quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

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

free products of compact quantum groups we construct and study compact quantum groups from free products ofc algebras in this connection we discover two mysterious classes of natural compact quantum groups a u m anda o m thea u m s respectivelya o m s are non isomorphic to each other for differentm s and are not obtainable by the ordinary quantization method we also clarify some basic concepts in the theory of compact quantum groups

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

l 2 homology for von neumann algebras the aim of this paper is to introduce a notion of l homology in the context of von neumann algebras finding a suitable co homology theory for von neumann algebras has been a dream for several generations see kr71a kr71b jkr72 ss95 and references therein one s hope is to have a powerful invariant to distinguish von neumann algebras unfortunately little positive is known about the kadison ringrose cohomology h b m m except that it vanishes in many cases furthermore there does not seem to be a good connection between the bounded cohomology theory of a group and of the bounded cohomology of its von neumann algebra our interest in developing an l cohomology theory was revived by the introduction of lcohomology invariants in the field of ergodic equivalence relations in the paper of gaboriau gab02 his results in particular imply that l betti numbers 2 i of a discrete group are the same for measure equivalent groups i e for groups that can generate isomorphic ergodic measure preserving equivalence relations parallels between the worlds of von neumann algebras and measurable equivalence relations have been noted for a long time starting with the parallel between the work of murray and von neumann mvn and that of h dye dy thus there is hope that an invariant of a group that survives measure equivalence will survive also von neumann algebra equivalence i e will be an invariant of the von neumann algebra of the group the original motivation for our construction comes from the well understood analogy between the theory of ii1 factors and that of discrete groups based on the theory of correspondences con con94 this analogy has been remarkably efficient to transpose analytic properties such as amenability or property t from the group context to the factor context con80 cj and more recently in the breakthrough work of popa popa con03 we use the theory of correspondences together with the algebraic description of l betti numbers given by luck his definition involves the computation of the algebraic group homology with coefficients in the group von neumann algebra following the guiding idea that the category of bimodules over a von neumann algebra is the analogue of the category of modules over a group we are led to the following algebraic definition of l homology of a von neumann algebra m

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

algorithms of maximum likelihood data clustering with applications abstract we address the problem of data clustering by introducing an unsupervised parameter free approach based on maximum likelihood principle starting from the observation that data sets belonging to the same cluster share a common information we construct an expression for the likelihood of any possible cluster structure the likelihood in turn depends only on the pearson s coefficient of the data we discuss clustering algorithms that provide a fast and reliable approximation to maximum likelihood configurations compared to standard clustering methods our approach has the advantages that i it is parameter free ii the number of clusters need not be fixed in advance and iii the interpretation of the results is transparent in order to test our approach and compare it with standard clustering algorithms we analyze two very different data sets time series of financial market returns and gene expression data we find that different maximization algorithms produce similar cluster structures whereas the outcome of standard algorithms has a much wider variability

quantum deformation of lorentz group a one parameter quantum deformations l 2 ofsl 2 is introduced and investigated an analog of the iwasawa decomposition is proved the compact part of this decomposition coincides withs u 2 whereas the solvable part is identified as a pontryagin dual ofs u 2 it shows thats l 2 is the result of the dual version of drinfeld s double group construction applied tos u 2 the same construction applied to any compact quantum groupgc is discussed in detail in particular the explicit formulae for the haar measures on the pontryagin dualgd ofgc and on the double groupg are given we show that there exists remarkable 1 1 correspondence between representations ofg and bicovariant bimodules tensor bundles overgc the theory of smooth representations ofs l 2 is the same as that ofsl 2 clebsh gordon coefficients are however modified the corresponding tame bicovariant bimodules ons u 2 are classified an application to 4d differential calculus is presented the nonsmooth case is also discussed

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

orthogonal free quantum group factors are strongly 1 bounded abstract we prove that the orthogonal free quantum group factors l f o n are strongly 1 bounded in the sense of jung in particular they are not isomorphic to free group factors this result is obtained by establishing a spectral regularity result for the edge reversing operator on the quantum cayley tree associated to f o n and combining this result with a recent free entropy dimension rank theorem of jung and shlyakhtenko

detrending moving average based bivariate regression estimator in this work a detrending moving average dma based bivariate linear regression analysis method is proposed the method is combination of detrended moving average analysis and standard regression methodology which allows us to estimate the scale dependent regression coefficients for nonstationary and power law correlated time series by using synthetic simulations with error of estimation for different position parameter ensuremath theta of detrending windows we test our dma based bivariate linear regression algorithm and find that the centered detrending technique ensuremath theta 0 5 is of best performance which provides the most accurate estimates in addition the estimated regression coefficients are in good agreement with the theoretical values the center dma based bivariate linear regression estimator is applied to analyze the return series of shanghai stock exchange composite index the hong kong hangseng index and the nikkei 225 index the dependence among the asian stock market across timescales is confirmed furthermore two statistics based on the scale dependent t statistic and the partial detrending moving average cross correlation coefficient are used to demonstrate the significance of the dependence the scale dependent evaluation parameters also show that the dma based bivariate regression model can provide rich information than standard regression analysis

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

the full classification of orthogonal easy quantum groups we study easy quantum groups a combinatorial class of orthogonal quantum groups introduced by banica speicher in 2009 we show that there is a countable descending chain of easy quantum groups interpolating between bichon s free wreath product with the permutation group s n and a semi direct product of a permutation action of s n on a free product this reveals a series of new commutation relations interpolating between a free product construction and the tensor product furthermore we prove a dichotomy result saying that every hyperoctahedral easy quantum group is either part of our new interpolating series of quantum groups or belongs to a class of semi direct product quantum groups recently studied by the authors this completes the classification of easy quantum groups we also study combinatorial and operator algebraic aspects of the new interpolating series

the boundary of universal discrete quantum groups exactness and factoriality we study the c algebras and von neumann algebras associated with the universal discrete quantum groups they give rise to full prime factors and simple exact c algebras the main tool in our work is the study of an amenable boundary action yielding the akemann ostrand property finally this boundary can be identified with the martin or the poisson boundary of a quantum random walk

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

on the decomposition of generalized incomplete gamma functions with applications to fourier transforms abstract in this paper we introduce decomposition functions c x s x c x and s x of the generalized gamma functions these functions are found useful in the analytic study of the temperature distribution of a semi infinite solid with periodic boundary conditions and to the theory of fourier transforms several new identities involving the fourier transforms are investigated and some of the classical ones are recovered as special cases for numerical and scientific computations tabular and graphical representations of the functions c x and s x are also given

stochastic dynamical model for stock stock correlations we propose a model of coupled random walks for stock stock correlations the walks in the model are coupled via a mechanism that the displacement price change of each walk stock is activated by the price gradients over some underlying network we assume that the network has two underlying structures describing the correlations among the stocks of the whole market and among those within individual groups respectively each with a coupling parameter controlling the degree of correlation the model provides the interpretation of the features displayed in the distribution of the eigenvalues for the correlation matrix of real market on the level of time sequences we verify that such modeling indeed gives good fitting for the market data of us stocks

extended incomplete gamma functions with applications an extension of the generalized inverse gaussian density function is proposed analogous to a recent useful generalization of the incomplete gamma functions extensions of the generalized incomplete gamma functions are presented for which the usual properties and representations are naturally and simply extended several classical functions including abramowitz s functions dowson s integral function goodwin and stalon s function and astrophysical thermonuclear functions are proved to be special cases of these extensions in addition extended meijer g functions and fox s h functions are defined

strongly solid group factors which are not interpolated free group factors we give examples of non amenable infinite conjugacy classes groups with the haagerup property weakly amenable with constant cb 1 for which we show that the associated ii1 factors l are strongly solid i e the normalizer of any diffuse amenable subalgebra p subset l gamma generates an amenable von neumann algebra nevertheless for these examples of groups l is not isomorphic to any interpolated free group factor l ft for 1 t

free wreath product quantum groups the monoidal category approximation properties and free probability in this paper we find the fusion rules of the free wreath product quantum groups g sn for all compact matrix quantum groups of kac type g and n 4 this is based on a combinatorial description of the intertwiner spaces between certain generating representations of g sn the combinatorial properties of the intertwiner spaces in g sn allow us to obtain several probabilistic applications we prove also the monoidal equivalence between g sn and a compact quantum group whose dual is a discrete quantum subgroup of the free product g suq 2 for some 0 q 1 we obtain as a corollary certain stability results for the operator algebras associated with the free wreath products of quantum groups such as the acpap property and exactness

the connes embedding property for quantum group von neumann algebras for a compact quantum group g of kac type we study the existence of a haar trace preserving embedding of the von neumann algebra l g into an ultrapower of the hyperfinite ii 1 factor the connes embedding property for l g we establish a connection between the connes embedding property for l g and the structure of certain quantum subgroups of g and use this to prove that the ii 1 factors l o n and l u n associated to the free orthogonal and free unitary quantum groups have the connes embedding property for all n 4 as an application we deduce that the free entropy dimension of the standard generators of l o n equals 1 for all n 4 we also mention an application of our work to the problem of classifying the quantum subgroups of o n

examples of weakly amenable discrete quantum groups abstract we prove that the free orthogonal and free unitary quantum groups f o n and f u n are weakly amenable and that their cowling haagerup constant is equal to 1 this is achieved by estimating the completely bounded norm of the projections on the coefficients of irreducible representations of their compact duals an argument of monoidal equivalence then allows us to extend this result to quantum automorphism groups of finite spaces and even yields some examples of weakly amenable non unimodular discrete quantum groups with the haagerup property

extension of gamma beta and hypergeometric functions the main object of this paper is to present generalizations of gamma beta and hypergeometric functions some recurrence relations transformation formulas operation formulas and integral representations are obtained for these new generalizations

residually finite quantum group algebras abstract we show that provided n 3 the involutive hopf algebra a u n coacting universally on an n dimensional hilbert space has enough finite dimensional representations in the sense that every non zero element acts non trivially in some finite dimensional representation this implies that the discrete quantum group with group algebra a u n is maximal almost periodic i e it embeds in its quantum bohr compactification answering a question posed by p soltan in 21 we also prove analogous results for the involutive hopf algebra b u n coacting universally on an n dimensional hilbert space equipped with a non degenerate bilinear form

liberation of orthogonal lie groups abstract we show that under suitable assumptions we have a one to one correspondence between classical groups and free quantum groups in the compact orthogonal case we classify the groups under correspondence with the result that there are exactly 6 of them o n s n h n b n s n b n we investigate the representation theory aspects of the correspondence with the result that for o n s n h n b n this is compatible with the bercovici pata bijection finally we discuss some more general classification problems in the compact orthogonal case notably with the construction of a new quantum group

detrending moving average algorithm a closed form approximation of the scaling law abstract the hurst exponent h of long range correlated series can be estimated by means of the detrending moving average dma method the computational tool on which the algorithm is based is the generalized variance dma 2 1 n n i n n y i y n i 2 with y n i 1 n k 0 n y i k being the average over the moving window n and n the dimension of the stochastic series y i the ability to yield h relies on the property of dma 2 to vary as n 2 h over a wide range of scales e alessio a carbone g castelli v frappietro eur j phys b 27 2002 197 here we give a closed form proof that dma 2 is equivalent to c h n 2 h and provide an explicit expression for c h we furthermore compare the values of c h with those obtained by applying the dma algorithm to artificial self similar signals

hyperlinearity essentially free actions and l2 invariants the sofic property we prove that connes embedding conjecture holds for the von neumann algebras of sofic groups that is sofic groups are hyperlinear hence we provide some new examples of hyperlinearity we also show that the determinant conjecture holds for sofic groups as well we introduce the notion of essentially free actions and amenable actions and study their properties

detrended partial cross correlation analysis of two nonstationary time series influenced by common external forces when common factors strongly influence two power law cross correlated time series recorded in complex natural or social systems using detrended cross correlation analysis dcca without considering these common factors will bias the results we use detrended partial cross correlation analysis dpxa to uncover the intrinsic power law cross correlations between two simultaneously recorded time series in the presence of nonstationarity after removing the effects of other time series acting as common forces the dpxa method is a generalization of the detrended cross correlation analysis that takes into account partial correlation analysis we demonstrate the method by using bivariate fractional brownian motions contaminated with a fractional brownian motion we find that the dpxa is able to recover the analytical cross hurst indices and thus the multiscale dpxa coefficients are a viable alternative to the conventional cross correlation coefficient we demonstrate the advantage of the dpxa coefficients over the dcca coefficients by analyzing contaminated bivariate fractional brownian motions we calculate the dpxa coefficients and use them to extract the intrinsic cross correlation between crude oil and gold futures by taking into consideration the impact of the u s dollar index we develop the multifractal dpxa mf dpxa method in order to generalize the dpxa method and investigate multifractal time series we analyze multifractal binomial measures masked with strong white noises and find that the mf dpxa method quantifies the hidden multifractal nature while the multifractal dcca method fails

large deviation bounds for matrix brownian motion we prove large deviation bounds for the convergence of hermitian matrix valued brownian motion towards free brownian motion as a consequence we obtain upper and lower bounds on the microstates entropy introduced by voiculescu 24

detrended moving average partial cross correlation analysis on financial time series abstract cross correlations between nonlinear time series widely exist in complex systems it is of great importance to accurately measure the correlations between time series in this work we suggest a combination methodology of detrended moving average processing and partial cross correlation analysis to quantify the correlations between different time series which we call as detrended moving average partial cross correlation analysis d m p c c a this novel approach combines the advantages of detrended moving average processing and partial cross correlation analysis not only exploring power law cross correlations between two signals but removing underlying impacts of other signals on those two signals to demonstrate the advantages of this approach we carry out experiments with synthetic data generated by correlated processes and compare the performance of this measurement to traditional cross correlation techniques it is found that this method can reveal the real cross correlations between systems even when the indirect cross correlations established by other common factors exist then we go further study into the application of d m p c c a to financial time series in order to report its performance in stock markets and investigate cross correlations between different stock indices furthermore the rolling windows method is used in conjunction with d m p c c a to capture the changes of cross correlations between stock indices as time goes on we notice that there is a special period when d m p c c a coefficients between stock indices are obviously different from those of other periods

estimating long range dependence finite sample properties and confidence intervals abstract a major issue in financial economics is the behavior of asset returns over long horizons various estimators of long range dependence have been proposed even though some have known asymptotic properties it is important to test their accuracy by using simulated series of different lengths we test r s analysis detrended fluctuation analysis and periodogram regression methods on samples drawn from gaussian white noise the dfa statistics turns out to be the unanimous winner unfortunately no asymptotic distribution theory has been derived for this statistics so far we were able however to construct empirical i e approximate confidence intervals for all three methods the obtained values differ largely from heuristic values proposed by some authors for the r s statistics and are very close to asymptotic values for the periodogram regression method

the analogues of entropy and of fisher s information measure in free probability theory i analogues of the entropy and fisher information measure for random variables in the context of free probability theory are introduced monotonicity properties and an analogue of the cramer rao inequality are proved

detrending moving average cross correlation coefficient measuring cross correlations between non stationary series abstract in the paper we introduce a new measure of correlation between possibly non stationary series as the measure is based on the detrending moving average cross correlation analysis dmca we label it as the dmca coefficient d m c a with a moving average window length we analytically show that the coefficient ranges between 1 and 1 as a standard correlation does in the simulation study we show that the values of d m c a very well correspond to the true correlation between the analyzed series regardless the non stationarity level dependence of the newly proposed measure on other parameters correlation level moving average window length and time series length is discussed as well

topological generation and matrix models for quantum reflection groups abstract we prove that the von neumann algebras of quantum permutation groups and quantum reflection groups have the connes embedding property we do this by establishing several new topological generation results for the quantum permutation groups s n and the quantum reflection groups h n s we use these results to show that these quantum groups admit sufficiently many matrix models in particular all of these quantum groups have residually finite discrete duals and are in particular hyperlinear and certain flat matrix models for s n are inner faithful

paths in quantum cayley trees and l 2 cohomology abstract we study existence uniqueness and triviality of path cocycles in the quantum cayley graph of universal discrete quantum groups in the orthogonal case we find that the unique path cocycle is trivial in contrast with the case of free groups where it is proper in the unitary case it is neither bounded nor proper from this geometrical result we deduce the vanishing of the first l 2 betti number of a o i n