rank one property for derivatives of functions with bounded variation when u is a function of bounded variation of the open set r into r du is a measure on which takes values in the space rm n of all m n matrices such that du i j ui xj for every i j with 1 i m 1 j n and we denote by dsu the part of the measure du which is singular with respect to lebesgue measure we recall that the rank of a matrix a rm n is dimension of the space spanned by its columns in r or by its rows in r and in particular the rank of a is one if and only if there exist e r and r with e 6 0 6 0 so that a e i e ai j ei j for all i j cf remark 1 7 when is a measure which takes values in the space rm n and d d denotes the radon nikodym derivative of with respect to the total variation we say that has rank one when the rank of the matrix d d x is one for almost every x in this paper we prove we prove the following statement see theorem 4 5 corollary 4 6 and remark 4 9

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

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

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

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

shape analysis via oriented distance functions the object of this paper is twofold we first present constructions which induce topologies on subsets of a fixed domain or hold all d in rn by using set parameterized functions in an appropriate function space second we study the role of the family of oriented distance functions also known as algebraic or signed distance functions in the analysis of shape optimization problems they play an important role in the introduction of topologies which retain the classical geometric properties associated with sets convexity exterior normals mean curvature ck boundaries etc

boundary conditions at fluid permeable interfaces in porous media a variational approach abstract a general set of boundary conditions at fluid permeable interfaces between dissimilar fluid filled porous matrices is established starting from an extended hamilton rayleigh principle these conditions do include friction and inertial effects once linearized they encompass boundary conditions relative to volume darcy brinkman and to surface saffman beavers joseph dissipation effects

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

robust passivity and passification of stochastic fuzzy time delay systems in this paper the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time varying delays the fuzzy system is based on the takagi sugeno t s model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning to reflect more realistic dynamical behaviors of the system both the parameter uncertainties and the stochastic disturbances are considered where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a brownian motion we first propose the definition of robust passivity in the sense of expectation then by utilizing the lyapunov functional method the ito differential rule and the matrix analysis techniques we establish several sufficient criteria such that for all admissible parameter uncertainties and stochastic disturbances the closed loop stochastic fuzzy time delay system is robustly passive in the sense of expectation the derived criteria which are either delay independent or delay dependent are expressed in terms of linear matrix inequalities lmis that can be easily checked by using the standard numerical software illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results

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

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

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

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

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

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

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

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

superposition and chain rule for bounded hessian functions abstract we study the properties of superposition of bounded hessian functions establishing the validity of a second order chain rule we prove rectifiability properties of all noncritical level sets ofbh functions by showing a geometric measure theory analogous of dini s theorem

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

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

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

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

brief paper stability and stabilization of markovian jump linear systems with partly unknown transition probabilities in this paper the stability and stabilization problems of a class of continuous time and discrete time markovian jump linear system mjls with partly unknown transition probabilities are investigated the system under consideration is more general which covers the systems with completely known and completely unknown transition probabilities as two special cases the latter is hereby the switched linear systems under arbitrary switching moreover in contrast with the uncertain transition probabilities studied recently the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements the sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via lmis formulation and the relation between the stability criteria currently obtained for the usual mjls and switched linear systems under arbitrary switching are exposed by the proposed class of hybrid systems two numerical examples are given to show the validity and potential of the developed results

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

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

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

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

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

passivity and passification of fuzzy systems with time delays takagi sugeno t s fuzzy model provides an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output submodels recently a number of authors studied the t s fuzzy systems with time delays in this paper the passivity and feedback passification of t s fuzzy systems with time delays are considered both delay independent and delay dependent results are presented and the theoretical results are given in terms of linear matrix inequalities lmis numerical examples are given which illustrate the effectiveness of the theoretical results

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

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

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

analysis and synthesis of markov jump linear systems with time varying delays and partially known transition probabilities in this note the stability analysis and stabilization problems for a class of discrete time markov jump linear systems with partially known transition probabilities and time varying delays are investigated the time delay is considered to be time varying and has a lower and upper bounds the transition probabilities of the mode jumps are considered to be partially known which relax the traditional assumption in markov jump systems that all of them must be completely known a priori following the recent study on the class of systems a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality lmi formulation and the design of the stabilizing controller is further given a numerical example is used to illustrate the developed theory

brief paper static output feedback stabilization of discrete time markovian jump linear systems a system augmentation approach this paper studies the static output feedback sof stabilization problem for discrete time markovian jump systems from a novel perspective the closed loop system is represented in a system augmentation form in which input and gain output matrices are separated by virtue of the system augmentation a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities which possess a monotonic structure for a linearized computation and a convergent iteration algorithm is given to solve such inequalities in addition a special property of the feasible solutions enables one to further improve the solvability via a simple d k type optimization on the initial values an extension to mode independent sof stabilization is provided as well compared with some existing approaches to sof synthesis the proposed one has several advantages that make it specific for markovian jump systems the effectiveness and merit of the theoretical results are shown through some numerical examples

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

robust output feedback h control of uncertain markovian jump systems with mode dependent time delays this paper describes the synthesis of robust output feedback h control for a class of uncertain markovian jump linear systems with time delays which are time varying and depend on the system modes of operation under the assumption of known bounds of system uncertainties and the control system gain variations we present sufficient conditions on the existence of robust stochastic stability and disturbance h attenuation through the changes of variables and schur complements these sufficient conditions can be rewritten in a set of coupled linear matrix inequalities with which robust control can be easily constructed as an added advantage the control design depends only on the measured parameter of markovian jumping at time t which might be corrupted by measurement noises numerical examples are provided to demonstrate the effectiveness of the proposed approach

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

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

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

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

an image denoising model based on a fourth order nonlinear partial differential equation abstract image denoising is a challenging task in the fields of image processing and computer vision inspired by the good performance of nonlinear fourth order models in recovering smooth region we proposed a fourth order image denoising model using the fixed point theorem we established the existence and uniqueness of the entropy solution based on the fast explicit diffusion scheme fed numerical experiments illustrate the effectiveness of the suggested method in image denoising the results have been compared with three famous fourth order models you and kaveh yk model lysaker lundervold and tai llt model and the more recent mean curvature mc model the proposed model has the superiority in terms of removing noise while preserving image features

entropy solutions for a fourth order nonlinear degenerate problem for noise removal abstract in this paper we establish the existence and uniqueness of entropy solutions for a fourth order nonlinear degenerate parabolic problem for noise removal in dimension 1 d 4

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

passivity analysis and passification of uncertain markovian jump systems with partially known transition rates and mode dependent interval time varying delays in this paper the problem of delay dependent robust passivity analysis and robust passification of uncertain markovian jump linear systems mjlss with partially known transition rates and mode dependent time varying delays are investigated in the deterministic model the time varying delay is in a given range and the uncertainties are assumed to be norm bounded by constructing an appropriate lyapunov krapunov functional lkf combining with jensen s inequality and the free weighting matrix method delay dependent passification conditions are obtained in term of linear matrix inequalities lmis for the robust passification problem desired passification controllers are designed which guarantee that the closed loop mjls is passive finally a numerical example is given to illustrate the effectiveness of the proposed approach

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

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

delay dependent stability analysis and controller synthesis for markovian jump systems with state and input delays this paper focuses on the problem of delay dependent robust stochastic stability analysis and controller synthesis for markovian jump systems with state and input delays it is assumed that the delays are constant and unknown but their upper bounds are known by constructing a new lyapunov krasovskii functional and introducing some appropriate slack matrices new delay dependent stochastic stability and stabilization conditions are proposed by means of linear matrix inequalities lmis an important feature of the results proposed here is that all the robust stability and stabilization conditions are dependent on the upper bound of the delays memoryless state feedback controllers are designed such that the closed loop system is robustly stochastically stable some numerical examples are provided to illustrate the effectiveness of the proposed method