model categories of diagram spectra working in the category mathcal t of based spaces we give the basic theory of diagram spaces and diagram spectra these are functors mathcal d longrightarrow mathcal t for a suitable small topological category mathcal d when mathcal d is symmetric monoidal there is a smash product that gives the category of mathcal d spaces a symmetric monoidal structure examples include begin enumerate item prespectra as defined classically item symmetric spectra as defined by jeff smith item orthogonal spectra a coordinate free analogue of symmetric spectra with symmetric groups replaced by orthogonal groups in the domain category item gamma spaces as defined by graeme segal item mathcal w spaces an analogue of gamma spaces with finite sets replaced by finite cw complexes in the domain category end enumerate we construct and compare model structures on these categories with the caveat that gamma spaces are always connective these categories and their simplicial analogues are quillen equivalent and their associated homotopy categories are equivalent to the classical stable homotopy category monoids in these categories are strict ring spectra often the subcategories of ring spectra module spectra over a ring spectrum and commutative ring spectra are also model categories when this holds the respective categories of ring and module spectra are quillen equivalent and thus have equivalent homotopy categories this allows interchangeable use of these categories in applications 2000 mathematics subject classification primary 55p42 secondary 18a25 18e30 55u35

symmetric powers in abstract homotopy categories abstract we study symmetric powers in the homotopy categories of abstract closed symmetric monoidal model categories in both unstable and stable settings as an outcome we prove that symmetric powers preserve the nisnevich and etale homotopy type in the unstable and stable motivic homotopy theories of schemes over a base more precisely if f is a weak equivalence of motivic spaces or a weak equivalence between positively cofibrant motivic spectra with respect to the nisnevich or etale topology then all symmetric powers sym n f are weak equivalences too this gives left derived symmetric powers in the corresponding motivic homotopy categories of schemes over a base which aggregate into a categorical structures on these categories

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

codes based on a trellis cut set transformation i rotationally invariant codes let a trellis section spl tscr generate a trellis code spl cscr we study two trellis sections based on spl tscr a cut set trellis section spl tscr sub cs and a differential encoder trellis section spl tscr sub de we show that spl tscr can be transformed to a cut set trellis section spl tscr sub cs which is equivalent to spl tscr in the sense that both spl tscr and spl tscr sub cs generate spl cscr and both spl tscr and spl tscr sub cs have the same decoding complexity a differential encoder trellis section is equivalent to the trellis section obtained by following spl tscr with a differential encoder it is shown that both spl tscr sub cs and spl tscr sub de have inverse transform trellis sections a differential encoder trellis section generates a rotationally invariant ri code in a particularly simple and straightforward way but an ri code need not have a differential encoder trellis section however for all of the ri codes examined here we show that the cut set trellis section can be arranged into a differential encoder trellis section this means that these codes can be decomposed into an encoder followed by a differential encoder further we show that when spl tscr is formed using a linear binary convolutional encoder and a mapping by set partitioning then spl tscr followed by a differential encoder gives an ri code which in some cases is as good as the best previously known codes after applying the inverse transform to spl tscr sub de

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

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

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

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

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

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

volatility aggregation intensity energy futures series on stochastic finite range exclusion dynamics abstract the stochastic finite range exclusion process one of statistical physics systems is introduced to construct a new agent based financial price model to study the mechanism of market dynamics a novel volatility aggregation intensity vai time series describing the fluctuation aggregation intensity of the volatility series is developed for further investigating the nonlinear volatility behaviors in energy markets for studying the proposed vai series and the proposed price model the new york mercantile exchange energy futures data is selected and analyzed further cross correlation analysis auto correlation analysis with multiscale and multifractal detrended fluctuation analysis are applied to analyze the correlation volatility clustering and multifractal natures of the vai time series the empirical results show that the proposed model has the parallel behaviors with the authentic markets indicating that it is rational and available the new concept of vai series is of great value and can enrich the study of volatility behaviors in energy markets to some extent

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

detrended fluctuation analysis for fractals and multifractals in higher dimensions one dimensional detrended fluctuation analysis dfa and multifractal detrended fluctuation analysis mfdfa are widely used in the scaling analysis of fractal and multifractal time series because they are accurate and easy to implement in this paper we generalize the one dimensional dfa and mfdfa to higher dimensional versions the generalization works well when tested with synthetic surfaces including fractional brownian surfaces and multifractal surfaces the two dimensional mfdfa is also adopted to analyze two images from nature and experiment and nice scaling laws are unraveled

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

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

transitions between superstatistical regimes validity breakdown and applications abstract superstatistics is a widely employed tool of non equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems yet its canonical formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data here we show that a multi scale generalization of the superstatistics paradigm is more versatile allowing to address such pertinent issues as transmutation of statistics or inter scale stochastic behavior to put some flesh on the bare bones we provide a numerical evidence for a transition between two superstatistics regimes by analyzing high frequency minute tick data for share price returns of seven selected companies salient issues such as breakdown of superstatistics in fractional diffusion processes or connection with brownian subordination are also briefly discussed

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

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

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