areawise significance tests for windowed recurrence network analysis many time series analysis techniques use sliding window approaches or are repeatedly applied over a continuous range of parameters when combined with a significance test intrinsic correlations among the pointwise analysis results can make falsely positive significant points appear as continuous patches rather than as isolated points to account for this effect we present an areawise significance test that identifies such false positive patches for this purpose we numerically estimate the decorrelation length of the statistic of interest by calculating correlation functions between the analysis results and require an areawise significant point to belong to a patch of pointwise significant points that is larger than this decorrelation length we apply our areawise test to results from windowed traditional and scale specific recurrence network analysis in order to identify dynamical anomalies in time series of a non stationary rossler system and tree ring width index values from eastern canada especially in the palaeoclimate context the areawise testing approach markedly reduces the number of points that are identified as significant and therefore highlights only the most relevant features in the data this provides a crucial step towards further establishing recurrence networks as a tool for palaeoclimate data analysis

chaotic pattern alternations can reproduce properties of dominance durations in multistable perception we propose a pulse neural network that exhibits chaotic pattern alternations among stored patterns as a model of multistable perception which is reflected in phenomena such as binocular rivalry and perceptual ambiguity when we regard the mixed state of patterns as a part of each pattern the durations of the retrieved pattern obey unimodal distributions we confirmed that no chaotic properties are observed in the time series of durations consistent with the findings of previous psychological studies moreover it is shown that our model also reproduces two properties of multistable perception that characterize the relationship between the contrast of inputs and the durations

testing for nonlinearity in unevenly sampled time series we generalize the method of surrogate data of testing for nonlinearity in time series to the case that the data are sampled with uneven time intervals the null hypothesis will be that the data have been generated by a linear stochastic process possibly rescaled and sampled at times chosen independently from the generating process the surrogate data are generated with their linear properties specified by the lomb periodogram the inversion problem is solved by combinatorial optimization

aging regularity and variability in maximum isometric moments this study examined the variability and regularity of maximum isometric moment production of the plantar flexors in young and old subjects it was hypothesized that in the development of maximum isometric moments there would be greater regularity in the moment profiles for older subjects compared with young subjects due to the reduced number of motor units present in elderly muscle two groups of subjects produced three maximal isometric plantar flexions young n 11 mean age 23 8 2 8 years mean mass 81 2 10 4 kg mean height 1 78 0 05 m elderly n 13 mean age 74 0 3 3 years mean mass 78 5 3 4 kg mean height 1 73 0 05 m the plateau of the moment time curve was analyzed for each trial a repeat measures analysis of variance showed the young subjects produced statistically greater peak plantar flexion moments than the elderly subjects but similar coefficients of variation signal regularity was determined by computing the signal s approximate entropy which demonstrated that the older group had greater regularity in their generation of moment profiles the hypothesis was accepted with a potential explanation for this increased regularity in old age being the reduced number of motor units to coordinate

impact and importance of hyperdiffusion on the spectral element method a linear dispersion analysis abstract the spectral element method sem is a mimetic finite element method with several properties that make it a desirable choice for numerical modeling although the linear dispersion properties of this method have been analyzed extensively for the case of the 1d inviscid advection equation practical implementations of the sem frequently employ hyperdiffusion for stabilization as argued in this paper hyperdiffusion has a pronounced impact on the accuracy of the discrete wave modes and the dispersive properties of the sem when applied with an appropriately large coefficient hyperdiffusion is effective at removing the spectral gap and improving the stability of the 1d advection equation this study also considers the sem as applied to the 2d linearized shallow water equations where hyperdiffusion in the form of scalar diffusion divergence damping and vorticity damping are analyzed to the extent possible guidance on the choice of hyperdiffusion coefficients is provided a brief discussion of the comparative impact of local element filtering is included

a chebyshev collocation method for solving two phase flow stability problems this paper describes a chebyshev collocation method for solving the eigenvalue problem that governs the stability of parallel two phase flow the method is based on the expansion of the eigenfunctions in terms of chebyshev polynomials point collocation and the subsequent solution of the resulting generalized eigenvalue problem with the qz algorithm we concentrate on the question how to handle difficulties that arise when these standard techniques are applied to the stability problem of a thin film of liquid that is sheared by a gas after discussing this specific problem in detail it is argued that the method of solution can readily be applied to other two phase flow configurations as well

a spectral element basin model for the shallow water equations abstract a spectral element model is built for the shallow water equations in complex geometry it is proved to be an efficient computational model in solving oceanic problems in particular the equatorial rossby modon s reflection process is simulated

characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments we study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep deep sleep and rapid eye movement rem sleep using the detrended fluctuation analysis method we find short range anticorrelations in the sign time series which are strong during deep sleep weaker during light sleep and even weaker during rem sleep in contrast we find long range positive correlations in the magnitude time series which are strong during rem sleep and weaker during light sleep we observe uncorrelated behavior for the magnitude during deep sleep since the magnitude series relates to the nonlinear properties of the original time series while the sign series relates to the linear properties our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during rem sleep thus the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages

how random is your heart beat we measure the content of random uncorrelated noise in heart rate variability using a general method of noise level estimation using a coarse grained entropy we show that usually except for atrial fibrillation the level of such noise is within 5 15 of the variance of the data and that the variability due to the linearly correlated processes is dominant in all cases analyzed but atrial fibrillation the nonlinear deterministic content of heart rate variability remains significant and may not be ignored

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

stochastic heart rate model can reveal pathologic cardiac dynamics a simple one dimensional langevin type stochastic difference equation can simulate the heart rate fluctuations in a time scale from minutes to hours the model consists of a deterministic nonlinear part and a stochastic part typical of gaussian noise and both parts can be directly determined from measured heart rate data data from healthy subjects typically exhibit the deterministic part with two or more stable fixed points studies of 15 congestive heart failure subjects reveal that the deterministic part of pathologic heart dynamics has no clear stable fixed points direct simulations of the stochastic model for normal and pathologic cases can produce statistical parameters similar to those of real subjects results directly indicate that pathologic situations simplify the heart rate control system

extreme value statistics in records with long term persistence many natural records exhibit long term correlations characterized by a power law decay of the autocorrelation function c s ensuremath sim s ensuremath ensuremath gamma with time lag s and correlation exponent 0l ensuremath gamma l1 we study how the presence of such correlations affects the statistics of the extreme events i e the maximum values of the signal within time segments of the fixed duration r we find numerically that i the integrated distribution function of the maxima converges to a gumbel distribution for large r similar to uncorrelated signals ii the deviations for finite r depend on the initial distribution of the records and on their correlation properties iii the maxima series exhibit long term correlations similar to those of the original data and most notably iv the maxima distribution as well as the mean maxima significantly depend on the history in particular on the previous maximum the last item implies that conditional mean maxima and conditional maxima distributions with the value of the previous maximum as condition should be considered for an improved extreme event prediction we provide indications that this dependence of the mean maxima on the previous maximum occurs also in observational long term correlated records

research on the relationship between the multifractality and long memory of realized volatility in the sseci abstract we examine the multifractal properties of the realized volatility rv and realized bipower variation rbv series in the shanghai stock exchange composite index sseci by using the multifractal detrended fluctuation analysis mf dfa method we find that there exist distinct multifractal characteristics in the volatility series the contributions of two different types of source of multifractality namely fat tailed probability distributions and nonlinear temporal correlations are studied by using the unit root test we also find the strength of the multifractality of the volatility time series is insensitive to the sampling frequency but that the long memory of these series is sensitive

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

a time domain test for some types of nonlinearity the bispectrum and third order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series this is because the bispectrum is the fourier transform of the third order moment an advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity an advantage of the third order moment is that its values in any subset of joint lags can be used in the test whereas when using the bispectrum the entire or truncated third order moment is required to construct the fourier transform we propose a test for nonlinearity based upon the estimated third order moment we use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis using a simulation study we demonstrate that the test obtains its target significance level with large power when compared to an existing standard parametric test that uses the bispectrum further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies we also investigate implications for heuristic diagnosis of nonstationarity

the compound matrix method for ordinary differential systems abstract a generalization of the compound matrix method is presented to deal with eigenvalue and boundary value problems involving unstable systems of ordinary differential equations details are given for fourth and sixth order problems next is shown that a simple equivalence relation exists between the compounds of the solution matrices of the eigenvalue problems and their adjoints and how this relation can be exploited to simplify the calculation of the adjoint eigenfunctions is discussed using the orr sommerfeld problem as an example it is also shown how the techniques used in the derivation of certain auxiliary systems which play a crucial role in the generalization of the compound matrix method can also provide an alternate method for the direct computation of certain quantities defined in terms of the eigenfunctions finally there is a brief discussion of the relationship between the compound matrix method anf the riccati method

re evaluating the performance of the nonlinear prediction error for the detection of deterministic dynamics the nonlinear prediction error in combination with appropriately generated surrogate data is widely used as a discriminating statistic for weak nonlinearity in this paper two of the most widely used formulations of this particular measure are evaluated using data from exemplary nonlinear and linear systems it is found that both methods contrary to expectation and accepted utility give rise to substantial false positive and false negative detection rates in purely linear and nonlinear systems respectively these findings suggest that the nonlinear prediction error should be used with considerable caution the implications of these findings for the search for nonlinearity in the human electroencephalogram are briefly discussed

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

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

price clustering and discreteness is there chaos behind the noise abstract we investigate the compass rose patterns introduced by crack and ledoit j finance 51 2 1996 751 as revealed in phase portraits delay plots of stock returns the structures observed in these diagrams have been attributed mainly to price clustering and discreteness and the tick size using wavelet based denoising we examine the noise free versions of a set of ftse100 stock returns time series we reveal evidence of non periodic cyclical dynamics as a second stage we apply surrogate data analysis on the original and denoised stock returns our results suggest that there is a strong nonlinear and possibly deterministic signature in the data generating processes of the stock returns sequences

rewiring induced chaos in pulse coupled neural networks the dependence of the dynamics of pulse coupled neural networks on random rewiring of excitatory and inhibitory connections is examined when both excitatory and inhibitory connections are rewired periodic synchronization emerges with a hopf like bifurcation and a subsequent period doubling bifurcation chaotic synchronization is also observed when only excitatory connections are rewired periodic synchronization emerges with a saddle node like bifurcation and chaotic synchronization is also observed this result suggests that randomness in the system does not necessarily contaminate the system and sometimes it even introduces rich dynamics to the system such as chaos

a discontinuous galerkin conservative level set scheme for interface capturing in multiphase flows the accurate conservative level set acls method of desjardins et al o desjardins v moureau h pitsch an accurate conservative level set ghost fluid method for simulating turbulent atomization j comput phys 227 18 2008 8395 8416 is extended by using a discontinuous galerkin dg discretization dg allows for the scheme to have an arbitrarily high order of accuracy with the smallest possible computational stencil resulting in an accurate method with good parallel scaling this work includes a dg implementation of the level set transport equation which moves the level set with the flow field velocity and a dg implementation of the reinitialization equation which is used to maintain the shape of the level set profile to promote good mass conservation a near second order converging interface curvature is obtained by following a height function methodology common amongst volume of fluid schemes in the context of the conservative level set various numerical experiments are conducted to test the properties of the method and show excellent results even on coarse meshes the tests include zalesak s disk two dimensional deformation of a circle time evolution of a standing wave and a study of the kelvin helmholtz instability finally this novel methodology is employed to simulate the break up of a turbulent liquid jet

a fourier spectral element algorithm for thermal convection in rotating axisymmetric containers we present a fourier spectral element approach for modeling thermal convection in a rotating axisymmetric container following the theory detailed in bernardi et al c bernardi m dauge y maday spectral methods for axisymmetric domains gauthier villars paris 1999 a fourier expansion of the field variables is performed in the periodic direction and the resulting collection of meridional problems is discretized by means of a parallel spectral element method a gauss lobatto jacobi 0 1 quadrature which incorporates the cylindrical radius in its weight is introduced to avoid a potential degeneracy of the discrete set of equations due to those nodes located on the axis of symmetry a second order timestepping scheme is presented which treats the coriolis and viscous forces implicitly numerical comparisons with analytical and published numerical solutions in spherical and cylindrical geometries are presented which highlight the accuracy of the model and demonstrate its spectral convergence properties

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

constrained realization monte carlo method for hypothesis testing abstract we compare two theoretically distinct approaches to generate artificial or surrogate data for testing hypotheses about a given data set the first and more straightforward approach is to fit a single best model to the original data and then to generate surrogate data sets that are typical realizations of that model the second approach concentrates not on the model but directly on the original data it attempts to constrain the surrogate data sets so that they exactly agree with the original data for a specified set of sample statistics examples of these two approaches are provided for two simple cases a test for deviations from a gaussian distribution and a test for serial dependence in a time series additionally we consider test for nonlinearity in time series based on a fourier transform ft method and on more conventional autoregressive moving average arma fits to the data the comparative performance of hypothesis testing schemes based on these two approaches is found to depend on whether or not the discriminating statistic is pivotal a statistic is pivotal if its distribution is the same for all processes consistent with the null hypothesis the typical realization method requires that the discriminating statistic satisfy this property the constrained realization approach on the other hand does not share this requirement and can provide an accurate and powerful test without having to sacrifice flexibility in the choice of discriminating statistic

universal scaling behaviors of meteorological variables volatility and relations with original records abstract volatility series defined as the magnitude of the increments between successive elements of five different meteorological variables over china are analyzed by means of detrended fluctuation analysis dfa for short universal scaling behaviors are found in all volatility records whose scaling exponents take similar distributions with similar mean values and standard deviations to reconfirm the relation between long range correlations in volatility and nonlinearity in original series dfa is also applied to the magnitude records defined as the absolute values of the original records the results clearly indicate that the nonlinearity of the original series is more pronounced in the magnitude series

complex networks in confined comminution the physical process of confined comminution is investigated within the framework of complex networks we first characterize the topology of the unweighted contact networks as generated by the confined comminution process we find this process gives rise to an ultimate contact network which exhibits a scale free degree distribution and small world properties in particular if viewed in the context of networks through which information travels along shortest paths we find that the global average of the node vulnerability decreases as the comminution process continues with individual node vulnerability correlating with grain size a possible application to the design of synthetic networks e g sensor networks is highlighted next we turn our attention to the physics of the granular comminution process and examine force transmission with respect to the weighted contact networks where each link is weighted by the inverse magnitude of the normal force acting at the associated contact we find that the strong forces i e force chains are transmitted along pathways in the network which are mainly following shortest path routing protocols as typically found for example in communication systems motivated by our earlier studies of the building blocks for self organization in dense granular systems we also explore the properties of the minimal contact cycles the distribution of the contact strain energy intensity of 4 cycle motifs in the ultimate state of the confined comminution process is shown to be consistent with a scale free distribution with infinite variance thereby suggesting that 4 cycle arrangements of grains are capable of storing vast amounts of energy in their contacts without breaking

discrimination power of measures for nonlinearity in a time series the performance of a number of different measures of nonlinearity in a time series is compared numerically their power to distinguish noisy chaotic data from linear stochastic surrogates is determined by monte carlo simulation for a number of typical data problems the main result is that the ratings of the different measures vary from example to example it therefore seems preferable to use an algorithm with good overall performance that is higher order autocorrelations or nonlinear prediction errors

spectral hp discontinuous galerkin methods for modelling 2d boussinesq equations we present spectral hp discontinuous galerkin methods for modelling weakly nonlinear and dispersive water waves described by a set of depth integrated boussinesq equations on unstructured triangular meshes when solving the equations two different formulations are considered directly solving the coupled momentum equations and the scalar method in which a wave continuity equation is solved as an intermediate step we demonstrate that the approaches are fully equivalent and give identical results in terms of accuracy convergence and restriction on the time step however the scalar method is shown to be more cpu efficient for high order expansions in addition to requiring less storage

power of surrogate data testing with respect to nonstationarity surrogate data testing is a method frequently applied to evaluate the results of nonlinear time series analysis since the null hypothesis tested against is a linear gaussian stationary stochastic process a positive outcome may not only result from an underlying nonlinear or even chaotic system but also from e g a non stationary linear one we investigate the power of the test against non stationarity

volatility of linear and nonlinear time series previous studies indicated that nonlinear properties of gaussian distributed time series with long range correlations u i can be detected and quantified by studying the correlations in the magnitude series ensuremath mid u i ensuremath mid the volatility however the origin for this empirical observation still remains unclear and the exact relation between the correlations in u i and the correlations in ensuremath mid u i ensuremath mid is still unknown here we develop analytical relations between the scaling exponent of linear series u i and its magnitude series ensuremath mid u i ensuremath mid moreover we find that nonlinear time series exhibit stronger or the same correlations in the magnitude time series compared with linear time series with the same two point correlations based on these results we propose a simple model that generates multifractal time series by explicitly inserting long range correlations in the magnitude series the nonlinear multifractal time series is generated by multiplying a long range correlated time series that represents the magnitude series with uncorrelated time series that represents the sign series mathrm sgn u i we apply our techniques on daily deep ocean temperature records from the equatorial pacific the region of the el nin o phenomenon and find i long range correlations from several days to several years with 1 f power spectrum ii significant nonlinear behavior as expressed by long range correlations of the volatility series and iii broad multifractal spectrum

entropy in the natural time domain a surrogate data analysis is presented which is based on the fluctuations of the entropy s defined in the natural time domain phys rev e 68 031106 2003 this entropy is not a static one as for example the shannon entropy the analysis is applied to three types of time series i e seismic electric signals artificial noises and electrocardiograms and recognizes the nonmarkovianity in all these signals furthermore it differentiates the electrocardiograms of healthy

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

strong and weak lagrange galerkin spectral element methods for the shallow water equations the lagrange galerkin spectral element method for the two dimensional shallow water equations is presented the equations are written in conservation form and the domains are discretized using quadrilateral elements lagrangian methods integrate the governing equations along the characteristic curves thus being well suited for resolving the nonlinearities introduced by the advection operator of the fluid dynamics equations two types of lagrange galerkin methods are presented the strong and weak formulations the strong form relies mainly on interpolation to achieve high accuracy while the weak form relies pri marily on integration lagrange galerkin schemes offer an increased efficiency by virtue of their less stringent cfl condition the use of quadrilateral elements permits the construction of spectral type finite element methods that exhibit exponential convergence as in the conventional spectral method yet they are constructed locally as in the finite element method this is the spectral element method in this paper we show how to fuse the lagrange galerkin methods with the spectral element method and present results for two standard test cases in order to compare and contrast these two hybrid schemes 2003 published by elsevier science ltd

pseudospectra of the orr sommerfeld operator this paper investigates the pseudospectra and the numerical range of the orr sommerfeld operator for plane poiseuille flow a number z in bf c is in the epsilon pseudospectrum of a matrix or operator a if zi a 1 geq epsilon 1 or equivalently if z is in the spectrum of a e for some perturbation e satisfying e leq epsilon the numerical range of a is the set of numbers of the form au u where cdot cdot is the inner product and u is a vector or function with huh u 1 the spectrum of the orr sommerfeld operator consists of three branches it is shown that the eigenvalues at the intersection of the branches are highly sensitive to perturbations and that the sensitivity increases dramatically with the reynolds number the associated eigenfunctions are nearly linearly dependent even though they form a complete set to understand the high sensitivity of the eigenvalues a model operator is considered related to the airy equation tha

the level crossing and inverse statistic analysis of german stock market index dax and daily oil price time series a b s t r a c t the level crossing and inverse statistics analysis of dax and oil price time series are given we determine the average frequency of positive slope crossings where t 1 is the average waiting time for observing the level again we estimate the probability p k which provides us the probability of observing k times of the level with positive slope in time scale t for analyzed time series we found that maximum k is about 6 we show that by using the level crossing analysis one can estimate how the dax and oil time series will develop we carry out the same analysis for the increments of dax and oil price log returns which is known as inverse statistics and provide the distribution of waiting times to observe some level for the increments 2011 elsevier b v all rights reserved stochastic processes occur in many natural and man made phenomena ranging from various indicators of economic activities in the stock market velocity fluctuations in turbulent flows and heartbeat dynamics etc 1 the level crossing analysis of stochastic processes has been introduced by rice 1944 1945 2 26 and used to describe the turbulence 16 rough surfaces 27 stock markets 28 burgers turbulence and kardar parisi zhang equation 29 30 the level crossing analysis of the data set has the advantage that it gives important global properties of the time series and do not need the scaling feature the almost of the methods in time series analysis are using the scaling features of time series and their applications are restricted to the time series with scaling properties our goal with the level crossing analysis is to characterize the statistical properties of the data set with the hope to better understand the underlying stochastic dynamics and provide a possible tool to estimate its dynamics the level crossing and inverse statistics analysis can be viewed as the complementary method to the other well known methods such as detrended fluctuation analysis dfa 31 detrended moving average dma 32 wavelet transform modulus maxima wtmm 33 rescaled range analysis r s 34 scaled windowed variance swv 35 langevin dynamics 36 detrended cross correlation analysis 37 multifactor analysis of

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

generalized redundancies for time series analysis abstract extensions to various information theoretic quantities such as entropy redundancy and mutual information are discussed in the context of their role in nonlinear time series analysis we also discuss linearized versions of these quantities and their use as benchmarks in tests for nonlinearity many of these quantities can be expressed in terms of the generalized correlation integral and this expression permits us to more clearly exhibit the relationships of these quantities to each other and to other commonly used nonlinear statistics such as the bds and green savit statistics further numerical estimation of these quantities is found to be more accurate and more efficient when the the correlation integral is employed in the computation finally we consider several local versions of these quantities including a local kolmogorov sinai entropy which gives an estimate of variability of the short term predictability

surrogates for finding unstable periodic orbits in noisy data sets recently searches for unstable periodic orbits in biological and medical applications have become of interest the motivations for this research range in order of ascending complexity from efforts to understand the dynamics of simple sensory neurons through speculations regarding neural coding to the hopeful development of new diagnostic and or control techniques for cardiac and epileptic pathologies biological and medical data are however noisy and nonstationary findings of unstable periodic orbits in such data thus require convincing assessments of their statistical significance such tests are accomplished by comparison with surrogate data files designed to test an appropriate null hypothesis in this paper we test surrogates generated by three different algorithms against correlated noise as well as stable periodic orbits one of the surrogates is new and has been specifically designed to preserve the shape of the attractor we discuss the suitability of these surrogates and argue that the simple shuffled one correctly tests the appropriate null hypothesis

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

monofractal and multifractal analysis of simulated heat release fluctuations in a spark ignition heat engine abstract we study data from cycle by cycle variations in heat release for a simulated spark ignited engine our analyses are based on nonlinear scaling properties of heat release fluctuations obtained from a turbulent combustion model we apply monofractal and multifractal methods to characterize the fluctuations for several fuel air ratio values from lean mixtures to stoichiometric situations the monofractal approach reveals that for lean and stoichiometric conditions the fluctuations are characterized by the presence of weak anticorrelations whereas for intermediate mixtures we observe complex dynamics characterized by a crossover in the scaling exponents for short scales the variations display positive correlations while for large scales the fluctuations are close to white noise moreover a broad multifractal spectrum is observed for intermediate fuel ratio values while for low and high the fluctuations lead to a narrow spectrum finally we explore the origin of correlations by using the surrogate data method to compare the findings of multifractality and scaling exponents between original simulated and randomized data

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

nonlinear strength quantifier based on phase correlation abstract distinguishing linear series from nonlinear ones is of great importance for not only understanding the processes generating these series but also their modeling and prediction there are many methods and their nonlinear quantifiers to reach this goal but no one is powerful enough to deal with any given series in this study the artificially generating series with given tailored phase correlation strength is applied to test the performance of some widely used methods and their nonlinear quantifiers given in the previous studies both advantages and shortcomings are shown for these methods and their nonlinear metrics especially spurious results from these methods and their nonlinear metrics can be found for some cases much weak or strong phase correlations in order to avoid these spurious results modified phase correlation quantifiers are proposed at the same time multiple stripes found in the phase map can be explained from the view point of enhanced nonlinear strength

random vector and time series definition and synthesis from matrix product representations from statistical physics to hidden markov models inspired from modern out of equilibrium statistical physics models a matrix product based framework is defined and studied that permits the formal definition of random vectors and time series whose desired joint distributions are a priori prescribed its key feature consists of preserving the writing of the joint distribution as the simple product structure it has under independence while inputing controlled dependencies amongst components this is obtained by replacing the product of probability densities by a product of matrices of probability densities it is first shown that this matrix product model can be remapped onto the framework of hidden markov models second combining this dual perspective enables us both to study the statistical properties of this model in terms of marginal distributions and dependencies a stationarity condition is notably devised and to devise an efficient and accurate numerical synthesis procedure a design procedure is also described that permits the tuning of model parameters to attain targeted statistical properties pedagogical well chosen examples of times series and multivariate vectors aim at illustrating the power and versatility of the proposed approach and at showing how targeted statistical properties can actually be prescribed

constrained surrogate time series with preservation of the mean and variance structure a method is presented for generating surrogates that are constrained realizations of a time series but which preserve the local mean and variance of the original signal the method is based on the popular iterated amplitude adjusted fourier transform method but makes use of a wavelet transform to constrain behavior in the time domain using this method it is possible to test for local changes in the nonlinear properties of the signal we present an example for a change in hurst exponent in a time series produced by fractional brownian motion

algorithms for generating surrogate data for sparsely quantized time series abstract the method of surrogate data is frequently used for a statistical examination of nonlinear properties underlying original data if surrogate data sets are generated by a null hypothesis that the data are derived by a linear process a rejection of the hypothesis means that the original data have more complex properties however we found that if an algorithm for generating surrogate data for example amplitude adjusted fourier transformed is applied to sparsely quantized data there are large discrepancies between their power spectrum and that of the original data in lower frequency regions we performed some simulations to confirm that these errors often lead to false rejections in this paper in order to prevent such drawbacks we advance an extended hypothesis and propose two improved algorithms for generating surrogate data that reduce the discrepancies of the power spectra we also confirm the validity of the two improved algorithms with numerical simulations by showing that the extended null hypothesis can be rejected if the time series is produced from chaotic dynamical systems finally we applied these algorithms for analyzing financial tick data as a real example then we showed that the extended null hypothesis cannot be rejected because the nonlinear statistics or nonlinear prediction errors exhibited are the same as those of the original financial tick time series

a wetting and drying treatment for the runge kutta discontinuous galerkin solution to the shallow water equations this paper proposes a wetting and drying treatment for the piecewise linear runge kutta discontinuous galerkin approximation to the shallow water equations the method takes a fixed mesh approach as opposed to mesh adaptation techniques and applies a post processing operator to ensure the positivity of the mean water depth within each finite element in addition special treatments are applied in the numerical flux computation to prevent an instability due to excessive drying the proposed wetting and drying treatment is verified through comparisons with exact solutions and convergence rates are examined the obtained orders of convergence are close to or approximately equal to 1 for solutions with discontinuities and are improved for smooth solutions the combination of the proposed wetting and drying treatment and a tvb slope limiter is also tested and is found to be applicable on condition that they are applied exclusively to an element at the same runge kutta step

fractal rock slope dynamics anticipating a collapse time series of dilatometric measurements of relative displacements on rock cracks on stable and unstable sandstone slopes were analyzed the inherent dynamics of rock slopes lack any significant nonlinearity however the residuals obtained by removing meteorological influences are fat tailed non gaussian fluctuations with short range correlations in the case of stable slopes the fluctuations of unstable slopes exhibit self affine dynamics of fractional brownian motions with power law long range correlations and are characterized by asymptotic power law probability distributions with decay coefficients outside the range of stable l evy distributions

critical scale invariance in a healthy human heart rate we demonstrate the robust scale invariance in the probability density function pdf of detrended healthy human heart rate increments which is preserved not only in a quiescent condition but also in a dynamic state where the mean level of the heart rate is dramatically changing this scale independent and fractal structure is markedly different from the scale dependent pdf evolution observed in a turbulentlike cascade heart rate model these results strongly support the view that a healthy human heart rate is controlled to converge continually to a critical state

detection of synchronization between chaotic signals an adaptive similarity based approach we present an adaptive similarity based approach to detect generalized synchronization gs with n m phase synchronization ps where n and m are integers and one of them is 1 this approach is based on the similarity index si and gaussian mixture model with the minimum description length criterion the clustering method which is shown to be superior to the closeness and connectivity of a continuous function is employed in this study to detect the existence of gs with n m ps we conducted a computer simulation and a finger lifting experiment to illustrate the effectiveness of the proposed method in the simulation of a rossler lorenz system our method outperformed the conventional si and gs with 2 1 ps within the coupled system was found in the experiment of self paced finger lifting movement cortico muscular gs with 1 2 and 1 3 ps was found between the surface electromyogram signals on the first dorsal interossei muscle and the magnetoencephalographic data in the motor area the gs with n m ps n or m 1 has been simultaneously resolved from both simulation and experiment the proposed approach thereby provides a promising means for advancing research into both nonlinear dynamics and brain science

the spectral element method for the shallow water equations on the sphere the spectral element method is implemented for the shallow water equations in spherical geometry and its performance is compared with other models this is the first step in evaluating the suitability of spectral elements for climate modeling the potential advantages and disadvantages of spectral elements over more conventional models used for climate studies are discussed the method requires that the sphere be tiled with rectangles for which we make use of the gnomonic projection to map the sphere onto the cube to measure the performance of the method relative to other models results are presented from a standard suite of shallow water test cases for the sphere these results confirm the spectral accuracy of the method

an information theoretic algorithm for finding periodicities in stellar light curves we propose a new information theoretic metric for finding periodicities in stellar light curves light curves are astronomical time series of brightness over time and are characterized as being noisy and unevenly sampled the proposed metric combines correntropy generalized correlation with a periodic kernel to measure similarity among samples separated by a given period the new metric provides a periodogram called correntropy kernelized periodogram ckp whose peaks are associated with the fundamental frequencies present in the data the ckp does not require any resampling slotting or folding scheme as it is computed directly from the available samples ckp is the main part of a fully automated pipeline for periodic light curve discrimination to be used in astronomical survey databases we show that the ckp method outperformed the slotted correntropy and conventional methods used in astronomy for periodicity discrimination and period estimation tasks using a set of light curves drawn from the macho survey the proposed metric achieved 97 2 of true positives with 0 of false positives at the confidence level of 99 for the periodicity discrimination task and 88 of hits with 11 6 of multiples and 0 4 of misses in the period estimation task

stochastic model for heart rate fluctuations a normal human heart rate shows complex fluctuations in time which is natural because the heart rate is controlled by a large number of different feedback control loops these unpredictable fluctuations have been shown to display fractal dynamics long term correlations and 1 f noise these characterizations are statistical and they have been widely studied and used but much less is known about the detailed time evolution dynamics of the heart rate control mechanism here we show that a simple one dimensional langevin type stochastic difference equation can accurately model the heart rate fluctuations in a time scale from minutes to hours the model consists of a deterministic nonlinear part and a stochastic part typical to gaussian noise and both parts can be directly determined from the measured heart rate data studies of 27 healthy subjects reveal that in most cases the deterministic part has a form typically seen in bistable systems there are two stable fixed points and one unstable one

detecting determinism in short time series using a quantified averaged false nearest neighbors approach we propose a criterion to detect determinism in short time series this criterion is based on the estimation of the parameter e 2 defined by the averaged false neighbors method for analyzing time series cao physica d 110 43 1997 using surrogate data testing with several chaotic and stochastic simulated time series we show that the variation coefficient of e 2 over a few values of the embedding dimension d defines a suitable statistic to detect determinism in short data sequences this result holds for a time series generated by a high dimensional chaotic system such as the mackey glass one different decreasing lengths of the time series are included in the numerical experiments for both synthetic and real world data we also investigate the robustness of the criterion in the case of deterministic time series corrupted by additive noise

the lagrange galerkin spectral element method on unstructured quadrilateral grids the purpose of this paper is to introduce a new method formed by fusing the lagrange galerkin and spectral element methods the lagrange galerkin method traces the characteristic curves of the solution and consequently is very well suited for resolving the nonlinearities introduced by the advection operator of the fluid dynamics equations spectral element methods are essentially higher order finite element methods that exhibit spectral exponential convergence provided that the solution is a smooth function by combining these two methods a numerical scheme can be constructed that resolves with extremely high precision the nonlinearities of the advection terms and the smooth regions of the flow generated by the diffusion terms this paper describes the construction of the lagrange galerkin spectral element method which permits the use of any grid type including unstructured grids the only restriction at the moment is that the grid elements be quadrilaterals the stability analysis of both methods demonstrates why these two methods are so powerful individually and how their fusion leads to an improved scheme the lagrange galerkin spectral element method is validated using the 1d and 2d advection and advection diffusion equations the results of the stability analysis and the numerical experiments demonstrate the utility of such an approach

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

a multiscale pressure splitting of the shallow water equations abstract direct representation of the free surface in ocean circulation models leads to a number of computational difficulties that are due to the fast time scales associated with free surface waves these fast time scales generally result in severe time step restrictions when the free surface is advanced using an explicit scheme and may result in large phase errors when the free surface is treated implicitly with a large time step a multiple scale analysis of the shallow water equations is used to analyze this stiffness and to guide the construction of a computational methodology that overcomes the associated difficulties specifically we explore a class of fractional step methods that utilize coarsened grids in the propagation of long wave data the behavior of the corresponding schemes is examined in detail in light of one dimensional model problems based on finite difference or spectral element discretizations

nonlinear dynamical system identification with dynamic noise and observational noise in this paper we consider the problem of whether a nonlinear system has dynamic noise and then estimate the level of dynamic noise to add to any model we build the method we propose relies on a nonlinear model and an improved least squares method recently proposed on the assumption that observational noise is not large we do not need any a priori knowledge for systems to be considered and we can apply the method to both maps and flows we demonstrate with applications to artificial and experimental data the results indicate that applying the proposed method can detect presence or absence of dynamic noise from scalar time series and give a reliable level of dynamic noise to add to the model built in some cases

scaling multifractality and long range correlations in well log data of large scale porous media abstract three distinct methods namely the spectral density the multifractal random walk approach and the multifractal detrended fluctuation analysis are utilized to study the properties of four distinct types of well logs from three oil and gas fields namely the natural gamma ray emission neutron porosity bulk density and the sonic transient time logs such well logs have never been analyzed by the methods that we utilize in the present study the results indicate that the well logs exhibit multifractal characteristics and the estimated hurst exponents by the three methods are close to each other using multifractal detrended fluctuation analysis and the shuffled and surrogated data we find that the source of multifractality is due to both broad probability density functions of the data and long range correlations in them the correlations are persistent and are characterized by a hurst exponent h 0 5 despite very significant differences in the geology of the three reservoirs ranging from shaly sands to fractured carbonate reservoirs there is a rough universality in the log data in that the hurst exponents for all the logs vary in a very narrow range

numerical solution of eigenvalue problems using spectral techniques abstract two algorithms based on spectral chebyshev and pseudospectral chebyshev methods are presented for solving difficult eigenvalue problems that are valid over connected domains coupled through interfacial conditions to demonstrate the applicability of these methods we have examined the eigenvalue problems that describe the linear stability of two superposed newtonian and inelastic power law fluids in plane poiseuille flow for a selected range of parameters both algorithms provide accurate results and the pseudospectral code appears to be more efficient in handling linear stability problems

nonstationary langevin equation statistical properties and application to explain effects observed in cardiological time series using the langevin equation we develop the model of a stochastic process subject to a given time dependent regulatory mechanism the effects of this nonstationarity on the statistical properties of the time series i e on global and conditional probability densities and on the moments of the distribution are derived application of these results on simple model trends allows one to approximate cardiological data and thus to explain effects recently observed in the reconstruction of the deterministic part of the langevin equation for time series of heart rate

construction of multivariate surrogate sets from nonlinear data using the wavelet transform abstract the use of surrogate data has become a crucial first step in the study of nonlinearity in time series data a widely used technique to construct surrogate data is to randomize the phases of the data in the fourier domain in this paper an alternative technique based on the resampling of wavelet coefficients is discussed this approach exploits between scale correlations that exist within nonlinear data but which are either absent or weak in stochastic data it proceeds by transforming the data into the wavelet domain and permuting the wavelet coefficients experimental and numerical time series data are used to demonstrate that the performance of the wavelet resampling technique is comparable to phase randomization in terms of the preservation of linear properties removal of nonlinear structure and computational demands however the wavelet technique may have specific and distinct advantages in the application to complex data sets such as numerical analysis of turbulence and experimental brain imaging data where wavelets give a more parsimonious representation of spatio temporal patterns than fourier modes it is shown that different techniques of resampling the data in the wavelet domain may optimize the construction of surrogate data according to the properties of the experimental time series and computational constraints

stochastic aspects of cardiac arrhythmias abnormal cardiac rhythms cardiac arrhythmias often display complex changes over time that can have a random or haphazard appearance mathematically these changes can on occasion be identified with bifurcations in difference or differential equation models of the arrhythmias one source for the variability of these rhythms is the fluctuating environment however in the neighborhood of bifurcation points the fluctuations induced by the stochastic opening and closing of individual ion channels in the cell membrane which results in membrane noise may lead to randomness in the observed dynamics to illustrate this we consider the effects of stochastic properties of ion channels on the resetting of pacemaker oscillations and on the generation of early afterdepolarizations the comparison of the statistical properties of long records showing arrhythmias with the predictions from theoretical models should help in the identification of different mechanisms underlying cardiac arrhythmias

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

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

detecting generalized synchronization between chaotic signals a kernel based approach a unified framework for analysing generalized synchronization in coupled chaotic systems from data is proposed the key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning several successful applications are presented which show the capability of the kernel based approach for detecting generalized synchronization and dynamical change of the coupling strength between two chaotic systems can be captured by the proposed approach it is also discussed how the kernel parameter is suitably chosen from data

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

deterministic dynamics of neural activity during absence seizures in rats the study of brain electrical activities in terms of deterministic nonlinear dynamics has recently received much attention forbidden ordinal patterns fop is a recently proposed method to investigate the determinism of a dynamical system through the analysis of intrinsic ordinal properties of a nonstationary time series the advantages of this method in comparison to others include simplicity and low complexity in computation without further model assumptions in this paper the fop of the eeg series of genetic absence epilepsy rats from strasbourg was examined to demonstrate evidence of deterministic dynamics during epileptic states experiments showed that the number of fop of the eeg series grew significantly from an interictal to an ictal state via a preictal state these findings indicated that the deterministic dynamics of neural networks increased significantly in the transition from the interictal to the ictal states and also suggested that the fop measures of the eeg series could be considered as a predictor of absence seizures

randomness and degrees of irregularity the fundamental question are sequential data random arises in myriad contexts often with severe data length constraints furthermore there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness e g to evaluate the efficacy of therapy in medicine we address both these issues from a computable framework via a quantification of regularity apen approximate entropy defining maximal randomness for sequences of arbitrary length indicating the applicability to sequences as short as n 5 points an infinite sequence formulation of randomness is introduced that retains the operational and computable features of the finite case in the infinite sequence setting we indicate how the foundational definition of independence in probability theory and the definition of normality in number theory reduce to limit theorems without rates of convergence from which we utilize apen to address rates of convergence of a deficit from maximal randomness refining the aforementioned concepts in a computationally essential manner representative applications among many are indicated to assess i random number generation output ii well shuffled arrangements and iii the quality of bootstrap replicates

detrended fluctuation analysis of short datasets an application to fetal cardiac data abstract using detrended fluctuation analysis dfa we perform scaling analysis of short datasets of length 500 1500 data points we quantify the long range correlation exponent by computing the mean value of the local exponents l in the asymptotic regime the local exponents are obtained as the numerical derivative of the logarithm of the fluctuation function f s with respect to the logarithm of the scale factor s l d log 10 f s d log 10 s these local exponents display huge variations and complicate the correct quantification of the underlying correlations we propose the use of the phase randomized surrogate prs which preserves the long range correlations of the original data to minimize the variations in the local exponents using the numerically generated uncorrelated and long range correlated data we show that performing dfa on several realizations of prs and estimating l from the averaged fluctuation functions of all realizations can minimize the variations in l the application of this approach to the fetal cardiac data rr intervals is discussed and we show that there is a statistically significant correlation between and the gestation age

numerical solution of eigenvalue problem using the compound matrix method abstract an algorithm based on the compound matrix method is presented for solving difficult eigen value problems details are given for systems of ordinary differential equations of fourth order that are valid over connected domains coupled through interfacial conditions as an example we examine the linear stability of two superposed fluids in plane poiseuille flow and consider both interfacial and shear modes the orr sommerfeld system that describes linear stability is solved for a selected range of parameters

fluctuation analysis of high frequency electric power load in the czech republic abstract we analyze the electric power load in the czech republic cr which exhibits a seasonality as well as other oscillations typical for european countries moreover we detect the 1 f noise property of electrical power load with extra additional peaks that allows to separate it into a deterministic and stochastic part we then focus on the analysis of the stochastic part using improved multi fractal detrended fluctuation analysis method mfdfa to investigate power load datasets with a minute resolution extracting the noise part of the signal by using fourier transform allows us to apply this method to obtain the fluctuation function and to estimate the generalized hurst exponent together with the correlated hurst exponent its improvement for the non gaussian datasets the results exhibit a strong presence of persistent behavior or strong anti persistent behavior for the differences and the dataset is characterized by a non gaussian skewed distribution there are also indications for the presence of the probability distribution that has heavier tail than the gaussian distribution

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

analysis of time series from stochastic processes analysis of time series from stochastic processes governed by a langevin equation is discussed several applications for the analysis are proposed based on estimates of drift and diffusion coefficients of the fokker planck equation the coefficients are estimated directly from a time series the applications are illustrated by examples employing various synthetic time series and experimental time series from metal cutting