quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

fast adaptive 2d vortex methods we present a new approach to vortex methods for the 2d euler equations we obtain long time high order accuracy at almost optimal cost by using three tools fast adaptive quadrature rules a free lagrangian formulation and a useful new analysis of the consistency error our error analysis halves the order of differentiability required of the flow and suggests an efficient new balance of smoothing parameters which works well with fast summation schemes numerical experiments with our methods confirm our theoretical predictions and display excellent long time accuracy

recursive estimation of autoregressions this paper is concerned with the recursive estimation of autoregressive models in particular the realtime determination of the order of such a specification a model selection criterion based on the minimum description length principle due to rissanen is discussed and strong consistency in the stationary situation is shown alternative criteria are also considered and modifications required to introduce forgetting when the procedures are implemented in the non stationary case are presented some simulation evidence on the performance of the criteria when applied to stationary and non stationary processes is given

an improved unsteady unstructured artificial compressibility finite volume scheme for viscous incompressible flows part i theory and implementation a robust artificial compressibility scheme has been developed for modelling laminar steady state and transient incompressible flows over a wide range of reynolds and rayleigh numbers artificial compressibility is applied in a consistant manner resulting in a system of preconditioned governing equations a locally generalized preconditioner is introduced designed to be robust and offer good convergence rates free artificial compressibility parameters in the equations are automated to allow ease of use while facilitating improved or comparable convergence rates as compared with the standard artificial compressibility scheme memory efficiency is achieved through a multistage pseudo time explicit time marching solution procedure a node centred dual cell edge based finite volume discretization technique suitable for unstructured grids is used due to its computational efficiency and high resolution spatial accuracy in the interest of computational efficiency and ease of implementation stabilization is achieved via a scalar valued artificial dissipation scheme temporal accuracy is facilitated by employing a second order accurate dual time stepping method in this part of the paper the theory and implementation details are discussed in part 11 the scheme will be applied to a number of example problems to solve flows over a wide range of reynolds and rayleigh numbers

exploiting sparsity in adaptive filters this paper studies a class of algorithms called natural gradient ng algorithms the least mean square lms algorithm is derived within the ng framework and a family of lms variants that exploit sparsity is derived this procedure is repeated for other algorithm families such as the constant modulus algorithm cma and decision directed dd lms mean squared error analysis stability analysis and convergence analysis of the family of sparse lms algorithms are provided and it is shown that if the system is sparse then the new algorithms will converge faster for a given total asymptotic mse simulations are provided to confirm the analysis in addition bayesian priors matching the statistics of a database of real channels are given and algorithms are derived that exploit these priors simulations using measured channels are used to show a realistic application of these algorithms

multifractal spectra of multi affine functions abstract self affine functions f x with multiscaling height correlations cq x xqhq are described in terms of the standard multifractal formalism with a modified assumption for the partition the corresponding quantities and expressions are shown to exhibit some characteristic differences from the standard ones according to our calculations the f type spectra are not uniquely determined by the hq spectrum but depend on the particular choice which is made for the dependence of n on x where n is the number of points over which the average is taken our results are expected to be relevant in the analysis of signal type data obtained in experiments on systems with an underlying multiplicative process

a cut cell non conforming cartesian mesh method for compressible and incompressible flow this paper details a multigrid accelerated cut cell non conforming cartesian mesh methodology for the modelling of inviscid compressible and incompressible flow this is done via a single equation set that describes sub trans and supersonic flows cut cell technology is developed to furnish body fitted meshes with an overlapping mesh as starting point and in a manner which is insensitive to surface definition inconsistencies spatial discretization is effected via an edge based vertex centred finite volume method an alternative dual mesh construction strategy similar to the cell centred method is developed incompressibility is dealt with via an artificial compressibility algorithm and stabilization achieved with artificial dissipation in compressible flow shocks are captured via pressure switch activated upwinding the solution process is accelerated with full approximation storage fas multigrid where coarse meshes are generated automatically via a volume agglomeration methodology this is the first time that the proposed discretization and solution methods are employed to solve a single compressible incompressible equation set on cut cell cartesian meshes the developed technology is validated by numerical experiments the standard discretization and alternative methods were found equivalent in accuracy and computational cost the multigrid implementation achieved decreases in cpu time of up to one order of magnitude copyright 2007 john wiley sons ltd

parsimonious extreme learning machine using recursive orthogonal least squares novel constructive and destructive parsimonious extreme learning machines cp and dp elm are proposed in this paper by virtue of the proposed elms parsimonious structure and excellent generalization of multiinput multioutput single hidden layer feedforward networks slfns are obtained the proposed elms are developed by innovative decomposition of the recursive orthogonal least squares procedure into sequential partial orthogonalization spo the salient features of the proposed approaches are as follows 1 initial hidden nodes are randomly generated by the elm methodology and recursively orthogonalized into an upper triangular matrix with dramatic reduction in matrix size 2 the constructive spo in the cp elm focuses on the partial matrix with the subcolumn of the selected regressor including nonzeros as the first column while the destructive spo in the dp elm operates on the partial matrix including elements determined by the removed regressor 3 termination criteria for cp and dp elm are simplified by the additional residual error reduction method and 4 the output weights of the slfn need not be solved in the model selection procedure and is derived from the final upper triangular equation by backward substitution both single and multi output real world regression data sets are used to verify the effectiveness and superiority of the cp and dp elm in terms of parsimonious architecture and generalization accuracy innovative applications to nonlinear time series modeling demonstrate superior identification results

explicit and semi implicit cbs procedures for incompressible viscous flows this paper presents a numerical comparison of two different numerical procedures based on the characteristic based split cbs algorithm for the solution of incompressible flows the first procedure is based on the original semi implicit version of the cbs introduced in the early days of the scheme development the second was proposed more recently in order to have a fully explicit version of the scheme and is based on the introduction of an artificial compressibility type of formulation the interest in fully explicit schemes has increased because of the easy and efficient parallelization the main differences between the two versions of the schemes are highlighted in this work and a numerical comparison is presented on the basis of several benchmark solutions both steady and unsteady flows are considered with the explicit version of the scheme a dual time stepping procedure is needed to recover unsteady solutions copyright 2006 john wiley sons ltd

extracting fractal components from time series abstract we present a technique for extracting random fractal components from a given time series in the frequency domain the method was based on characteristics of the fractal time series that the original and the renormalized coarse grained time series had a random phase relationship an ordinary fft based cross spectral method was used to measure the phase relationship the method was tested on simulated data with known fractal and or simple harmonic properties and with a mixture of these the percent fractal components derived by this technique were closely matched to the theoretical values we set the extracted fractal power showed power law dependence expressed as spectral exponent by which we could calculate the hurst exponent h of the time series from it was also shown that the calculated h for the simulated time series gave good estimates for the true h of the random fractal process

levels of complexity in scale invariant neural signals many physical and physiological signals exhibit complex scale invariant features characterized by 1 f scaling and long range power law correlations indicating a possibly common control mechanism specifically it has been suggested that dynamical processes influenced by inputs and feedback on multiple time scales may be sufficient to give rise to 1 f scaling and scale invariance two examples of physiologic signals that are the output of hierarchical multiscale physiologic systems under neural control are the human heartbeat and human gait here we show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable 1 f scaling they still may belong to different complexity classes our analysis of the multifractal scaling exponents of the fluctuations in these two signals demonstrates that in contrast to the multifractal behavior found in healthy heartbeat dynamics gait time series exhibit less complex close to monofractal behavior further we find strong anticorrelations in the sign and close to random behavior for the magnitude of gait fluctuations at short and intermediate time scales in contrast to weak anticorrelations in the sign and strong positive correlation for the magnitude of heartbeat interval fluctuations suggesting that the neural mechanisms of cardiac and gait control exhibit different linear and nonlinear features these findings are of interest because they underscore the limitations of traditional two point correlation methods in fully characterizing physiological and physical dynamics in addition these results suggest that different mechanisms of control may be responsible for varying levels of complexity observed in physiological systems under neural regulation and in physical systems that possess similar 1 f scaling

online sparse system identification and signal reconstruction using projections onto weighted ell_ 1 balls this paper presents a novel projection based adaptive algorithm for sparse signal and system identification the sequentially observed data are used to generate an equivalent sequence of closed convex sets namely hyperslabs each hyperslab is the geometric equivalent of a cost criterion that quantifies data mismatch sparsity is imposed by the introduction of appropriately designed weighted l1 balls and the related projection operator is also derived the algorithm develops around projections onto the sequence of the generated hyperslabs as well as the weighted l1 balls the resulting scheme exhibits linear dependence with respect to the unknown system s order on the number of multiplications additions and an o llog2l dependence on sorting operations where l is the length of the system signal to be estimated numerical results are also given to validate the performance of the proposed method against the least absolute shrinkage and selection operator lasso algorithm and two very recently developed adaptive sparse schemes that fuse arguments from the lms rls adaptation mechanisms with those imposed by the lasso rational

bayesian like autoregressive spectrum estimation in the case of unknown process order initially the problem of estimation of the spectral density function of a stationary multivariate autoregressive gaussian process of unknown order is considered two new solutions to this problem are presented the proposed estimators suggested by the form of the bayesian predictor in autoregressive systems can be characterized as the average model spectrum and the spectrum corresponding to the averaged model with the averages being computed over the set of competitive autoregressive models of different orders and with respect to the sequence of the posterior probabilities of the process order given its observation history the obtained results are then extended to the case of nonstationary autoregressive processes identified by means of the exponentially weighted estimators and more general weighting sequences although not bayesian in the strict sense the proposed approaches seem to be interesting from the theoretical point of view and give better results than the classical one the efficient computational algorithms are indicated and the results of computer simulations are discussed

region based wavelet packet adaptive algorithm for identification of sparse impulse responses identification of systems with sparse impulse response encounters large applicability numerous techniques have been proposed to identify such systems efficiently one strategy that leads to specially good results is to detect the active nonzero response samples and update only the corresponding adaptive coefficients wavelet based approaches have been shown to be specially effective to this end this paper proposes a new region based wavelet packet rbwp algorithm for efficient identification of systems with sparse impulse responses with arbitrary frequency spectra and with any delay of the effective response the discrete wavelet packet transform dwpt is adaptively tailored to the energy distribution of the unknown system s response spectrum the new algorithm leads to a reduced number of active weights and to a reduced computational complexity when compared with competing wavelet based algorithms monte carlo simulation results show good performances regarding convergence speed and robustness to design parameter choice

an efficient artificial compressibility ac scheme based on the characteristic based split cbs method for incompressible flows in this paper an artificial compressibility scheme using the finite element method is introduced 2002 zienkiewicz silver medal and prize winning paper the multi purpose cbs scheme is implemented in its fully explicit form to solve incompressible fluid dynamics problems it is important to note that the scheme developed here includes split and velocity correction the proposed method takes advantage of good features from both velocity correction and standard artificial compressibility schemes unlike many other artificial compressibility schemes the proposed one works on a variety of grids and gives results for a wide range of reynold s numbers the paper presents some bench mark two and three dimensional steady and unsteady incompressible flow solutions obtained from the proposed scheme copyright 2003 john wiley sons ltd

footswitch system for measurement of the temporal parameters of gait gait analysis relies upon accurate measurement of initial and end foot contact times these times act as a reference point for correlating all other gait data and as a mean of distinguishing normal and pathologic gait we have developed a simple inexpensive footswitch system that provides accurate estimates of the start and end of stance phase for sequential steps the estimates of the beginning and end of stance phase do not require custom footwear extensive calibration or precise placement of the sensor within the shoe the system is based on a commercially available transducer and can be readily reproduced for use in a laboratory setting for less than 50 we describe this system as well as its validation to assess the accuracy of this footswitch system we compared footswitch based estimates of initial and end foot contact times with those obtained using a force platform as 10 people took 30 steps 10 each at slow normal and fast walking rates across a force platform both estimates coincided within 10 ms mean 0 3 ms n 300 for the start of stance phase and within 22 ms mean 1 8 ms n 300 for the end of stance phase for stance duration the differences ranged from 24 to 28 ms mean 1 10 ms n 300 in combination these measures can be used to estimate stance duration to within 3 of force plate determined values for steps with stance durations ranging from 446 to 1594 ms estimates of swing and stride duration also are within 5 of force plate determined values this system should therefore prove to be a useful tool for augmenting laboratory based investigations of gait

online hyperparameter free sparse estimation method in this paper we derive an online estimator for sparse parameter vectors which unlike the lasso approach does not require the tuning of any hyperparameters the algorithm is based on a covariance matching approach and is equivalent to a weighted version of the square root lasso the computational complexity of the estimator is of the same order as that of the online versions of regularized least squares rls and lasso we provide a numerical comparison with feasible and infeasible implementations of the lasso and rls to illustrate the advantage of the proposed online hyperparameter free estimator

a compact difference scheme for the navier stokes equations in vorticity velocity formulation this paper presents a new numerical method for solving the incompressible unsteady navier stokes equations in vorticity velocity formulation the method is applicable to spatial simulations of transitional and turbulent boundary layer flows it is based on a compact difference discretization of the streamwise and wall normal derivatives in cartesian coordinates a fourier collocation approach is used for the spanwise derivatives important new features of the numerical method are the use of nonequidistant differences in the wall normal direction the use of split compact differences in the streamwise direction a new fast iteration for a semi implicit time integration of the wall normal diffusion terms and an improvement of the buffer domain technique to prevent reflections of waves at the outflow boundary results of test calculations are presented to verify the improvements obtained by the use of these new techniques

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 stochastic model of human gait dynamics abstract we present a stochastic model of gait rhythm dynamics based on transitions between different neural centers that reproduces distinctive statistical properties of normal human walking by tuning one model parameter the transition hopping range the model can describe alterations in gait dynamics from childhood to adulthood including a decrease in the correlation and volatility exponents with maturation the model also generates time series with multifractal spectra whose broadness depends only on this parameter moreover we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum suggesting the possibility of a change in multifractality with maturation

steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility ac based characteristic based split cbs scheme in this paper the explicit characteristic based split cbs scheme has been employed to solve both steady and unsteady flows inside a non rectangular double driven cavity this problem is recently suggested as a benchmark problem for incompressible flows both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible the results obtained show the existence of steady state at lower reynolds numbers 1000 and transient states at higher reynolds numbers the flow approaches a turbulent state as the reynolds number is increased to 10 000 copyright 2005 john wiley sons ltd

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

a novel vector potential formulation of 3d navier stokes equations with through flow boundaries by a local meshless method an alternative vector potential formulation is used to solve the navier stokes n s equations in 3d incompressible viscous flow problems with and without through flow boundaries difficulties of the vector potential formulation include the implementation of boundary conditions for through flow boundaries and the numerical treatment of fourth order partial differential equations the advantages on the other hand are the automatic satisfaction of the continuity equation and pressure is decoupled from the velocity the objective of this paper is to introduce the appropriate gauge and boundary conditions on the vector potential formulation by a localized meshless method to handle the divergence free property a coulomb gauge condition is enforced on the vector potential to ensure its existence and uniqueness mathematically we further improve the algorithm to through flow problems for the boundary conditions of vector potential by introducing the concept of stokes theorem based on this innovation there is no need to include an additional variable to tackle the through flow fields this process will greatly simplify the imposition of boundary conditions by the vector potential approach under certain conditions the coupled fourth order partial differential equations can be easily solved by using this meshless local differential quadrature ldq method due to the ldq capability to deal with the high order differential equations this algorithm is very attractive to solve this fourth order vector potential formulation for the n s equations as comparing to the conventional numerical schemes such as finite element or finite difference methods the proposed vector potential formulation is simpler and has improved accuracy and efficiency compared to other pressure free or pressure coupled algorithms this investigation can be regarded as the first complete study to obtain the n s solutions by vector potential formulation through a ldq method two classic 3d benchmark problems lid driven cavity and backward facing step flows are numerically solved to examine the feasibility of the improved algorithm results show the flexibility of the proposed vector potential formulation for the 3d navier stokes equations

multifractal formalism for fractal signals the structure function approach versus the wavelet transform modulus maxima method several attempts have been made recently to generalize the multifractal formalism originally introduced for singular measures to fractal signals we report on a systematic comparison between the structure function approach pioneered by parisi and frisch in 2 proceedings of the international school on turbulence and predictability in geophysical fluid dynamics and climate dynamics edited by m ghil r benzi and g parisi north holland amsterdam 1985 p 84 to account for the multifractal nature of fully developed turbulent signals and an alternative method we have developed within the framework of the wavelet transform analysis we comment on the intrinsic limitations of the structure function approach this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases we demonstrate that our method based on the wavelet transform modulus maxima representation works in most situations and is likely to be the ground of a unified multifractal description of self affine distributions our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

investigation on gait time series by means of factorial moments abstract by means of factorial moments fm the fractal structures embedded in gait time series are investigated intermittency is found in records for healthy objects and this kind of intermittency is much sensitive to disease or outside influences it is found that fm is an effective tool to deal with this kind of time series

multi affine model for the velocity distribution in fully turbulent flows a simple multi affine model for the velocity distribution in fully developed turbulent flows is introduced to capture the essential features of the underlying geometry of the velocity field the authors show that in this model the various relevant quantities characterizing different aspects of turbulence can be readily calculated a simultaneous good agreement is found with the available experimental data for the velocity structure functions the dq spectra obtained from studies of the velocity derivatives and the exponent describing the scaling of the spectrum of the kinetic energy fluctuations their results are obtained analytically assuming a single free parameter the fractal dimension of the region where the dominating contribution to dissipation comes from is estimated to be d approximately 2 88

correlation differences in heartbeat fluctuations during rest and exercise we study the heartbeat activity of healthy individuals at rest and during exercise we focus on correlation properties of the intervals formed by successive peaks in the pulse wave and find significant scaling differences between rest and exercise for exercise the interval series is anticorrelated at short time scales and correlated at intermediate time scales while for rest we observe the opposite crossover pattern from strong correlations in the short time regime to weaker correlations at larger scales we also suggest a physiologically motivated stochastic scenario to provide an intuitive explanation of the scaling differences between rest and exercise

comparison of pressure based and artificial compressibility methods for solving 3d steady incompressible viscous flows pressure based and artificial compressibility methods for calculating three dimensional steady incompressible viscous flows are compared in this work each method is applied to the prediction of three dimensional laminar flows in strongly curved ducts of square and circular cross sections numerical predictions from each method are compared with available experimental data and previously reported predictions using a multigrid numerical method the accuracy grid independence convergence behavior and computational efficiency of each method are critically examined hence some of the merits and demerits of each method are revealed in this study

sparls the sparse rls algorithm we develop a recursive l1 regularized least squares sparls algorithm for the estimation of a sparse tap weight vector in the adaptive filtering setting the sparls algorithm exploits noisy observations of the tap weight vector output stream and produces its estimate using an expectation maximization type algorithm we prove the convergence of the sparls algorithm to a near optimal estimate in a stationary environment and present analytical results for the steady state error simulation studies in the context of channel estimation employing multipath wireless channels show that the sparls algorithm has significant improvement over the conventional widely used recursive least squares rls algorithm in terms of mean squared error mse moreover these simulation studies suggest that the sparls algorithm with slight modifications can operate with lower computational requirements than the rls algorithm when applied to tap weight vectors with fixed support

greedy sparse rls starting from the orthogonal greedy least squares method we build an adaptive algorithm for finding online sparse solutions to linear systems the algorithm belongs to the exponentially windowed recursive least squares rls family and maintains a partial orthogonal factorization with pivoting of the system matrix for complexity reasons the permutations that bring the relevant columns into the first positions are restrained mainly to interchanges between neighbors at each time moment the storage scheme allows the computation of the exact factorization implicitly working on indefinitely long vectors the sparsity level of the solution i e the number of nonzero elements is estimated using information theoretic criteria in particular bayesian information criterion bic and predictive least squares we present simulations showing that for identifying sparse time varying fir channels our algorithm is consistently better than previous sparse rls methods based on the norm regularization of the rls criterion we also use our sparse greedy rls algorithm for computing linear predictions in a lossless audio coding scheme and obtain better compression than mpeg4 als using an rls lms cascade

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state

scaling and universality in heart rate variability distributions we find that a universal homogeneous scaling form describes the distribution of cardiac variations for a group of healthy subjects which is stable over a wide range of time scales however a similar scaling function does not exist for a group with a common cardiopulmonary instability associated with sleep apnea subtle differences in the distributions for the day and night phase dynamics for healthy subjects are detected