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

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

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

regularity for solutions of nonlinear second order evolution equations this paper deals with the existence of solutions for the class of nonlinear second order evolution equations the regularity and a variation of solutions of the given equations are also given as particular cases of our general formulation some results for volterra integrodifferential equations of the hyperbolic type are given

integral equations as evolution equations abstract we study a class of time dependent linear integrodifferential equations ve with the evolution equation approach we determine the generators of a time dependent evolution equation de which is equivalent to the given integrodifferential equation under very general assumptions we prove the well posedness and continuity of ve from the stability of de the related question of convergence of a family of approximate solutions is examined as an application we include an example of hyperbolic integro partial differential equation to illustrate the theory

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

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

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

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

local existence for nonlinear volterra integrodifferential equations with infinite delay abstract in this paper we investigate the local existence and uniqueness of solutions to integrodifferential equations with infinite delay which are more general than those in previous studies we assume that the linear part of the equation is nondensely defined and satisfies a hille yosida condition moreover the continuity of solutions with respect to initial conditions is also studied in order to illustrate our abstract results we conclude this work with an example

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

an abstract transmission problem in a thin layer i sharp estimates we study an elliptic transmission problem in banach spaces the problem is considered on the juxtaposition of two intervals one of which of small length and models physical phenomena in media constituted by two parts with different physical characteristics we obtain results of existence uniqueness maximal regularity and optimal dependence on the parameter for lp solutions of the problem the main tools of our approach are impedance and admittance operators i e dirichlet to neumann and neumann to dirichlet operators and h functional calculus for sectorial operators in banach spaces

controllability of sobolev type integrodifferential systems in banach spaces sufficient conditions for controllability of sobolev type integrodifferential systems in banach spaces are established the results are obtained using compact semigroups and the schauder fixed point theorem as an example is provided to illustrate the results

an abstract semilinear hyperbolic volterra integrodifferential equation abstract we consider semilinear integrodifferential equations of the form u t a t u t 0 t g t s u s ds f t u 0 u 0 for each t 0 the operator a t is assumed to be the negative generator of a strongly continuous semigroup in a banach space x the domain d a t of a t is allowed to vary with t thus our models are volterra integrodifferential equations of hyperbolic type these types of equations arise naturally in the study of viscoelasticity our main results are the proofs of existence uniqueness continuation and continuous dependence of the solutions

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