significance testing for wavelet bicoherence and its application in analyzing nonlinearity in turbulent shear flows wavelet based bispectral analysis has been applied in various physical and engineering fields in recent years but discussion of its significance testing which distinguishes statistically meaningful results from those due to random noise has been scarce and incomplete in the literature previously derived significance levels for wavelet bicoherence were either preliminary or based on numerical simulations of a limited sample size the present study reviewed relevant previous works analytically identified the sampling distribution of the estimated wavelet bicoherence and derived expressions for its significance levels for any given probability value its application in analyzing a turbulent shear flow around a bluff body was demonstrated in detail the significance testing developed here helped to identify significant quadratic couplings among a triad of scales in a separated turbulent shear layer over very short time intervals the results obtained here can be applied to a wide variety of research topics for detecting nonlinearity in physical systems

measuring time frequency information content using the renyi entropies the generalized entropies of renyi inspire new measures for estimating signal information and complexity in the time frequency plane when applied to a time frequency representation tfr from cohen s class or the affine class the renyi entropies conform closely to the notion of complexity that we use when visually inspecting time frequency images these measures possess several additional interesting and useful properties such as accounting and cross component and transformation invariances that make them natural for time frequency analysis this paper comprises a detailed study of the properties and several potential applications of the renyi entropies with emphasis on the mathematical foundations for quadratic tfrs in particular for the wigner distribution we establish that there exist signals for which the measures are not well defined

rank deficient submatrices of fourier matrices we consider the maximal rank deficient submatrices of fourier matrices with order a power of a prime number we do this by considering a hierarchical subdivision of these matrices into low rank blocks we also explore some connections with the fast fourier transform fft and with an uncertainty principle for fourier transforms over finite abelian groups

generalized entropic uncertainty relations a new class of uncertainty relations is derived for pairs of observables in a finite dimensional hilbert space which do not have any common eigenvector this class contains an entropic uncertainty relation which improves a previous result of deutsch and confirms a recent conjecture by kraus some comments are made on the extension of these relations to the case where the hilbert space is infinite dimensional

uncertainty principles for kac algebras in this paper we introduce the notation of bi shift of biprojections in subfactor theory to unimodular kac algebras we characterize the minimizers of the hirschman beckner uncertainty principle and the donoho stark uncertainty principle for unimodular kac algebras with biprojections and prove hardy s uncertainty principle in terms of the minimizers

predictive updating methods with application to bayesian classification we propose algorithms based on random draws from predictive distributions of unknown quantities missing values for instance this procedure can either be iterative which is a special variation of the gibbs sampler or be sequential which is a variation of sequential imputation in the latter case one can update the posterior distribution with new observations easily the methods proposed have intuitive statistical implications and can be generalized to accommodate other bayesian like procedures we display some applications of the method in connection with the bayesian bootstrap classification hierarchical models and selection of variables in particular as an application of the method we present a unified treatment of switching regression models driven by a general binary process and we develop a bayesian testing procedure some simulations and a real example are used to illustrate the methods proposed

posterior distribution of nondifferentiable functions abstract this paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g where is a finite dimensional parameter of either a parametric or semiparametric model the main assumption is that the distribution of a suitable estimator n its bootstrap approximation and the bayesian posterior for all agree asymptotically it is shown that whenever g is locally lipschitz though not necessarily differentiable the posterior distribution of g and the bootstrap distribution of g n coincide asymptotically one implication is that bayesians can interpret bootstrap inference for g as approximately valid posterior inference in a large sample another implication built on known results about bootstrap inconsistency is that credible intervals for a nondifferentiable parameter g cannot be presumed to be approximately valid confidence intervals even when this relation holds true for

analysis in a finite time frequency plane we revise our conjecture concerning signals realizing the lower bound on compaction in the phase plane to include a forgotten case of periodization and indicate that this case can be used to develop an orthonormal basis for data lengths n that are the square of an integer

on classes of non gaussian asymptotic minimizers in entropic uncertainty principles abstract in this paper we revisit the bialynicki birula and mycielski uncertainty principle and its cases of equality this shannon entropic version of the well known heisenberg uncertainty principle can be used when dealing with variables that admit no variance in this paper we extend this uncertainty principle to renyi entropies we recall that in both shannon and renyi cases and for a given dimension n the only case of equality occurs for gaussian random vectors we show that as n grows however the bound is also asymptotically attained in the cases of n dimensional student t and student r distributions a complete analytical study is performed in a special case of a student t distribution we also show numerically that this effect exists for the particular case of a n dimensional cauchy variable whatever the renyi entropy considered extending the results of abe and illustrating the analytical asymptotic study of the student t case in the student r case we show numerically that the same behavior occurs for uniformly distributed vectors these particular cases and other ones investigated in this paper are interesting since they show that this asymptotic behavior cannot be considered as a gaussianization of the vector when the dimension increases

lapped multiple bases algorithms for still image compression without blocking effect we describe a system for still image compression that uses several transform sets in a multiple bases realization algorithm our algorithms reduce the number of encoded transform coefficients 20 beyond dct only compression we extend these algorithms to use several newly developed lapped orthogonal transform lot bases resulting in useful algorithms for low bit rate high compression operation without blocking effect

hardy and uncertainty inequalities on stratified lie groups abstract we prove various hardy type and uncertainty inequalities on a stratified lie group g in particular we show that the operators t f l 2 f where is a homogeneous norm 0 q p and l is the sub laplacian are bounded on the lebesgue space l p g as consequences we estimate the norms of these operators sufficiently precisely to be able to differentiate and prove a logarithmic uncertainty inequality we also deduce a general version of the heisenberg pauli weyl inequality relating the l p norm of a function f to the l q norm of f and the l r norm of l 2 f

on the dynamics of the error floor behavior in regular ldpc codes it is shown that dominant trapping sets of regular low density parity check ldpc codes so called absorption sets undergo a two phased dynamic behavior in the iterative message passing decoding algorithm using a linear dynamic model for the iteration behavior of these sets it is shown that they undergo an initial geometric growth phase which stabilizes in a final bit flipping behavior where the algorithm reaches a fixed point this analysis is shown to lead to very accurate numerical calculations of the error floor bit error rates down to error rates that are inaccessible by simulation the topology of the dominant absorption sets of an example code the ieee 802 3an 2048 1723 regular ldpc code are identified and tabulated using topological relationships in combination with search algorithms

reply to comments on resolution in time frequency the authors reply that the first sentence of the conjecture numbered 5 as stated by dr knockaert see ibid vol 48 no 12 p 3585 86 2000 in his comments was proven first by dembo et al 1991 this they discovered in march 1999 furthermore dr m doroslovacki of george washington university pointed out in march 1999 that a time sequence used by donoho et al 1989 was a counter example to conjecture 5 in that paper they correspondingly revised their conjecture to the improved conjecture presented

time phase bispectral analysis bispectral analysis a technique based on high order statistics is extended to encompass time dependence for the case of coupled nonlinear oscillators it is applicable to univariate as well as to multivariate data obtained respectively from one or more of the oscillators it is demonstrated for a generic model of interacting systems whose basic units are the poincare oscillators their frequency and phase relationships are explored for different coupling strengths both with and without gaussian noise the distinctions between additive linear or quadratic and parametric frequency modulated interactions in the presence of noise are illustrated

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

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

finite alphabet iterative decoders part i decoding beyond belief propagation on the binary symmetric channel we introduce a new paradigm for finite precision iterative decoding on low density parity check codes over the binary symmetric channel the messages take values from a finite alphabet and unlike traditional quantized decoders which are quantized versions of the belief propagation bp decoder the proposed finite alphabet iterative decoders faids do not propagate quantized probabilities or log likelihoods and the variable node update functions do not mimic the bp decoder rather the update functions are maps designed using the knowledge of potentially harmful subgraphs that could be present in a given code thereby rendering these decoders capable of outperforming the bp in the error floor region on certain column weight three codes of practical interest we show that there exist faids that surpass the floating point bp decoder in the error floor region while requiring only three bits of precision for the representation of the messages hence faids are able to achieve a superior performance at much lower complexity we also provide a methodology for the selection of faids that is not code specific but gives a set of candidate faids containing potentially good decoders in the error floor region for any column weight three code we validate the code generality of our methodology by providing particularly good three bit precision faids for a variety of codes with different rates and lengths

the lot transform coding without blocking effects an exact derivation of an optimal lapped orthogonal transform lot is presented the optimal lot is related to the discrete cosine transform dct in such a way that a fast algorithm for a nearly optimal lot is derived compared to the dct the fast lot requires about 20 30 more computations mostly additions an image coding example demonstrates the effectiveness of the lot in reducing blocking effects the lot actually leads to slightly smaller signal reconstruction errors than does the dct

wavelet bispectral analysis for the study of interactions among oscillators whose basic frequencies are significantly time variable bispectral analysis recently introduced as a technique for revealing time phase relationships is extended to make use of wavelets rather than fourier analysis it is thus able to encompass instantaneous phase time dependence for the case of two or more coupled nonlinear oscillators the method is demonstrated and evaluated by use of test signals from a pair of coupled poincare oscillators it promises to be useful in a wide range of scientific contexts for studies of interacting oscillators whose basic frequencies are significantly time variable

polynomial wigner ville distributions and their relationship to time varying higher order spectra the wigner ville distribution wvd has optimal energy concentration for linear frequency modulated fm signals this paper presents a generalization of the wvd in order to effectively process nonlinear polynomial fm signals a class of polynomial wvd s pwvd s that give optimal concentration in the time frequency plane for fm signals with a modulation law of arbitrary polynomial form are defined a class of polynomial time frequency distributions ptfd s are also defined based on the class of pwvd s the optimal energy concentration of the pwvd enables it to be used for estimation of the instantaneous frequency if of polynomial fm signals finally a link between pwvd s and time varying higher order spectra tvhos is established just as the expected value of the wvd of a nonstationary random signal is the time varying power spectrum the expected values of the pwvd s have interpretations as reduced tvhos

bootstrapping empirical functions in our previous sections we have established weak convergence of mean residual life total time of test lorenz and goldie processes to appropriate gaussian processes apart from a few special cases cf section 8 these limiting processes are functions of the underlying distributions consequently when testing for statistical hypotheses for example one would have to compute the resulting limiting distribution for each f of interest the same is true when trying to use our results for constructing confidence bands for the theoretical functionals of the said empirical processes this type of problems can be solved by adapting the bootstrap method proposed by efron 1979 1982 to the present situation as we will see the bootstrap method is simply a monte carlo simulation determined by the given observations

a rank statistics approach to the consistency of a general bootstrap a general notion of a bootstrapped mean constructed by exchangeably weighting sample points is introduced consistency of this generalized bootstrapped mean which includes proposals of efron and rubin among others is proved by classical linear rank statistics theory the consistency of generalized bootstrapped empirical and quantile processes is also established

expander codes using expander graphs we construct a new family of asymptotically good linear error correcting codes these codes have linear time sequential decoding algorithms and logarithmic time parallel decoding algorithms that use a linear number of processors we present both randomized and explicit constructions of these codes experimental results demonstrate the good performance of the randomly chosen codes

direction of coupling from phases of interacting oscillators an information theoretic approach a directionality index based on conditional mutual information is proposed for application to the instantaneous phases of weakly coupled oscillators its abilities to distinguish unidirectional from bidirectional coupling as well as to reveal and quantify asymmetry in bidirectional coupling are demonstrated using numerical examples of quasiperiodic chaotic and noisy oscillators as well as real human cardiorespiratory data

on the error correction of regular ldpc codes using the flipping algorithm the iterative bit flipping algorithm is applied to the standard regular low density parity check ldpc code ensemble in the past it was shown for a typical code in the ensemble with left degree at least five and block length sufficiently large that this algorithm can correct a linear in the block length number of worst case errors in this paper this result is extended to the case where the left degree is at least four for the case where the left degree is larger than four an improvement compared to existing results of several orders of magnitude is obtained on the fraction of worst case errors that can be corrected it is also shown how the results can be further improved when random errors produced by the channel as opposed to worst case errors are considered

an entropy based uncertainty principle for a locally compact abelian group abstract we classify all functions on a locally compact abelian group giving equality in an entropy inequality generalizing the heisenberg uncertainty principle in particular for functions on a real line we proof a conjecture of hirschman published in 1957

entropy based uncertainty measures for l sup 2 spl ropf sup n spl lscr sup 2 spl zopf and spl lscr sup 2 spl zopf n spl zopf with a hirschman optimal transform for spl lscr sup 2 spl zopf n spl zopf the traditional heisenberg weyl measure quantifies the joint localization uncertainty or concentration of a signal in the phase plane based on a product of energies expressed as signal variances in time and in frequency in the image processing literature the term compactness also has been used to refer to this same notion of joint localization in the sense of a signal representation that is efficient simultaneously in time or space and frequency in this paper we consider hirschman uncertainty principles based not on energies and variances directly but rather on entropies computed with respect to normalized energy densities in time and frequency unlike the heisenberg weyl measure this entropic hirschman notion of joint uncertainty extends naturally from the case of infinitely supported continuous time signals to the cases of both finitely and infinitely supported discrete time signals for the first time we consider these three cases together and study them relative to one another in the case of infinitely supported continuous time signals we find that consistent with the energy based heisenberg principle the optimal time frequency concentration with respect to the hirschman uncertainty principle is realized by translated and modulated gaussian functions in the two discrete cases however the entropy based measure yields optimizers that may be generated by applying compositions of operators to the kronecker delta study of the discrete cases yields two interesting results first in the finitely supported case the hirschman optimal functions coincide with the so called picket fence functions that are also optimal with respect to the joint time frequency counting measure of donoho and stark second the hirschman optimal functions in the infinitely supported case can be reconciled with continuous time gaussians through a certain limiting process while a different limiting process can be used to reconcile the finitely and infinitely supported discrete cases there does not appear to be a straightforward limiting process that unifies all three cases the optimizers from the finitely supported discrete case are decidedly non gaussian we perform a very simple experiment that indicates that the hirschman optimal transform hot is superior to the discrete fourier transform dft and discrete cosine transform dct in terms of its ability to separate or resolve two limiting cases of localization in frequency viz pure tones and additive white noise we believe that these differences arise from the use of entropy rather than energy as an optimality criterion and are intimately related to the apparent incongruence between the infinitely supported continuous time case and the finitely supported discrete time case

on computing and implementing the running bispectra the paper extends recursion to bispectrum estimation problems and presents the systolic array implementation of the recursive higher order spectrum in which the bispectrum estimate is updated every data sample forward and reverse sequence running fourier transforms are first systolically realized the results are then used to drive a second systolic array whose outputs represent the ft of the data third order moment the proposed systolic arrays have no global communications with a number of processing elements independent of the size of the employed 2d lag window

on scale and concentration invariance in entropies renyi entropies are compared to generalized log fisher information and variational entropies in the context of translation scale and concentration invariance it is proved that the renyi entropies occupy a special place amongst these entropies it is also shown that shannon entropy is centrally positioned amidst the renyi entropies

phase synchronization of chaotic attractors in the presence of two competing periodic signals we discuss the situation where two periodic signals compete to phase synchronize a chaotic attractor depending on the relative position of the periods with respect to the synchronization tongue for a single frequency signal we distinguish several different cases we find that depending on parameters it is possible that one or the other signal will entrain exclusively or that they will entrain alternately at their average frequency or not at all

cyclic and quasi cyclic ldpc codes on constrained parity check matrices and their trapping sets this paper is concerned with construction and structural analysis of both cyclic and quasi cyclic codes particularly low density parity check ldpc codes it consists of three parts the first part shows that a cyclic code given by a parity check matrix in circulant form can be decomposed into descendant cyclic and quasi cyclic codes of various lengths and rates some fundamental structural properties of these descendant codes are developed including the characterization of the roots of the generator polynomial of a cyclic descendant code the second part of the paper shows that cyclic and quasi cyclic descendant ldpc codes can be derived from cyclic finite geometry ldpc codes using the results developed in the first part of the paper this enlarges the repertoire of cyclic ldpc codes the third part of the paper analyzes the trapping set structure of regular ldpc codes whose parity check matrices satisfy a certain constraint on their rows and columns several classes of finite geometry and finite field cyclic and quasi cyclic ldpc codes with large minimum distances are shown to have no harmful trapping sets of size smaller than their minimum distances consequently their error floor performances are dominated by their minimum distances

error floor approximation for ldpc codes in the awgn channel this paper addresses the prediction of error floors of low density parity check codes transmitted over the additive white gaussian noise channel using a linear state space model to estimate the behavior of the sum product algorithm spa decoder in the vicinity of trapping sets tss we study the performance of the spa decoder in the log likelihood ratio llr domain as a function of the llr saturation level when applied to several widely studied codes the model accurately predicts a significant decrease in the error floor as the saturation level is allowed to increase for nonsaturating decoders however we find that the state space model breaks down after a small number of iterations due to the strong correlation of llr messages we then revisit richardson s importance sampling methodology for estimating error floors due to tss when those floors are too low for monte carlo simulation we propose modifications that account for the behavior of a nonsaturating decoder and present the resulting error floor estimates for the margulis code these estimates are much lower significantly steeper and more sensitive to iteration count than those previously reported

bayesian bootstrap for proportional hazards models we propose two bayesian bootstrap extensions the binomial and poisson forms for proportional hazards models the binomial form bayesian bootstrap is the limit of the posterior distribution with a beta process prior as the amount of the prior information vanishes and thus can be considered as a default nonparametric bayesian analysis it is also the same as lo s bayesian bootstrap for censored data when covariates are absent the poisson form bayesian bootstrap is equivalent to the bayesian analysis with cox s profile likelihood when the baseline distribution is discrete thus when the data set has many ties simulation study suggests that the binomial form bayesian bootstrap performs better than standard frequentist procedures in the frequentist sense an advantage of the proposed bayesian bootstrap procedures over the standard bayesian analysis is conceptual and computational simplicity finally it is shown that both bayesian bootstrap posteriors are asymptotically equivalent to the sampling distribution of the maximum likelihood estimator

gaussian and bootstrap approximations for high dimensional u statistics and their applications this paper studies the gaussian and bootstrap approximations for the probabilities of a nondegenerate u statistic belonging to the hyperrectangles in mathbb r d when the dimension d is large a two step gaussian approximation procedure that does not impose structural assumptions on the data distribution is proposed subject to mild moment conditions on the kernel we establish the explicit rate of convergence uniformly in the class of all hyperrectangles in mathbb r d that decays polynomially in sample size for a high dimensional scaling limit where the dimension can be much larger than the sample size we also provide computable approximation methods for the quantiles of the maxima of centered u statistics specifically we provide a unified perspective for the empirical bootstrap the randomly reweighted bootstrap and the gaussian multiplier bootstrap with the jackknife estimator of covariance matrix as randomly reweighted quadratic forms and we establish their validity we show that all three methods are inferentially first order equivalent for high dimensional u statistics in the sense that they achieve the same uniform rate of convergence over all d dimensional hyperrectangles in particular they are asymptotically valid when the dimension d can be as large as o e n c for some constant c in 0 1 7 the bootstrap methods are applied to statistical applications for high dimensional non gaussian data including i principled and data dependent tuning parameter selection for regularized estimation of the covariance matrix and its related functionals ii simultaneous inference for the covariance and rank correlation matrices in particular for the thresholded covariance matrix estimator with the bootstrap selected tuning parameter we show that for a class of sub gaussian data error bounds of the bootstrapped thresholded covariance matrix estimator can be much tighter than those of the minimax estimator with a universal threshold in addition we also show that the gaussian like convergence rates can be achieved for heavy tailed data which are less conservative than those obtained by the bonferroni technique that ignores the dependency in the underlying data distribution

exact multivariate bayesian bootstrap distributions of moments the common unknown probability law p of a random sample y 1 y n is assigned a dirichlet process prior with index it is shown that the posterior joint density of several moments of p converges as r 0 to a multivariate b spline which is therefore the bayesian bootstrap joint density of the moments the result provides the basis for possible default nonparametric bayesian inference on unknown moments

detecting the harmonics of oscillations with time variable frequencies a method is introduced for the spectral analysis of complex noisy signals containing several frequency components it enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency the method is based on mutual information and surrogate testing combined with the wavelet transform and it is applicable to relatively short time series containing frequencies that are time variable where the fundamental frequency and harmonics of a process can be identified the characteristic shape of the corresponding oscillation can be determined enabling adaptive filtering to remove other components and nonoscillatory noise from the signal thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately the method is first demonstrated on numerical examples it is then used to identify the higher harmonics of oscillations in human skin blood flow both spontaneous and associated with periodic iontophoresis of a vasodilatory agent the method should be equally relevant to all situations where signals of comparable complexity are encountered including applications in astrophysics engineering and electrical circuits as well as in other areas of physiology and biology

uncertainty principles for locally compact quantum groups abstract in this paper we prove the donoho stark uncertainty principle for locally compact quantum groups and characterize the minimizer which are bi shifts of group like projections we also prove the hirschman beckner uncertainty principle for compact quantum groups and discrete quantum groups furthermore we show hardy s uncertainty principle for locally compact quantum groups in terms of bi shifts of group like projections

a sub graph expansion contraction method for error floor computation in this paper we present a computationally efficient method for estimating error floors of low density parity check ldpc codes over the binary symmetric channel bsc without any prior knowledge of its trapping sets tss given the tanner graph g of a code and the decoding algorithm mathcal d the method starts from a list of short cycles in g and expands each cycle by including its sufficiently large neighborhood in g variable nodes of the expanded sub graphs mathcal g text exp are then corrupted exhaustively by all possible error patterns and decoded by mathcal d operating on mathcal g text exp union of support of the error patterns for which mathcal d fails on each mathcal g text exp defines a subset of variable nodes that is a ts the knowledge of the minimal error patterns and their strengths in each tss is used to compute an estimation of the frame error rate this estimation represents the contribution of error events localized on tss and therefore serves as an accurate estimation of the error floor performance of mathcal d at low bsc cross over probabilities we also discuss trade offs between accuracy and computational complexity our analysis shows that in some cases the proposed method provides a million fold improvement in computational complexity over standard monte carlo simulation

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

jackknife multiplier bootstrap finite sample approximations to the u process supremum with applications this paper is concerned with finite sample approximations to the supremum of a non degenerate u process of a general order indexed by a function class we are primarily interested in situations where the function class as well as the underlying distribution change with the sample size and the u process itself is not weakly convergent as a process such situations arise in a variety of modern statistical problems we first consider gaussian approximations namely approximate the u process supremum by the supremum of a gaussian process and derive coupling and kolmogorov distance bounds such gaussian approximations are however not often directly applicable in statistical problems since the covariance function of the approximating gaussian process is unknown this motivates us to study bootstrap type approximations to the u process supremum we propose a novel jackknife multiplier bootstrap jmb tailored to the u process and derive coupling and kolmogorov distance bounds for the proposed jmb method all these results are non asymptotic and established under fairly general conditions on function classes and underlying distributions key technical tools in the proofs are new local maximal inequalities for u processes which may be useful in other problems we also discuss applications of the general approximation results to testing for qualitative features of nonparametric functions based on generalized local u processes

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

the bispectrum of sampled data part 1 detection of the sampling jitter the effect of timing error jitter on the power spectrum second order spectrum of sampled data has been investigated previously the current increasing interest in higher order spectra calls for investigation of the effect of sam pling jitter on the discrete higher than order two spectra in this paper we present results concerning the bispectrum third order spectrum we derive expressions for the bispectrum of sampled data under the assumption that the timing errors are independently identically distributed i i d random variables it is shown that while the discrete bispectrum of a uniformly sampled third order stationary signal is zero in a triangle that is a proper subset of the principal domain it differs from zero in the presence of jitter exploiting this effect we propose a test for detection of sampling jitter using the bispectrum namely given estimates of the discrete bispectrum of an un known band limited signal we can decide whether jitter is present or not the performance of the proposed detector is analyzed and its dependence on the jitter variance signal skewness and observation time is shown

a large sample study of the bayesian bootstrap on donne une justification asymptotique du bootstrap bayesien on obtient des resultats lies a l article de rubin 1981 dans le meme sens que bickel et freedman 1981 et singh 1981 se rapportant a l article d efron 1979

the uncertainty principle on groups the classical uncertainty principle asserts that both a function and its fourier transform cannot be largely concentrated on intervals of small measure donoho and stark siam j app math 49 1989 pp 906 931 have shown recently that both cannot be largely concentrated on any sets of small measure in the case of functions on the line or functions on finite cyclic groups and with concentrations measured in l 2 the purpose of this note is to extend these results to functions on sigma finite locally compact abelian groups with concentrations measured in l p 1 leqq p leqq 2 the first uncertainty principle on groups due to matolcsi and szucs d r acad sci paris 277 1973 pp 841 843 deals with full rather than large concentration asserting that if a function and its fourier transform are supported by sets t and w then the product of the haar measures of t and w must be at least 1 for the case of full concentration in r n benedicks j math anal appl 106 1985 pp 1

error rate estimation of low density parity check codes on binary symmetric channels using cycle enumeration the performance of low density parity check ldpc codes decoded by hard decision iterative decoding algorithms can be accurately estimated if the weight j and the number ej of the smallest error patterns that cannot be corrected by the decoder are known to obtain j and ej one would need to perform the direct enumeration of error patterns with weight i les j the complexity of enumeration increases exponentially with j essentially as nj where n is the code block length this limits the application of direct enumeration to codes with small n and j in this letter we approximate j and ej by enumerating and testing the error patterns that are subsets of short cycles in the code s tanner graph this reduces the computational complexity by several orders of magnitude compared to direct enumeration making it possible to estimate the error rates for almost any practical ldpc code to obtain the error rate estimates we propose an algorithm that progressively improves the estimates as larger cycles are enumerated through a number of examples we demonstrate that the proposed method can accurately estimate both the bit error rate ber and the frame error rate fer of regular and irregular ldpc codes decoded by a variety of hard decision iterative decoding algorithms

detecting couplings between interacting oscillators with time varying basic frequencies instantaneous wavelet bispectrum and information theoretic approach in the natural world the properties of interacting oscillatory systems are not constant but evolve or fluctuating continuously in time thus the basic frequencies of the interacting oscillators are time varying which makes the system analysis complex for studying their interactions we propose a complementary approach combining wavelet bispectral analysis and information theory we show how these methods uncover the interacting properties and reveal the nature strength and direction of coupling wavelet bispectral analysis is generalized as a technique for detecting instantaneous phase time dependence for the case of two or more coupled nonlinear oscillators whereas the information theory approach can uncover the directionality of coupling and extract driver response relationships in complex systems we generate bivariate time series numerically to mimic typical situations that occur in real measured data apply both methods to the same time series and discuss the results the approach is applicable quite generally to any system of coupled nonlinear oscillators

entropic uncertainty bound for open pointer based simultaneous measurements of conjugate observables we discuss the information entropy for a general open pointer based simultaneous measurement and show how it is bound from below this entropic uncertainty bound is a direct consequence of the structure of the entropy and can be obtained from the formal solution of the measurement dynamics furthermore the structural properties of the entropy allow us to give an intuitive interpretation of the noisy influence of the pointers and the environmental heat bath on the measurement results

wigner higher order moment spectra definition properties computation and application to transient signal analysis the wigner higher order moment spectra whos are defined as extensions of the wigner ville distribution wd to higher order moment spectra domains a general class of time frequency higher order moment spectra is also defined in terms of arbitrary higher order moments of the signal as gen eralizations of the cohen s general class of time frequency rep resentations the properties of the general class of time fre quency higher order moment spectra can be related to the properties of whos which are in fact extensions of the prop erties of the wd discrete time and frequency wigner higher order moment spectra dtf whos distributions are intro duced for signal processing applications and are shown to be implemented with two fft based algorithms one application is presented where the wigner bispectrum wb which is a whos in the third order moment domain is utilized for the detection of transient signals embedded in noise the wb is compared with the wd in terms of simulation examples and analysis of real sonar data it is shown that better detection schemes can be derived in low signal to noise ratio when the wb is applied

gaussian kernels have only gaussian maximizers a gaussian integral kernel g x y on rn x rn is the exponential of a quadratic form in x and y the fourier transform kernel is an example the problem addressed here is to find the sharp bound of g as an operator from l p rp to l q rn and to prove that the l p rn functions that saturate the bound are necessarily gaussians this is accomplished generally for 1 q in some special cases besides greatly extending previous results in this area the proof technique is also essentially different from earlier ones a corollary of these results is a fully multidimensional multilinear generalization of young s inequality

estimation of bit and frame error rates of finite length low density parity check codes on binary symmetric channels a method for estimating the performance of low density parity check ldpc codes decoded by hard decision iterative decoding algorithms on binary symmetric channels bscs is proposed based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder this method estimates both the frame error rate fer and the bit error rate ber of a given ldpc code with very good precision for all crossover probabilities of practical interest through a number of examples we show that the proposed method can be effectively applied to both regular and irregular ldpc codes and to a variety of hard decision iterative decoding algorithms compared with the conventional monte carlo simulation the proposed method has a much smaller computational complexity particularly for lower error rates

sampling requirements and aliasing for higher order correlations while sampling at a nyquist frequency equal to the highest frequency present in the data critical sampling is sufficient to prevent aliasing in both the data and the autocorrelation of a bandlimited energy signal the sampling requirements for the avoidance of aliasing in higher order correlations and spectra are not the same also there is a difference in aliasing effects depending on whether one samples the original continuous time signal and calculates the autocorrelation or one samples the continuous time autocorrelation this distinction between sampling procedures must be made for correlations of higher order as well for which not only the type of aliasing but also the sampling requirements to prevent aliasing differ in particular if one samples the continuous time autobicorrelation or autotricorrelation critical sampling is sufficient to prevent aliasing in practice however it is not usually the continuous time autobicorrelation or autotricorrelation that is sampled generally it is the

renyi s entropy as an index of diversity in simple stage cluster sampling abstract shannon s measure of entropy and gini simpson s diversity index are usually used by social scientists for measuring diversity of a multinomial population in this paper entropy of order r renyi a 1961 in proceedings of fourth berkeley symposium on mathematics statistics and probability 1 547 561 renyi 1961 is presented as a generalization of shannon s entropy to measure and analyze the diversity asymptotic properties of r order index in a simple stage cluster sampling are investigated also applications to testing hypotheses are discussed finite sample results are computed and to finish a comparison of family members via moments is given

sampling requirements for nth order correlations as has been derived previously pflug ms thesis univ of new orleans 1990 pflug et al j acoust soc am 91 975 988 1992 pflug et al j acoust soc am 94 2159 2172 1993 the sampling intervals required to prevent nonremovable and removable aliasing in higher order correlations calculated from discrete time data are t3 1 3ft for the bicorrelation and t4 1 4ft for the tricorrelation where ft is the highest or top frequency present in a signal it is shown here that a general expression for the sampling required to prevent aliasing for each order n of correlation calculated from discrete time data is tn 1 nft time domain computer calculations of correlation central ordinate values for orders two through eight are consistent with this result removable aliasing can be eliminated for data which are sampled such that t 1 2 ft by 1 the application of n dimensional transform or time domain masking filters 2 one dimensional filtering of the transform domain diagonal factor o

four bootstrap confidence intervals for the binomial error model confidence intervals for the mean function of the true proportion score x where andx respectively denote the true proportion and observed test scores can be approximated by the efron bayesian and parametric empirical bayes peb bootstrap procedures the similarity of results yielded by all the bootstrap methods suggests the following the unidentifiability problem of the prior distributiong can be bypassed with respect to the construction of confidence intervals for the mean function and a beta distribution forg is a reasonable assumption for the test scores in compliance with a negative hypergeometric distribution the peb bootstrap which reflects the construction of morris intervals is introduced for computing predictive confidence bands for x it is noted that the effect of test reliability on the precision of interval estimates varies with the two types of confidence statements concerned

on the principal domain of the discrete bispectrum of a stationary signal the paper presents a simplifying yet general approach to determining the symmetry structure of a bispectrum the principal domain pd of the bispectrum and its region of positive support are derived in a way that illuminates the controversy surrounding the triangle in the pd which is called the outer triangle ot by hinich and wolinsky 1988 where the bispectrum is zero for a stationary random sampled process that is not aliased the basic statistical issues of testing for nonzero bispectral structure are reviewed

lp decoding corrects a constant fraction of errors we show that for low density parity check ldpc codes whose tanner graphs have sufficient expansion the linear programming lp decoder of feldman karger and wainwright can correct a constant fraction of errors a random graph will have sufficient expansion with high probability and recent work shows that such graphs can be constructed efficiently a key element of our method is the use of a dual witness a zero valued dual solution to the decoding linear program whose existence proves decoding success we show that as long as no more than a certain constant fraction of the bits are flipped by the channel we can find a dual witness this new method can be used for proving bounds on the performance of any lp decoder even in a probabilistic setting our result implies that the word error rate of the lp decoder decreases exponentially in the code length under the binary symmetric channel bsc this is the first such error bound for ldpc codes using an analysis based on pseudocodewords recent work by koetter and vontobel shows that lp decoding and min sum decoding of ldpc codes are closely related by the graph cover structure of their pseudocodewords in their terminology our result implies that that there exist families of ldpc codes where the minimum bsc pseudoweight grows linearly in the block length

the optimal transform for the discrete hirschman uncertainty principle we determine all signals giving equality for the discrete hirschman uncertainty principle we single out the case where the entropies of the time signal and its fourier transform are equal these signals up to scalar multiples form an orthonormal basis giving an orthogonal transform that optimally packs a finite duration discrete time signal the transform may be computed via a fast algorithm due to its relationship to the discrete fourier transform

least squares channel equalization performance versus equalization delay linear channel equalization has been a successful way to combat intersymbol interference isi introduced by physical communication channels at high enough symbol rates we consider the performance of least squares equalizers in the single input multi output simo channel context when the true channel is composed of an mth order significant part and tails of small leading and or trailing terms using a perturbation analysis approach we show that if the diversity of the significant part is sufficiently large with respect to the size of the tails then the lth order least squares equalizers with l spl ges m 1 perform well for all the delays corresponding to the significant part on the other hand the performance of the equalizers for the delays corresponding to the tails may be poor

resolution in time frequency we introduce a new measure h sub p that is related to the heisenberg uncertainty principle the measure predicts the compactness of discrete time signal descriptions in the sample frequency phase plane we conjecture a lower limit on the compaction in the phase plane and show that discretized gaussians may not provide the most compact basis

on the construction of structured ldpc codes free of small trapping sets we present a method to construct low density parity check ldpc codes with low error floors on the binary symmetric channel codes are constructed so that their tanner graphs are free of certain small trapping sets these trapping sets are selected from the trapping set ontology for the gallager a b decoder they are selected based on their relative harmfulness for a given decoding algorithm we evaluate the relative harmfulness of different trapping sets for the sum product algorithm by using the topological relations among them and by analyzing the decoding failures on one trapping set in the presence or absence of other trapping sets we apply this method to construct structured ldpc codes to facilitate the discussion we give a new description of structured ldpc codes whose parity check matrices are arrays of permutation matrices this description uses latin squares to define a set of permutation matrices that have disjoint support and to derive a simple necessary and sufficient condition for the tanner graph of a code to be free of four cycles

convergence rates for density estimation with bernstein polynomials mixture models for density estimation provide a very useful set up for the bayesian or the maximum likelihood approach for a density on the unit interval mixtures of beta densities form a flexible model the class of bernstein densities is a much smaller subclass of the beta mixtures defined by bernstein polynomials which can approximate any continuous density a bernstein polynomial prior is obtained by putting a prior distribution on the class of bernstein densities the posterior distribution of a bernstein polynomial prior is consistent under very general conditions in this article we present some results on the rate of convergence of the posterior distribution if the underlying distribution generating the data is itself a bernstein density then we show that the posterior distribution converges at nearly parametric rate log n sqrt n for the hellinger distance if the true density is not of the bernstein type we show that the posterior converges at a rate n 1 3 log n 5 6 provided that the true density is twice differentiable and bounded away from 0 similar rates are also obtained for sieve maximum likelihood estimates these rates are inferior to the pointwise convergence rate of a kernel type estimator we show that the bayesian bootstrap method gives a proxy for the posterior distribution and has a convergence rate at par with that of the kernel estimator

asymptotic theory of mixed time averages and kth order cyclic moment and cumulant statistics we generalize parzen s 1961 analysis of asymptotically stationary processes to mixtures of deterministic stationary nonstationary and generally complex time series under certain mixing conditions expressed in terms of joint cumulant summability we show that time averages of such mixtures converge in the mean square sense to their ensemble averages we additionally show that sample averages of arbitrary orders are jointly complex normal and provide their covariance expressions these conclusions provide us with statistical tools that treat random and deterministic signals on a common framework and are helpful in defining generalized moments and cumulants of mixed processes as an important consequence we develop consistent and asymptotically normal estimators for time varying and cyclic moments and cumulants of kth order cyclostationary processes and provide computable variance expressions some examples are considered to illustrate the salient features of the analysis

comments on resolution in time frequency the author comments that the first line of conjecture 5 in the paper of debrunner ozaydin and przebinda see ibid vol 47 p 783 88 1999 was proven by dembo et al 1991 the proof is a consequence of the properties of the discrete renyi entropies conjecture 5 is a special case of the renyi hirschman inequality