measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

robustness of sentence length measures in written texts abstract hidden structural patterns in written texts have been subject of considerable research in the last decades in particular mapping a text into a time series of sentence lengths is a natural way to investigate text structure typically sentence length has been quantified by using measures based on the number of words and the number of characters but other variations are possible to quantify the robustness of different sentence length measures we analyzed a database containing about five hundred books in english for each book we extracted six distinct measures of sentence length including the number of words and number of characters taking into account lemmatization and stop words removal we compared these six measures for each book by using i pearson s coefficient to investigate linear correlations ii kolmogorov smirnov test to compare distributions and iii detrended fluctuation analysis dfa to quantify auto correlations we have found that all six measures exhibit very similar behavior suggesting that sentence length is a robust measure related to text structure

error threshold in optimal coding numerical criteria and classes of universalities for complexity the free energy of the random energy model at the transition point between the ferromagnetic and spin glass phases is calculated at this point equivalent to the decoding error threshold in optimal codes the free energy has finite size corrections proportional to the square root of the number of degrees the response of the magnetization to an external ferromagnetic phase is maximal at values of magnetization equal to one half we give several criteria of complexity and define different universality classes according to our classification at the lowest class of complexity are random graphs markov models and hidden markov models at the next level is the sherrington kirkpatrick spin glass connected to neuron network models on a higher level are critical theories the spin glass phase of the random energy model percolation and self organized criticality the top level class involves highly optimized tolerance design error thresholds in optimal coding language and maybe financial markets living systems are also related to the last class the concept of antiresonance is suggested for complex systems

topology induced coarsening in language games we investigate how very large populations are able to reach a global consensus out of local microscopic interaction rules in the framework of a recently introduced class of models of semiotic dynamics the so called naming game we compare in particular the convergence mechanism for interacting agents embedded in a low dimensional lattice with respect to the mean field case we highlight that in low dimensions consensus is reached through a coarsening process that requires less cognitive effort of the agents with respect to the mean field case but takes longer to complete in one dimension the dynamics of the boundaries is mapped onto a truncated markov process from which we analytically computed the diffusion coefficient more generally we show that the convergence process requires a memory per agent scaling as n and lasts a time n 1 2 d in dimension d 4 the upper critical dimension while in mean field both memory and time scale as n 3 2 for a population of n agents we present analytical and numerical evidence supporting this picture

can analysis of word frequency distinguish between writings of different authors abstract various literature writings are compared by the rank distance d between two word frequency zipf plots introduced by s havlin physica a 216 1995 148 we studied 22 books written by six authors for this ensemble of books we find that the mean distance between books written by the same authors d 15 2 2 6 is considerably smaller than that between books written by different authors d 21 8 3 2 in good agreement with earlier results on a smaller sample of books our results suggest that the distribution of the rank difference of the same words in different books decays exponentially

testing the order of discrete markov chains using surrogate data tests of the null hypothesis that a symbolic sequence is of nth markov order are described these tests are based on resampling methods similar to the method of surrogate data used to test continuous time series for nonlinear structure the size and power of these symbolic surrogate tests are estimated using binary and heptary test sequences of known order conditioning on a sufficient statistic under the null hypothesis yields an estimated true size which closely approximates the nominal size and increases the power of the test with respect to the unconditional test we apply one method to a symbolic sequence derived from the rossler system and to a binary and heptary representation of an interspike interval sequence of an electroreceptor of the weakly electric eel apteronotus leptorhynchus

analysis of tbzn resistivity temperature derivative above the curie point using singular fitting equations new analyses were carried out of previously published tbzn resistivity temperature derivative data just above the curie temperature tc fitting was accomplished using a weighted nonlinear least squares program genls which allows one to take proper account of errors present in both the independent and the dependent variables the utility of fitting with equations of either logarithmic or power law form involving a critical exponent both with a pole at the curie point was investigated in detail fitting results were uncertain for the four parameter power law choice but with one parameter fixed led to estimates of tc of 199 61 0 02 k and of of 0 16 0 01 the latter value is rather far removed from the value of 0 104 which is expected for a three dimensional n 1 ising model and from the value of 0 014 for a three dimensional n 2 xy model by contrast fitting with a three parameter logarithmic law corresponding to a three dimensional n 2 xy model led to estimated standard deviations of all three free parameters much smaller than the corresponding ones of the four parameter power law fit and to a tc estimate of 199 56 0 03k the present results thus indicate the presence of marked xy or even ising anisotropy quadrupolar effects seem irrelevant

the derivation of the regularized chiral jacobian using the zeta function method using the zeta function method a general formula for the regularized chiral jacobian to theories including non hermitian dirac operators d defined in arbitrary even dimensional euclidean space is derived the agreement of this formula with the results obtained in the differential geometric approach is also clarified

language evolution and population dynamics in a system of two interacting species we use monte carlo simulations and assumptions from evolutionary game theory in order to study the evolution of words and the population dynamics of a system made of two interacting species which initially speak two different languages the species are characterized by their identity vocabulary and have different initial fitness i e reproduction capability we investigate how different initial fitness affects the vocabulary of the species or the population dynamics by leading to a permanent populational advantage we further find that the spatial distributions of the species may cause the system to exhibit pattern formation or segregation we show that an initial fitness advantage even though very quickly balanced leads to better spatial arrangement and enhances survival probabilities of the species in most cases the system will arrive at a final state where both languages coexist however in cases where one species greatly outnumbers the other in population and fitness then only one species survives with its final language having a slightly richer vocabulary than its initial language thus our results offer an explanation for the existence and origin of synonyms in spoken languages

on the regularized determinant for non invertible elliptic operators we propose a technique for regularizing the determinant of a non invertible elliptic operator restricted to the complement of its nilpotent elements we apply this approach to the study of chiral changes in the fermionic path integral variables

prediction and entropy of nonlinear dynamical systems and symbolic sequences with lro abstract following shannon we introduce higher order entropies and derive dynamic entropies the nth order dynamic entropy conditional entropy is a measure of the uncertainty of the next state which follows after the observation of n foregoing states the asymptotic behaviour of the dynamic entropies at large n is studied for several nonlinear model systems and for symbolic sequences with long range order lro for example we investigate 1d maps texts dna strings and time series it is shown that the existence of long correlations improves the possibility of predictions characteristic scaling laws for the higher order shannon entropies and the conditional entropies are derived and a new interpolation formula is tested finally instead of the dynamic entropies which yield mean values of the uncertainty predictability we investigate the local values of the uncertainty predictability

modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti persistent processes abstract detrended fluctuation analysis dfa is a simple but very efficient method for investigating the power law long term correlations of non stationary time series in which a detrending step is necessary to obtain the local fluctuations at different timescales we propose to determine the local trends through empirical mode decomposition emd and perform the detrending operation by removing the emd based local trends which gives an emd based dfa method similarly we also propose a modified multifractal dfa algorithm called an emd based mfdfa the performance of the emd based dfa and mfdfa methods is assessed with extensive numerical experiments based on fractional brownian motion and multiplicative cascading process we find that the emd based dfa method performs better than the classic dfa method in the determination of the hurst index when the time series is strongly anticorrelated and the emd based mfdfa method outperforms the traditional mfdfa method when the moment order q of the detrended fluctuations is positive we apply the emd based mfdfa to the 1 min data of shanghai stock exchange composite index and the presence of multifractality is confirmed we also analyze the daily austrian electricity prices and confirm its anti persistence

mutual information functions versus correlation functions this paper studies one application of mutual information to symbolic sequences the mutual information functionm d this function is compared with the more frequently used correlation function d an exact relation betweenm d and d is derived for binary sequences for sequences with more than two symbols no such general relation exists in particular d 0 may or may not lead tom d 0 this linear but not general independence between symbols separated by a distance is studied for ternary sequences also included is the estimation of the finite size effect on calculating mutual information finally the concept of symbolic noise is discussed

on perturbation theory for regularized determinants of differential operators a perturbation theory for determinants of differential operators regularized through the function technique is presented the application of this approach to the study of chiral changes in the fermionic path integral variables is discussed

entropy analysis of natural language written texts abstract the aim of the present work is to investigate the relative contribution of ordered and stochastic components in natural written texts and examine the influence of text category and language on these to this end a binary representation of written texts and the generated symbolic sequences are examined by the standard block entropy analysis and the shannon and kolmogorov entropies are obtained it is found that both entropies are sensitive to both language and text category with the text category sensitivity to follow almost the same trends in both languages english and greek considered the values of these entropies are compared with those of stochastically generated symbolic sequences and the nature of correlations present in this representation of real written texts is identified

limit theorems for toeplitz quadratic functionals of continuous time stationary processes let x t t in mathbb r be a centered real valued stationary gaussian process with spectral density f the paper considers a question concerning asymptotic distribution of toeplitz type quadratic functional qt of the process x t generated by an integrable even function g sufficient conditions in terms of f and g ensuring central limit theorems for standard normalized quadratic functionals qt are obtained extending the results of fox and taqqu prob theory relat fields 74 213 240 1987 avram prob theory relat fields 79 37 45 1988 giraitis and surgailis prob theory relat fields 86 87 104 1990 ginovian and sahakian theory prob appl 49 612 628 2004 for discrete time processes

convergence in distribution of sums of bivariate appell polynomials with long range dependence normalized quadratic forms of moving averages converge to double wiener ito integrals if the summands are sufficiently dependent this result extends to sums of bivariate appell polynomials of arbitrary degree

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

theoretical model for the evolution of the linguistic diversity abstract here we describe how some important scaling laws observed in the distribution of languages on earth can emerge from a simple computer simulation the proposed language dynamics includes processes of selective geographic colonization linguistic anomalous diffusion and mutation and interaction among populations that occupy different regions it is found that the dependence of the linguistic diversity on the area after colonization displays two power law regimes both described by critical exponents which are dependent on the mutation probability most importantly for the future prospect of world s population our results show that the linguistic diversity always decrease to an asymptotic very small value if large areas and sufficiently long times of interaction among populations are considered

multifractality in stock indexes fact or fiction abstract multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes including hsi szsc s p 500 and nasdaq to check whether the indexes instead of the returns possess multifractality we find that the mass exponent q is linear and the singularity q is close to 1 for all trading days and all indexes furthermore we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series hence the so called multifractality in the intraday stock market indexes is merely an illusion

shakespeare and other english renaissance authors as characterized by information theory complexity quantifiers abstract we introduce novel information theory quantifiers in a computational linguistic study that involves a large corpus of english renaissance literature the 185 texts studied 136 plays and 49 poems in total with first editions that range from 1580 to 1640 form a representative set of its period our data set includes 30 texts unquestionably attributed to shakespeare in addition we also included a lover s complaint a poem which generally appears in shakespeare collected editions but whose authorship is currently in dispute our statistical complexity quantifiers combine the power of jensen shannon s divergence with the entropy variations as computed from a probability distribution function of the observed word use frequencies our results show among other things that for a given entropy poems display higher complexity than plays that shakespeare s work falls into two distinct clusters in entropy and that his work is remarkable for its homogeneity and for its closeness to overall means

possible origin of power law behavior in n tuple zipf analysis in n tuple zipf analysis words are defined as strings of n digits and their normalized frequency of occurrence v is measured for a given text sequence of digits in the case of various non markovian sequences the probability density of the frequencies p v has a power law tail here we argue that a broad class of unbiased binary texts exhibiting a nonexponential distribution of cluster sizes can indeed yield a power law behavior of p v where we define clusters to be strings of identical digits we support this result by numerical studies of long range correlated sequences generated by three different methods that result in

multifractal analyses of music sequences multifractal analysis is applied to study the fractal property of music in this paper a method is proposed to transform both the melody and rhythm of a music piece into individual sets of distributed points along a one dimensional line the structure of the musical composition is thus manifested and characterized by the local clustering pattern of these sequences of points specifically the local holder exponent and the multifractal spectrum are calculated for the transformed music sequences according to the multifractal formalism the observed fluctuations of the holder exponent along the music sequences confirm the non uniformity feature in the structures of melodic and rhythmic motions of music our present result suggests that the shape and opening width of the multifractal spectrum plot can be used to distinguish different styles of music in addition a characteristic curve is constructed by mapping the point sequences converted from the melody and rhythm of a musical work into a two dimensional graph each different pieces of music has its own unique characteristic curve this characteristic curve which also exhibits a fractal trait unveils the intrinsic structure of music

on the quotient of the regularized determinant of two elliptic operators we study the quotient of the regularized determinants of two elliptic operators having the same principal symbol we prove that under general conditions a method recently proposed by tamura coincides with the function approach

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

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

the n zipf analysis of financial data series and biased data series the zipf analysis of n words in random sequences and financial data series like the stock prices of a company has been performed the bias as well as the resulting staircase structure of the zipf plots are taken into account in the subsequent analysis it is found that correlations for the sign of the fluctuations as well as for the amplitude of the fluctuations can be found in financial time series the relevance of the n zipf analysis to financial sequences is underlined to be only weakly predictive for a binary transformation level but could be more interesting for higher translation levels

quantifying origin and character of long range correlations in narrative texts in natural language using short sentences is considered efficient for communication however a text composed exclusively of such sentences looks technical and reads boring a text composed of long ones on the other hand demands significantly more effort for comprehension studying characteristics of the sentence length variability slv in a large corpus of world famous literary texts shows that an appealing and aesthetic optimum appears somewhere in between and involves selfsimilar cascade like alternation of various lengths sentences a related quantitative observation is that the power spectra s f of thus characterized slv universally develop a convincing 1 fs scaling with the average exponent s 1 2 close to what has been identified before in musical compositions or in the brain waves an overwhelming majority of the studied texts simply obeys such fractal attributes but especially spectacular in this respect are hypertext like stream of consciousness novels in addition they appear to develop structures characteristic of irreducibly interwoven sets of fractals called multifractals scaling of s f in the present context implies existence of the long range correlations in texts and appearance of multifractality indicates that they carry even a nonlinear component a distinct role of the full stops in inducing the long range correlations in texts is evidenced by the fact that the above quantitative characteristics on the long range correlations manifest themselves in variation of the full stops recurrence times along texts thus in slv but to a much lesser degree in the recurrence times of the most frequent words in this latter case the nonlinear correlations thus multifractality disappear even completely for all the texts considered treated as one extra word the full stops at the same time appear to obey the zipfian rank frequency distribution however

equilibrium and dynamic methods when comparing an english text and its esperanto translation abstract a comparison of two english texts written by lewis carroll one alice in wonderland also translated into esperanto the other through the looking glass are discussed in order to observe whether natural and artificial languages significantly differ from each other one dimensional time series like signals are constructed using only word frequencies fts or word lengths lts the data is studied through i a zipf method for sorting out correlations in the fts and ii a grassberger procaccia gp technique based method for finding correlations in lts the methods correspond to an equilibrium and a dynamic approach respectively to human texts features there are quantitative statistical differences between the original english text and its esperanto translation but the qualitative differences are very minutes however different power laws are observed with characteristic exponents for the ranking properties and the phase space attractor dimensionality the zipf exponent can take values much less than unity 0 50 or 0 30 depending on how a sentence is defined this variety in exponents can be conjectured to be an intrinsic measure of the book style or purpose rather than the language or author vocabulary richness since a similar exponent is obtained whatever the text moreover the attractor dimension r is a simple function of the so called phase space dimension n i e r n with 0 79 such an exponent could also be conjectured to be a measure of the author style versatility here well preserved in the translation

modeling the average shortest path length in growth of word adjacency networks we investigate properties of evolving linguistic networks defined by the word adjacency relation such networks belong to the category of networks with accelerated growth but their shortest path length appears to reveal the network size dependence of different functional form than the ones known so far we thus compare the networks created from literary texts with their artificial substitutes based on different variants of the dorogovtsev mendes model and observe that none of them is able to properly simulate the novel asymptotics of the shortest path length then we identify the local chainlike linear growth induced by grammar and style as a missing element in this model and extend it by incorporating such effects it is in this way that a satisfactory agreement with the empirical result is obtained

random texts exhibit zipf s law like word frequency distribution it is shown that the distribution of word frequencies for randomly generated texts is very similar to zipf s law observed in natural languages such as english the facts that the frequency of occurrence of a word is almost an inverse power law function of its rank and the exponent of this inverse power law is very close to 1 are largely due to the transformation from the word s length to its rank which stretches an exponential function to a power law function

long range correlations between letters and sentences in texts abstract we mapped three long texts to random walks and calculated several correlation measures as holder exponents higher order cumulants and power spectra by means of computer experiments we have found that shuffling on or below the sentence level generates strings showing no anomalous diffusion no higher order cumulants and no power spectra with 1 f shape in this way we have shown that the long correlations reflected in these measures are not based on correlations inside sentences but reflect the large scale structure beyond the sentence level

wavelet versus detrended fluctuation analysis of multifractal structures we perform a comparative study of applicability of the multifractal detrended fluctuation analysis mfdfa and the wavelet transform modulus maxima wtmm method in proper detecting of monofractal and multifractal character of data we quantify the performance of both methods by using different sorts of artificial signals generated according to a few well known exactly soluble mathematical models monofractal fractional brownian motion bifractal levy flights and different sorts of multifractal binomial cascades our results show that in the majority of situations in which one does not know a priori the fractal properties of a process choosing mfdfa should be recommended in particular wtmm gives biased outcomes for the fractional brownian motion with different values of hurst exponent indicating spurious multifractality in some cases wtmm can also give different results if one applies different wavelets we do not exclude using wtmm in real data analysis but it occurs that while one may apply mfdfa in a more automatic fashion wtmm must be applied with care in the second part of our work we perform an analogous analysis on empirical data coming from the american and from the german stock market for this data both methods detect rich multifractality in terms of broad f alpha but mfdfa suggests that this multifractality is poorer than in the case of wtmm

scaling features of texts images and time series in the given paper we consider the scaling features of long letter sequences like human writings discretized images and discretized 3nancial data using several approaches we show that the symbolic strings and time series being analyzed have a complex multiscale structure and demonstrate di5erent scalings for large and small 6uctuations we discuss complex phenomena in the scaling behavior of partition functions in the case of high frequency dax future data c 2001 elsevier science b v all rights reserved

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

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

network properties of written human language we investigate the nature of written human language within the framework of complex network theory in particular we analyze the topology of orwell s 1984 focusing on the local properties of the network such as the properties of the nearest neighbors and the clustering coefficient we find a composite power law behavior for both the average nearest neighbor s degree and average clustering coefficient as a function of the vertex degree this implies the existence of different functional classes of vertices furthermore we find that the second order vertex correlations are an essential component of the network architecture to model our empirical results we extend a previously introduced model for language due to dorogovtsev and mendes we propose an accelerated growing network model that contains three growth mechanisms linear preferential attachment local preferential attachment and the random growth of a predetermined small finite subset of initial vertices we find that with these elementary stochastic rules we are able to produce a network showing syntacticlike structures

beyond the zipf mandelbrot law in quantitative linguistics abstract in this paper the zipf mandelbrot law is revisited in the context of linguistics despite its widespread popularity the zipf mandelbrot law can only describe the statistical behaviour of a rather restricted fraction of the total number of words contained in some given corpus in particular we focus our attention on the important deviations that become statistically relevant as larger corpora are considered and that ultimately could be understood as salient features of the underlying complex process of language generation finally it is shown that all the different observed regimes can be accurately encompassed within a single mathematical framework recently introduced by c tsallis

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

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

generalized hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series a nonlinear dynamics approach can be used in order to quantify complexity in written texts as a first step a one dimensional system is examined two written texts by one author lewis carroll are considered together with one translation into an artificial language i e esperanto are mapped into time series their corresponding shuffled versions are used for obtaining a baseline two different one dimensional time series are used here one based on word lengths lts the other on word frequencies fts it is shown that the generalized hurst exponent h q and the derived f curves of the original and translated texts show marked differences the original texts are far from giving a parabolic f function in contrast to the shuffled texts moreover the esperanto text has more extreme values this suggests cascade model like with multiscale time asymmetric features as finally written texts a discussion of the difference and complementarity of mapping into a lts or fts is presented the fts f curves are more opened than the lts ones

the effects of observational correlated noises on multifractal detrended fluctuation analysis abstract we have numerically investigated the effects that observational correlated noises have on the generalized hurst exponents h q estimated by using the multifractal generalization of detrended fluctuation analysis mf dfa more precisely artificially generated stochastic binomial multifractals with increased amount of colored noises were analyzed via mf dfa it has been recently shown that for moderate additions of white noise the generalized hurst exponents are significantly underestimated for q 2 and they are nearly unchanged for q 2 j ludescher m i bogachev j w kantelhardt a y schumann a bunde on spurious and corrupted multifractality the effects of additive noise short term memory and periodic trends physica a 390 2011 2480 2490 in this paper we have found that h q with q 2 are also affected when correlated noises are considered this is due to the fact that the spurious correlations influence the scaling behaviors associated to large fluctuations the results obtained are significant for practical situations where noises with different correlations are inherently present

punctuation effects in english and esperanto texts abstract a statistical physics study of punctuation effects on sentence lengths is presented for written texts alice in wonderland and through a looking glass the translation of the first text into esperanto is also considered as a test for the role of punctuation in defining a style and for contrasting natural and artificial but written languages several log log plots of the sentence length rank relationship are presented for the major punctuation marks different power laws are observed with characteristic exponents the exponent can take a value much less than unity c a 0 50 or 0 30 depending on how a sentence is defined the texts are also mapped into time series based on the word frequencies the quantitative differences between the original and translated texts are very minutes at the exponent level it is argued that sentences seem to be more reliable than word distributions in discussing an author style

multifractal geometry in stock market time series it has been recently noticed that time series of returns in stock markets are of multifractal multiscaling character in that context multifractality has been always evidenced by its statistical signature i e the scaling exponents associated to a related variable however a direct geometrical framework much more revealing about the underlying dynamics is possible in this paper we present the techniques allowing the multifractal decomposition we will show that there exists a particular fractal component the most singular manifold msm which contains the relevant information about the dynamics of the series it is possible to reconstruct the series at a given precision from the msm we analyze the dynamics of the msm which shows revealing features about the evolution of this type of series