estimating the proportion of true null hypotheses with application to dna microarray data summary we consider the problem of estimating the proportion of true null hypotheses 0 i n a multiple hypothesis set up the tests are based on observed p values we first review published estimators based on the estimator that was suggested by schweder and spjotvoll then we derive new estimators based on nonparametric maximum likelihood estimation of the p value density restricting to decreasing and convex decreasing densities the estimators of 0 are all derived under the assumption of independent test statistics their performance under dependence is investigated in a simulation study we find that the estimators are relatively robust with respect to the assumption of independence and work well also for test statistics with moderate dependence

on asymptotic stabilization of driftless systems a simple approach is proposed to investigate the stabilization of driftless systems by taking the control input as a function of system states we can transform the stabilization design into a stability problem the known stability results on the nonlinear autonomous system are then employed to derive the asymptotically stabilizing controllers by solving an algebraic equation existence conditions of the asymptotic stabilizing feedback controller for the driftless systems by employing the stability criteria on linear systems and a class of third order homogeneous systems are obtained to demonstrate the application of the approach

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

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

optimal multiple testing under a gaussian prior on the effect sizes we develop a new method for large scale frequentist multiple testing with bayesian prior information we find optimal formula see text value weights that maximize the average power of the weighted bonferroni method due to the nonconvexity of the optimization problem previous methods that account for uncertain prior information are suitable for only a small number of tests for a gaussian prior on the effect sizes we give an efficient algorithm that is guaranteed to find the optimal weights nearly exactly our method can discover new loci in genome wide association studies and compares favourably to competitors an open source implementation is available

characterization of ellipsoids as k dense sets let k n be any convex body containing the origin a measurable set g n with finite and positive lebesgue measure is said to be k dense if for any fixed r 0 the measure of g x rk is constant when x varies on the boundary of g here x rk denotes a translation of a dilation of k in a previous work we proved for the case n 2 that if g is k dense then both g and k must be homothetic to the same ellipse here we completely characterize k dense sets in n if g is k dense then both g and k must be homothetic to the same ellipsoid our proof which builds upon results obtained in our previous work relies on an asymptotic formula for the measure of g x rk for large values of the parameter r and a classical characterization of ellipsoids due to petty

power enhanced multiple decision functions controlling family wise error and false discovery rates improved procedures in terms of smaller missed discovery rates mdr for performing multiple hypotheses testing with weak and strong control of the family wise error rate fwer or the false discovery rate fdr are developed and studied the improvement over existing procedures such as the sidak procedure for fwer control and the benjamini hochberg bh procedure for fdr control is achieved by exploiting possible differences in the powers of the individual tests results signal the need to take into account the powers of the individual tests and to have multiple hypotheses decision functions which are not limited to simply using the individual p values as is the case for example with the sidak bonferroni or bh procedures they also enhance understanding of the role of the powers of individual tests or more precisely the receiver operating characteristic roc functions of decision processes in the search for better multiple hypotheses testing procedures a decision theoretic framework is utilized and through auxiliary randomizers the procedures could be used with discrete or mixed type data or with rank based nonparametric tests this is in contrast to existing p value based procedures whose theoretical validity is contingent on each of these p value statistics being stochastically equal to or greater than a standard uniform variable under the null hypothesis proposed procedures are relevant in the analysis of high dimensional large m small n data sets arising in the natural physical medical economic and social sciences whose generation and creation is accelerated by advances in high throughput technology notably but not limited to microarray technology

optimal motion planning for nonholonomic systems using genetic algorithm with wavelet approximation an optimal motion planning scheme using genetic algorithm with wavelet approximation is proposed for nonholonomic systems the motion planning of nonholonomic systems can be formulated as an optimal control of a driftfree system a cost function is introduced to incorporate the control energy and the final state errors the control inputs are determined to minimize the cost functional by using the method of wavelet the infinite dimensional optimal control problem is truncated to a finite dimensional one based on the wavelet bases the genetic algorithm is employed to solve a feasible trajectory satisfying nonholonomic constraints the proposed scheme is applied to a free floating robot consisting of two one link arms connected to a main base via revolute joints the numerical results demonstrate that the genetic algorithm with the wavelet approximation is an effective approach to steer a nonholonomic system from its initial state to its final state 2006 published by elsevier inc

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

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

application of center manifold reduction to nonlinear system stabilization the center manifold theorem is applied to the local feedback stabilization of nonlinear systems in critical cases the paper addresses two particular critical cases of which the system linearization at the equilibrium point of interest is assumed to possess either a simple zero eigenvalue or a complex conjugate pair of simple and pure imaginary eigenvalues in either case the noncritical eigenvalues are taken to be stable the results on stabilizability and stabilization are given explicitly in terms of the nonlinear model of interest in its original form i e before reduction to the center manifold moreover the formulation given in this paper uncovers connections between results obtained using the center manifold reduction and those of an alternative approach

weighted false discovery rate control in large scale multiple testing abstractthe use of weights provides an effective strategy to incorporate prior domain knowledge in large scale inference this article studies weighted multiple testing in a decision theoretical framework we develop oracle and data driven procedures that aim to maximize the expected number of true positives subject to a constraint on the weighted false discovery rate the asymptotic validity and optimality of the proposed methods are established the results demonstrate that incorporating informative domain knowledge enhances the interpretability of results and precision of inference simulation studies show that the proposed method controls the error rate at the nominal level and the gain in power over existing methods is substantial in many settings an application to a genome wide association study is discussed supplementary materials for this article are available online

continuous finite time stabilization of the translational and rotational double integrators a class of bounded continuous time invariant finite time stabilizing feedback laws is given for the double integrator lyapunov theory is used to prove finite time convergence for the rotational double integrator these controllers are modified to obtain finite time stabilizing feedback that avoid unwinding

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

an embedded minimal surface with no symmetries we construct embedded minimal surfaces of finite total curvature in euclidean space by gluing catenoids and planes we use weierstrass representation and we solve the period problem using the implicit function theorem as a corollary we obtain the existence of minimal surfaces with no symmetries

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

a bayesian discovery procedure we discuss a bayesian discovery procedure for multiple comparison problems we show that under a coherent decision theoretic framework a loss function combining true positive and false positive counts leads to a decision rule based on a threshold of the posterior probability of the alternative under a semi parametric model for the data we show that the bayes rule can be approximated by the optimal discovery procedure odp recently introduced by storey 2007a improving the approximation leads us to a bayesian discovery procedure bdp which exploits the multiple shrinkage in clusters implied by the assumed nonparametric model we compare the bdp and the odp estimates in a simple simulation study and in an assessment of differential gene expression based on microarray data from tumor samples we extend the setting of the odp by discussing modifications of the loss function that lead to different single thresholding statistics finally we provide an application of the previous arguments to dependent spatial data

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

stabilization of parameters perturbation chaotic system via adaptive backstepping technique abstract the work of yassen m t yassen chaos control of chaotic dynamical systems using backstepping design chaos soliton fract 27 2006 537 548 which mainly investigated the stabilization problem for a class of chaotic systems without the parameters perturbation this paper is concerned with stabilization problem for a class of parameters perturbation chaotic systems via both backstepping design method and adaptive technique the proposed controllers can guarantee that the parameters perturbation systems will be stabilized at a fixed bounded point furthermore the paper also proposes controllers to stabilize the uncertain chaotic system at equilibrium point with only backstepping design method finally numerical simulations are given to illustrate the effectiveness of the proposed controllers

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

multiple testing of composite null hypotheses in heteroscedastic models in large scale studies the true effect sizes often range continuously from zero to small to large and are observed with heteroscedastic errors in practical situations where the failure to reject small deviations from the null is inconsequential specifying an indifference region or forming composite null hypotheses can greatly reduce the number of unimportant discoveries in multiple testing the heteroscedasticity issue poses new challenges for multiple testing with composite nulls in particular the conventional framework in multiple testing which involves rescaling or standardization is likely to distort the scientific question we propose the concept of a composite null distribution for heteroscedastic models and develop an optimal testing procedure that minimizes the false nondiscovery rate subject to a constraint on the false discovery rate the proposed approach is different from conventional methods in that the effect size statistical significance and multiplicity issues are addressed in

complete embedded minimal surfaces of finite total curvature we will survey what is known about minimal surfaces s r 3 which are complete embedded and have finite total curvature int s k da infty the only classically known examples of such surfaces were the plane and the catenoid the discovery by costa 14 15 early in the last decade of a new example that proved to be embedded sparked a great deal of research in this area many new examples have been found even families of them as will be described below the central question has been transformed from whether or not there are any examples except surfaces of rotation to one of understanding the structure of the space of examples

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 optimality of stepdown and stepup multiple test procedures consider the multiple testing problem of testing k null hypotheses where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption attention is restricted to procedures that control the familywise error rate in the strong sense and which satisfy a monotonicity condition under these assumptions we prove certain maximin optimality results for some well known stepdown and stepup procedures

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

stationary isothermic surfaces and uniformly dense domains we establish a relationship between stationary isothermic surfaces and uniformly dense domains a stationary isothermic surface is a level surface of temperature which does not evolve with time a domain in the n dimensional euclidean space r n is said to be uniformly dense in a surface r n of codimension 1 if for every small r 0 the volume of the intersection of with a ball of radius r and center x does not depend on x for x we prove that the boundary of every uniformly dense domain which is bounded or whose complement is bounded must be a sphere we then examine a uniformly dense domain with unbounded boundary and we show that the principal curvatures of satisfy certain identities the case in which the surface coincides with is particularly interesting in fact we show that if the boundary of a uniformly dense domain is connected then i if n 2 it must be either a circle or a straight line and ii if n 3 it must be either a sphere a spherical cylinder or a minimal surface we conclude with a discussion on uniformly dense domains whose boundary is a minimal surface

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

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

matzoh ball soup heat conductors with a stationary isothermic surface we consider a bounded heat conductor that satisfies the exterior sphere condition suppose that initially the conductor has temperature 0 and at all times its boundary is kept at temperature 1 we show that if the conductor contains a proper sub domain satisfying the interior cone condition and having constant boundary temperature at each given time then the conductor must be a ball

discrete sequential boundaries for clinical trials summary pocock 1977 o brien fleming 1979 and slud wei 1982 have proposed different methods to construct discrete sequential boundaries for clinical trials these methods require that the total number of decision times be specified in advance in the present paper we propose a more flexible way to construct discrete sequential boundaries the method is based on the choice of a function a t which characterizes the rate at which the error level ac is spent the boundary at a decision time is determined by a t and by past and current decision times but does not depend on the future decision times or the total number of decision times

explicit design of time varying stabilizing control laws for a class of controllable systems without drift abstract this paper gives a systematic way to design time variant feedback control laws for a class of controllable nonlinear systems this class contains a lot of systems which cannot be stabilized via a time invariant feedback control law the interest of this work lies in the design method since a general existence results is already available the techniques employed here are basic they mainly involve classical lyapunov analysis

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

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

statistical discoveries and effect size estimation abstract current methods of statistical inference are correct but incomplete small probability of wrong null hypothesis rejections can be misunderstood definitive rejections of null hypotheses as well as interval assessments of effect sizes are impossible in single cases with significance probabilities like 05 sufficiently large sets of independent experiments and attained significance levels p values should be registered from such data it is possible to calculate least upper bounds for proportions of fallacies in sets of null hypothesis rejections or effect size assessments a provisional rejection of a null hypothesis in a one tailed test or a one sided confidence interval showing a nonzero effect is here called a discovery consider a large number n of independent experiments with r discoveries for r rejections of null hypotheses the proportion of fallacies q has least upper bound q max n r 1 1 1 for r confidence intervals the proportion of fallacies is e n r assumi

α investing a procedure for sequential control of expected false discoveries summary investing is an adaptive sequential methodology that encompasses a large family of procedures for testing multiple hypotheses all control mfdr which is the ratio of the expected number of false rejections to the expected number of rejections mfdr is a weaker criterion than the false discovery rate which is the expected value of the ratio we compensate for this weakness by showing that investing controls mfdr at every rejected hypothesis investing resembles spending that is used in sequential trials but it has a key difference when a test rejects a null hypothesis investing earns additional probability towards subsequent tests investing hence allows us to incorporate domain knowledge into the testing procedure and to improve the power of the tests in this way investing enables the statistician to design a testing procedure for a specific problem while guaranteeing control of mfdr

the optimal discovery procedure a new approach to simultaneous significance testing summary the neyman pearson lemma provides a simple procedure for optimally testing a single hypothesis when the null and alternative distributions are known this result has played a major role in the development of significance testing strategies that are used in practice most of the work extending single testing strategies to multiple tests has focused on formulating and estimating new types of significance measures such as the false discovery rate these methods tend to be based on p values that are calculated from each test individually ignoring information from the other tests i show here that one can improve the overall performance of multiple significance tests by borrowing information across all the tests when assessing the relative significance of each one rather than calculating p values for each test individually the optimal discovery procedure is introduced which shows how to maximize the number of expected true positive results for each fixed number of expected false positive results the optimality that is achieved by this procedure is shown to be closely related to optimality in terms of the false discovery rate the optimal discovery procedure motivates a new approach to testing multiple hypotheses especially when the tests are related as a simple example a new simultaneous procedure for testing several normal means is defined this is surprisingly demonstrated to outperform the optimal single test procedure showing that a method which is optimal for single tests may no longer be optimal for multiple tests connections to other concepts in statistics are discussed including stein s paradox shrinkage estimation and the bayesian approach to hypothesis testing

time varying exponential stabilization of a rigid spacecraft with two control torques rigid body models with two controls cannot be locally asymptotically stabilized by continuous feedbacks which are functions of the state only this impossibility no longer holds when the feedback is also a function of time and time varying asymptotically stabilizing feedbacks have already been proposed however due to the smoothness of the feedbacks the convergence rate is only polynomial in this paper exponential convergence is obtained by considering time varying feedbacks which are only continuous

generalizing simes test and hochberg s stepup procedure in a multiple testing problem where one is willing to tolerate a few false rejections procedure controlling the familywise error rate fwer can potentially be improved in terms of its ability to detect false null hypotheses by generalizing it to control the k fwer the probability of falsely rejecting at least k null hypotheses for some fixed k 1 simes test for testing the intersection null hypothesis is generalized to control the k fwer weakly that is under the intersection null hypothesis and hochberg s stepup procedure for simultaneous testing of the individual null hypotheses is generalized to control the k fwer strongly that is under any configuration of the true and false null hypotheses the proposed generalizations are developed utilizing joint null distributions of the k dimensional subsets of the p values assumed to be identical the generalized simes test is proved to control the k fwer weakly under the multivariate totally positive of order two mtp 2 condition j multivariate analysis 10 1980 467 498 of the joint null distribution of the p values by generalizing the original simes inequality it is more powerful to detect k or more false null hypotheses than the original simes test when the p values are independent a stepdown procedure strongly controlling the k fwer a version of generalized holm s procedure that is different from and more powerful than ann statist 33 2005 1138 1154 with independent p values is derived before proposing the generalized hochberg s procedure the strong control of the k fwer for the generalized hochberg s procedure is established in situations where the generalized simes test is known to control its k fwer weakly

oracle and adaptive compound decision rules for false discovery rate control we develop a compound decision theory framework for multiple testing problems and derive an oracle rule based on the z values that minimizes the false nondiscovery rate fnr subject to a constraint on the false discovery rate fdr we show that many commonly used multiple testing procedures which are p value based are inefficient and propose an adaptive procedure based on the z values the z value based adaptive procedure asymptotically attains the performance of the z value oracle procedure and is more efficient than the conventional p value based methods we investigate the numerical performance of the adaptive procedure using both simulated and real data in particular we demonstrate our method in an analysis of the microarray data from a human immunodeficiency virus study that involves testing a large number of hypotheses simultaneously

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

on the stabilization in finite time of locally controllable systems by means of continuous time varying feedback law it is proven that if for any positive time t there exists an open loop control u a t depending continuously on the initial data a vanishing for a 0 and steering a small neighborhood of 0 into 0 in time t then the control system can be locally stabilized in small time by means of continuous time varying feedback law provided that the dimension of the state space is at least 4 and the strong accessibility rank condition holds

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

approximation theorems for parabolic equations and movement of local hot spots the authors were supported by european research council starting grants 633152 enciso and garcia ferrero and 335079 peralta salas this work was also supported by instituto de ciencias matematicas severo ochoa grant sev 2015 0554

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

adding an integrator for the stabilization problem abstract we study the relationship between the following two properties p1 the system x f x y y v is locally asymptotically stabilizable and p2 the system x f x u is locally asymptotically stabilizable where x r n y r dayawansa martin and knowles have proved that these properties are equivalent if the dimension n 1 here using the so called control lyapunov function approach a we propose another more constructive and somewhat simpler proof of dayawansa martin and knowles s result b we show that in general p1 does not imply p2 for dimensions n larger than 1 c we prove that p2 implies p1 if some extra assumptions are added like homogeneity of the system by using the latter result recursively we obtain a sufficient condition for the local asymptotic stabilizability of systems in a triangular form

covariate assisted ranking and screening for large scale two sample inference author s cai t tony sun wenguang wang weinan abstract two sample multiple testing has a wide range of applications the conventionalpractice first reduces the original observations to a vector of p values and then chooses a cutoffto adjust for multiplicity however this data reduction step could cause significant loss ofinformation and thus lead to suboptimal testing procedures we introduce a new framework fortwo sample multiple testing by incorporating a carefully constructed auxiliary variable in inferenceto improve the power a data driven multiple testing procedure is developed by employinga covariate assisted ranking and screening cars approach that optimally combines the informationfrom both the primary and the auxiliary variables the proposed cars procedureis shown to be asymptotically valid and optimal for false discovery rate control the procedureis implemented in the r package cars numerical results confirm the effectiveness of carsin false discovery rate control and show that it achieves substantial power gain over existingmethods cars is also illustrated through an application to the analysis of a satellite imagingdata set for supernova detection

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

the matzoh ball soup problem a complete characterization abstract we characterize all the solutions of the heat equation that have their spatial equipotential surfaces which do not vary with the time such solutions are either isoparametric or split in space time the result gives a final answer to a problem raised by m s klamkin extended by g alessandrini and that was named the matzoh ball soup problem by l zalcman similar results can also be drawn for a class of quasi linear parabolic partial differential equations with coefficients which are homogeneous functions of the gradient variable this class contains the isotropic or anisotropic evolution p laplace and normalized p laplace equations

on the rational stability of autonomous dynamical systems applications to control chained systems in this paper several sufficient conditions for rational stability are provided we applied our conditions to show that all chained systems are rationally stabilized by holderian feedback laws in partial sense in addition we show that the backstepping techniques can be extended to rational stabilizability theory

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

false discovery control with p value weighting we present a method for multiple hypothesis testing that maintains control of the false discovery rate while incorporating prior information about the hypotheses the prior information takes the form of p value weights if the assignment of weights is positively associated with the null hypotheses being false the procedure improves power except in cases where power is already near one even if the assignment of weights is poor power is only reduced slightly as long as the weights are not too large we also provide a similar method to control false discovery exceedance

optimal sample size for multiple testing the case of gene expression microarrays we consider the choice of an optimal sample size for multiple comparison problems the motivating application is the choice of the number of microarray experiments to be carried out when learning about differential gene expression however the approach is valid in any application that involves multiple comparisons in a large number of hypothesis tests we discuss two decision problems in the context of this setup the sample size selection and the decision about the multiple comparisons we adopt a decision theoretic approach using loss functions that combine the competing goals of discovering as many differentially expressed genes as possible while keeping the number of false discoveries manageable for consistency we use the same loss function for both decisions the decision rule that emerges for the multiple comparison problem takes the exact form of the rules proposed in the recent literature to control the posterior expected falsediscovery rate for the sample size selection we combine the expe

practical stability of nonlinear differential equation with initial time difference this paper develops the concept of practical stability to nonlinear differential equations with solutions starting with different initial times several practical stability criteria of nonlinear dynamical systems relative to initial time difference are presented by employing two lyapunov like functions the method of two lyapunov like functions enables us to obtain results under weaker assumptions

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 the orientation of a rigid body using point masses in this paper we consider a new approach to study the problem of the orientation of a rigid body containing moving masses in this approach the exponential asymptotic stability of the equilibrium positions of a rigid body with the help of moving masses are investigated a non linear feedback control law that ensuring asymptotic stability of these positions is obtained as functions of the phase coordinates of the system the control forces ensuring exponential stability of these positions are obtained the general solution of the equations of controlled system is obtained and analyzed

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

exponential stabilization of driftless nonlinear control systems using homogeneous feedback this paper focuses on the problem of exponential stabilization of controllable driftless systems using time varying homogeneous feedback the analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control lie algebra it can be shown that any continuous time varying controller that achieves exponential stability relative to the euclidean norm is necessarily non lipschitz despite these restrictions we provide a set of constructive sufficient conditions for extending smooth asymptotic stabilizers to homogeneous exponential stabilizers the modified feedbacks are everywhere continuous smooth away from the origin and can be extended to a large class of systems with torque inputs the feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

stationary isothermic surfaces in euclidean 3 space let omega be a domain in mathbb r 3 with partial omega partial mathbb r 3 setminus overline omega where partial omega is unbounded and connected and let u be the solution of the cauchy problem for the heat equation partial t u delta u over mathbb r 3 where the initial data is the characteristic function of the set omega c mathbb r 3 setminus omega we show that if there exists a stationary isothermic surface gamma of u with gamma cap partial omega varnothing then both partial omega and gamma must be either parallel planes or co axial circular cylinders this theorem completes the classification of stationary isothermic surfaces in the case that gamma cap partial omega varnothing and partial omega is unbounded to prove this result we establish a similar theorem for uniformly dense domains in mathbb r 3 a notion that was introduced by magnanini et al trans am math soc 358 4821 4841 2006 in the proof we use methods from the theory of surfaces with constant mean curvature combined with a careful analysis of certain asymptotic expansions and a surprising connection with the theory of transnormal functions