the berry esseen bound for student s statistic we prove the berry esseen bound for the student t statistic under the assumption of a third moment this bound coincides up to an absolute constant with the classical berry esseen bound for the mean in general the distribution of the student statistic converges to the standard normal distribution function at least as fast as the distribution of the mean and sometimes faster for example rates of convergence can be proved if the underlying distribution is in the domain of attraction of the normal law

tests for high dimensional covariance matrices we propose tests for sphericity and identity of high dimensional covariance matrices the tests are nonparametric without assuming a specific parametric distribution for the data they can accommodate situations where the data dimension is much larger than the sample size namely the large p small n situations we demonstrate by both theoretical and empirical studies that the tests have good properties for a wide range of dimensions and sample sizes we applied the proposed test on a microarray dataset on yorkshire gilts and tested for the covariance structure for the expression levels for sets of genes

a cdma multiuser detection algorithm on the basis of belief propagation an iterative algorithm for the multiuser detection problem that arises in code division multiple access cdma systems is developed on the basis of pearl s belief propagation bp we show that the bp based algorithm exhibits nearly optimal performance in a practical time scale by utilizing the central limit theorem and self averaging property appropriately whereas direct application of bp to the detection problem is computationally difficult and far from practical we further present close relationships of the proposed algorithm to the thouless anderson palmer approach and replica analysis known in spin glass research

to how many simultaneous hypothesis tests can normal student s t or bootstrap calibration be applied in the analysis of microarray data and in some other contemporary statistical problems it is not uncommon to apply hypothesis tests in a highly simultaneous way the number n say of tests used can be much larger than the sample sizes n to which the tests are applied yet we wish to calibrate the tests so that the overall level of the simultaneous test is accurate often the sampling distribution is quite different for each test so there may not be an opportunity to combine data across samples in this setting how large can n be as a function of n before level accuracy becomes poor here we answer this question in cases where the statistic under test is of student s t type we show that if either the normal or student t distribution is used for calibration then the level of the simultaneous test is accurate provided that log n increases at a strictly slower rate than n 1 3 as n diverges on the other hand if bootstrap methods are used for calibration then we may choose log n almost as large as

frequency synchronization in a random oscillator network we study the frequency synchronization of a randomly coupled oscillators by analyzing the continuum limit we obtain a sufficient condition for the mean field type synchronization we especially find that the critical coupling constant k becomes 0 in the random scale free network p k ensuremath propto k ensuremath ensuremath gamma if 2l ensuremath gamma ensuremath leqslant 3 numerical simulations in finite networks are consistent with this analysis

cramer type moderate deviation for the maximum of the periodogram with application to simultaneous tests in gene expression time series where 1 j q and q n 1 2 the periodogram is a fundamental tool in spectral analysis and is often used to detect periodic patterns in various real applications such as the analysis of gene expression data and the study of earthquake theoretical properties of the periodogram have been extensively studied an chen and hannan 1983 obtained the logarithm law for the maximum of the periodogram davis and mikosch 1999 mikosch resnick and samorodnitsky 2000 lin and liu 2009a obtained the asymptotic distribution for the maximum of the periodogram under the i i d and linear process cases the heavy tailed case and nonlinear time series case respectively fay and soulier 2001 proved the central limit theorem for functionals of the periodogram shao and wu 2007 obtained asymptotic distributions for the periodogram and the empirical distribution function of the periodogram for a wide class of nonlinear processes when xn are independent and identically distributed i i d random variables with var x1 2 and e x1 2 0 davis and mikosch 1999 show that

inference and testing breaks in large dynamic panels with strong cross sectional dependence in this paper we provide a new central limit theorem for estimators of the slope papers in large dynamic panel data models where both n and t increase without bound in the presence of possibly strong cross sectional dependence we proceed by providing two related tests for breaks homogeneity in the time dimension the first test is based on the cusum principle the second test is based on a hausman durbin wu approach some of the key features of the tests are that they have nontrivial power when the number of individuals for which the slope parameters may differ is a negligible fraction or when the break happens to be towards the end of the sample and do not suffer from the incidental parameter problem we provide a simple bootstrap algorithm to obtain asymptotic valid critical values for our statistics an important feature of the bootstrap is that there is no need to know the underlying model of the cross sectional dependence a monte carlo simulation analysis sheds some light on the small sample behaviour of the tests and their bootstrap analogues we implement our test to some real economic data

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

a new perspective on robust m estimation finite sample theory and applications to dependence adjusted multiple testing heavy tailed errors impair the accuracy of the least squares estimate which can be spoiled by a single grossly outlying observation as argued in the seminal work of peter huber in 1973 ann statist 1 1973 799 821 robust alternatives to the method of least squares are sorely needed to achieve robustness against heavy tailed sampling distributions we revisit the huber estimator from a new perspective by letting the tuning parameter involved diverge with the sample size in this paper we develop nonasymptotic concentration results for such an adaptive huber estimator namely the huber estimator with the tuning parameter adapted to sample size dimension and the variance of the noise specifically we obtain a sub gaussian type deviation inequality and a nonasymptotic bahadur representation when noise variables only have finite second moments the nonasymptotic results further yield two conventional normal approximation results that are of independent interest the berry esseen inequality and cramer type moderate deviation as an important application to large scale simultaneous inference we apply these robust normal approximation results to analyze a dependence adjusted multiple testing procedure for moderately heavy tailed data it is shown that the robust dependence adjusted procedure asymptotically controls the overall false discovery proportion at the nominal level under mild moment conditions thorough numerical results on both simulated and real datasets are also provided to back up our theory

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

onset of synchronization in large networks of coupled oscillators we study the transition from incoherence to coherence in large networks of coupled phase oscillators we present various approximations that describe the behavior of an appropriately defined order parameter past the transition and generalize recent results for the critical coupling strength we find that under appropriate conditions the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix we show how with an additional assumption a mean field approximation recently proposed is recovered from our results we test our theory with numerical simulations and find that it describes the transition when our assumptions are satisfied we find that our theory describes the transition well in situations in which the mean field approximation fails we study the finite size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase

coupled effects of local movement and global interaction on contagion abstract by incorporating segregated spatial domain and individual based linkage into the sis susceptible infected susceptible model we propose a generalized epidemic model which can change from the territorial epidemic model to the networked epidemic model the role of the individual based linkage between different spatial domains is investigated as we adjust the timescale parameter from 0 to unity which represents the degree of activation of the individual based linkage three regions are found within the region of 0 0 02 the epidemic is determined by local movement and is sensitive to the timescale within the region of 0 02 0 5 the epidemic is insensitive to the timescale within the region of 0 5 1 the outbreak of the epidemic is determined by the structure of the individual based linkage as we keep an eye on the first region the role of activating the individual based linkage in the present model is similar to the role of the shortcuts in the two dimensional small world network only activating a small number of the individual based linkage can prompt the outbreak of the epidemic globally the role of narrowing segregated spatial domain and reducing mobility in epidemic control is checked these two measures are found to be conducive to curbing the spread of infectious disease only when the global interaction is suppressed a log log relation between the change in the number of infected individuals and the timescale is found by calculating the epidemic threshold and the mean first encounter time we heuristically analyze the microscopic characteristics of the propagation of the epidemic in the present model

exact solution of site and bond percolation on small world networks we study percolation on small world networks which has been proposed as a simple model of the propagation of disease the occupation probabilities of sites and bonds correspond to the susceptibility of individuals to the disease and the transmissibility of the disease respectively we give an exact solution of the model for both site and bond percolation including the position of the percolation transition at which epidemic behavior sets in the values of the critical exponents governing this transition the mean and variance of the distribution of cluster sizes disease outbreaks below the transition and the size of the giant component epidemic above the transition

strong control conservative point estimation and simultaneous conservative consistency of false discovery rates a unified approach summary the false discovery rate fdr is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses benjamini and hochberg introduced this quantity and proved that a particular step up p value method controls the fdr storey introduced a point estimate of the fdr for fixed significance regions the former approach conservatively controls the fdr at a fixed predetermined level and the latter provides a conservatively biased estimate of the fdr for a fixed predetermined significance region in this work we show in both finite sample and asymptotic settings that the goals of the two approaches are essentially equivalent in particular the fdr point estimates can be used to define valid fdr controlling procedures in the asymptotic setting we also show that the point estimates can be used to estimate the fdr conservatively over all significance regions simultaneously which is equivalent to controlling the fdr at all levels simultaneously the main tool that we use is to translate existing fdr methods into procedures involving empirical processes this simplifies finite sample proofs provides a framework for asymptotic results and proves that these procedures are valid even under certain forms of dependence

cascading parity check error correcting codes a method for improving the performance of sparse matrix based parity check codes is proposed based on insight gained from methods of statistical physics the advantages of this approach are demonstrated on an existing encoding decoding paradigm suggested by sourlas we also discuss the application of the same method to more advanced codes of a similar type

finite size effects and error free communication in gaussian channels the efficacy of a specially constructed gallager type error correcting code to communication in a gaussian channel is examined the construction is based on the introduction of complex matrices used in both encoding and decoding which comprise sub matrices of cascading connection values the finite size effects are estimated for comparing the results with the bounds set by shannon the critical noise level achieved for certain code rates and infinitely large systems nearly saturates the bounds set by shannon even when the connectivity used is low

generation of uncorrelated random scale free networks uncorrelated random scale free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks we propose and analyze a model capable of generating random uncorrelated scale free networks with no multiple and self connections the model is based on the classical configuration model with an additional restriction on the maximum possible degree of the vertices we check numerically that the proposed model indeed generates scale free networks with no two and three vertex correlations as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k respectively complex networks constitute a general framework for the topological characterization of many natural and technological systems whose complexity prevents a more detailed microscopic description f1 3g within this framework these systems are represented in terms of networks or graphs f4g in which vertices stand for the units composing the system while edges among vertices represent the interactions or relations between pairs of units the focus is thus shift to the topological characterization of the representative network a task which is largely more feasible and yields nevertheless a noticeable amount of information on the structure and properties of the original system the empirical analysis of many real complex networks has unveiled the presence of several typical properties widely found in systems belonging to a large variety of realms one of the most relevant is given by the scale free nature of the degree distribution pskd f1 3 5g defined as the probability that a randomly chosen vertex has degree k si e it is connected to other k verticesd in mathematical terms the scale free property translates into a power law function of the form psk d k g

asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity consider a sample of size n from a regular exponential family in p n dimensions let hat theta n denote the maximum likelihood estimator and consider the case where p n tends to infinity with n and where theta n is a sequence of parameter values in r p n moment conditions are provided under which hat theta n theta n o p sqrt p n n and hat theta n theta n overline x n o p p n n where overline x n is the sample mean the latter result provides normal approximation results when p 2 n n rightarrow 0 it is shown by example that even for a single coordinate of hat theta n theta n p 2 n n rightarrow 0 may be needed for normal approximation however if p 3 2 n n rightarrow 0 the likelihood ratio test statistic lambda for a simple hypothesis has a chi square approximation in the sense that 2 log lambda p n sqrt 2p n rightarrow d mathscr n 0 1

marginal asymptotics for the large p small n paradigm with applications to microarray data the large p small n paradigm arises in microarray studies image analysis high throughput molecular screening astronomy and in many other high dimensional applications false discovery rate fdr methods are useful for resolving the accompanying multiple testing problems in cdna microarray studies for example p values may be computed for each of p genes using data from n arrays where typically p is in the thousands and n is less than 30 for fdr methods to be valid in identifying differentially expressed genes the p values for the nondifferentially expressed genes must simultaneously have uniform distributions marginally while feasible for permutation p values this uniformity is problematic for asymptotic based p values since the number of p values involved goes to infinity and intuition suggests that at least some of the p values should behave erratically we examine this neglected issue when n is moderately large but p is almost exponentially large relative to n we show the somewhat surprising result that under very general dependence structures and for both mean and median tests the p values are simultaneously valid a small simulation study and data analysis are used for illustration

asymptotic comparison of step down and step up multiple test procedures based on exchangeable test statistics in this paper interest is focused on some theoretical investigations concerning the comparison of two popular multiple test procedures so called step down and step up procedures in terms of their defining critical values such procedures can be applied for example to multiple comparisons with a control in the definition of the critical values for these procedures order statistics play a central role for k n 0 fixed we consider the joint cumulative distribution function cdf p y 1 n c 1 y n k n c n k of the first n k order statistics and the cdf p y n k n c n k of the k 1 th largest order statistic y n k n of n random variables y1 y n belonging to a sequence of exchangeable real valued random variables our interest is focused on the asymptotic behavior of these cdf s and their interrelation if n tends to it turns out that they sometimes behave completely differently compared with the iid case treated in finner and roters so that positive results are only possible under additional assumptions concerning the underlying distribution we consider different sets of assumptions which then allow analogous results for the exchangeable case recently dalal and mallows derived a result concerning the monotonicity of a certain set of critical values in connection with the joint cdf of order statistics in the iid case we give a counterexample for the exchangeable case underlining the difficulties occurring in this situation as an application we consider the comparison of certain step down and step up procedures in multiple comparisons with a control the results of this paper yield a more theoretical explanation of the superiority of the step up procedure which has been observed earlier by comparing tables of critical values as a byproduct we are able to quantify the tightness of the bonferroni inequality in connection with maximum statistics

tests for high dimensional regression coefficients with factorial designs we propose simultaneous tests for coefficients in high dimensional linear regression models with factorial designs the proposed tests are designed for the large p small n situations where the conventional f test is no longer applicable we derive the asymptotic distribution of the proposed test statistic under the high dimensional null hypothesis and various scenarios of the alternatives which allow power evaluations we also evaluate the power of the f test for models of moderate dimension the proposed tests are employed to analyze a microarray data on yorkshire gilts to find significant gene ontology terms which are significantly associated with the thyroid hormone after accounting for the designs of the experiment

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

finite size scaling in complex networks a finite size scaling fss theory is proposed for various models in complex networks in particular we focus on the fss exponent which plays a crucial role in analyzing numerical data for finite size systems based on the droplet excitation hyperscaling argument we conjecture the values of the fss exponents for the ising model the susceptible infected susceptible model and the contact process all of which are confirmed reasonably well in numerical simulations

criterion for the emergence of explosive synchronization transitions in networks of phase oscillators the emergence of explosive synchronization transitions in networks of phase oscillators recently has become one of the most interesting topics it is widely believed that the large frequency mismatch of a pair of oscillators also known as disassortativity in frequency is a direct cause of an explosive synchronization it is found that besides the disassortativity in frequency the disassortativity in node degree also shows up in connection with the first order synchronization transition in this paper we simulate the kuramoto model on top of a family of networks with different degree degree and frequency frequency correlation patterns results show that only when the degrees and natural frequencies of the network s nodes are both disassortative can an explosive synchronization occur

pattern transitions and complexity for a nonlocal logistic map abstract we examine the pattern solutions in a generalized nonlocal logistic map that includes spatial kernels in both growth and competition terms we show that this map includes as a particular case the nonlocal fisher kolmogorov equation and we demonstrate the existence of three kinds of stationary nonlinear solutions one uniform one cosine type that we refer to as wavelike solution and another in the form of gaussian we also obtain analytical expressions that describe the nonlinear pattern behavior in the system and we establish the stability criterion we define thermodynamics quantities such as entropy and the order parameter based on this the pattern no pattern and pattern pattern transitions are properly analyzed we show that these pattern solutions may be related to the recently observed peak adding phenomenon in nonlinear optics

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

survey propagation for the cascading sourlas code we investigate how insights from statistical physics namely survey propagation can improve decoding of a particular class of sparse error correcting codes we show that a recently proposed algorithm time averaged belief propagation is in fact intimately linked to a specific survey propagation for which parisi s replica symmetry breaking parameter is set to zero and that the latter is always superior to belief propagation in the high connectivity limit we briefly look at further improvements available by going to the second level of replica symmetry breaking

high dimensional classification using features annealed independence rules classification using high dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high throughput data the impact of dimensionality on classifications is largely poorly understood in a seminal paper bickel and levina 2004 show that the fisher discriminant performs poorly due to diverging spectra and they propose to use the independence rule to overcome the problem we first demonstrate that even for the independence classification rule classification using all the features can be as bad as the random guessing due to noise accumulation in estimating population centroids in high dimensional feature space in fact we demonstrate further that almost all linear discriminants can perform as bad as the random guessing thus it is paramountly important to select a subset of important features for high dimensional classification resulting in features annealed independence rules fair the conditions under which all the important features can be selected by the two sample t statistic are established the choice of the optimal number of features or equivalently the threshold value of the test statistics are proposed based on an upper bound of the classification error simulation studies and real data analysis support our theoretical results and demonstrate convincingly the advantage of our new classification procedure

a two way semilinear model for normalization and analysis of cdna microarray data a basic question in analyzing cdna microarray data is normalization the purpose of which is to remove systematic bias in the observed expression values by establishing a normalization curve across the whole dynamic range a proper normalization procedure ensures that the normalized intensity ratios provide meaningful measures of relative expression levels we propose a two way semilinear model tw slm for normalization and analysis of microarray data this method does not make the usual assumptions underlying some of the existing methods for example it does not assume that the percentage of differentially expressed genes is small or that there is symmetry in the expression levels of up regulated and down regulated genes as required in the lowess normalization method the tw slm also naturally incorporates uncertainty due to normalization into significance analysis of microarrays we use a semiparametric approach based on polynomial splines in the tw slm to estimate the normalization curves and the no

synchronization transition of heterogeneously coupled oscillators on scale free networks we investigate the synchronization transition of the modified kuramoto model where the oscillators form a scale free network with degree exponent ensuremath lambda an oscillator of degree k i is coupled to its neighboring oscillators with asymmetric and degree dependent coupling in the form of j k i ensuremath eta ensuremath 1 by invoking the mean field approach we find eight different synchronization transition behaviors depending on the values of ensuremath eta and ensuremath lambda and derive the critical exponents associated with the order parameter and the finite size scaling in each case the synchronization transition point j c is determined as being zero finite when ensuremath eta g ensuremath lambda ensuremath 2 ensuremath eta l ensuremath lambda ensuremath 2 the synchronization transition is also studied from the perspective of cluster formation of synchronized vertices the cluster size distribution and the largest cluster size as a function of the system size are derived for each case using the generating function technique our analytic results are confirmed by numerical simulations

error correcting codes that nearly saturate shannon s bound gallager type error correcting codes that nearly saturate shannon s bound are constructed using insight gained from mapping the problem onto that of an ising spin system the performance of the suggested codes is evaluated for different code rates in both finite and infinite message length

factors that predict better synchronizability on complex networks while shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network the suppressing tendency of the heterogeneity of the degree distribution even for shorter characteristic path length has also been reported to see this we investigate the effects of various factors such as the degree characteristic path length heterogeneity and betweenness centrality on synchronization and find a consistent trend between the synchronization and the betweenness centrality the betweenness centrality is thus proposed as a good indicator for synchronizability

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

robustness and accuracy of methods for high dimensional data analysis based on student s t statistic summary student s t statistic is finding applications today that were never envisaged when it was introduced more than a century ago many of these applications rely on properties e g robustness against heavy tailed sampling distributions that were not explicitly considered until relatively recently we explore these features of the t statistic in the context of its application to very high dimensional problems including feature selection and ranking the simultaneous testing of many different hypotheses and sparse high dimensional signal detection robustness properties of the t ratio are highlighted and it is established that those properties are preserved under applications of the bootstrap in particular bootstrap methods correct for skewness and therefore lead to second order accuracy even in the extreme tails indeed it is shown that the bootstrap and also the more popular but less accurate t distribution and normal approximations are more effective in the tails than towards the middle of the distribution these properties motivate new methods e g bootstrap based techniques for signal detection that confine attention to the significant tail of a statistic

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

survey propagation at finite temperature application to a sourlas code as a toy model in this paper we investigate a finite temperature generalization of survey propagation by applying it to the problem of finite temperature decoding of a biased finite connectivity sourlas code for temperatures lower than the nishimori temperature we observe that the result is a shift of the location of the dynamical critical channel noise to larger values than the corresponding dynamical transition for belief propagation as suggested recently by migliorini and saad for ldpc codes we show how the finite temperature 1rsb sp gives accurate results in the regime where competing approaches fail to converge or fail to recover the retrieval state

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

ising model on networks with an arbitrary distribution of connections we find the exact critical temperature t c of the nearest neighbor ferromagnetic ising model on an equilibrium random graph with an arbitrary degree distribution p k we observe an anomalous behavior of the magnetization magnetic susceptibility and specific heat when p k is fat tailed or loosely speaking when the fourth moment of the distribution diverges in infinite networks when the second moment becomes divergent t c approaches infinity the phase transition is of infinite order and size effect is anomalously strong

synchronization transition in scale free networks clusters of synchrony we study the synchronization transition in scale free networks that display power law asymptotic behaviors in their degree distributions the critical coupling strength and the order parameter critical exponent derived by the mean field approach depend on the degree exponent ensuremath lambda which implies a close connection between structural organization and the emergence of dynamical order in complex systems we also derive the finite size scaling behavior of the order parameter finding that the giant cluster of synchronized nodes is formed in different ways between scale free networks with 2l ensuremath lambda l3 and those with ensuremath lambda g3

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

higher criticism for detecting sparse heterogeneous mixtures higher criticism or second level significance testing is a multiplecomparisons concept mentioned in passing by tukey it concerns a situation where there are many independent tests of significance and one is interested in rejecting the joint null hypothesis tukey suggested comparing the fraction of observed significances at a given level to the expected fraction under the joint null in fact he suggested standardizing the difference of the two quantities and forming a z score the resulting z score tests the significance of the body of significance tests we consider a generalization where we maximize this z score over a range of significance levels 0 0 we are able to show that the resulting higher criticism statistic is effective at resolving a very subtle testing problem testing whether n normal means are all zero versus the alternative that a small fraction is nonzero the subtlety of this sparse normal means testing problem can be seen from work of ingster and jin who studied such problems in great detail in their studies they identified an interesting range of cases where the small fraction of nonzero means is so small that the alternative hypothesis exhibits little noticeable effect on the distribution of the p values either for the bulk of the tests or for the few most highly significant tests in this range when the amplitude of nonzero means is calibrated with the fraction of nonzero means the likelihood ratio test for a precisely specified alternative would still succeed in separating the two hypotheses we show that the higher criticism is successful throughout the same region of amplitude sparsity where the likelihood ratio test

efficient estimation of the number of false positives in high throughput screening this paper develops tail estimation methods to handle false positives in multiple testing problems where testing is done at extreme significance levels and with low degrees of freedom and where the true null distribution may differ from the theoretical one we show that the number of false positives conditional on the total number of positives has an approximately binomial distribution and we find estimators of the distribution parameter we also develop methods for estimation of the true null distribution as well as techniques to compare it with the theoretical one analysis is based on a simple polynomial model for very small p values asymptotics that motivate the model properties of the estimators and model checking tools are provided the methods are applied to two large genomic studies and an fmri brain scan experiment

quenched randomness at first order transitions abstract a rigorous theorem due to aizenman and wehr asserts that there can be no latent heat in a two dimensional system with quenched random impurities we examine this result and its possible extensions to higher dimensions in the context of several models for systems whose pure versions undergo a strong first order transition we show that there is an asymptotically exact mapping to the random field ising model at the level of the interface between the ordered and disordered phases this provides a physical explanation for the above result and also implies a correspondence between the problems in higher dimensions including scaling relations between their exponents the particular example of the q state potts model in two dimensions has been considered in detail by various authors and we review the numerical results obtained for this case turning to weak fluctuation driven first order transitions we describe analytic renormalization group calculations which show how the continuous nature of the transition is restored by randomness in two dimensions

finite size scaling of synchronized oscillation on complex networks the onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated using a mean field approximation we characterize sample to sample fluctuations for networks of finite size and derive the corresponding scaling properties in the critical region for scale free networks with the degree distribution p k approximately k gamma at large k we found that the finite size exponent nu takes on the value 5 2 when gamma 5 the same as in the globally coupled kuramoto model for highly heterogeneous networks 3 gamma 5 nu and the order parameter exponent beta depend on gamma the analytical expressions for these exponents obtained from the mean field theory are shown to be in excellent agreement with data from extensive numerical simulations

criticality on networks with topology dependent interactions weighted scale free networks with topology dependent interactions are studied it is shown that the possible universality classes of critical behavior which are known to depend on topology can also be explored by tuning the form of the interactions at fixed topology for a model of opinion formation simple mean field and scaling arguments show that a mapping gamma gamma mu 1 mu describes how a shift of the standard exponent gamma of the degree distribution can absorb the effect of degree dependent pair interactions j ij proportional to k i k j mu where k i stands for the degree of vertex i this prediction is verified by extensive numerical investigations using the cavity method and monte carlo simulations the critical temperature of the model is obtained through the bethe peierls approximation and with the replica technique the mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network

first and second order phase transitions in scale free networks we study first and second order phase transitions of ferromagnetic lattice models on scale free networks with a degree exponent gamma using the example of the q state potts model we derive a general self consistency relation within the frame of the weiss molecular field approximation which presumably leads to exact critical singularities depending on the value of gamma we have found three different regimes of the phase diagram as a general trend first order transitions soften with decreasing gamma and the critical singularities at the second order transitions are gamma dependent

random k satisfiability problem from an analytic solution to an efficient algorithm we study the problem of satisfiability of randomly chosen clauses each with k boolean variables using the cavity method at zero temperature we find the phase diagram for the k 3 case we show the existence of an intermediate phase in the satisfiable region where the proliferation of metastable states is at the origin of the slowdown of search algorithms the fundamental order parameter introduced in the cavity method which consists of surveys of local magnetic fields in the various possible states of the system can be computed for one given sample these surveys can be used to invent new types of algorithms for solving hard combinatorial optimizations problems one such algorithm is shown here for the k 3 satisfiability problem with very good performances

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

self normalized cramer type moderate deviations under dependence we establish a cramer type moderate deviation result for self normalized sums of weakly dependent random variables where the moment requirement is much weaker than the non self normalized counterpart the range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes we consider three types of self normalization the equal block scheme the big block small block scheme and the interlacing scheme simulation study shows that the latter can have a better finite sample performance our result is applied to multiple testing and construction of simultaneous confidence intervals for ultra high dimensional time series mean vectors

a two sample test for high dimensional data with applications to gene set testing we proposed a two sample test for means of high dimensional data when the data dimension is much larger than the sample size the classical hotelling s t 2 test does not work for this large p small n situation the proposed test does not require explicit conditions on the relationship between the data dimension and sample size this offers much flexibility in analyzing high dimensional data an application of the proposed test is in testing significance for sets of genes which we demonstrate in an empirical study on a leukemia data set

nonlinear waves on circle networks with excitable nodes in this paper we propose a new model of the kuramoto type to study nonlinear wave generation and propagation on a circle network with excitable node dynamics and reveal certain common features of traveling wave solutions which are independent of local dynamics but strongly related to the diffusive coupling of neighboring nodes in view of the stability and size of the basin of attraction regular nonlinear waves and in the case of a large number of nodes circulating pulses are the most important ones the period t and the functional expression for regular nonlinear waves are computed analytically which matches well with the numerical result a new type of solution the special nonlinear wave existing only for the discrete node dynamics is studied and compared with the regular solution

semilinear high dimensional model for normalization of microarray data a theoretical analysis and partial consistency normalization of microarray data is essential for removing experimental biases and revealing meaningful biological results motivated by a problem of normalizing microarray data a semilinear in slide model slim has been proposed to aggregate information from other arrays slim is generalized to account for across array information resulting in an even more dynamic semiparametric regression model this model can be used to normalize microarray data even when there is no replication within an array we demonstrate that this semiparametric model has a number of interesting features the parametric component and the nonparametric component that are of primary interest can be consistently estimated the former having a parametric rate and the latter having a nonparametric rate whereas the nuisance parameters cannot be consistently estimated this is an interesting extension of the partial consistent phenomena which itself is of theoretical interest the asymptotic normality for the parametric component

instability of one step replica symmetry broken phase in satisfiability problems we reconsider the one step replica symmetry breaking 1rsb solutions of two random combinatorial problems k xorsat and k sat we present a general method for establishing the stability of these solutions with respect to further steps of replica symmetry breaking our approach extends the ideas of montanari and ricci tersenghi 2003 eur phys j b 33 339 to more general combinatorial problems it turns out that 1rsb is always unstable at sufficiently small clause density or high energy in particular the recent 1rsb solution to 3 sat is unstable at zero energy for m with m 4 153 on the other hand the sat unsat phase transition seems to be correctly described within 1rsb

detecting differential expressions in genechip microarray studies a quantile approach in this article we consider testing for differentially expressed genes in genechip studies by modeling and analyzing the quantiles of gene expression through probe level measurements by developing a robust rank score test for linear quantile models with a random effect we propose a reliable test for detecting differences in certain quantiles of the intensity distributions by using a genomewide adjustment to the test statistic to account for within array correlation we demonstrate that the proposed rank score test is highly effective even when the number of arrays is small our empirical studies with real experimental data show that detecting differences in the quartiles for the probe level data is a valuable complement to the usual mixed model analysis based on gaussian likelihood the methodology proposed in this article is a first attempt to develop inferential tools for quantile regression in mixed models