information theoretic determination of minimax rates of convergence we present some general results determining minimax bounds on statistical risk for density estimation based on certain information theoretic considerations these bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence

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

a simpler approach to matrix completion this paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix these results improve on prior work by candes and recht 2009 candes and tao 2009 and keshavan et al 2009 the reconstruction is accomplished by minimizing the nuclear norm or sum of the singular values of the hidden matrix subject to agreement with the provided entries if the underlying matrix satisfies a certain incoherence condition then the number of entries required is equal to a quadratic logarithmic factor times the number of parameters in the singular value decomposition the proof of this assertion is short self contained and uses very elementary analysis the novel techniques herein are based on recent work in quantum information theory

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

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

choosing parameters for renyi and tsallis entropies within a two dimensional multilevel image segmentation framework abstract in this work the effect of renyi and tsallis entropies parameters on the image segmentation quality within a two dimensional multilevel thresholding framework is assessed and analyzed the problems of automatically tuning entropy s parameter and determining the optimal thresholding values are solved in a single task this is done by using the quantum genetic algorithm qga the numerical experiments conducted on different types of images demonstrated that renyi and tsallis entropies perform approximately similarly and they are optimal when their parameters are null moreover it was shown that optimizing the entropy does not lead to maximize the peak signal to noise ratio psnr and the structural similarity ssim criteria then we have proved that these two criteria are not sufficiently consistent with human visual perception finally the comparative study performed on some synthetic and real images demonstrated the effectiveness of the proposed method

detecting switching points using asymmetric detrended fluctuation analysis abstract this work uses the concept of asymmetric detrended fluctuation analysis a dfa to investigate and characterize the occurrence of trend switching in financial series a dfa introduces two new roughness exponents h and h which differ from the usual one h by separately taking into account contributions to the fluctuations according to whether the local trend is respectively upward or downward the developed methodology requires the evaluation of local values of h t h t and h t by restricting the size of the largest window around the value t we show that h t and h t behave differently in the neighborhoods of switching points sps where trends change sign properly taken differences between shifted local values of h t h t and h t allow to identify and characterize sp s tests with weiertrasse functions isolated peaks and actual financial series are presented supporting the validity of the proposed method

statistical properties of the yuan exchange rate index abstract we choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after china s exchange rate system reform on the 21st july 2005 after dividing the time series into two parts according to the change in the yuan exchange rate regime in july 2008 we compare the statistical properties of the yuan exchange rate index during these two periods we find that the distribution of the two return series has the exponential form we also perform the detrending moving average analysis dma and the multifractal detrending moving average analysis mfdma the two periods possess different degrees of long range correlations and the multifractal nature is also unveiled in these two time series significant difference is found in the scaling exponents q and singularity spectra f of the two periods obtained from the mfdma analysis besides in order to detect the sources of multifractality shuffling and phase randomization procedures are applied to destroy the long range temporal correlation and fat tailed distribution of the yuan exchange rate index respectively we find that the fat tailedness plays a critical role in the sources of multifractality in the first period while the long memory is the major cause in the second period the results suggest that the change in china s exchange rate regime in july 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st july 2005

a new image segmentation method based on multifractal detrended moving average analysis abstract in order to segment and delineate some regions of interest in an image we propose a novel algorithm based on the multifractal detrended moving average analysis mf dma in this method the generalized hurst exponent h q is calculated for every pixel firstly and considered as the local feature of a surface and then a multifractal detrended moving average spectrum mf dms d h q is defined by the idea of box counting dimension method therefore we call the new image segmentation method mf dms based algorithm the performance of the mf dms based method is tested by two image segmentation experiments of rapeseed leaf image of potassium deficiency and magnesium deficiency under three cases namely backward 0 centered 0 5 and forward 1 with different q values the comparison experiments are conducted between the mf dms method and other two multifractal segmentation methods namely the popular mfs based and latest mf dfs based methods the results show that our mf dms based method is superior to the latter two methods the best segmentation result for the rapeseed leaf image of potassium deficiency and magnesium deficiency is from the same parameter combination of 0 5 and d h 10 when using the mf dms based method an interesting finding is that the d h 10 outperforms other parameters for both the mf dms based method with centered case and mf dfs based algorithms by comparing the multifractal nature between nutrient deficiency and non nutrient deficiency areas determined by the segmentation results an important finding is that the gray value s fluctuation in nutrient deficiency area is much severer than that in non nutrient deficiency area

multilevel image thresholding based on 2d histogram and maximum tsallis entropy a differential evolution approach multilevel thresholding amounts to segmenting a gray level image into several distinct regions this paper presents a 2d histogram based multilevel thresholding approach to improve the separation between objects recent studies indicate that the results obtained with 2d histogram oriented approaches are superior to those obtained with 1d histogram based techniques in the context of bi level thresholding here a method to incorporate 2d histogram related information for generalized multilevel thresholding is proposed using the maximum tsallis entropy differential evolution de a simple yet efficient evolutionary algorithm of current interest is employed to improve the computational efficiency of the proposed method the performance of de is investigated extensively through comparison with other well known nature inspired global optimization techniques such as genetic algorithm particle swarm optimization artificial bee colony and simulated annealing in addition the outcome of the proposed method is evaluated using a well known benchmark the berkley segmentation data set bsds300 with 300 distinct images

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

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

restricted strong convexity and weighted matrix completion optimal bounds with noise we consider the matrix completion problem under a form of row column weighted entrywise sampling including the case of uniformentrywise sampling as a special case we analyze the associated random observation operator and prove that with high probability it satisfies a form of restricted strong convexity with respect to weighted frobenius norm using this property we obtain as corollaries a number of error bounds on matrix completion in the weighted frobenius norm under noisy sampling and for both exact and near low rank matrices our results are based on measures of the spikiness and low rankness of matrices that are less restrictive than the incoherence conditions imposed in previous work our technique involves an m estimator that includes controls on both the rank and spikiness of the solution and we establish non asymptotic error bounds in weighted frobenius norm for recovering matrices lying with lq balls of bounded spikiness using information theoretic methods we show that no algorithm can achieve better estimates up to a logarithmic factor over these same sets showing that our conditions on matrices and associated rates are essentially optimal

efficiency and multifractality analysis of csi 300 based on multifractal detrending moving average algorithm abstract we apply the multifractal detrending moving average mfdma to investigate and compare the efficiency and multifractality of 5 min high frequency china securities index 300 csi 300 the results show that the csi 300 market becomes closer to weak form efficiency after the introduction of csi 300 future we find that the csi 300 is featured by multifractality and there are less complexity and risk after the csi 300 index future was introduced with the shuffling surrogating and removing extreme values procedures we unveil that extreme events and fat distribution are the main origin of multifractality besides we discuss the knotting phenomena in multifractality and find that the scaling range and the irregular fluctuations for large scales in the f q s vs s plot can cause a knot

a thresholding method based on two dimensional renyi s entropy in this paper we present a new thresholding technique based on two dimensional renyi s entropy the two dimensional renyi s entropy was obtained from the two dimensional histogram which was determined by using the gray value of the pixels and the local average gray value of the pixels this new method extends a method due to sahoo et al pattern recognition 30 1997 71 and includes a previously proposed global thresholding method due to abutaleb pattern recognition 47 1989 22 further our method extends a global thresholding method due to chang et al ieee trans image process 4 1995 370 to the two dimensional setting the effectiveness of the proposed method is demonstrated by using examples from the real world and synthetic images

the power of convex relaxation near optimal matrix completion this paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries this is known as the matrix completion problem and comes up in a great number of applications including the famous netflix prize and other similar questions in collaborative filtering in general accurate recovery of a matrix from a small number of entries is impossible but the knowledge that the unknown matrix has low rank radically changes this premise making the search for solutions meaningful this paper presents optimality results quantifying the minimum number of entries needed to recover a matrix of rank r exactly by any method whatsoever the information theoretic limit more importantly the paper shows that under certain incoherence assumptions on the singular vectors of the matrix recovery is possible by solving a convenient convex program as soon as the number of entries is on the order of the information theoretic limit up to logarithmic factors this convex program simply finds among all matrices consistent with the observed entries that with minimum nuclear norm as an example we show that on the order of nr log n samples are needed to recover a random n x n matrix of rank r by any method and to be sure nuclear norm minimization succeeds as soon as the number of entries is of the form nr polylog n

asymmetric multifractal detrending moving average analysis in time series of pm2 5 concentration abstract in this paper we propose the asymmetric multifractal detrending moving average analysis a mfdma method to explore the asymmetric correlation in non stationary time series the proposed method is applied to explore the asymmetric correlation of pm2 5 daily average concentration with uptrends or downtrends in china in addition shuffling and phase randomization procedures are applied to detect the sources of multifractality the results show that existences of asymmetric correlations and the asymmetric correlations are multifractal further the multifractal scaling behavior in the chinese pm2 5 is caused not only by long range correlation but also by fat tailed distribution but the major source of multifractality is fat tailed distribution

a dfa approach for assessing asymmetric correlations abstract here we propose a method based on detrended fluctuation analysis to investigate asymmetric correlations in nonstationary time series the aim is to show that for a certain range of time scales different scaling properties are found if signal trending is either positive and negative we illustrate the method by selected examples from physics and finance

analysis of clusters formed by the moving average of a long range correlated time series we analyze the stochastic function c n i ensuremath equiv y i ensuremath y n i where y i is a long range correlated time series of length n mathrm max and y n i ensuremath equiv 1 n ensuremath sum k 0 n ensuremath 1 y i ensuremath k is the moving average with window n we argue that c n i generates a stationary sequence of self affine clusters mathcal c with length mathcal l lifetime ensuremath tau and area s the length and the area are related to the lifetime by the relationships mathcal l ensuremath sim ensuremath tau ensuremath psi mathcal l and s ensuremath sim ensuremath tau ensuremath psi s where ensuremath psi mathcal l 1 and ensuremath psi s 1 h we also find that mathcal l ensuremath tau and s are power law distributed with exponents depending on h p mathcal l ensuremath sim mathcal l ensuremath ensuremath alpha p ensuremath tau ensuremath sim ensuremath tau ensuremath ensuremath beta and p s ensuremath sim s ensuremath ensuremath gamma with ensuremath alpha ensuremath beta 2 ensuremath h and ensuremath gamma 2 1 h these predictions are tested by extensive simulations on series generated by the midpoint displacement algorithm of assigned hurst exponent h ranging from 0 05 to 0 95 of length up to n mathrm max 2 21 and n up to 2 13

multi q pattern analysis a case study in image classification abstract this paper compares the effectiveness of the tsallis entropy over the classic boltzmann gibbs shannon entropy for general pattern recognition and proposes a multi q approach to improve pattern analysis using entropy a series of experiments were carried out for the problem of classifying image patterns given a dataset of 40 pattern classes the goal of our image case study is to assess how well the different entropies can be used to determine the class of a newly given image sample our experiments show that the tsallis entropy using the proposed multi q approach has great advantages over the boltzmann gibbs shannon entropy for pattern classification boosting image recognition rates by a factor of 3 we discuss the reasons behind this success shedding light on the usefulness of the tsallis entropy and the multi q approach

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

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

coupling detrended fluctuation analysis of the relationship between pm2 5 concentration and weather elements abstract pm2 5 pollution in china is getting worse the relationship between pm2 5 concentration and weather elements exhibits complex non linear feature therefore it is very important to study the sophisticated mathematical and nonlinear method about the relationship between pm2 5 concentration and weather elements coupling detrended fluctuation analysis cdfa method can reveal the multifractal properties of more than two series the coupled correlations between pm2 5 concentration and weather elements in hangzhou and guangzhou are explored by cdfa we find that coupled correlations are not only multifractal but also anti persistent compared with guangzhou hangzhou has stronger correlations both long range correlation and fat tailed distribution can cause the coupled multifractality and the long range correlation has a greater influence on the coupled multifractality in addition the coupling sensitivity degree csd y is used to study which weather element plays a key role in the change of pm2 5 concentration

exponential wavelet iterative shrinkage thresholding algorithm for compressed sensing magnetic resonance imaging it is beneficial for both hospitals and patients to accelerate mri scanning recently a new fast mri technique based on cs was proposed however the reconstruction quality and computation time of cs mri did not meet the standard of clinical use therefore we proposed a novel algorithm based on three successful components the sparsity of ewt the rapidness of fista and the excellent tuning in sista the proposed method was dubbed exponential wavelet iterative shrinkage threshold algorithm ewista experiments over four kinds of mr images brain ankle knee and adhd indicated that the proposed ewista showed better reconstruction performance than the state of the art algorithms such as fcsa ista fista sista and ewt ista moreover ewista was faster than ista and ewt ista but slightly slower than fcsa fista and sista