on the spaces lp x ω and wm p x ω in this paper we present some basic results on the generalized lebesgue spaces l p x omega and generalized lebesgue sobolev spaces w m w p x omega these results provide the necessary framework for the study of variational problems and elliptic equations with non standard p x growth conditions c 2001 academic press

kramers like escape driven by fractional gaussian noise we investigate the escape from a potential well of a test particle driven by fractional gaussian noise with hurst exponent 0 h 1 from a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time on the hurst exponent h and the particle diffusivity d we observe different behavior for the subdiffusive antipersistent and superdiffusive persistent domains in particular we find that the escape becomes increasingly faster for decreasing values of h consistent with previous findings on the first passage behavior approximate analytical calculations are shown to support the numerically observed dependencies

empirical mode decomposition and correlation properties of long daily ozone records sreceived 16 november 2004 revised manuscript received 17 march 2005 published 27 may 2005d correlations for daily data of total ozone column are investigated by detrended fluctuation analysis sdfad the removal of annual periodicity does not result in a background free signal for the tropical station mauna loa in order to identify the remaining quasiperiodic constituent the relatively new method of empirical mode decomposition semdd is tested we found that the so called intrinsic mode functions do not represent real signal components of the ozone time series their amplitude modulation is very sensitive to local changes such as random data removal or smoothing tests on synthetic data further corroborate the limitations of decomposing quasiperiodic signals from noise with emd nevertheless the emd algorithm helps to identify dominating frequencies in the time series which allows to separate fluctuations from the remaining background we demonstrate that dfa analysis for the cleaned mauna loa record yields scaling comparable to a mid latitude station

global attractors for p laplacian equation abstract the existence of a l 2 w 0 1 p l q global attractor is proved for the p laplacian equation u t div u p 2 u f u g on a bounded domain r n n 3 with dirichlet boundary condition where p 2 the nonlinear term f is supposed to satisfy the polynomial growth condition of arbitrary order c 1 u q k f u u c 2 u q k and f u l where q 2 is arbitrary there is no other restriction on p and q the asymptotic compactness of the corresponding semigroup is proved by using a new a priori estimate method called asymptotic a priori estimate

scale invariant distribution and multifractality of volatility multipliers in stock markets abstract the statistical properties of the multipliers of the absolute returns are investigated using 1 min high frequency data of financial time series the multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale providing direct evidence of the existence of scale invariance in financial data the multipliers with base a 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a we unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers that is the values of s and a

modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti persistent processes abstract detrended fluctuation analysis dfa is a simple but very efficient method for investigating the power law long term correlations of non stationary time series in which a detrending step is necessary to obtain the local fluctuations at different timescales we propose to determine the local trends through empirical mode decomposition emd and perform the detrending operation by removing the emd based local trends which gives an emd based dfa method similarly we also propose a modified multifractal dfa algorithm called an emd based mfdfa the performance of the emd based dfa and mfdfa methods is assessed with extensive numerical experiments based on fractional brownian motion and multiplicative cascading process we find that the emd based dfa method performs better than the classic dfa method in the determination of the hurst index when the time series is strongly anticorrelated and the emd based mfdfa method outperforms the traditional mfdfa method when the moment order q of the detrended fluctuations is positive we apply the emd based mfdfa to the 1 min data of shanghai stock exchange composite index and the presence of multifractality is confirmed we also analyze the daily austrian electricity prices and confirm its anti persistence

using detrended fluctuation analysis for lagged correlation analysis of nonstationary signals here we propose a method based on detrended fluctuation analysis dfa to investigate lagged correlations for nonstationary time series the aim is to show that the largest correlation can be found at positive lags reflecting the existence of underlying delays in the evolution of real time sequences the performance of the lagged dfa method is illustrated by selected real examples

the capacity of the arbitrarily varying channel revisited positivity constraints a well known result of r ahlswede 1970 asserts that the deterministic code capacity of an arbitrarily varying channel avc under the average error probability criterion either equals its random code capacity or else is zero a necessary and sufficient condition is identified for deciding between these alternative namely the capacity is zero if and only if the avc is symmetrizable the capacity of the avc is determined with constraints on the transmitted codewords as well as on the channel state sequences and it is demonstrated that it may be positive but less than the corresponding random code capacity a special case of the results resolves a weakened version of a fundamental problem of coding theory

sobolev embedding theorems for spaces wk p x ω this paper gives a sobolev type embedding theorem for the generalized lebesgue sobolev space wk p x where is an open domain in rn n 2 with cone property and p x is a lipschitz continuous function defined on satisfying 1 p p nk the main result can be stated as follows for any measurable function q x x formula with p x q x p x np x n kp x there exists a continuous embedding from wk p x to lq x

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

strong secrecy from channel resolvability we analyze physical layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability instead of considering capacity based constructions which associate to each message a subcode that operates just below the capacity of the eavesdropper s channel we consider channel resolvability based constructions which associate to each message a subcode that operates just above the resolvability of the eavesdropper s channel building upon the work of csiszar and hayashi we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels specifically we show that at least for symmetric wiretap channels random capacity based constructions fail to achieve the strong secrecy capacity while channel resolvability based constructions achieve it we then leverage channel resolvability to establish the secrecy capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics finally we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information csi mixed channels and compound channels with receiver csi as well as the secret key capacity of source models for secret key agreement by tying secrecy to channel resolvability we obtain achievable rates for strong secrecy metrics with simple proofs

multifractality in stock indexes fact or fiction abstract multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes including hsi szsc s p 500 and nasdaq to check whether the indexes instead of the returns possess multifractality we find that the mass exponent q is linear and the singularity q is close to 1 for all trading days and all indexes furthermore we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series hence the so called multifractality in the intraday stock market indexes is merely an illusion

fluctuation analysis of electric power loads in europe correlation multifractality vs distribution function multifractality abstract we analyzed the timeseries of power loads of 35 separate countries which publicly share hourly data through the entso e platform for more than 5 years moreover we applied multifractal detrended fluctuation analysis for the demonstration of the multifractal nature autocorrelation and the distribution function fundamentals additionally we improved the basic method described by kantelhardt et al using uniform shuffling and surrogation of the datasets in order to prove the robustness of the results with respect to the non linear effects of the processes all the datasets exhibited multifractality in the distribution function as well as in the autocorrelation function the basic differences between individual states are manifested in the width of the multifractal spectra and in the location of the maxima we present the hypothesis concerning the production portfolio and the export import dependencies

stochastic fractional evolution equations with fractional brownian motion and infinite delay abstract in this paper we consider a class of stochastic fractional evolution equations with infinite delay and a fractional brownian motion in a hilbert space by the stochastic analysis technique we establish the existence and uniqueness of mild solutions for these equations under non lipschitz condition with lipschitz conditions being considered as a special case an example is provided to illustrate the theory

global attractors for the p laplacian equations with nonregular data abstract let be a smooth bounded domain in r n n 3 we consider the long time behavior of solutions to the p laplacian equation u t p u f u g where 2 p n p div u p 2 u is the p laplace operator assume that g and the initial condition u 0 lie in l 1 f r r is of class c 1 and satisfies proper growth conditions firstly we prove the uniqueness of the entropy solution and establish some regularity results then we show the existence of a global attractor a in l r 1 w 0 1 s with s max n p 1 n 1 p r 1 r to obtain the results a decomposition method and a bootstrap technique are used

modeling electricity spot prices using mean reverting multifractal processes abstract we discuss stochastic modeling of volatility persistence and anti correlations in electricity spot prices and for this purpose we present two mean reverting versions of the multifractal random walk mrw in the first model the anti correlations are modeled in the same way as in an ornstein uhlenbeck process i e via a drift damping term and in the second model the anti correlations are included by letting the innovations in the mrw model be fractional gaussian noise with h 1 2 for both models we present approximate maximum likelihood methods and we apply these methods to estimate the parameters for the spot prices in the nordic electricity market the maximum likelihood estimates show that electricity spot prices are characterized by scaling exponents that are significantly different from the corresponding exponents in stock markets confirming the exceptional nature of the electricity market in order to compare the damped mrw model with the fractional mrw model we use ensemble simulations and wavelet based variograms and we observe that certain features of the spot prices are better described by the damped mrw model the characteristic correlation time is estimated to approximately half a year

statistical analysis of dwt coefficients of fgn processes using arfima p d q models abstract fractional gaussian noise fgn provides an important parametric representation for the data recorded from long memory processes also it has been well established in literature that the orthogonal wavelet transforms prove to be the optimal bases to represent the data as fgn or fbm fractional brownian motion models this paper highlights the statistical properties of discrete wavelet transform dwt coefficients in the wavelet expansion of fgn statistical analysis was carried out by analyzing the inter scale and intra scale correlations of the dwt coefficients for wavelets with varying vanishing moments two types of auto regressive moving average arma models were fit to the wavelet coefficients of fgn namely i arma p q and ii arfima p d q models the latter represents the arma models with fractional differencing using the akaike information criteria aic and the bayesian information criteria bic it has been shown that arfima models best represent the wavelet coefficients of fgn the above observation holds good when wavelets with increasing number of vanishing moments are used for obtaining dwt coefficients after estimating the optimal model and its parameters different properties pertaining to the inter scale and intra scale correlations were verified using these models

discrepancy between subcritical and fast rupture roughness a cumulant analysis rough crack fronts in a sheet of paper obtained during a creep experiment do not follow true scaling laws local roughness exponents are estimated using the first order cumulant a quantity recently introduced in the turbulence literature j delour j f muzy and a arneodo eur phys j b 23 243 2001 using a large data set 102 fronts we find a significant difference in local roughness between the slow subcritical and the fast growth regime

stochastic interpolation of sparsely sampled time series via multipoint fractional brownian bridges we propose and test a method to interpolate sparsely sampled signals by a stochastic process with a broad range of spatial and or temporal scales to this end we extend the notion of a fractional brownian bridge defined as fractional brownian motion with a given scaling hurst exponent h and with prescribed start and end points to a bridge process with an arbitrary number of intermediate and nonequidistant points determining the optimal value of the hurst exponent h opt appropriate to interpolate the sparse signal is a very important step of our method we demonstrate the validity of our method on a signal from fluid turbulence in a high reynolds number flow and discuss the implications of the non self similar character of the signal the method introduced here could be instrumental in several physical problems including astrophysics particle tracking and specific tailoring of surrogate data as well as in domains of natural and social sciences

establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes stochastic fractal signals can be characterized by the hurst coefficient h which is related to the exponents of various power law statistics characteristic of these processes two techniques widely used to estimate h are spectral analysis and detrended fluctuation analysis dfa this paper examines the analytical link between these two measures and shows that they are related through an integral transform numerical simulations confirm this relationship for ideal synthesized fractal signals their performance as estimators of h is compared based on a mean square error criterion and found to be similar dfa measures are derived for physiological signals of heartbeat r ensuremath r intervals through the integral transform of a spectral density estimate these agree with directly calculated dfa estimates indicating that the relationship holds for signals with nonideal fractal properties it is concluded that dfa and spectral measures provide equivalent characterizations of stochastic signals with long term correlation

multifractal analysis of ssec in chinese stock market a different empirical result from heng seng index abstract in this paper high frequency per 5 min data of shanghai stock exchange composite index ssec from january 1999 to july 2001 is analyzed by multifractal we find that the correlation of the parameters of the multifractal spectra with the variation of daily return z in ssec is noticeably different from that in previous studies of heng seng index in hong kong stock market sun et al phys a 291 2001 553 562 sun et al phys a 301 2001 473 482 so we suppose that there may not be a universal rule for the dependence of the parameters of the multifractal spectra with daily return of a stock index then we construct a new measurement of market risk based on multifractal spectra and test its ability of predicting index fluctuations with a more thorough method than that in sun et al phys a 301 2001 473 482

asymmetric multiscale detrended fluctuation analysis of california electricity spot price abstract in this paper we develop a new method called asymmetric multiscale detrended fluctuation analysis which is an extension of asymmetric detrended fluctuation analysis a dfa and can assess the asymmetry correlation properties of series with a variable scale range we investigate the asymmetric correlations in california 1999 2000 power market after filtering some periodic trends by empirical mode decomposition emd our findings show the coexistence of symmetric and asymmetric correlations in the price series of 1999 and strong asymmetric correlations in 2000 what is more we detect subtle correlation properties of the upward and downward price series for most larger scale intervals in 2000 meanwhile the fluctuations of s asymmetry and s absolute asymmetry are more significant in 2000 than that in 1999 for larger scale intervals and they have similar characteristics for smaller scale intervals we conclude that the strong asymmetry property and different correlation properties of upward and downward price series for larger scale intervals in 2000 have important implications on the collapse of california power market and our findings shed a new light on the underlying mechanisms of power price

measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis abstract analyzing the shanghai stock price index daily returns using mf dfa method it is found that there are two different types of sources for multifractality in time series namely fat tailed probability distributions and non linear temporal correlations based on that a sliding window of 240 frequency data in 5 trading days was used to study stock price index fluctuation it is found that when the stock price index fluctuates sharply a strong variability is clearly characterized by the generalized hurst exponents h q therefore two measures h and based on generalized hurst exponents were proposed to compare financial risks before and after price limits and reform of non tradable shares the empirical results verify the validity of the measures and this has led to a better understanding of complex stock markets

global attractors for nonlinear parabolic equations with nonstandard growth and irregular data abstract we investigate the large time behavior of solutions to the following nonlinear parabolic equations u t div u p x 2 u f x u g in r u 0 on r u x 0 u 0 x in where u 0 g l 1 we first provide the existence and uniqueness of an entropy solution for the problem then through some delicate analysis we establish some regularity results on the solution by which we prove the existence of a global attractor for the solution semigroup

the critical forms of the attractors for semigroups and the existence of critical attractors the critical forms of the minimal closed global attractor m and the minimal closed global b attractor m for operator semigroups are given i e if the set x x x x attracts each point x in the phase space x then it must be the unique minimal closed global attractor m and if the set b b x x attracts each bounded set in x then it must be the unique minimal closed global b attractor m on this basis the sufficient conditions for the existence of m and m interrelation between m and m are discussed we introduce some classes of semigroups and study a variety of relations of them and the different classes of semigroups considered by ladyzhenskaya hale and temam when a semigroup9s continuity is not required it is proved that the semigroups with b acp introduced by us coincide with the asymptotically smooth semigroups the semigroups of class ak or b ak respectively and that if these semigroups are b bounded and x x x b then each of them possesses the unique non empty minimal invariant compact global attractor x x x x and the unique non empty minimal invariant compact global b attractor m b b x x m omega o where 0is a small number furthermore the sufficient conditions for m and m are given it is further proved that these conditions which guarantee the existence of the compact invariant global b attractor m are not only sufficient but also necessary so in order to guarantee a semigroup to have such attractor m the conditions which are put on the semigroup cannot be weakened again these results will be useful in studying the existence and construction of attractors

a global attractor for a p x laplacian parabolic problem abstract in this work we study the asymptotic behavior of a p x laplacian parabolic problem of the form u t p x u b u in a bounded smooth domain in r n under dirichlet boundary conditions we prove under suitable assumptions the existence of a compact invariant global b attractor in l 2

finite and infinite dimensional attractors for porous media equations the fractal dimension of the global attractors of porous media equations in bounded domains is studied the conditions which guarantee this attractor to be finite dimensional are found and the examples of infinite dimensional attractors that do not satisfy these conditions are constructed the upper and lower bounds for the kolmogorov e entropy of infinite dimensional attractors are also obtained

upscaling levy motions in porous media with long range correlations bacterial motility has been modeled by levy motions which were upscaled in porous media with drift processes such as levy processes and time changed brownian motion via central limit theorems it was possible to prove the limit theorems and upscale the processes because of the independence of their increments therefore it has not been applied to processes with correlated increments such as fractional brownian motions in this paper the upscaling approach is generalized to porous media with long range correlated processes the processes are modeled by a fractional brownian velocity process and p diffusive position processes that were defined and used to classify diffusion processes by o malley and cushman a renormalization group classification of nonstationary and or infinite second moment diffusive processes j stat phys 146 989 1000 2012 10 1007 s10955 012 0448 3 a few examples of p diffusive processes are discussed by computing the values of the parameter p

measuring anti correlations in the nordic electricity spot market by wavelets abstract we consider the nordic electricity spot market from mid 1992 to the end of year 2000 this market is found to be well approximated by an anti persistent self affine mean reverting walk it is characterized by a hurst exponent of h 0 41 over three orders of magnitude in time ranging from days to years we argue that in order to see such a good scaling behavior and to locate cross overs it is crucial that an analyzing technique is used that decouples scales this is in our case achieved by utilizing a multi scale wavelet approach the shortcomings of methods that do not decouple scales are illustrated by applying to the same data set the classic r s and fourier techniques for which scaling regimes and or positions of cross overs are hard to define

multifractal detrended cross correlation analysis on gold crude oil and foreign exchange rate time series abstract we apply the recently developed multifractal detrended cross correlation analysis method to investigate the cross correlation behavior and fractal nature between two non stationary time series we analyze the daily return price of gold west texas intermediate and brent crude oil foreign exchange rate data over a period of 18 years the cross correlation has been measured from the hurst scaling exponents and the singularity spectrum quantitatively from the results the existence of multifractal cross correlation between all of these time series is found we also found that the cross correlation between gold and oil prices possess uncorrelated behavior and the remaining bivariate time series possess persistent behavior it was observed for five bivariate series that the cross correlation exponents are less than the calculated average generalized hurst exponents ghe for q 0 and greater than ghe when q 0 and for one bivariate series the cross correlation exponent is greater than ghe for all q values

generation of long range correlations in large systems as an optimization problem we propose an efficient method of generating long range correlations in large systems the development of this method was motivated by the problem of constructing an optimal model for a large scale porous medium there are typically long range correlations in the properties of such porous media such as their permeability and porosity for which there are usually only limited data the optimal model must not only honor preserve the available data and their correlation function but also accurately predict the future behavior of fluid flow in the media we formulate the problem of generating the long range correlations as one of optimization and utilize simulated annealing to generate a d dimensional array which contains the correlations and honors the existing data the optimization process is based on the data s correlation function the method is therefore free of the many numerical difficulties and or limitations that most previous techniques suffer from it is completely general and may be used for generating long range correlations with any type of correlation function in both isotropic and anisotropic media representative examples are presented and the method s efficiency and accuracy are discussed

wavelet based estimators of scaling behavior various wavelet based estimators of self similarity or long range dependence scaling exponent are studied extensively these estimators mainly include the bi orthogonal wavelet estimators and the wavelet transform modulus maxima wtmm estimator this study focuses both on short and long time series in the framework of fractional autoregressive integrated moving average farima processes we advocate the use of approximately adapted wavelet estimators for these ideal processes the scaling behavior actually extends down to the smallest scale i e the sampling period of the time series if an adapted decomposition is used but in practical situations there generally exists a cutoff scale below which the scaling behavior no longer holds we test the robustness of the set of wavelet based estimators with respect to that cutoff scale as well as to the specific density of the underlying law of the process in all situations the wtmm estimator is shown to be the best or among the best estimators in terms of the mean squared error mse we also compare the wavelet estimators with the detrended fluctuation analysis dfa estimator which was previously proved to be among the best estimators which are not wavelet based estimators the wtmm estimator turns out to be a very competitive estimator which can be further generalized to characterize multiscaling behavior

multifractal detrended cross correlation analysis of coding and non coding dna sequences through chaos game representation abstract we propose a new approach combining the chaos game representation and the two dimensional multifractal detrended cross correlation analysis methods to examine multifractal behavior in power law cross correlation between any pair of nucleotide sequences of unequal lengths in this work we analyzed the characteristic behavior of coding and non coding dna sequences of eight prokaryotes the results show the presence of strong multifractal nature between coding and non coding sequences of all data sets we found that this integrative approach helps us to consider complete dna sequences for characterization and further it may be useful for classification clustering identification of class affiliation of nucleotide sequences etc with high precision

characterization of long range correlations in complex distributions and profiles characterizing long range correlations in complex distributions such as the porosity logs of field scale porous media and profiles such as the fracture surfaces of rock and materials is an important problem we carry out an extensive analysis of such distributions represented by synthetic and real data to determine which method provides the most efficient and accurate tool for characterizing them the synthetic data and profiles are generated by a fractional brownian motion fbm and the real data analyzed are a porosity log of an oil reservoir and time variations of the pressure fluctuations in three phase flow in a fluidized bed the fbm is generated by three different numerical methods and the data are analyzed by seven different techniques our analysis indicates that the size of the data array greatly influences the accuracy of characterization of its long range correlations we also find that if the size of the data array is large enough the commonly used rescaled range r s method of analyzing fbm series fails to provide accurate estimates of the hurst exponent although it can provide a reasonably accurate analysis of a data array that is generated by a fractional gaussian noise in contrast the maximum entropy and wavelet decomposition methods offer highly accurate and efficient tools of characterizing long range correlations in complex distributions and profiles new methods that are somewhat similar to the r s method are also suggested

pde and ode limit problems for p x laplacian parabolic equations in this work we prove continuity of solutions with respect to initial conditions and parameters and we prove upper semicontinuity of a family of global attractors for problems of the form ut div d u p x 2 u b u in a bounded smooth domain in rn

multifractal description of stock price index fluctuation using a quadratic function fitting abstract in order to obtain a quantitative multifractal characterization of the stock price index the multifractal spectrum of shanghai stock price index time series in 2005 was investigated and the multifractal spectrum was fitted using a quadratic function a sliding window of 240 frequency data in 5 trading days was used to investigate the stock price index fluctuation the multifractal parameters and coefficients in each window were obtained by fitting the local multifractal spectrum using a quadratic function it is found that when the stock price index fluctuates sharply a strong variability is clearly characterized by the multifractal parameters and the quadratic function coefficients this has led to a better understanding of complex stock markets

wavelet analysis of dominant scales of heterogeneous porous media 1 heterogeneity of aquifer permeability has a significant influence on the transport of solutes therefore characterization of aquifer heterogeneity is needed to accurately predict the behavior of solutes a critical characteristic of heterogeneity is a characteristic length scale that is a measure of the distance over which property values are correlated we show that the characteristic length scale of a statistically homogeneous permeability field can be identified through wavelet analysis using the global wavelet energy spectrum gwes the relationship between the wavelet scale and the characteristic length scale of a random field is investigated for the mexican hat and morlet wavelets and different covariance structures the ability of the gwes to identify multiple characteristic length scales in a random field with nested covariance structures is also investigated we use the technique to identify the characteristic length scales of a laboratory collected permeability transect from massillon sandstone

use and misuse of some hurst parameter estimators applied to stationary and non stationary financial time series abstract the detection of long range dependence lrd is an important task in time series analysis lrd is often summarized by the well known hurst parameter or exponent h 0 1 which can be estimated by a number of methods some of these techniques are designed to be applied to signals behaving as a stationary fractional gaussian noise fgn whereas others imply that the analyzed time series behave as a non stationary fractional brownian motion fbm moreover some estimators do not yield the hurst parameter but indexes related to h and ranging outside the unit interval therefore the fgn or fbm nature of the studied time series has to be preliminarily analyzed before applying any estimation method and the relationships between h and the indexes resulting from the analyses have to be taken into account to obtain coherent results since fgn like series represent the increments of fbm like processes and both the signals are characterized by the same h value by definition estimators designed for fgn like series can be applied to fbm like sequences after preventive differentiation and conversely estimators designed for fbm like processes can be applied to fgn like series after preventive integration the signal characterization is particularly important when h is estimated on financial time series because the returns represent the first difference of price time series which are often assumed to behave like self affine sequences the analysis of simulated fgn and fbm time series shows that all the considered methods yield comparable h values when properly applied the reanalysis of several market price time series already studied in the literature points out that a correct application of the estimators supported by a preventive signal classification yields homogeneous h values allowing for a useful cross validation of results reported in different works moreover some conclusions reported in the literature about the anti persistence of some financial series are shown to be incorrect because of the inappropriate application of the estimation methods

the effect of linear mixing in the eeg on hurst exponent estimation although the long range temporal correlation lrtc of the amplitude fluctuations of neuronal eeg meg oscillations is widely acknowledged the majority of studies to date have been performed in sensor space disregarding the mixing effects implied by volume conduction and confounding noise while the effect of mixing on the evaluation of evoked responses and connectivity measures has been extensively studied there are to date no studies reporting on the differences in the values of the estimated hurst exponents when moving between sensor and source space representations of the multivariate data or on the effect of noise such differences if not duly acknowledged may lead to erroneous data interpretations we show in simulations and in theory that measuring hurst exponents in sensor space may lead to an incomplete picture of the lrtc properties of the underlying data and that noise may significantly bias the estimate of the hurst exponent of the underlying signal moreover these predictions are confirmed in real data where we analyze the amplitude dynamics of neuronal oscillations in the resting state from eeg data by moving either to an independent components representation or to a source representation which maximizes the signal to noise ratio in the alpha frequency range we observe greater variance skewness and kurtosis over measured hurst exponents than in sensor space we confirm the suitability of conventional source separation methodology by introducing a novel algorithm hemax which obtains a source maximizing the hurst exponent in the amplitude dynamics of narrow band oscillations our findings imply that the long range correlative properties of the eeg should be studied in source space in such a way that the snr is maximized or at least with spatial decomposition techniques approximating source activities rather than in sensor space

exponential error bounds for random codes in the arbitrarily varying channel random codes for the arbitrarily varying channel are investigated the code ensemble is restricted to increase only exponentially with codeword length a quantity called key rate is used as a measure of the rate of increase the reliability function for such codes is related to the reliability function for codes with unlimited key rate explicit results are obtained in some examples of practical interest

renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and l1 data abstract in this paper we prove the existence and uniqueness of both renormalized solutions and entropy solutions for nonlinear parabolic equations with variable exponents and l 1 data and moreover we obtain the equivalence of renormalized solutions and entropy solutions

an introduction to white noise theory and malliavin calculus for fractional brownian motion fractional brownian motion fbm with hurst parameter index between 0 and 1 is a stochastic process originally introduced by kolmogorov in a study of turbulence many other applications have subsequently been suggested in order to obtain good mathematical models based on fbm it is necessary to have a stochastic calculus for such processes the purpose of this paper is to give an introduction to this newly developed theory of stochastic integration for fbm based on white noise theory and malliavin type differentiation

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

on the z2 index of the global attractor for a class of p laplacian equations by means of the z 2 index we study the geometrical property of the global attractor for a class of symmetric p laplacian equations u t div vertical bar del u vertical bar p 2 del u vertical bar u vertical bar r 2 u lambda vertical bar u vertical bar s 2 u f x u 0 where lambda 0 2 s p r we first provide under suitable assumptions the existence result for the symmetric global attractor a then when 2 s p r we prove that the z 2 index of the global attractor is infinite as a corollary we obtain that the fractal dimension of the global attractor is infinite for when 2 s p r we provide the lower bound of the z 2 index of the global attractor c 2010 elsevier ltd all rights reserved

multifractal cross correlation analysis in electricity spot market abstract in this paper we investigate the multiscale cross correlations between electricity price and trading volume in czech market based on a newly developed algorithm called multifractal cross correlation analysis mfcca the new algorithm is a natural multifractal generalization of the detrended cross correlation analysis dcca and is sensitive to cross correlation structure and free from limitations of other algorithms by considering the original sign of the cross covariance it allows us to properly quantify and detect the subtle characteristics of two simultaneous recorded time series first the multifractality and the long range anti persistent auto correlations of price return and trading volume variation are confirmed using multifractal detrended fluctuation analysis mf dfa furthermore we show that there exist long range anti persistent cross correlations between price return and trading volume variation by mfcca and we also identify that the cross correlations disappear on the level of relative small fluctuations in order to obtain deeper insight into the dynamics of the electricity market we analyze the relation between generalized hurst exponent and the multifractal cross correlation scaling exponent q we find that the difference between the generalized hurst exponent and the multifractal cross correlation scaling exponent is significantly different for smaller fluctuation which indicates that the multifractal character of cross correlations resembles more each other for electricity price and trading volume on the level of large fluctuations and weakens for the smaller ones

generalized arcsine laws for fractional brownian motion the three arcsine laws for brownian motion are a cornerstone of extreme value statistics for a brownian b t starting from the origin and evolving during time t one considers the following three observables i the duration t the process is positive ii the time t mathrm last the process last visits the origin and iii the time t mathrm max when it achieves its maximum or minimum all three observables have the same cumulative probability distribution expressed as an arcsine function thus the name arcsine laws we show how these laws change for fractional brownian motion x t a non markovian gaussian process indexed by the hurst exponent h it generalizes standard brownian motion i e h frac 1 2 we obtain the three probabilities using a perturbative expansion in h ensuremath frac 1 2 while all three probabilities are different this distinction can only be made at second order in our results are confirmed to high precision by extensive numerical simulations

multifractal detrended cross correlation analysis of genome sequences using chaos game representation abstract we characterized the multifractal nature and power law cross correlation between any pair of genome sequence through an integrative approach combining 2d multifractal detrended cross correlation analysis and chaos game representation in this paper we have analyzed genomes of some prokaryotes and calculated fractal spectra h q and f from our analysis we observed existence of multifractal nature and power law cross correlation behavior between any pair of genome sequences cluster analysis was performed on the calculated scaling exponents to identify the class affiliation and the same is represented as a dendrogram we suggest this approach may find applications in next generation sequence analysis big data analytics etc

on global attractor for nonlinear parabolic equations of m laplacian type abstract existence and some regularity results of global attractor in l q q 1 for m laplacian type quasilinear parabolic equation with a perturbation like a x u u u u f x with 0 a x 0 are proved for the proofs moser s technique is used extensively

markov analysis and kramers moyal expansion of nonstationary stochastic processes with application to the fluctuations in the oil price we describe a general method for analyzing a nonstationary stochastic process x t which unlike many of the previous analysis methods does not require x t to have any scaling feature the method is used to study the fluctuations in the daily price of oil it is shown that the returns time series y t ln x t 1 x t is a stationary and markov process characterized by a markov time scale t m the coefficients of the kramers moyal expansion for the probability density function p y tmid r y 0 t 0 are computed p y tmid r y 0 t 0 satisfies a fokker planck equation which is equivalent to a langevin equation for y t that provides quantitative predictions for the oil price over times that are of the order of t m also studied is the average frequency of positive slope crossings nu alpha p y i alpha y i 1 alpha for the returns where t alpha 1nu alpha is the average waiting time for observing y t alpha again

multifractal detrending moving average cross correlation analysis there are a number of situations in which several signals are simultaneously recorded in complex systems which exhibit long term power law cross correlations the multifractal detrended cross correlation analysis mfdcca approaches can be used to quantify such cross correlations such as the mfdcca based on the detrended fluctuation analysis mfxdfa method we develop in this work a class of mfdcca algorithms based on the detrending moving average analysis called mfxdma the performances of the proposed mfxdma algorithms are compared with the mfxdfa method by extensive numerical experiments on pairs of time series generated from bivariate fractional brownian motions two component autoregressive fractionally integrated moving average processes and binomial measures which have theoretical expressions of the multifractal nature in all cases the scaling exponents h xy extracted from the mfxdma and mfxdfa algorithms are very close to the theoretical values for bivariate fractional brownian motions the scaling exponent of the cross correlation is independent of the cross correlation coefficient between two time series and the mfxdfa and centered mfxdma algorithms have comparative performances which outperform the forward and backward mfxdma algorithms for two component autoregressive fractionally integrated moving average processes we also find that the mfxdfa and centered mfxdma algorithms have comparative performances while the forward and backward mfxdma algorithms perform slightly worse for binomial measures the forward mfxdma algorithm exhibits the best performance the centered mfxdma algorithms performs worst and the backward mfxdma algorithm outperforms the mfxdfa algorithm when the moment order q 0 we apply these algorithms to the return time series of two stock market indexes and to their volatilities for the returns the centered mfxdma algorithm gives the best estimates of h xy q since its h xy 2 is closest to 0 5 as expected and the mfxdfa algorithm has the second best performance for the volatilities the forward and backward mfxdma algorithms give similar results while the centered mfxdma and the mfxdfa algorithms fail to extract rational multifractal nature

statistical behaviors for renormalization of correlated permeability field abstract in this article the statistical properties for the renormalized permeability obtained from the renormalization of the correlated permeability field are investigated in contrast to the uncorrelated porous media the scaling of the variance of the renormalized permeability field exhibits a crossover behavior when the correlation lengths are larger compared with the domain scale covered by the renormalization procedure the variance of the renormalized permeability will decrease slowly and the scaling exponent will be close to zero as the renormalization number increases the covered domain scale will eventually become larger than the correlation lengths and then the scaling property will transit to the uncorrelated case the convergent values of the renormalized permeability for isotropic and anisotropic correlated media are also investigated both the theoretical analysis and the simulation results show that larger correlation length in one direction will lead to a larger convergent value in the corresponding direction for the log normal permeability field numerical simulations show that the crossover scaling and also the convergent value for the renormalized permeability can be fitted very well by simple mathematical functions

a model porous medium equation with variable exponent of nonlinearity existence uniqueness and localization properties of solutions abstract we study the localization properties of weak solutions to the dirichlet problem for the degenerate parabolic equation u t div u x t u f with variable exponent of nonlinearity we prove the existence and uniqueness of weak solutions and establish conditions on the problem data and the exponent x t sufficient for the existence of such properties as finite speed of propagation of disturbances the waiting time effect finite time vanishing of the solution it is shown that the solution may instinct in a finite time even if x 0 in the problem domain but max 0

forecasting volatility of ssec in chinese stock market using multifractal analysis abstract in this paper taking about 7 years high frequency data of the shanghai stock exchange composite index ssec as an example we propose a daily volatility measure based on the multifractal spectrum of the high frequency price variability within a trading day an arfima model is used to depict the dynamics of this multifractal volatility mfv measures the one day ahead volatility forecasting performances of the mfv model and some other existing volatility models such as the realized volatility model stochastic volatility model and garch are evaluated by the superior prediction ability spa test the empirical results show that under several loss functions the mfv model obtains the best forecasting accuracy

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

mimo multiple access channel with an arbitrarily varying eavesdropper secrecy degrees of freedom a two transmitter gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated the channel matrices of the legitimate users are fixed and revealed to all the terminals whereas the channel matrices of the eavesdropper are arbitrarily varying and only known to the eavesdropper the secrecy degrees of freedom s d o f region under a strong secrecy constraint is characterized a transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver and uses a single user wiretap code for each user is shown to achieve the s d o f region the converse involves establishing an upper bound on a weighted sum rate expression this is accomplished by using induction where at each step one combines the secrecy and multiple access constraints associated with an adversary eavesdropping a carefully selected group of sub channels

rotation algorithm generation of gaussian self similar stochastic processes in this paper we introduce a simple and practical method to generate gaussian self similar stochastic processes fractional gaussian noises fgns and fractional brownian motions fbms by interpolating between two known series of them we apply the rotation algorithm to different cases including different pairs of fbms fgns and also different pairs each composed of an fbm and an fgn our results show that the sensitivity of our method for two fbms fgns is higher when approaching the series with a larger smaller hurst exponent and for the case with one fbm and one fgn by approaching the hurst exponent of the selected fbm the hurst exponent of the produced series changes more surprisingly by using this method we can generate positively and or negatively correlated series from two uncorrelated ones one brownian motion and one white gaussian noise or it is possible to generate uncorrelated signals one or two depending on the choice of two input signals from two correlated ones for two fgns using the rotation algorithm the evolution starts from larger scales in the system while for two fbms the evolution starts from smaller scales in the system

statistics of event by event fluctuations abstract following hwa and wu r c hwa y wu phys rev c 60 1999 0544904 we characterize the fluctuation behavior of the hadron density produced during quark hadron phase transition as modeled by a 2d ising model using a recently developed discrete wavelet based approach the scaling behavior is studied at temperatures below at and above t c at t c we find the hurst exponent h 1 as observed in a recent experimental finding l qin m ta chung phys rev d 72 2005 014011 however as compared to the r s analysis which yields only the hurst exponent our local approach finds a correlation behavior and multifractal properties at temperatures below at and above t c we find evidence for a transition from brownian to fractional browian motion near t c the correlation behavior compares well with the results obtained from a continuous wavelet based average wavelet co efficient method as well as with fourier power spectral analysis

wavelet transforms in a critical interface model for barkhausen noise we discuss the application of wavelet transforms to a critical interface model which is known to provide a good description of barkhausen noise in soft ferromagnets the two dimensional version of the model one dimensional interface is considered mainly in the adiabatic limit of very slow driving on length scales shorter than a crossover length which grows with the strength of the surface tension the effective interface roughness exponent zeta is approximately 1 20 close to the expected value for the universality class of the quenched edwards wilkinson model we find that the waiting times between avalanches are fully uncorrelated as the wavelet transform of their autocorrelations scales as white noise similarly detrended size size correlations give a white noise wavelet transform consideration of finite driving rates still deep within the intermittent regime shows the wavelet transform of correlations scaling as 1 f 1 5 for intermediate frequencies this behavior is ascribed to intra avalanche correlations

positive periodic solutions for a system of anisotropic parabolic equations abstract we consider a system of two degenerate parabolic equations with nonlocal terms and dirichlet boundary conditions more precisely the degeneracy in each equation of the system is of the type r x laplacian where r x is a function depending on x where is a bounded smooth domain of r n the system models the diffusion and the interaction between two different biological species sharing the same territory the paper provides conditions on the parameters of the problem that guarantee the coexistence of a t periodic non negative solution u v with both non trivial u v

localization of solutions of anisotropic parabolic equations abstract we study the localization properties of solutions of the dirichlet problem for the anisotropic parabolic equations u t i 1 n d i a i z u d i u p i 2 d i u f z z x t 0 t with constant exponents p i 1 and x r n n 2 such equations arise from the mathematical description of diffusion processes it is shown that if the equation combines the directions of slow diffusion for which p i 2 and the directions of fast or linear diffusion corresponding to p i 1 2 or p 2 then the solutions may simultaneously display the properties intrinsic for the solutions of isotropic equations of fast or slow diffusion under the assumptions that f 0 for t t f and u 0 0 f 0 for x 1 s we show on the one hand that the solution vanishes in a finite time if n 2 i 1 n 1 p i 1 n 2 and on the other hand that the support of the same solution never reaches the plane x 1 s provided that 1 n 1 1 n 1 i 2 n 1 p i 1 p 1

characterizing limit order prices abstract a computational model of a limit order book is used to study the effect of different limit order distribution offsets reference prices such as same side contra side best market prices and last traded price are considered in combination with different price offset distributions we show that when characterizing limit order prices varying the offset distribution only produces different behavior when the reference price is the contra side best price irrespective of the underlying mechanisms used in computing the limit order prices the shape of the price graph and the behavior of the average order book profile distribution are strikingly similar in all the considered reference prices offset distributions this implies that existing averaging methods can cancel variabilities in limit order book shape attributes and may be misleading

the existence of global attractors for the norm to weak continuous semigroup and application to the nonlinear reaction diffusion equations abstract in this paper first we introduce a new concept called the norm to weak continuous semigroup in a banach space and give a technical theorem to verify this notion of continuity then we establish a general method which is necessary and sufficient to obtain the existence of the global attractor for this kind of semigroup as an application we obtain the existence of the global attractor for a nonlinear reaction diffusion equation with a polynomial growth nonlinearity of arbitrary order and with some weak derivatives in the inhomogeneous term the global attractors are obtained in l p h 0 1 and h 2 h 0 1 respectively a new a priori estimate method called asymptotic a priori estimate has been introduced since the solutions of the equation has no higher regularity and the semigroup associated the solutions is not continuous in l p h 0 1 and h 2 h 0 1 the results in this part are new and appear to be optimal

comparison of detrending methods for fluctuation analysis abstract we examine several recently suggested methods for the detection of long range correlations in data series based on similar ideas as the well established detrended fluctuation analysis dfa in particular we present a detailed comparison between the regular dfa and two recently suggested methods the centered moving average cma method and a modified detrended fluctuation analysis mdfa we find that cma performs the same as dfa in long data with weak trends and is slightly superior to dfa in short data with weak trends when comparing standard dfa to mdfa we observe that dfa performs slightly better in almost all examples we studied we also discuss how several types of trends affect different types of dfa for weak trends in the data the new methods are comparable with dfa in these respects however if the functional form of the trend in data is not a priori known dfa remains the method of choice only a comparison of dfa results using different detrending polynomials yields full recognition of the trends a comparison with independent methods is recommended for proving long range correlations

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

existence and non existence results for nonlinear elliptic equations with nonstandard growth abstract we consider the existence and non existence of solutions for nonlinear elliptic equations whose model is div v p x 2 v v q x 1 v in v 0 on where is a smooth bounded domain in r n n 2 is a bounded radon measure our results are twofold when is absolutely continuous with respect to the p capacity the problem admits a unique solution when is concentrated on a set of zero r capacity r p in then the problem does not admit a solution if q is large enough

correlation between the hurst exponent and the maximal lyapunov exponent examining some low dimensional conservative maps the chirikov standard map and the 2d froeschle map are investigated a few thousand values of the hurst exponent he and the maximal lyapunov exponent mle are plotted in a mixed space of the nonlinear parameter versus the initial condition both characteristic exponents reveal remarkably similar structures in this space a tight correlation between the hes and mles is found with the spearman rank 0 83 and 0 75 for the chirikov and 2d froeschle maps respectively based on this relation a machine learning ml procedure using the nearest neighbor algorithm is performed to reproduce the he distribution based on the mle distribution alone a few thousand he and mle values from the mixed spaces were used for training and then using 2 2 4 105 mles the hes were retrieved the ml procedure allowed to reproduce the structure of the mixed spaces in great detail

anti correlation and multifractal features of spain electricity spot market we use multifractal detrended fluctuation analysis mf dfa to numerically investigate correlation persistence multifractal properties and scaling behavior of the hourly spot prices for the spain electricity exchange compania o peradora del mercado de electricidad omel through multifractal analysis fluctuations behavior the scaling exponents and generalized hurst exponents are studied moreover contribution of fat tailed probability distributions and nonlinear temporal correlations to multifractality is studied

long time behavior for a nonlinear parabolic problem with variable exponents abstract this paper addresses the question of the asymptotic behavior of solutions to the p x laplacian problem u t div u p x 2 u f x u g with general assumptions on f x u and the exponent p x we prove the existence of global attractors in proper spaces then we consider the fractal dimension of global attractors for the problem under suitable conditions we show that the problem admits an infinite dimensional global attractor

determination of the hurst exponent by use of wavelet transforms we propose a method for global hurst exponent determination based on wavelets using this method we analyze synthetic data with predefined hurst exponents fracture surfaces and data from economy the results are compared to those obtained with fourier spectral analysis when many samples are available the wavelet and fourier methods are comparable in accuracy however when one or only a few samples are available the wavelet method outperforms the fourier method by a large margin

renormalized solutions for a nonlinear parabolic equation with variable exponents and l 1 data abstract we prove the well posedness existence and uniqueness of a renormalized solution to nonlinear parabolic equations with variable exponents and l 1 data the functional setting involves lebesgue sobolev spaces with variable exponents

a channel under simultaneous jamming and eavesdropping attack correlated random coding capacities under strong secrecy criteria we give a complete characterization of the correlated random coding secrecy capacity of arbitrarily varying wiretap channels avwcs we apply two alternative strong secrecy criteria which both lead to the same multi letter formula the difference of these criteria lies in the treatment of correlated randomness they coincide in the case of uncorrelated codes on the basis of the derived formula we show that the correlated random coding secrecy capacity is continuous as a function of the avwc in contrast to the discontinuous uncorrelated coding secrecy capacity in the proof of the secrecy capacity formula for correlated random codes we apply an auxiliary channel which is compound from the sender to the intended receiver and arbitrarily varying from the sender to the eavesdropper

asymptotic regularity for p laplacian equation this paper is devoted to proving some asymptotic regularity of the solutions of the p laplacian equation ut div u p 2 u f u g x p 2 n considered on a bounded domain rn n 3 the nonlinear term f satisfies the polynomial growth condition of arbitrary order c1 u q k f u u c2 u q k where q 2 is arbitrary as an application of the asymptotic regularity results we not only can obtain the existence of a l2 w01 p lq global attractor a immediately but also can show further that a attracts every bounded subsets of l2 under the w01 p lq norm for any 0 furthermore the fractal dimension of a is finite in lq for any 0

hurst exponent a brownian approach to characterize the nonlinear behavior of red blood cells deformability abstract ektacytometry techniques quantifies red blood cells rbcs deformability by measuring the elongation of suspended rbcs subjected to shear stress raw shear stress elongation plots are difficult to understand thus most research papers apply data reduction methods characterizing the relationship between curve fitting our approach works with the naturally generated photometrically recorded time series of the diffraction pattern of several million of rbcs subjected to shear stress and applies nonlinear quantifiers to study the fluctuations of these elongations the development of new quantitative methods is crucial for restricting the subjectivity in the study of the cells behavior mainly if they are capable of analyze at the same time biological and mechanical aspects of the cells in flowing conditions and compare their dynamics a patented optical system called erythrocyte rheometer was used to evaluate viscoelastic properties of erythrocytes by ektacytometry to analyze cell dynamics we used the technique of time delay coordinates false nearest neighbors the forecasting procedure proposed by sugihara and may and hurst exponent the results have expressive meaning on comparing healthy samples with parasite treated samples suggesting that apparent noise associated with deterministic chaos can be used not only to distinguish but also to characterize biological and mechanical aspects of cells at the same time in flowing conditions

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

multifractal properties of chinese stock market in shanghai abstract in this article we apply three methods of multifractal analysis partition function method singular spectrum method and multifractal detrended fluctuation analysis method to analyze the closing index fluctuations of shanghai stock market during the past seven years we have found that shanghai stock market has weak multifractal features and there are long range power law correlations between index series the shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten but when the orders of partition function increase the strengths of multifractal increase the singular spectrums become rougher and the general hurst exponents decrease these results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation

strong converse for identification via quantum channels we present a simple proof of the strong converse for identification via discrete memoryless quantum channels based on a novel covering lemma the new method is a generalization to quantum communication channels of ahlswede s 1979 1992 approach to classical channels it involves a development of explicit large deviation estimates to the case of random variables taking values in self adjoint operators on a hilbert space this theory is presented separately in an appendix and we illustrate it by showing its application to quantum generalizations of classical hypergraph covering problems

on the relationship between the hurst exponent the ratio of the mean square successive difference to the variance and the number of turning points abstract the long range dependence of the fractional brownian motion fbm fractional gaussian noise fgn and differentiated fgn dfgn is described by the hurst exponent h considering the realizations of these three processes as time series they might be described by their statistical features such as half of the ratio of the mean square successive difference to the variance a and the number of turning points t this paper investigates the relationships between a and h and between t and h it is found numerically that the formulae a h a e b h in case of fbm and a h a b h c for fgn and dfgn describe well the a h relationship when t h is considered no simple formula is found and it is empirically found that among polynomials the fourth and second order description applies best the most relevant finding is that when plotted in the space of a t the three process types form separate branches hence it is examined whether a and t may serve as hurst exponent indicators some real world data stock market indices sunspot numbers chaotic time series are analyzed for this purpose and it is found that the h s estimated using the h a relations expressed as inverted a h functions are consistent with the h s extracted with the well known wavelet approach this allows to efficiently estimate the hurst exponent based on fast and easy to compute a and t given that the process type fbm fgn or dfgn is correctly classified beforehand finally it is suggested that the a h relation for fgn and dfgn might be an exact shifted 3 2 power law

empirical distributions of chinese stock returns at different microscopic timescales abstract we study the distributions of event time returns and clock time returns at different microscopic timescales using ultra high frequency data extracted from the limit order books of 23 stocks traded in the chinese stock market in 2003 we find that the returns at the one trade timescale obey the inverse cubic law for larger timescales 2 32 trades and 1 5 min the returns follow the student distribution with power law tails with the decrease in timescale the tail becomes fatter which is consistent with the variational theory in turbulence