one dimensional cellular automata characterization by the roughness exponent abstract cellular automata ca are discrete spatially homogeneous locally interacting dynamical systems of very simple construction but which exhibit a rich intrinsic behavior ca can even starting from disordered initial configurations evolve into ordered states with complex structures crystallized in its space time patterns in this paper we concentrate on the several wolfram qualitative classes of ca behavior in order to better characterize these classes we apply the roughness exponent method to the profiles generated by the spatiotemporal patterns of one dimensional elementary ca rules we find that this method can separate wolfram class iv from other ones

conditions on unimodality and logconcavity for densities of coherent systems with an application to bernstein operators abstract in this note the distribution of the lifetime of a coherent system with independent and identically distributed component lifetimes is considered conditions yielding unimodality or logconcavity of the density function of the system lifetime are obtained in the conditions only assumptions on the density function of the components and on the signature of the system are imposed the results are illustrated with several examples additionally a problem on preservation of logconcavity under the classical bernstein operator is solved

on the preservation of log convexity and log concavity under some classical bernstein type operators this paper analyzes the preservation of both the log convexity and the log concavity under certain bernstein type operators some results are provided for the bernstein szasz baskakov the gamma type and the weierstrass operators probabilistic methods support the proofs of these results

log concavity preserving property of bernstein operators and bernstein semigroup abstract we prove that bernstein operators preserve log concavity of functions we give a proof which bases solely on elementary properties of the binomial coefficients we prove that the bernstein semigroup t t t 0 also has the log concavity preserving property we also solve two problems presented recently by i rasa

blocks adjustment reduction of bias and variance of detrended fluctuation analysis using monte carlo simulation abstract the length of minimal and maximal blocks equally distant on log log scale versus fluctuation function considerably influences bias and variance of dfa through a number of extensive monte carlo simulations and different fractional brownian motion fractional gaussian noise generators we found the pair of minimal and maximal blocks that minimizes the sum of mean squared error of estimated hurst exponents for the series of length n 2 p p 7 15 sensitivity of dfa to sort range correlations was examined using arfima p d q generator due to the bias of the estimator for anti persistent processes we narrowed down the range of hurst exponent to 1 2 h 1

fractal structure of digital speckle patterns produced by rough surfaces abstract we report on the fractal analysis of digital speckle patterns experimentally generated using an optical setup to record the light scattered from metallic rough surfaces in the normal direction using the differential box counting technique we have calculated the fractal dimension of digital speckle patterns for six samples with different roughness our results show a quadratic dependence between the surface roughness and the fractal dimension of the corresponding digital speckle pattern as an application a method to determine the surface roughness of metallic surfaces is proposed

on uniform approximation by some classical bernstein type operators abstract we investigate the functions for which certain classical families of operators of probabilistic type over noncompact intervals provide uniform approximation on the whole interval the discussed examples include the szasz operators the szasz durrmeyer operators the gamma operators the baskakov operators and the meyer konig and zeller operators we show that some results of totik remain valid for unbounded functions at the same time that we give simple rates of convergence in terms of the usual modulus of continuity we also show by a counterexample that the result for meyer konig and zeller operators does not extend to cheney and sharma operators

roughness exponent in the domany kinzel cellular automaton we propose a method to detect phase transitions in discrete lattice models based on the roughness exponent this approach is applied to the one dimensional domany kinzel cellular automaton ca our results obtained by numerical simulations show that the roughness exponent method detects the frozen active phase transition directly from the ca spatio temporal configurations without any reference to thermodynamical potentials order parameters or response functions

similarity and fractality in the modelling of roughness by a multilevel profile with hierarchical structure some modern scaling and fractal approaches to the characterization of surface roughness are under consideration a new mathematical model of a multilevel profile suitable for flexible simulation of roughness is presented as a development from these approaches the iterative construction of the model is described it is shown that the profile is a hierarchical structure with self affine and fractal features its geometrical properties are studied both analytically and numerically and some of them are proved to be of the renormalization type the profile contour length can be finite or infinite depending on the chosen values of the structural parameters some characteristics including the bearing curve and the upper volume function of the profile and the corresponding prestructures are calculated

detecting switching points using asymmetric detrended fluctuation analysis abstract this work uses the concept of asymmetric detrended fluctuation analysis a dfa to investigate and characterize the occurrence of trend switching in financial series a dfa introduces two new roughness exponents h and h which differ from the usual one h by separately taking into account contributions to the fluctuations according to whether the local trend is respectively upward or downward the developed methodology requires the evaluation of local values of h t h t and h t by restricting the size of the largest window around the value t we show that h t and h t behave differently in the neighborhoods of switching points sps where trends change sign properly taken differences between shifted local values of h t h t and h t allow to identify and characterize sp s tests with weiertrasse functions isolated peaks and actual financial series are presented supporting the validity of the proposed method

evaluating scaled windowed variance methods for estimating the hurst coefficient of time series three scaled windowed variance methods standard linear regression detrended and brdge detrended for estimating the hurst coefficient h are evaluated the hurst coefficient with 0 h 1 characterizes self similar decay in the time series autocorrelation function the scaled windowed variance methods estimate h for fractional brownian motion fbm signals which are cumulative sums of fractional gaussian noise fgn signals for all three methods both the bias and standard deviation of estimates are less than 0 05 for series having n 2 9 points estimates for short series n 2 8 are unreliable to have a 0 95 probability of distinguishing between two signals with true h differing by 0 1 more than 2 15 points are needed all three methods proved more reliable based on bias and variance of estimates than hurst s rescaled range analysis periodogram analysis and autocorrelation analysis and as reliable as dispersional analysis the latter methods can only be applied to fgn or differences of fbm while the scaled windowed variance methods must be applied to fbm or cumulative sums of fgn

fractal characterization of the distribution of reactive sites over a rough catalyst surface abstract the amount of reactive sites usually dispersed noble metal atoms on the top of a catalyst rough surface is characterized within the framework of fractal geometry the problem is reduced to evaluating properties of a fractal set built on a self affine profile numerical simulations are used to generate both support and different amounts of dispersed atoms three different parameters local and global fractal dimension and roughness exponent are used to analyze profiles obtained by three different processes results indicate that the quantitative characterization of dispersed atoms follows from the direct evaluation of the local fractal dimension this in turn is achieved after a simple adaptation of an optimized box counting algorithm

random fractals self affinity in noise music mountains and clouds abstract many of nature s seemingly complex shapes can be effectively characterized and modeled as random fractals based on generalizations of fractional brownian motion fbm as a function of one dimension t the trace vh t provides a model for the 1 noises extending fbm s to higher dimensions gives vh x y as landscapes and vh x y z as clouds although all such fbm s are statistically self affine as characterized by the parameter h or the spectral density exponent either zerosets or trails of independent fbm s are statistically self similar and may be represented by the fractal dimension d

scaling exponents of rough surfaces generated by the domany kinzel cellular automaton the critical behavior at the frozen active transition in the domany kinzel stochastic cellular automaton is studied via a surface growth process in 1 1 dimensions at criticality this process presents a kinetic roughening transition we measure the critical exponents in simulations two update schemes are considered in the symmetric scheme the growth surfaces belong to the directed percolation dp universality class except at one terminal point at this point the phase transition is discontinuous and the surfaces belong to the compact directed percolation universality class the relabeling of space time points in the nonsymmetric scheme alters significantly the surface growth changing the values of the critical exponents the critical behavior of rough surfaces at the nonchaotic chaotic transition is also studied using the damage spreading technique the exponents confirm dp values for the symmetric scheme

log concavity for bernstein type operators using stochastic orders abstract this paper aims to study the preservation of log concavity for bernstein type operators in particular attention is focused on positive linear operators defined on the positive semi axis admitting a probabilistic representation in terms of a process with independent increments this class includes the classical gamma szasz and szasz durrmeyer operators with respect to the first and second operators the results of this paper correct two erroneous counterexamples in 10 as a main tool in our results we use stochastic order techniques our results include as a particular case the log concavity of certain functions related to the incomplete gamma function

how fast do stock prices adjust to market efficiency evidence from a detrended fluctuation analysis abstract in this paper we analyse price fluctuations with the aim of measuring how long the market takes to adjust prices to weak form efficiency i e how long it takes for prices to adjust to a fractional brownian motion with a hurst exponent of 0 5 the hurst exponent is estimated for different time horizons using detrended fluctuation analysis a method suitable for non stationary series with trends in order to identify at which time scale the hurst exponent is consistent with the efficient market hypothesis using high frequency share price exchange rate and stock data we show how price dynamics exhibited important deviations from efficiency for time periods of up to 15 min thereafter price dynamics was consistent with a geometric brownian motion the intraday behaviour of the series also indicated that price dynamics at trade opening and close was hardly consistent with efficiency which would enable investors to exploit price deviations from fundamental values this result is consistent with intraday volume volatility and transaction time duration patterns

on the fractal dimension of self affine profiles one dimensional profiles f x can be characterized by a minkowski bouligand dimension d and by a scale dependent generalized roughness w f epsilon this roughness can be defined as the dispersion around a chosen fit to f x in an epsilon scale it is shown that d limepsilon to 0 2 in w f epsilon in epsilon holds for profiles nowhere differentiable this establishes a close connection between the roughness and the fractal dimension and proves that d 2 h for self affine profiles h is the roughness or hurst exponent two numerical algorithms based on the roughness one around the local average f x epsilon usual roughness and the other around the local rms straight line a generalized roughness are discussed the estimates of d for standard self affine profiles are reliable and robust especially for the last method

is the expression h 1 3 q valid for real financial data non extensive thermodynamics is one of the most intriguing physics new frontiers a large number of researchers have been successfully finding connections between the new concepts introduced by this new field and other complex systems already presented in particular borland phys rev e 57 1998 6634 6642 has introduced a very interesting relation between the entropic index q that arises in the non extensive entropy and the well known hurst exponent h used to measure long range dependence in complex systems in this paper we provide statistical support to borland results and test the validity of these results in real financial data

riemann surfaces with maximal real symmetry abstract let s be a compact riemann surface of genus g 1 and let s s be any anti conformal automorphism of s of order 2 such an anti conformal involution is known as a symmetry of s and the species of all conjugacy classes of all symmetries of s constitute what is known as the symmetry type of s the surface s is said to have maximal real symmetry if it admits a symmetry s s such that the compact klein surface s has maximal symmetry which means that s has the largest possible number of automorphisms with respect to its genus if has fixed points which is the only case we consider here then the maximum number of automorphisms of s is 12 g 1 in the first part of this paper we develop a computational procedure to compute the symmetry type of every riemann surface of genus g with maximal real symmetry for given small values of g 1 we have used this to find all of them for 1 g 101 and give details for 1 g 25 in an appendix in the second part we determine the symmetry types of four infinite families of riemann surfaces with maximal real symmetry we also determine the full automorphism group of the klein surface s associated with each symmetry s s

roughness exponents to calculate multi affine fractal exponents abstract we propose a new method to determine the multi affine fractal exponents based on a generalization of the roughness concept for synthetic multi affine fractal profiles with exactly known exponents we show that the results obtained in this method are more accurate than the results obtained with the height height correlation function method also in the present method scaling is observed using profiles with a number of points more than one order mangnitude smaller

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

on the approximation of convex functions by bernstein type operators abstract as a consequence of jensen s inequality centered operators of probabilistic type also called bernstein type operators approximate convex functions from above starting from this fact we consider several pairs of classical operators and determine in each case which one is better to approximate convex functions in almost all the discussed examples the conclusion follows from a simple argument concerning composition of operators however when comparing szasz mirakyan operators with bernstein operators over the positive semi axis the result is derived from the convex ordering of the involved probability distributions analogous results for non centered operators are also considered

involutions of compact klein surfaces let x be a compact klein surface of topological genus g and k bounda ry components and let tp x x be a dianalytic involution we are interested in determining q0 up to topological conjugacy by a finite number of invariants mainly connected with fix q the fixed point set of qo we shall also investigate corresponding inclusions between non eucl idean crystal lographic groups and use these to consider the subspaces of teichmfiller space of klein surfaces admitting involutions as we shall see fix cp consists of a a finite number of isolated fixed points b a finite number of simple closed curves by analogy with the case of plane algebraic curves we shall call a fixed simple closed curve an oval ovals will be called twisted or untwisted according to whether they have m6bius band or annular ne ighbourhoods respectively of course twisted ovals can only occur on non orientable surfaces

dynamic scaling and phase transitions in interface growth abstract the dynamic scaling approach is an effective tool for understanding the temporal evolution of fluctuating interfaces the surface width w obeys the scaling form w l t l t l where and are exponents which characterize how the surface width grows with the length scale l and the time t applications of dynamic scaling to a number of surface growth models are discussed the results of a large scale simulation of the ballistic deposition model in three dimensions are presented and compared with recent conjectures the question of universality in interface growth is addressed and a finite temperature generalization of the restricted solid on solid model is studied this model appears to undergo a phase transition from the usual rough phase at high temperatures to a new phase at low temperatures numerical solutions of the generalized langevin equation indicate that there is no phase transition in 2 1 dimensions thus the relation between the continuum equation and the discrete models is still an open question

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

use and misuse of some hurst parameter estimators applied to stationary and non stationary financial time series abstract the detection of long range dependence lrd is an important task in time series analysis lrd is often summarized by the well known hurst parameter or exponent h 0 1 which can be estimated by a number of methods some of these techniques are designed to be applied to signals behaving as a stationary fractional gaussian noise fgn whereas others imply that the analyzed time series behave as a non stationary fractional brownian motion fbm moreover some estimators do not yield the hurst parameter but indexes related to h and ranging outside the unit interval therefore the fgn or fbm nature of the studied time series has to be preliminarily analyzed before applying any estimation method and the relationships between h and the indexes resulting from the analyses have to be taken into account to obtain coherent results since fgn like series represent the increments of fbm like processes and both the signals are characterized by the same h value by definition estimators designed for fgn like series can be applied to fbm like sequences after preventive differentiation and conversely estimators designed for fbm like processes can be applied to fgn like series after preventive integration the signal characterization is particularly important when h is estimated on financial time series because the returns represent the first difference of price time series which are often assumed to behave like self affine sequences the analysis of simulated fgn and fbm time series shows that all the considered methods yield comparable h values when properly applied the reanalysis of several market price time series already studied in the literature points out that a correct application of the estimators supported by a preventive signal classification yields homogeneous h values allowing for a useful cross validation of results reported in different works moreover some conclusions reported in the literature about the anti persistence of some financial series are shown to be incorrect because of the inappropriate application of the estimation methods

on symmetries of p hyperelliptic riemann surfaces let x be a compact riemann surface of genus g 1 the surface x is p hyperelliptic with p 0 if x admits a conformal involution p such that x p has genus p if p 0 then x is hyperelliptic and if p 1 then x is elliptic hyperelliptic the involution p is called a p hyperelliptic involution the topological type of a p hyperelliptic involution p is determined by the number p because the xed point set of p f p consists of 2g 2 4p points and this number determines the topological type of a conformal involution a symmetry of x is an anticonformal involution x x of x the topological type of a symmetry is determined by properties of its xed point set f the set f consists of k disjoint jordan curves 05k 5 g 1 harnack s theorem h the space x f has either one or two components it consists of one component if x is nonorientable and of two components if x is orientable let be a symmetry of x and suppose that f has k disjoint curves then we shall say that the species of is k or k according to whether x f has two or one component respectively in this work we shall study the species of symmetries of p hyperelliptic riemann surfaces if x is p hyperelliptic having genus g g 4p 1 and is a symmetry of x then the p hyperelliptic involution p of x is unique and therefore p is another symmetry in general not conformally conjugate to f klein in k see also bs studied the species of these pairs p in the case p 0 the hyperelliptic case we shall study such species in the general case p 0 in sect 3 we shall de ne m r with r 0 riemann surface as a riemann surface admitting a symmetry with g 1 r xed curves s m natanzon n1 n2 n3 n4 has studied the automorphisms