on the finite escape phenomena for matrix riccati equations we show a necessary and sufficient condition for the solution of riccati differential equations to escape to the infinity in finite time this implies that we obtain a necessary and sufficient condition for the existence of the solution of all time t geq 0 this condition is given as a rank condition of the matrix which we refer to as the escape criterion matrix this matrix consists of the equation matrices and an equilibrium point of riccati differential equation

brief paper root mean square gains of switched linear systems a variational approach we consider the problem of computing the root mean square rms gain of switched linear systems we develop a new approach which is based on an attempt to characterize the worst case switching law wcsl that is the switching law that yields the maximal possible gain our main result provides a sufficient condition guaranteeing that the wcsl can be characterized explicitly using the differential riccati equations dres corresponding to the linear subsystems this condition automatically holds for first order siso systems so we obtain a complete solution to the rms gain problem in this case

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

effect of coarse graining on detrended fluctuation analysis several studies have investigated the scaling behavior in naturally occurring biological and physical processes using techniques such as detrended fluctuation analysis dfa data acquisition is an inherent part of these studies and maps the continuous process into digital data the resulting digital data is discretized in amplitude and time and shall be referred to as coarse grained realization in the present study since coarse graining precedes scaling exponent analysis it is important to understand its effects on scaling exponent estimators such as dfa in this brief communication k means clustering is used to generate coarse grained realizations of data sets with different correlation properties namely anti correlated noise long range correlated noise and uncorrelated noise it is shown that the coarse graining can significantly affect the scaling exponent estimates it is also shown that scaling exponent can be reliably estimated even at low levels of coarse graining and the number of the clusters required varies across the data sets with different correlation properties

application of the detrended fluctuation analysis dfa method for describing cloud breaking abstract a method to sort out correlations and decorrelations in stratus cloud formation persistence and breakup is introduced the detrended fluctuation analysis dfa statistical method is applied to microwave radiometer data the existence of long range power law correlations in stratus cloud liquid water content fluctuations is demonstrated over a 2 h period moreover using a finite size time interval window a change from brownian to non brownian fluctuation regimes is clearly shown to define the cloud structure changes such findings are similar to those found in dna and financial data sequences when mosaics of persistent and antipersistent patches are present the occurrence of these statistics in stratus cloud liquid water content suggests the usefulness of similar studies on cloud resolving model output and for better meteorological predictability

dynamic scaling approach to study time series fluctuations we propose an approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface growth problem in this framework the fluctuation sampling time interval plays the role of time variable whereas the physical time is treated as the analog of spatial variable in this way we found that the fluctuations of many real world time series satisfy the analog of the family viscek dynamic scaling ansatz this finding permits us to use the powerful tools of kinetic roughening theory to classify model and forecast the fluctuations of real world time series

h sub spl infin differential riccati equations convergence properties and finite escape phenomena the paper studies the transient and asymptotic behavior of the solution of the sign indefinite differential riccati equation dre arising in finite horizon h sub spl infin filtering and control problems differently from the sign definite h sub spl infin dre the solution of the h sub spl infin dre can have finite escape times even for nonnegative initial conditions sufficient and necessary conditions for boundedness and convergence are derived in correspondence to a fixed value of the h sub spl infin norm attenuation level spl gamma finally a stepwise spl gamma switching strategy is devised to guarantee boundedness as well as asymptotic performance

method for generating long range correlations for large systems we propose a new method to generate a sequence of random numbers with long range power law correlations that overcomes known difficulties associated with large systems the new method presents an improvement on the commonly used methods we apply the algorithm to generate enhanced diffusion isotropic and anisotropic self affine surfaces and isotropic and anisotropic correlated percolation

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

long term memory in extreme returns of financial time series abstract it is well known that while daily price returns of financial markets are uncorrelated their absolute values volatility are long term correlated here we provide evidence that certain subsequences of the returns themselves also exhibit long term memory these subsequences consist of maxima or minima of returns in consecutive time windows of r days our analysis shows that for both stocks and currency exchange rates long term correlations are significant for r 4 we argue that this long term memory which is similar to that observed in volatility clustering sheds further insight on price dynamics that might be used for risk estimation

robust spl hscr sub spl infin filtering for continuous time varying uncertain systems with deterministic input signals many dynamical systems involve not only process and measurement noise signals but also parameter uncertainty and known input signals when spl lscr sub 2 or spl hscr sub spl infin filters that were designed based on a nominal model of the system are applied the presence of parameter uncertainty will not only affect the noise attenuation property of the filter but also introduce a bias proportional to the known input signal and the latter may be very appreciable we introduce a finite horizon robust spl hscr sub spl infin filtering method that provides a guaranteed spl hscr sub spl infin bound for the estimation error in the presence of both parameter uncertainty and a known input signal this method is developed by using a game theoretic approach and the results generalize those obtained for cases without parameter uncertainty or without a known input signal it is also demonstrated via an example that the proposed method provides significantly improved signal estimates

h control of linear time varying systems a state space approach in this paper the standard problem of h infty control theory for finite dimensional linear time varying continuous time plants is considered the problem is given a real number gamma 0 f

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

a structure preserving algorithm for the minimum h norm computation of finite time state feedback control problem the algorithm being developed here is based on the generating function approach for finite time h control and application of canonical transformation of linear hamiltonian system first an equivalent finite time h control law in terms of the third type generating function is derived then by using symplectic structure of the hamiltonian system s state transition matrix a group of matrix recursive formulae are deduced for the evaluation of the finite time h control law combining with a matrix singularity testing procedure this recursive algorithm verifies the existence condition of sub optimal h controllers and gives the minimum h norm of finite time control systems inherited from the canonical transformation the matrix recursive formulae have a standard symplectic form this structure preserving property helps facilitate reliable and effective computation numerical results show the effectiveness of the proposed algorithm

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

on the existence of solutions of the riccati differential equation abstract we generalize a technique given in c martin 1 to obtain a characterization of finite escape times for time varying riccati equations which also apply to the non definite case

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

phase portrait of the matrix riccati equation the matrix riccati equation which arises from optimal control and filtering problems is a quadratic differential equation on the space of real symmetric n times n matrices it is closely related via compactification of the phase space to the differential equations on the grassmann manifold and the lagrange grassmann manifold whose flows are generated by the action of one parameter subgroups of the general linear group and of the symplectic group respectively we determine the complete phase portraits of the riccati equations on all three spaces the asymptotic behavior of every solution is described the phase portraits are characterized topologically as well as set theoretically although the riccati equation is not generally a morse smale vector field we are able to show that it possesses suitable generalizations of many of the important properties of morse smale vector fields in particular the riccati equation satisfies a generalized version of the morse inequalities for a morse smale dynamica

universal scaling behaviors of meteorological variables volatility and relations with original records abstract volatility series defined as the magnitude of the increments between successive elements of five different meteorological variables over china are analyzed by means of detrended fluctuation analysis dfa for short universal scaling behaviors are found in all volatility records whose scaling exponents take similar distributions with similar mean values and standard deviations to reconfirm the relation between long range correlations in volatility and nonlinearity in original series dfa is also applied to the magnitude records defined as the absolute values of the original records the results clearly indicate that the nonlinearity of the original series is more pronounced in the magnitude series

is non gaussianity sufficient to produce long range volatile correlations abstract scaling analysis of the magnitude series volatile series has been proposed recently to identify possible non linear multifractal signatures in the given data y ashkenazy et al phys rev lett 86 2001 1900 y ashkenazy et al physica a 323 2003 19 t kalisky y ashkenazy s havlin phys rev e 72 2005 011913 in this article correlations of volatile series generated from stationary first order linear feedback process with gaussian and non gaussian innovations are investigated while volatile correlations corresponding to gaussian innovations exhibited uncorrelated behavior across all time scales those of non gaussian innovations showed significant deviation from uncorrelated behavior even at large time scales the results presented raise the intriguing question whether non gaussian innovations can be sufficient to realize long range volatile correlations

modeling heart rate variability in healthy humans a turbulence analogy many complex systems share similar statistical characteristics in this letter a turbulence analogy is proposed for the long term heart rate variability of healthy humans based on such an analogy the equivalence of an inertial range is found and a cascade model which captures the statistical properties of the heart rate data is given

volatility of linear and nonlinear time series previous studies indicated that nonlinear properties of gaussian distributed time series with long range correlations u i can be detected and quantified by studying the correlations in the magnitude series ensuremath mid u i ensuremath mid the volatility however the origin for this empirical observation still remains unclear and the exact relation between the correlations in u i and the correlations in ensuremath mid u i ensuremath mid is still unknown here we develop analytical relations between the scaling exponent of linear series u i and its magnitude series ensuremath mid u i ensuremath mid moreover we find that nonlinear time series exhibit stronger or the same correlations in the magnitude time series compared with linear time series with the same two point correlations based on these results we propose a simple model that generates multifractal time series by explicitly inserting long range correlations in the magnitude series the nonlinear multifractal time series is generated by multiplying a long range correlated time series that represents the magnitude series with uncorrelated time series that represents the sign series mathrm sgn u i we apply our techniques on daily deep ocean temperature records from the equatorial pacific the region of the el nin o phenomenon and find i long range correlations from several days to several years with 1 f power spectrum ii significant nonlinear behavior as expressed by long range correlations of the volatility series and iii broad multifractal spectrum

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

multifractal characterization of stochastic resonance we use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals to characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence we use wavelet transform modulus maxima method for the singularity spectrum computations it is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic stochastic or chaotic input signals we show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization this fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also moreover our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence we use also the proposed approach to characterize the noise enhanced dynamics of a coupled stochastic neurons model

auxiliary signal design for robust multimodel identification under the assumption that one of two given linear models is the real underlying model of the system a proper auxiliary signal is defined as an input signal that allows the selection of the correct model under the assumption that model noises have bounded energy the separability index is defined as the inverse of the energy of the proper auxiliary signal of least energy a method for the computation of this index and the construction of the auxiliary signal is presented finally an efficient procedure for online identification called the hyperplane test is developed

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

magnitude and sign of long range correlated time series decomposition and surrogate signal generation we systematically study the scaling properties of the magnitude and sign of the fluctuations in correlated time series which is a simple and useful approach to distinguish between systems with different dynamical properties but the same linear correlations first we decompose artificial long range power law linearly correlated time series into magnitude and sign series derived from the consecutive increments in the original series and we study their correlation properties we find analytical expressions for the correlation exponent of the sign series as a function of the exponent of the original series such expressions are necessary for modeling surrogate time series with desired scaling properties next we study linear and nonlinear correlation properties of series composed as products of independent magnitude and sign series these surrogate series can be considered as a zero order approximation to the analysis of the coupling of magnitude and sign in real data a problem still open in many fields we find analytical results for the scaling behavior of the composed series as a function of the correlation exponents of the magnitude and sign series used in the composition and we determine the ranges of magnitude and sign correlation exponents leading to either single scaling or to crossover behaviors finally we obtain how the linear and nonlinear properties of the composed series depend on the correlation exponents of their magnitude and sign series based on this information we propose a method to generate surrogate series with controlled correlation exponent and multifractal spectrum

on global existence of solutions to coupled matrix riccati equations in closed loop nash games presents comparison and global existence results for solutions of coupled matrix riccati differential equations appearing in closed loop nash games and in mixed h sub 2 h sub spl infin type problems convergence of solutions is established for the diagonal case solutions of the corresponding algebraic equations are discussed using numerical examples

power spectrum and detrended fluctuation analysis application to daily temperatures the variability measures of fluctuation analysis fa and detrended fluctuation analysis dfa are expressed in terms of the power spectral density and of the autocovariance of a given process the diagnostic potential of these methods is tested on several model power spectral densities in particular we find that both fa and dfa reveal an algebraic singularity of the power spectral density at small frequencies corresponding to an algebraic decay of the autocovariance a scaling behavior of the power spectral density in an intermediate frequency regime is better reflected by dfa than by fa we apply fa and dfa to ambient temperature data from the 20th century with the primary goal to resolve the controversy in literature whether the low frequency behavior of the corresponding power spectral densities are better described by a power law or a stretched exponential as a third possible model we suggest a weibull distribution however it turns out that neither fa nor dfa can reliably distinguish between the proposed models

appropriateness of correlated first order auto regressive processes for modeling daily temperature records abstract the present study investigates linear and volatile nonlinear correlations of first order auto regressive process with uncorrelated ar 1 and long range correlated car 1 gaussian innovations as a function of the process parameter in the light of recent findings a kiraly i m janosi phys rev e 65 2002 0511021 we discuss the choice of car 1 in modeling daily temperature records we demonstrate that while car 1 is able to capture linear correlations it is unable to capture nonlinear volatile correlations in daily temperature records

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 horizon h sup infinity control problems with terminal penalties the standard h sup infinity control problem is generalized to the finite horizon case with two possibly singular terminal penalties at the initial and final times the major objective of the generalization is to increase flexibility of h sup infinity controls transients in the finite horizon and the terminal penalties are taken into account within the framework of h sup infinity control problems a complete solution a necessary and sufficient condition and a parameterization to the finite horizon h sup infinity control problem are given the solution is a natural extension of the riccati equation solution in the special case when all the terminal penalties vanish the solution is reduced to the existing one and to the finite horizon standard h sup infinity control problem this approach to the problem is based on completing the square argument of a particular quadratic form which is at least technically different from the previous ones

long range correlation properties of coding and noncoding dna sequences genbank analysis an open question in computational molecular biology is whether long range correlations are present in both coding and noncoding dna or only in the latter to answer this question we consider all 33301 coding and all 29453 noncoding eukaryotic sequences each of length larger than 512 base pairs bp in the present release of the genbank to dtermine whether there is any statistically significant distinction in their long range correlation properties standard fast fourier transform fft analysis indicates that coding sequences have practically no correlations in the range from 10 bp to 100 bp spectral exponent beta 0 00 0 04 where the uncertainty is two standard deviations in contrast for noncoding sequences the average value of the spectral exponent beta is positive 0 16 0 05 which unambiguously shows the presence of long range correlations we also separately analyze the 874 coding and the 1157 noncoding sequences that have more than 4096 bp and find a larger region of power law behavior we calculate the probability that these two data sets coding and noncoding were drawn from the same distribution and we find that it is less than 10 10 we obtain independent confirmation of these findings using the method of detrended fluctuation analysis dfa which is designed to treat sequences with statistical heterogeneity such as dna s known mosaic structure patchiness arising from the nonstationarity of nucleotide concentration the near perfect agreement between the two independent analysis methods fft and dfa increases the confidence in the reliability of our conclusion

nonlinear transformation on the transfer entropy of financial time series abstract transfer entropy te now is widely used in the data mining and economic field however te itself demands that time series intend to be stationary and meet markov condition naturally we are interested in investigating the effect of the nonlinear transformation of the two series on the te therefore the paper is designed to study the te of five nonlinear volatile transformations based on the data which are generated by the linear modeling and the logistic maps modeling as well as the dataset that come from financial markets with only one of the te of nonlinear transformations fluctuating around the te of original series the te of others all have increased with different degrees

detrended fluctuation analysis of time series of a firing fusimotor neuron abstract we study the interspike intervals isi time series of the spontaneous fusimotor neuron activity by applying the detrended fluctuation analysis that is a modification of the random walk model analysis thus we have found evidence for the white noise characteristics of the isi time series which means that the fusimotor activity does not possess temporal correlations we conclude that such an activity represents the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles

derived categories of keum s fake projective planes abstract we conjecture that derived categories of coherent sheaves on fake projective n spaces have a semi orthogonal decomposition into a collection of n 1 exceptional objects and a category with vanishing hochschild homology we prove this for fake projective planes with non abelian automorphism group such as keum s surface then by passing to equivariant categories we construct new examples of phantom categories with both hochschild homology and grothendieck group vanishing

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

finite horizon h filter and its 2n algorithm a 2n algorithm will double a time or space step in each evaluation for initial value problem the 2n algorithm for the integration of filtering differential equation of the finite horizon h filter is presented in this paper since it is a boundary value problem within a time range a new 2n algorithm is introduced by merging two intervals each time so that the time interval is doubled in each evaluation if one divides the original time range into one million intervals 20 evaluations will complete the whole process owing to the extremely small initial time interval the first few terms of the taylor expansion of the interval matrices are sufficient for very accurate results since the filter gain matrices are the solution of the riccati differential equation and the existence of the solution depends on the induced norm the computation of critical value is reviewed first then according to the result and the prespecified performance index the suitable parameter 2 can be selected and the precise numerical solution of the riccati differential equation and the filtering differential equation can be obtained by using the 2n algorithm although the filtering equation is time varying the 2n algorithm for interval merging is given explicitly copyright 2001 john wiley sons ltd

on the multifractal effects generated by monofractal signals we study quantitatively the level of false multifractal signal one may encounter while ana lyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis mf dfa the investigated effect appears as a result of finite length of used data series and is additionally amplified by the long term memory the data eventually may contain we pro vide the detailed quantitative description of such apparent multifractal background signal as a threshold in spread of generalized hurst exponent valuesh or a threshold in the width of multifractal spectrum below which multifractal properties of the system are only apparent i e do not exist despite 6 0 orh 6 0 we find this effect quite important for shorter or persistent series and we argue it is linear with respect to autocorrelation exponent its strength decays according to power law with respect to the length of time series the influ ence of basic linear and nonlinear transformations applied to initial data in finite time series with various levels of long memory is also investigated this provides additional set of semi analytical results the obtained formulas are significant in any interdisciplinary application of multifractality including physics financial data analysis or physiology because they allow to separate the true multifractal phenomena from the apparent artificial multifractal effects they should be a helpful tool of the first choice to decide whether we do in particular case with the signal with real multiscaling properties or not

cal h _ infty and dwell time specifications of continuous time switched linear systems this technical note deals with continuous time switched linear systems and addresses the problem of characterizing open loop switching strategies based on dwell time specifications assuring a pre specified root mean square gain rms as a natural consequence of treating general systems of this particular class in terms of order and number of subsystems only sufficient conditions are worked out however as positive features they are expressed through linear matrix inequalities lmi being thus numerically solvable in polynomial time and allow the treatment of stable switched linear systems which do not admit a common lyapunov function the conservativeness of the proposed design method is evaluated by comparison with other results available in the literature by means of two simple illustrative examples

magnitude and sign scaling in power law correlated time series a time series can be decomposed into two sub series a magnitude series and a sign series here we analyze separately the scaling properties of the magnitude series and the sign series using the increment time series of cardiac interbeat intervals as an example we 6nd that time series having identical distributions and long range correlation properties can exhibit quite di8erent temporal organizations of the magnitude and sign sub series from the cases we study it follows that the long range correlations in the magnitude series indicate nonlinear behavior speci6cally our results suggest that the correlation exponent of the magnitude series is a monotonically increasing function of the multifractal spectrum width of the original series on the other hand the sign series mainly relates to linear properties of the original series we also show that the magnitude and sign series of the heart interbeat interval series can be used for diagnosis purposes c

random cascades on wavelet dyadic trees we introduce a new class of random fractal functions using the orthogonal wavelet transform these functions are built recursively in the space scale half plane of the orthogonal wavelet transform cascading from an arbitrary given large scale towards small scales to each random fractal function corresponds a random cascading process referred to as a w cascade on the dyadic tree of its orthogonal wavelet coefficients we discuss the convergence of these cascades and the regularity of the so obtained random functions by studying the support of their singularity spectra then we show that very different statistical quantities such as correlation functions on the wavelet coefficients or the wavelet based multifractal formalism partition functions can be used to characterize very precisely the underlying cascading process we illustrate all our results on various numerical examples

h control with transients in h infty or uniformly optimal control problems it is usually assumed that the system initial conditions are zero in this paper an h infty like control problem that incorporates uncertainty in initial conditions is formulated this is done by defining a worst case performance measure both finite and infinite horizon problems are considered necessary and sufficient conditions are derived for the existence of controllers that yield a closed loop system for which the above mentioned performance measure is less than a prespecified value state space formulae for the controllers are also presented

difference and differential riccati equations a note on the convergence to the strong solution the convergence of the solutions of the differential difference riccati equations to the strong solution of the corresponding algebraic riccati equation are is addressed detectability only is required in the analysis and no assumption is made on the eigenvalues on the real imaginary axis on the unit circle in the discrete time case in particular from the results it follows that under the sole assumption of detectability a positive definite initial condition guarantees convergence to the strong solution even in the presence of unreachable eigenvalues on the imaginary axis or on the unit circle

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

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

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

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

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

attempt to distinguish long range temporal correlations from the statistics of the increments by natural time analysis most probable value of 1 of the shuffled data is found to be approximately equal to that of the original data the difference most likely arising from temporal correlation finally it is found that the differential entropy associated with the probability p1 maximizes for around 1 6 1 7 which is comparable to the value determined experimentally in diverse phenomena e g solar flares icequakes dislocation glide in stressed single crystals of ice etc it also agrees with the b value in the gutenberg richter law of earthquakes in addition the case of multiplicative cascades is studied in the natural time domain

preservation of long range temporal correlations under extreme random dilution abstract many natural time series exhibit long range temporal correlations that may be characterized by power law scaling exponents however in many cases the time series have uneven time intervals due to for example missing data points noisy data and outliers here we study the effect of randomly missing data points on the power law scaling exponents of time series that are long range temporally correlated the fourier transform and detrended fluctuation analysis dfa techniques are used for scaling exponent estimation we find that even under extreme dilution of more than 50 the value of the scaling exponent remains almost unaffected random dilution is also applied on heart interbeat interval time series it is found that dilution of 70 80 of the data points leads to a reduction of only 8 in the scaling exponent it is also found that it is possible to discriminate between healthy and heart failure subjects even under extreme dilution of more than 90

sur la rigidite de certains groupes fondamentaux l arithmeticite des reseaux hyperboliques complexes et les faux plans projectifs the motivation of this work comes from the study of lattices in real simple lie groups the famous margulis s superrigidity theorem claims that finite dimensional reductive representations of any lattice of a real simple lie group of real rank 2 are superrigid as a corollary such a lattice is arithmetic these results extend to the real rank one case for lattices in sp n 1 and f4 20 by the work of corlette and gromov schoen on the other hand mostow and deligne mostow exhibited arithmetic lattices with non superrigid representations as well as non arithmetic lattices in the unitary group pu 2 1 a natural question is then to find simple sufficient conditions for superrigidity or arithmeticity of lattices in pu 2 1 rogawski conjectured the following let be a torsion free cocompact lattice in pu 2 1 such that the hyperbolic quotient m b2 verifies the cohomogical conditions b1 m 0 and h1 1 m h2 m then is arithmetic in this paper we consider a smooth complex projective surface m verifying the above cohomological assumptions and study zariski dense representations of the fundamental group 1 m in a simple k group h of k rank 2 where k denotes a local field our main result states that there are strong restrictions on such representations especially when k is non archimedean theorem 5 we then consider some cocompact lattices in pu 2 1 of special geometric interest recall that a fake p2 is a smooth complex surface distinct from p2 having the same betti numbers as p2 fake p2 exist by a result of mumford and are complex hyperbolic quotients h2 by yau s proof of the calabi conjecture they obviously verify the hypotheses of rogawski s conjecture in this case we prove that every zariski dense representation of in pgl 3 is superrigid in the sense of margulis theorem 3 as a corollary every fake p2 is an arithmetic quotient of the ball b2

are the phases in the anderson model long range correlated we investigate the local cumulative phases at single sites of the lattice for time dependent wave functions in the anderson model in d 2 and 3 in addition to a local linear trend the phases exhibit some fluctuations we study the time correlations of these fluctuations using detrended fluctuation analysis our results suggest that the phase fluctuations are long range correlated decaying as a power law with time it seems that the exponent depends on the degree of disorder in d 3 close to the critical disorder wc 16 5 the correlation exponent exhibits a maximum value of 0 6 which is significantly above random fluctuations 0 5

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

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

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

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

explicit equations of a fake projective plane fake projective planes are smooth complex surfaces of general type with betti numbers equal to those of the usual projective plane they come in complex conjugate pairs and have been classified as quotients of the 2 dimensional ball by explicitly written arithmetic subgroups in the following we find equations of a projective model of a conjugate pair of fake projective planes by studying the geometry of the quotient of such surface by an order 7 automorphism

multifractal random walk we introduce a class of multifractal processes referred to as multifractal random walks mrws to our knowledge it is the first multifractal process with continuous dilation invariance properties and stationary increments mrws are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio the mrws are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments we briefly explain how in the same way one can build stationary multifractal processes or positive random measures

receding horizon revisited an easy way to robustly stabilize an ltv system stabilization schemes are often based on infinite horizon optimization of a non singular cost functional for such schemes to make sense in a time varying context a fairly good knowledge of the system parameters at all times is a prerequisite that is a major disadvantage in adaptive implementations when applicable the receding horizon approach overcomes this difficulty as though it relies on general qualitative long term properties such as controllability it requires quantitative knowledge only of temporally local parameter values work done on receding horizon stabilization during the 1970 s focused on lq h2 optimization criteria looking for a stabilization method which carries also the robustness properties of infinite horizon h design we consider here local minimization of the l2 induced i o norm h optimization as the design objective both state and observation based feedback scheme are derived and relations to finite and infinite horizon optimization are discussed

nonextensivity and natural time the case of seismicity nonextensive statistical mechanics pioneered by tsallis has recently achieved a generalization of the gutenberg richter law for earthquakes this remarkable generalization is combined here with natural time analysis which enables the distinction of two origins of self similarity i e the process memory and the process increments infinite variance by using also detrended fluctuation analysis for the detection of long range temporal correlations we demonstrate the existence of both temporal and magnitude correlations in real seismic data of california and japan natural time analysis reveals that the nonextensivity parameter q in contrast to some published claims cannot be considered as a measure of temporal organization but the tsallis formulation does achieve a satisfactory description of real seismic data for japan for q 1 66 when supplemented by long range temporal correlations

new conditions for the convergence of h sub spl infin filters and predictors the finite horizon h sub spl infin filtering and prediction problems in the discrete time case admit solutions only if a suitable difference riccati equation is solved by a matrix sequence satisfying feasibility conditions in this work sufficient conditions ensuring the existence of filters and predictors over an arbitrarily long time interval are derived moreover it is shown that under these conditions finite horizon estimators tend to stable stationary ones as the time horizon increases