on the linear normal modes of planar pre stressed curved beams the natural frequencies and mode shapes of planar shear undeformable beams around their curved pre stressed post buckling configurations are investigated neglecting rotary inertia effects two mechanical models are considered depending on the assumed boundary conditions in the buckling and post buckling phases with the first model the beam is considered inextensible because it is hinged at one end and is acted upon by an axial compressive force on the other end a sliding hinge in the second case the beam is assumed inextensible in the pre stressed phase same boundary conditions as above whereas it is extensible in the subsequent free linear dynamic phase because the sliding hinged boundary is changed into a stationary hinged end linear vibrations are governed by partial differential equations with non constant coefficients and the solutions for the frequencies and mode shapes are found employing two approximate approaches a fully numerical method based on a finite element formulation and a semi analytical method based on a weak formulation galerkin method the main results are compared and a close agreement in the outcomes is found the leading mechanical differences in the linear normal modes of the two pre stressed curved beam models are discussed

information based detection of nonlinear granger causality in multivariate processes via a nonuniform embedding technique we present an approach framed in information theory to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system the approach follows a sequential procedure for nonuniform embedding of multivariate time series whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states a corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure the causal coupling is detected according to the granger notion of predictability improvement and is quantified in terms of information transfer we apply the approach to simulations of deterministic and stochastic systems showing its superiority over standard uniform embedding effects of quantization data length and noise contamination are investigated as practical applications we consider the assessment of cardiovascular regulatory mechanisms from the analysis of heart period arterial pressure and respiration time series and the investigation of the information flow across brain areas from multichannel scalp electroencephalographic recordings

a new domain decomposition method for an hjb equation in this paper we propose a new domain decompostion method for solving a hamilton jacobi bellman equation of second order the basic idea is to solve an equivalent quasivariational inequality instead of the original discretized hjb equation

the poor bending response of the four node plane stress quadrilateral many plane stress finite elements which can exactly represent rigid body and constant strain modes are too stiff in their response to the simple flexural action of a beam this problem has received considerable interest this paper explores a new interpretation of the problem and shows that the poor bending response of the original 4 node plane stress quadrilateral can be quantitatively predicted by an error model

computational analysis of elastic field of deep curved beams rings using displacement function equilibrium method a new computational approach is proposed for determining the elastic field of deep curved beams rings which is based on a displacement function equilibrium method the displacement function is defined in terms of the radial and circumferential components of displacements which is governed by a single partial differential equation of equilibrium solution of the elastic field is obtained in terms of the displacement function in which both the uniform and the mixed mode of boundary conditions are treated with equal sophistication the application of the single function computational method is demonstrated through the numerical solutions of a number of problems of curved beams and rings with mixed boundary conditions the soundness and accuracy of the investigation are verified through the comparison of results with those obtained by conventional computational and analytical approaches available

quantifying and interpreting collective behavior in financial markets firms having similar business activities are correlated we analyze two different cross correlation matrices c constructed from i 30 min price fluctuations of 1000 us stocks for the two year period 1994 95 and ii one day price fluctuations of 422 us stocks for the 35 year period 1962 96 we find that the eigenvectors of c corresponding to the largest eigenvalues allow us to partition the set of all stocks into distinct subsets these subsets are similar to business sectors and are stable for extended periods of time we find that price fluctuations of these subsets are characterized by power law decaying time correlations reminiscent of strongly interacting systems the internal structure of a complex system manifests itself in correlations among its constituents in complex physical systems interactions between constituents cause collective modes having special statistical properties which reflect the underlying dynamics can we quantify collective movement of stock prices in analogous terms to address this question we analyze the equal time correlation matrix c constructed from the price fluctuations of a large number of stocks first we find that the collective modes for the stock market problem partition the set of all stocks studied into distinct subsets typically these subsets are formed by combinations of related industries and in some cases they go beyond grouping by industry due to company diversification the traditional partitioning of firms into subsets by products and services is difficult and sometimes arbitrary and thus our results could be viewed as a statistical alternative to traditional industry classification 1 furthermore we find that the price fluctuations of the collective modes display long range power law time correla

detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble a method to characterize dynamical interdependence among nonlinear systems is derived based on mutual nonlinear prediction systems with nonlinear correlation will show mutual nonlinear prediction when standard analysis with linear cross correlation might fail mutual nonlinear prediction also provides information on the directionality of the coupling between systems furthermore the existence of bidirectional mutual nonlinear prediction in unidirectionally coupled systems implies generalized synchrony numerical examples studied include three classes of unidirectionally coupled systems systems with identical parameters nonidentical parameters and stochastic driving of a nonlinear system this technique is then applied to the activity of motoneurons within a spinal cord motoneuron pool the interrelationships examined include single neuron unit firing the total number of neurons discharging at one time as measured by the integrated monosynaptic reflex and intracellular measurements of integrated excitatory postsynaptic potentials epsp s dynamical interdependence perhaps generalized synchrony was identified in this neuronal network between simultaneous single unit firings between units and the population and between units and intracellular epsp s

financial networks based on granger causality a case study connectivity analysis is performed on a long financial record of 21 international stock indices employing a linear and a nonlinear causality measure the conditional granger causality index cgci and the partial mutual information on mixed embedding pmime respectively both measures aim to specify the direction of the interrelationships among the international stock indexes and portray the links of the resulting networks by the presence of direct couplings between variables exploiting all available information however their differences are assessed due to the presence of nonlinearity the weighted networks formed with respect to the causality measures are transformed to binary ones using a significance test the financial networks are formed on sliding windows in order to examine the network characteristics and trace changes in the connectivity structure subsequently two statistical network quantities are calculated the average degree and the average shortest path length the empirical findings reveal interesting time varying properties of the constructed network which are clearly dependent on the nature of the financial cycle

uniform approach to linear and nonlinear interrelation patterns in multivariate time series currently a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series whereas the former are by definition insensitive to nonlinear effects the latter detect both nonlinear and linear interrelation in the present contribution we employ a uniform surrogate based approach which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation the bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation to demonstrate applicability of the approach to multivariate real world time series we investigate resting state functional magnetic resonance imaging rsfmri data of two healthy subjects as well as intracranial electroencephalograms ieeg of two epilepsy patients with focal onset seizures the main findings are that for our rsfmri data interrelations can be described by linear cross correlation rejection of the null hypothesis of linear ieeg interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures

distributions of singular values for some random matrices the singular value decomposition is a matrix decomposition technique widely used in the analysis of multivariate data such as complex space time images obtained in both physical and biological systems in this paper we examine the distribution of singular values of low rank matrices corrupted by additive noise past studies have been limited to uniform uncorrelated noise using diagrammatic and saddle point integration techniques we extend these results to heterogeneous and correlated noise sources we also provide perturbative estimates of error bars on the reconstructed low rank matrix obtained by truncating a singular value decomposition 1999 the american physical society

analysis of locking and stress oscillations in a general curved beam element the exactly integrated general quadratic curved beam element has both membrane and shear locking and significant quadratic oscillations in the axial force and cubic oscillations in the shear force the functional re constitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations the orthogonally correct field consistent interpolations are determined for the optimal form of the element and it is shown that the popular two point gaussian integrated13 version of the element is non orthogonal and has a cubic13 oscillation in the shear force that curiously vanishes at the barlow points

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

the curved beam deep arch finite ring element revisited an attempt is made to understand the errors arising in curved finite elements which undergo both flexural and membrane deformation it is shown that with elements of finite size i e a practical level of discretization at which reasonably accurate results can be expected there can be errors of a special nature that arise because the membrane strain fields are not consistently interpolated with terms from the two independent field functions that characterize such a problem these lead to errors described here as of the second kind and a physical phenomenon called membrane locking it seems possible to determine optimal integration rules that will allow the extensional deformation of a curved beam deep arch finite ring element to be modelled by independently chosen low order polynomial functions and which will recover the inextensional case in the penalty limit of extreme thinness without spurious locking constraints what is emphasized is that the choice of shape functions or subsequent operations to determine the discretized functionals must consistently model the physical requirements the problem imposes on the field variables

a gaussian sinc collocation approach for a whipping cantilever with a follower shear force at its tip a spatial discretization scheme based on a set of gaussian sinc functions is proposed for the temporal projection of a set of partial differential equations pdes describing the non linear dynamics of an elastic plastic hardening softening ephs cantilever subjected to a follower shear force at its tip the dynamics so described correspond to planar whipping of a pipe conveying fluid ruptured near a right angled bend the constitutive ephs moment curvature relationship used here follows the earlier work of reid et al proceedings of the royal society of london series a 1998 454 997 1029 compared to the more classical lagrangian polynomial based collocation functions the gaussian sine functions have better localization properties moreover for a relatively large number of collocation points use of such functions does not lead to numerical overflow or underflow problems often associated with the use of higher order polynomial collocation functions the spatial discretization leads to a set of non linear ordinary differential equations odes in time which are in turn integrated via a fourth order adaptive runge kutta scheme some numerical results for a cantilever whipping in a plane are presented to further illustrate the present approach the method is a step forward towards the development of a mesh free non linear beam element suitable for dynamic analyses of pipe networks and pipe on pipe impact problems

information and entropy in strange attractors a technique for analyzing time series data from experiments is presented that provides estimates of four basic characteristics of a system 1 the measure theoretic entropy 2 the accuracy of the measurements 3 the number of measurements necessary to specify a system state and 4 the best delay time t to use in order to construct phase space portraits by the method of delays these characteristics are obtained by separating the entropy of measurements into a part due to noise and parts due to deterministic effects for the technique to work the noise associated with each measurement must be independent of the noise associated with all other measurements an algorithm for implementing the analysis is presented with three examples

markov chain order estimation with conditional mutual information abstract we introduce the conditional mutual information cmi for the estimation of the markov chain order for a markov chain of k symbols we define cmi of order m i c m as the mutual information of two variables in the chain being m time steps apart conditioning on the intermediate variables of the chain we find approximate analytic significance limits based on the estimation bias of cmi and develop a randomization significance test of i c m where the randomized symbol sequences are formed by random permutation of the components of the original symbol sequence the significance test is applied for increasing m and the markov chain order is estimated by the last order for which the null hypothesis is rejected we present the appropriateness of cmi testing on monte carlo simulations and compare it to the akaike and bayesian information criteria the maximal fluctuation method peres shields estimator and a likelihood ratio test for increasing orders using divergence the order criterion of cmi testing turns out to be superior for orders larger than one but its effectiveness for large orders depends on data availability in view of the results from the simulations we interpret the estimated orders by the cmi testing and the other criteria on genes and intergenic regions of dna chains

significance testing of information theoretic functionals abstract a transformation is derived such that under the transformation the mutual information of two unrelated variables is a normally distributed random variable with zero mean and unit variance it is demonstrated that the transformed mutual information can be used as a test statistic to test the statistical significance of the relationship between variables and provides an alternative to the method of surrogate data if the mutual information is regarded as a generalization of the linear correlation coefficient then this test statistic can be regarded as analogous to the fisher z test statistic

stochastic verification theorems within the framework of viscosity solutions this paper studies controlled systems governed by ito s stochastic differential equations in which control variables are allowed to enter both drift and diffusion terms a new verification theorem is derived within the framework of viscosity solutions without involving any derivatives of the value functions this theorem is shown to have wider applicability than the restrictive classical verification theorems which require the associated dynamic programming equations to have smooth solutions based on the new verification result optimal stochastic feedback controls are obtained by maximizing the generalized hamiltonians over both the control regions and the superdifferentials of the value functions

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

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

dynamic mean variance portfolio selection with no shorting constraints this paper is concerned with mean variance portfolio selection problems in continuous time under the constraint that short selling of stocks is prohibited the problem is formulated as a stochastic optimal linear quadratic lq control problem however this lq problem is not a conventional one in that the control portfolio is constrained to take nonnegative values due to the no shorting restriction and thereby the usual riccati equation approach involving a completion of squares does not apply directly in addition the corresponding hamilton jacobi bellman hjb equation inherently has no smooth solution to tackle these difficulties a continuous function is constructed via two riccati equations and then it is shown that this function is a viscosity solution to the hjb equation solving these riccati equations enables one to explicitly obtain the efficient frontier and efficient investment strategies for the original mean variance problem an example illustrating these results is also presented

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

free vibration analysis of planar curved beams by wave propagation in this paper a systematic approach for the free vibration analysis of a planar circular curved beam system is presented the system considered includes multiple point discontinuities such as elastic supports attached masses and curvature changes neglecting transverse shear and rotary inertia harmonic wave solutions are found for both extensional and inextensional curved beam models dispersion equations are obtained and cut off frequencies are determined wave reflection and transmission matrices are formulated accounting for general support conditions these matrices are combined with the aid of field transfer matrices to provide a concise and efficient method for the free vibration problem of multi span planar circular curved beams with general boundary conditions and supports the solutions are exact since the effects of attenuating wave components are included in the formulation several examples are presented and compared with other methods

nonuniform state space reconstruction and coupling detection we investigate the state space reconstruction from multiple time series derived from continuous and discrete systems and propose a method for building embedding vectors progressively using information measure criteria regarding past current and future states the embedding scheme can be adapted for different purposes such as mixed modeling cross prediction and granger causality in particular we apply this method in order to detect and evaluate information transfer in coupled systems as a practical application we investigate in records of scalp epileptic eeg the information flow across brain areas

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

test your surrogate data before you test for nonlinearity the schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis in particular we pinpoint some important caveats of the prominent algorithm of amplitude adjusted fourier transform surrogates aaft and compare it to the iterated aaft which is more consistent in representing the null hypothesis it turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be reinvestigated taking into account the inaccuracies in the aaft algorithm mainly concerning the mismatching of the linear correlations in order to deal with such inaccuracies we propose the use of linear together with nonlinear polynomials as discriminating statistics the application of this setup to some well known real data sets cautions against the use of the aaft algorithm

state space reconstruction parameters in the analysis of chaotic time series the role of the time window length abstract the most common state space reconstruction method in the analysis of chaotic time series is the method of delays mod many techniques have been suggested to estimate the parameters of mod i e the time delay and the embedding dimension m we discuss the applicability of these techniques with a critical view as to their validity and point out the necessity of determining the overall time window length w for successful embedding emphasis is put on the relation between w and the dynamics of the underlying chaotic system and we suggest to set w p the mean orbital period p is approximated from the oscillations of the time series the procedure is assessed using the correlation dimension for both synthetic and real data for clean synthetic data values of w larger than p always give good results given enough data and thus p can be considered as a lower limit w p for noisy synthetic data and real data an upper limit is reached for w which approaches p for increasing noise amplitude

numerical solution of continuous time mean variance portfolio selection with nonlinear constraints an investment problem is considered with dynamic mean variance m v portfolio criterion under discontinuous prices described by jump diffusion processes some investment strategies are restricted in the study this m v portfolio with restrictions can lead to a stochastic optimal control model the corresponding stochastic hamilton jacobi bellman equation of the problem with linear and nonlinear constraints is derived numerical algorithms are presented for finding the optimal solution in this article finally a computational experiment is to illustrate the proposed methods by comparing with m v portfolio problem which does not have any constraints

embedding as a modeling problem abstract standard approaches to time delay embedding will often fail to provide an embedding that is useful for many common applications this happens in particular when there are multiple timescales in the dynamics we present a modified procedure non uniform embedding which overcomes such problems in many cases for more complex nonlinear dynamics we introduce variable embedding where in a suitable sense the embedding changes with the state of the system we show how to implement these procedures by combining embedding and modeling into a single procedure with a single optimization goal

an additional stiffness parameter measure of error of the second kind in the finite element method conventional error analyses norms in the finite element method are based on the percentage error or its equivalent in some computed value as compared to the theoretically predicted value in problems where two or more field variables are coupled it is possible that if the field interpolation functions do not consistently reproduce limiting situations of physical behaviour there may be very large errors which are exaggerated enormously when some structural parameters become indefinitely large in a penalty limiting sense the percentage error norms therefore saturate quickly to a value approaching 100 per cent and do not sensibly reflect the relationship between error and the structural parameter even on a logarithmic plot errors due to these spurious constraints have recently been recognized as belonging to a special class described as errors of the second kind a new error norm called the additional stiffening parameter helps to recognize the manner in which errors of the second kind can be blown out of propprtion by a large variation in some structural parameter recent investigations in some multi field problems are summarized here to demonstrate the usefulness of this concept

estimating mutual information we present two classes of improved estimators for mutual information m x y from samples of random points distributed according to some joint probability density mu x y in contrast to conventional estimators based on binnings they are based on entropy estimates from k nearest neighbor distances this means that they are data efficient with k 1 we resolve structures down to the smallest possible scales adaptive the resolution is higher where data are more numerous and have minimal bias indeed the bias of the underlying entropy estimates is mainly due to nonuniformity of the density at the smallest resolved scale giving typically systematic errors which scale as functions of k n for n points numerically we find that both families become exact for independent distributions i e the estimator m x y vanishes up to statistical fluctuations if mu x y mu x mu y this holds for all tested marginal distributions and for all dimensions of x and y in addition we give estimators for redundancies between more than two random variables we compare our algorithms in detail with existing algorithms finally we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis ica for improving ica and for estimating the reliability of blind source separation

reliable detection of directional couplings using rank statistics to detect directional couplings from time series various measures based on distances in reconstructed state spaces were introduced these measures can however be biased by asymmetries in the dynamics structure noise color or noise level which are ubiquitous in experimental signals using theoretical reasoning and results from model systems we identify the various sources of bias and show that most of them can be eliminated by an appropriate normalization we furthermore diminish the remaining biases by introducing a measure based on ranks of distances this rank based measure outperforms existing distance based measures concerning both sensitivity and specificity for directional couplings therefore our findings are relevant for a reliable detection of directional couplings from experimental signals

sparse model from optimal nonuniform embedding of time series an approach to obtaining a parsimonious polynomial model from time series is proposed an optimal minimal nonuniform time series embedding schema is used to obtain a time delay kernel this scheme recursively optimizes an objective functional that eliminates a maximum number of false nearest neighbors between successive state space reconstruction cycles a polynomial basis is then constructed from this time delay kernel a sparse model from this polynomial basis is obtained by solving a regularized least squares problem the constraint satisfaction problem is made computationally tractable by keeping the ratio between the number of constraints to the number of variables small by using fewer samples spanning all regions of the reconstructed state space this helps the structure selection process from an exponentially large combinatorial search space a forward stagewise algorithm is then used for fast discovery of the optimization path results are presented for the mackey glass system

dynamics from multivariate time series abstract multivariate time series data are common in experimental and industrial systems if the generating system has nonlinear dynamics we may be able to construct a model that reproduces the dynamics and can be used for control and other purposes in principle multivariate time series are not necessary for recovering dynamics according to the embedding theorem only one time series should be needed however for real data there may be large gains in using all of the measurements in this paper we examine the issues of how to use multiple data streams most effectively for modeling and prediction for example perhaps the data are redundant in that only a subset of the data streams is useful and how should we embed the data if indeed embedding is required at all we show how these questions can be answered and describe some numerical experiments which show that using multivariate time series can significantly improve predictability we also demonstrate a somewhat surprising synchronization between different reconstructions

relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data commonly used dependence measures such as linear correlation cross correlogram or kendall s tau cannot capture the complete dependence structure in data unless the structure is restricted to linear periodic or monotonic mutual information mi has been frequently utilized for capturing the complete dependence structure including nonlinear dependence recently several methods have been proposed for the mi estimation such as kernel density estimators kde k nearest neighbors knn edgeworth approximation of differential entropy and adaptive partitioning of the xy plane however outstanding gaps in the current literature have precluded the ability to effectively automate these methods which in turn have caused limited adoptions by the application communities this study attempts to address a key gap in the literature specifically the evaluation of the above methods to choose the best method particularly in terms of their robustness for short and noisy data based on comparisons with the theoretical mi estimates which can be computed analytically as well with linear correlation and kendall s tau here we consider smaller data sizes such as 50 100 and 1 000 where this study considers 50 and 100 data points as very short and 1 000 as short we consider a broader class of functions specifically linear quadratic periodicmore and chaotic contaminated with artificial noise with varying noise to signal ratios the case studies presented here are motivated by domain consideration in the earth sciences where the data are short and noisy our results indicate kde as the best choice for very short data at relatively high noise to signal levels whereas the performance of knn is the best for short data at relatively low noise levels as well as for short data consistently across noise levels in addition the optimal smoothing parameter of a gaussian kernel appears to be the best choice for kde while three nearest neighbors appear optimal for knn thus in situations where the approximate data sizes are known in advance and exploratory data analysis and or domain knowledge can be used to provide a priori insights on the noise to signal ratios the results in the paper point to a way forward for automating the process of mi estimation less

granger causality in multivariate time series using a time ordered restricted vector autoregressive model granger causality has been used for the investigation of the inter dependence structure of the underlying systems of multivariate time series in particular the direct causal effects are commonly estimated by the conditional granger causality index cgci in the presence of many observed variables and relatively short time series cgci may fail because it is based on vector autoregressive models var involving a large number of coefficients to be estimated in this paper the var is restricted by a scheme that modifies the recently developed method of backward in time selection bts of the lagged variables and the cgci is combined with bts further the proposed approach is compared favorably to other restricted var representations such as the top down strategy the bottom up strategy and the least absolute shrinkage and selection operator lasso in terms of sensitivity and specificity of cgci this is shown by using simulations of linear and nonlinear low and high dimensional systems and different time series lengths for nonlinear systems cgci from the restricted var representations are compared with analogous nonlinear causality indices further cgci in conjunction with bts and other restricted var representations is applied to multichannel scalp electroencephalogram eeg recordings of epileptic patients containing epileptiform discharges cgci on the restricted var and bts in particular could track the changes in brain connectivity before during and after epileptiform discharges which was not possible using the full var representation

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

an approach for characterizing coupling in dynamical systems abstract the study of coupling in dynamical systems dates back to christian hyugens who in 1665 discovered that pendulum clocks with the same length pendulum synchronize when they are near to each other in that case the observed synchronous motion was out of phase in this paper we propose a new approach for measuring the degree of coupling and synchronization of a dynamical system consisting of interacting subsystems the measure is based on quantifying the active degrees of freedom e g correlation dimension of the coupled system and the constituent subsystems the time delay embedding scheme is extended to coupled systems and used for attractor reconstruction of the coupled dynamical system we use the coupled lorenz rossler and henon model systems with a coupling strength variable for evaluation of the proposed approach results show that we can measure the active degrees of freedom of the coupled dynamical systems and can quantify and distinguish the degree of synchronization or coupling in each of the dynamical systems studied furthermore using this approach the direction of coupling can be determined

measuring statistical dependences in a time series we propose two methods to measure all linear and nonlinear statistical dependences in a stationary time series presuming ergodicity the measures can be obtained from efficient numerical algorithms

a locking free finite element formulation and reduced models for geometrically exact kirchhoff rods in this work we suggest a locking free geometrically exact finite element formulation incorporating the modes of axial tension torsion and bending of thin kirchhoff beams with arbitrary initial curvatures and cross section shapes the proposed formulation has been designed in order to represent general load cases and three dimensional problem settings in the geometrically nonlinear regime of large deformations from this comprehensive theory we not only derive a general beam model but also several reduced formulations which deliver accurate solutions for special problem classes concerning the beam geometry and the external loads the advantages of these reduced models arise for example in terms of simplified finite element formulations less degrees of freedom per element and consequently a higher computational efficiency of the corresponding numerical models a second core topic of this publication is the treatment of membrane locking which is a locking phenomenon predominantly occurring in highly slender curved structures thus exactly in the prime field of application for kirchhoff theories in order to address the membrane locking effect we will propose a new interpolation strategy for the axial strain field and compare this method with common approaches such as assumed natural strains ans or reduced integration the effectiveness of this method as well as the consistency and accuracy of the general finite element formulation and the reduced beam models will be illustrated with selected numerical examples

field consistent strain interpolations for the quadratic shear flexible beam element a shear flexible i e timoshenko quadratic isoparametric beam element with two degrees of freedom per node is critically examined from the point of view of the consistency of the constrained strain fields that arise in the thin beam limits the errors in terms of convergence of displacement fields and violent oscillations of stress fields that emerge when exactly integrated elements are used are predicted a priori and confirmed with numerical experiments the rationale behind the use of optimal stress sampling at gaussian points is also derived directly from these arguments

reduced integration and the shear flexible beam element the timoshenko beam element is studied in an investigation of shear locking in the development of c 0 continuous elements using shear flexible or penalty function type formulations a penalty type argument is used to degenerate thick elements to thin elements and the various approximations of the shear related energy terms act as different types of constraints depending on the formulation two types of constraints may emerge which are classified as true or spurious formulations that ensure only true constraints in the extreme penalty limit cases display superior performance in the thick element situation the argument is extended to a shallow curved timoshenko beam and another mechanism inplane locking arises if all energy terms corresponding to the membrane energy are exactly integrated

multivariate phase space reconstruction by nearest neighbor embedding with different time delays a recently proposed nearest neighbor based selection of time delays for phase space reconstruction is extended to multivariate time series with an iterative selection of variables and time delays a case study of numerically generated solutions of the x and z coordinates of the lorenz system and an application to heart rate and respiration data are used for illustration

testing for nonlinearity using redundancies quantitative and qualitative aspects abstract a method for testing nonlinearity in time series is described based on information theoretic functionals redundancies linear and nonlinear forms of which allow either qualitative or after incorporating the surrogate data technique quantitative evaluation of dynamical properties of scrutinized data an interplay of quantitative and qualitative testing on both the linear and nonlinear levels is analyzed and robustness of this combined approach against spurious nonlinearity detection is demonstrated evaluation of redundancies and redundancy based statistics as functions of time lag and embedding dimension can further enhance insight into dynamics of a system under study

reconstructing embedding spaces of coupled dynamical systems from multivariate data a method for reconstructing dimensions of subspaces for weakly coupled dynamical systems is offered the tool is able to extrapolate the subspace dimensions from the zero coupling limit where the division of dimensions as per the algorithm is exact implementation of the proposed technique to multivariate data demonstrates its effectiveness in disentangling subspace dimensionalities also in the case of emergent synchronized motions for both numerical and experimental systems

identifying phase synchronization clusters in spatially extended dynamical systems we investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended nonstationary systems with regard to field applications the starting point of both techniques is a matrix whose entries are the mean phase coherence values measured between pairs of time series the first method is a mean field approach which allows one to define the strength of participation of a subsystem in a single synchronization cluster the second method is based on an eigenvalue decomposition from which a participation index is derived that characterizes the degree of involvement of a subsystem within multiple synchronization clusters simulating multiple clusters within a lattice of coupled lorenz oscillators we explore the limitations and pitfalls of both methods and demonstrate a that the mean field approach is relatively robust even in configurations where the single cluster assumption is not entirely fulfilled and b that the eigenvalue decomposition approach correctly identifies the simulated clusters even for low coupling strengths using the eigenvalue decomposition approach we studied spatiotemporal synchronization clusters in long lasting multichannel eeg recordings from epilepsy patients and obtained results that fully confirm findings from well established neurophysiological examination techniques multivariate time series analysis methods such as synchronization cluster analysis which account for nonlinearities in the data are expected to provide complementary information which allows one to gain deeper insights into the collective dynamics of spatially extended complex systems

analytical and numerical results for vibration analysis of multi stepped and multi damaged circular arches this paper investigates the in plane linear dynamic behaviour of multi stepped and multi damaged circular arches under different boundary conditions cracked cross sections are modelled as massless elastic rotational hinges in damaged configuration cracks can be located both at the interface between two adjacent portions as well as inside the portion itself for each arch portion bounded by two cracks the differential equations of motion have been established considering axial extension transverse shear effects and rotatory inertia the equilibrium equations of arch portions are combined in the coupled fundamental system in terms of radial displacement tangential displacement and rotation analytical and numerical solutions for multi stepped arches in undamaged as well as in damaged configurations are proposed the analytical solution is based on the euler characteristic exponent procedure involving the roots of characteristic polynomials while the numerical method is focused on the generalized differential quadrature gdq method and the generalized differential quadrature element gdqe technique numerical results are shown in terms of the first 10 analytical and numerical frequencies of multi stepped and multi damaged arches with different boundary conditions finally convergence and stability characteristics of the gdqe procedure are investigated the convergence rate of the natural frequencies is shown to be very fast and the stability of the numerical procedure is very good

a simple plate shell triangle a simple shear flexible triangular plate shell element with three five displacement degrees of freedom at the three corner nodes only is identified it does not lock or have zero energy mechanisms the specific geometrical configurations in which this is possible are derived through field consistency patch tests

a three noded shear flexible curved beam element based on coupled displacement field interpolations an efficient shear flexible three noded curved beam element is proposed herein the shear flexibility is based on timoshenko beam theory and the element has three degrees of freedom viz tangential displacement u radial displacement w and the section rotation a quartic polynomial interpolation for flexural rotation is assumed a priori making use of the physical composition of in terms of and u a novel way of deriving the polynomial interpolations for u and w is presented by solving force moment and moment shear equilibrium equations simultaneously the field interpolation for is then constructed from that of and u the procedure leads to high order polynomial field interpolations which share some of the generalized degrees of freedom by means of coefficients involving material and geometric properties of the element when applied to a straight euler bernoulli beam all the coupled coefficients vanish and the formulation reduces to classical quintic in w and quadratic in u element with u w and w x as degrees of freedom the element is totally devoid of membrane and shear locking phenomena the formulation presents an efficient utilization of the nine generalized degrees of freedom available for the polynomial interpolation of field variables for a three noded curved beam element numerical examples on static and free vibration analyses demonstrate the efficacy and locking free property of the element copyright 2001 john wiley sons ltd

mean variance portfolio selection with random parameters in a complete market this paper concerns the continuous time mean variance portfolio selection problem in a complete market with random interest rate appreciation rates and volatility coef cients the problem is tackled using the results of stochastic linear quadratic lq optimal control and backward stochastic differential equations bsdes two theories that have been extensively studied and developed in recent years specifically the mean variance problem is formulated as a linearly constrained stochastic lq control problem solvability of this lq problem is reduced in turn to proving global solvability of a stochastic riccati equation the proof of existence and uniqueness of this riccati equation which is a fully nonlinear and singular bsde with random coefficients is interesting in its own right and relies heavily on the structural properties of the equation efficient investment strategies as well as the mean variance efficient frontier are then analytically derived in terms of the solution of this equation in particular it is demonstrated that the efficient frontier in the mean standard deviation diagram is still a straight line or equivalently risk free investment is still possible even when the interest rate is random finally a version of the mutual fund theorem is presented

locking free curved beam element based on curvature the formulation of a curved beam element with 3 nodes for curvature to eliminate the shear membrane locking phenomenon is presented the element is based on curvature so that it may represent the bending energy fully and the shear membrane strain energy is incorporated into the formulation by the equilibrium equations to deal with general boundary conditions a transformation matrix between nodal curvature and nodal displacement vector is introduced several examples are presented in order to verify the element formulation and its analytical capability the solutions obtained reveal that the element describes the curved beam behaviour quite correctly and efficiently showing no locking phenomena and that it is also applicable to the analysis of both thin and thick curved beams

a comment on accuracy of some finite element models for arch problems by f kikuchi comput meths appl mech engrg 35 1982 315 345

application of the finite element difference method to vibration problems the so called finite element difference method introduced in references 1 and 2 yields a continuous stress field by finite difference operations and finite element interpolations in the present paper applications of the method to vibration problems are discussed the inverse iteration procedure is modified for this method numerical results show that the accuracy of solutions depends strongly on the type of finite difference operator chosen for reliable and accurate solutions in modal analysis problems element internal strains must be included in the strain field used to compute nodal forces associated with element deformations

regularized local linear prediction of chaotic time series abstract local linear prediction based on the ordinary least squares ols approach is one of several methods that have been applied to prediction of chaotic time series apart from potential linearization errors a drawback of this approach is the high variance of the predictions under certain conditions here a different set of so called linear regularization techniques originally derived to solve ill posed regression problems are compared to ols for chaotic time series corrupted by additive measurement noise these methods reduce the variance compared to ols but introduce more bias a main tool of analysis is the singular value decomposition svd and a key to successful regularization is to damp the higher order svd components several of the methods achieve improved prediction compared to ols for synthetic noise corrupted data from well known chaotic systems similar results were found for real world data from the r r intervals of ecg signals good results are also obtained for real sunspot data compared to published predictions using nonlinear techniques

field consistency and violent stress oscillations in the finite element method the fact that finite element models can give rise to13 violent stress oscillations has been known for some time it is also well known that in many problems there are optimal locations where stresses can be correctly sampled in spite of the presence of these violent stress fluctuations however it is less well known that these oscillations arise in a specific class of problems where there are multiple strain fields arising from one or more field variables and where one or more of these strain fields must be constrained in particular physical13 limits in this paper we show that unless the interpolations for these constrained strain fields are x2018 field consistentx2019 violent oscillations would set in these oscillations represent spurious self equilibrating stress fields generating spurious energy terms that lead to x2018 lockingx2019

random matrix theory analysis of cross correlations in financial markets we confirm universal behaviors such as eigenvalue distribution and spacings predicted by random matrix theory rmt for the cross correlation matrix of the daily stock prices of tokyo stock exchange from 1993 to 2001 which have been reported for new york stock exchange in previous studies it is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present some deviations in the small eigenvalue statistics outside the bounds of the universality class of rmt are not completely explained with the deterministic correlations as proposed in previous studies we study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues this is interpreted as a reminiscent of level repulsion in rmt and explains some deviations from the previous studies observed in the market data we also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on rmt some characteristic differences between properties of tokyo stock exchange and new york stock exchange are found

nearest neighbor embedding with different time delays a nearest neighbor based selection of time delays for phase space reconstruction is proposed and compared to the standard use of time delayed mutual information the possibility of using different time delays for consecutive dimensions is considered a case study of numerically generated solutions of the lorenz system is used for illustration the effect of contamination with various levels of additive gaussian white noise is discussed

estimation of the direction of the coupling by conditional probabilities of recurrence we introduce a method to detect and quantify the asymmetry of the coupling between two interacting systems based on their recurrence properties this method can detect the direction of the coupling in weakly as well as strongly coupled systems it even allows detecting the asymmetry of the coupling in the more challenging case of structurally different systems and it is very robust against noise we also address the problem of detecting the asymmetry of the coupling in passive experiments i e when the strength of the coupling cannot be systematically changed which is of great relevance for the analysis of experimental time series

consistency aspects of out of plane bending torsion and shear in a quadratic curved beam element curved beams in civil engineering applications call for out of plane bending and torsion under the action of out of plane transverse shear loads the design of a quadratic displacement type curved beam element capable of representing shear deformation as in the timoshenko beam theory will call for special attention to be paid to the manner in which the shear strain is to be represented field inconsistent representations of the out of plane transverse shear strain will result in a loss gf efficiency and introduce spuriou oscillations in the bending moment torsional moment and shear force the optimal field consistent assumed strain interpolation for the shear is derived here and it is demonstrated that it has very high accuracy and is free from spurious force and moment oscillations

surrogate time series before we apply nonlinear techniques e g those inspired by chaos theory to dynamical phenomena occurring in nature it is necessary to first ask if the use of such advanced techniques is justified by the data while many processes in nature seem very unlikely a priori to be linear the possible nonlinear nature might not be evident in specific aspects of their dynamics the method of surrogate data has become a very popular tool to address such a question however while it was meant to provide a statistically rigorous foolproof framework some limitations and caveats have shown up in its practical use in this paper recent efforts to understand the caveats avoid the pitfalls and to overcome some of the limitations are reviewed and augmented by new material in particular we will discuss specific as well as more general approaches to constrained randomisation providing a full range of examples new algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains the main limitation which lies in the interpretability of the test results will be illustrated through instructive case studies we will also discuss some implementational aspects of the realisation of these methods in the tisean software package

mixed models and reduced selective integration displacement models for nonlinear analysis of curved beams simple mixed models are developed for the geometrically nonlinear analysis of deep arches a total lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included the fundamental unknowns consist of the six internal forces and generalized displacements of the arch and the element characteristic arrays are obtained by using hellinger reissner mixed variational principle the polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements and the forces are discontinuous at the interelement boundaries the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed the advantages of mixed models over equivalent displacement models are outlined numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and compare their performance with other mixed models reported in the literature

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

improved surrogate data for nonlinearity tests current tests for nonlinearity compare a time series to the null hypothesis of a gaussian linear stochastic process for this restricted null assumption random surrogates can be constructed which are constrained by the linear properties of the data we propose a more general null hypothesis allowing for nonlinear rescalings of a gaussian linear process we show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity an iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution

locking and robustness in the finite element method for circular arch problem in this paper we discuss locking and robustness of the finite element method for a model circular arch problem it is shown that in the primal variable i e the standard displacement formulation the p version is free from locking and uniformly robust with order p k and hence exhibits optimal rate of convergence on the other hand the h version shows locking of order h 2 and is uniformly robust with order h p 2 for p 2 which explains the fact that the quadratic element for some circular arch problems suffers from locking for thin arches in computational experience if mixed method is used both the h version and the p version are free from locking furthermore the mixed method even converges uniformly with an optimal rate for the stress

spatio temporal dynamics of human eeg electroencephalogram eeg recording of spontaneous brain electrical activity resulting from collective dynamical behaviour of the neural mass was traditionally treated as a random signal and processed by stochastic methods like spectral analysis qualitatively new views were opened by approaches derived from synergetics non linear dynamics and theory of deterministic chaos introduced into eeg research in the last six years see refs 1 2 and references therein in this approach the eeg signal is supposed to be a deterministic signal generated by chaotic dynamics of finite and even low dimensional dynamical system evolving on its strange attractor processing eeg data consists then of the reconstruction of a hypothetical strange attractor from experimental data and computations of relevant dynamical topological invariants fractal dimensions lyapunov exponents kolmogorov entropy the goal of this treatment is using measures of complexity and chaos for characterization of brain processes reflected in the eeg signal i e developing new tools for computerized eeg analysis with applications in psychiatry neurology and pharmacology of psychoactive drugs eeg signals can be simultaneously registered from several locations on the scalp 16 32 64 two ways of reconstructing the brain attractor are presently used one channel reconstruction a one dimensional one channel eeg signal registered from a particular location on the scalp is considered as a smooth projection of n dimensional chaotic dynamics on the strange attractor an n dimensional trajectory is reconstructed using the time delay method based affiliated to 3rd school of medicine charles university prague e mail pcpmp csearn bitnet 0378 4371 92 05 00 1992 elsevier science publishers b v all rights reserved

optimal embedding parameters a modelling paradigm the reconstruction of a dynamical system from a time series requires the selection of two parameters the embedding dimension de and the embedding lag many competing criteria to select these parameters exist and all are heuristic within the context of modelling the evolution operator of the underlying dynamical system we show that one only need be concerned with the product de we introduce an information theoretic criterion for the optimal selection of the embedding window dw de for infinitely long time series this method is equivalent to selecting the embedding lag that minimises the nonlinear model prediction error for short and noisy time series we find that the results of this new algorithm are data dependent and are superior to estimation of embedding parameters with the standard techniques

invariant hermitian finite elements for thin kirchhoff rods i the linear plane case abstract the objective of this work is to develop finite elements for the simulation of thin kirchhoff rods that is rods where the influence of transverse shear strain can be neglected leading to governing equations that require c 1 continuous finite element interpolations we start in this paper with the formulation of new finite elements for the infinitesimal plane deformations of otherwise generally curved rods addressing in particular the lack of invariance observed in related traditional treatments of plane arches by non invariance we mean that the classical rigid body modes of translations and infinitesimal rotations of the underlying structural theory lead to non zero strains in the element an effect sometimes referred to as self straining this phenomenon occurs in curved configurations of the elements and in the infinitesimal setting of interest in this paper it results in the elements stiffness matrix not to exhibit the correct zero energy modes associated with these physical rigid body motions as a consequence the basic equilibrium relations of balance of forces and moments are not satisfied for the associated nodal forces and moments in non invariant finite elements in this context we propose a new framework for the formulation of c 1 continuous finite elements based on hermitian shape functions that do lead to the satisfaction of this fundamental invariance property accounting fully for the rod s curvature and associated kirchhoff s kinematics in contrast to common straight framework element approximations based on the simplified euler bernoulli beam kinematics the formulation relies crucially on a consistent treatment of the kinematics and the assumed interpolation of the rods geometry an additional assumed strain treatment is considered to avoid limitations of membrane locking complete rigorous analyses and several numerical simulations are presented to prove and illustrate the properties and performance of the newly proposed finite element methods

reconstructing attractors from scalar time series a comparison of singular system and redundancy criteria abstract a delay vector phase space reconstruction in which the delay time satisfiesa minimum redundancy criterion is compared with a reconstruction obtained using a singular system approach minimum redundancy produces the better reconstruction the reconstructions are compared using a distortion functional d which measures how well the location of a point in the original phase space can be determined on the basis of its image under the reconstruction process the superiority of the redundancy analysis over the singular system analysis is found to arise from the former s foundation on the notion of general independence as opposed to the latter s foundation on the notion of linear independence