detection of couplings in ensembles of stochastic oscillators the problem of detection and quantitative characterization of directional couplings in an ensemble of noisy oscillators from a time series is addressed we suggest estimators for the strengths of couplings which are based on modeling the observed oscillations with a set of stochastic phase oscillators and easily interpreted from a physical viewpoint moreover we present an analytic formula for a statistical significance level allowing to reveal an architecture of couplings reliably from a relatively short time series the technique applies to weakly coupled nonsynchronized oscillators it is introduced for oscillators with close basic frequencies but can be readily generalized to the case of arbitrary frequencies efficiency of the technique is demonstrated in numerical experiments

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

symmetrically trimmed least squares estimation for tobit models this paper proposes alternatives to maximum likelihood estimation of the censored and truncated regression models known to economists as tobit models the proposed estimators are based upon symmetric censoring or truncation of the upper tail of the distribution of the dependent variable unlike methods based on the assumption of identically distributed gaussian errors the estimators are semiparametric in the sense that they are consistent and asymptotically normal for a wide class of symmetric error distributions with heteroskedasticity of unknown form the paper gives the regularity conditions and proofs of these large sample properties demonstrates how to construct consistent estimators of the asymptotic covariance matrices and presents the results of a simulation study for the censored case extensions and limitations of the approach are also considered

a robust method for detecting interdependences application to intracranially recorded eeg we present a measure for characterizing statistical relationships between two time sequences in contrast to commonly used measures like cross correlations coherence and mutual information the proposed measure is non symmetric and provides information about the direction of interdependence it is closely related to recent attempts to detect generalized synchronization however we do not assume a strict functional relationship between the two time sequences and try to define the measure so as to be robust against noise and to detect also weak interdependences we apply our measure to intracranially recorded electroencephalograms of patients suffering from severe epilepsies

a simple resampling method by perturbing the minimand suppose that under a semiparametric setting an estimator of a vector of parameters of interest is obtained by optimising an objective function which has a u process structure the covariance matrix of the estimator is generally a function of the underlying density function which may be difficult to estimate well by conventional methods in this paper we present a simple resampling method by perturbing the objective function repeatedly inferences of the parameters can then be made based on a large collection of the resulting optimisers we illustrate our proposal by three examples with a heteroscedastic regression model

construction and properties of multiwavelet packets with arbitrary scale and the related algorithms of decomposition and reconstruction a more flexible method of constructing multiwavelet packets with the scale a 2 from the same set of multiwavelets is discussed in this paper the properties of these packets are studied the formulae for performing iterations and decomposition are given l2 r can be further decomposed by these multiwavelet packets and good bases of l2 r are given finally we provide the algorithms for the decomposition and reconstruction using these multiwavelet packets

bias testing bias correction and confounder selection using an instrumental variable model instrumental variable iv analysis can be used to address bias due to unobserved confounding when estimating the causal effect of a treatment on an outcome of interest however if a proposed iv is correlated with unmeasured confounders and or weakly correlated with the treatment the standard iv estimator may be more biased than an ordinary least squares ols estimator several methods have been proposed that compare the bias of the iv and ols estimators relying on the belief that measured covariates can be used as proxies for the unmeasured confounder despite these developments there is lack of discussion about approaches that can be used to formally test whether the iv estimator may be less biased than the ols estimator thus we have developed a testing framework to compare the bias and a criterion to select informative measured covariates for bias comparison and regression adjustment we also have developed a bias correction method which allows one to use an invalid iv to correct the bias of the ols or iv estimator numerical studies demonstrate that the proposed methods perform well with realistic sample sizes

on the relationship between instantaneous phase synchrony and correlation based sliding windows for time resolved fmri connectivity analysis abstract correlation based sliding window analysis cswa is the most commonly used method to estimate time resolved functional mri fmri connectivity however instantaneous phase synchrony analysis ipsa is gaining popularity mainly because it offers single time point resolution of time resolved fmri connectivity we aim to provide a systematic comparison between these two approaches on temporal topological and anatomical levels for this purpose we used resting state fmri data from two separate cohorts with different temporal resolutions 45 healthy subjects from human connectome project fmri data with repetition time of 0 72 s and 25 healthy subjects from a separate validation fmri dataset with a repetition time of 3 s for time resolved functional connectivity analysis we calculated tapered cswa over a wide range of different window lengths that were compared to ipsa we found a strong association in connectivity dynamics between ipsa and cswa when considering the absolute values of cswa the association between cswa and ipsa was stronger for a window length of 20 s shorter than filtered fmri wavelength than 100 s longer than filtered fmri wavelength irrespective of the sampling rate of the underlying fmri data narrow band filtering of fmri data 0 03 0 07 hz yielded a stronger relationship between ipsa and cswa than wider band 0 01 0 1 hz on a topological level time averaged ipsa and cswa nodes were non linearly correlated for both short 20 s and long 100 s windows mainly because nodes with strong negative correlations cswa displayed high phase synchrony ipsa ipsa and cswa were anatomically similar in the default mode network sensory cortex insula and cerebellum our results suggest that ipsa and cswa provide comparable characterizations of time resolved fmri connectivity for appropriately chosen window lengths although ipsa requires narrow band fmri filtering it does not mandate a semi arbitrary choice of window length and window overlap a code for calculating ipsa is provided

synchronization likelihood an unbiased measure of generalized synchronization in multivariate data sets the study of complex systems consisting of many interacting subsystems requires the use of analytical tools which can detect statistical dependencies between time series recorded from these subsystems typical examples are the electroencephalogram eeg and magnetoencephalogram meg which may involve the simultaneous recording of 150 or more time series coherency which is often used to study such data is only sensitive to linear and symmetric interdependencies and cannot deal with non stationarity recently several algorithms based upon the concept of generalized synchronization have been introduced to overcome some of the limitations of coherency estimates e g physica d 134 1999 419 brain res 792 1998 24 however these methods are biased by the degrees of freedom of the interacting subsystems physica d 134 1999 419 physica d 148 2001 147 we propose a novel measure for generalized synchronization in multivariate data sets which avoids this bias and can deal with non stationary dynamics

spurious detection of phase synchronization in coupled nonlinear oscillators coupled nonlinear systems under certain conditions exhibit phase synchronization which may change for different frequency bands or with the presence of additive system noise in both cases fourier filtering is traditionally used to preprocess data we investigate to what extent the phase synchronization of two coupled r ossler oscillators depends on 1 the broadness of their power spectrum 2 the width of the bandpass filter and 3 the level of added noise we find that for identical coupling strengths oscillators with broader power spectra exhibit weaker synchronization further we find that within a broad bandwidth range bandpass filtering reduces the effect of noise but can lead to a spurious increase in the degree of phase synchronization with narrowing bandwidth even when the coupling between the two oscillators remains the same

generalising the kuramoto model for the study of neuronal synchronisation in the brain abstract in this article we have generalised the kuramoto model to allow one to model neuronal synchronisation more appropriately the generalised version allows for different connective arrangements time varying natural frequencies and time varying coupling strengths to be realised within the framework of the original kuramoto model by incorporating the above mentioned features into the original kuramoto model one can allow for the adaptive nature of neurons in the brain to be accommodated extensive tests using the generalised kuramoto model were performed on a n 4 coupled oscillator network examination of how different connective arrangements time varying natural frequencies and time varying coupling strengths affected synchronisation separately and in combination are reported the effects on synchronisation for large n are also reported

measuring synchronization in coupled model systems a comparison of different approaches the investigation of synchronization phenomena on measured experimental data such as biological time series has recently become an increasing focus of interest different approaches for measuring synchronization have been proposed that rely on certain characteristic features of the dynamical system under investigation for experimental data the underlying dynamics are usually not completely known therefore it is difficult to decide a priori which synchronization measure is most suitable for an analysis in this study we use three different coupled model systems to create a controlled setting for a comparison of six different measures of synchronization all measures are compared to each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise results show that the measure to be applied to a certain task can not be chosen according to a fixed criterion but rather pragmatically as the measure which most reliably yields plausible information in test applications although certain dynamical features of a system under investigation e g power spectra dimension may render certain measures more suitable than others c 2006 elsevier b v all rights reserved

information theoretic wavelet noise removal for inverse elastic wave scattering theory a discussion of noise removal in ultrasound elastic wave scattering for nondestructive evaluation is given the methods used in this paper include a useful suboptimal wiener filter information theory and orthonormal wavelets the multiresolution analysis mra due to mallat is the key wavelet feature used here whereas fourier transforms have a translational symmetry wavelets have a dilation or affine symmetry which consists of the semi direct product of a translation with a change of scale of the variable the mra describes the scale change features of orthonormal wavelet families first an empirical method of noise removal from scattered elastic waves using wavelets is shown to markedly improve the l 1 and l 2 error norms this suggests that the wavelet scale can act as dial to tune out noise maximization of the kullback liebler information is also shown to provide a scale dependent noise removal technique that supports but does not prove the intuition that certain small energy coefficients that are retained contain large information content the wavelet mra thereby locates islands of information in the phase space of the signal it is conjectured that this method holds more generally

large sample theory of a modified buckley james estimator for regression analysis with censored data this approach we introduce herein a slight modification of the buckley james estimator to get around the difficulties caused by the instability at the upper tail of the associated kaplan meier estimate of the underlying error distribution and show that the modified buckleyjames estimator is consistent and asymptotically normal under certain regularity conditions a simple formula for the asymptotic variance of the modified buckley james estimator is also derived and is used to study the asymptotic efficiency of the estimator extensions of these results to the multiple regression model are also given

synchronous chaos in coupled oscillator systems we investigate the synchronization of chaotic oscillations in coupled oscillator systems both theoretically and in analog electronic circuits particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift invariant symmetry these cases include the well studied cases of nearest neighbor diffusive coupling and all to all or global coupling an approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit when the oscillators are coupled through a single coordinate scalar coupling this stability criterion is illustrated numerically in a set of coupled r ossler like oscillators synchronization experiments with coupled r ossler like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems

bivariate surrogate techniques necessity strengths and caveats the concept of surrogates allows testing results from time series analysis against specified null hypotheses in application to bivariate model dynamics we here compare different types of surrogates each designed to test against a different null hypothesis e g an underlying bivariate linear stochastic process two measures that aim at a characterization of interdependence between nonlinear deterministic dynamics were used as discriminating statistics we analyze eight different stochastic and deterministic models not only to demonstrate the power of the surrogates but also to reveal some pitfalls and limitations

data driven estimates of the number of clusters in multivariate time series an important problem in unsupervised data clustering is how to determine the number of clusters here we investigate how this can be achieved in an automated way by using interrelation matrices of multivariate time series two nonparametric and purely data driven algorithms are expounded and compared the first exploits the eigenvalue spectra of surrogate data while the second employs the eigenvector components of the interrelation matrix compared to the first algorithm the second approach is computationally faster and not limited to linear interrelation measures

detecting synchronization clusters in multivariate time series via coarse graining of markov chains synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series starting from a matrix r of bivariate synchronization indices a previous method utilized the eigenvectors of r for cluster identification analogous to several recent attempts at group identification using eigenvectors of the correlation matrix all of these approaches assumed a one to one correspondence of dominant eigenvectors and clusters which has however been shown to be wrong in important cases we clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes and derive an enhanced clustering method harnessing recent insights from the coarse graining of finite state markov processes we illustrate the operation of our method using a simulated system of coupled lorenz oscillators and we demonstrate its superior performance over the previous approach finally we investigate the question of robustness of the algorithm against small sample size which is important with regard to field applications

mixing properties of the rossler system and consequences for coherence and synchronization analysis cross spectral and synchronization analysis of two independent identical chaotic rossler systems suggest a coupling although there is no interaction this spuriously detected interaction can either be explained by the absence of mixing or by finite size effects to decide which alternative holds the phase dynamics is studied by a model of the fluctuations derived from the system s equations the basic assumption of the model is a diffusive character for the system which corresponds to mixing comparison of theoretical properties of the model with empirical properties of the rossler system suggests that the system is mixing but the rate of mixing appears to be rather low

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

detection of weak directional coupling phase dynamics approach versus state space approach we compare two conceptually different approaches to the detection of weak directional couplings between two oscillatory systems from bivariate time series the first approach is based on the analysis of the systems phase dynamics whereas the other one tests for interdependencies in the reconstructed state spaces of the systems we analyze the sensitivity of both techniques to weak couplings in numerical experiments by considering couplings between almost identical as well as between significantly different nonlinear systems we study different degrees of phase diffusion test the robustness of the two techniques against observational noise and investigate the influence of the time series length our results show that none of the two approaches is generally superior to the other and we conclude that it is probably the combination of both techniques that would allow the most comprehensive and reliable characterization of coupled systems

synchronization between main rhythmic processes in the human cardiovascular system for the cases of spontaneous respiration and paced respiration with a fixed frequency and linearly increasing frequency we investigate synchronization between three main rhythmic processes governing the cardiovascular dynamics in humans namely the main heart rhythm respiration and the process whose fundamental frequency is close to 0 1 hz the analysis of the experimental records reveals synchronous regimes of different orders n m between all the three main rhythms the influence of the regime of breathing and the magnitude of heart rate variability on the degree of synchronization is considered

wavelet transforms associated with finite cyclic groups multiresolution analysis via decomposition on wavelet bases has emerged as an important tool in the analysis of signals and images when these objects are viewed as sequences of complex or real numbers an important class of multiresolution decompositions are the laplacian pyramid schemes in which the resolution is successively halved by recursively low pass filtering the signal under analysis and decimating it by a factor of two in general the principal framework within which multiresolution techniques have been studied and applied is the same as that used in the discrete time fourier analysis of sequences of complex numbers an analogous framework is developed for the multiresolution analysis of finite length sequences of elements from arbitrary fields attention is restricted to sequences of length 2 sup n for n a positive integer so that the resolution may be recursively halved to completion as in finite length fourier analysis a cyclic group structure of the index set of such sequences is exploited to characterize the transforms of interest for the particular cases of complex and finite fields

an alternative two stage least squares 2sls estimator for latent variable equations the maximum likelihood estimator dominates the estimation of general structural equation models noniterative equation by equation estimators for factor analysis have received some attention but little has been done on such estimators for latent variable equations i propose an alternative 2sls estimator of the parameters in lisrel type models and contrast it with the existing ones the new 2sls estimator allows observed and latent variables to originate from nonnormal distributions is consistent has a known asymptotic covariance matrix and is estimable with standard statistical software diagnostics for evaluating instrumental variables are described an empirical example illustrates the estimator

assessment of eeg synchronization based on state space analysis cortical computation involves the formation of cooperative neuronal assemblies characterized by synchronous oscillatory activity a traditional method for the identification of synchronous neuronal assemblies has been the coherence analysis of eeg signals here we suggest a new method called s estimator whereby cortical synchrony is defined from the embedding dimension in a state space we first validated the method on clusters of chaotic coupled oscillators and compared its performance to that of other methods for assessing synchronization then nine adult subjects were studied with high density eeg recordings while they viewed in the two hemifields hence with separate hemispheres identical sinusoidal gratings either arranged collinearly and moving together or orthogonally oriented and moving at 90 degrees the estimated synchronization increased with the collinear gratings over a cluster of occipital electrodes spanning both hemispheres whereas over temporo parietal regions of both hemispheres it decreased with the same stimulus and it increased with the orthogonal gratings separate calculations for different eeg frequencies showed that the occipital clusters involved synchronization in the beta band and the temporal clusters in the alpha band the gamma band appeared to be insensitive to stimulus diversity different stimulus configurations therefore appear to cause a complex rearrangement of synchronous neuronal assemblies distributed over the cortex in particular over the visual cortex

a note on the phase locking value and its properties we investigate the properties of the phase locking value plv and the phase lag index pli as metrics for quantifying interactions in bivariate local field potential lfp electroencephalography eeg and magnetoencephalography meg data in particular we describe the relationship between nonparametric estimates of plv and pli and the parameters of two distributions that can both be used to model phase interactions the first of these is the von mises distribution for which the sample plv is a maximum likelihood estimator the second is the relative phase distribution associated with bivariate circularly symmetric complex gaussian data we derive an explicit expression for the plv for this distribution and show that it is a function of the cross correlation between the two signals we compare the bias and variance of the sample plv and the plv computed from the cross correlation we also show that both the von mises and gaussian models are suitable for representing relative phase in application to lfp data from a visually cued motor study in macaque we then compare results using the two different plv estimators and conclude that for this data the sample plv provides equivalent information to the cross correlation of the two complex time series

conditional correlation as a measure of mediated interactivity in fmri and meg eeg many measures have been proposed so far to extract brain functional interactivity from functional magnetic resonance imaging fmri and magnetoencephalography electroencephalography meg eeg data sets unfortunately none has been able to provide a relevant self contained and common definition of brain interaction in this paper we propose a first step in this direction we first introduce a common terminology together with a cross modal definition of interaction in this setting we investigate the commonalities shared by some measures of interaction proposed in the literature we show that temporal correlation nonlinear correlation mutual information generalized synchronization phase synchronization coherence and phase locking value plv actually measure the same quantity namely correlation when one is investigating linear interactions between independently and identically distributed gaussian variables we also demonstrate that these data driven measures can only partly account for the interaction patterns that can be expressed by the effective connectivity of structural equation modeling sem to bridge this gap we suggest the use of conditional correlation which is shown to be related to mediated interaction

weak signal transmission in complex networks and its application in detecting connectivity we present a network model of coupled oscillators to study how a weak signal is transmitted in complex networks through both theoretical analysis and numerical simulations we find that the response of other nodes to the weak signal decays exponentially with their topological distance to the signal source and the coupling strength between two neighboring nodes can be figured out by the responses this finding can be conveniently used to detect the topology of unknown network such as the degree distribution clustering coefficient and community structure etc by repeatedly choosing different nodes as the signal source through four typical networks i e the regular one dimensional small world random and scale free networks we show that the features of network can be approximately given by investigating many fewer nodes than the network size thus our approach to detect the topology of unknown network may be efficient in practical situations with large network size

the phase corrected undecimated discrete wavelet packet transform and its application to interpreting the timing of events this paper is concerned with the development and application of the phase corrected maximal overlap discrete wavelet packet transform modwpt the discrete cyclic filtering steps of the modwpt are fully explained energy preservation is proven with filter coefficients chosen from daubechie s least asymmetric class the optimum time shifts to apply to ensure approximate zero phase filtering at every level of the modwpt are studied and applied to the wavelet packet coefficients to give phase corrections which ensure alignment with the original time series also the time series values at each time are decomposed into details associated with each frequency band and these line up perfectly with features in the original time series since the details are shown to arise through exact zero phase filtering the phase corrected modwpt is applied to a non stationary time series of hourly averaged southern hemisphere solar magnetic field magnitude data acquired by the ulysses spacecraft the occurrence times of the shock waves previously determined via manual pattern matching on the raw data match those times in the time frequency plot where a broadband spectrum is obtained in other words the phase corrected modwpt provides an approach to picking the location of complicated events we demonstrate the superiority of the modwpt in interpreting timing information over two competing methods namely the cosine packet transform or local cosine transform and the short time fourier transform

inferring the directionality of coupling with conditional mutual information uncovering the directionality of coupling is a significant step in understanding drive response relationships in complex systems in this paper we discuss a nonparametric method for detecting the directionality of coupling based on the estimation of information theoretic functionals we consider several different methods for estimating conditional mutual information the behavior of each estimator with respect to its free parameter is shown using a linear model where an analytical estimate of conditional mutual information is available numerical experiments in detecting coupling directionality are performed using chaotic oscillators where the influence of the phase extraction method and relative frequency ratio is investigated

tensor least angle regression for sparse representations of multidimensional signals sparse signal representations have gained much interest recently in both signal processing and statistical communities compared to orthogonal matching pursuit omp and basis pursuit which solve

amplitude envelope synchronization in coupled chaotic oscillators a peculiar type of synchronization has been found when two van der pol duffing oscillators evolving in different chaotic attractors are coupled as the coupling increases the frequencies of the two oscillators remain different while a synchronized modulation of the amplitudes of a signal of each system develops and a null lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value this phenomenon is characterized by an appropriate correlation function between the returns of the signals and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra this form of synchronization also occurs in other systems but it shows up mixed with or screened by other forms of synchronization as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators

mean phase coherence as a measure for phase synchronization and its application to the eeg of epilepsy patients abstract we apply the concept of phase synchronization of chaotic and or noisy systems and the statistical distribution of the relative instantaneous phases to electroencephalograms eegs recorded from patients with temporal lobe epilepsy using the mean phase coherence as a statistical measure for phase synchronization we observe characteristic spatial and temporal shifts in synchronization that appear to be strongly related to pathological activity in particular we observe distinct differences in the degree of synchronization between recordings from seizure free intervals and those before an impending seizure indicating an altered state of brain dynamics prior to seizure activity

from granger causality to long term causality application to climatic data quantitative characterization of interaction between processes from time series is often required in different fields of natural science including geophysics and biophysics typically one estimates short term influences e g the widely used granger causality is defined via one step ahead predictions such an approach does not reveal how strongly the long term behavior of one process under study is affected by the others to overcome this problem we introduce the concept of long term causality which extends the concept of granger causality the long term causality is estimated from data via empirical modeling and analysis of model dynamics under different conditions apart from mathematical examples we apply both approaches to find out how strongly the global surface temperature gst is affected by variations in carbon dioxide atmospheric content solar activity and volcanic activity during the last 150 years influences of all the three factors on gst are detected with the granger causality however the long term causality shows that the rise in gst during the last decades can be explained only if the anthropogenic factor co 2 is taken into account in a model

on denoising and best signal representation we propose a best basis algorithm for signal enhancement in white gaussian noise the best basis search is performed in families of orthonormal bases constructed with wavelet packets or local cosine bases we base our search for the best basis on a criterion of minimal reconstruction error of the underlying signal this approach is intuitively appealing because the enhanced or estimated signal has an associated measure of performance namely the resulting mean square error previous approaches in this framework have focused on obtaining the most compact signal representations which consequently contribute to effective denoising these approaches however do not possess the inherent measure of performance which our algorithm provides we first propose an estimator of the mean square error based on a heuristic argument and subsequently compare the reconstruction performance based upon it to that based on the stein 1981 unbiased risk estimator we compare the two proposed estimators by providing both qualitative and quantitative analyses of the bias term having two estimators of the mean square error we incorporate these cost functions into the search for the best basis and subsequently provide a substantiating example to demonstrate their performance

intraburst versus interburst locking in networks of driven nonidentical oscillators we investigate the effect of common periodic drive applied to mean field coupled oscillators and observe a specific realization of synchronization for particular ranges of drive frequency this synchronization occurs when the phase difference variability between a pair of oscillators on a given cycle is larger than that between consecutive cycles this synchrony may have implications for neural systems in which case the apparent locking between neurons based on the magnitude of their interspike intervals may not be consistent with their dynamical locking

improved transient signal detection using a wavepacket based detector with an extended translation invariant wavelet transform this paper presents the theory of m band extended translation invariant eti wavelet transforms the eti generalizes the translation invariant wavelet transform of weiss 1933 it is shown that iteration of the eti in a tree structure provides a signal decomposition into an orthonormal wavepacket basis other properties such as translation invariance and invertibility of the transform are proven the theory is then applied to transient signal detection through development of a family of translation invariant wavepacket based detectors this family of detectors provides improved the performance over previously defined wavepacket based detectors a performance analysis is conducted roc curves generated by monte carlo simulation are presented indicating the detector performance the detector performance is demonstrated to be independent of the signal translation

discrete frequency warped wavelets theory and applications we extend the definition of dyadic wavelets to include frequency warped wavelets the new wavelets are generated and the transform computed in discrete time by alternating the laguerre transform with perfect reconstruction filterbanks this scheme provides the unique implementation of orthogonal or biorthogonal warped wavelets by means of rational transfer functions we show that the discrete time warped wavelets lead to well defined continuous time wavelet bases satisfying a warped form of the two scale equation the shape of the wavelets is not invariant by translation rather the wavelet translates are obtained from one another by allpass filtering we show that the phase of the delay element is asymptotically a fractal a feature of the warped wavelet transform is that the cut off frequencies of the wavelets may be arbitrarily assigned while preserving a dyadic structure the new transform provides an arbitrary tiling of the time frequency plane which can be designed by selecting as little as a single parameter this feature is particularly desirable in cochlear and perceptual models of speech and music where accurate bandwidth selection is an issue as our examples show by defining pitch synchronous wavelets based on warped wavelets the analysis of transients and denoising of inharmonic pseudo periodic signals is greatly enhanced

positive solutions of elliptic systems with bounded nonlinearities on considere des systemes d equations elliptiques semilineaires d ordre 2 a couplage faible dans des domaines exterieurs r n n 3 on donne des conditions sur les non linearites qui garantissent l existence des solutions u a composantes positives dans telles que u 0 et u x 0 uniformement quand x on etablit la decroissance asymptotique des solutions

the relationship between structural and functional connectivity graph theoretical analysis of an eeg neural mass model we investigated the relationship between structural network properties and both synchronization strength and functional characteristics in a combined neural mass and graph theoretical model of the electroencephalogram eeg thirty two neural mass models nmms each representing the lump activity of reasonably large groups of interacting excitatory and inhibitory neurons were reciprocally and excitatory coupled using random rewiring as described by watts and strogatz numerical analysis of the network revealed an abrupt transition towards a synchronized state as a function of increasing coupling strength alpha synchronization increased with increasing degree and decreasing regularity of the network parameters of the functional network showed a diverse dependency on structural connectivity normalized clustering coefficient gamma and path length lambda increased with increasing alpha for sufficiently large alpha however gamma decreased with increasing rewiring probability p while lambda increased hence a structured functional network exists despite the randomness of the underlying structural network that is patterns of functional connectivity are influenced by patterns of the corresponding structural level but do not necessarily agree with those

matching wavelet packets to gaussian random processes we consider the problem of approximating a set of arbitrary discrete time gaussian random processes by a single representative wavelet based gaussian process we measure the similarity between the original processes and the wavelet based process with the bhattacharyya 1943 coefficient by manipulating the bhattacharyya coefficient we reduce the task of defining the representative process to finding an optimal unitary matrix of wavelet based eigenvectors an associated diagonal matrix of eigenvalues and a mean vector the matching algorithm we derive maximizes the nonadditive bhattacharyya coefficient in three steps a migration algorithm that determines the best basis by searching through a wavelet packet tree for the optimal unitary matrix of wavelet based eigenvectors and two separate fixed point algorithms that derive an appropriate set of eigenvalues and a mean vector we illustrate the method with two different classes of processes first order markov and bandlimited the technique is also applied to the problem of robust terrain classification in polarimetric sar images

a biased look at phase locking brief critical review and proposed remedy a number of popular measures of dependence between pairs of bandlimited signals rely on analytic phase a common misconception is that the dependence revealed by these measures must be specific to the spectral range of the filtered input signals implicitly or explicitly obtaining analytic phase involves normalizing the signal by its own envelope which is a nonlinear operation that introduces broad spectral leakage we review how this generates bias and complicates the interpretation of commonly used measures of phase locking a specific example of this effect may create spurious phase locking as a consequence of nonzero circular mean in the phase of input signals which can be viewed as spectral leakage to 0 hz corrections for this problem which recenter or uniformize the distribution of phase may fail when the amplitudes of the compared signals are correlated to address the more general problem of spectral bias a novel measure of phase locking is proposed the amplitude weighted phase locking value this measure is closely related to coherence but it removes ambiguities of interpretation that detract from the latter

finding effective points by surrogate models with overcomplete bases we develop algorithms to find the so called effective points eps email protected email protected r n such that the corresponding responses f x r belong to a specific region of interest roi examples of an roi include extreme values bounded intervals and positivity we are especially interested in the problem defined by the following characteristics i the definition of f x is either complicated or implicit ii the response surface f x does not fit simple patterns and iii computational costs of function evaluations is high to solve this problem we iteratively approximate the true yet unknown response surface with simplified surrogate models and then use the surrogate models to predict the possible eps unlike interpolation schemes the surrogate models are formed by linear combinations of a set of overcomplete bases and they are not obliged to fit the known response value a numerical example that involves finding positive lyapunov exponents of a dynamical system shows that the algorithm is efficient and practical

multiple imputation for m regression with censored covariates we develop a new multiple imputation approach for m regression models with censored covariates instead of specifying parametric likelihoods our method imputes the censored covariates by their conditional quantiles given the observed data where the conditional quantiles are estimated through fitting a censored quantile regression process the resulting estimator is shown to be consistent and asymptotically normal and it improves the estimation efficiency by using information from cases with censored covariates compared with existing methods the proposed method is more flexible as it does not require stringent parametric assumptions on the distributions of either the regression errors or the covariates the finite sample performance of the proposed method is assessed through a simulation study and the analysis of a c reactive protein dataset in the 2007 2008 national health and nutrition examination survey this article has supplementary material online

mapping and assessment of epileptogenic foci using frequency entropy templates much effort has been devoted to developing analysis methods of subdural electroencephalogram and depth electrode recordings of epileptic patients being evaluated for surgical resection the general approach is to investigate the brain activity at different locations as recorded by the different electrodes in an attempt to localize the epileptogenic focus or foci currently most of the methods are based on the notion that epileptogenic brain activity is associated with changes in synchronization and in complexity here we present a method that is based on the temporal dynamics combined with the spectral distribution of energy in terms of frequency entropy fe templates the fe templates are based upon maximum information partitioning into a set of frequency bands the fe template is calculated by wavelet packet decomposition followed by an application of the best basis algorithm minimizing the entropy cost function a comparison between two fe templates is performed by a special quantitative similarity measure according to the overlap in the partitioning into frequency bands and weighted by the bands entropy for localization of the epileptogenic foci the templates of each electrode during the interictal period are compared with a representative template evaluated from the ensemble of all electrodes during the ictal period we suggest associating the locations that reveal high template similarity to the ictal template with the epileptogenic foci to test the method and the underlying assumptions we perform retrospective analysis of the recorded brain activity from both grid and depth electrodes from 11 patients suffering from medically intractable epilepsy application of the ictal interictal fe template similarity analysis revealed regions in the epileptic brain in which the interictal characteristics are highly similar to those of the ictal period to asses the foci we compared the interictal templates of the different electrodes to each other forming interelectrode similarity matrices investigation of these similarity matrices revealed the existence of a single distinct subcluster of electrodes with high interelectrode similarity in the brain activity of seven patients type i activity and the existence of multiple high interelectrode similarity subclusters in the activity of four patients type ii activity comparisons of the analysis results to the medical presurgical evaluations and the outcomes of the surgical resections suggest that the method may be helpful in the chronic evaluation of the epileptogenic zone before operation and in some cases type i activity without the need to wait for seizures to occur

a peak synchronization measure for multiple signals peaks signify important events in a signal in a pair of signals how peaks are occurring with mutual correspondence may offer us significant insights into the mutual interdependence between the two signals based on important events in this work we proposed a novel synchronization measure between two signals called peak synchronization which measures the simultaneity of occurrence of peaks in the signals we subsequently generalized it to more than two signals we showed that our measure of synchronization is largely independent of the underlying parameter values a time complexity analysis of the algorithm has also been presented we applied the measure on intracranial eeg signals of epileptic patients and found that the enhanced synchronization during an epileptic seizure can be modeled better by the new peak synchronization measure than the classical amplitude correlation method

synchronization properties of heterogeneous neuronal networks with mixed excitability type we study the synchronization of neuronal networks with dynamical heterogeneity showing that network structures with the same propensity for synchronization as quantified by master stability function analysis may develop dramatically different synchronization properties when heterogeneity is introduced with respect to neuronal excitability type specifically we investigate networks composed of neurons with different types of phase response curves prcs which characterize how oscillating neurons respond to excitatory perturbations neurons exhibiting type 1 prc respond exclusively with phase advances while neurons exhibiting type 2 prc respond with either phase delays or phase advances depending on when the perturbation occurs we find that watts strogatz small world networks transition to synchronization gradually as the proportion of type 2 neurons increases whereas scale free networks may transition gradually or rapidly depending upon local correlations between node degree and excitability type random placement of type 2 neurons results in gradual transition to synchronization whereas placement of type 2 neurons as hubs leads to a much more rapid transition showing that type 2 hub cells easily hijack neuronal networks to synchronization these results underscore the fact that the degree of synchronization observed in neuronal networks is determined by a complex interplay between network structure and the dynamical properties of individual neurons indicating that efforts to recover structural connectivity from dynamical correlations must in general take both factors into account

efficient instrumental variables estimation of nonlinear models this paper considers asymptotically efficient instrumental variables estimation of nonlinear models in an i i d environment the class of models includes nonlinear simultaneous equations models and other models of interest a problem in constructing efficient instrumental variables estimators for such models is that the optimal instruments involve a conditional expectation calculation of which can require functional form assumptions for the conditional distribution of endogenous variables as well as integration nonparametric methods provide a way of avoiding this difficulty here it is shown that nonparametric estimates of the optimal instruments can give asymptotically efficient instrumental variables estimators also ways of choosing the nonparametric estimate in applications are discussed two types of nonparametric estimates of the optimal instruments are considered each involves nonparametric regression one by nearest neighbor and the other by series approximation the finite sample properties of the estimators are considered in a small sampling experiment involving an endogenous dummy variable model

quantifying time varying coordination of multimodal speech signals using correlation map analysis this paper demonstrates an algorithm for computing the instantaneous correlation coefficient between two signals the algorithm is the computational engine for analyzing the time varying coordination between signals which is called correlation map analysis cma correlation is computed around any pair of points in the two input signals thus coordination can be assessed across a continuous range of temporal offsets and be detected even when changing over time due to temporal fluctuations the correlation algorithm has two major features i it is structurally similar to a tunable filter requiring only one parameter to set its cutoff frequency and sensitivity ii it can be applied either uni directionally computing correlation based only on previous samples or bi directionally computing correlation based on both previous and future samples computing instantaneous correlation for a range of time offsets between two signals produces a 2d correlation map in which correlation is characterized as

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

instrumental variable additive hazards models summary instrumental variable iv methods are popular in non experimental studies to estimate the causal effects of medical interventions these approaches allow for the consistent estimation of treatment effects even if important confounding factors are unobserved despite the increasing use of these methods there have been few extensions of iv methods to censored data problems in this article we discuss challenges in applying iv techniques to the proportional hazards model and demonstrate the utility of the additive hazards formulation for iv analyses with censored data assuming linear structural equation models for the hazard function we develop a closed form two stage estimator for the causal effect in the additive hazard model the methods permit both continuous and discrete exposures and enable the estimation of causal relative survival measures the asymptotic properties of the estimators are derived and the resulting inferences are shown to perform well in simulation studies and in an application to a data set on the effectiveness of a novel chemotherapeutic agent for colon cancer

on least squares regression with censored data summary the semiparametric accelerated failure time model relates the logarithm of the failure time linearly to the covariates while leaving the error distribution unspecified the present paper describes simple and reliable inference procedures based on the least squares principle for this model with right censored data the proposed estimator of the vector valued regression parameter is an iterative solution to the buckley james estimating equation with a preliminary consistent estimator as the starting value the estimator is shown to be consistent and asymptotically normal a novel resampling procedure is developed for the estimation of the limiting covariance matrix extensions to marginal models for multivariate failure time data are considered the performance of the new inference procedures is assessed through simulation studies illustrations with medical studies are provided

instrumental variable estimation in semi parametric additive hazards models instrumental variable methods allow unbiased estimation in the presence of unmeasured confounders when an appropriate instrumental variable is available two stage least squares and residual inclusion methods have recently been adapted to additive hazard models for censored survival data the semi parametric additive hazard model which can include time independent and time dependent covariate effects is particularly suited for the two stage residual inclusion method since it allows direct estimation of time independent covariate effects without restricting the effect of the residual on the hazard in this article we prove asymptotic normality of two stage residual inclusion estimators of regression coefficients in a semi parametric additive hazard model with time independent and time dependent covariate effects we consider the cases of continuous and binary exposure estimation of the conditional survival function given observed covariates is discussed and a resampling scheme is proposed to obtain simultaneous confidence bands the new methods are compared to existing ones in a simulation study and are applied to a real data set the proposed methods perform favourably especially in cases with exposure dependent censoring

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

linear frequency modulated signal detection using radon ambiguity transform a novel time frequency technique for linear frequency modulated lfm signal detection is proposed the design of the proposed detectors is based on the radon transform of the modulus square or the envelope amplitude of the ambiguity function af of the signal a practical assumption is made that the chirp rate is the only parameter of interest since the af of lfm signals will pass through the origin of the ambiguity plane the line integral of the radon transform is performed over all lines passing through the origin of the ambiguity plane the proposed detectors yield maxima over chirp rates of the lfm signals this reduces the two dimensional 2 d problem of the conventional wigner ville distribution wvd based detection or the radon wigner transform rwt based detector to a one dimensional 1 d problem and consequently reduces the computation load and keeps the feature of built in filtering related issues such as the finite length effect the resolution and the effect of noise are studied the result is a tool for lfm detection as well as the time varying filtering and adaptive kernel design for multicomponent lfm signals

visualization of coupling in time series by order recurrence plots we introduce a method to visualize dependencies between two time series by applying the concept of cross recurrence plots to the local ordinal structure we derive a measure of the coupling strength which is robust against observational noise nonlinear distortion of the amplitude and low frequency trends connections to the instantaneous phase and the determination of phase coupling of two coupled rossler systems in the standard and funnel regimes are shown an application to electroencephalogram data demonstrates that the method is robust with respect to artifacts

on positive l solutions of a class of elliptic systems on considere le systeme elliptique faiblement couple l 0 u f x u dans r n n 3 ou l 0 est l expression elliptique l 0 u d i a ij d j u b j d j u et u s f r n s t s t avec s 1 m t i r 1 s t s i 0 on etablit des conditions sur f qui impliquent l existence de solutions dans r n dont les composantes sont bornees positives et bornees loin de zero

comparison of three nonlinear seizure prediction methods by means of the seizure prediction characteristic epilepsy is characterized by the spontaneous and unforeseeable occurrence of seizures during which the perception or behavior of patients is disturbed the predictability of these seizures would render novel therapeutic approaches possible several prediction methods have claimed to be able to predict seizures based on eeg recordings minutes in advance however the term seizure prediction is not unequivocally defined different criteria to assess prediction methods exist and only little attention has been paid to issues of sensitivity and false prediction rate we introduce an assessment criterion called the seizure prediction characteristicthat incorporates the assessment of sensitivity and false prediction rate within this framework three nonlinear seizure prediction methods were evaluated on a large eeg data pool of 21 patients altogether 582 h intracranial eeg data and 88 seizures were examined with a rate of 1 3 6 false predictions per day the dynamical similarity index achieves a sensitivity between 21 and 42 which was the best result of the three methods sensitivity was between 18 and 31 for the extended prospective version of the accumulated energy and between 13 and 30 for the effective correlation dimension these results still are not sufficient for clinical applications

inferring direct directed information flow from multivariate nonlinear time series estimating the functional topology of a network from multivariate observations is an important task in nonlinear dynamics we introduce the nonparametric partial directed coherence that allows disentanglement of direct and indirect connections and their directions we illustrate the performance of the nonparametric partial directed coherence by means of a simulation with data from synchronized nonlinear oscillators and apply it to real world data from a patient suffering from essential tremor

wavelet footprints theory algorithms and applications wavelet based algorithms have been successful in different signal processing tasks the wavelet transform is a powerful tool because it manages to represent both transient and stationary behaviors of a signal with few transform coefficients discontinuities often carry relevant signal information and therefore they represent a critical part to analyze we study the dependency across scales of the wavelet coefficients generated by discontinuities we start by showing that any piecewise smooth signal can be expressed as a sum of a piecewise polynomial signal and a uniformly smooth residual theorem 1 we then introduce the notion of footprints which are scale space vectors that model discontinuities in piecewise polynomial signals exactly we show that footprints form an overcomplete dictionary and develop efficient and robust algorithms to find the exact representation of a piecewise polynomial function in terms of footprints this also leads to efficient approximation of piecewise smooth functions finally we focus on applications and show that algorithms based on footprints outperform standard wavelet methods in different applications such as denoising compression and nonblind deconvolution in the case of compression we also prove that at high rates footprint based algorithms attain optimal performance theorem 3

electroencephalograms in epilepsy analysis and seizure prediction within the framework of lyapunov theory abstract epileptic seizures are defined as the clinical manifestation of excessive and hypersynchronous activity of neurons in the cerebral cortex and represent one of the most frequent malfunctions of the human central nervous system therefore the search for precursors and predictors of a seizure is of utmost clinical relevance and may even guide us to a deeper understanding of the seizure generating mechanisms we extract chaos indicators such as lyapunov exponents and kolmogorov entropies from different types of electroencephalograms eegs this covers mainly intracranial eegs semi invasive and invasive recording techniques but also scalp eegs from the surface of the skin among the analytical methods we tested up to now we find that the spectral density of the local expansion exponents is best suited to predict the onset of a forthcoming seizure we also evaluate the time evolution of the dissipation in these signals it exhibits strongly significant variations that clearly relate to the time relative to a seizure onset this article is mainly devoted to an assessment of these methods with respect to their sensitivity to eeg changes e g prior to a seizure further we investigate interictal eegs i e far away from a seizure in order to characterize their more general properties such as the convergence of the reconstructed quantities with respect to the number of phase space dimensions generally we use multichannel reconstruction but we also present a comparison with the delay embedding technique