application of the detrended fluctuation analysis dfa method for describing cloud breaking abstract a method to sort out correlations and decorrelations in stratus cloud formation persistence and breakup is introduced the detrended fluctuation analysis dfa statistical method is applied to microwave radiometer data the existence of long range power law correlations in stratus cloud liquid water content fluctuations is demonstrated over a 2 h period moreover using a finite size time interval window a change from brownian to non brownian fluctuation regimes is clearly shown to define the cloud structure changes such findings are similar to those found in dna and financial data sequences when mosaics of persistent and antipersistent patches are present the occurrence of these statistics in stratus cloud liquid water content suggests the usefulness of similar studies on cloud resolving model output and for better meteorological predictability

delay dependent exponential stability for a class of neural networks with time delays this paper is concerned with the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type in terms of a linear matrix inequality lmi a sufficient condition guaranteeing the existence uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks is proposed this condition is dependent on the size of the time delay which is usually less conservative than delay independent ones the proposed lmi condition can be checked easily by recently developed algorithms solving lmis examples are provided to demonstrate the effectiveness and applicability of the proposed criteria

method for generating long range correlations for large systems we propose a new method to generate a sequence of random numbers with long range power law correlations that overcomes known difficulties associated with large systems the new method presents an improvement on the commonly used methods we apply the algorithm to generate enhanced diffusion isotropic and anisotropic self affine surfaces and isotropic and anisotropic correlated percolation

a semi free weighting matrices approach for neutral type delayed neural networks in this paper a new approach is proposed for stability issues of neutral type neural networks dnns with constant delay first the semi free weighting matrices are proposed and used instead of the known free weighting matrices to express the relationship between the terms in the leibniz newton formula to simplify the system synthesis and to obtain less computation demand second global exponential stability conditions which are less conservative and restrictive than the known results are derived at the same time based on the above approach fewer variable matrices are introduced in the construction of the lyapunov functional and augmented lyapunov functional two examples are given to show their effectiveness and advantages over others

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

empirical regularities of opening call auction in chinese stock market abstract we study the statistical regularities of an opening call auction using the ultra high frequency data of 22 liquid stocks traded on the shenzhen stock exchange in 2003 the distribution of the relative price defined as the relative difference between the order price in the opening call auction and the closing price on the last trading day is asymmetric and that the distribution displays a sharp peak at the zero relative price and a relatively wide peak at the negative relative price the detrended fluctuation analysis dfa method is adopted to investigate the long term memory of relative order prices we further study the statistical regularities of order sizes in the opening call auction and observe a phenomenon of number preference known as order size clustering the probability density function pdf of order sizes could be well fitted by a q gamma function and the long term memory also exists in order sizes in addition both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit order book lob established immediately after the opening call auction and a price clustering phenomenon is observed

new results for global stability of a class of neutral type neural systems with time delays this paper studies the global convergence properties of a class of neutral type neural networks with discrete time delays this class of neutral systems includes cohen grossberg neural networks hopfield neural networks and cellular neural networks based on the lyapunov stability theorems some delay independent sufficient conditions for the global asymptotic stability of the equilibrium point for this class of neutral type systems are derived it is shown that the results presented in this paper for neutral type delayed neural networks are the generalization of a recently reported stability result a numerical example is also given to demonstrate the applicability of our proposed stability criteria

power spectrum and detrended fluctuation analysis application to daily temperatures the variability measures of fluctuation analysis fa and detrended fluctuation analysis dfa are expressed in terms of the power spectral density and of the autocovariance of a given process the diagnostic potential of these methods is tested on several model power spectral densities in particular we find that both fa and dfa reveal an algebraic singularity of the power spectral density at small frequencies corresponding to an algebraic decay of the autocovariance a scaling behavior of the power spectral density in an intermediate frequency regime is better reflected by dfa than by fa we apply fa and dfa to ambient temperature data from the 20th century with the primary goal to resolve the controversy in literature whether the low frequency behavior of the corresponding power spectral densities are better described by a power law or a stretched exponential as a third possible model we suggest a weibull distribution however it turns out that neither fa nor dfa can reliably distinguish between the proposed models

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

visibility graph analysis of economy policy uncertainty indices abstract uncertainty plays an important role in the global economy in this paper the economic policy uncertainty epu indices of the united states and china are selected as the proxy variable corresponding to the uncertainty of national economic policy by adopting the visibility graph algorithm the four economic policy uncertainty indices of the united states and china are mapped into complex networks and the topological properties of the corresponding networks are studied the hurst exponents of all the four indices are within 0 5 1 which implies that the economic policy uncertainty is persistent the degree distributions of the epu networks have power law tails and thus the networks are scale free the average clustering coefficients of the four epu networks are high and close to each other while these networks exhibit weak assortative mixing we also find that the epu network in united states based on daily data shows the small world feature since the average shortest path length increases logarithmically with the network size such that l n 0 626 ln n 0 405 our research highlights the possibility to study the epu from the view angle of complex networks

long range correlation properties of coding and noncoding dna sequences genbank analysis an open question in computational molecular biology is whether long range correlations are present in both coding and noncoding dna or only in the latter to answer this question we consider all 33301 coding and all 29453 noncoding eukaryotic sequences each of length larger than 512 base pairs bp in the present release of the genbank to dtermine whether there is any statistically significant distinction in their long range correlation properties standard fast fourier transform fft analysis indicates that coding sequences have practically no correlations in the range from 10 bp to 100 bp spectral exponent beta 0 00 0 04 where the uncertainty is two standard deviations in contrast for noncoding sequences the average value of the spectral exponent beta is positive 0 16 0 05 which unambiguously shows the presence of long range correlations we also separately analyze the 874 coding and the 1157 noncoding sequences that have more than 4096 bp and find a larger region of power law behavior we calculate the probability that these two data sets coding and noncoding were drawn from the same distribution and we find that it is less than 10 10 we obtain independent confirmation of these findings using the method of detrended fluctuation analysis dfa which is designed to treat sequences with statistical heterogeneity such as dna s known mosaic structure patchiness arising from the nonstationarity of nucleotide concentration the near perfect agreement between the two independent analysis methods fft and dfa increases the confidence in the reliability of our conclusion

a delayed neural network for solving linear projection equations and its analysis in this paper we present a delayed neural network approach to solve linear projection equations the lyapunov krasovskii theory for functional differential equations and the linear matrix inequality lmi approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network compared with the existing linear projection neural network theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems

detrended fluctuation analysis of time series of a firing fusimotor neuron abstract we study the interspike intervals isi time series of the spontaneous fusimotor neuron activity by applying the detrended fluctuation analysis that is a modification of the random walk model analysis thus we have found evidence for the white noise characteristics of the isi time series which means that the fusimotor activity does not possess temporal correlations we conclude that such an activity represents the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles

further remarks on additional dynamics in various model transformations of linear delay systems this paper focuses on the analysis of conservatism introduced due to some model transformations used in the control literature this work is an extension of a previous paper by the authors 1999 on additional dynamics the additional dynamics of the second order and parametrized model transformations are examined the neutral model transformation introduces additional constraints for stability which can be analyzed in a very similar manner to additional dynamics

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

a new delay dependent criterion for neural systems with multiple delays in this paper the problem of the stability analysis for neutral systems with multiple delays is investigated using lyapunov method we present a new delay dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities lmis which can be easily solved by various convex optimization algorithms a numerical example is given to illustrate the effectiveness of the proposed method

lmi optimization approach on stability for delayed neural networks of neutral type in this paper the global asymptotic stability of delayed cellular neural networks of neutral type is investigated a novel delay dependent criterion for the stability using the lyapunov stability theory and linear matrix inequality lmi framework is presented since the condition is dependent on the size of time delay it is usually less conservative than delay independent ones two numerical examples are given to show the effectiveness of proposed method

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

detecting long range correlations with detrended fluctuation analysis abstract we examine the detrended fluctuation analysis dfa which is a well established method for the detection of long range correlations in time series we show that deviations from scaling which appear at small time scales become stronger in higher orders of dfa and suggest a modified dfa method to remove them the improvement is necessary especially for short records that are affected by non stationarities furthermore we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of dfa

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

applications of statistical physics to economic and financial topics abstract problems in economy and finance have started to attract the interest of statistical physicists fundamental problems pertain to the existence or not of long medium short range power law correlations in economic systems as well as to the presence of financial cycles methods like the extended detrended fluctuation analysis and the multi affine analysis are recalled emphasizing their value in sorting out correlation ranges and predictability among spectacular results the possibility of crash predictions is indicated the well known financial analyst technique the so called moving average is shown to raise questions about fractional brownian motion properties finally the m k zipf method and the i variability diagram technique are presented for sorting out short range correlations analogies with other fields of modern applied statistical physics are also presented in view of some universal openess

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

distribution of natural trends in long term correlated records a scaling approach we estimate the exceedance probability w x ensuremath alpha l that in a long term correlated gaussian distributed sub record of length l characterized by a fluctuation exponent ensuremath alpha between 0 5 and 1 5 a relative increase ensuremath delta ensuremath sigma t of size larger than x occurs where ensuremath delta is the total observed increase measured by linear regression and ensuremath sigma t is the standard deviation around the regression line we consider l between 500 and 2000 which is the typical length scale of monthly local and reconstructed annual global temperature records we use scaling theory to obtain an analytical expression for w x ensuremath alpha l from this expression we can determine analytically for a given confidence probability q the boundaries ifmmode pm else textpm fi x q ensuremath alpha l of the confidence interval in the presence of an external linear trend the total observed increase is the sum of the natural and the external increase an observed relative increase ensuremath delta ensuremath sigma t is considered unnatural when it is above x q ensuremath alpha l in this case the size of the external relative increase is bounded by ensuremath delta ensuremath sigma t ifmmode pm else textpm fi x q ensuremath alpha l we apply this approach to various global and local climate data and discuss the different results for the significance of the observed trends

introducing false eur and false eur exchange rates abstract the euro eur is a new currency introduced by the european community its exchange rate is very puzzling we have invented a false euro feur dating back to 1993 and have derived the exchange rates of the feur with respect to currencies not belonging to the eur i e dkk chf jpy and usd this allows us to search for correlations between the fluctuations preexisting to the introduction of eur and present ones in such financial data the detrended fluctuation analysis dfa statistical method is used this leads to assume a power law behavior i e a scaling hypothesis through an exponent the latter has demonstrated its usefulness for the investigations of long range power law correlations in several types of financial sequences our findings show that the exponent interestingly characterizes fractional brownian motion of the currency exchange rates between eur and dkk over a 25 day interval and usual brownian motion otherwise and for the three other investigated exchange rates we can devise an investment strategy based on the local technique and obtain appreciable gains for the time being

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

are the phases in the anderson model long range correlated we investigate the local cumulative phases at single sites of the lattice for time dependent wave functions in the anderson model in d 2 and 3 in addition to a local linear trend the phases exhibit some fluctuations we study the time correlations of these fluctuations using detrended fluctuation analysis our results suggest that the phase fluctuations are long range correlated decaying as a power law with time it seems that the exponent depends on the degree of disorder in d 3 close to the critical disorder wc 16 5 the correlation exponent exhibits a maximum value of 0 6 which is significantly above random fluctuations 0 5

nonlinear analysis of cardiac rhythm fluctuations using dfa method abstract after a brief overview of classical techniques used to explore cardiac rhythm variability we show how the dfa method can help diagnose heart failure

design of state estimator for neural networks with leakage discrete and distributed delays abstract in this paper the design problem of state estimator for neural networks with mixed time varying delays and leakage delays has been investigated by using appropriate model transformation that shifts the considered systems into the neutral type time delay systems adapting a new lyapunov krasovskii functional which takes into account the range of time delay and by making use of some inequality techniques delay dependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable the criteria are formulated in terms of a set of linear matrix inequalities lmis which can be checked efficiently by use of some standard numerical packages finally three numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the presented results

a hybrid detrending method for fractional gaussian noise abstract determining trend and implementing detrending operations are important steps in data analysis yet there is neither precise definition of trend nor any logical algorithm for extracting it in this paper we propose a hybrid detrending method hdm which is based on the empirical mode decomposition emd and the detrended fluctuation analysis dfa our method can remove the polynomial and sinusoidal trends from the fractional gaussian noise fgn background we illustrate the method by selected examples from artificial time series and climate data in comparison with existing frequency domain based detrending methods our method is a posteriori the trend defined by our method is only derived from the data further our method also preserves the scaling behavior of the original signals

the eikonal equation stability of reaction diffusion waves on a sphere abstract the eikonal approach to excitable reaction diffusion systems provides an analytical hold on the phenomenon of wave propagation on curved surfaces and the evolution of toroidal scroll structures in the neighbourhood of organising filaments the extent to which the eikonal equation contains information on the stability of these wave solutions is important from a theoretical and experimental point of view we initiated this study in 1987 by demonstrating the stability of an expanding spherical wave recent experiments on wave propagation on a sphere encouraged us further to investigate stability of waves on surfaces we analyse in this paper the geometrical stability of symmetric counter rotating spiral waves propagating on the unit sphere we demonstrate that these solutions are stable under small perturbations normal to the wave fron lying on the unit sphere

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

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