on the statistical efficiency of the lms algorithm with nonstationary inputs a fundamental relationship exists between the quality of an adaptive solution and the amount of data used in obtaining it quality is defined here in terms of misadjustment the ratio of the excess mean square error mse in an adaptive solution to the minimum possible mse the higher the misadjustment the lower the quality is the quality of the exact least squares solution is compared with the quality of the solutions obtained by the orthogonalized and the conventional least mean square lms algorithms with stationary and nonstationary input data when adapting with noisy observations a filter trained with a finite data sample using an exact least squares algorithms will have a misadjustment given by m frac n n frac number of weights number of training samples if the same adaptive filter were trained with a steady flow of data using an ideal orthogonalized lms algorithm the misadjustment would be m frac n 4 tau mse frac number of weights number of training samples thus for a given time constant tau mse of the learning process the ideal orthogonalized lms algorithm will have about as low a misadjustment as can be achieved since this algorithm performs essentially as an exact least squares algorithm with exponential data weighting it is well known that when rapid convergence with stationary data is required exact least squares algorithms can in certain cases outperform the conventional widrow hoff lms algorithm it is shown here however that for an important class of nonstationary problems the misadjustment of conventional lms is the same as that of orthogonalized lms which in the stationary case is shown to perform essentially as an exact least squares algorithm

detrended fluctuation analysis based on higher order moments of financial time series in this paper a generalized method of detrended fluctuation analysis dfa is proposed as a new measure to assess the complexity of a complex dynamical system such as stock market we extend dfa and local scaling dfa to higher moments such as skewness and kurtosis labeled smdfa and kmdfa so as to investigate the volatility scaling property of financial time series simulations are conducted over synthetic and financial data for providing the comparative study we further report the results of volatility behaviors in three american countries three chinese and three european stock markets by using dfa and lsdfa method based on higher moments they demonstrate the dynamics behaviors of time series in different aspects which can quantify the changes of complexity for stock market data and provide us with more meaningful information than single exponent and the results reveal some higher moments volatility and higher moments multiscale volatility details that cannot be obtained using the traditional dfa method

long range power law correlations in stock returns abstract this study investigates long range power law correlations in us uk japanese german french and spanish stock markets using daily data and applying a recently developed residual analysis termed detrended fluctuation analysis dfa we quantify correlations for the returns absolute value of returns and square of returns the results show that there is little evidence of long range correlations in returns but there is strong evidence of long range correlation in absolute and squared returns for the absolute returns a cross over of approximately 41 days is found

multiscale statistical behaviors for ising financial dynamics with continuum percolation jump abstract a financial dynamics of interaction and jump is developed and investigated by two statistical physics systems ising model and continuum percolation this proposed model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price in an attempt to describe interacting micromechanism and sudden jump for stock price changes further the corresponding fluctuation behaviors and various complexity properties of logarithmic returns for the financial model are investigated by some statistical and complex analyses then p order multiscale autocorrelation function and q order multiscale entropy are also introduced to study the financial model with scaled analysis methods moreover the real stock market indexes are used to compare with the simulation returns from the financial model the empirical research shows that the simulation time series exhibits the similar fluctuation patterns with real time series

block adaptive filters with deterministic reference inputs for event related signals blms and brls adaptive estimation of the linear coefficient vector in truncated expansions is considered for the purpose of modeling noisy recurrent signals two different criteria are studied for block wise processing of the signal the mean square error mse and the least squares ls error the block lms blms algorithm being the solution of the steepest descent strategy for minimizing the mse is shown to be steady state unbiased and with a lower variance than the lms algorithm it is demonstrated that blms is equivalent to an exponential averager in the subspace spanned by the truncated set of basis functions the block recursive least squares brls solution is shown to be equivalent to the blms algorithm with a decreasing step size the brls is unbiased at any occurrence number of the signal and has the same steady state variance as the blms but with a lower variance at the transient stage the estimation methods can be interpreted in terms of linear time variant filtering the performance of the methods is studied on an ecg signal and the results show that the performance of the block algorithms is superior to that of the lms algorithm in addition measurements with clinical interest are found to be more robustly estimated in noisy signals

self similarity and network perspective of the chinese fund market abstract by testing 88 different funds of the chinese fund market cfm we find fractal behavior and long range correlations in the return series which are insensitive to the kind of funds meanwhile a power law relationship between the deviation d of prices and the hurst exponent h has been obtained which may be useful for predicting the price time series in addition with funds being viewed as nodes and the connections among the funds being determined by the cross correlation coefficients using a winner takes all approach we investigate the topological properties of the fund network our analysis reveals that during different time periods the cumulative degree distributions of the fund network all obey the double power law format moreover the small world property is also found for the fund network

generalized aic method based on higher order moments and entropy of financial time series abstract in this paper a generalized method of traditional akaike information criterion is proposed as a new measurement to compare and evaluate the volatility behaviors of time series in stock market this new method is modified by extending variance to high order statistics such as skewness kurtosis and permutation entropy so as to demonstrate the different aspects of volatility behaviors of time series compared to low order method furthermore a new model of creating an aic plane is proposed in order to derive more accurate results numerical simulations are conducted over synthetic data to provide comparative study in addition further reports about the results of distinguishing behaviors in stock market composite index of america china and hong kong by using generalized aic method and aic plane are utilized to reflect the feasibility our results can effectively differentiate multiscale volatility details of time series from three areas

modified dfa and dcca approach for quantifying the multiscale correlation structure of financial markets abstract we use multiscale detrended fluctuation analysis msdfa and multiscale detrended cross correlation analysis msdcca to investigate auto correlation ac and cross correlation cc in the us and chinese stock markets during 1997 2012 the results show that us and chinese stock indices differ in terms of their multiscale ac structures stock indices in the same region also differ with regard to their multiscale ac structures we analyze ac and cc behaviors among indices for the same region to determine similarity among six stock indices and divide them into four groups accordingly we choose s p500 nqci hsi and the shanghai composite index as representative samples for simplicity msdfa and msdcca results and average msdfa spectra for local scaling exponents lses for individual series are presented we find that the msdcca spectrum for lse cc between two time series generally tends to be greater than the average msdfa lse spectrum for individual series we obtain detailed multiscale structures and relations for cc between the four representatives msdfa and msdcca with secant rolling windows of different sizes are then applied to reanalyze the ac and cc vertical and horizontal comparisons of different window sizes are made the msdfa and msdcca results for the original window size are confirmed and some new interesting characteristics and conclusions regarding multiscale correlation structures are obtained

adaptive mesh refinement for nonparametric image registration three dimensional 3d image registration is a computationally intensive problem which is commonly solved in medical imaging the complexity of the problem stems from its size and nonlinearity in this paper we present an approach that drastically reduces the problem size by using adaptive mesh refinement our approach requires special and careful discretization of the variational form on adaptive quad octree grids it further requires an appropriate refinement criterion we show that in some cases this approach can reduce the computational time by a factor of approximately 10 or so in two dimensions and 5 in three dimensions compared to the nonadaptive approach

a unified approach to time and frequency domain realization of fir adaptive digital filters specific implementations of the finite impulse response fir block adaptive filter in the frequency domain are presented and some of their important properties are discussed the time domain block adaptive filter implemented in the frequency domain is shown to be equivalent to the frequency domain adaptive filter derived in the frequency domain provided data sectioning is done properly all of the known time and frequency domain adaptive filters 1 12 16 18 are contained in the set of possible block adaptive filter structures thus the block adaptive filter is generic and its formulation unifies the current theory of time and frequency domain fir adaptive filter structures a detailed analysis of overlap save and overlap add implementations shows that the former is to be preferred for adaptive applications because it requires less computation a fact that is not true for fixed coefficient filters

a unified approach to fast image registration and a new curvature based registration technique abstract image registration is central to many challenges in medical imaging today it has a vast range of applications the purpose of this note is twofold first we review some of the most promising non linear registration strategies currently used in medical imaging we show that all these techniques may be phrased in terms of a variational problem and allow for a unified treatment second we introduce within the variational framework a new non linear registration model based on a curvature type smoother we show that affine linear transformations belong to the kernel of this regularizer as a result the approach becomes more robust against poor initializations of a pre registration step furthermore we develop a stable and fast implementation of the new scheme based on a real discrete cosine transformation we demonstrate the advantages of the new technique for synthetic data sets and present an application of the algorithm for registering mr mammography images

iterative multigrid regularization techniques for image matching in this paper we consider the problem of matching images i e to find a deformation u which transforms a digital image into another such that the images have nearly equal gray values in every image element the difference of the two images is measured by their l2 difference which should be minimized this yields a nonlinear ill conditioned inverse problem for u so the numerical solution is quite difficult a tikhonov regularization method is considered to rule out discontinuous and irregular solutions to the minimization problem an important problem is a proper choice of the regularization parameter alpha for the practical choice of alpha we use iterative regularization methods based on multigrid techniques to obtain a suitable initial guess we use an approach similar to the full multigrid fmg developed by brandt math comp 31 1977 pp 333 390 the algorithms have optimal complexity the amount of work is proportional to the number of picture elements finally we present some experimental results for synthetic and real images

realization of adaptive digital filters using the fermat number transform an efficient realization of the block least mean square adaptive digital filters using fast transforms is discussed the computational complexities of the fermat number transform realization and the fixed point fast fourier transform realization are compared and their convergence properties are studied through the computer simulation of practical applications

block realization of multirate adaptive digital filters in this paper we study multirate transversal adaptive digital filters adf s based on the block least mean square blms algorithms these include an adf with decimation adfd and an adf with interpolation adfi we first formulate these filters based on the block mean squared error bmse criterion and derive blms multi rate weight adjustment algorithms and then study efficient realization of those filters it is shown that the blms adfd can be realized efficiently in the direct form or in the filter bank structure both using the fast fourier transform fft and an appropriate sectioning procedure according to our analysis of computational complexity the fft realization of the blms adfd in the filter bank structure is more efficient than in the direct form and the two structures using the fft become more efficient in comparison to the lms adfd as the number of weights increases unlike the direct form realization the filter bank realization of the blms adfd using the fft becomes more efficient as the decimation ratio increases similar results have been obtained for the blms adfi finally we investigate by computer simulation the effects of different weight adjustment algorithms and several system parameters on the performances of adfd s the results of simulation indicate that as expected the convergence speed of the blms adfd can be significantly improved by self orthogonalization of weight adjustment in the frequency domain furthermore the convergence factor of the self orthogonalizing blms adfd can be chosen such that the steady state performance of the new adfd is the same as that of the existing lms adfd

on two multigrid algorithms for modeling variational multiphase image segmentation in this paper we present two related multigrid algorithms for multiphase image segmentation algorithm i solves the model by vese chan we first generalize our recently developed multigrid method to this multiphase segmentation model mg1 we also give a local fourier analysis for the local smoother which leads to a new and more effective smoother although mg1 is found many magnitudes faster than the fast method of additive operator splitting aos both algorithms are not robust with regard to the initial guess to overcome this dependence on the initial guess we consider a hierarchical segmentation model which achieves multiphase segmentation by repeated use of the chan vese two phase model our algorithm ii solves this model by a multigrid algorithm mg2 numerical experiments show that both algorithms are efficient and in particular mg2 is more robust than mg1 with respect to initial guesses ams subject classifications 68u10 65f10 65k10

adaptive linearly constrained inverse qrd rls beamforming algorithm for moving jammers suppression a general linearly constrained lc recursive least squares rls array beamforming algorithm based on an inverse qr decomposition is developed for suppressing moving jammers efficiently in fact by using the inverse qr decomposition recursive least squares qrd rls algorithm approach the least squares ls weight vector can be computed without back substitution and is suitable for implementation using a systolic array to achieve fast convergence and good numerical properties the merits of this new constrained algorithm are verified by evaluating the performance in terms of the learning curve to investigate the convergence property and numerical efficiency and the output signal to interference and noise ratio we show that our proposed algorithm outperforms the conventional linearly constrained lms lclms algorithm and the one using the fast linear constrained rls algorithm and its modified version

performance analysis of structured gradient algorithm antenna array processing the structured gradient algorithm uses a structured estimate of the array correlation matrix to estimate the gradient required for the constrained least mean square algorithm this structure reflects the structure of the exact array correlation matrix for an equispaced linear array and is obtained by spatial averaging of the elements of the noisy correlation matrix in its standard form the lms algorithm does not exploit the structure of the array correlation matrix the gradient is estimated by multiplying the array output with the receiver outputs an analysis of the two algorithms is presented to show that the covariance of the gradient estimated by the structured method is less sensitive to the look direction signal than that estimated by the standard method the effect of the number of elements on the signal sensitivity of the two algorithms is studied

performance of transform domain lms adaptive digital filters in this paper we analyze the performance particularly the convergence behavior of the transform domain least mean square lms adaptive digital filter adf using the discrete fourier transform and discrete orthogonal transforms such as discrete cosine and sine transforms we first obtain the optimum wiener solution and the minimum mean squared error mse in the transform domain it is shown that the two minimum mse s in the time and transform domains are identical independently of the transforms used we then study the convergence conditions and the steady state excess mse s of the transform domain lms trlms algorithms both for the cases of having a constant and a time varying convergence factors when a constant convergence factor is used the convergence behaviors of the lms and trlms adf s appear to be almost identical provided that each has an appropriate value of the convergence factor depending on the transform used also based on the concept of a self orthogonalizing algorithm in the transform domain it is shown that the convergence speed of the trlms adf can be improved significantly for the same excess mse as that of the lms adf in addition we compare the computational complexities of the lms and trlms adf s finally we investigate by computer simulation the effects of system parameter values and different transforms on the convergence behavior of the trlms adf

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

a structured gradient algorithm for adaptive beamforming the constrained least mean square lms algorithm uses a noisy estimate of the required gradient to adaptively estimate the weights of an optimal antenna array the gradient is estimated by multiplying the array output with the array receiver outputs an alternative scheme for estimating the required gradient is proposed in this paper the new scheme uses a structured estimate of the array correlation matrix to estimate the gradient this structure reflects the structure of the exact array correlation matrix and is obtained by a spatial averaging of the elements of the noisy array correlation matrix used in the standard algorithm it is shown that the estimated gradient is unbiased and the array weights converge to the optimal weights in the mean sense furthermore the weights estimated by the structured gradient algorithm are less noisy than those estimated by the standard algorithm

transform domain lms algorithm the concept of transform domain adaptive filtering is introduced in certain applications filtering in the transform domain results in great improvements in convergence rate over the conventional time domain adaptive filtering the relationship between several existing frequency domain adaptive filtering algorithms is established applications of the discrete fourier transform dft and the discrete cosine transform dct domain adaptive filtering algorithms in the areas of speech processing and adaptive line enhancers are discussed

a multilevel method for image registration in this paper we introduce a new framework for image registration our formulation is based on consistent discretization of the optimization problem coupled with a multigrid solution of the linear system which evolves in a gauss newton iteration we show that our discretization is h elliptic independent of parameter choice and therefore a simple multigrid implementation can be used to overcome potential large nonlinearities and to further speed up computation we use a multilevel continuation technique we demonstrate the efficiency of our method on a realistic highly nonlinear registration problem

volatility distribution in the s p500 stock index abstract we study the volatility of the s p500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log normal function further using detrended fluctuation analysis we show that the volatility is power law correlated with hurst exponent 0 9

volatility behavior of visibility graph emd financial time series from ising interacting system abstract a financial market dynamics model is developed and investigated by stochastic ising system where the ising model is the most popular ferromagnetic model in statistical physics systems applying two graph based analysis and multiscale entropy method we investigate and compare the statistical volatility behavior of return time series and the corresponding imf series derived from the empirical mode decomposition emd method and the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further we find that the degree distribution of visibility graph for the simulation series has the power law tails and the assortative network exhibits the mixing pattern property all these features are in agreement with the real market data the research confirms that the financial model established by the ising system is reasonable

a more robust multigrid algorithm for diffusion type registration models abstract registration refers to the useful process of aligning two similar but different intensity image functions in order to either track changes or combine information variational models are capable of finding transform maps containing large and non uniform deformations between such a pair of images since finding a transform map is an inverse problem as with all models suitable regularisation is necessary to overcome the non uniqueness of the problem in the case of diffusion type models regularisation terms impose smoothness on the transformation by minimising the gradient of the flow field the diffusion model also coincides with the basic model for optical flow frameworks of horn and schunck 1981 the biggest drawback with variational models is the large computational cost required to solve the highly non linear system of pdes chumchob and chen 2011 developed a non linear multigrid nmg method to address this cost problem however a closer look at the analysis of the nmg scheme highlighted omissions which affected the convergence of the nmg scheme moreover the nmg method proposed by chumchob and chen did not impose any control of non physical folding which invalidates a map this paper has proposed several key ideas first we re evaluate the analysis of the nmg method to show how the omissions in chumchob and chen 2011 have a noticeable impact on the convergence of the nmg method in addition we also provide a way of estimating the convergence rate of a solver on the coarsest grid in order to estimate the number of iterations that will be required to obtain a solution with appropriate accuracy second we propose an extension to the chumchob chen nmg method which controls any folding within the deformation experimental results on the proposed multigrid framework demonstrate improvements in convergence and the accuracy of registrations compared with previous methods

time varying hurst exponent for us stock markets abstract in this work the dynamical behavior of the us stock markets is characterized on the basis of the temporal variations of the hurst exponent estimated with detrended fluctuation analysis dfa over moving windows for the historical dow jones 1928 2007 and the s p 500 1950 2007 daily indices according to the results drawn i the hurst exponent displays an erratic dynamics with some episodes alternating low and high persistent behavior ii the major breakthrough of the long term trend of the scaling behavior occurred in 1972 at the end of the bretton woods system when the hurst exponent shifted form a positive to a negative long term trend other effects such as the 1987 crisis and the emergence of anti correlated behavior in the recent two years are also discussed

bootstrap testing for detrended fluctuation analysis abstract detrended fluctuation analysis dfa is a scaling method that allows the detection of long memory in a time series until now no asymptotic distribution has been found for this statistic the bootstrap technique allows the simulation of the probability distribution of any statistic in this paper the results of the monte carlo study using bootstrap method show that the dfa test has reasonably good power for short time series another advantage of the bootstrap technique is that allows the calculation of finite sample critical values as an example we calculate bootstrap p values for financial returns time series using dfa

fourier mode analysis of multigrid methods for partial differential equations with random coefficients partial differential equations with random coefficients appear for example in reliability problems and uncertainty propagation models various approaches exist for computing the stochastic characteristics of the solution of such a differential equation in this paper we consider the spectral expansion approach this method transforms the continuous model into a large discrete algebraic system we study the convergence properties of iterative methods for solving this discretized system we consider one level and multi level methods the classical fourier mode analysis technique is extended towards the stochastic case this is done by taking the eigenstructure into account of a certain matrix that depends on the random structure of the problem we show how the convergence properties depend on the particulars of the algorithm on the discretization parameters and on the stochastic characteristics of the model numerical results are added to illustrate some of our theoretical findings

variational optical flow computation in real time this paper investigates the usefulness of bidirectional multigrid methods for variational optical flow computations although these numerical schemes are among the fastest methods for solving equation systems they are rarely applied in the field of computer vision we demonstrate how to employ those numerical methods for the treatment of variational optical flow formulations and show that the efficiency of this approach even allows for real time performance on standard pcs as a representative for variational optic flow methods we consider the recently introduced combined local global method it can be considered as a noise robust generalization of the horn and schunck technique we present a decoupled as well as a coupled version of the classical gau spl szlig seidel solver and we develop several multigrid implementations based on a discretization coarse grid approximation in contrast with standard bidirectional multigrid algorithms we take advantage of intergrid transfer operators that allow for nondyadic grid hierarchies as a consequence no restrictions concerning the image size or the number of traversed levels have to be imposed in the experimental section we juxtapose the developed multigrid schemes and demonstrate their superior performance when compared to unidirectional multigrid methods and nonhierachical solvers for the well known 316 spl times 252 yosemite sequence we succeeded in computing the complete set of dense flow fields in three quarters of a second on a 3 06 ghz pentium4 pc this corresponds to a frame rate of 18 flow fields per second which outperforms the widely used gau spl szlig seidel method by almost three orders of magnitude

improved lms algorithm for adaptive beamforming two adaptive algorithms which make use of all the available samples to estimate the required gradient are proposed and studied the first algorithm is referred to as the recursive lms least mean squares and is applicable for a general array the second algorithm is referred to as the improved lms algorithm and exploits the toeplitz structure of the array correlation matrix and can be used only for an equispaced linear array

the performance of hybrid adaptive beamforming algorithm for jammers suppression adaptive array processing is of growing importance in the fields of communications radar and sonar where the designer almost invariably faces the problem of interference suppression in general under some situations the conventional frost s 1972 beamforming algorithm may have some problems associated with performance degradation in multiple jammers environment it causes the convergence time to be essentially dependent on the jammer powers ratio a new hybrid adaptive beamforming algorithm is derived in the transformed domain for multiple jammers suppression here three popular orthonormal transformations i e discrete hartley discrete cosine and discrete fourier transforms are considered overall performance improvement in terms of convergence rate and the computational requirement is investigated from the simulation results we observed that the new presented beamforming algorithm is more robust than the conventional frost s beamforming algorithm in terms of jammers suppression and the convergence rate

a robust multigrid approach for variational image registration models variational registration models are non rigid and deformable imaging techniques for accurate registration of two images as with other models for inverse problems using the tikhonov regularization they must have a suitably chosen regularization term as well as a data fitting term one distinct feature of registration models is that their fitting term is always highly nonlinear and this nonlinearity restricts the class of numerical methods that are applicable this paper first reviews the current state of the art numerical methods for such models and observes that the nonlinear fitting term is mostly avoided in developing fast multigrid methods it then proposes a unified approach for designing fixed point type smoothers for multigrid methods the diffusion registration model second order equations and a curvature model fourth order equations are used to illustrate our robust methodology analysis of the proposed smoothers and comparisons to other methods are given as expected of a multigrid method being many orders of magnitude faster than the unilevel gradient descent approach the proposed numerical approach delivers fast and accurate results for a range of synthetic and real test images

does the singular value decomposition entropy have predictive power for stock market evidence from the shenzhen stock market abstract this paper analyzes the predictive ability of the singular value decomposition entropy for the shenzhen component index based on different scales it is found that the predictive ability of the entropy for the index is affected by the width of moving time windows and the structural break in stock market by moving time windows with one year the predictive power of singular value decomposition entropy of shenzhen stock market for its component index is found after the reform of non tradable shares

magnitude squared conherence function estimation an adaptive approach this paper concerns an adaptive approach for estimating the magnitude squared coherence msc function via widrow s least mean square lms algorithm analytical expressions for the bias and variance of the estimate so obtained are derived for the case when the input signals are stationary some computer simulation results are also included for both stationary and nonstationary signals

vectorial total variation based regularization for variational image registration to use interdependence between the primary components of the deformation field for smooth and non smooth registration problems the channel by channel total variation or standard vectorial total variation svtv based regularization has been extended to a more flexible and efficient technique allowing high quality regularization procedures based on this method this paper proposes a fast nonlinear multigrid nmg method for solving the underlying euler lagrange system of two coupled second order nonlinear partial differential equations numerical experiments using both synthetic and realistic images not only confirm that the recommended vtv based regularization yields better registration qualities for a wide range of applications than those of the svtv based regularization but also that the proposed nmg method is fast accurate and reliable in delivering visually pleasing registration results

shrinkage linear and widely linear complex valued least mean squares algorithms for adaptive beamforming in this paper shrinkage linear complex valued least mean squares sl clms and shrinkage widely linear complex valued least mean squares swl clms algorithms are devised for adaptive beamforming by exploiting the relationship between the noise free a posteriori and a priori error signals the sl clms method is able to provide a variable step size to update the weight vector for the adaptive beamformer significantly enhancing the convergence speed and decreasing the steady state misadjustment on the other hand besides adopting a variable step size determined by minimizing the square of the augmented noise free a posteriori errors the swl clms approach exploits the noncircular properties of the signal of interest which considerably improves the steady state performance simulation results are presented to illustrate their superiority over the clms complex valued normalized lms variable step size recursive least squares rls algorithms and their corresponding widely linear based schemes additionally our proposed algorithms are more computationally efficient than the rls solutions though they may have a slightly slower convergence rate

self orthogonalizing adaptive equalization in the discrete frequency domain a self orthogonalizing discrete adaptive equalizer for synchronous data transmission is presented based on the overlapsave filtering technique self orthogonalization in the discrete frequency domain is adaptively performed by premultiplying by a diagonal matrix the mse gradient estimates before projecting by means of rosen s gradient projection method the diagonal of the matrix is the inverse of the power spectrum of the received sequence taken at equally spaced frequencies and estimates are obtained by using bartlett s procedure of periodograms averaging for spectrum estimation projection is accomplished by means of an off line derived projection matrix confidence of gradient estimates is improved by means of a block correlated estimation technique using available dft s of blocks of data this equalizer is compared to time domain self orthogonalizing algorithms as regards speed of convergence and ease of implementation during the short startup phase convergence is competitive with that of godard s algorithm which is the fastest algorithm known and in the decision directed mode fast convolution performed by blocks results in a considerable reduction of the number of multiplications with respect to the time domain algorithms a computationally simpler unconstrained startup algorithm is also examined obtained by removing the projection while retaining gradient block estimates in the dfd

identification of short term and long term time scales in stock markets and effect of structural break abstract the paper presents the comparative study of the nature of stock markets in short term and long term time scales with and without structural break in the stock data structural break point has been identified by applying zivot and andrews structural trend break model to break the original time series t s o into two time series time series before structural break t s b and time series after structural break t s a in order to identify the of short term and long term market the hurst exponent h technique has been applied on the intrinsic mode functions i m f obtained from the t s o t s b and t s a by using empirical mode decomposition method h 0 5 for all the imfs of t s o t s b and t s a having in the range of few days d to 3 months m and h 0 75 for all the imfs of t s o t s b and t s a having 5 m based on the value of h the market has been divided into two time horizons short term market having 3 d 3 m and h 0 5 and long term market having 5 m and h 0 75 as h 0 5 in short term and h 0 75 in long term the market is random in short term and has long range correlation in long term robustness of the results has also been verified by using detrended fluctuation exponent analysis and normalised variance n v techniques we obtained 0 5 for reconstructed short term time series and 1 68 for long term reconstructed time series separation of short term and long term market are also identified using n v technique the time scales for short term and long term markets are independent of structural break happened due to extreme event the obtained using the proposed method for short term and long term market may be useful for investors to identify the investment time horizon and hence to design the investment and trading strategies

unconstrained frequency domain adaptive filter an unconstrained frequency domain least mean squares uflms algorithm is presented the algorithm is based on the overlap save technique used in frequency domain filtering the proposed algorithm converges to the wiener solution without the time domain constraint on the impulse response as proposed by ferrara for a large number of taps geq32 the uflms algorithm offers a significant reduction in computation another advantage is its fast convergence for highly correlated input signals the performance of the algorithm is illustrated by a simulation

correlations in economic time series a financial index of the new york stock exchange the sp here f is called the crossover frequency iii we confirm these results using the dfa detrended fluctuation analysis method see fig 2b which allows accurate estimates of exponents independent of local trends

a multigrid platform for real time motion computation with discontinuity preserving variational methods variational methods are among the most accurate techniques for estimating the optic flow they yield dense flow fields and can be designed such that they preserve discontinuities estimate large displacements correctly and perform well under noise and varying illumination however such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution consequently variational methods are considered to be too slow for real time performance in our paper we address this problem in two ways i we present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions thereby our work focuses particularly on regularisation strategies that preserve discontinuities ii we show by the examples of five classical and two recent variational techniques that real time performance is possible in all cases even for very complex optic flow models that offer high accuracy experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 120 can be achieved on a standard pc compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude

wavelet transform based adaptive filters analysis and new results in this paper the wavelet transform is used in an adaptive filtering structure the coefficients of the adaptive filter are updated by the help of the least mean square lms algorithm first the wavelet transform based adaptive filter wtaf is described and it is analyzed for its wiener optimal solution then the performance of the wtaf is studied by the help of learning curves for three different convergence factors 1 constant convergence factor 2 time varying convergence factor and 3 exponentially weighted convergence factor the exponentially weighted convergence factor is proposed to introduce scale based variation to the weight update equation it is shown for two different sets of data that the rate of convergence increases significantly for all three wtaf structures as compared to that of time domain lms the high convergence rates of the wtaf give us reason to expect that it will perform well in tracking rapid changes in a signal

a multigrid method for a fourth order diffusion equation with application to image processing in this paper we are concerned with the efficient solution of the elliptic system alpha l nobreak i u nobreak f where l is the biharmonic operator supplemented by higher order boundary conditions this is a core task in image processing arising from the minimization of rotation invariant energy functionals for the purpose of numerical solution we approximate the partial differential equation by finite differences in order to obtain efficient and robust solution methods we discuss how the system can be treated efficiently by multigrid methods finally experimental results are reported that demonstrate the effectiveness of the multigrid approach

recurrence duration statistics and time dependent intrinsic correlation analysis of trading volumes a study of chinese stock indices abstract the trading volume in stock markets is known as an important variable which reflects the liquidity of the financial markets and therefore is regarded to be greatly important for the measurement of market liquidity risk in this work a new concept called recurrence duration is introduced for study of daily trading volumes which is inspired by idea of the volatility duration that was proposed and studied in our previous work the recurrence duration is thought as the shortest passing time that the following days trading volume takes to exceed or go below the current trading volume which is time varying similar to the volatility duration distribution of the price returns the power law function could describe the empirical probability distribution of recurrence durations of trading volumes and their tail distributions can be fitted by two stretched exponential functions further the correlation relationships of trading volumes between chinese stock indices as well as the correlations of recurrence durations are investigated one approach employed is a recently proposed method time dependent intrinsic correlation tdic which is based on the empirical mode decomposition emd to decompose nonlinear and nonstationary signals into the intrinsic mode functions imfs the instantaneous periods of which are used then in determination of the sizes of sliding windows to compute the running correlation coefficients for the multiscale signals the empirical results reveal rich patterns of correlations for both trading volumes and recurrence durations at different scales for different modes another approach is the widely used dcca cross correlation coefficient by which the level of cross correlation is measured for both original series and imf modes of the stock indices

deviations from uniform power law scaling in nonstationary time series a classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long range correlations here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat to beat fluctuations in the human heart rate we develop techniques based on the fano factor and allan factor functions as well as on detrended fluctuation analysis for quantifying deviations from uniform power law scaling in nonstationary time series by analyzing extremely long data sets of up to n 10 5 beats for 11 healthy subjects we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude by contrast we find that in data sets of comparable length for 14 subjects with heart disease the fluctuations grow erratically indicating a loss of scaling stability