a markov model of financial returns abstract we address the general problem of how to quantify the kinematics of time series with stationary first moments but having non stationary multifractal long range correlated second moments we show that a markov process is sufficient to model important aspects of the multifractality observed in financial time series and propose a kinematic model of price fluctuations we test the proposed model by analyzing index closing prices of the new york stock exchange and the dem usd tick by tick exchange rates obtained from reuters efx we show that the model captures the characteristic features observed in actual financial time series including volatility clustering time scaling and fat tails in the probability density functions power law behavior of volatility correlations and most importantly the observed nonuniversal multifractal singularity spectrum motivated by our finding of strong agreement between the model and the data we argue that at least two independent stochastic gaussian variables are required to adequately model price fluctuations

establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes stochastic fractal signals can be characterized by the hurst coefficient h which is related to the exponents of various power law statistics characteristic of these processes two techniques widely used to estimate h are spectral analysis and detrended fluctuation analysis dfa this paper examines the analytical link between these two measures and shows that they are related through an integral transform numerical simulations confirm this relationship for ideal synthesized fractal signals their performance as estimators of h is compared based on a mean square error criterion and found to be similar dfa measures are derived for physiological signals of heartbeat r ensuremath r intervals through the integral transform of a spectral density estimate these agree with directly calculated dfa estimates indicating that the relationship holds for signals with nonideal fractal properties it is concluded that dfa and spectral measures provide equivalent characterizations of stochastic signals with long term correlation

empirical scaling relations of market event rates in foreign currency market abstract the mechanism of order book dynamic is studied by using ultra high frequency data in terms of three market events injection cancellation and transaction we analyzed the empirical decision making process of market participants focusing on the event rates conditional on the depth from the mid price we observed that both injection and cancellation rates depend on the market depth with exponential decay near the mid price which is different from the conventional assumption of the homogeneous poisson process for the order book formation we also found scaling relations between injection cancellation transaction and diffusion of the mid price highlighting the correlation between these market events we finally discussed a theoretical model based on our findings to reproduce the empirical order book profiles

modeling stylized facts for financial time series abstract multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series they describe the well established deviations from the gaussian random walk such as an approximate scaling and heavy tails of the return distributions long ranged volatility volatility correlations volatility clustering and return volatility correlations leverage effect the model is tested successfully to fit joint distributions of the 100 years of daily price returns of the dow jones 30 industrial average

statistical analysis of 5 s index data of the budapest stock exchange abstract a statistical analysis of the budapest stock index bux is presented the high time resolution 5 s sampling makes it possible to extract information on market functioning which does not emerge from daily data the main results are as follows from a statistical point of view the large drop in october 1997 was a normal event strong autocorrelation has been detected in the volatility and market activity data detrended fluctuation analysis reveals superdiffusive scaling without persistence finally we report on a simple method for mapping local trends to represent sequences in order to obtain pattern statistics

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

equilibrium econophysics a unified formalism for neoclassical economics and equilibrium thermodynamics abstract we develop a unified conceptual and mathematical structure for equilibrium econophysics i e the use of concepts and tools of equilibrium thermodynamics in neoclassical microeconomics and vice versa within this conceptual structure the results obtained in microeconomic theory are 1 the definition of irreversibility in economic behavior 2 the clarification that the engel curve and the offer curve are not descriptions of real processes dictated by the maximization of utility at constant endowment 3 the derivation of a relation between elasticities proving that economic elasticities are not all independent 4 the proof that giffen goods do not exist in a stable equilibrium 5 the derivation that economic integrability is equivalent to the generalized le chatelier principle and 6 the definition of a first order phase transition i e a transition between separate points in the utility function in thermodynamics the results obtained are 1 a relation between the non dimensional isothermal and adiabatic compressibilities and the increase or decrease in the thermodynamic potentials 2 the distinction between mathematical integrability and optimization behavior and 3 the generalization of the clapeyron equation

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

wavelet correlation coefficient of strongly correlated time series abstract in this paper wavelet concepts are used to study two strongly correlated financial time series apart from obtaining wavelet spectra we also calculate the wavelet correlation coefficient and show that strong correlation or strong anti correlation depends on scale

codes in permutations and error correction for rank modulation codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors we study basic coding theoretic problems for such codes representing them as subsets of the set of permutations of n elements equipped with the kendall tau distance we derive several lower and upper bounds on the size of codes these bounds enable us to establish the exact scaling of the size of optimal codes for large values of n we also show the existence of codes whose size is within a constant factor of the sphere packing bound for any fixed number of errors

bounds for permutation rate distortion we study the rate distortion relationship in the set of permutations endowed with the kendall tau metric and the chebyshev metric the ell infty metric this paper is motivated by the application of permutation rate distortion to the average case and worst case distortion analysis of algorithms for ranking with incomplete information and approximate sorting algorithms for the kendall tau metric we provide bounds for various distortion regimes while for the chebyshev metric we present bounds that are valid for all distortions and are especially accurate for small distortions in addition for the chebyshev metric we provide a construction for covering codes

quantification of scaling exponent with crossover type phenomena for different types of forcing in dc glow discharge plasma abstract we have carried out a detailed study of scaling region using detrended fractal analysis test by applying different forcing likewise noise sinusoidal square on the floating potential fluctuations acquired under different pressures in a dc glow discharge plasma the transition in the dynamics is observed through recurrence plot techniques which is an efficient method to observe the critical regime transitions in dynamics the complexity of the nonlinear fluctuation has been revealed with the help of recurrence quantification analysis which is a suitable tool for investigating recurrence an ubiquitous feature providing a deep insight into the dynamics of real dynamical system an informal test for stationarity which checks for the compatibility of nonlinear approximations to the dynamics made in different segments in a time series has been proposed in case of sinusoidal noise square forcing applied on fluctuation acquired at p 0 12 mbar only one dominant scaling region is observed whereas the forcing applied on fluctuation p 0 04 mbar two prominent scaling regions have been explored reliably using different forcing amplitudes indicating the signature of crossover phenomena furthermore a persistence long range behavior has been observed in one of these scaling regions a comprehensive study of the quantification of scaling exponents has been carried out with the increase in amplitude and frequency of sinusoidal square type of forcings the scalings exponent is envisaged to be the roughness of the time series the method provides a single quantitative idea of the scaling exponent to quantify the correlation properties of a signal

on the labeling problem of permutation group codes under the infinity metric we consider codes over permutations under the infinity norm given such a code we show that a simple relabeling operation which produces an isomorphic code may drastically change the minimal distance of the code thus we may choose a code structure for efficient encoding procedures and then optimize the code s minimal distance via relabeling to establish that the relabeling problem is hard and is of interest we formally define it and show that all codes may be relabeled to get a minimal distance at most 2 on the other hand the decision problem of whether a code may be relabeled to distance 2 or more is shown to be np complete and calculating the best achievable minimal distance after relabeling is proved to be hard to approximate up to a factor of 2 we then consider general bounds on the relabeling problem we specifically construct the optimal relabeling for transitive cyclic groups we conclude with the main result a general probabilistic bound which we then use to show both the agl p group and the dihedral group on p elements may be relabeled to a minimal distance of p o p in p

exponentially damped levy flights multiscaling and exchange rates abstract we employ our previously suggested exponentially damped levy flight physica a 326 2003 544 to study the multiscaling properties of 30 daily exchange rates against the us dollar together with a fictitious euro dollar rate physica a 286 2000 353 though multiscaling is not theoretically seen in either stable levy processes or abruptly truncated levy flights it is even characteristic of smoothly truncated levy flights phys lett a 266 2000 282 eur phys j b 4 1998 143 we have already defined a class of quasi stable processes in connection with the finding that single scaling is pervasive among the dollar price of foreign currencies physica a 323 2003 601 here we show that the same goes as far as multiscaling is concerned our novel findings incidentally reinforce the case for real world relevance of the levy flights for modeling financial prices

efficiently computing the permanent and hafnian of some banded toeplitz matrices we present a new efficient method for computing the permanent and hafnian of certain banded toeplitz matrices the method covers non trivial cases for which previous known methods do not apply the main idea is to use the elements of the first row and column which determine the entire toeplitz matrix to construct a digraph in which certain paths correspond to permutations that the permanent and hafnian count since counting paths can be done efficiently the permanent and hafnian for those matrices is easily obtainable

on the scaling ranges of detrended fluctuation analysis for long term memory correlated short series of data abstract we examine the scaling regime for the detrended fluctuation analysis dfa the most popular method used to detect the presence of long term memory in data and the fractal structure of time series first the scaling range for dfa is studied for uncorrelated data as a function of time series length l and the correlation coefficient of the linear regression r 2 at various confidence levels next a similar analysis for artificial short series of data with long term memory is performed in both cases the scaling range is found to change linearly both with l and r 2 we show how this dependence can be generalized to a simple unified model describing the relation l r 2 h where h 1 2 h 1 stands for the hurst exponent of the long range autocorrelated signal our findings should be useful in all applications of dfa technique particularly for instantaneous local dfa where a huge number of short time series has to be analyzed at the same time without possibility of checking the scaling range in each of them separately

volatility in the italian stock market an empirical study we study the volatility of the mib30 stock index high frequency data from november 28 1994 through september 15 1995 our aim is to empirically characterize the volatility random walk in the framework of continuous time finance to this end we compute the index volatility by means of the log return standard deviation we choose an hourly time window in order to investigate intraday properties of volatility a periodic component is found for the hourly time window in agreement with previous observations fluctuations are studied by means of detrended fluctuation analysis and we detect long range correlations volatility values are log stable distributed we discuss the implications of these results for stochastic volatility modelling

effect of extreme data loss on long range correlated and anticorrelated signals quantified by detrended fluctuation analysis detrended fluctuation analysis dfa is an improved method of classical fluctuation analysis for nonstationary signals where embedded polynomial trends mask the intrinsic correlation properties of the fluctuations to better identify the intrinsic correlation properties of real world signals where a large amount of data is missing or removed due to artifacts we investigate how extreme data loss affects the scaling behavior of long range power law correlated and anticorrelated signals we introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of long range correlations the surrogate signals we generate are characterized by four parameters i the dfa scaling exponent alpha of the original correlated signal u i ii the percentage p of the data removed from u i iii the average length mu of the removed or remaining data segments and iv the functional form p l of the distribution of the length l of the removed or remaining data segments we find that the global scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90 in contrast the global scaling of anticorrelated signals changes to uncorrelated behavior even when a very small fraction of the data is lost these observations are confirmed on two examples of real world signals human gait and commodity price fluctuations we further systematically study the local scaling behavior of surrogate signals with missing data to reveal subtle deviations across scales we find that for anticorrelated signals even 10 of data loss leads to significant monotonic deviations in the local scaling at large scales from the original anticorrelated to uncorrelated behavior in contrast positively correlated signals show no observable changes in the local scaling for up to 65 of data loss while for larger percentage of data loss the local scaling shows overestimated regions with higher local exponent at small scales followed by underestimated regions with lower local exponent at large scales finally we investigate how the scaling is affected by the average length probability distribution and percentage of the remaining data segments in comparison to the removed segments we find that the average length mu r of the remaining segments is the key parameter which determines the scales at which the local scaling exponent has a maximum deviation from its original value interestingly the scales where the maximum deviation occurs follow a power law relationship with mu r whereas the percentage of data loss determines the extent of the deviation the results presented in this paper are useful to correctly interpret the scaling properties obtained from signals with extreme data loss

longest increasing subsequences from patience sorting to the baik deift johansson theorem we describe a simple one person card game patience sorting its analysis leads to a broad circle of ideas linking young tableaux with the longest increasing subsequence of a random permutation via the schensted correspondence a recent highlight of this area is the work of baik deift johansson which yields limiting probability laws via hard analysis of toeplitz determinants

levy walks and enhanced diffusion in milan stock exchange abstract we perform statistical analyses of the general and sectorial historical m i b indices of the milan stock exchange our analyses show that the price indices have statistical properties which are compatible with a levy random walk the time evolution of the daily variations of indices is intermittent on a time scale of years and the variance of almost all indices displays a superdiffusive behavior by using the theory of enhanced diffusion in levy walks as theoretical framework we ascribe the superdiffusive behavior to a nonlocal memory coupling price and time

constructions of rank modulation codes rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines modeling rank modulation involves construction of packings of the space of permutations equipped with the kendall tau distance as our main set of results we present several general constructions of codes in permutations that cover a broad range of code parameters in particular we show a number of ways in which conventional error correcting codes can be modified to correct errors in the kendall space our constructions are nonasymptotic and afford simple encoding and decoding algorithms of essentially the same complexity as required to correct errors in the hamming metric as an example from binary bose chaudhuri hocquenghem codes we obtain codes correcting t kendall errors in n memory cells that support the order of n log2n t messages for any constant t 1 2 we give many examples of rank modulation codes with specific parameters turning to asymptotic analysis we construct families of rank modulation codes that correct a number of errors that grows with n at varying rates from n to n2 one of our constructions gives rise to a family of rank modulation codes for which the tradeoff between the number of messages and the number of correctable kendall errors approaches the optimal scaling rate

precise m k zipf diagram analysis of mathematical and financial time series when m 6 k 2 for studying short range time correlations in nancial signals we have envisaged to combine the zipf method and the i variability diagrams vd as useful tools the 2 vd describes the local curvature short range correlations we have resulted into ranking the 2 vd data according to their frequency of occurrence after having tested the ideas and estimated the error bars on a brownian motion signal we have examined two stocks i e sgp and oxhp closing price and volume of transaction long series a precise m k zipf diagram analysis when m 6 k 2 has been shown to lead to a non immediate information on the signal behavior even taking into account error bars the set of curvatures translated into words indicates a brownian motion like set for the closing price local curvature of such signals over a 6 day span moreover it has been shown that the conjecture about a simple relationship between the hurst exponent h and the exponent of zipf plots does not seem to be substantiated here c 1999 elsevier science b v all rights reserved

bootstrap testing for detrended fluctuation analysis abstract detrended fluctuation analysis dfa is a scaling method that allows the detection of long memory in a time series until now no asymptotic distribution has been found for this statistic the bootstrap technique allows the simulation of the probability distribution of any statistic in this paper the results of the monte carlo study using bootstrap method show that the dfa test has reasonably good power for short time series another advantage of the bootstrap technique is that allows the calculation of finite sample critical values as an example we calculate bootstrap p values for financial returns time series using dfa

correcting charge constrained errors in the rank modulation scheme we investigate error correcting codes for a the rank modulation scheme with an application to flash memory devices in this scheme a set of n cells stores information in the permutation induced by the different charge levels of the individual cells the resulting scheme eliminates the need for discrete cell levels overcomes overshoot errors when programming cells a serious problem that reduces the writing speed and mitigates the problem of asymmetric errors in this paper we study the properties of error correcting codes for charge constrained errors in the rank modulation scheme in this error model the number of errors corresponds to the minimal number of adjacent transpositions required to change a given stored permutation to another erroneous one a distance measure known as kendall s distance we show bounds on the size of such codes and use metric embedding techniques to give constructions which translate a wealth of knowledge of codes in the lee metric to codes over permutations in kendall s metric specifically the one error correcting codes we construct are at least half the ball packing upper bound

asymptotic behavior of nonlinear evolution equations in banach spaces abstract in this study we show how yosida s approach for the approximation of the derivative obtains new results for evolution systems using this method we obtain multivalued time dependent perturbation results in addition we consider translation invariant subspaces y of the bounded and uniformly continuous functions to obtain criteria for the existence of solutions u y to the equation u t a t u t u t f t t r or of solutions u which are asymptotically close to y for the inhomogeneous differential equation u t a t u t u t f t t 0 u 0 u 0 in general banach spaces where a t denotes a possibly nonlinear time dependent dissipative operator particular examples of the space y are spaces of functions with various properties of almost periodicity and more general types of asymptotic behavior furthermore an application to functional differential equations is described

toward a phase diagram for stocks abstract a display of the tentatively basic parameters of stocks i e the daily closing price and the daily transaction volume is presented eliminating the time variable between them the phase diagram looks like a triangular region similar to the two phase region of traffic diagrams the data is taken for two companies sgp and oxhp which present different long range correlations in the closing price value as examined by the linearly detrended fluctuation analysis dfa statistical method substructures are observed in the phase diagram as due to changes in management policy e g stock splits

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

asymptotically almost periodic solutions of evolution equations in banach spaces abstract tile linear abstract evolution equation u t au t t t r is considered where a d a e e is the generator of a strongly continuous semigroup of operators in the banach space e starting from analogs of kadets and loomis theorems for vector valued almost periodic functions we show that if a i r is countable and r e is asymptotically almost periodic then every bounded and uniformly continuous solution u to is asymptotically almost periodic provided e tu t has uniformly convergent means for all a i r related results on eberlein weakly asymptotically almost periodic periodic asymptotically periodic and c0 solutions of as well as on the discrete case of solutions of difference equations are included

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

introducing false eur and false eur exchange rates abstract the euro eur is a new currency introduced by the european community its exchange rate is very puzzling we have invented a false euro feur dating back to 1993 and have derived the exchange rates of the feur with respect to currencies not belonging to the eur i e dkk chf jpy and usd this allows us to search for correlations between the fluctuations preexisting to the introduction of eur and present ones in such financial data the detrended fluctuation analysis dfa statistical method is used this leads to assume a power law behavior i e a scaling hypothesis through an exponent the latter has demonstrated its usefulness for the investigations of long range power law correlations in several types of financial sequences our findings show that the exponent interestingly characterizes fractional brownian motion of the currency exchange rates between eur and dkk over a 25 day interval and usual brownian motion otherwise and for the three other investigated exchange rates we can devise an investment strategy based on the local technique and obtain appreciable gains for the time being

flow invariance for solutions to nonlinear nonautonomous partial differential delay equations we investigate the problem of existence and flow invariance of mild solutions to nonautonomous partial differential delay equations u t b t u t f t ut t s us where b t is a family of nonlinear multivalued accretive operators with d b t possibly depending on t and the operators f t being defined and lipschitz continuous possibly only on thin subsets of the initial history space e the results are applied to population dynamics models we also study the asymptotic behavior of solutions to this equation our analysis will be based on the evolution operator associated to the equation in the initial history space e

an axiomatic approach to constructing distances for rank comparison and aggregation we propose a new family of distance measures on rankings derived through an axiomatic approach that consider the nonuniform relevance of the top and bottom of ordered lists and similarities between candidates the proposed distance functions include specialized weighted versions of the kendall distance and the cayley distance and are suitable for comparing rankings in a number of applications including information retrieval and rank aggregation in addition to proposing the distance measures and providing the theoretical underpinnings for their applications we also analyze algorithmic and computational aspects of weighted distance based rank aggregation we present an aggregation method based on approximating weighted distance measures by a generalized version of spearman s footrule distance as well as a markov chain method inspired by pagerank where transition probabilities of the markov chain reflect the chosen weighted distances

correcting limited magnitude errors in the rank modulation scheme we study error correcting codes for permutations under the infinity norm motivated by a novel storage scheme for flash memories called rank modulation in this scheme a set of n flash cells are combined to create a single virtual multilevel cell information is stored in the permutation induced by the cell charge levels spike errors which are characterized by a limited magnitude change in cell charge levels correspond to a low distance change under the infinity norm we define codes protecting against spike errors called limited magnitude rank modulation codes lmrm codes and present several constructions for these codes some resulting in optimal codes these codes admit simple recursive and sometimes direct encoding and decoding procedures we also provide lower and upper bounds on the maximal size of lmrm codes both in the general case and in the case where the codes form a subgroup of the symmetric group in the asymptotic analysis the codes we construct outperform the gilbert varshamov like bound estimate

long correlations and truncated levy walks applied to the study latin american market indices abstract this work is devoted to the study of long correlations and other statistical properties of latin american market indices we concluded that the behavior of the return is compatible with a slow convergence to a gaussian distribution we also detected long range correlations in the absolute value of the return analyzing the effects of working with short data series this fact has relevant consequences in the volatility dynamics

the origin of fat tailed distributions in financial time series abstract a classic problem in physics is the origin of fat tailed distributions generated by complex systems we study the distributions of stock returns measured over different time lags we find that destroying all correlations without changing the 1 d distribution by shuffling the order of the daily returns causes the fat tails to almost vanish for 1 d we argue that the fat tails are caused by the well known long range volatility correlations that have already been systematically studied previously indeed destroying only sign correlations by shuffling the order of only the signs but not the absolute values of the daily returns allows the fat tails to persist for 1 d

low order variability diagrams for short range correlation evidence in financial data bgl usd exchange rate dow jones industrial average gold ounce price a method to sort out short range correlations and decorrelations in financial data is tested on three typical sets the bulgarian lev usa dollar bgl usd exchange rate the dow jones industrial average the gold ounce price the method makes use of the so called variability diagram technique three toys are used as models in order to understand features our findings indicate that some predictability can be found at short range time intervals c 1999 elsevier science b v all rights reserved

improved lower bounds on the size of balls over permutations with the infinity metric we study the size or volume of balls in the metric space of permutations s n under the infinity metric we focus on the regime of balls with radius r rho cdot n 1 rho in 0 1 i e a radius that is a constant fraction of the maximum possible distance we provide new lower bounds on the size of such balls these new lower bounds reduce the asymptotic gap to the known upper bounds to at most 0 029 bits per symbol additionally they imply an improved ball packing bound for error correcting codes and an improved upper bound on the size of optimal covering codes

error correction in flash memories via codes in the ulam metric we consider rank modulation codes for flash memories that allow for handling arbitrary charge drop errors unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked elements the proposed translocation rank codes account for more general forms of errors that arise in storage systems translocations represent a natural extension of the notion of adjacent transpositions and as such may be analyzed using related concepts in combinatorics and rank modulation coding our results include derivation of the asymptotic capacity of translocation rank codes construction techniques for asymptotically good codes as well as simple decoding methods for one class of constructed codes as part of our exposition we also highlight the close connections between the new code family and permutations with short common subsequences deletion and insertion error correcting codes for permutations and permutation codes in the hamming distance

almost periodicity of mild solutions of inhomogeneous periodic cauchy problems abstract we consider a mild solution u of a well posed inhomogeneous cauchy problem u t a t u t f t on a banach space x where a is periodic for a problem on r we show that u is asymptotically almost periodic if f is asymptotically almost periodic u is bounded uniformly continuous and totally ergodic and the spectrum of the monodromy operator v contains only countably many points of the unit circle for a problem on r we show that a bounded uniformly continuous solution u is almost periodic if f is almost periodic and various supplementary conditions are satisfied we also show that there is a unique bounded solution subject to certain spectral assumptions on v f and u

nonlinear analysis of cardiac rhythm fluctuations using dfa method abstract after a brief overview of classical techniques used to explore cardiac rhythm variability we show how the dfa method can help diagnose heart failure

modeling of financial data comparison of the truncated levy flight and the arch 1 and garch 1 1 processes we compare our results on empirical analysis of nancia l data with simulations of two stochastic models of the dynamics of stock market prices the two models are i the truncated l evy igh t recently introduced by us and ii the arch 1 and garch 1 1 processes we n d that the tlf well describes the scaling and its breakdown observed in empirical data while it is not able to properly describe the uctuation s of volatility empirically detected the arch 1 and garch 1 1 models are able to describe the probability density function of price changes at a given time horizon but both fail to describe the scaling properties of the pdfs for short time horizons c 1998 elsevier science b v all rights reserved

coherent and random sequences in financial fluctuations abstract the detrended fluctuation analysis dfa is used to sort out temporal correlations in financial data its usefulness for the investigations of long range power law correlations in economic sequences is shown our findings of persistent and antipersistent sequences are suprisingly similar to those for dna sequences which appeared as a mosaic of coding and non coding patches

long range correlation analysis of economic news flow intensity abstract the goal of the paper is to examine the auto correlation properties for time series of the news flow intensity using different methods such as the fluctuation analysis the detrended fluctuation analysis and the detrending moving average analysis empirical findings for news analytics data show the presence of long range correlations for the time series of news intensity data

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

periodic solutions to functional evolution equations the object of the present paper is the study of a class of functional evolution equations of the type u t a t ut u t 0 t r where a t are nonlinear operators acting on a banach space x we establish under certain additional assumptions on x and the operator a the existence of a periodic generalized solution

the use of the hurst exponent to investigate the global maximum of the warsaw stock exchange wig20 index abstract the wig20 index the index of the 20 biggest companies traded on the warsaw stock exchange reached the global maximum on 29th october 2007 i have used the local dfa detrended functional analysis to obtain the hurst exponent diffusion exponent and investigate the signature of anti correlation of share price evolution around the maximum the analysis was applied to the share price evolution for variable dfa parameters for many values of parameters the evidence of anti correlation near the wig20 maximum was pointed out

wavelet methods in financial time series processing abstract we briefly describe the major advantages of using the wavelet transform for the processing of financial time series on the example of the sp fractals 8 2 2000 163 we use it to display the local spectral multifractal contents of the s p index in addition to this we analyse the collective properties of the local correlation exponent as perceived by the trader exercising various time horizon analyses of the index we observe an intriguing interplay between such different time horizons heavy oscillations at shorter time horizons which seem to be accompanied by a steady decrease of correlation level for longer time horizons seem to be characteristic patterns before the biggest crashes of the index we find that this way of local presentation of scaling properties may be of economic importance

long range correlations and nonstationarity in the brazilian stock market abstract we report an empirical study of the ibovespa index of the sao paulo stock exchange in which we detect the existence of long range correlations to analyze our data we introduce a rescaled variant of the usual detrended fluctuation analysis that allows us to obtain the hurst exponent through a one parameter fitting we also compute a time dependent hurst exponent h t using 3 year moving time windows in particular we find that before the launch of the collor plan in 1990 the curve h t remains in general well above 1 2 while afterwards it stays close to 1 2 we thus argue that the structural reforms set off by the collor plan has lead to a more efficient stock market in brazil we also suggest that the time dependence of the ibovespa hurst exponent could be described in terms of a multifractional brownian motion

strategy for investments from zipf law s abstract we have applied the zipf method to extract the exponent for seven financial indices dax ftse djia nasdaq sp hang seng and nikkei 225 after having translated the signals into a text based on two letters we follow considerations based on the signal hurst exponent and the notion of a time dependent zipf law and exponent in order to implement two simple investment strategies for such indices we show the time dependence of the returns

on the relationship between the hurst exponent the ratio of the mean square successive difference to the variance and the number of turning points abstract the long range dependence of the fractional brownian motion fbm fractional gaussian noise fgn and differentiated fgn dfgn is described by the hurst exponent h considering the realizations of these three processes as time series they might be described by their statistical features such as half of the ratio of the mean square successive difference to the variance a and the number of turning points t this paper investigates the relationships between a and h and between t and h it is found numerically that the formulae a h a e b h in case of fbm and a h a b h c for fgn and dfgn describe well the a h relationship when t h is considered no simple formula is found and it is empirically found that among polynomials the fourth and second order description applies best the most relevant finding is that when plotted in the space of a t the three process types form separate branches hence it is examined whether a and t may serve as hurst exponent indicators some real world data stock market indices sunspot numbers chaotic time series are analyzed for this purpose and it is found that the h s estimated using the h a relations expressed as inverted a h functions are consistent with the h s extracted with the well known wavelet approach this allows to efficiently estimate the hurst exponent based on fast and easy to compute a and t given that the process type fbm fgn or dfgn is correctly classified beforehand finally it is suggested that the a h relation for fgn and dfgn might be an exact shifted 3 2 power law

applications of statistical physics to economic and financial topics abstract problems in economy and finance have started to attract the interest of statistical physicists fundamental problems pertain to the existence or not of long medium short range power law correlations in economic systems as well as to the presence of financial cycles methods like the extended detrended fluctuation analysis and the multi affine analysis are recalled emphasizing their value in sorting out correlation ranges and predictability among spectacular results the possibility of crash predictions is indicated the well known financial analyst technique the so called moving average is shown to raise questions about fractional brownian motion properties finally the m k zipf method and the i variability diagram technique are presented for sorting out short range correlations analogies with other fields of modern applied statistical physics are also presented in view of some universal openess

hurst exponent of very long birth time series in xx century romania social and religious aspects abstract the hurst exponent of very long birth time series in romania has been extracted from official daily records i e over 97 years between 1905 and 2001 included the series result from distinguishing between families located in urban u or rural r areas and belonging ox or not nox to the orthodox religion four time series combining both criteria u r and ox nox are also examined a statistical information is given on these sub populations measuring their xx th century state as a snapshot however the main goal is to investigate whether the daily production of babies is purely noisy or is fluctuating according to some non trivial fractional brownian motion in the four types of populations characterized by either their habitat or their religious attitude yet living within the same political regime one of the goals was also to find whether combined criteria implied a different behavior moreover we wish to observe whether some seasonal periodicity exists the detrended fluctuation analysis technique is used for finding the fractal correlation dimension of such 9 signals it has been first necessary due to two periodic tendencies to define the range regime in which the hurst exponent is meaningfully defined it results that the birth of babies in all cases is a very strongly persistent signal it is found that the signal fractal correlation dimension is weaker i for nox than for ox and ii or u with respect to r moreover it is observed that the combination of u or r with nox or ox enhances the unox uox and rox fluctuations but smoothens the rnox signal thereby suggesting a stronger conditioning on religiosity rituals or rules