quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average we present a bottom up derivation of fluctuation analysis with detrending for the detection of long range correlations in the presence of additive trends or intrinsic nonstationarities while the well known detrended fluctuation analysis dfa and detrending moving average dma were introduced ad hoc we claim basic principles for such methods where dfa and dma are then shown to be specific realizations the mean squared displacement of the summed time series contains the same information about long range correlations as the autocorrelation function but has much better statistical properties for large time lags however the scaling exponent of its estimator on a single time series is affected not only by trends on the data but also by intrinsic nonstationarities we therefore define the fluctuation function as mean squared displacement with weighting kernel we require that its estimator be unbiased and exhibit the correct scaling behavior for the random component of a signal which is only achieved if the weighting kernel implies detrending we show how dfa and dma satisfy these requirements and we extract their kernel weights

critical behaviour of directed self avoiding walks a new directed self avoiding walk directed saw is proposed and studied on a square lattice the critical behaviour of such directed saws in two dimensions is established and shown to be of different universality class from that of an ordinary saw

special solutions from the variable separation approach the davey stewartson equation a variable separation procedure for the davey stewartson ds equation is proposed by using a prior ansatz to its bilinear form the reduced equations for two variable separated fields have the same trilinear form although they possess different independent variables the trilinear equation can be changed to a spacetime symmetric form and can be solved by means of a boussinesq type equation system whenever a pair of solutions of the reduced fields are obtained a corresponding solution of the ds equation can be obtained algebraically the single dromion solution and some kinds of positon solutions are obtained explicitly

feature matching constrained by cross ratio invariance abstract the main aim of this work is to propose a new technique to solve the well known feature correspondence problem for motion estimation the problem is formulated as an optimization process whose energy function includes constraints based on projective invariance of cross ratio of five coplanar points starting from some approximated correspondences estimated by radiometric similarity for features with high directional variance optimal matches are obtained through an optimization technique the new contribution of this work consists of a matching process refining the raw measurements based on an energy function minimization technique converging to an optimal solution for most of the features by taking advantage of some good initial guess and in the use of cross ratio as geometrical invariant constraint to detect and correct the mismatches due to wrong radiometric similarity measures though the method is based on geometrical invariance of coplanar points it is not required that all features have to be coplanar or to preprocess the images to detect the planar regions experimental results are presented for real and synthetic images and the performance of the novel approach is evaluated on different image sequences and compared to well known techniques

directed fixed energy sandpile model we numerically study the directed version of the fixed energy sandpile on a closed square lattice the dynamical evolution of a fixed density of sand grains is studied the activity of the system shows a continuous phase transition around a critical density while the deterministic version has the set of nontrivial exponents the stochastic model is characterized by mean field like exponents

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

a direct method for dromion solutions of the davey stewartson equations and their asymptotic properties a new direct approach to determining a class of solutions including the dromion solutions of the davey stewartson equations is presented the form of solution obtained allows a detailed asymptotic analysis of the dromion solutions and compact expression for the phase shifts and changes of amplitude as a result of interaction of the dromions to be determined a class of solutions describing dromion scattering is discussed and computer plots of the interactions of such solutions are presented

critical behavior and conservation in directed sandpiles we perform large scale simulations of directed sandpile models with both deterministic and stochastic toppling rules our results show the existence of two distinct universality classes we also provide numerical simulations of directed models in the presence of bulk dissipation the numerical results indicate that the way in which dissipation is implemented is irrelevant for the determination of the critical behavior the analysis of the self affine properties of avalanches shows the existence of a subset of superuniversal exponents whose value is independent of the universality class this feature is accounted for by means of a phenomenological description of the energy balance condition in these models

class of cellular automata for reaction diffusion systems finite difference methods for solving the pde s finite difference methods then proceed to solve the resulting coupled system of n s ordinary differential equations n points in space s equations in the pde system by any of a number of numerical methods operating on floating point numbers the use of floating point numbers on computers implies a discretization of the continuous variables the errors introduced by this discretization and the ensuing roundoff errors are often not considered explicitly but assumed to be small because the precision is rather high 8 decimal digits for usual floating point numbers in contrast in the ca approach all variables are explicitly discretized into relatively small integers this discretization allows the use of lookup tables to replace the evaluation of the nonlinear rate functions it is this table lookup combined with the fact that all calculations are performed using integers instead of floating point variables that accounts for an improvement in speed of orders of magnitude on a conventional multi purpose computer the undesirable effects of discretization are overcome by using probabilistic rules for the updating of the ca the state of the ca is given by a regular array of concentration vectors y residing on a d dimensional lattice each y r is a s vector of integers s is the number of reactive species for reasons of efficiency and to fulfill the finiteness condition of the definition of cellular automata each component yi r can only take integer values between 0 and bi where the bi s can be different for each species i the position index r is a d dimensional vector in the ca lattice for cubic lattices r is a d vector of integers the central operation of the automaton consists of calculating the sum

confirming and extending the hypothesis of universality in sandpiles stochastic sandpiles self organize to an absorbing state critical point with scaling behavior different from directed percolation dp and characterized by the presence of an additional conservation law this is usually called the c dp or manna universality class there remains however an exception to this universality principle a sandpile automaton introduced by maslov and zhang which was claimed to be in the dp class despite the existence of a conservation law we show by means of careful numerical simulations as well as by constructing and analyzing a field theory that contrarily to what was previously thought this sandpile is also in the c dp or manna class this confirms the hypothesis of universality for stochastic sandpiles and gives rise to a fully coherent picture of self organized criticality in systems with conservation in passing we obtain a number of results for the c dp class and introduce a strategy to easily discriminate between dp and c dp scaling

variable separation approach for a differential difference system special toda equation a bilinear variable separation approach is used to construct some special solutions for a differential difference toda equation the semi discrete form of the continuous formula which describes some types of special solutions for many 2 1 dimensional continuous systems is found for a suitable quantity of the differential difference toda equation thus abundant semi discrete localized coherent structures are constructed by appropriately selecting the arbitrary functions

dromion can be remote controlled the one dromion solution of the davey stewartson 1 equations with driving boundaries is analysed numerically it is shown that the dromion can follow the motion of the crosspoint of the mean flows even if it is not of exact solutions moreover it is found that the localized structure keeps its shape when it is exposed to the forced motion of the mean flows in the case where dromion runs on a circle path the decay ratio of the localized structure versus the radius is given several types of movement of mean flows are also studied it is expected that dromion can be controlled arbitrarily by driving mean flows at the boundaries

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

scaling properties and entropy of long range correlated time series we calculate the shannon entropy of a time series by using the probability density functions of the characteristic sizes of the long range correlated clusters introduced in a carbone g castelli h e stanley phys rev e 69 2004 026105 we define three different measures of the entropy related respectively to the length the duration and the area of the clusters for all the three cases the entropy increases as the logarithm of a power of the size with exponents equal to the fractal dimension of the cluster length duration and area respectively r 2007 elsevier b v all rights reserved

characteristics of deterministic and stochastic sandpile models in a rotational sandpile model rotational constraint representing a local external bias generally has a nontrivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena in order to study the effect of rotational bias in an out of equilibrium situation like self organized criticality a two state quasideterministic rotational sandpile model is developed here imposing rotational constraint on the flow of sand grains an extended set of critical exponents are estimated to characterize the avalanche properties at the nonequilibrium steady state of the model the probability distribution functions are found to obey usual finite size scaling supported by negative time autocorrelation between the toppling waves the model exhibits characteristics of both deterministic and stochastic sandpile models

detrending fluctuation analysis based on high pass filtering abstract detrended fluctuation analysis dfa is a scaling method commonly used for detecting long range correlations in non stationary time series the dfa method uses a trend based on polynomial fitting to extract and quantify fluctuations at different time scales basically such procedure acts as a non dynamical high pass filter that removes time series components below a given time scale as an alternative to the polynomial fitting approach this paper proposes a dfa method based on well known high pass filters e g butterworth elliptic etc numerical results show that the proposed dfa approach yields results similar to traditional dfa method maybe the main advantage of the proposed dfa method is that efficient implementations of high pass filters are available commercially

concrete construction and properties of the difference equation derived from the cellular automaton using the filtration technique following the proposal of a filtration technique by nobe satsuma and tokihiro we concretely construct partial difference equations which preserve any time evolution patterns of cellular automaton ca stably by the filtration technique we illustrate how to develop a method of filtration for applying to the typical two spatial dimensional ca rule the game of life and verify that the filtration method provides the stable difference equation associated with the ca compared with the inverse ultradiscretization besides in order to discuss whether the filtration technique can lead one to partial differential equations from ca rules we show a derivation of the burgers equation from rule 184 ca via the discrete burgers equation constructed by the filtration method as an example

economic fluctuations and statistical physics quantifying extremely rare and less rare events in finance one challenge of economics is that the systems treated by these sciences have no perfect metronome in time and no perfect spatial architecture crystalline or otherwise nonetheless as if by magic out of nothing but randomness one finds remarkably fine tuned processes in time we present an overview of recent research joining practitioners of economic theory and statistical physics to try to better understand puzzles regarding economic fluctuations one of these puzzles is how to describe outliers phenomena that lie outside of patterns of statistical regularity we review evidence consistent with the possibility that such outliers may not exist this possibility is supported by recent analysis of databases containing information about each trade of every stock r 2007 elsevier b v all rights reserved

extended multilinear variable separation approach and multivalued localized excitations for some 2 1 dimensional integrable systems the multilinear variable separation approach and the related universal formula have been applied to many 2 1 dimensional nonlinear systems starting from the universal formula abundant 2 1 dimensional localized excitations have been found in this paper the universal formula is extended in two different ways one is obtained for the modified nizhnik novikov veselov equation such that two universal terms can be combined linearly and this type of extension is also valid for the 2 1 dimensional symmetric sine gordon system the other is for the dispersive long wave equation the broer kaup kupershmidt system the higher order broer kaup kupershmidt system and the burgers system where arbitrary number of variable separated functions can be involved because of the existence of the arbitrary functions in both the original universal formula and its extended forms the multivalued functions can be used to construct a new type of localized excitations folded solitary waves fsws and foldons the fsws

on solutions of the camassa holm equation the techniques that have been developed for the application of the inverse scattering transform method to the solution of the camassa holm equation principally by constantin are implemented we use this approach first to represent the known solitary wave solution in a simple parametric form and then second to obtain the general two and three soliton solutions these latter two solutions require rather extensive use of mathematical packages mathematica and maple in order to complete the construction of solutions a number of examples are presented the phase shifts evident after an interaction are found and the special limit that recovers the peakon solutions is discussed

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

some novel nonlinear coherent excitations of the davey stewartson system exact solutions of many integrable 2 1 2 spatial and 1 temporal dimensional systems of nonlinear evolution equations e g the davey stewartson model can be obtained by a special separation of variables procedure by choosing the jacobi elliptic functions as the building blocks exact doubly periodic solutions are obtained analytically here two sets of elliptic functions with two different independent moduli are employed and the resulting wave packets are expressed as rational functions of elliptic functions by taking the long wave limit in one spatial variable peculiar wave patterns localized in one direction but periodic in the other direction will arise by taking the long wave limit in both spatial variables exponentially localized wave patterns which differ from the known dromions will result the boundary conditions relating to these localized structures are studied

3d euclidean versus 2d non euclidean two approaches to 3d recovery from images methods of 3d recovery in computer vision for computing the shape and motion of an object from projected images when an object model is available are classified into two types the 3d euclidean approach which is based on geometrical constraints in 3d euclidean space and the 2d non euclidean space implications of these two approaches are discussed and some illustrating examples are presented

sandpile on directed small world networks we numerically investigate the avalanche dynamics of the bak tang wiesenfeld sandpile model on directed small world networks we find that the avalanche size and duration distribution follow a power law for all rewiring probabilities p specially we find that approaching the thermodynamic limit l the values of critical exponents do not depend on p and are consistent with the mean field solution in euclidean space for any p 0 in addition we measure the dynamic exponent in the relation between avalanche size and avalanche duration and find that the values of the dynamic exponents are also consistent with the mean field values for any p 0

using projective geometry to recover planar surfaces in stereovision our purpose is to build the planar surfaces called three dimensional 3d faces of the objects of a polyhedral scene using a stereovision system composed of three cameras in each image our system builds structures known as 2d faces which are 2d polygons which are supposed to be the projections of 3d faces and then matches the 2d faces of each given triplet of images due to the large errors caused by the stereo reconstruction it is difficult to check for planar surfaces after the 3d process instead we prefer to search among the set of triplets of matched 2d faces for the triplets which really correspond to planar 3d surfaces before the reconstruction step for this purpose we propose a new approach to validate the 3d coplanarity of a set of 3d segments working only on their corresponding matched 2d images and using principles of projective geometry for each triplet of matched 2d segments new information known as trace is computed and added to the triplets then using this new characteristic related to each triplet of matched 2d segments 3d geometric properties such as the planarity and even coplanarity of a 3d structure are established in 2d space all these 3d properties 3d planarity and 3d coplanarity checked in 2d space lead to an accurate reconstruction of the surfaces in this paper we first introduce the required mathematical tools which explain our approach then we present our system for building 3d faces which includes a new unit in its stereovision part based on projective geometry some experimental results are presented at the end of this paper showing the efficiency of our method

directed self organized critical patterns emerging from fractional brownian paths abstract we discuss a family of clusters c corresponding to the region whose boundary is formed by a fractional brownian path y i and by the moving average function y n i 1 n k 0 n 1 y i k our model generates fractal directed patterns showing spatio temporal complexity and we demonstrate that the cluster area length and duration exhibit the characteristic scaling behavior of soc clusters the function cn i acts as a magnifying lens zooming in or out the avalanches formed by the cluster construction rule where the magnifying power of the zoom is set by the value of the amplitude window n on the basis of the construction rule of the clusters c n i y i y n i and of the relationship among the exponents we hypothesize that our model might be considered to be a generalized stochastic directed model including the dhar ramaswamy dr model and the stochastic models as particular cases as in the dr model the growth and annihilation of our clusters are obtained from the set of intersections of two random walk paths and we argue that our model is a variant of the directed self organized criticality scheme of the dr model

parameter estimation for the generalized fractional element network zener model based on the bayesian method abstract in the present study an inverse problem to estimate parameters in the zener model of viscoelasticity based on the generalized fractional element gfe network is studied the bayesian method is proposed to obtain the optimal estimation of the viscoelastic parameters three examples are performed to certify the validity of the method all numerical results lead to an excellent fitting between the calculative results and experimental data it is shown that the bayesian method is feasible in the inverse problem of parameter estimation for the fractional constitutive equation and the gfe network zener model is efficient in the modeling of the viscoelastic behavior

revisitation of the localized excitations of the 2 1 dimensional kdv equation in a previous paper lou s y 1995 j phys a math gen 28 7227 a generalized dromion structure was revealed for the 2 1 dimensional kdv equation which was first derived by boiti et al boiti m leon j j p manna m and pempinelli f 1986 inverse problems 2 271 using the idea of the weak lax pair in this paper using a backlund transformation and the variable separation approach we find there exist much more abundant localized structures for the 2 1 dimensional kdv equation the abundance of the localized structures of the model is introduced by the entrance of an arbitrary function of the seed solution some special types of dromion solution lumps breathers instantons and the ring type of soliton are discussed by selecting the arbitrary functions appropriately the dromion solutions can be driven by sets of straight line and curved line ghost solitons the dromion solutions may be located not only at the cross points of the lines but also at the closed points of the curves the breathers may breathe both in amplitude and in shape

spiral bond animals ratio approach bond animals with a constraint of a given winding direction on the square lattice are enumerated up to 14 bonds numerical evidence further confirms the previous conjecture using the position space renormalisation group approach that they belong to a new universality class

cnoidal waves as exact sums of repeated solitary waves new series for elliptic functions via poisson summation of the corresponding fourier series it is shown that the cnoidal wave of the korteweg de vries equation can be written as an infinite sum of periodically repeated solitary waves a result first proved by toda through a different method similar series of hyperbolic secant or tangent functions are also derived for the elliptic dn sn and cn functions which make it possible to express the cnoidal wave of almost any evolution equation in terms of a series of the corresponding solitary waves as a by product new series are also obtained for the complete elliptic integral k and modulus k

interactions among periodic waves and solitary waves of the n 1 dimensional sine gordon field exact solutions of the n 1 dimensional sine gordon field equation are studied with help of those of the cubic nonlinear klein gordon fields the mapping relations among the sine gordon field equation and the cubic nonlinear klein gordon fields are pure algebraic by solving the cubic nonlinear klein gordon equations many new types of exact explicit solutions such as the periodic periodic interaction waves periodic kink interaction waves periodic perturbed snake shape solitary waves etc are displayed both analytically and graphically

directed avalanche processes with underlying interface dynamics we describe a directed avalanche model a slowly unloading sandbox driven by lowering a retaining wall the directness of the dynamics allows us to interpret the stable sand surfaces as world sheets of fluctuating interfaces in one lower dimension in our specific case the interface growth dynamics belongs to the kardar parisi zhang kpz universality class we formulate relations between the critical exponents of the various avalanche distributions and those of the roughness of the growing interface the nonlinear nature of the underlying kpz dynamics provides a nontrivial test of such generic exponent relations the numerical values of the avalanche exponents are close to the conventional kpz values but differ sufficiently to warrant a detailed study of whether avalanche correlated monte carlo sampling changes the scaling exponents of kpz interfaces we demonstrate that the exponents remain unchanged but that the traces left on the surface by previous avalanches give rise to unusually strong finite size corrections to scaling this type of slow convergence seems intrinsic to avalanche dynamics

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

analysis of clusters formed by the moving average of a long range correlated time series we analyze the stochastic function c n i ensuremath equiv y i ensuremath y n i where y i is a long range correlated time series of length n mathrm max and y n i ensuremath equiv 1 n ensuremath sum k 0 n ensuremath 1 y i ensuremath k is the moving average with window n we argue that c n i generates a stationary sequence of self affine clusters mathcal c with length mathcal l lifetime ensuremath tau and area s the length and the area are related to the lifetime by the relationships mathcal l ensuremath sim ensuremath tau ensuremath psi mathcal l and s ensuremath sim ensuremath tau ensuremath psi s where ensuremath psi mathcal l 1 and ensuremath psi s 1 h we also find that mathcal l ensuremath tau and s are power law distributed with exponents depending on h p mathcal l ensuremath sim mathcal l ensuremath ensuremath alpha p ensuremath tau ensuremath sim ensuremath tau ensuremath ensuremath beta and p s ensuremath sim s ensuremath ensuremath gamma with ensuremath alpha ensuremath beta 2 ensuremath h and ensuremath gamma 2 1 h these predictions are tested by extensive simulations on series generated by the midpoint displacement algorithm of assigned hurst exponent h ranging from 0 05 to 0 95 of length up to n mathrm max 2 21 and n up to 2 13

some results and a conjecture for manna s stochastic sandpile model we present some analytical results for the stochastic sandpile model studied earlier by manna in this model the operators corresponding to particle addition at different sites commute the eigenvalues of operators satisfy a system of coupled polynomial equations for an l l square we construct a nontrivial toppling invariant and hence a ladder operator which acting on eigenvectors of the evolution operator gives new eigenvectors with different eigenvalues for periodic boundary conditions in one direction one more toppling invariant can be constructed we show that there are many forbidden subconfigurations and only an exponentially small fraction of all stable configurations are recurrent we obtain rigorous lower and upper bounds for the minimum number of particles in a recurrent configuration and conjecture a formula for its exact value for finite size rectangles

exactly solved model of self organized critical phenomena we define a variant of the model of bak tang and wiesenfeld of self organized critial behavior by introducing a preferred direction we characterize the critical state and by establishing equivalence to a voter model determine the critical exponents exactly in arbitrary dimension d the upper critical dimension for this model is three in two dimensions the model is equivalent to an earlier solved special case of directed percolation

fractal heterogeneous media a method is presented for generating compact fractal disordered media by generalizing the random midpoint displacement algorithm the obtained structures are invasive stochastic fractals with the hurst exponent varying as a continuous parameter as opposed to lacunar deterministic fractals such as the menger sponge by employing the detrending moving average algorithm a carbone phys rev e 76 056703 2007 the hurst exponent of the generated structure can be subsequently checked the fractality of such a structure is referred to a property defined over a three dimensional topology rather than to the topology itself consequently in this framework the hurst exponent should be intended as an estimator of compactness rather than of roughness applications can be envisaged for simulating and quantifying complex systems characterized by self similar heterogeneity across space for example exploitation areas range from the design and control of multifunctional self assembled artificial nanostructures and microstructures to the analysis and modeling of complex pattern formation in biology environmental sciences geomorphological sciences etc

distribution of the first return time in fractional brownian motion and its application to the study of on off intermittency herein the term fractional brownian motion is used to refer to a class of random walks with long range correlated steps where the mean square displacement of the walker at large time t is proportional to mathit t 2 mathit h with 0h1 for ordinary brownian motion we obtain h 1 2 let t denote the time at which the random walker starting at the origin first returns to the origin the purpose of this paper is to show that the probability distribution of t scales with t as p t ensuremath sim mathit t mathit h mathrm ensuremath 2 theoretical arguments and numerical simulations are presented to support the result additional issues explored include modification to the power law distribution when the random walk is biased and the application of the result to the characterization of on off intermittency a recently proposed mechanism for bursting

from waves to avalanches two different mechanisms of sandpile dynamics time series resulting from wave decomposition show the existence of different correlation patterns for avalanche dynamics for the d 2 bak tang wisenfeld model long range correlations determine a modification of the wave size distribution under coarse graining in time and multifractal scaling for avalanches in the manna model the distribution of avalanche coincides with that of waves which are uncorrelated and obey finite size scaling a result expected also for the d 3 bak tang wiesenfeld sandpile

detrending fluctuation analysis based on moving average filtering abstract detrended fluctuation analysis dfa is a scaling method commonly used for detecting long range correlations in nonstationary time series applications range from financial time series to physiological data however as the removal of trends in dfa is based on discontinuous polynomial fitting oscillations in the fluctuation function and significant errors in crossover locations can be introduced to reduce the problems induced by discontinuous fitting moving average ma methods have been proposed previously by alesio et al eur j phys b 27 2002 197 in this work a variant of such ma methods is studied specifically the performance and characteristics of a ma method based on central differences is studied some important properties of this ma method are analyzed and illustrated with several artificial and real time series

universality in sandpiles we perform extensive numerical simulations of different versions of the sandpile model we find that previous claims about universality classes are unfounded since the method previously employed to analyze the data suffered from a systematic bias we identify the correct scaling behavior and provide evidences suggesting that sandpiles with stochastic and deterministic toppling rules belong to the same universality class