integral versions of iss for sampled data nonlinear systems via their approximate discrete time models two integral versions of input to state stability are considered integral input to state stability iiss and integral input to integral state stability iiiss we present sufficient conditions that guarantee that if a controller achieves semiglobal practical iiss respectively iiiss of an ap proximate discrete time model of a nonlinear sampled data system then the same controller achieves semiglobal practical iiss respectively iiiss of the exact discrete time model by reducing the sampling period recent results on numerical methods for systems with measurable disturbances can be used to generate approximate models that we consider results are presented for arbitrary dynamic controllers that can be discontinuous in general

testing hypotheses in order in certain circumstances one wishes to test one hypothesis only if certain other hypotheses have been rejected this ordering of hypotheses simplifies the task of controlling the probability of rejecting any true hypothesis in an example from an observational study a treated group is shown to be further from both of two control groups than the two control groups are from each other

nonparametric tests for homogeneity based on non bipartite matching given a sequence of observations has a change occurred in the underlying probability distribution with respect to observation order this problem of detecting change points arises in a variety of applications including health prognostics for mechanical systems syndromic disease surveillance in geographically dispersed populations anomaly detection in information networks and multivariate process control in general detecting change points in high dimensional settings is challenging and most change point methods for multidimensional problems rely upon distributional assumptions or the use of observation history to model probability distributions we present three new nonparametric statistical tests for heterogeneity based on the combinatorial properties of minimum non bipartite matching mnbm the key idea underlying each of these tests is that if a sequence of independent random observations undergoes a change in distribution either an abrupt shift or a gradual drift a mnbm based on inter point

higher order numerical schemes for affinely controlled nonlinear systems a systematic method for the derivation of high order schemes for affinely controlled nonlinear systems is developed using an adaptation of the stochastic taylor expansion for control systems we construct taylor schemes of arbitrary high order and indicate how derivative free runge kutta type schemes can be obtained furthermore an approximation technique for the multiple control integrals appearing in the schemes is proposed

resampling based multiple testing methods with covariate adjustment application to investigation of antiretroviral drug susceptibility identifying genetic mutations that cause clinical resistance to antiretroviral drugs requires adjustment for potential confounders such as the number of active drugs in a hiv infected patient s regimen other than the one of interest motivated by this problem we investigated resampling based methods to test equal mean response across multiple groups defined by hiv genotype after adjustment for covariates we consider construction of test statistics and their null distributions under two types of model parametric and semiparametric the covariate function is explicitly specified in the parametric but not in the semiparametric approach the parametric approach is more precise when models are correctly specified but suffer from bias when they are not the semiparametric approach is more robust to model misspecification but may be less efficient to help preserve type i error while also improving power in both approaches we propose resampling approaches based on matching of observations with similar covariate values matching reduces the impact of model misspecification as well as imprecision in estimation these methods are evaluated via simulation studies and applied to a data set that combines results from a variety of clinical studies of salvage regimens our focus is on relating hiv genotype to viral susceptibility to abacavir after adjustment for the number of active antiretroviral drugs excluding abacavir in the patient s regimen

the false discovery rate for multiple testing in factorial experiments identifying the important factors and effects is an important goal in the analysis of two level fractional factorial experiments in moderate and large experiments the large number of potential effects presents problems of multiple statistical inference in this work we apply the false discovery rate fdr idea in multiple inference to effect identification in factorial experiments the fdr is the expected proportion of inert effects among those declared active which we believe is a more relevant quantity to control than the probability of a single erroneous declaration the criterion that has been adopted in previous studies we show how to combine the control of fdr with popular methods for estimating contrast standard error in unreplicated experiments we present simulations of unreplicated 16 and 32 run experiments that illustrate the improvements in power that can be obtained by controlling the fdr we also analyze data from an actual 128 run experiment with replication in which the fdr identifie

input to state stability for discrete time time varying systems with applications to robust stabilization of systems in power form input to state stability iss of a parameterized family of discrete time time varying nonlinear systems is investigated a converse lyapunov theorem for such systems is developed we consider parameterized families of discrete time systems and concentrate on a semiglobal practical type of stability that naturally arises when an approximate discrete time model is used to design a controller for a sampled data system an application of our main result to time varying periodic systems is presented and this is used to solve a robust stabilization problem namely to design a control law for systems in power form yielding semiglobal practical iss sp iss

gene identification using true discovery rate degree of association sets and estimates corrected for regression to the mean analyses intended to identify genes with expression that is associated with some clinical outcome or state are often based on ranked p values from tests of point null hypotheses of no association van de wiel and kim take the innovative approach of testing the interval null hypotheses that the degree of association for a gene is less than some value of interest against the alternative that it is greater combining this idea with the false discovery rate controlling methods of storey taylor and siegmund gives a computationally simple way to identify true discovery rate degree of association tdrda sets of genes among which a specified proportion are expected to have an absolute association of a specified degree or more this leads to a gene ranking method that uses the maximum lower bound degree of association for which each gene belongs to a tdrda set estimates of each gene s actual degree of association with approximate correction for selection bias due to regression to the mean rm can be derived using simple bivariate normal theory and efron and tibshirani s empirical bayes approach for a given data set all possible tdrda sets can be displayed along with the gene ranking and the rm corrected estimates of degree of association in a concise graphical summary

new characterisations of positive realness and static output feedback control of discrete time systems this article is concerned with the problems of positive real analysis and control synthesis for discrete time systems new linear matrix inequality lmi characterisations of positive realness are derived which enable one to check the positive realness by using parameter dependent lyapunov function the relationship between the proposed characterisations and the existing ones are clarified which shows that our new results are of less conservatism for characterising the positive realness of discrete time systems with polytopic uncertainty in addition sufficient conditions for static output feedback positive real controller design are given in terms of solutions to a set of linear matrix inequalities numerical examples are included for illustration

changing supply rates for input output to state stable discrete time nonlinear systems with applications we present results on changing supply rates for input output to state stable discrete time nonlinear systems our results can be used to combine two lyapunov functions none of which can be used to verify that the system has a certain property into a new composite lyapunov function from which the property of interest can be concluded the results are stated for parameterized families of discrete time systems that naturally arise when an approximate discrete time model is used to design a controller for a sampled data system we present several applications of our results i a lasalle criterion for input to state stability iss of discrete time systems ii constructing iss lyapunov functions for time varying discrete time cascaded systems iii testing iss of discrete time systems using positive semidefinite lyapunov functions iv observer based input to state stabilization of discrete time systems our results are exploited in a case study of a two link manipulator and some simulation results that illustrate advantages of our approach are presented

on uniform asymptotic stability of time varying parameterized discrete time cascades recently a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been proposed in the literature in this paper we develop novel tools that can be used within this framework and that are useful for tracking problems in particular results for stability analysis of parameterized time varying discrete time cascaded systems are given this class of models arises naturally when one uses an approximate discrete time model to design a stabilizing or tracking controller for a sampled data plant while some of our results parallel their continuous time counterparts the stability properties that are considered the conditions that are imposed and the the proof techniques that are used are tailored for approximate discrete time systems and are technically different from those in the continuous time context a result on constructing strict lyapunov functions from nonstrict ones that is of independent interest is also presented we illustrate the utility of our results in the case study of the tracking control of a mobile robot this application is fairly illustrative of the technical differences and obstacles encountered in the analysis of discrete time parameterized systems

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

optimization based stabilization of sampled data nonlinear systems via their approximate discrete time models we present results on numerical regulator design for sampled data nonlinear plants via their approximate discrete time plant models the regulator design is based on an approximate discrete time plant model and is carried out either via an infinite horizon optimization problem or via a finite horizon with terminal cost optimization problem in both cases we discuss situations when the sampling period t and the integration period h used in obtaining the approximate discrete time plant model are the same or they are independent of each other we show that using this approach practical and or semiglobal stability of the exact discrete time model is achieved under appropriate conditions

exact calculations for false discovery proportion with application to least favorable configurations in a context of multiple hypothesis testing we provide several new exact calculations related to the false discovery proportion fdp of step up and step down procedures for step up procedures we show that the number of erroneous rejections conditionally on the rejection number is simply a binomial variable which leads to explicit computations of the c d f the s th moment and the mean of the fdp the latter corresponding to the false discovery rate fdr for step down procedures we derive what is to our knowledge the first explicit formula for the fdr valid for any alternative c d f of the p values we also derive explicit computations of the power for both step up and step down procedures these formulas are explicit in the sense that they only involve the parameters of the model and the c d f of the order statistics of i i d uniform variables the p values are assumed either independent or coming from an equicorrelated multivariate normal model and an additional mixture model for the true false hypotheses is used this new approach is used to investigate new results which are of interest in their own right related to least most favorable configurations for the fdr and the variance of the fdp

an exact distribution free test comparing two multivariate distributions based on adjacency summary a new test is proposed comparing two multivariate distributions by using distances between observations unlike earlier tests using interpoint distances the new test statistic has a known exact distribution and is exactly distribution free the interpoint distances are used to construct an optimal non bipartite matching i e a matching of the observations into disjoint pairs to minimize the total distance within pairs the cross match statistic is the number of pairs containing one observation from the first distribution and one from the second distributions that are very different will exhibit few cross matches when comparing two discrete distributions with finite support the test is consistent against all alternatives the test is applied to a study of brain activation measured by functional magnetic resonance imaging during two linguistic tasks comparing brains that are impaired by arteriovenous abnormalities with normal controls a second exact distribution free test is also discussed it ranks the pairs and sums the ranks of the cross matched pairs

total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities total positivity properties of multivariate densities are useful in deducing positive dependence of random vector components and related probability inequalities in this paper we determine necessary and sufficient conditions for total positivity of absolute value multinormal variables the results are applied to obtain positive dependence and associated inequalities for the multinormal and related distributions e g the multivariate t and wishart distributions inequalities of this type yield bounds for multivariate confidence set probabilities

multiple testing via fdrl for large scale imaging data the multiple testing procedure plays an important role in detecting the presence of spatial signals for large scale imaging data typically the spatial signals are sparse but clustered this paper provides empirical evidence that for a range of commonly used control levels the conventional fdr procedure can lack the ability to detect statistical significance even if the p values under the true null hypotheses are independent and uniformly distributed more generally ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the fdr procedure this paper first introduces a scalar quantity to characterize the extent to which the lack of identification phenomenon lip of the fdr procedure occurs second we propose a new multiple comparison procedure called fdrl to accommodate the spatial information of neighboring p values via a local aggregation of p values theoretical properties of the fdrl procedure are investigated under weak dependence of p values it is shown that the fdrl procedure alleviates the lip of the fdr procedure thus substantially facilitating the selection of more stringent control levels simulation evaluations indicate that the fdrl procedure improves the detection sensitivity of the fdr procedure with little loss in detection specificity the computational simplicity and detection effectiveness of the fdrl procedure are illustrated through a real brain fmri dataset

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

a characterization of the lie algebra rank condition by transverse periodic functions the lie algebra rank condition plays a central role in nonlinear systems control theory the present paper establishes that the satisfaction of this condition by a set of smooth control vector fields is equivalent to the existence of smooth transverse periodic functions the proof here enclosed is constructive and provides an explicit method for the synthesis of such functions

stepup procedures controlling generalized fwer and generalized fdr in many applications of multiple hypothesis testing where more than one false rejection can be tolerated procedures controlling error rates measuring at least k false rejections instead of at least one for some fixed k 1 can potentially increase the ability of a procedure to detect false null hypotheses the k fwer a generalized version of the usual familywise error rate fwer is such an error rate that has recently been introduced in the literature and procedures controlling it have been proposed a further generalization of a result on the k fwer is provided in this article in addition an alternative and less conservative notion of error rate the k fdr is introduced in the same spirit as the k fwer by generalizing the usual false discovery rate fdr a k fwer procedure is constructed given any set of increasing constants by utilizing the kth order joint null distributions of the p values without assuming any specific form of dependence among all the p values procedures controlling the k fdr are also developed by using the kth order joint null distributions of the p values first assuming that the sets of null and nonnull p values are mutually independent or they are jointly positively dependent in the sense of being multivariate totally positive of order two mtp2 and then discarding that assumption about the overall dependence among the p values

system size dependence of the autocorrelation time for the swendsen wang ising model abstract we present monte carlo simulation results of the autocorrelation time for the swendsen wang method for the simulation of the ising model we have calculated the exponential and the integrated autocorrelation time at the critical point t c of the two dimensional ising model our results indicate that both autocorrelation times depend logarithmically on the linear system size l instead of a power law the simulations were carried out on the parallel computer of the condensed matter theory group at the university of mainz

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

sequential selection procedures and false discovery rate control summary we consider a multiple hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block of hypotheses a rejection rule in this setting amounts to a procedure for choosing the stopping point k this setting is inspired by the sequential nature of many model selection problems where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter we propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting we also show how the methods can be applied to model selection by using recent results on p values in sequential model selection settings

on uniform boundedness of parameterized discrete time systems with decaying inputs applications to cascades a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been established recently within this framework naturally arises the need to investigate stability properties of parameterized discrete time systems further results that guarantee appropriate stability of the parameterized family of discrete time systems that is used within this framework have been also established for systems with cascaded structure a fundamental condition that is required in this framework is uniform boundedness of solutions of the cascade however this is difficult to check in general in this paper we provide a range of sufficient conditions for uniform boundedness that are easier to check these results further contribute to the toolbox for controller design of sampled data nonlinear systems via their approximate discrete time models

stabilization of sampled data nonlinear systems by receding horizon control via discrete time approximations abstract results on stabilizing receding horizon control of sampled data nonlinear systems via their approximate discrete time models are presented the proposed receding horizon control is based on the solution of bolza type optimal control problems for the parametrized family of approximate discrete time models this paper investigates both situations when the sampling period t is fixed and the integration parameter h used in obtaining approximate model can be chosen arbitrarily small and when these two parameters coincide but they can be adjusted arbitrary sufficient conditions are established which guarantee that the controller that renders the origin to be asymptotically stable for the approximate model also stabilizes the exact discrete time model for sufficiently small integration and or sampling parameters

invaded cluster algorithm for potts models the invaded cluster algorithm a method for simulating phase transitions is described in detail theoretical albeit nonrigorous justification of the method is presented and the algorithm is applied to potts models in two and three dimensions the algorithm is shown to be useful for both first order and continuous transitions and evidently provides an efficient way to distinguish between these possibilities the dynamic properties of the invaded cluster algorithm are studied numerical evidence suggests that the algorithm has no critical slowing for ising models s1063 651x 96 09208 2

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

correlated z values and the accuracy of large scale statistical estimates we consider large scale studies in which there are hundreds or thousands of correlated cases to investigate each represented by its own normal variate typically a z value a familiar example is provided by a microarray experiment comparing healthy with sick subjects expression levels for thousands of genes this paper concerns the accuracy of summary statistics for the collection of normal variates such as their empirical cdf or a false discovery rate statistic it seems like we must estimate an n by n correlation matrix n the number of cases but our main result shows that this is not necessary good accuracy approximations can be based on the root mean square correlation over all n n 1 2 pairs a quantity often easily estimated a second result shows that z values closely follow normal distributions even under nonnull conditions supporting application of the main theorem practical application of the theory is illustrated for a large leukemia microarray study

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

a unifying integral iss framework for stability of nonlinear cascades we analyze nonlinear cascades in which the driven subsystem is integral input to state stable iss and we characterize the admissible integral iss gains for stability this characterization makes use of the convergence speed of the driving subsystem and allows a larger class of gain functions when the convergence is faster we show that our integral iss gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem the result is used to develop a new observer based backstepping design in which the growth of the nonlinear damping terms is reduced

fiber density estimation from single q shell diffusion imaging by tensor divergence diffusion weighted magnetic resonance imaging provides information about the nerve fiber bundle geometry of the human brain while the inference of the underlying fiber bundle orientation only requires single q shell measurements the absolute determination of their volume fractions is much more challenging with respect to measurement techniques and analysis unfortunately the usually employed multi compartment models cannot be applied to single q shell measurements because the compartment s diffusivities cannot be resolved this work proposes an equation for fiber orientation densities that can infer the absolute fraction up to a global factor this equation which is inspired by the classical mass preservation law in fluid dynamics expresses the fiber conservation associated with the assumption that fibers do not terminate in white matter simulations on synthetic phantoms show that the approach is able to derive the densities correctly for various configurations experiments with a pseudo ground truth phantom show that even for complex brain like geometries the method is able to infer the densities correctly in vivo results with 81 healthy volunteers are plausible and consistent a group analysis with respect to age and gender show significant differences such that the proposed maps can be used as a quantitative measure for group and longitudinal analysis

some probability inequalities for ordered rm mtp sb 2 random variables a proof of the simes conjecture some new probability inequalities involving the ordered components of an mtp 2 random vector are derived which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing this conjecture has been mostly validated so far using simulation

on stability of sets for sampled data nonlinear inclusions via their approximate discrete time models and summability criteria this paper consists of two main parts in the first part we provide a framework for stabilization of arbitrary not necessarily compact closed sets for sampled data nonlinear differential inclusions via their approximate discrete time models we generalize d nesic a r teel and p v kokotovic systems control lett 38 1999 pp 259 270 theorem 1 in several different directions we consider stabilization of arbitrary closed sets plants described as sampled data differential inclusions and arbitrary dynamic controllers in the form of difference inclusions our result does not require the knowledge of a lyapunov function for the approximate model which is a standing assumption in d nesic and a r teel ieee trans automat control 49 2004 pp 1103 1122 and d nesic a r teel and p v kokotovic systems control lett 38 1999 pp 259 270 theorem 2 we present checkable conditions that one can use to conclude semiglobal asymptotic stability or global exponential stability ges of the sampled data system via appropriate properties of its approximate discrete time model in the second part we present sufficient conditions for stability of parameterized difference inclusions that involve various summability criteria on trajectories of the system to conclude global asymptotic stability gas or ges and they represent discrete time counterparts of results given in a r teel e panteley and a loria math control signals systems 15 2002 pp 177 201 these summability criteria are not lyapunov based and they are tailored to be used within our above mentioned framework for stabilization of sampled data differential inclusions via their approximate discrete time models we believe that these tools will be a useful addition to the toolbox for controller design for sampled data nonlinear systems via their approximate discrete time models

sufficient conditions for stabilization of sampled data nonlinear systems via discrete time approximations given a parameterized by sampling period t family of approximate discrete time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all t sufficiently small we present conditions which guarantee that the same family of controllers semi globally practically stabilizes the exact discrete time model of the plant for sufficiently small sampling periods when the family of controllers is locally bounded uniformly in the sampling period the inter sample behavior can also be uniformly bounded so that the time varying sampled data model of the plant is uniformly semi globally practically stabilized the result justifies controller design for sampled data nonlinear systems based on the approximate discrete time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied our analysis is applicable to a wide range of time discretization schemes and general plant models

dependency and false discovery rate asymptotics some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step up procedure lsu for testing n hypotheses when test statistics are dependent in this paper we investigate the expected error rate eer and the false discovery rate fdr in some extreme parameter configurations when n tends to infinity for test statistics being exchangeable under null hypotheses all results are derived in terms of p values in a general setup we present a series of results concerning the interrelation of simes rejection curve and the limiting empirical distribution function of the p values main objects under investigation are largest limiting crossing points between these functions which play a key role in deriving explicit formulas for eer and fdr as specific examples we investigate equi correlated normal and t variables in more detail and compute the limiting eer and fdr theoretically and numerically a surprising limit behavior occurs if these models tend to independence

sensitivity of two sample permutation inferences in observational studies abstract in observational studies subjects are not randomly assigned to treatment or control so they may differ in their chances of receiving the treatment a simple method is developed and demonstrated for displaying the sensitivity of conventional two group permutation inferences to departures from random assignment of treatments the unmatched case discussed here differs in certain technical and computational details from the matched case discussed previously however the underlying model and the method for quantifying departures from randomization are the same the method may be applied to wilcoxon s rank sum test the gehan and log rank tests for censored outcomes mantel s test for scored categories and fisher s exact test for binary responses the method embeds the usual randomization reference distribution in a one parameter family of departures involving an unobserved covariate that would have been controlled by adjustments had it been observed as this parameter is varied the sensitivity

dynamic and static properties of the invaded cluster algorithm simulations of the two dimensional ising and three state potts models at their critical points are performed using the invaded cluster ic algorithm it is argued that observables measured on a sublattice of size l should exhibit a crossover to swendsen wang sw behavior for l sufficiently less than the lattice size l and a scaling form is proposed to describe the crossover phenomenon it is found that the energy autocorrelation time t l l for an l3l sublattice attains a maximum in the crossover region and a dynamic exponent z ic for the ic algorithm is defined according to t max l z ic simulation results for the three state model yield z ic 50 34660 002 which is smaller than values of the dynamic exponent found for the sw and wolff algorithms and also less than the li sokal bound the results are less conclusive for the ising model but it appears that z ic 0 21 and possibly that t max ln l so that z ic 50 similar to previous results for the sw and wolff algorithms s1063 651x 99 00902 2

multiple tests based on a gaussian approximation of the unitary events method with delayed coincidence count the unitary events ue method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons the detection of coincidences is usually based on binned coincidence count grun 1996 which is known to be subject to loss in synchrony detection grun diesmann grammont riehle aertsen 1999 this defect has been corrected by the multiple shift coincidence count grun et al 1999 the statistical properties of this count have not been further investigated until this work the formula being more difficult to deal with than the original binned count first we propose a new notion of coincidence count the delayed coincidence count which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains moreover it generalizes this notion to nondiscretized point processes allowing us to propose a new gaussian approximation of the count since unknown parameters are involved in the approximation we perform a plug in step where unknown parameters are replaced by estimated ones leading to a modification of the approximating distribution finally the method takes the multiplicity of the tests into account via a benjamini and hochberg approach benjamini hochberg 1995 to guarantee a prescribed control of the false discovery rate we compare our new method mtgaue multiple tests based on a gaussian approximation of the unitary events and the ue method proposed in grun et al 1999 over various simulations showing that mtgaue extends the validity of the previous method in particular mtgaue is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model furthermore mtgaue is applied on real data

a framework for stabilization of nonlinear sampled data systems based on their approximate discrete time models a unified framework for design of stabilizing controllers for sampled data differential inclusions via their approximate discrete time models is presented both fixed and fast sampling are considered in each case sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete time plant models also stabilizes the exact discrete time plant model for sufficiently small integration and or sampling periods previous results in the literature are extended to cover 1 continuous time plants modeled as differential inclusions 2 general approximate discrete time plant models 3 dynamical discontinuous controllers modeled as difference inclusions and 4 stability with respect to closed arbitrary not necessarily compact sets

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

detection of the number of signals using the benjamini hochberg procedure this paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array we formulate the detection problem as a multiple hypothesis test to control the global level of the multiple test we apply the false discovery rate fdr criterion proposed by benjamini and hochberg compared to the classical familywise error rate fwe criterion the fdr controling procedure leads to a significant gain in power for large size problems in addition we apply the bootstrap technique to estimate the observed significance level required by the fdr controling procedure simulations show that the fdr controling procedure always provides higher probability of correct detection than the fwe controling procedure furthermore the reliability of the proposed test procedure is not affected by the gain in power of the test

on false discovery control under dependence a popular framework for false discovery control is the random effects model in which the null hypotheses are assumed to be independent this paper generalizes the random effects model to a conditional dependence model which allows dependence between null hypotheses the dependence can be useful to characterize the spatial structure of the null hypotheses asymptotic properties of false discovery proportions and numbers of rejected hypotheses are explored and a large sample distributional theory is obtained

familywise robustness criteria for multiple comparison procedures a criticism of multiple comparison procedures is that the family of inferences over which an error rate is controlled is often arbitrarily selected yet the conclusion may depend heavily on the choice of the family such ambiguity is most likely in large exploratory studies requiring numerous simultaneous inferences in ambiguous situations it is desirable that results of multiple comparison procedures depend little on the chosen family to assess this we propose several familywise robustness criteria to evaluate such procedures and we find some of their properties theoretically and by simulation procedures that control the false discovery rate seem to be familywise robust

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

uniform semiglobal practical asymptotic stability for non autonomous cascaded systems and applications it is due to the modularity they provide that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on adding integrators nevertheless the standing assumptions in most of the present literature on cascaded systems is that when decoupled the subsystems constituting the cascade are uniformly globally asymptotically stable ugas hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable uspas this situation is often encountered in control practice e g in control of physical systems with external perturbations measurement noise unmodelled dynamics etc after giving a rigorous framework for the analysis of such stability properties this paper generalizes previous results for cascades by establishing that under a uniform boundedness condition on its solutions the cascade of two uspas systems remains uspas an analogous result is derived for uniformly semiglobally asymptotically stable usas systems in cascade furthermore we show the utility of our results in the pid control of mechanical systems affected by unknown non dissipative forces and considering the dynamics of the dc motors

passivity and absolute stabilization of a class of discrete time nonlinear systems abstract by using the theory of discrete time passive systems and the concept of feedback equivalence we present an approach toward deriving sufficient conditions for the global stabilization of discrete time nonlinear systems in the form x k 1 tf x k g x k u k the central feature of the approach is that a unifying set of stability criteria can be obtained and the stability results recover the previous stabilization schemes proposed in the literature

on global uniform asymptotic stability of nonlinear time varying systems in cascade abstract in this short paper we deal with the stability analysis problem of nonautonomous nonlinear systems in cascade in particular we give sufficient conditions to guarantee that i a globally uniformly stable gus nonlinear time varying nltv system remains gus when it is perturbed by the output of a globally uniformly asymptotically stable guas nltv system under the assumption that the perturbing signal is absolutely integrable ii if in addition the perturbed system is guas it remains guas under the cascaded interconnection iii two guas systems yield a guas cascaded system under some growth restrictions over the lyapunov function our proofs rely on the second method of lyapunov roughly speaking on a e stability analysis

brief growth rate conditions for uniform asymptotic stability of cascaded time varying systems in the last decade several results on cascaded autonomous systems have appeared in the literature the sufficient conditions for the stability and stabilizability of these systems are often related to certain growth rate conditions on the functions which define the dynamics of the system in this paper we analyze three complementary classes of nonlinear time varying systems according to these growth rates for each case we give further results to guarantee uniform global asymptotic stability of the cascade and relate our contributions to input to state stability and other growth rate conditions previously reported the advantage of this type of analysis is that it is often easier to verify such conditions than to find a lyapunov function with a negative definite derivative

support vector machines for dyadic data we describe a new technique for the analysis of dyadic data where two sets of objects row and column objects are characterized by a matrix of numerical values that describe their mutual relationships the new technique called potential support vector machine p svm is a large margin method for the construction of classifiers and regression functions for the column objects contrary to standard support vector machine approaches the p svm minimizes a scale invariant capacity measure and requires a new set of constraints as a result the p svm method leads to a usually sparse expansion of the classification and regression functions in terms of the row rather than the column objects and can handle data and kernel matrices that are neither positive definite nor square we then describe two complementary regularization schemes the first scheme improves generalization performance for classification and regression tasks the second scheme leads to the selection of a small informative set of row support objects and can be applied to feature selection benchmarks for classification regression and feature selection tasks are performed with toy data as well as with several real world data sets the results show that the new method is at least competitive with but often performs better than the benchmarked standard methods for standard vectorial as well as true dyadic data sets in addition a theoretical justification is provided for the new approach

adaptive linear step up procedures that control the false discovery rate we provide a new two stage procedure in which the linear step up procedure is used in stage one to estimate mo providing a new level q which is used in the linear step up procedure in the second stage we prove that a general form of the two stage procedure controls the false discovery rate at the desired level q this framework enables us to study analytically the properties of other procedures that exist in the literature a simulation study is presented that shows that two stage adaptive procedures improve in power over the original procedure mainly because they provide tighter control of the false discovery rate we further study the performance of the current suggestions some variations of the procedures and previous suggestions in the case where the test statistics are positively dependent a case for which the original procedure controls the false discovery rate in the setting studied here the newly proposed two stage procedure is the only one that controls the false discovery rate the procedures are illustrated with two examples of biological importance

joint mean and covariance estimation with unreplicated matrix variate data abstractit has been proposed that complex populations such as those that arise in genomics studies may exhibit dependencies among observations as well as among variables this gives rise to the challenging problem of analyzing unreplicated high dimensional data with unknown mean and dependence structures matrix variate approaches that impose various forms of inverse covariance sparsity allow flexible dependence structures to be estimated but cannot directly be applied when the mean and covariance matrices are estimated jointly we present a practical method utilizing generalized least squares and penalized inverse covariance estimation to address this challenge we establish consistency and obtain rates of convergence for estimating the mean parameters and covariance matrices the advantages of our approaches are i dependence graphs and covariance structures can be estimated in the presence of unknown mean structure ii the mean structure becomes more efficiently estimated when accounting for

on adjusting p values for multiplicity response 1 the development of proc multtest while controversial the use of multiplicity adjustments has gained acceptance recently in varied fields of scientific endeavor and their associated publications multiplicity adjustments have been considered important in pharmaceutical safety determinations involving multiple endpoints such as in adverse events analysis of clinical trials and in animal carcinogenicity studies in situations where the compound tested is completely safe it is likely to observe false positive indications of one or more untoward outcomes when unadjusted testing methods are used multiplicity adjustment is also important in epidemiology and other complicated areas of data analysis as it offers protection against conclusions that are driven by excessive data mining multiplicity concerns in toxicology and clinical trials prompted the development of the sas procedure proc multtest which calculates adjusted p values for a user supplied family of tests in a wide variety of applications biometrics readers will be interested to know that this software is readily available to calculate many but not all of the multiplicity adjusted p values described by wright 1992 in addition the software incorporates many improvements and enhancements such as the ability to incorporate correlations and nonnormal distributions the development of proc multtest started in may 1987 one of us westfall presented a resampling approach to calculating adjusted p values for multiple tests in multivariate binomial models with special application to the animal carcinogenicity problem the talk was entitled multivariate binomial testing and was given as the keynote address for the midwestern biopharmaceutical statistics workshop mbsw held in muncie indiana similar approaches to the same problem were developed concurrently and independently all of which have been published farrar and crump 1988 heyse and rom 1988 westfall and young 1989 an interesting biometrics connection should be mentioned here dr young thought that westfall s 1985 publication concerning simultaneous inference with multivariate binary data might be applied to the multiplicity problem in animal carcinogenicity studies dr young therefore invited dr westfall to speak at the mbsw conference on this application the initial precursor to proc multtest called proc mbin was developed in 1988 we wrote the specifications for the software and the coding was performed by youling lin at texas tech university under the auspices of the pharmaceutical manufacturing association a consortium of drug companies offered financial and intellectual support for the project specific individuals and companies who contributed are listed below in the acknowledgements section the development proceeded through a series of meetings at national and regional statistics conferences attendees included representatives from the funding organizations and from the united states food and drug administration from the outset it was decided that the primary form of output from the software would be the adjusted p value for the reasons wright describes in his opening paragraph the procedure proc mbin was described by westfall lin and young 1989 and was donated to sas institute inc the software performed multiplicity adjustments for multiple tests z score or exact permutation tests in multivariate possibly stratified multiple group binary outcome situations the main feature of the output of this software was the use of adjusted p values to summarize many statistical tests single step resampling bootstrap or permutation bonferroni and sidak methods were used to calculate the adjustments the tabular form of the output was much like tables 2 and 3 of wright showing unadjusted p values which we called raw p values side by side with various types of adjusted p values

a new factorization of special nonlinear discrete systems and their applications in this paper a new factorization of discrete nonlinear systems is presented this factorization is based on the star product an operation corresponding to the linear connection of systems a relevant algorithm is developed based on a theoretical background finally some applications to system analysis bibo stability and feedback design are provided

accumulation tests for fdr control in ordered hypothesis testing abstractmultiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses with relatively few true signals in this article we consider the multiple testing problem where prior information is available for instance from an earlier study under different experimental conditions that can allow us to test the hypotheses as a ranked list to increase the number of discoveries given an ordered list of n hypotheses the aim is to select a data dependent cutoff k and declare the first k hypotheses to be statistically significant while bounding the false discovery rate fdr generalizing several existing methods we develop a family of accumulation tests to choose a cutoff k that adapts to the amount of signal at the top of the ranked list we introduce a new method in this family the hingeexp method which offers higher power to detect true signals compared to existing techniques our theoretical results prove that these metho

formulas relating kl stability estimates of discrete time and sampled data nonlinear systems abstract we provide an explicit kl stability or input to state stability iss estimate for a sampled data nonlinear system in terms of the kl estimate for the corresponding discrete time system and a k function describing inter sample growth it is quite obvious that a uniform inter sample growth condition plus an iss property for the exact discrete time model of a closed loop system implies uniform iss of the sampled data nonlinear system our results serve to quantify these facts by means of comparison functions our results can be used as an alternative to prove and extend results in 1 or extend some results in 4 to a class of nonlinear systems finally the formulas we establish can be used as a tool for some other problems which we indicate

on uniform global asymptotic stability of nonlinear discrete time systems with applications this paper presents new characterizations of uniform global asymptotic stability for nonlinear and time varying discrete time systems under mild assumptions it is shown that weak zero state detectability is equivalent to uniform global asymptotic stability for globally uniformly stable systems by employing the notion of reduced limiting systems another characterization of uniform global asymptotic stability is proposed on the basis of the detectability for the reduced limiting systems associated with the original system as a by product we derive a generalized discrete time version of the well known krasovskii lasalle theorem for general time varying not necessarily periodic systems furthermore we apply the obtained stability results to analyze uniform asymptotic stability of cascaded time varying systems and show that some technical assumptions in recent papers can be relaxed through a practical application it is shown that our results play a similar role to the classic lasalle invariance principle in guaranteeing attractivity noting that reduced limiting systems are used instead of the original system to validate the conceptual characterizations we study the problem of sampled data stabilization for the benchmark example of nonholonomic mobile robots via the exact discrete time model rather than approximate models this case study also reveals that in general sampled data systems may become non periodic even though their original continuous time system is periodic a novel sampled data stabilizer design is proposed using the new stability results and is supported via simulation results

estimating the false discovery rate using the stochastic approximation algorithm testing of multiple hypotheses involves statistics that are strongly dependent in some applications but most work on this subject is based on the assumption of independence we propose a new method for estimating the false discovery rate of multiple hypothesis tests in which the density of test scores is estimated parametrically by minimizing the kullback leibler distance between the unknown density and its estimator using the stochastic approximation algorithm and the false discovery rate is estimated using the ensemble averaging method our method is applicable under general dependence between test statistics numerical comparisons between our method and several competitors conducted on simulated and real data examples show that our method achieves more accurate control of the false discovery rate in almost all scenarios

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

quantiles in nonrandom samples and observational studies abstract in a nonrandom sample or a nonrandomized comparison of treated and control groups methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection quantiles of a single distribution and for a shift in two distributions are both discussed these confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison the inequality has additional applications in particular it greatly accelerates the computations in a sensitivity analysis for the mantel haenszel statistic in a 2 2 s contingency table examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas an observational study of chromosome damage from mercury and a study of the drug allopurinol as a cause of skin rash the proof of the inequality makes use of savage s lattice for ranks and holley s inequality wh

sensitivity analysis for equivalence and difference in an observational study of neonatal intensive care units in randomized experiments it is sometimes important to demonstrate that two treatments do not differ greatly in their effects or to demonstrate that the treatments have very different effects on one outcome but similar effects on another outcome these demonstrations may take the form of rejecting a null hypothesis of inequivalence in an equivalence test or rejecting a null hypothesis of equal and inequivalent effects on two outcomes the procedures often express a complex hypothesis in terms of component hypotheses and combine the component significance levels to test the complex hypothesis if used in a randomized trial randomization provides valid significance levels for each component test and hence also for the combined procedure in an observational study that is in a study of treatments that were not randomly assigned there is typically concern that significance levels for testing hypotheses about treatment effects may be distorted by failure to control for some unobserved pretreatment cov

global stabilization of partially linear composite systems a linear stabilizable nonlinear asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if a the linear subsystem is right invertible and weakly minimum phase and b the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output both of these conditions are coordinate free and there is freedom of choice for the linear output variable this result generalizes several earlier sufficient conditions for stabilizability moreover the weak minimum phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem

invaded cluster algorithm for critical properties of periodic and aperiodic planar ising models we demonstrate that the invaded cluster algorithm introduced by machta et al 1995 phys rev lett 75 2792 5 is a fast and reliable tool for determining the critical temperature and the magnetic critical exponent of periodic and aperiodic ferromagnetic ising models in two dimensions the algorithm is shown to reproduce the known values of the critical temperature on various periodic and quasiperiodic graphs with an accuracy of more than three significant digits but only modest computational effort on two quasiperiodic graphs which were not investigated in this respect before the 12 fold symmetric square triangle tiling and the 10 fold symmetric tubingen triangle tiling we determine the critical temperature furthermore a generalization of the algorithm to non identical coupling strengths is presented and applied to a class of ising models on the labyrinth tiling for generic cases in which the heuristic harris luck criterion predicts deviations from the onsager universality class we find a magnetic critical exponent different from the onsager value but notable exceptions to the criterion are found which consist not only of the exactly solvable cases in agreement with a recent exact result but also of the self dual ones and maybe more

matrosov theorem for parameterized families of discrete time systems a version of matrosov s theorem for parameterized discrete time time varying systems is presented the theorem is a discrete time version of the continuous time result in loria et al 2002 d persistency of excitation a necessary and sufficient condition for uniform attractivity 2002 submitted for publication our result facilitates controller design for sampled data nonlinear systems via their approximate discrete time models an application of the theorem to establishing uniform asymptotic stability of systems controlled by model reference adaptive controllers designed via approximate discrete time plant models is presented

outlier detection and false discovery rates for whole genome dna matching we define a statistic called the matching statistic for locating regions of the genome that exhibit excess similarity among cases when compared to controls such regions are reasonable candidates for harboring disease genes we find the asymptotic distribution of the statistic while accounting for correlations among sampled individuals we then use the benjamini and hochberg false discovery rate fdr method for multiple hypothesis testing to find regions of excess sharing the p values for each region involve estimated nuisance parameters under appropriate conditions we show that the fdr method based on p values and with estimated nuisance parameters asymptotically preserves the fdr property finally we apply the method to a pilot study on schizophrenia

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

sensitivity analysis for the cross match test with applications in genomics the cross match test is an exact distribution free test of no treatment effect on a high dimensional outcome in a randomized experiment the test uses optimal nonbipartite matching to pair 2i subjects into i pairs based on similar outcomes and the cross match statistic a is the number of times that a treated subject was paired with a control rejecting for small values of a if the test is applied in an observational study in which treatments are not randomly assigned then it may be comparing treated and control subjects who are not comparable and thus may falsely reject a true null hypothesis of no treatment effect we develop a sensitivity analysis for the cross match test and apply it in an observational study of the effects of smoking on gene expression levels in addition we develop a sensitivity analysis for several multiple testing procedures using the cross match test and apply it to 1627 molecular function categories in gene ontology

is the simes improved bonferroni procedure conservative summary simes 1986 proposed a modified bonferroni procedure for conducting multiple tests of significance he proved that when the n test statistics are independent his procedure has exact size a already hommel 1983 had considered a similar procedure and shown that it need not be conservative he gave an attainable upper bound for its anticonservativeness here we show that for one sided tests based on positively correlated bivariate normal test statistics the procedure is conservative and for negatively correlated such variables it is anticonservative two sided tests based on bivariate normal variables are always conservative some numerical values are given which show that for all practical purposes the nominal a value can be used

brief strict lyapunov functions for time varying systems uniformly asymptotically stable periodic time varying systems for which is known a lyapunov function with a derivative along the trajectories non positive and negative definite in the state variable on non empty open intervals of the time are considered for these systems strict lyapunov functions are constructed

lyapunov sufficient conditions for uniform semiglobal exponential stability 2017 this manuscript version is made available under the cc by nc nd 4 0 license http creativecommons org licenses by nc nd 4 0

propensity score matching with time dependent covariates summary in observational studies with a time dependent treatment and time dependent covariates it is desirable to balance the distribution of the covariates at every time point a time dependent propensity score based on the cox proportional hazards model is proposed and used in risk set matching matching on this propensity score is shown to achieve a balanced distribution of the covariates in both treated and control groups optimal matching with various designs is conducted and compared in a study of a surgical treatment cystoscopy and hydrodistention given in response to a chronic bladder disease interstitial cystitis simulation studies also suggest that the statistical analysis after matching outperforms the analysis without matching in terms of both point and interval estimations

intrinsic robustness of global asymptotic stability abstract equivalence is shown for discrete time systems between global asymptotic stability and the so called integral input to state stability the latter is a notion of robust stability with respect to exogenous disturbances which informally translates into the statement no matter what is the initial condition if the energy of the inputs is small then the state must eventually be small

controlling nonlinear time varying systems via euler approximations abstract a discrete time model reference control algorithm for continuous time systems represented by essentially unknown nonlinear time varying ordinary differential equations is presented and analysed provided the reference model and the inverse dynamics of the plant are bounded input bounded output stable it is shown that a discrete control using state measurements based on euler approximations for the systems response can achieve arbitrary tracking accuracy the effect of unmodelled dynamics and disturbances is analysed