non linear observer based on the euler discretization in this paper we present an estimator based on the euler discretization first we show that the proposed estimator is an exponential observer in the case when the error between trajectories of continuous time and its associated euler discretized system can be neglected otherwise we show that the error of estimation is exponentially attracted by some neighbourhood of the origin which depends only on the sampling time finally numerical simulations using a bioreactor model are given in order to highlight the performance of the proposed estimator

direct transformation of nonlinear systems into state affine miso form for observer design this paper gives necessary and sufficient conditions to solve in a constructive way the transformation of a general multiple input single output nonlinear system into a state affine system this result is direct i e without solving the state elimination problem when computing the input output differential equation a kalman like observer can be designed for the obtained state affine system

reflective inductive inference of recursive functions in this paper we investigate reflective inductive inference of recursive functions a reflective iim is a learning machine that is additionally able to assess its own competence first we formalize reflective learning from arbitrary and from canonical example sequences here we arrive at four different types of reflection reflection in the limit optimistic pessimistic and exact reflection then we compare the learning power of reflective iims with each other as well as with the one of standard iims for learning in the limit for consistent learning of three different types and for finite learning

adapting to unknown sparsity by controlling the false discovery rate we attempt to recover an n dimensional vector observed in white noise where n is large and the vector is known to be sparse but the degree of sparsity is unknown we consider three different ways of defining sparsity of a vector using the fraction of nonzero terms imposing power law decay bounds on the ordered entries and controlling the lp norm for p small we obtain a procedure which is asymptotically minimax for l r loss simultaneously throughout a range of such sparsity classes the optimal procedure is a data adaptive thresholding scheme driven by control of the false discovery rate fdr fdr control is a relatively recent innovation in simultaneous testing ensuring that at most a certain fraction of the rejected null hypotheses will correspond to false rejections in our treatment the fdr control parameter qn also plays a determining role in asymptotic minimaxity if q lim qn 0 1 2 and also qn log n we get sharp asymptotic minimaxity simultaneously over a wide range of sparse parameter spaces and loss functions on the other hand q lim qn 1 2 1 forces the risk to exceed the minimax risk by a factor growing with q to our knowledge this relation between ideas in simultaneous inference and asymptotic decision theory is new our work provides a new perspective on a class of model selection rules which has been introduced recently by several authors these new rules impose complexity penalization of the form 2 log potential model size actual model size we exhibit a close connection with fdr controlling procedures under stringent control of the false discovery rate

size power and false discovery rates modern scientific technology has provided a new class of large scale simultaneous inference problems with thousands of hypothesis tests to consider at the same time microarrays epitomize this type of technology but similar situations arise in proteomics spectroscopy imaging and social science surveys this paper uses false discovery rate methods to carry out both size and power calculations on large scale problems a simple empirical bayes approach allows the false discovery rate fdr analysis to proceed with a minimum of frequentist or bayesian modeling assumptions closed form accuracy formulas are derived for estimated false discovery rates and used to compare different methodologies local or tail area fdr s theoretical permutation or empirical null hypothesis estimates two microarray data sets as well as simulations are used to evaluate the methodology the power diagnostics showing why nonnull cases might easily fail to appear on a list of significant discoveries

a new procedure for time varying linearization up to output injection new necessary and sufficient conditions for time varying linearization up to output injection tvloi are presented they yield a straightforward tvloi procedure

simultaneous testing of grouped hypotheses finding needles in multiple haystacks in large scale multiple testing problems data are often collected from heterogeneous sources and hypotheses form into groups that exhibit different characteristics conventional approaches including the pooled and separate analyses fail to efficiently utilize the external grouping information we develop a compound decision theoretic framework for testing grouped hypotheses and introduce an oracle procedure that minimizes the false nondiscovery rate subject to a constraint on the false discovery rate it is shown that both the pooled and separate analyses can be uniformly improved by the oracle procedure we then propose a data driven procedure that is shown to be asymptotically optimal simulation studies show that our procedures enjoy superior performance and yield the most accurate results in comparison with both the pooled and separate procedures a real data example with grouped hypotheses is studied in detail using different methods both theoretical and numerical results demonstrate that exploit

on the benjamini hochberg method we investigate the properties of the benjamini hochberg method for multiple testing and of a variant of storey s generalization of it extending and complementing the asymptotic and exact results available in the literature results are obtained under two different sets of assumptions and include asymptotic and exact expressions and bounds for the proportion of rejections the proportion of incorrect rejections out of all rejections and two other proportions used to quantify the efficacy of the method

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

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

false discovery control for random fields this article extends false discovery rates to random fields for which there are uncountably many hypothesis tests we develop a method for finding regions in the field s domain where there is a significant signal while controlling either the proportion of area or the proportion of clusters in which false rejections occur the method produces confidence envelopes for the proportion of false discoveries as a function of the rejection threshold from the confidence envelopes we derive threshold procedures to control either the mean or the specified tail probabilities of the false discovery proportion an essential ingredient of this construnction is a new algorithm to compute a confidence superset for the set of all true null locations we demonstrate our method with applications to scan statistics and functional neuroimaging

global time varying linearization up to output injection this paper following the purpose of synthesis of observers for nonlinear systems investigates the question of equivalence of a nonlinear system with a bilinear system or more generally a linear time dependent system plus an output injection in a previous work by the same authors such questions have already been dealt with from the local point of view the goal herein is to examine the global situation using basic facts from algebraic topology it is shown that in the single output case whenever the possibility to bilinearize up to output injection holds locally everywhere it also holds globally

observer design for mimo non uniformly observable systems the design of high gain observers is usually based on normal forms of observability if the system is observable for every input uniform observability the gain of the observer does not required a solution to differential equation for multiple input multiple output mimo non uniformly observable systems we give here a sufficient condition that the input must satisfy in order to design an observer unlike uniformly observable systems the observer gain of non uniformly observable systems is derived from a lyapunov differential equation

stability of polymerization reactors using i o linearization and a high gain observer we develop an observer based control structure for a standard nonlinear model of polymerization reactors we use a classical input output linearization technique for the controller synthesis and prove theoretically its global asymptotic stability because our stabilizing feedback laws require knowledge of the state of the model we solve the estimation problem by designing an exponentially converging observer the equations of which are close to those of the extended kalman filter finally by proving a nonlinear separation principle we conclude that our observer based control structure is capable of stabilizing polymerization reactors as a consequence polymerization reactors can be operated even on open loop unstable steady states

state equivalence of discrete time nonlinear control systems to state affine form up to input output injection in this paper the problem of transformation of a discrete time nonlinear control system into a state affine form up to input output injection is addressed a set of coordinate free necessary and sufficient conditions for such a transformation to be possible is first proposed and a more constructive procedure is then presented no restriction of invertibility of the state transition map is required

an intrinsic observer for a class of lagrangian systems we propose a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements our main contribution is to introduce a state position and velocity observer that is invariant under any changes of the configuration coordinates the observer dynamics equations as the euler lagrange equations are intrinsic the design method uses the riemannian structure defined by the kinetic energy on the configuration manifold the local convergence is proved by showing that the jacobian of the observer dynamics is negative definite contraction for a particular metric defined on the state space a metric derived from the kinetic energy and the observer gains from a practical point of view such intrinsic observers can be approximated when the estimated configuration is close to the true one by an explicit set of differential equations involving the riemannian curvature tensor these equations can be automatically generated via symbolic differentiations of the metric and potential up to order two numerical simulations for the ball and beam system an example where the scalar curvature is always negative show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics

plots of p values to evaluate many tests simultaneously summary when a large number of tests are made possibly on the same data it is proposed to base a simultaneous evaluation of all the tests on a plot of cumulative p values using the observed significance probabilities the points corresponding to true null hypotheses should form a straight line while those for false null hypotheses should deviate from this line the line may be used to estimate the number of true hypotheses the properties of the method are studied in some detail for the problems of comparing all pairs of means in a one way layout testing all correlation coefficients in a large correlation matrix and the evaluation of all 2 x 2 subtables in a contingency table the plot is illustrated on real data

on the linearization up to multi output injection for a class of systems with implicitly defined outputs for a class of nonlinear systems we investigate the problem of under what conditions there exists a coordinate transformation that yields a state affine linear system up to output injection with implicit outputs in particular we provide necessary and sufficient conditions for time varying linearization up to multi output injection we highlight that if the conditions hold as a consequence it is possible in the new coordinates to construct an observer with linear error dynamics we propose a methodology to find the coordinate transformation several examples illustrate the proposed procedure

empirical bayes analysis of a microarray experiment microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels a typical microarray experiment can produce millions of data points raising serious problems of data reduction and simultaneous inference we consider one such experiment in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on seven thousand human genes a simple nonparametric empirical bayes model is introduced which is used to guide the efficient reduction of the data to a single summary statistic per gene and also to make simultaneous inferences concerning which genes were affected by the radiation although our focus is on one specific experiment the proposed methods can be applied quite generally the empirical bayes inferences are closely related to the frequentist false discovery rate fdr criterion

signal classification for the integrative analysis of multiple sequences of large scale multiple tests the integrative analysis of multiple data sets is becoming increasingly important in many fields of research when the same features are studied in several independent experiments it can often be useful to analyse jointly the multiple sequences of multiple tests that result it is frequently necessary to classify each feature into one of several categories depending on the null and non null configuration of its corresponding test statistics the paper studies this signal classification problem motivated by a range of applications in large scale genomics two new types of misclassification rate are introduced and two oracle procedures are developed to control each type while also achieving the largest expected number of correct classifications corresponding data driven procedures are also proposed proved to be asymptotically valid and optimal under certain conditions and shown in numerical experiments to be nearly as powerful as the oracle procedures in an application to psychiatric genetics the procedures proposed are used to discover genetic variants that may affect both bipolar disorder and schizophrenia as well as variants that may help to distinguish between these conditions

the limiting behavior of a modified maximal symmetric 2s spacing with applications this paper presents a solution to an open problem in astrophysics namely that of estimating nonparametrically the strength of the pulsed signal in a series of high energy photon arrival times the newly proposed estimator based on a modified maximal symmetric 2s spacing is shown to be strongly consistent and asymptotically normally distributed and a monte carlo study shows that its small and moderate sample behavior is very satisfactory additionally new results regarding the weak and strong limiting behavior of modified maximal 2 s spacings are derived

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

multiple hypotheses testing and expected number of type i errors the performance of multiple test procedures with respect to error control is an old issue assuming that all hypotheses are true we investigate the behavior of the expected number of type i errors ene as a characteristic of certain multiple tests controlling the familywise error rate fwer or the false discovery rate fdr at a prespecified level we derive explicit formulas for the distribution of the number of false rejections as well as for the ene for single step step down and step up procedures based on independent p values moreover we determine the corresponding asymptotic distributions of the number of false rejections as well as explicit formulae for the ene if the number of hypotheses tends to infinity in case of fwer control we mostly obtain poisson distributions and in one case a geometric distribution as limiting distributions in case of fdr control we obtain limiting distributions which are apparently not named in the literature surprisingly the ene is bounded by a small number regardless of the number of hypotheses under consideration finally it turns out that in case of dependent test statistics the ene behaves completely differently compared to the case of independent test statistics

symbolic computing of nonlinear observable and observer forms observer design for highly nonlinear dynamics is an important issue particularly when the locally observable dynamics are not linearly observable in such circumstances the ability to reduce the system to observable or observer form is a useful first step to observer design we describe and illustrate symbolic computing tools to do that

properties of higher criticism under strong dependence the problem of signal detection using sparse faint information is closely related to a variety of contemporary statistical problems including the control of false discovery rate and classification using very high dimensional data each problem can be solved by conducting a large number of simultaneous hypothesis tests the properties of which are readily accessed under the assumption of independence in this paper we address the case of dependent data in the context of higher criticism methods for signal detection short range dependence has no first order impact on performance but the situation changes dramatically under strong dependence there although higher criticism can continue to perform well it can be bettered using methods based on differences of signal values or on the maximum of the data the relatively inferior performance of higher criticism in such cases can be explained in terms of the fact that under strong dependence the higher criticism statistic behaves as though the data were partitioned into very large blocks with all but a single representative of each block being eliminated from the dataset

local observer for infinitesimally observable nonlinear systems in this article we present a local observer based on infinitesimal observability along trajectories the gain of this observer derives from a dynamical lyapunov equation the inputs for which the observer converges are those which render the system observable at each point of the limit of the unknown trajectory infinitesimal observability at infinity along trajectories the performance of the proposed observer is illustrated with an application to dc machine

refuting learning revisited we consider within the framework of inductive inference the concept of refuting learning as introduced by mukouchi and arikawa where the learner is not only required to learn all concepts in a given class but also has to explicitly refute concepts outside the class in the first part of the paper we consider learning from text and introduce a concept of limit refuting learning that is intermediate between refuting learning and reliable learning we give characterizations for these concepts and show some results about their relative strength and their relation to confident learning in the second part of the paper we consider learning from texts that for some k contain all positive k formulae that are valid in the standard structure determined by the set to be learned in this model the following results are shown for the language with successor any countable axiomatizable class can be limit refuting learned from 1 texts for the language with successor and order any countable axiomatizable class can be reliably learned from 1 texts and can be limit refuting learned from 2 texts whereas the axiomatizable class of all finite sets cannot be limit refuting learned from 1 texts for the full language of arithmetic which contains in addition plus and times for any even k there is an axiomatizable class that can be limit refuting learned from k 1 texts but not from k texts a similar result with k 3 in place of k 1 holds with respect to the language of presburger s arithmetic

some results on false discovery rate in stepwise multiple testing procedures the concept of false discovery rate fdr has been receiving increasing attention by researchers in multiple hypotheses testing this paper produces some theoretical results on the fdr in the context of stepwise multiple testing procedures with dependent test statistics it was recently shown by benjamini and yekutieli that the benjamini hochberg step up procedure controls the fdr when the test statistics are positively dependent in a certain sense this paper strengthens their work by showing that the critical values of that procedure can be used in a much more general stepwise procedure under similar positive dependency it is also shown that the fdr controlling benjamini liu step down procedure originally developed for independent test statistics works even when the test statistics are positively dependent in some sense an explicit expression for the fdr of a generalized stepwise procedure and an upper bound to the fdr of a step down procedure are obtained in terms of probability distributions of ordered components of dependent random variables before establishing the main results 1 introduction the main purpose of this paper is to present some formulas and inequalities providing theoretical insight into when and what stepwise procedures control the false discovery rate fdr at a prespecified level in multiple hypotheses testing the fdr first introduced in multiple testing by benjamini and hochberg 1995 is the expected proportion of erroneously rejected null hypotheses with v and r representing respectively the number of true null hypotheses rejected and the total number of null hypotheses rejected in a multiple testing procedure let q v r if r 0a nd 0i fr 0 then e q is the fdr of that procedure as they have argued it is an appropriate error rate to control in many practical situations particularly where a large number of null hypotheses are involved they also put forward an fdr controlling stepup procedure that is more powerful than comparable procedures controlling the traditional familywise error fwe rate when the underlying test statistics are independent benjamini and liu 1999 recently introduced a step down procedure with the same property the concept of fdr is now being used in a wide variety of applications abramovich and benjamini 1996 basford and tukey 1997 drigalenko

learning by switching type of information the present work is dedicated to the study of modes of data presentation in the range between text and informant within the framework of inductive inference in this study the learner alternatingly requests sequences of positive and negative data we define various formalizations of valid data presentations in such a scenario we resolve the relationships between these different formalizations and show that one of these is equivalent to learning from informant we also show a hierarchy formed for each of the formalizations studied by considering the number of switches between requests for positive and negative data

a stochastic process approach to false discovery control this paper extends the theory of false discovery rates fdr pioneered by benjamini and hochberg j roy statist soc ser b 57 1995 289 300 we develop a framework in which the false discovery proportion fdp the number of false rejections divided by the number of rejections is treated as a stochastic process after obtaining the limiting distribution of the process we demonstrate the validity of a class of procedures for controlling the false discovery rate the expected fdp we construct a confidence envelope for the whole fdp process from these envelopes we derive confidence thresholds for controlling the quantiles of the distribution of the fdp as well as controlling the number of false discoveries we also investigate methods for estimating the p value distribution

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

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

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

the positive false discovery rate a bayesian interpretation and the q value multiple hypothesis testing is concerned with controlling the rate of false positives when testing several hypotheses simultaneously one multiple hypothesis testing error measure is the false discovery rate fdr which is loosely defined to be the expected proportion of false positives among all significant hypotheses the fdr is especially appropriate for exploratory analyses in which one is interested in finding several significant results among many tests in this work we introduce a modified version of the fdr called the positive false discovery rate pfdr we discuss the advantages and disadvantages of the pfdr and investigate its statistical properties when assuming the test statistics follow a mixture distribution we show that the pfdr can be written as a bayesian posterior probability and can be connected to classification theory these properties remain asymptotically true under fairly general conditions even under certain forms of dependence also a new quantity called the q value is introduced and investigated which is a natural bayesian posterior p value or rather the pfdr analogue of the p value 1 introduction when testing a single hypothesis one is usually concerned with controlling the false positive rate while maximizing the probability of detecting an effect when one really exists in statistical terms we maximize the power conditional on the type i error rate being at or below some level the field of multiple hypothesis testing tries to extend this basic paradigm to the situation where several hypotheses are tested simultaneously one must define an appropriate compound error measure according to the rate of false positives one is willing to encounter then a procedure is developed that allows one to control the error rate at a desired level while maintaining the power of each test as much as possible the most commonly controlled quantity when testing multiple hypotheses is the family wise error rate fwer which is the probability of yielding one or more false positives out of all hypotheses tested the most familiar example of this is the bonferroni method if there are m hypothesis tests each test is controlled so that the probability of a false positive is less than or equal to m for some chosen value of it then follows that the overall fwer is less than or equal to m any

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

on false discovery rate thresholding for classification under sparsity we study the properties of false discovery rate fdr thresholding viewed as a classification procedure the 0 class null is assumed to have a known density while the 1 class alternative is obtained from the 0 class either by translation or by scaling furthermore the 1 class is assumed to have a small number of elements w r t the 0 class sparsity we focus on densities of the subbotin family including gaussian and laplace models nonasymptotic oracle inequalities are derived for the excess risk of fdr thresholding these inequalities lead to explicit rates of convergence of the excess risk to zero as the number m of items to be classified tends to infinity and in a regime where the power of the bayes rule is away from 0 and 1 moreover these theoretical investigations suggest an explicit choice for the target level alpha m of fdr thresholding as a function of m our oracle inequalities show theoretically that the resulting fdr thresholding adapts to the unknown sparsity regime contained in the data this property is illustrated with numerical experiments

semi global observer for multi output nonlinear systems abstract we present an explicit form of nonlinear observers for a class of multi input multi output systems observer construction for multi output nonlinear systems is not a trivial extension of single output case especially when the global error convergence is of interest in this paper we consider a class of systems in which the subsystem for each output has a triangular dependence on the states of that subsystem itself and the overall system has a block triangular form for each subsystem hence the contribution is to extend the results existing in the literature in that interconnections between the subsystems are allowed the construction is based on the saturation of some estimates which is originated by khalil and esfandiari for the use of semi global output feedback control