survey two alternative adjustments to the test statistic are developed to deal with this a a modification of the effective sample size for each row of each table using the design effects extending a method proposed by donald and donner for familial aggregation studies b a taylor series approximation to the variance of the square root of the numerator of the mantel haenszel statistic both methods are evaluated by application to both simulated and real data the two methods perform equally well and offer a considerable improvement over the unadjusted test statistic when observations from the same cluster are highly correlated a simplified adjustment is also considered as is the need for correction to the variance of the odds ratio estimator

finite horizon covariance control for discrete time stochastic linear systems subject to input constraints abstract this work deals with a finite horizon covariance control problem for discrete time stochastic linear systems with complete state information subject to input constraints first we present the main steps for the transcription of the covariance control problem which is originally formulated as a stochastic optimal control problem into a deterministic nonlinear program nlp with a convex performance index and with both convex and non convex constraints in particular the convex constraints in this nonlinear program are induced by the input constraints of the stochastic optimal control problem whereas the non convex constraints are induced by the requirement that the terminal state covariance be equal to a prescribed positive definite matrix subsequently we associate this nonlinear program via a simple convex relaxation technique with a convex semi definite program which can be solved numerically by means of modern computational tools of convex optimization although in general the endpoints of a representative sample of closed loop trajectories generated by the control policy that corresponds to the solution of the relaxed convex program are not expected to follow exactly the goal terminal gaussian distribution they are more likely to be concentrated near the mean of this distribution than if they were drawn from the latter which is a desirable feature in practice numerical simulations that illustrate the key ideas of this work are also presented

a multicut algorithm for two stage stochastic linear programs outer linearization methods such as van slyke and wets s l shaped method for stochastic linear programs generally apply a single cut on the nonlinear objective at each major iteration the structure of stochastic programs allows for several cuts to be placed at once this paper describes a multicut algorithm to carry out this procedure it presents experimental and theoretical justification for reductions in major iterations

some results on green s higher abel jacobi map this paper is devoted to the study of the flrst higher abel jacobi invariant deflned by m green in 4 for zero cycles on a surface green s work is a very original attempt to understand at least over the graded pieces of the conjecturally deflned flltration on chow groups ch p x f 0 ch p x ae f 1 ch p x c h p x hom ae ae f p 1 ch p x 0

ensemble control of time invariant linear systems with linear parameter variation in this paper we study the control of a class of time invariant linear ensemble systems whose natural dynamics are linear in the system parameter this class of ensemble control systems arises from practical engineering and physical applications such as transport of quantum particles and control of uncertain harmonic systems we establish explicit algebraic criteria to examine controllability of such ensemble systems our derivation is based on the notion of polynomial approximation where the elements of the reachable set of the ensemble system are represented in polynomials of the system parameter and used to approximate the desired state of interest in addition we highlight the role of the spectra of the system matrices play in the determination of ensemble controllability finally illustrative examples and numerical simulations for optimal control of this class of linear ensemble systems are presented to demonstrate the theoretical results