bayesian sensitivity analysis for unmeasured confounding in observational studies we consider bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure binary response measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models a model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder simulation from the posterior distribution is accomplished using markov chain monte carlo because the model for unmeasured confounding is not identifiable standard large sample theory for bayesian analysis is not applicable consequently the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown using simulations we investigate the coverage probability when averaged with respect to various distributions over the parameter space the results indicate that credible intervals will have approximately nominal coverage probability on average when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies we motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure

on the spaces lp x ω and wm p x ω in this paper we present some basic results on the generalized lebesgue spaces l p x omega and generalized lebesgue sobolev spaces w m w p x omega these results provide the necessary framework for the study of variational problems and elliptic equations with non standard p x growth conditions c 2001 academic press

on lp x norms the relation between a banach function space x and its subspaces formed by i those functions with absolutely continuous norm ii those with continuous norm and iii the closure of the set of

identifiability improper priors and gibbs sampling for generalized linear models markov chain monte carlo algorithms are widely used in the fitting of generalized linear models glms such model fitting is somewhat of an art form requiring suitable trickery and tuning to obtain results in which one can have confidence a wide range of practical issues arise the focus here is on parameter identifiability and posterior propriety in particular we clarify that nonidentifiability arises for usual glms and discuss its implications for simulation based model fitting because often some part of the prior specification is vague we consider whether the resulting posterior is proper providing rather general and easily checked results for glms we also show that if a gibbs sampler is run with an improper posterior then it may be possible to use the output to obtain meaningful inference for certain model unknowns

properties of a nonparametric test for early comparison of treatments in clinical trials in the presence of surrogate endpoints summary a nonparametric test is derived for comparing treatments with respect to the final endpoint in clinical trials in which the final endpoint has been observed for a random subset of patients but results are available for a surrogate endpoint for a larger sample of patients the test is an adaptation of the wilcoxon mann whitney two sample test with an adjustment that involves a comparison of the ranks of the surrogate endpoints between patients with and without final endpoints the validity of the test depends on the assumption that the patients with final endpoints represent a random sample of the patients registered in the study this assumption is viable in trials in which the final endpoint is evaluated at a landmark timepoint in the patients natural history a small sample simulation study demonstrates that the test has a size that is close to the nominal value for all configurations evaluated when compared with the conventional test based only on the final endpoints the new test delivers substantial increases in power only when the surrogate endpoint is highly correlated with the true endpoint our research indicates that in the absence of modeling assumptions auxiliary information derived from surrogate endpoints can provide significant additional information only under special circumstances

the real structured singular value is hardly approximable this paper investigates the problem of approximating the real structured singular value real spl mu a negative result is provided which shows that the problem of checking if spl mu 0 is np hard this result is much more negative than the known np hard result for the problem of checking if spl mu 0 even exponential functions of n unless np p a similar statement holds for the lower bound of spl mu our result strengthens a recent result by toker which demonstrates that obtaining a sublinear approximation for spl mu is np hard

randomized algorithms for robust controller synthesis using statistical learning theory by now it is known that several problems in the robustness analysis and synthesis of control systems are np complete or np hard these negative results force us to modify our notion of solving a given problem an approach that is recently gaining popularity is that of using randomized algorithms which can be used to solve a problem approximately most of the time we begin with the premise that many problems in robustness analysis and synthesis can be formulated as the minimization of an objective function with respect to the controller parameters it is argued that in order to assess the performance of a controller as the plant varies over a prespecified family it is better to use the average performance of the controller as the objective function to be minimized rather than its worst case performance as the worst case objective function usually leads to rather conservative designs then it is shown that a property from statistical learning theory known as uniform convergence of empirical means ucem plays an important role in allowing us to construct efficient randomized algorithms for a wide variety of controller synthesis problems in particular whenever the ucem property holds there exists an efficient i e polynomial time randomized algorithm using very recent results in statistical learning theory it is shown that the ucem property holds in any problem in which the satisfaction of a performance constraint can be expressed in terms of a finite number of polynomial inequalities in particular several problems such as robust stabilization and weighted h 2 h norm minimization are amenable to the randomized approach

eigenvalues of p x laplacian dirichlet problem abstract this paper studies the eigenvalues of the p x laplacian dirichlet problem div u p x 2 u u p x 2 u in u 0 on where is a bounded domain in rn and p x is a continuous function on such that p x 1 we show that the set of eigenvalues is a nonempty infinite set such that sup we present some sufficient conditions for inf 0 and for inf 0 respectively

a multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids the goal of this correction is to correct a mistake that appears in the proof of both lemma 3 9 and 3 10 in the article mih ilescu r dulescu 2006 1 the mistake in the proof of lemma 3 9 and 3 10 is mainly owing to the fact that we wrongly computed the expression of function g x t

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

improved upper bounds for the mixed structured singular value in this paper we take a new look at the mixed structured singular value problem a problem of finding important applications in robust stability analysis several new upper bounds are proposed using a very simple approach which we call the multiplier approach these new bounds are convex and computable by using linear matrix inequality lmi techniques we show most importantly that these upper bounds are actually lower bounds of a well known upper bound which involves the so called d scaling for complex perturbations and g scaling for real perturbations

a bayesian hierarchical model for categorical data with nonignorable nonresponse les modeles log lineaires ont montre leur utilite pour lisser des tableaux de contingence lorsque les variables categorielles sont sujettes a des non reponses qu on ne peut ignorer un modele log lineaire peut etre ajuste a un tableau de donnees augmente qui inclut une variable indicatrice indiquant si les individus sont repondants ou non les estimateurs calcules par maximum de vraisemblance a partir de tableaux de donnees augmentes sont connus pour leur instabilite en raison de solutions frontieres park et brown 1994 et park 1998 ont developpe des modeles bayesiens empiriques qui tendent a lisser les estimateurs a distance de la frontiere avec ces approches les estimateurs pour les non repondants ont ete calcules en maximisant une distribution a posteriori par l algorithme em pour etendre leur precedent travail nous avons developpe un modele hierarchique bayesien qui incorpore un modele log lineaire pour specifier la distribution a priori de plus du fait de l incertitude dans le processus de selection des variables associe a un seul modele log lineaire un nombre fini des modeles en nombre fini ont ete consideres simultanement en utilisant la procedure stochastique de selection de variables ssvs de mcculloch 1997 l integration de la procedure ssvs dans un echantillonneur de monte carlo par chaines de markov mcmc est direct et conduit a des estimations des frequences dans les cellules pour les non repondants qui sont les moyennes resultantes de plusieurs modeles log lineaires les methodes sont demontrees avec un exemple de donnees de niveaux de creatinine chez des patients ayant survecus a des transplantations renales une etude de simulation a ete conduite afin de rechercher les proprietes du modele

a dual formulation of mixed spl mu and on the losslessness of d g scaling this paper studies the mixed structured singular value spl mu and the well known d g scaling upper bound spl nu a dual characterization of spl mu and spl nu is derived which intimately links the two values using the duals it is shown that spl nu is guaranteed to be lossless i e equal to spl mu if and only if 2 m sub r m sub e m sub c spl les 3 where m sub r m sub c and m sub c are the numbers of repeated real scalar blocks repeated complex scalar blocks and full complex blocks respectively the losslessness result further leads to a variation of the well known kalman yakubovich popov lemma and lyapunov inequalities

comparing and combining biomarkers as principal surrogates for time to event clinical endpoints principal surrogate endpoints are useful as targets for phase i and ii trials in many recent trials multiple post randomization biomarkers are measured however few statistical methods exist for comparison of or combination of biomarkers as principal surrogates and none of these methods to our knowledge utilize time to event clinical endpoint information we propose a weibull model extension of the semi parametric estimated maximum likelihood method of huang and gilbert 1 that allows for the inclusion of multiple biomarkers in the same risk model as multivariate candidate principal surrogates we propose several methods for comparing candidate principal surrogates and evaluating multivariate principal surrogates these include the time dependent and surrogate dependent true and false positive fraction the time dependent and the integrated standardized total gain and the cumulative distribution function of the risk difference we illustrate the operating characteristics of our proposed methods in simulations and outline how these statistics can be used to evaluate and compare candidate principal surrogates we use these methods to investigate candidate surrogates in the diabetes control and complications trial

a bayesian approach to surrogacy assessment using principal stratification in clinical trials a surrogate marker s is a variable that can be measured earlier and often more easily than the true endpoint t in a clinical trial most previous research has been devoted to developing surrogacy measures to quantify how well s can replace t or examining the use of s in predicting the effect of a treatment z however the research often requires one to fit models for the distribution of t given s and z it is well known that such models do not have causal interpretations because the models condition on a postrandomization variable s in this article we directly model the relationship among t s and z using a potential outcomes framework introduced by frangakis and rubin 2002 biometrics 58 21 29 we propose a bayesian estimation method to evaluate the causal probabilities associated with the cross classification of the potential outcomes of s and t when s and t are both binary we use a log linear model to directly model the association between the potential outcomes of s and t through the odds ratios the quantities derived from this approach always have causal interpretations however this causal model is not identifiable from the data without additional assumptions to reduce the nonidentifiability problem and increase the precision of statistical inferences we assume monotonicity and incorporate prior belief that is plausible in the surrogate context by using prior distributions we also explore the relationship among the surrogacy measures based on traditional models and this counterfactual model the method is applied to the data from a glaucoma treatment study

bounds on treatment effects from studies with imperfect compliance abstract this article establishes nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect the bounds provided are the tightest possible given the distribution of assignments treatments and responses the formulas show that even with high rates of noncompliance experimental data can yield useful and sometimes accurate information on the average effect of a treatment on the population

links between causal effects and causal association for surrogacy evaluation in a gaussian setting two paradigms for the evaluation of surrogate markers in randomized clinical trials have been proposed the causal effects paradigm and the causal association paradigm each of these paradigms rely on assumptions that must be made to proceed with estimation and to validate a candidate surrogate marker s for the true outcome of interest t we consider the setting in which s and t are gaussian and are generated from structural models that include an unobserved confounder under the assumed structural models we relate the quantities used to evaluate surrogacy within both the causal effects and causal association frameworks we review some of the common assumptions made to aid in estimating these quantities and show that assumptions made within one framework can imply strong assumptions within the alternative framework we demonstrate that there is a similarity but not exact correspondence between the quantities used to evaluate surrogacy within each framework and show that the conditions for identifiability of the surrogacy parameters are different from the conditions which lead to a correspondence of these quantities

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

bayesian inference for causal effects in randomized experiments with noncompliance for most of this century randomization has been a cornerstone of scientific experimentation especially when dealing with humans as experimental units in practice however noncompliance is relatively common with human subjects complicating traditional theories of inference that require adherence to the random treatment assignment in this paper we present bayesian inferential methods for causal estimands in the presence of noncompliance when the binary treatment assignment is random and hence ignorable but the binary treatment received is not ignorable we assume that both the treatment assigned and the treatment received are observed we describe posterior estimation using em and data augmentation algorithms also we investigate the role of two assumptions often made in econometric instrumental variables analyses the exclusion restriction and the monotonicity assumption without which the likelihood functions generally have substantial regions of maxima we apply our procedures to real and artificial data thereby demonstrating the technology and showing that our new methods can yield valid inferences that differ in practically important ways from those based on previous methods for analysis in the presence of noncompliance including intention to treat analyses and analyses based on econometric instrumental variables techniques finally we perform a simulation to investigate the operating characteristics of the competing procedures in a simple setting which indicates relatively dramatic improvements in frequency operating characteristics attainable using our bayesian procedures

criteria for the validation of surrogate endpoints in randomized experiments the validation of surrogate endpoints has been studied by prentice 1989 statistics in medicine 8 431 440 and freedman graubard and schatzkin 1992 statistics in medicine 11 167 178 we extended their proposals in the cases where the surrogate and the final endpoints are both binary or normally distributed letting t and s be random variables that denote the true and surrogate endpoint respectively and z be an indicator variable for treatment prentice s criteria are fulfilled if z has a significant effect on t and on s if s has a significant effect on t and if z has no effect on t given s freedman relaxed the latter criterion by estimating pe the proportion of the effect of z on t that is explained by s and by requiring that the lower confidence limit of pe be larger than some proportion say 0 5 or 0 75 this condition can only be verified if the treatment has a massively significant effect on the true endpoint a rare situation we argue that two other quantities must be considered in the validation of a surrogate endpoint re the effect of z on t relative to that of z on s and gamma z the association between s and t after adjustment for z a surrogate is said to be perfect at the individual level when there is a perfect association between the surrogate and the final endpoint after adjustment for treatment a surrogate is said to be perfect at the population level if re is 1 a perfect surrogate fulfills both conditions in which case s and t are identical up to a deterministic transformation fieller s theorem is used for the estimation of pe re and their respective confidence intervals logistic regression models and the global odds ratio model studied by dale 1986 biometrics 42 909 917 are used for binary endpoints linear models are employed for continuous endpoints in order to be of practical value the validation of surrogate endpoints is shown to require large numbers of observations

some properties of an upper bound for spl mu a convex upper bound of the mixed structured singular value spl mu is analyzed the upper bound is based on a multiplier method it is simple it can exploit low rank properties and it is shown to be less conservative than the well known d g scaling a direct relationship with d g scaling is given the upper bound can be modified to one that is continuous with an explicit lipschitz constant

frequency sweeping tests for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems given in a state space form we consider specifically the notion of asymptotic stability independent of delay systems with both commensurate and noncommensurate delays are investigated we present for each class of systems a necessary and sufficient condition in terms of structured singular values and further we demonstrate how these conditions may be extended to study stability independent of delay for uncertain systems our results consist of several frequency sweeping tests that can be systematically implemented and that should complement the previous work

latent class model diagnosis summary in many areas of medical research such as psychiatry and gerontology latent class variables are used to classify individuals into disease categories often with the intention of hierarchical modeling problems arise when it is not clear how many disease classes are appropriate creating a need for model selection and diagnostic techniques previous work has shown that the pearson 2 statistic and the log likelihood ratio g2 statistic are not valid test statistics for evaluating latent class models other methods such as information criteria provide decision rules without providing explicit information about where discrepancies occur between a model and the data identifiability issues further complicate these problems this paper develops procedures for assessing markov chain monte carlo convergence and model diagnosis and for selecting the number of categories for the latent variable based on evidence in the data using markov chain monte carlo techniques simulations and a psychiatric example are presented to demonstrate the effective use of these methods

the boundedness of all products of a pair of matrices is undecidable we show that the boundedness of the set of all products of a given pair sigma of rational matrices is undecidable furthermore we show that the joint or generalized spectral radius rho sigma is not computable because testing whether rho sigma less than or equal to1 is an undecidable problem as a consequence the robust stability of linear systems under time varying perturbations is undecidable and the same is true for the stability of a simple class of hybrid systems we also discuss some connections with the so called finiteness conjecture our results are based on a simple reduction from the emptiness problem for probabilistic finite automata which is known to be undecidable c 2000 elsevier science b v all rights reserved

continuity properties of the real complex structured singular value the structured singular value function mu is defined with respect to a given uncertainty set this function is continuous if the uncertainties are allowed to be complex however if some uncertainties are required to be real then it can be discontinuous it is shown that mu is always upper semi continuous and conditions are derived under which it is also lower semi continuous with these results the real parameter robustness problem is reexamined a related although not equivalent problem is formulated which is always continuous and the relationship between the new problem and the original real mu m problem is made explicit a numerical example and results obtained via this related problem are presented

an information theoretic approach for the evaluation of surrogate endpoints based on causal inference in this work a new metric of surrogacy the so called individual causal association ica is introduced using information theoretic concepts and a causal inference model for a binary surrogate and true endpoint the ica has a simple and appealing interpretation in terms of uncertainty reduction and in some scenarios it seems to provide a more coherent assessment of the validity of a surrogate than existing measures the identifiability issues are tackled using a two step procedure in the first step the region of the parametric space of the distribution of the potential outcomes compatible with the data at hand is geometrically characterized further in a second step a monte carlo approach is proposed to study the behavior of the ica on the previous region the method is illustrated using data from the collaborative initial glaucoma treatment study a newly developed and user friendly r package surrogate is provided to carry out the evaluation exercise

sobolev embedding theorems for spaces wk p x ω this paper gives a sobolev type embedding theorem for the generalized lebesgue sobolev space wk p x where is an open domain in rn n 2 with cone property and p x is a lipschitz continuous function defined on satisfying 1 p p nk the main result can be stated as follows for any measurable function q x x formula with p x q x p x np x n kp x there exists a continuous embedding from wk p x to lq x

on continuity discontinuity in robustness indicators continuity discontinuity of robustness indicators is reviewed for the case of real or mixed uncertainty a regularization of a conservative bound to the robustness margin is proposed and its properties are discussed in the case of polynomial families with affine dependency on the uncertainty a regularization of the robustness margin results

counterfactual links to the proportion of treatment effect explained by a surrogate marker in a randomized clinical trial a statistic that measures the proportion of treatment effect on the primary clinical outcome that is explained by the treatment effect on a surrogate outcome is a useful concept we investigate whether a statistic proposed to estimate this proportion can be given a causal interpretation as defined by models of counterfactual variables for the situation of binary surrogate and outcome variables two counterfactual models are considered both of which include the concept of the proportion of the treatment effect which acts through the surrogate in general the statistic does not equal either of the two proportions from the counterfactual models and can be substantially different conditions are given for which the statistic does equal the counterfactual model proportions a randomized clinical trial with potential surrogate endpoints is undertaken in a scientific context this context will naturally place constraints on the parameters of the counterfactual model we conducted a simulation experiment to investigate what impact these constraints had on the relationship between the proportion explained pe statistic and the counterfactual model proportions we found that observable constraints had very little impact on the agreement between the statistic and the counterfactual model proportions whereas unobservable constraints could lead to more agreement

surrogate marker evaluation from an information theory perspective the last 20 years have seen lots of work in the area of surrogate marker validation partly devoted to frame the evaluation in a multitrial framework leading to definitions in terms of the quality of trial and individual level association between a potential surrogate and a true endpoint buyse et al 2000 biostatistics 1 49 67 a drawback is that different settings have led to different measures at the individual level here we use information theory to create a unified framework leading to a definition of surrogacy with an intuitive interpretation offering interpretational advantages and applicable in a wide range of situations our method provides a better insight into the chances of finding a good surrogate endpoint in a given situation we further show that some of the previous proposals follow as special cases of our method we illustrate our methodology using data from a clinical study in psychiatry

prior induction in log linear models for general contingency table analysis log linear modelling plays an important role in many statistical applications particularly in the analysis of contingency table data with the advent of powerful new computational techniques such as reversible jump mcmc bayesian analyses of these models and in particular model selection and averaging have become feasible coupled with this is the desire to construct and use suitably flexible prior structures which allow efficient computation while facilitating prior elicitation the latter is greatly improved in the case where priors can be specified on interpretable parameters about which relevant experts can express their beliefs in this paper we show how the specification of a general multivariate normal prior on the log linear parameters induces a multivariate lognormal prior on the corresponding cell counts of a contingency table we derive the parameters of this distribution in an explicit practical form and state the corresponding mean and covariances of the cell counts we discuss the importance of these results in terms of applying both uninformative and informative priors to the model parameters and provide an illustration in the context of the analysis of a 2 3 contingency table 1 introduction the analysis of general k way contingency table data is of interest in a wide variety of areas of statistical application model selection is notoriously difficult in suchsituations since th e number of models rises doubly exponentially withdimension obviously exhaustive comparisons are impossible but various computational techniques have been proposed for obtaining posterior model probabilities for problems of this sort depending upon the parameters upon which the analyst wishes to express prior opinions with the introduction of powerful new computational techniques these forms of analysis have been greatly simplified and are becoming increasingly common in the applied literature in undertaking a bayesian analysis of contingency table data it is necessary to specify priors either for the cell counts which could alternatively be expressed in terms of the cell probabilities and total cell count or equivalently the log linear parameters madigan and york 1997 choose to choose to place hyper dirichlet priors dawid and lauritzen 1993 on the cell probabilities which has the advantage that priors of this form allow a factorization of the likelihood through the identification of cliques within the corresponding model graph giudici green and tarantola 1999 illustrate how this decomposition

some np complete problems in quadratic and nonlinear programming in continuous variable smooth nonconvex nonlinear programming we analyze the complexity of checking whether a a given feasible solution is not a local minimum and b the objective function is not bounded below on the set of feasible solutions we construct a special class of indefinite quadratic programs with simple constraints and integer data and show that checking a or b on this class is np complete as a corollary we show that checking whether a given integer square matrix is not copositive is np complete

on computational complexity of invalidating structured uncertainty models abstract in this paper we study a class of uncertainty model validation invalidation problems for linear discrete time systems we consider models described by a linear fractional transformation lft of modeling uncertainties which are structured time invariant or time varying and are bounded in h or l 1 norms the experimental data available for use in invalidation are either input output time series observations or frequency response measurements we analyze the computational complexity associated with these problems while earlier work showed that for lft models with an unstructured uncertainty the invalidation problems can be reduced to one of solving linear matrix inequalities and hence may be tackled readily using well developed numerical methods in this paper we provide a simple proof to show that in the presence of structured uncertainties they are all np hard with respect to the number of uncertainty blocks suggesting that the problems are inherently intractable from a computational standpoint additionally we also demonstrate that the problems do become tractable when the lft model description is changed to an additive one leading to lmi based invalidation tests similar to those obtained elsewhere these results indicate that the main source of the computational difficulty lies in the lft description together with the structured nature of the uncertainties

computational complexity of spl mu calculation the structured singular value spl mu measures the robustness of uncertain systems numerous researchers over the last decade have worked on developing efficient methods for computing spl mu this paper considers the complexity of calculating spl mu with general mixed real complex uncertainty in the framework of combinatorial complexity theory in particular it is proved that the spl mu recognition problem with either pure real or mixed real complex uncertainty is np hard this strongly suggests that it is futile to pursue exact methods for calculating spl mu of general systems with pure real or mixed uncertainty for other than small problems

the rank one mixed m problem and kharitonov type analysis the general mixed problem has been shown to be np hard so that the exact solution of the general problem is computationally intractable except for small problems in this paper we consider not the general problem but a particular special case of this problem the rank one mixed problem we show that for this case the mixed problem is equivalent to its upper bound which is convex and it can in fact be computed easily and exactly this special case is shown to be equivalent to the so called affine parameter variation problem for a polynomial with perturbed coefficients which has been examined in detail in the literature and for which several celebrated kharitonov type results have been proven

sufficient conditions for concluding surrogacy based on observed data in this paper we show that prentice s criteria for surrogates can be strengthened to remedy some weaknesses of the criteria and we also propose some sufficient conditions under which the treatment effects on a surrogate and on the true endpoint have qualitative implication and equivalence relations with or without requiring prentice s criteria we discuss what conditions are required to qualitatively assess the causal effect of treatment on an unobserved endpoint in terms of an observed surrogate rather than a correlation between a surrogate and an endpoint we require stricter measurements of association for the qualitative assessment further we show that these conditions can be satisfied by commonly used models such as generalized linear models and cox s proportional hazard models copyright 2011 john wiley sons ltd

controller design with real parametric uncertainty a number of techniques have been developed in recent years for the analysis and design of controllers which are robust with respect to structured complex uncertainty in particular the complex synthesis procedure has been successfully applied to a number of engineering problems however the presence of real parametric uncertainty in the problem description substantially complicates matters so that standard complex synthesis techniques are no longer adequate in this paper we develop a procedure to tackle the mixed real and complex synthesis problem this procedure involves a d g k iteration between computing the mixed upper bound and solving an h optimal control problem and has guaranteed convergence to a local minimum of the nonconvex problem the procedure has been implemented in software and several controller designs are compared with the corresponding complex synthesis designs

a survey of extreme point results for robustness of control systems abstract this paper surveys a subset of the body of research which was sparked by kharitonov s theorem the focal point is extreme point results for robust stability and robust performance that is we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family the results which are surveyed apply mainly to systems with structured real parametric uncertainty in addition a number of counterexamples are given to illustrate cases for which an extreme point result does not hold for such cases a solution via the so called edge theorem is often possible

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

efficient computation of a guaranteed lower bound on the robust stability margin for a class of uncertain systems sufficient conditions for the robust stability of a class of uncertain systems with several different assumptions on the structure and nature of the uncertainties can be derived in a unified manner in the framework of integral quadratic constraints these sufficient conditions in turn can be used to derive lower bounds on the robust stability margin for such systems the lower bound is typically computed with a bisection scheme with each iteration requiring the solution of a linear matrix inequality feasibility problem we show how this bisection can be avoided altogether by reformulating the lower bound computation problem as a single generalized eigenvalue minimization problem which can be solved very efficiently using standard algorithms we illustrate this with several important commonly encountered special cases diagonal nonlinear uncertainties diagonal memoryless time invariant sector bounded popov uncertainties structured dynamic uncertainties and structured parametric uncertainties we also present a numerical example that demonstrates the computational savings that can be obtained with our approach

structured singular values and stability analysis of uncertain polynomials part 2 a missing link abstract in part 1 of this paper a generalized notion of structured singular value is introduced and studied specifically in the case when a certain matrix is of rank one in part 2 of this series we demonstrate that the framework developed in part 1 is particularly suitable for a class of stability problems and its unifies several frequency based stability conditions obtained via alternative approaches generally these problems correspond to a class of uncertain polynomials whose coefficients are perturbed in an affine fashion several stability conditions are derived readily from solution of the structured singular value presented in part 1 which either extend or coincide with previously known results in particular for family of interval and diamond polynomials we further show that the stability conditions based on the structured singular value and the corresponding results in the spirit of kharitonov theorem lead to one another thus establishing a link between the two types of drastically different results and accomplishing one of our main goals in this series a related robust stabilization problem is also investigated in this framework

integral quadratic constraint approach vs multiplier approach integral quadratic constraints iqc arise in many optimal and or robust control problems the iqc approach can be viewed as a generalization of the classical multiplier approach in the absolute stability theory in this paper we study the relationship between the two approaches for robust stability analysis using a slightly modified multiplier approach we show that the existence of an iqc is equivalent to the existence of a multiplier in most known cases it is hoped that this result provides some new insight into both approaches and makes them more useful in robust control applications

an entropy based nonparametric test for the validation of surrogate endpoints we present a nonparametric test to validate surrogate endpoints based on measure of divergence and random permutation this test is a proposal to directly verify the prentice statistical definition of surrogacy the test does not impose distributional assumptions on the endpoints and it is robust to model misspecification our simulation study shows that the proposed nonparametric test outperforms the practical test of the prentice criterion in terms of both robustness of size and power we also evaluate the performance of three leading methods that attempt to quantify the effect of surrogate endpoints the proposed method is applied to validate magnetic resonance imaging lesions as the surrogate endpoint for clinical relapses in a multiple sclerosis trial copyright 2012 john wiley sons ltd

the dirichlet problem of higher order quasilinear elliptic equation abstract the paper is concerned with the dirichlet problem of higher order quasilinear elliptic equation m 1 d a x m u g f x u x d u 0 x m 1 where r n is a bounded domain 1 p p n m g is a bounded linear functional on w 0 m p x and a x m u f x u satisfy caratheodory condition and some p x growth conditions respectively we show that there exists at least one non trivial solution for the above problem in w 0 m p x

on the gap between the complex structured singular value and its convex upper bound the gap between the complex structured singular value of a complex matrix m and its convex upper bound is considered new necessary and sufficient conditions for the existence of the gap are derived it is shown that determining whether there exists such a gap is as difficult as evaluating a structured singular value of a reduced rank matrix whose rank is equal to the multiplicity of the largest singular value of m furthermore if an upper bound on this reduced rank problem can be obtained it is shown that this provides an upper bound on the original problem that is lower than the convex relaxation upper bound an example that illustrates our procedure is given we also give the solution of several structured approximation problems of independent interest

criteria for surrogate end points summary a surrogate end point is often used to evaluate the effects of treatments or exposures on the true end point in medical researches various criteria for the statistical surrogate principal surrogate and strong surrogate have been proposed we first illustrate that with a surrogate end point that is defined by these criteria it is possible that a treatment has a positive effect on the surrogate which in turn has a positive effect on the true end point but the treatment has a negative effect on the true end point we define such a phenomenon as a surrogate paradox the surrogate paradox also means that the sign of the treatment effect on the true end point is unpredictable by the effect signs of both the treatment on the surrogate and the surrogate on the true end point then we propose two notions for a consistent surrogate and a strictly consistent surrogate to avoid the surrogate paradox with the causal network that was presented by lauritzen we discuss the conditions for a strong surrogate to be a consistent surrogate and a strictly consistent surrogate

existence of solutions for p x laplacian problems on a bounded domain in this paper we study the following p x laplacian problem div a x vd uv p x 2 d u b x v uv p x 2 u f x u x e u u 0 on p u where 1 p 1 l p x l p 2 n u s r n is a bounded domain and applying the mountain pass theorem we obtain the existence of solutions in w 0 1 p x for the p x laplacian problems in the superlinear and sublinear cases 2004 elsevier inc all rights reserved

computational complexity of real structured singular value in l sub p setting this paper studies a generalized real structured singular value spl mu problem where uncertain parameters are bounded by an l sub p norm two results are presented the first one shows that this generalized spl mu problem is np hard for any given rational number p spl isin 1 spl infin the np hardness holds as long as le the size of the largest repeated block exceeds one this result generalizes the known np hardness result for the conventional spl mu problem with p spl infin the second result which strengthens the first one considers the approximability problem of the generalized spl mu we show that the problem of obtaining an estimate for the generalized spl mu with some guaranteed bounds on the relative error remains to be np hard regardless how large this bound is