an efficient two step iterative method for solving a class of complex symmetric linear systems abstract in this paper a new two step iterative method called the two step parameterized tsp iteration method for a class of complex symmetric linear systems is developed we investigate its convergence conditions and derive the quasi optimal parameters which minimize the upper bound of the spectral radius of the iteration matrix of the tsp iteration method meanwhile some more practical ways to choose iteration parameters for the tsp iteration method are proposed furthermore comparisons of the tsp iteration method with some existing ones are given which show that the upper bound of the spectral radius of the tsp iteration method is smaller than those of the modified hermitian and skew hermitian splitting mhss the preconditioned mhss pmhss the combination method of real part and imaginary part cri and the parameterized variant of the fixed point iteration adding the asymmetric error pfpae iteration methods proposed recently inexact version of the tsp iteration itsp method and its convergence properties are also presented numerical experiments demonstrate that both tsp and itsp are effective and robust when they are used either as linear solvers or as matrix splitting preconditioners for the krylov subspace iteration methods and they have comparable advantages over some known ones for the complex symmetric linear systems

the congruence class of the solutions of some matrix equations the congruence class of a least square solution for the following matrix equations ax b a xa d axb dand axxb ef is presented also we derive necessary and sufficient conditions for the existence of a least square solution and present a general form of such solutions using the singular value decomposition svd and generalized singular value decomposition gsvd

generalized aor method for solving a class of generalized saddle point problems abstract in this paper by constructing appropriate splitting a generalized aor gaor method for solving a class of generalized saddle point problems has been presented and the convergence of the method is studied the numerical experiments results show the efficiency and robustness of the new method

a modified gpss method for non hermitian positive definite linear systems this paper is concerned with a modified version of the generalization of positive definite and skew hermitian splitting iteration mgpss to solve the non hermitian positive definite linear systems the theoretical analysis shows that the mgpss iteration method will converge unconditionally numerical examples are reported to confirm the efficiency of the proposed methods

surrogate testing of linear feedback processes with non gaussian innovations abstract surrogate testing is used widely to determine the nature of the process generating the given empirical sample in the present study the usefulness of phase randomized surrogates amplitude adjusted fourier transform and iterated amplitude adjusted fourier transform surrogates on statistical inference of linearly correlated noise with non gaussian innovations and their static invertible nonlinear transforms from their empirical samples are discussed existing surrogate testing procedures which retain the auto correlation function in the surrogates may not be appropriate in the presence of non gaussian innovations

alternating direction method for generalized sylvester matrix equation axb cyd e this paper presents alternating direction methods of multipliers for finding the solution the best approximate solution and the nonnegative solution of the generalized sylvester matrix equation axb cyd e where a b c d and e are given matrices of suitable sizes preliminary convergence properties of the proposed algorithms are given numerical experiments show that the proposed algorithms tend to deliver higher quality solutions with less iteration steps and less computing times than recent algorithms on the tested problems

probing the linearity and nonlinearity in dna sequences abstract in this paper we apply the principles of information theory that relate to the definition of nonlinear predictability which is a measure that describes both the linear and nonlinear components of a system by comparing this measure to a measure of linear predictability one can assess whether a given system has a strong linear or a strong nonlinear component this provides insights as to whether the system should be modeled by a nonlinear or a linear model we apply these ideas to dna sequences our results which extend previous results on this issue indicate that all dna sequences coding and noncoding exhibit strong nonlinear structure at the same time the results provide insights to understand dna structure and possible clues about evolutionary mechanisms

solving shifted linear systems with restarted gmres augmented with error approximations abstract in this paper we investigate a variant of the restarted gmres method for solving a series of large sparse linear systems restarting is carried out by augmenting krylov subspaces with some recently generated error approximations from the seed system the method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix vector multiplication per iteration compared with solving each added linear system separately the advantage of the new scheme is to lower down the overall cost of solving all added linear systems numerical experiments illustrate the efficiency of the acceleration strategy

fredholm determinants and the camassa holm hierarchy the equation of camassa and holm 2 2 is an approximate description of long waves in shallow water

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

extreme value statistics in records with long term persistence many natural records exhibit long term correlations characterized by a power law decay of the autocorrelation function c s ensuremath sim s ensuremath ensuremath gamma with time lag s and correlation exponent 0l ensuremath gamma l1 we study how the presence of such correlations affects the statistics of the extreme events i e the maximum values of the signal within time segments of the fixed duration r we find numerically that i the integrated distribution function of the maxima converges to a gumbel distribution for large r similar to uncorrelated signals ii the deviations for finite r depend on the initial distribution of the records and on their correlation properties iii the maxima series exhibit long term correlations similar to those of the original data and most notably iv the maxima distribution as well as the mean maxima significantly depend on the history in particular on the previous maximum the last item implies that conditional mean maxima and conditional maxima distributions with the value of the previous maximum as condition should be considered for an improved extreme event prediction we provide indications that this dependence of the mean maxima on the previous maximum occurs also in observational long term correlated records

iterative solutions of the generalized sylvester matrix equations by using the hierarchical identification principle abstract in this paper by extending the well known jacobi and gauss seidel iterations for ax b we study iterative solutions of matrix equations axb f and generalized sylvester matrix equations axb cxd f including the sylvester equation ax xb f as a special case and present a gradient based and a least squares based iterative algorithms for the solution it is proved that the iterative solution always converges to the exact solution for any initial values the basic idea is to regard the unknown matrix x to be solved as the parameters of a system to be identified and to obtain the iterative solutions by applying the hierarchical identification principle finally we test the algorithms and show their effectiveness using a numerical example

geometry of kdv 2 three examples let q be a 1 dimensional schroedinger operator with spectrum bounded from infinity by addition i mean a map of the form q q q 2d sup 2 1g e with qe lambdae lambda to the left of spec q and either integral sub infinity sup 0 e sup 2 or integral sub 0 sup infinity e sup 2 finite the additive class of q is obtained by composite addition and a subsequent closure it is a substitute for the kdv invariant manifold even if the individual kdv flows have no existence kdv 1 mckean 1987 suggested that the additive class of q is the same as its unimodular spectral class defined in terms of the 2 x 2 spectral weight df by fixing a the measure class of df and b the value of sqrt det df the present paper verifies this for 1 the scattering case 2 hill s case and 3 when the additive class is finite dimensional neumann case

what is a linear process abstract we argue that given even an infinitely long data sequence it is impossible with any test statistic to distinguish perfectly between linear and nonlinear processes including slightly noisy chaotic processes our approach is to consider the set of moving average linear processes and study its closure under a suitable metric we give the precise characterization of this closure which is unexpectedly large containing nonergodic processes which are poisson sums of independent and identically distributed copies of a stationary process proofs of these results will appear elsewhere

a generalization of the hermitian and skew hermitian splitting iteration method for solving sylvester equations this paper is concerned with a generalization of the hermitian and skew hermitian splitting hss iteration method for solving large sparse continuous sylvester equations the analysis shows that the ghss iteration method will converge under certain assumptions numerical results show that this new method is more efficient and robust than the existing ones

image processing using newton based algorithm of nonnegative matrix factorization in this paper we propose a newton based algorithm for nonnegative matrix factorization in image processing we employ the new algorithm to three real world databases extensive numerical results show the feasibility and validity of the proposed algorithm

functional connectivity in resting state fmri is linear correlation sufficient functional connectivity fc analysis is a prominent approach to analyzing fmri data especially acquired under the resting state condition the commonly used linear correlation fc measure bears an implicit assumption of gaussianity of the dependence structure if only the marginals but not all the bivariate distributions are gaussian linear correlation consistently underestimates the strength of the dependence to assess the suitability of linear correlation and the general potential of nonlinear fc measures we present a framework for testing and estimating the deviation from gaussianity by means of comparing mutual information in the data and its gaussianized counterpart we apply this method to 24 sessions of human resting state fmri for each session matrix of connectivities between 90 anatomical parcel time series is computed using mutual information and compared to results from its multivariate gaussian surrogate that conserves the correlations but cancels any nonlinearity while the group level tests confirmed non gaussianity in the fc the quantitative assessment revealed that the portion of mutual information neglected by linear correlation is relatively minor on average only about 5 of the mutual information already captured by the linear correlation the marginality of the non gaussianity was confirmed in comparisons using clustering of the parcels the disagreement between clustering obtained from mutual information and linear correlation was attributable to random error we conclude that for this type of data practical relevance of nonlinear methods trying to improve over linear correlation might be limited by the fact that the data are indeed almost gaussian

efficient single step preconditioned hss iteration methods for complex symmetric linear systems abstract we propose a single step preconditioned variant of hss sphss and an efficient parameterized sphss psphss iteration method for solving a class of complex symmetric linear systems under suitable conditions we analyze the convergence properties of the sphss and psphss iteration methods theoretical analysis shows that the minimal upper bounds for the spectral radius of the sphss and psphss iteration matrices are less than those of the shss and pshss iteration matrices when using the optimal parameters respectively numerical results show that the psphss iteration method has comparable advantage over several other iteration methods whether the experimental optimal parameters are used or not

commuting solutions of the yang baxter like matrix equation for a class of rank two updated matrices abstract let a i p q t where p and q are two n 2 complex matrices of full column rank and det q t p 0 all the commuting solutions with a of the quadratic matrix equation a x a x a x have been founded

preconditioned hss iteration method and its non alternating variant for continuous sylvester equations abstract bai 2010 proposed an efficient hermitian and skew hermitian splitting hss iteration method for solving a broad class of large sparse continuous sylvester equations to further improve the efficiency of the hss method in this paper we present a preconditioned hss phss iteration method and its non alternating variant nphss for this matrix equation the convergence properties of the phss and nphss methods are studied in depth and the quasi optimal values of the iteration parameters for the two methods are also derived moreover to reduce the computational cost we establish the inexact variants of the two iteration methods numerical experiments illustrate the efficiency and robustness of the two iteration methods and their inexact variants

on the detection of determinism in a time series the nonlinearly scaled distributions of the strengths of the orthogonal modes in the data of a time series are compared with that derived from its surrogate counterpart to assess its chaoticity or the stochastic nature chaoticity manifests in the relatively decreasing strengths of the weaker modes with increasing dimension of the orthogonal spaces mapping the process the distributions of the strengths of the modes for the data and the surrogate are compared statistically singular value decomposition is used for the implementation the ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated series including linear and nonlinear stochastic noise and processes described by lorenz rossler and mackey glass equations henon map and ecological map and some real life examples

constrained realization monte carlo method for hypothesis testing abstract we compare two theoretically distinct approaches to generate artificial or surrogate data for testing hypotheses about a given data set the first and more straightforward approach is to fit a single best model to the original data and then to generate surrogate data sets that are typical realizations of that model the second approach concentrates not on the model but directly on the original data it attempts to constrain the surrogate data sets so that they exactly agree with the original data for a specified set of sample statistics examples of these two approaches are provided for two simple cases a test for deviations from a gaussian distribution and a test for serial dependence in a time series additionally we consider test for nonlinearity in time series based on a fourier transform ft method and on more conventional autoregressive moving average arma fits to the data the comparative performance of hypothesis testing schemes based on these two approaches is found to depend on whether or not the discriminating statistic is pivotal a statistic is pivotal if its distribution is the same for all processes consistent with the null hypothesis the typical realization method requires that the discriminating statistic satisfy this property the constrained realization approach on the other hand does not share this requirement and can provide an accurate and powerful test without having to sacrifice flexibility in the choice of discriminating statistic

complex hill s equation and the complex periodic korteweg de vries equations on etudie la classe spectrale des operateurs differentiels l d 2 dx 2 q avec un potentiel q de periode un on traite des potentiels complexes et des operateurs auto adjoints

on soliton type solutions of equations associated with n component systems the algebraic geometric approach to n component systems of nonlinear integrable pde s is used to obtain and analyze explicit solutions of the coupled kdv and dym equations detailed analysis of soliton fission kink to anti kink transitions and multi peaked soliton solutions is carried out transformations are used to connect these solutions to several other equations that model physical phenomena in fluid dynamics and nonlinear optics

stochastic modelling replacing fast degrees of freedom by noise in systems with timescale separation where the fast degrees of freedom exhibit chaotic motion the latter are replaced by suitable stochastic processes a projection technique is employed to derive equations of motion for the phase space density of the slow variables by eliminating the fast ones the resulting equations can be approximated in a controlled way by fokker planck equations or equivalently by stochastic differential equations for slow degrees of freedom we discuss some model situations and explore the accuracy of the approximations by numerical simulations

effects of non stationarity on the magnitude and sign scaling in the multi scale vertical velocity increment abstract we study the scaling properties of multi scale increment series from the stationary and non stationary vertical velocity records by the detrended fluctuation analysis dfa and series decomposition methods and show the impact of non stationarity on the magnitude and sign scaling properties firstly we show it is difficult to define a significant scaling range for stationary records themselves secondly for increment series with lag one the nonlinear correlation found in magnitude fluctuation i e volatility fluctuation is obvious for both cases and over the smaller scale range the linear correlation found usually in the sign series is the same for both cases however over the larger scale range the difference is sharp and marked nonlinear correlation is also incorporated for the non stationary sign series thirdly with the lags in increment increasing there exist two scaling ranges in both the magnitude and sign fluctuations the nonlinear correlation in the magnitude series over both small and large scale ranges decreases with the lags increasing for the sign series the linear correlation is dominant over both small and large scale ranges for stationary case however the nonlinear correlation can be found over the large scale ranges for non stationary case and will decrease with lags increasing the nonlinear correlation found in the sign series over large scale range is resulted from the modulation of the large scale structures found in the non stationary data which will incorporate parts of the magnitude information into the sign series

a wavelet based method for surrogate data generation hypothesis testing based on surrogate data has emerged as a popular way to test the null hypothesis that a signal is a realisation of a linear gaussian stochastic process if these surrogates are constrained to the values and power spectrum of the original data there is no need to formulate a pivotal test statistic in this paper a method is presented for generating constrained surrogates using a wavelet transform introducing a threshold above which wavelet detail coefficients are pinned to their original values such surrogates avoid problems of nonstationarity for pseudo periodic data and appear to be more robust than conventional approaches for situations where period modulation is corrupting a gaussian stochastic process when used for generating ensemble realisations of a process the approach used here avoids some of the difficulties of methods based on simple randomisation of wavelet coefficients

the infinite period limit of the inverse formalism for periodic potentials soit l operateur de hill h p d 2 dx 2 v p x quand v p x est une fonction p periodique de x on montre que les formules pour la solution du probleme inverse ont une limite si on prend v p comme une repetition periodique d une fonction a support compact v x et que l on fait tendre p vers l infini

surrogate analysis of volatility series from long range correlated noise detrended fluctuation analysis dfa c k peng s v buldyrev a l goldberger s havlin f sciortino m simons h e stanley nature 356 1992 168 of volatility series has been proposed to identify possible nonlinear multifractal signatures in the given empirical sample y ashkenazy p ch ivanov s havlin c k peng a l goldberger h e stanley phys rev lett 86 2001 1900 y ashkenazy s havlin p ch ivanov c k peng v schulte frohlinde h e stanley physica a 323 2003 19 t kalisky y ashkenazy s havlin phys rev e 72 2005 011913 long range volatility correlation can be an outcome of static as well as dynamical nonlinearity in order to argue in favor of dynamical nonlinearity surrogate testing is used in conjunction with volatility analysis y ashkenazy p ch ivanov s havlin c k peng a l goldberger h e stanley phys rev lett 86 2001 1900 y ashkenazy s havlin p ch ivanov c k peng v schulte frohlinde h e stanley physica a 323 2003 19 t kalisky y ashkenazy s havlin phys rev e 72 2005 011913 in this brief communication surrogate testing of volatility series from long range correlated monofractal noise and their static invertible nonlinear transforms is investigated long range correlated noise is generated from fractional auto regressive integrated moving average farima 0 d 0 with gaussian and non gaussian innovations we show significant deviation in the scaling behavior between the empirical sample and the surrogate counterpart at large time scales in the case of farima 0 d 0 with non gaussian innovations whereas no such discrepancy was observed in the case of gaussian innovations the results encourage cautious interpretation of surrogate analysis of volatility series in the presence of non gaussian innovations

finite size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method abstract analysis of freight rate volatility characteristics attracts more attention after year 2008 due to the effect of credit crunch and slowdown in marine transportation the multifractal detrended fluctuation analysis technique is employed to analyze the time series of baltic dry bulk freight rate index and the market trend of two bulk ship sizes namely capesize and panamax for the period march 1st 1999 february 26th 2015 in this paper the degree of the multifractality with different fluctuation sizes is calculated besides multifractal detrending moving average mf dma counting technique has been developed to quantify the components of multifractal spectrum with the finite size effect taken into consideration numerical results show that both capesize and panamax freight rate index time series are of multifractal nature the origin of multifractality for the bulk freight rate market series is found mostly due to nonlinear correlation

on modified hss iteration methods for continuous sylvester equations we introduce and analyze a modification of the hermitian and skew hermitian splitting iteration method for solving large sparse continuous sylvester equations with non hermitian and complex symmetric positive definite semidefinite matrices it is found that the modified hermitian and skew hermitian splitting mhss iteration method is unconditionally convergent each iteration in this method requires the solution of two linear systems with real symmetric positive definite coefficient matrices these two systems can be solved inexactly numerical results show that the mhss iteration method and its inexact variant are efficient and robust solvers for this class of continuous sylvester equations

an iterative method for obtaining the least squares solutions of quadratic inverse eigenvalue problems over generalized hamiltonian matrix with submatrix constraints abstract in this paper we consider a class of constrained matrix quadratic inverse eigenvalue problem and its optimal approximation problem it is proved that the proposed algorithm always converge to the generalized hamiltonian solutions with a submatrix constraint of problem 1 1 within finite iterative steps in the absence of roundoff error in addition by choosing a special kind of initial matrices it is shown that the minimum norm solution of problem 1 1 can be obtained consequently at last for a given matrix group in the solution set of problem 1 1 it is proved that the unique optimal approximation solution of problem 1 2 can be also obtained some numerical results are reported to demonstrate the efficiency of our algorithm

new matrix iterative methods for constraint solutions of the matrix equation axb c in this paper two new matrix iterative methods are presented to solve the matrix equation axb c the minimum residual problem min x email protected email protected and the matrix nearness problem min x s email protected x x where s is the set of constraint matrices such as symmetric symmetric r symmetric and r s symmetric and s e is the solution set of above matrix equation or minimum residual problem these matrix iterative methods have faster convergence rate and higher accuracy than the matrix iterative methods proposed in deng et al 2006 13 huang et al 2008 15 peng 2005 16 and lei and liao 2007 17 paige s algorithms are used as the frame method for deriving these matrix iterative methods numerical examples are used to illustrate the efficiency of these new methods

algorithms for generating surrogate data for sparsely quantized time series abstract the method of surrogate data is frequently used for a statistical examination of nonlinear properties underlying original data if surrogate data sets are generated by a null hypothesis that the data are derived by a linear process a rejection of the hypothesis means that the original data have more complex properties however we found that if an algorithm for generating surrogate data for example amplitude adjusted fourier transformed is applied to sparsely quantized data there are large discrepancies between their power spectrum and that of the original data in lower frequency regions we performed some simulations to confirm that these errors often lead to false rejections in this paper in order to prevent such drawbacks we advance an extended hypothesis and propose two improved algorithms for generating surrogate data that reduce the discrepancies of the power spectra we also confirm the validity of the two improved algorithms with numerical simulations by showing that the extended null hypothesis can be rejected if the time series is produced from chaotic dynamical systems finally we applied these algorithms for analyzing financial tick data as a real example then we showed that the extended null hypothesis cannot be rejected because the nonlinear statistics or nonlinear prediction errors exhibited are the same as those of the original financial tick time series

nonlinear strength quantifier based on phase correlation abstract distinguishing linear series from nonlinear ones is of great importance for not only understanding the processes generating these series but also their modeling and prediction there are many methods and their nonlinear quantifiers to reach this goal but no one is powerful enough to deal with any given series in this study the artificially generating series with given tailored phase correlation strength is applied to test the performance of some widely used methods and their nonlinear quantifiers given in the previous studies both advantages and shortcomings are shown for these methods and their nonlinear metrics especially spurious results from these methods and their nonlinear metrics can be found for some cases much weak or strong phase correlations in order to avoid these spurious results modified phase correlation quantifiers are proposed at the same time multiple stripes found in the phase map can be explained from the view point of enhanced nonlinear strength

genesis of solitons arising from individual flows of the camassa holm hierarchy the present work offers a detailed account of the large time development of the velocity profile run by a single individual hamiltonian flow of the camassa holm ch hierarchy the hamiltonian employed being the reciprocal of any eigenvalue of the underlying spectral problem in this simpler scenario i prove some of the conjectures raised by mckean 27 notably i confirm the ultimate shaping into solitons of the cusps that appear near blowup sites of any velocity profile emanating from an initial disposition for which breakdown of the wave in finite time is sure to happen the careful large time asymptotic analysis is carried from exact expressions describing the velocity in terms of initial data the integration involving a lagrangian scale and three theta functions the rates at which the latter reach their common values at each end of the line characterizing the region where soliton genesis is expected in fact the present method also suggests how solitons may arise from initial conditions not leading to breakdown the full ch flow is nothing but a superposition of such commuting individual actions therein lies the hope that the present account will pave the way to elucidate soliton formation for more complex flows in particular for the ch flow itself 2005 wiley periodicals inc

multiplicative cascade dynamics in pole balancing pole balancing is a key task for probing the prospective control that organisms must engage in for purposeful action the temporal structure of pole balancing behaviors will reflect the on line operation of control mechanisms needed to maintain an upright posture in this study signatures of multifractality are sought and found in time series of the vertical angle of a pole balanced on the fingertip comparisons to surrogate time series reveal multiplicative cascade dynamics and interactivity across scales in addition simulations of a pole balancing model generating on off intermittency j l cabrera and j g milton phys rev lett 89 158702 2002 were analyzed evidence of multifractality is also evident in simulations though comparing simulated and participant series reveals a significantly greater contribution of cross scale interactivity for the latter these findings suggest that multiplicative cascade dynamics are an extension of on off intermittency and play a role in prospective coordination

on geometric phases for soliton equations this paper develops a new complex hamiltonian structure forn soliton solutions for a class of integrable equations such as the nonlinear schrodinger sine gordon and korteweg de vries hierarchies of equations that yields amongst other things geometric phases in the sense of hannay and berry for example one of the possible soliton geometric phases is manifested by the well known phase shift that occurs for interacting solitons the main new tools are complex angle representations that linearize the corresponding hamiltonian flows on associated noncompact jacobi varieties this new structure is obtained by taking appropriate limits of the differential equations describing the class of quasi periodic solutions a method of asymptotic reduction of the angle representations is introduced for investigating soliton geometric phases that are related to the presence of monodromy at singularities in the space of parameters in particular the phase shift of interacting solitons can be expressed as an integral over a cycle on an associated riemann surface in this setting soliton geometric asymptotics are constructed for studying geometric phases in the quantum case the general approach is worked out in detail for the three specific hierarchies of equations mentioned some links with functions the braid group and geometric quantization are pointed out as well

geometry of kdv 4 abel sums jacobi variety and theta function in the scattering case the study of the general projective curve x defined by the vanishing of an irreducible polynomial p x y originated in the discovery of addition formulas for integrals v r x y dx of rational functions on such a curve

gradient based and least squares based iterative algorithms for matrix equations axb cxtd f abstract this paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation axb cx t d f the basic idea is to decompose the matrix equation system under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving ax b and axb f the analysis shows that when the matrix equation has a unique solution under the sense of least squares the iterative solution converges to the exact solution for any initial values a numerical example verifies the proposed theorems

detecting determinism in short time series using a quantified averaged false nearest neighbors approach we propose a criterion to detect determinism in short time series this criterion is based on the estimation of the parameter e 2 defined by the averaged false neighbors method for analyzing time series cao physica d 110 43 1997 using surrogate data testing with several chaotic and stochastic simulated time series we show that the variation coefficient of e 2 over a few values of the embedding dimension d defines a suitable statistic to detect determinism in short data sequences this result holds for a time series generated by a high dimensional chaotic system such as the mackey glass one different decreasing lengths of the time series are included in the numerical experiments for both synthetic and real world data we also investigate the robustness of the criterion in the case of deterministic time series corrupted by additive noise

distribution of natural trends in long term correlated records a scaling approach we estimate the exceedance probability w x ensuremath alpha l that in a long term correlated gaussian distributed sub record of length l characterized by a fluctuation exponent ensuremath alpha between 0 5 and 1 5 a relative increase ensuremath delta ensuremath sigma t of size larger than x occurs where ensuremath delta is the total observed increase measured by linear regression and ensuremath sigma t is the standard deviation around the regression line we consider l between 500 and 2000 which is the typical length scale of monthly local and reconstructed annual global temperature records we use scaling theory to obtain an analytical expression for w x ensuremath alpha l from this expression we can determine analytically for a given confidence probability q the boundaries ifmmode pm else textpm fi x q ensuremath alpha l of the confidence interval in the presence of an external linear trend the total observed increase is the sum of the natural and the external increase an observed relative increase ensuremath delta ensuremath sigma t is considered unnatural when it is above x q ensuremath alpha l in this case the size of the external relative increase is bounded by ensuremath delta ensuremath sigma t ifmmode pm else textpm fi x q ensuremath alpha l we apply this approach to various global and local climate data and discuss the different results for the significance of the observed trends

on hermitian and skew hermitian splitting iteration methods for the linear matrix equation axb c in this paper a hermitian and skew hermitian splitting hss iteration method for solving the linear matrix equation axb c is proposed this method is formed by extending the corresponding hss iteration method for solving ax b the analysis shows that the hss iteration method will converge under certain assumptions moreover the optimal parameter of this iteration method is presented numerical results show that this new method is more efficient and robust than existing methods

nonlinear dynamical system identification with dynamic noise and observational noise in this paper we consider the problem of whether a nonlinear system has dynamic noise and then estimate the level of dynamic noise to add to any model we build the method we propose relies on a nonlinear model and an improved least squares method recently proposed on the assumption that observational noise is not large we do not need any a priori knowledge for systems to be considered and we can apply the method to both maps and flows we demonstrate with applications to artificial and experimental data the results indicate that applying the proposed method can detect presence or absence of dynamic noise from scalar time series and give a reliable level of dynamic noise to add to the model built in some cases

interpreting non random signatures in biomedical signals with lempel ziv complexity abstract lempel ziv complexity lz j ziv a lempel on the complexity of finite sequences ieee trans inform theory 22 1976 75 81 and its variants have been used widely to identify non random patterns in biomedical signals obtained across distinct physiological states non random signatures of the complexity measure can occur under nonlinear deterministic as well as non deterministic settings surrogate data testing have also been encouraged in the past in conjunction with complexity estimates to make a finer distinction between various classes of processes in this brief letter we make two important observations 1 non gaussian noise at the dynamical level can elude existing surrogate algorithms namely phase randomized surrogates ft amplitude adjusted fourier transform aaft and iterated amplitude adjusted fourier transform iaaft thus any inference nonlinear determinism as an explanation for the non randomness is incomplete 2 decrease in complexity can be observed even across two linear processes with identical auto correlation functions the results are illustrated with a second order auto regressive process with gaussian and non gaussian innovations ar 2 processes have been used widely to model several physiological phenomena hence their choice the results presented encourage cautious interpretation of non random signatures in experimental signals using complexity measures

iterative least squares solutions of coupled sylvester matrix equations abstract in this paper we present a general family of iterative methods to solve linear equations which includes the well known jacobi and gauss seidel iterations as its special cases the methods are extended to solve coupled sylvester matrix equations in our approach we regard the unknown matrices to be solved as the system parameters to be identified and propose a least squares iterative algorithm by applying a hierarchical identification principle and by introducing the block matrix inner product the star product for short we prove that the iterative solution consistently converges to the exact solution for any initial value the algorithms proposed require less storage capacity than the existing numerical ones finally the algorithms are tested on computer and the results verify the theoretical findings

periodic limit of inverse scattering i t is well known that a p periodic potential q x can be reconstructed from spectral data of the corresponding hill operator d2 dx2 q x in terms of a riemann function we regard the periodic potential q x as the pointwise limit of a scattering potential qn c x defined to equal q x when np x np to equal zero when x np as n and c2 the scattering potential qn c x can be recovered from the scattering data of the corresponding schrodinger operator in terms of a dyson determinant according to a well known theory we derive the riemann function corresponding to the periodic potential q x by taking the above limit of the dyson determinant for the scattering potential we first calculate the scattering data of the potential qn c x through recursive formulas in terms of the left transmission and reflection coefficients t and r of the potential which is equal to q x when 0 x p and equal to zero otherwise we use these data to express the dyson determinant of qn c x we then expand the dyson determinant into a fredholm series and compute the main contributions to the expansion in the asymptotic limit n and c2 using a method developed by lax levermore and venakides in their study of the small dispersion limit of the initial value problem of korteweg de vries equation the computation of the leading order contributions reduces to a quadratic functional maximization problem constrained by a positivity condition and by a mass quantization condition the solutions to this maximization problem constitute the differentials on a riemann surface the main ingredients for the riemann function corresponding to the periodic potential the limit of the dyson determinant for qn c x as n and c2 is shown to equal the exact riemann function corresponding to the periodic potential q x times an exponential function with exponent being a quadratic polynomial in x our calculation includes the correct phase shifts of the function 1993 john wiley sons inc

on positive definite and skew hermitian splitting iteration methods for continuous sylvester equation ax xb c in this paper we present a positive definite and skew hermitian splitting pss iteration method for continuous sylvester equations ax xb c with positive definite semi definite matrices the theoretical analysis shows that the pss iteration method will converge unconditionally and the optimal parameter of the new method is presented moreover to reduce the computing cost an inexact variant of the pss iteration method ipss and the analysis of its convergence property in detail have been established numerical results show that this new method and its inexact invariant are efficient and robust solvers for this class of continuous sylvester equations

kronecker products unitary matrices and signal processing applications discrete unitary transforms are extensively used in many signal processing applications and in the development of fast algorithms kronecker products have proved quite useful in this semitutorial paper we briefly review properties of kronecker products and direct sums of matrices which provide a compact notation in treating patterned matrices a generalized matrix product which inherits some useful algebraic properties from the standard kronecker product and allows a large class of discrete unitary transforms to be generated from a single recursion formula is then introduced the notation is intimately related to sparse matrix factorizations and examples are included illustrating the utility of the new notation in signal processing applications finally some novel characteristics of hadamard transforms and polyadic permutations are derived in the framework of kronecker products

signatures of chaotic and stochastic dynamics uncovered with recurrence networks an old and important problem in the field of nonlinear time series analysis entails the distinction between chaotic and stochastic dynamics recently recurrence networks have been proposed as a t

the geometry of minimal surfaces of finite genus ii nonexistence of one limit end examples we demonstrate that a properly embedded minimal surface in 3 with finite genus cannot have one limit end

some uniqueness and nonexistence theorems for embedded minimal surfaces thanks to the works of callahan costa hoffman karcher meeks rosenberg wei etc see for example 1 2 3 5 8 11 12 16 20 we dispose now of a large number of properly embedded minimal surfaces in the euclidean space ir other than the classical examples all those surfaces can be viewed as minimal surfaces with finite total curvature properly embedded in complete flat three manifolds the most basic invariants associated to a surface of this type are its topology and its periodicity it is an interesting problem to decide if the simplest examples like the catenoid the helicoid the scherk s surfaces or the riemann example can be characterized in terms of some of these invariants in the non periodic case there are two important uniqueness theorems in this direction the first one obtained by schoen 17 characterizes the catenoid as the only complete minimal surface embedded

revisiting sample entropy analysis abstract we modify the definition of sample entropy saen by incorporating a time delay between the components of the block from which the densities are estimated and show that the modified method characterizes the complexity of the system better than the original version we apply the modified saen to the standard deterministic systems and stochastic processes uncorrelated and long range correlated lrc processes and show that the underlying complexity of the system is better quantified by the modified method we extend this analysis to the rr intervals of the normal and congestive heart failure chf subjects available via www physionet org and show that there is a good degree of separation between the two groups

parameterized preconditioned hermitian and skew hermitian splitting iteration method for a class of linear matrix equations recently wang et al 2013 proposed an efficient hermitian and skew hermitian splitting hss iteration method to approximate the solution of linear matrix equation to further improve the efficiency of the hss method we in this paper establish a parameterized preconditioned hss pphss iteration method by introducing two hermitian positive definite preconditioners and two more different iteration parameters for the hss method the convergence properties of the pphss method used for solving linear matrix equation a x b c are strictly analyzed and the quasi optimal values of the iteration parameters for the pphss method are also derived numerical results demonstrate the feasibility and the efficiency of the pphss iteration method

on tau functions for orthogonal polynomials and matrix models let v be a real polynomial of even degree and let rho be the equilibrium probability measure for v with support s to that v x greeater than or equal to int 2log x y rho dy c for some constant c with equality on s then s is the union of finitely many boundd intervals with endpoints delta j and rho is given by an algebraic weight w x on s then the system of orthogonal polynomials for w gives rise to a system of differential equations known as the schlesinger equations this paper identifies the tau function of this system with the hankel determinant det int x j k rho dx the solutions of the magnus schlesinger equation are realised by a linear system which is used to compute the tau functions in terms of a gelfand levitan equation the tau function is associated with a potential q and a scattering problem for the schrodinger equation with potential q the paper describes cases where this is integrable in terms of the nonlinear fourier transform

stationary splitting iterative methods for the matrix equation axb c abstract stationary splitting iterative methods for solving a x b c are considered in this paper the main tool to derive our new method is the induced splitting of a given nonsingular matrix a m n by a matrix h such that i h 1 exists convergence properties of the proposed method are discussed and numerical experiments are presented to illustrate its computational efficiency and the effectiveness of some preconditioned variants in particular for certain surface fitting applications our method is much more efficient than the progressive iterative approximation pia a conventional iterative method often used in computer aided geometric design cagd

construction of multivariate surrogate sets from nonlinear data using the wavelet transform abstract the use of surrogate data has become a crucial first step in the study of nonlinearity in time series data a widely used technique to construct surrogate data is to randomize the phases of the data in the fourier domain in this paper an alternative technique based on the resampling of wavelet coefficients is discussed this approach exploits between scale correlations that exist within nonlinear data but which are either absent or weak in stochastic data it proceeds by transforming the data into the wavelet domain and permuting the wavelet coefficients experimental and numerical time series data are used to demonstrate that the performance of the wavelet resampling technique is comparable to phase randomization in terms of the preservation of linear properties removal of nonlinear structure and computational demands however the wavelet technique may have specific and distinct advantages in the application to complex data sets such as numerical analysis of turbulence and experimental brain imaging data where wavelets give a more parsimonious representation of spatio temporal patterns than fourier modes it is shown that different techniques of resampling the data in the wavelet domain may optimize the construction of surrogate data according to the properties of the experimental time series and computational constraints

on the korteweg de vries equation convergent birkhoff normal form abstract the korteweg de vries equation kdv formula is a completely integrable hamiltonian system of infinite dimension with phase space the sobolev spacehn s1 r n 1 hamiltonian h q s1 1 2 xq x 2 q x 3 dx and poisson structure x the functionq 0 is an elliptic fixed point we prove that for anyn 1 the korteweg de vries equation and thus the entire kdv hierarchy admits globally defined real analytic action angle variables as a consequence it follows that in a neighborhood ofq 0 inh1 s1 r the kdv hamiltonian h and similarly any hamiltonian in the kdv hierarchy admits a convergent birkhoff normal form to the best of our knowledge this is the first such example in infinite dimension moreover using the constructed action angle variables we analyze the regularity properties of the hamiltonian vectorfield of kdv

on normal and skew hermitian splitting iteration methods for large sparse continuous sylvester equations this paper is concerned with some generalizations of the hermitian and skew hermitian splitting hss iteration for solving continuous sylvester equations the main contents we will introduce are the normal and skew hermitian splitting nss iteration methods for the continuous sylvester equations it is shown that the new schemes can outperform the standard hss method in some situations theoretical analysis shows that the nss methods converge unconditionally to the exact solution of the continuous sylvester equations moreover we derive the upper bound of the contraction factor of the nss iterations numerical experiments further show the effectiveness of our new methods

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

detecting generalized synchronization between chaotic signals a kernel based approach a unified framework for analysing generalized synchronization in coupled chaotic systems from data is proposed the key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning several successful applications are presented which show the capability of the kernel based approach for detecting generalized synchronization and dynamical change of the coupling strength between two chaotic systems can be captured by the proposed approach it is also discussed how the kernel parameter is suitably chosen from data

improved surrogate data for nonlinearity tests current tests for nonlinearity compare a time series to the null hypothesis of a gaussian linear stochastic process for this restricted null assumption random surrogates can be constructed which are constrained by the linear properties of the data we propose a more general null hypothesis allowing for nonlinear rescalings of a gaussian linear process we show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity an iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution

multifractal moving average analysis and test of multifractal model with tuned correlations we address two common major problems in the study of time series characterizing fluctuations in complex systems multifractal analysis and multifractal modeling specifically we introduce a multi fractal centered moving average mf cma analysis which is computationally easier but equivalently performing compared with the well established multi fractal detrended fluctuation analysis mf dfa with linear detrending in addition we study in detail a generalized binomial multi fractal model gb mfm to conveniently and reliably generate multifractal surrogate data with arbitrary singularity strengths and arbitrary long term persistence we use the data generated by this model as well as realistic by construction monofractal data series with crossovers and trends to test and compare the multifractal analysis methods and discuss finite size effects as well as limitations due to spurious multifractality

the jacobi and gauss seidel type iteration methods for the matrix equation a x b c in this paper the jacobi and gauss seidel type iteration methods are proposed for solving the matrix equation a x b c which are based on the splitting schemes of the matrices a and b the convergence and computational cost of these iteration methods are discussed furthermore we give the preconditioned jacobi and gauss seidel type iteration methods numerical examples are given to demonstrate the efficiency of these methods proposed in this paper

detrended fluctuation analysis of short datasets an application to fetal cardiac data abstract using detrended fluctuation analysis dfa we perform scaling analysis of short datasets of length 500 1500 data points we quantify the long range correlation exponent by computing the mean value of the local exponents l in the asymptotic regime the local exponents are obtained as the numerical derivative of the logarithm of the fluctuation function f s with respect to the logarithm of the scale factor s l d log 10 f s d log 10 s these local exponents display huge variations and complicate the correct quantification of the underlying correlations we propose the use of the phase randomized surrogate prs which preserves the long range correlations of the original data to minimize the variations in the local exponents using the numerically generated uncorrelated and long range correlated data we show that performing dfa on several realizations of prs and estimating l from the averaged fluctuation functions of all realizations can minimize the variations in l the application of this approach to the fetal cardiac data rr intervals is discussed and we show that there is a statistically significant correlation between and the gestation age

the least squares anti bisymmetric solution and the optimal approximation solution for sylvester equation in this paper a modified conjugate gradient iterative method for solving sylvester equation is presented by using this iterative method the least squares anti bisymmetric solution and the optimal approximation solution can be obtained here we present the derivation and theoretical analysis of our iterative method numerical results illustrate the feasibility and effectiveness of the proposed iterative method

price volume multifractal analysis of the moroccan stock market abstract in this paper we analyzed price volume multifractal cross correlations of moroccan stock exchange we chose the period from january 1st 2000 to january 20th 2017 to investigate the multifractal behavior of price change and volume change series then we used multifractal detrended cross correlations analysis method mf dcca and multifractal detrended fluctuation analysis mf dfa to analyze the series we computed bivariate generalized hurst exponent renyi exponent and spectrum of singularity for each pair of indices to measure quantitatively cross correlations furthermore we used detrended cross correlations coefficient dcca and cross correlation test q m to analyze cross correlation quantitatively and qualitatively by analyzing results we found existence of price volume multifractal cross correlations the spectrum width has a strong multifractal cross correlation we remarked that volume change series is anti persistent when we analyzed the generalized hurst exponent for all moments q the cross correlation test showed the presence of a significant cross correlation however dcca coefficient had a small positive value which means that the level of correlation is not very significant finally we analyzed sources of multifractality and their degree of contribution in the series

efficient preconditioned nhss iteration methods for solving complex symmetric linear systems abstract based on the new hss nhss iteration method introduced by pour and goughery 2015 we propose a preconditioned variant of nhss p nhss and an efficient parameterized p nhss ppnhss iteration methods for solving a class of complex symmetric linear systems the convergence properties of the p nhss and the ppnhss iteration methods show that the iterative sequences are convergent to the unique solution of the linear system for any initial guess when the parameters are properly chosen moreover we discuss the quasi optimal parameters which minimize the upper bounds for the spectral radius of the iteration matrices numerical results show that the ppnhss iteration method is superior to several iteration methods whether the experimental optimal parameters are used or not

the reflexive solutions of the matrix equation ax b c in this paper we study the existence of a reflexive with respect to the generalized reflection matrix p solution of the matrix equation ax b c for the special case when b i we get the result of peng and hu 1

scattering theory for the korteweg de vries kdv equation and its hamiltonian interpretation abstract it is shown that the scattering transform for the kdv equation is not canonical in the naive sense an explanation of this phenomenon is found and a correct hamiltonian formulation of the scattering theory is proposed

a single step iteration method for non hermitian positive definite linear systems abstract an efficient single step iteration method is presented for solving the large sparse non hermitian positive definite linear systems we theoretically prove that this method converges to the unique solution of the system of linear equations under suitable restrictions moreover we derive an upper bound for the spectral radius of the new iteration matrix furthermore we consider acceleration of the new iteration by krylov subspace methods and some special properties of the new preconditioned matrix are proposed numerical experiments on a few model problems are presented to further examine the effectiveness of our new method