detrended fluctuation analysis made flexible to detect range of cross correlated fluctuations the detrended cross correlation coefficient dcca has recently been proposed to quantify the strength of cross correlations on different temporal scales in bivariate nonstationary time series it is based on the detrended cross correlation and detrended fluctuation analyses dcca and dfa respectively and can be viewed as an analog of the pearson coefficient in the case of the fluctuation analysis the coefficient dcca works well in many practical situations but by construction its applicability is limited to detection of whether two signals are generally cross correlated without the possibility to obtain information on the amplitude of fluctuations that are responsible for those cross correlations in order to introduce some related flexibility here we propose an extension of dcca that exploits the multifractal versions of dfa and dcca multifractal detrended fluctuation analysis and multifractal detrended cross correlation analysis respectively the resulting new coefficient q not only is able to quantify the strength of correlations but also allows one to identify the range of detrended fluctuation amplitudes that are correlated in two signals under study we show how the coefficient q works in practical situations by applying it to stochastic time series representing processes with long memory autoregressive and multiplicative ones such processes are often used to model signals recorded from complex systems and complex physical phenomena like turbulence so we are convinced that this new measure can successfully be applied in time series analysis in particular we present an example of such application to highly complex empirical data from financial markets the present formulation can straightforwardly be extended to multivariate data in terms of the q dependent counterpart of the correlation matrices and then to the network representation

forward propagation of time evolving acoustic pressure formulation and investigation of the impulse response in time wavenumber domain the aim of this work is to continuously provide the acoustic pressure field radiated from nonstationary sources from the acquisition in the nearfield of the sources of a planar acoustic field which fluctuates in time the method gives instantaneous sound field with respect to time by convolving wavenumber spectra with impulse response and then inverse fourier transforming into space for each time step the quality of reconstruction depends on the impulse response which is composed of investigated parameters as transition frequency and propagation distance sampling frequency also affects errors of the practically discrete impulse response used for calculation to avoid aliasing the impulse response is low pass filtered with chebyshev or kaiser bessel filter another approach to implement the impulse response consists of applying an inverse fourier transform to the theoretical transfer function for propagation to estimate the performance of each processing method a simulation test involving several sou

coupling detrended fluctuation analysis for analyzing coupled nonstationary signals when many variables are coupled to each other a single case study could not give us thorough and precise information when these time series are stationary different methods of random matrix analysis and complex networks can be used but in nonstationary cases the multifractal detrended cross correlation analysis mf dxa method was introduced for just two coupled time series in this article we have extended the mf dxa to the method of coupling detrended fluctuation analysis cdfa for the case when more than two series are correlated to each other here we have calculated the multifractal properties of the coupled time series and by comparing cdfa results of the original series with those of the shuffled and surrogate series we can estimate the source of multifractality and the extent to which our series are coupled to each other we illustrate the method by selected examples from air pollution and foreign exchange rates

duality in entanglement assisted quantum error correction the dual of an entanglement assisted quantum error correcting eaqec code is defined from the orthogonal group of a simplified stabilizer group from the poisson summation formula this duality leads to the macwilliams identities and linear programming bounds for eaqec codes we establish a table of upper and lower bounds on the minimum distance of any maximal entanglement eaqec code with length up to 15 channel qubits

all the stabilizer codes of distance 3 we give necessary and sufficient conditions for the existence of stabilizer codes n k 3 of distance 3 for qubits n k log2 3n 1 n where n 1 if n 84m 1 3 1 2 or n 4m 2 1 3 1 2 3 for some integer m 1 and n 0 otherwise or equivalently a code n n r 3 exists if and only if n 4r 1 3 4r 1 3 n 1 2 3 for even r and n 8 4r 3 1 3 8 4 3 1 3 n 1 for odd r given an arbitrary length n we present an explicit construction for an optimal quantum stabilizer code of distance 3 that saturates the above bound

on the interplay between short and long term memory in the power law cross correlations setting abstract we focus on emergence of the power law cross correlations from processes with both short and long term memory properties in the case of correlated error terms the power law decay of the cross correlation function comes automatically with the characteristics of separate processes bivariate hurst exponent is then equal to an average of separate hurst exponents of the analyzed processes strength of short term memory has no effect on these asymptotic properties implications of these findings for the power law cross correlations concept are further discussed

dcca cross correlation coefficient quantifying level of cross correlation abstract in this paper a new coefficient is proposed with the objective of quantifying the level of cross correlation between nonstationary time series this cross correlation coefficient is defined in terms of the dfa method and the dcca method the implementation of this cross correlation coefficient will be illustrated with selected time series

the minimum distance problem for two way entanglement purification entanglement purification takes a number of noisy epr pairs 00 11 and processes them to produce a smaller number of more reliable pairs if this is done with only a forward classical side channel the procedure is equivalent to using a quantum error correcting code qecc we instead investigate entanglement purification protocols with two way classical side channels 2 epps for finite block sizes in particular we consider the analog of the minimum distance problem for qeccs and show that 2 epps can exceed the quantum hamming bound and the quantum singleton bound we also show that 2 epps can achieve the rate k n 1 t n log sub 2 3 h t n o 1 n asymptotically reaching the quantum hamming bound where the epp produces at least k good pairs out of n total pairs with up to t arbitrary errors and h x xlog sub 2 x 1 x log sub 2 1 x is the usual binary entropy in contrast the best known lower bound on the rate of qeccs is the quantum gilbert varshamov bound k n spl ges 1 2t n log sub 2 3 h 2t n indeed in some regimes the known upper bound on the asymptotic rate of good qeccs is strictly below our lower bound on the achievable rate of 2 epps

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

nonbinary quantum codes we present several results on quantum codes over general alphabets that is in which the fundamental units may have more than two states in particular we consider codes derived from finite symplectic geometry assumed to have additional global symmetries from this standpoint the analogs of calderbank shor steane codes and of gf 4 linear codes turn out to be special cases of the same construction this allows us to construct families of quantum codes from certain codes over number fields in particular we get analogs of quadratic residue codes including a single error correcting code encoding one letter in five for any alphabet size we also consider the problem of fault tolerant computation through such codes generalizing ideas of gottesman see phys rev a vol 57 no 1 p127 37 1998

on the macwilliams identity for classical and quantum convolutional codes the weight generating functions associated with convolutional codes ccs are based on state space realizations or the weight adjacency matrices wams the macwilliams identity for ccs on the wams was first established by gluesing luerssen and schneider in the case of minimal encoders and generalized by forney we consider this problem in the viewpoint of constraint codes and obtain a simple and direct proof of this macwilliams identity in the case of minimal encoders for our purpose we choose a different representation for the exact weight generating function ewgf of a block code by defining it as a linear combination of orthonormal vectors in dirac bra ket notation this representation provides great flexibility so that general split weight generating functions and their macwilliams identities can be easily obtained from the macwilliams identity for ewgfs as a result we also obtain the macwilliams identity for the input parity wams of a systematic convolutional code and its dual finally paralleling the development of the classical case we establish the macwilliams identity for quantum ccs

non linear approach to study the dynamics of neurodegenerative diseases by multifractal detrended cross correlation analysis a quantitative assessment on gait disease abstract this paper studies the human gait pattern of normal people and patients suffering from parkinson s disease using the mfdxa multifractal detrended cross correlation analysis methodology the auto correlation and cross correlation of the time series of the total force under the left foot and right foot were studied the study reveals that the degree of multifractality w and degree of correlation are generally more for normal patients than the diseased set it is also observed that the values of w and are nearly same for left foot and right it is also observed that the study of autocorrelation alone is not sufficient cross correlations should also be studied to get a better concept of neurodegenerative diseases

nonbinary stabilizer codes over finite fields one formidable difficulty in quantum communication and computation is to protect information carrying quantum states against undesired interactions with the environment to address this difficulty many good quantum error correcting codes have been derived as binary stabilizer codes fault tolerant quantum computation prompted the study of nonbinary quantum codes but the theory of such codes is not as advanced as that of binary quantum codes this paper describes the basic theory of stabilizer codes over finite fields the relation between stabilizer codes and general quantum codes is clarified by introducing a galois theory for these objects a characterization of nonbinary stabilizer codes over fq in terms of classical codes over fq 2 is provided that generalizes the well known notion of additive codes over f4 of the binary case this paper also derives lower and upper bounds on the minimum distance of stabilizer codes gives several code constructions and derives numerous families of stabilizer codes including quantum hamming codes quadratic residue codes quantum melas codes quantum bose chaudhuri hocquenghem bch codes and quantum character codes the puncturing theory by rains is generalized to additive codes that are not necessarily pure bounds on the maximal length of maximum distance separable stabilizer codes are given a discussion of open problems concludes this paper

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

detrended cross correlation analysis consistently extended to multifractality we propose an algorithm multifractal cross correlation analysis mfcca which constitutes a consistent extension of the detrended cross correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross correlations between two time series our motivation for introducing this algorithm is that the already existing methods like multifractal extension have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross correlations when there are none the principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments furthermore we present a broad analysis of the model fractal stochastic processes as well as of the real world signals and show that mfcca is a robust and selective tool at the same time and therefore allows for a reliable quantification of the cross correlative structure of analyzed processes in particular it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized hurst exponent and the multifractal scaling parameter ensuremath lambda q this relation provides information about the character of potential multifractality in cross correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far by using examples of time series from the stock market we show that financial fluctuations typically cross correlate multifractally only for relatively large fluctuations whereas small fluctuations remain mutually independent even at maximum of such cross correlations finally we indicate possible utility of mfcca to study effects of the time lagged cross correlations

a semidefinite program for distillable entanglement we show that the maximum fidelity obtained by a positive partial transpose p p t distillation protocol is given by the solution to a certain semidefinite program this gives a number of new lower and upper bounds on p p t distillable entanglement and thus new upper bounds on 2 locally distillable entanglement in the presence of symmetry the semidefinite program simplifies considerably becoming a linear program in the case of isotropic and werner states using these techniques we determine the p p t distillable entanglement of asymmetric werner states and maximally correlated states we conclude with a discussion of possible applications of semidefinite programming to quantum codes and 1 local distillation

high performance single error correcting quantum codes for amplitude damping we construct families of high performance quantum amplitude damping codes all of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension one family is built from nonlinear error correcting codes for classical asymmetric channels with which we systematically construct quantum amplitude damping codes with parameters better than any prior construction known for any block length n 8 except n 2r 1 we generalize this construction to employ classical codes over gf 3 with which we numerically obtain better performing codes up to length 14 because the resulting codes are of the codeword stabilized cws type conceptually simple though potentially computationally expensive encoding and decoding circuits are available

on the units of bipartite entanglement is sixteen ounces of entanglement always equal to one pound in a good physical theory dimensionless quantities such as the ratio mp me of the mass of the proton to the mass of the electron do not depend on the system of units being used this paper demonstrates that one widely used method for defining measures of entanglement violates this principle specifically in this approach dimensionless ratios e e of entanglement measures may depend on what state is chosen as the basic unit of entanglement this observation leads us to suggest three novel approaches to the quantification of entanglement these approaches lead to unit free definitions for the entanglement of formation and the distillable entanglement and suggest natural measures of entanglement for multipartite systems we also show that the behaviour of one of these novel measures the entanglement of computation is related to some open problems in computational complexity

chaos based nonlinear analysis to study cardiovascular responses to changes in posture abstract cardiovascular responses to changes in posture have been the focus of numerous investigations in the past analysis of ecg and arterial blood pressure abp data for different postures obtained from physionet was done from a new perspective of analyzing nonlinear time series having multifractal features multifractal detrended fluctuation analysis mfdfa and also the cross correlation between ecg and bp with another technique multifractal detrended cross correlation analysis mfdxa reveals ecg and abp time series of different subjects to be multifractal in nature with different degree of complexity different degree of auto and cross correlation for both ecg and abp signals is also observed for all subjects further significant information obtained from the cross correlation parameters obtained from mfdxa analysis is very important and relevant particularly for understanding the dynamics of orthostatic stress

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

acoustic imaging using under determined inverse approaches frequency limitations and optimal regularization this paper presents an acoustic imaging technique based on an under determined inverse approach the principle is to quantify an elementary source distribution on a source surface from acoustic pressure measurements the acoustic transfer system between elementary sources and microphone positions very under determined is then reduced to a square system using singular value decomposition the high frequency limitation of this method is studied as well as the regularization techniques that have to be used at low frequency a monte carlo simulation is carried out to compare the efficiency of generalized cross validation and l curve validation to choose the tikhonov regularization parameter a combined validation criterion is finally proposed to take advantage of both approaches

multifractal fourier detrended cross correlation analysis of traffic signals abstract multifractal detrended cross correlation analysis mf dxa has been developed to detect the long range power law cross correlation of considered signals in the presence of non stationarity however crossovers arising from extrinsic periodic trends make the scaling behavior difficult to analyze we introduce a fourier filtering method to eliminate the trend effects and systematically investigate the multifractal cross correlation of simulated and real traffic signals the crossover locations are found approximately corresponding to the periods of underlying trend traffic velocity on one road and flows on adjacent roads show strong cross correlation they also present weak multifractality after periodic trends are removed the traffic velocity and flow are cross correlated in opposite directions which is accordant to their actual evolution

mixed correlated arfima processes for power law cross correlations abstract we introduce a general framework of the mixed correlated arfima mc arfima processes which allows for various specifications of univariate and bivariate long term memory apart from a standard case when h x y 1 2 h x h y mc arfima also allows for processes with h x y 1 2 h x h y but also for long range correlated processes which are either short range cross correlated or simply correlated the major contribution of mc arfima lies in the fact that the processes have well defined asymptotic properties for h x h y and h x y which are derived in the paper so that the processes can be used in simulation studies comparing various estimators of the bivariate hurst exponent h x y moreover the framework allows for modeling of processes which are found to have h x y 1 2 h x h y

linear programming bounds for entanglement assisted quantum error correcting codes by split weight enumerators linear programming approaches have been applied to derive upper bounds on the size of classical and quantum codes in this paper we derive similar results for general quantum codes with entanglement assistance by considering a type of split weight enumerator after deriving the macwilliams identities for these enumerators we are able to prove algebraic linear programming bounds such as the singleton bound the hamming bound and the first linear programming bound our singleton bound and hamming bound are more general than the previous bounds for entanglement assisted quantum stabilizer codes in addition we show that the first linear programming bound improves the hamming bound when the relative distance is sufficiently large on the other hand we obtain additional constraints on the size of pauli subgroups for quantum codes which allow us to improve the linear programming bounds on the minimum distance of quantum codes of small length in particular we show that there is no 27 15 5 or 28 14 6 stabilizer code we also discuss the existence of some entanglement assisted quantum stabilizer codes with maximal entanglement as a result the upper and lower bounds on the minimum distance of maximal entanglement quantum stabilizer codes with length up to 20 are significantly improved

new asymptotic bounds for self dual codes and lattices we give an independent proof of the krasikov litsyn bound d n spl lsim 1 5 sup 1 4 2 on doubly even self dual binary codes the technique used a refinement of the mallows odlyzko sloane approach extends easily to other families of self dual codes modular lattices and quantum codes in particular we show that the krasikov litsyn bound applies to singly even binary codes and obtain an analogous bound for unimodular lattices we also show that in each case our bound differs from the true optimum by an amount growing faster than o spl radic n

cubic spline interpolation based time domain equivalent source method for modeling transient acoustic radiation abstract transient acoustic radiation from an arbitrarily shaped source is modeled using a cubic spline interpolation based time domain equivalent source method in the method the cubic spline interpolation function is introduced to approximate the equivalent source strengths in the time domain for establishing the relationships between the acoustic quantities in the field the normal acceleration on the source surface and the equivalent sources and the least squares solution of the equivalent source strengths at each time step is determined by an iterative solving process with the singular value decomposition technique the proposed method has the abilities of calculating the acoustic quantities directly in the time domain and applying to arbitrarily shaped sources numerical examples of calculating the transient acoustic fields from a baffled planar piston and an impulsively accelerating sphere demonstrate that the proposed method can model the transient acoustic radiation very well the experimental results also further verify the validity of the proposed method

a wave vector time domain method of forward projecting time dependent pressure fields a wave vector time domain k t method of forward projecting time dependent pressure fields from complex vibrators is developed using space time fourier transform methods axisymmetric fields are included as a special case of the general formulation in which a pressure field at one plane can be forward projected to other planes in brief a wave vector time domain representation of the field at one plane is forward projected via a temporal convolution with a wave vector time domain impulse response that is dependent on the projection distance the projected field is then obtained via the use of an inverse spatial fourier transform a numerical study of the method illustrates the accuracy of the approach when implemented using fast fourier transform fft algorithms the forward projections of simulated pressure fields from a planar ultrasonic transducer are shown to be in excellent agreement with corresponding results from the use of a time domain impulse response method

multifractal detrended cross correlation analysis of sunspot numbers and river flow fluctuations abstract we use the detrended cross correlation analysis dcca to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators specifically rivers represented by river flow fluctuation for daugava holston nolichucky and french broad rivers the multifractal detrended cross correlation analysis mf dxa shows that there exist some crossovers in the cross correlation fluctuation function versus time scale of the river flow and sunspot series one of these crossovers corresponds to the well known cycle of solar activity demonstrating a universal property of the mentioned rivers the scaling exponent given by dcca for original series at intermediate time scale 12 24 s 130 months is 1 17 0 04 which is almost similar for all underlying rivers at 1 confidence interval showing the second universal behavior of river runoffs to remove the sinusoidal trends embedded in data sets we apply the singular value decomposition svd method our results show that there exists a long range cross correlation between the sunspot numbers and the underlying streamflow records the magnitude of the scaling exponent and the corresponding cross correlation exponent are 0 76 0 85 and 0 30 0 48 respectively different values for scaling and cross correlation exponents may be related to local and external factors such as topography drainage network morphology human activity and so on multifractal cross correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series in addition the empirical relation between scaling exponent derived by dcca and detrended fluctuation analysis dfa h sun h river 2 is confirmed

modeling long range cross correlations in two component arfima and fiarch processes we investigate how simultaneously recorded long range power law correlated multivariate signals cross correlate to this end we introduce a two component arfima stochastic process and a two component fiarch process to generate coupled fractal signals with long range power law correlations which are at the same time long range cross correlated we study how the degree of cross correlations between these signals depends on the scaling exponents characterizing the fractal correlations in each signal and on the coupling between the signals our findings have relevance when studying parallel outputs of multiple component of physical physiological and social systems

two infinite families of nonadditive quantum error correcting codes we construct explicitly two infinite families of genuine nonadditive 1 error correcting quantum codes and prove that their coding subspaces are 50 larger than those of the optimal stabilizer codes of the same parameters via the linear programming bound all these nonadditive codes can be characterized by a stabilizer like structure and thus their encoding circuits can be designed in a straightforward manner

quantum error detection i statement of the problem this paper is devoted to the problem of error detection with quantum codes we show that it is possible to give a consistent definition of the undetected error event to prove this we examine possible problem settings for quantum error detection our goal is to derive a functional that describes the probability of undetected error under natural physical assumptions concerning transmission with error detection with quantum codes we discuss possible transmission protocols with stabilizer and unrestricted quantum codes the set of results proved in the paper shows that in all the cases considered the average probability of undetected error for a given code is essentially given by one and the same function of its weight enumerators we examine polynomial invariants of quantum codes and show that coefficients of rains s see ibid vol44 p 1388 94 1998 unitary weight enumerators are known for classical codes under the name of binomial moments of the distance distribution as in the classical situation these enumerators provide an alternative expression for the probability of undetected error

dcca cross correlation coefficient differentiation theoretical and practical approaches abstract we propose in this paper to establish a well defined relationship between d f a the long range auto correlation exponent and d c c a the long range cross correlation exponent respectively described by the dfa and dcca methods this relationship will be accomplished theoretically by differentiating the dcca cross correlation coefficient d c c a n also for some specific times series we apply this theory in order to establish its validity

regularization methods for near field acoustical holography the reconstruction of the pressure and normal surface velocity provided by near field acoustical holography nah from pressure measurements made near a vibrating structure is a linear ill posed inverse problem due to the existence of strongly decaying evanescentlike waves regularization provides a technique of overcoming the ill posedness and generates a solution to the linear problem in an automated way we present four robust methods for regularization the standard tikhonov procedure along with a novel improved version landweber iteration and the conjugate gradient approach each of these approaches can be applied to all forms of interior or exterior nah problems planar cylindrical spherical and conformal we also study two parameter selection procedures the morozov discrepancy principle and the generalized cross validation which are crucial to any regularization theory in particular we concentrate here on planar and cylindrical holography these forms of nah which rely on the discrete fourier transform are important due to their popularity and to their tremendous computational speed in order to use regularization theory for the separable geometry problems we reformulate the equations of planar cylindrical and spherical nah into an eigenvalue problem the resulting eigenvalues and eigenvectors couple easily to regularization theory which can be incorporated into the nah software with little sacrifice in computational speed the resulting complete automation of the nah algorithm for both separable and nonseparable geometries overcomes the last significant hurdle for nah

polynomial invariants of quantum codes the weight enumerators shor and laflamme 1997 of a quantum code are quite powerful tools for exploring its structure as the weight enumerators are quadratic invariants of the code this suggests the consideration of higher degree polynomial invariants we show that the space of degree k invariants of a code of length n is spanned by a set of basic invariants in one to one correspondence with s sub k sup n we then present a number of equations and inequalities in these invariants in particular we give a higher order generalization of the shadow enumerator of a code and prove that its coefficients are nonnegative we also prove that the quartic invariants of a 4 4 2 sub 2 code are uniquely determined an important step in a proof that any 4 4 2 sub 2 code is additive rains 1999

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

the need for structure in quantum ldpc codes the existence of quantum ldpc codes with minimal distance scaling linearly in the number of qubits is a central open problem in quantum information despite years of research good quantum ldpc codes are not known to exist but at the very least it is known they cannot be defined on very regular topologies like low dimensional grids in this work we establish a complementary result showing that good quantum css codes which are sparsely generated require structure in the local terms that constrain the code space so as not to be too random in a well defined sense to show this we prove a weak converse to a theorem of krasikov and litsyn on weight distributions of classical codes due to which may be of independent interest subspaces for which the distribution of weights in the dual space is approximately binomial have very few codewords of low weight tantamount to having a non negligible approximate minimal distance while they may not have a large minimal non zero weight they still have very few words of low hamming weight

instantaneous bayesian regularization applied to real time near field acoustic holography real time near field acoustic holography rt nah is used to recover non stationary sound sources using a planar microphone array direct propagation is described by the convolution of the wavenumber spectrum of the source under study with a known impulse response the deconvolution operation is achieved by a singular value decomposition of the propagator and tikhonov regularization is performed to stabilize the solution the inverse problem has an innate ill posed characteristic and the regularization process is the key factor in obtaining acceptable results the purpose of this paper is to present the instantaneous regularization process applied to rt nah method bayesian estimation of the regularization parameter is introduced from prior knowledge of the problem the computation of the regularization parameter is updated for each block of constant time interval allowing one to take into account the fluctuating properties of the sound field the superiority of bayesian regularization compared to state of the art methods is observed numerically and experimentally for reconstruction of non stationary sources rt nah is also enhanced to allow the reconstruction of long signals updating the regularization parameter accordingly to the fluctuations of the snr is revealed to be a necessary effort to reconstruct highly non stationary sources

parallel quantum computation and quantum codes we study the class qnc of efficient parallel quantum circuits the quantum analog of nc we exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth including circuits for encoding and decoding standard quantum error correcting codes or more generally any circuit consisting of controlled not gates controlled pi shifts and hadamard gates finally while we note the exact quantum fourier transform can be parallelized to linear depth we conjecture that neither it nor a simpler staircase circuit can be parallelized to less than this

monotonicity of the quantum linear programming bound the most powerful technique known at present for bounding the size of quantum codes of prescribed minimum distance is the quantum linear programming bound unlike the classical linear programming bound it is not immediately obvious that if the quantum linear programming constraints are satisfiable for dimension k then the constraints can be satisfied for all lower dimensions we show that the quantum linear programming bound is monotonic in this sense and give an explicitly monotonic reformulation

price volume multifractal analysis and its application in chinese stock markets abstract an empirical research on chinese stock markets is conducted using statistical tools first the multifractality of stock price return series r i r i ln p t 1 ln p t and trading volume variation series v i v i ln v t 1 ln v t is confirmed using multifractal detrended fluctuation analysis furthermore a multifractal detrended cross correlation analysis between stock price return and trading volume variation in chinese stock markets is also conducted it is shown that the cross relationship between them is also found to be multifractal second the cross correlation between stock price p i and trading volume v i is empirically studied using cross correlation function and detrended cross correlation analysis it is found that both shanghai stock market and shenzhen stock market show pronounced long range cross correlations between stock price and trading volume third a composite index r based on price and trading volume is introduced compared with stock price return series r i and trading volume variation series v i r variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume finally we analyze the multifractal characteristics of r variation series before and after three financial events in china namely price limits reform of non tradable shares and financial crisis in 2008 in the whole period of sample to study the changes of stock market fluctuation and financial risk it is found that the empirical results verified the validity of r

a family of asymptotically good quantum codes based on code concatenation we explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer codes use quantum reed solomon codes and the inner codes use a set of special quantum codes in the field of quantum error correcting codes this is the first time that a family of asymptotically good quantum codes is derived from bad codes its occurrence supplies a gap in quantum coding theory

a nonadditive quantum code every good quantum error correcting code discovered thus far such as those known as stabilizer or additive codes has had the structure of an eigenspace of an abelian group generated by tensor products of pauli matrices in this letter we present the first example of a code that is better than any code of this type it encodes six states in five qubits and can correct the erasure of any single qubit

quantum codes of minimum distance two it is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2 thus it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize with this in mind we present a number of results on codes of minimum distance 2 we first compute the linear programming bound on the dimension of such a code then show that this bound can only be attained when the code either is of even length or is of length 3 or 5 we next consider questions of uniqueness showing that the optimal code of length 2 or 1 is unique implying that the well known one qubit in five single error correcting code is unique and presenting nonadditive optimal codes of all greater even lengths finally we compute the full automorphism group of the more important distance 2 codes allowing us to determine the full automorphism group of any gf 4 linear code

source identification system based on the time domain nearfield equivalence source imaging fundamental theory and implementation abstract a nearfield equivalence source imaging nesi technique is proposed to identify locations and strengths of noise sources the nesi is based on the time domain formulation that applies not only to stationary but also a transient noise multichannel inverse filters are designed using the least square optimization tikhonov regularization is called for to mitigate the ill posedness inherent in the underdetermined model matching problem the design parameters such as array aperture microphone spacing focal point spacing and distance of projection have profound impact on the resulting sound image resolution the distance of reconstruction dor is selected according to the condition number of the propagation matrix a windowing design is also suggested to cope with boundary defocusing problem beam pattern is calculated for the inverse filters with window design in addition a modified approach based on focal point points is devised to avoid the singularity problem in reconstructing sound images the multichannel inverse filters are implemented in light of a highly efficient state space minimal realization technique the nesi is applicable to one dimensional 1d linear array two dimensional 2d rectangular array and even other arrays of irregular geometries as indicated by the simulation results the proposed nesi technique proves effective in the identification of noise sources

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

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

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

shadow bounds for self dual codes conway and sloane 1990 have previously given an upper bound on the minimum distance of a singly even self dual binary code using the concept of the shadow of a self dual code we improve their bound finding that the minimum distance of a self dual binary code of length n is at most 4 n 24 4 except when n mod 24 22 when the bound is 4 n 24 6 we also show that a code of length a multiple of 24 meeting the bound cannot be singly even the same technique gives similar results for additive codes over gf 4 relevant to quantum coding theory

reconstruction of nonstationary sound fields based on the time domain plane wave superposition method a time domain plane wave superposition method is proposed to reconstruct nonstationary sound fields in this method the sound field is expressed as a superposition of time convolutions between the estimated time wavenumber spectrum of the sound pressure on a virtual source plane and the time domain propagation kernel at each wavenumber by discretizing the time convolutions directly the reconstruction can be carried out iteratively in the time domain thus providing the advantage of continuously reconstructing time dependent pressure signals in the reconstruction process the tikhonov regularization is introduced at each time step to obtain a relevant estimate of the time wavenumber spectrum on the virtual source plane because the double infinite integral of the two dimensional spatial fourier transform is discretized directly in the wavenumber domain in the proposed method it does not need to perform the two dimensional spatial fast fourier transform that is generally used in time domain holography and real time near field acoustic holography and therefore it avoids some errors associated with the two dimensional spatial fast fourier transform in theory and makes possible to use an irregular microphone array the feasibility of the proposed method is demonstrated by numerical simulations and an experiment with two speakers

quantum shadow enumerators in a previous paper shor and laflamme see phys rev lett vol 78 p 1600 02 1997 define two weight enumerators for quantum error correcting codes connected by a macwilliams 1977 transform and use them to give a linear programming bound for quantum codes we extend their work by introducing another enumerator based on the classical theory of shadow codes that tightens their bounds significantly in particular nearly all of the codes known to be optimal among additive quantum codes codes derived from orthogonal geometry can be shown to be optimal among all quantum codes we also use the shadow machinery to extend a bound on additive codes to general codes obtaining as a consequence that any code of length can correct at most n 1 6 errors

communicating over adversarial quantum channels using quantum list codes in this correspondence we study quantum communication in the presence of adversarial noise in this setting communicating with perfect fidelity requires a quantum code of bounded minimum distance for which the best known rates are given by the quantum gilbert varshamov qgv bound asking only for arbitrarily high fidelity and letting the sender and receiver use a secret key of length logarithmic in the number of qubits sent we find a dramatic improvement over the qgv rates in fact our protocols allow high fidelity transmission at noise levels for which perfect fidelity is impossible to achieve such rates we introduce fully quantum list codes which may be of independent interest

regularization for improving the deconvolution in real time near field acoustic holography near field acoustic holography is a measuring process for locating and characterizing stationary sound sources from measurements made by a microphone array in the near field of the acoustic source plane a technique called real time near field acoustic holography rt nah has been introduced to extend this method in the case of nonstationary sources this technique is based on a formulation which describes the propagation of time dependent sound pressure signals on a forward plane using a convolution product with an impulse response in the time wavenumber domain thus the backward propagation of the pressure field is obtained by deconvolution taking the evanescent waves into account in rt nah improves the spatial resolution of the solution but makes the deconvolution problem ill posed and often yields inappropriate solutions the purpose of this paper is to focus on solving this deconvolution problem two deconvolution methods are compared one uses a singular value decomposition and a standard tikhonov regularization and the other one is based on optimum wiener filtering a simulation involving monopoles driven by nonstationary signals demonstrates by means of objective indicators the accuracy of the time dependent reconstructed sound field the results highlight the advantage of using regularization and particularly in the presence of measurement noise

quantum weight enumerators in a recent paper shor and laflamme see phys rev lett vol 78 p 1600 2 1997 defined two weight enumerators for quantum error correcting codes connected by a macwilliams transform and used them to give a linear programming bound for quantum codes we introduce two new enumerators which while much less powerful at producing bounds are useful tools nonetheless the new enumerators are connected by a much simpler duality transform clarifying the duality between shor and laflamme s enumerators we also use the new enumerators to give a simpler condition for a quantum code to have specified minimum distance and to extend the enumerator theory to codes with block size greater than 2

forward projection of transient sound pressure fields radiated by impacted plates using numerical laplace transform forward propagation of the transient sound pressure radiated by an impacted plate is presented it is shown that direct and inverse time domain discrete fourier transforms involved in fourier transform based near field acoustical holography nah lead to aliasing errors in the reconstructed time signals adding trailing zeros to the initial time signals is an inefficient way to reduce time aliasing errors hence the numerical laplace transform is introduced and a fourier transform based transient nah tnah approach is formulated an error measure is introduced to compare both nah and tnah with respect to the propagation distance and the location of the observation point in the projection plane the percentage of error with tnah is reduced by more than a factor of 10 without adding trailing zeros to the initial signals simulation results are validated experimentally using a free plexiglas plate impacted at its center

a bayesian approach to sound source reconstruction optimal basis regularization and focusing the reconstruction of acoustical sources from discrete field measurements is a difficult inverse problem that has been approached in different ways classical methods beamforming near field acoustical holography inverse boundary elements wave superposition equivalent sources etc all consist implicitly or explicitly in interpolating the measurements onto some spatial functions whose propagation are known and in reconstructing the source field by retropropagation this raises the fundamental question as whether for a given source topology and array geometry there exists an optimal interpolation basis which minimizes the reconstruction error this paper provides a general answer to this question by proceeding from a bayesian formulation that is ideally suited to combining information of physical and probabilistic natures the main findings are the followings 1 the optimal basis functions are the m eigen functions of a specific continuous discrete propagation operator with m being the number of microphones in the array 2 the a priori inclusion of spatial information on the source field causes super resolution according to a phenomenon coined bayesian focusing 3 the approach is naturally endowed with an internal regularization mechanism and results in a robust regularization criterion with no more than one minimum 4 it admits classical methods as particular cases

can the bivariate hurst exponent be higher than an average of the separate hurst exponents abstract in this note we investigate possible relationships between the bivariate hurst exponent h x y and an average of the separate hurst exponents 1 2 h x h y we show that two cases are well theoretically founded these are the cases when h x y 1 2 h x h y and h x y 1 2 h x h y however we show that the case of h x y 1 2 h x h y is not possible regardless of stationarity issues further discussion of the implications is provided as well together with a note on the finite sample effect

a new upper bound on the minimal distance of self dual codes it is shown that the minimal distance d of a binary self dual code of length n or 74 is at most 2 n 6 10 this bound is a consequence of some new conditions on the weight enumerator of a self dual code obtained by considering a particular translate of the code called its shadow these conditions also enable one to find the highest possible minimal distance of a self dual code for all n or 60 to show that self dual codes with d or 22 with d or 8 exist precisely for n 24 32 and n or 26 and with d or 10 exist precisely for n or 46 and to show that there are exactly eight self dual codes of length 32 with d 8 several of the self dual codes of length 34 have trivial group this appears to be the smallest length where this can happen