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

universal features and tail analysis of the order parameter distribution of the two dimensional ising model an entropic sampling monte carlo study we present a numerical study of the order parameter probability density function pdf of the square ising model for lattices with linear sizes l 80 140 a recent efficient entropic sampling scheme combining the wang landau and broad histogram methods and based on the high levels of the wang landau process in dominant energy subspaces is employed we find that for large lattices there exists a stable window of the scaled order parameter in which the full ansatz including the pre exponential factor for the tail regime of the universal pdf is well obeyed this window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal pdf the probability densities are used to estimate the universal privman fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime

noise and determinism in cardiovascular dynamics s ignals derived from the human cardiovascular system are well known to exhibit highly complex nearly periodic oscillatory behaviour whose nature is something of an enigma it has for example been variously described as chaotic fractal stochastic and subject to 1 f fluctuations and its true nature is still the subject of vigorous debate we review and describe some recent experiments that illuminate the problem and discuss a combination of noise and almost periodic frequency modulation as a signature of the system dynamics

multifractal spectra of multi affine functions abstract self affine functions f x with multiscaling height correlations cq x xqhq are described in terms of the standard multifractal formalism with a modified assumption for the partition the corresponding quantities and expressions are shown to exhibit some characteristic differences from the standard ones according to our calculations the f type spectra are not uniquely determined by the hq spectrum but depend on the particular choice which is made for the dependence of n on x where n is the number of points over which the average is taken our results are expected to be relevant in the analysis of signal type data obtained in experiments on systems with an underlying multiplicative process

non linear approach to study the dynamics of neurodegenerative diseases by multifractal detrended cross correlation analysis a quantitative assessment on gait disease abstract this paper studies the human gait pattern of normal people and patients suffering from parkinson s disease using the mfdxa multifractal detrended cross correlation analysis methodology the auto correlation and cross correlation of the time series of the total force under the left foot and right foot were studied the study reveals that the degree of multifractality w and degree of correlation are generally more for normal patients than the diseased set it is also observed that the values of w and are nearly same for left foot and right it is also observed that the study of autocorrelation alone is not sufficient cross correlations should also be studied to get a better concept of neurodegenerative diseases

application of the detrended fluctuation analysis dfa method for describing cloud breaking abstract a method to sort out correlations and decorrelations in stratus cloud formation persistence and breakup is introduced the detrended fluctuation analysis dfa statistical method is applied to microwave radiometer data the existence of long range power law correlations in stratus cloud liquid water content fluctuations is demonstrated over a 2 h period moreover using a finite size time interval window a change from brownian to non brownian fluctuation regimes is clearly shown to define the cloud structure changes such findings are similar to those found in dna and financial data sequences when mosaics of persistent and antipersistent patches are present the occurrence of these statistics in stratus cloud liquid water content suggests the usefulness of similar studies on cloud resolving model output and for better meteorological predictability

characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments we study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep deep sleep and rapid eye movement rem sleep using the detrended fluctuation analysis method we find short range anticorrelations in the sign time series which are strong during deep sleep weaker during light sleep and even weaker during rem sleep in contrast we find long range positive correlations in the magnitude time series which are strong during rem sleep and weaker during light sleep we observe uncorrelated behavior for the magnitude during deep sleep since the magnitude series relates to the nonlinear properties of the original time series while the sign series relates to the linear properties our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during rem sleep thus the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages

when human walking becomes random walking fractal analysis and modeling of gait rhythm fluctuations abstract we present a random walk fractal analysis of the stride to stride fluctuations in the human gait rhythm the gait of healthy young adults is scale free with long range correlations extending over hundreds of strides this fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases stochastic modeling of the gait rhythm dynamics based on transitions between different neural centers reproduces distinctive statistical properties of the gait pattern by tuning one model parameter the hopping transition range the model can describe alterations in gait dynamics from childhood to adulthood including a decrease in the correlation and volatility exponents with maturation

monte carlo analysis of the critical properties of the two dimensional randomly bond diluted ising model via wang landau algorithm abstract the influence of random bond dilution on the critical properties of the two dimensional ising model on a square lattice with periodic boundary conditions is presented using the monte carlo process with wang landau sampling the lattice linear size is l 20 140 and the concentration of the diluted bonds spans a wide range from weak to strong dilution namely q 0 05 0 1 0 2 0 3 0 4 the respective percolation limit for the square lattice is q c p e r c 0 5 its pure version q 0 has a second order phase transition with vanishing specific heat critical exponent an example of inapplicability of the harris criterion the main effort is focused on the temperature dependence of the specific heat and magnetic susceptibility to estimate the respective maximum values and subsequent pseudocritical temperatures for extracting the relative critical exponents we have also looked at the probability distribution of the susceptibility pseudocritical temperature and specific heat for assessing self averaging the study is carried out in the appropriately restricted but dominant energy subspaces by applying the finite size scaling analysis the critical exponents are estimated the specific heat exponent vanishes the correlation length exponent is equal to one and the critical exponents ratio retains its pure ising model value thus supporting the strong universality hypothesis

extracting fractal components from time series abstract we present a technique for extracting random fractal components from a given time series in the frequency domain the method was based on characteristics of the fractal time series that the original and the renormalized coarse grained time series had a random phase relationship an ordinary fft based cross spectral method was used to measure the phase relationship the method was tested on simulated data with known fractal and or simple harmonic properties and with a mixture of these the percent fractal components derived by this technique were closely matched to the theoretical values we set the extracted fractal power showed power law dependence expressed as spectral exponent by which we could calculate the hurst exponent h of the time series from it was also shown that the calculated h for the simulated time series gave good estimates for the true h of the random fractal process

determining the density of states for classical statistical models a random walk algorithm to produce a flat histogram we describe an efficient monte carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models the density of states is modified at each step when the energy level is visited to produce a flat histogram by carefully controlling the modification factor we allow the density of states to converge to the true value very quickly even for large systems from the density of states at the end of the random walk we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature using this method we not only can avoid repeating simulations at multiple temperatures but we can also estimate the free energy and entropy quantities that are not directly accessible by conventional monte carlo simulations this algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability as with the multicanonical monte carlo technique our method overcomes the tunneling barrier between coexisting phases at first order phase transitions in this paper we apply our algorithm to both first and second order phase transitions to demonstrate its efficiency and accuracy we obtained direct simulational estimates for the density of states for two dimensional ten state potts models on lattices up to 200 x 200 and ising models on lattices up to 256 x 256 our simulational results are compared to both exact solutions and existing numerical data obtained using other methods applying this approach to a three dimensional j spin glass model we estimate the internal energy and entropy at zero temperature and using a two dimensional random walk in energy and order parameter space we obtain the rough canonical distribution and energy landscape in order parameter space preliminary data suggest that the glass transition temperature is about 1 2 and that better estimates can be obtained with more extensive application of the method this simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space

time and frequency domain characteristics of detrending operation based scaling analysis exact dfa and dma frequency responses we develop a general framework to study the time and frequency domain characteristics of detrending operation based scaling analysis methods such as detrended fluctuation analysis dfa and detrending moving average dma analysis in this framework using either the time or frequency domain approach the frequency responses of detrending operations are calculated analytically although the frequency domain approach based on conventional linear analysis techniques is only applicable to linear detrending operations the time domain approach presented here is applicable to both linear and nonlinear detrending operations furthermore using the relationship between the time and frequency domain representations of the frequency responses the frequency domain characteristics of nonlinear detrending operations can be obtained based on the calculated frequency responses it is possible to establish a direct connection between the root mean square deviation of the detrending operation based scaling analysis and the power spectrum for linear stochastic processes here by applying our methods to dfa and dma including higher order cases exact frequency responses are calculated in addition we analytically investigate the cutoff frequencies of dfa and dma detrending operations and show that these frequencies are not optimally adjusted to coincide with the corresponding time scale

levels of complexity in scale invariant neural signals many physical and physiological signals exhibit complex scale invariant features characterized by 1 f scaling and long range power law correlations indicating a possibly common control mechanism specifically it has been suggested that dynamical processes influenced by inputs and feedback on multiple time scales may be sufficient to give rise to 1 f scaling and scale invariance two examples of physiologic signals that are the output of hierarchical multiscale physiologic systems under neural control are the human heartbeat and human gait here we show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable 1 f scaling they still may belong to different complexity classes our analysis of the multifractal scaling exponents of the fluctuations in these two signals demonstrates that in contrast to the multifractal behavior found in healthy heartbeat dynamics gait time series exhibit less complex close to monofractal behavior further we find strong anticorrelations in the sign and close to random behavior for the magnitude of gait fluctuations at short and intermediate time scales in contrast to weak anticorrelations in the sign and strong positive correlation for the magnitude of heartbeat interval fluctuations suggesting that the neural mechanisms of cardiac and gait control exhibit different linear and nonlinear features these findings are of interest because they underscore the limitations of traditional two point correlation methods in fully characterizing physiological and physical dynamics in addition these results suggest that different mechanisms of control may be responsible for varying levels of complexity observed in physiological systems under neural regulation and in physical systems that possess similar 1 f scaling

quantification of heart rate variability by discrete nonstationary non markov stochastic processes we develop the statistical theory of discrete nonstationary non markov random processes in complex systems the objective of this paper is to find the chain of finite difference non markov kinetic equations for time correlation functions tcf in terms of nonstationary effects the developed theory starts from careful analysis of time correlation through nonstationary dynamics of vectors of initial and final states and nonstationary normalized tcf using the projection operators technique we find the chain of finite difference non markov kinetic equations for discrete nonstationary tcf and for the set of nonstationary discrete memory functions mf s the last one contains supplementary information about nonstationary properties of the complex system on the whole another relevant result of our theory is the construction of the set of dynamic parameters of nonstationarity which contains some information of the nonstationarity effects the full set of dynamic spectral and kinetic parameters and kinetic functions tcf short mf s statistical spectra of non markovity parameter and statistical spectra of nonstationarity parameter has made it possible to acquire the in depth information about discreteness non markov effects long range memory and nonstationarity of the underlying processes the developed theory is applied to analyze the long time holter series of rr intervals of human ecg s we had two groups of patients the healthy ones and the patients after myocardial infarction in both groups we observed effects of fractality standard and restricted self organized criticality and also a certain specific arrangement of spectral lines the received results demonstrate that the power spectra of all orders n 1 2 mf m n t exhibit the neatly expressed fractal feat ures we have found out that the full sets of non markov discrete and nonstationary parameters can serve as reliable and powerful means of diagnosis of the cardiovascular system states and can he used to distinguish healthy data from pathologic data

bridge functions near the liquid vapor coexistence curve in binary lennard jones mixtures we have carried out extensive molecular dynamics simulation studies of binary lennard jones mixtures to calculate directly the bridge function at state points lying in a very narrow single fluid phase region between the vapor liquid and solid liquid coexistence lines lamm and hall fluid phase equilib 182 37 2001 194 197 197 2002 by varying the density close to the liquid vapor coexistence line significant deviations are observed at intermediate distances between the simulated bridge function and two widely used approximate closures in the integral equation theory of liquids viz the hybrid mean spherical approximation and the duh henderson closures the overall qualitative agreement remains the same with small variation in temperature that brings the system closer to either the liquid vapor or liquid solid coexistence curve we also report a comparison of the direct and indirect correlation functions obtained from our simulation studies as well as from the integral equation theory of liquids our results emphasize the need for developing new closures applicable to binary fluid mixtures over a wide range of thermodynamic parameters

establishing a direct connection between detrended fluctuation analysis and fourier analysis to understand methodological features of the detrended fluctuation analysis dfa using a higher order polynomial fitting we establish the direct connection between dfa and fourier analysis based on an exact calculation of the single frequency response of the dfa the following facts are shown analytically 1 in the analysis of stochastic processes exhibiting a power law scaling of the power spectral density psd s f f a higher order detrending in the dfa has no adverse effect in the estimation of the dfa scaling exponent which satisfies the scaling relation 1 2 2 the upper limit of the scaling exponents detectable by the dfa depends on the order of polynomial fit used in the dfa and is bounded by m 1 where m is the order of the polynomial fit 3 the relation between the time scale in the dfa and the corresponding frequency in the psd are distorted depending on both the order of the dfa and the frequency dependence of the psd we can improve the scale distortion by introducing the corrected time scale in the dfa corresponding to the inverse of the frequency scale in the psd in addition our analytical approach makes it possible to characterize variants of the dfa using different types of detrending as an application properties of the detrending moving average algorithm are discussed

scaling analysis of trends using dfa we study two aspects of the detrended uctuation analysis dfa method namely the scaling behavior of the leading terms of the best 0t polynomials and the detection of trends we show analytically and numerically that the standard deviation of the leading terms of the best 0t polynomials used in dfa displays scaling behavior furthermore we demonstrate that the distribution of these terms can be used to reveal the presence of trends in the data we also argue that this distribution can be used as a sensitive tool for identifying weak trends c 2001 elsevier science b v all rights reserved

critical end point behavior in a binary fluid mixture we consider the liquid gas phase boundary in a binary fluid mixture near its critical end point using general scaling arguments we show that the diameter of the liquid gas coexistence curve exhibits singular behaviour as the critical end point is approached this prediction is tested by means of extensive monte carlo simulations of a symmetrical lennard jones binary mixture within the grand canonical ensemble the simulation results show clear evidence for the proposed singularity as well as confirming a previously predicted singularity in the coexistence chemical potential fisher and upton phys rev lett 65 2402 1990 the results suggest that the observed singularities particularly that in the coexistence diameter should also be detectable experimentally

understanding and improving the wang landau algorithm we present a mathematical analysis of the wang landau algorithm prove its convergence and identify sources of errors and strategies for optimization in particular we found the histogram increases uniformly with small fluctuations after a stage of initial accumulation and the statistical error is found to scale as sqrt mathrm ln phantom rule 0 2em 0ex f with the modification factor f this has implications for strategies for obtaining fast convergence

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

fractal ion channel behavior generates fractal firing patterns in neuronal models fractal behavior has been observed in both ion channel gating and neuronal spiking patterns but a causal relationship between the two has not yet been established here we examine the effects of fractal ion channel activity in modifications of two classical neuronal models fitzhugh nagumo fhn and hodgkin huxley hh for the modified fhn model the recovery variable was represented as a population of ion channels with either fractal or markov gating characteristics fractal gating characteristics changed the form of the interspike interval histogram isih and also induced fractal behavior in the firing rate for the hh model the k conductance was represented as a collection of ion channels with either quasifractal or markov gating properties fractal gating induced fractal rate behavior without changing the isih we conclude that fractal ion channel gating activity is sufficient to account for fractal rate firing behavior

scale invariance and universality organizing principles in complex systems this paper is a brief summary of a talk that was designed to address the question of whether two of the pillars of the eld of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on a broad class of complex phenomena we shall see that while scale invariance has been tested for many years universality is relatively more rarely discussed in particular we shall develop a heuristic argument that serves to make more plausible the universality hypothesis in both thermal critical phenomena and percolation phenomena and suggest that this argument could be developed into a possible coherent approach to understanding the ubiquity of scale invariance and universality in a wide range of complex systems c 2000 elsevier science b v all rights reserved

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

size rules life but does it in the assessment of medical vigilance best practice towards a testable hypothesis abstract the goal of this paper is to infer the applicability of scaling concepts to haemovigilance based on the study of the relationship between severe adverse reactions and events sare and blood transfusions bt we hypothesize that in a haemovigilance operating optimally sare should be a power law function of bt as sare bt we investigated the relationship between yearly bt and the related sare reported in 12 french hospitals of the picardie state from 2004 to 2015 first we found that when integrated over the whole period 2004 2015 sare were significantly described by a power law function sare bt 1 51 for 10 of the 12 hospitals considered the numbers of sare in these two hospitals is drastically over estimated by this power law that is 1 9 to 4 3 fold lower than those predicted by the power law when considered on a yearly basis we consistently found that sare was also significantly described by a power law function of the form sare bt 1 44 for 10 of the 12 hospitals considered in turn the occurrence of sare in the two other hospitals was strongly over estimated by this power law though it is also significantly described by another power law sare bt 1 11 we specified these results through separate yearly analyses and found the relationship between sare and bt was best described by a power law with 0 90 in 2004 a linear relationship from 2005 to 2007 and a power law with ranging from 1 49 and 1 92 from 2008 to 2014 finally in 2015 the relationship between sare and bt was significantly described by a power law sare bt 1 17 for the 12 hospitals considered overall our results suggest that hospitals performing more blood transfusions are more efficient as the observed negative effects of blood transfusions increase relatively slower than in hospitals performing less transfusions

monte carlo study of the triangular blume capel model under bond randomness the effects of bond randomness on the universality aspects of a two dimensional d 2 blume capel model embedded in the triangular lattice are discussed the system is studied numerically in both its first and second order phase transition regimes by a comprehensive finite size scaling analysis for a particularly suitable value of the disorder strength we find that our data for the second order phase transition emerging under random bonds from the second order regime of the pure model are compatible with the universality class of the two dimensional 2d random ising model furthermore we find evidence that the second order transition emerging under bond randomness from the first order regime of the pure model belongs again to the same universality class although the first finding reinforces the scenario of strong universality in the 2d ising model with quenched disorder the second is in difference from the critical behavior emerging under randomness in the cases of the ex first order transitions of the potts model finally our results verify previous renormalization group calculations on the blume capel model with disorder in the crystal field coupling

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

footswitch system for measurement of the temporal parameters of gait gait analysis relies upon accurate measurement of initial and end foot contact times these times act as a reference point for correlating all other gait data and as a mean of distinguishing normal and pathologic gait we have developed a simple inexpensive footswitch system that provides accurate estimates of the start and end of stance phase for sequential steps the estimates of the beginning and end of stance phase do not require custom footwear extensive calibration or precise placement of the sensor within the shoe the system is based on a commercially available transducer and can be readily reproduced for use in a laboratory setting for less than 50 we describe this system as well as its validation to assess the accuracy of this footswitch system we compared footswitch based estimates of initial and end foot contact times with those obtained using a force platform as 10 people took 30 steps 10 each at slow normal and fast walking rates across a force platform both estimates coincided within 10 ms mean 0 3 ms n 300 for the start of stance phase and within 22 ms mean 1 8 ms n 300 for the end of stance phase for stance duration the differences ranged from 24 to 28 ms mean 1 10 ms n 300 in combination these measures can be used to estimate stance duration to within 3 of force plate determined values for steps with stance durations ranging from 446 to 1594 ms estimates of swing and stride duration also are within 5 of force plate determined values this system should therefore prove to be a useful tool for augmenting laboratory based investigations of gait

finite size scaling analysis of the critical behavior of the baxter wu model abstract we use the recently developed critical minimum energy subspace crmes approximation scheme to study the critical behavior of the baxter wu model this scheme uses only a properly determined part of the energy spectrum and allows us to obtain high accuracy for relatively large systems with considerably reduced computational effort the density of states is constructed by a multi range wang landau sampling and from this we obtain the critical properties of specific heat and of the reduced binder cummulant the good agreement of our results with existing exact solutions demonstrates the accuracy of our approximation technique

time singularity multifractal spectrum distribution based on detrended fluctuation analysis abstract the time singularity multifractal spectrum distribution ts mfsd generalizes the singularity spectrum in a time varying framework in this paper a new method to compute mfsd based on detrended fluctuation analysis dfa mfsd is introduced we relate dfa mfsd method to the standard partition function based multifractal spectrum distribution formalism and prove that both approaches are equivalent for fractal time series with compact support furthermore we find that dfa mfsd has equivalent results better mathematic foundation less computational cost and is more adapted for fractal time series with arbitrary length compared with mfsd based on wavelet transform modulus maxima wtmm mfsd by analyzing several examples this paper shows that dfam mfsd with different polynomial fitting orders can reliably determine the time varying multifractal scaling behavior of time series including processes embodying chirp type or oscillating singularities to illustrate these results simulations are executed using binomial multiplicative cascades wavelet series and real sea clutter and simulations indicate that dfa m mfsd benefits from excellent theoretical and practical performances

multifractals embedded in short time series an unbiased estimation of probability moment an exact estimation of probability moments is the base for several essential concepts such as the multifractals the tsallis entropy and the transfer entropy by means of approximation theory we propose a new method called factorial moment based estimation of probability moments theoretical prediction and computational results show that it can provide us an unbiased estimation of the probability moments of continuous order calculations on probability redistribution model verify that it can extract exactly multifractal behaviors from several hundred recordings its powerfulness in monitoring evolution of scaling behaviors is exemplified by two empirical cases i e the gait time series for fast normal and slow trials of a healthy volunteer and the closing price series for shanghai stock market by using short time series with several hundred lengths a comparison with the well established tools displays significant advantages of its performance over the other methods the factorial moment based estimation can evaluate correctly the scaling behaviors in a scale range about three generations wider than the multifractal detrended fluctuation analysis and the basic estimation the estimation of partition function given by the wavelet transform modulus maxima has unacceptable fluctuations besides the scaling invariance focused in the present paper the proposed factorial moment of continuous order can find its various uses such as finding nonextensive behaviors of a complex system and reconstructing the causality relationship network between elements of a complex system

modeling heart rate variability in healthy humans a turbulence analogy many complex systems share similar statistical characteristics in this letter a turbulence analogy is proposed for the long term heart rate variability of healthy humans based on such an analogy the equivalence of an inertial range is found and a cascade model which captures the statistical properties of the heart rate data is given

finite size scaling of the three dimensional conserved order parameter ising model via wang landau algorithm abstract the critical properties of the conserved order parameter cop version of the three dimensional ising model with zero magnetization were investigated by means of the monte carlo mc wang landau algorithm the study was carried out in appropriate restricted but dominant energy subspaces the main effort was focused on the specific heat and binder energy cumulant by using the density of states of the model for lattices with linear size l 4 60 by applying finite size scaling analysis the estimated values for the thermal critical exponent y t and critical temperature k c are in agreement with the considered as best values leading to the conclusion that this model belongs to the ising universality class the analysis revealed the necessity of corrections to scaling functions for interpreting correctly the mc data

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

field theoretical analysis of singularities at critical end points abstract continuum models with critical end points are considered whose hamiltonian h depends on two densities and field theoretic methods are used to show the equivalence of the critical behavior on the critical line and at the critical end point and to give a systematic derivation of critical end point singularities like the thermal singularity t 2 of the spectator phase boundary and the coexistence singularities t 1 or t of the secondary density the appearance of a discontinuity eigenexponent associated with the critical end point is confirmed and the mechanism by which it arises in field theory is clarified

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

critical behavior of the pure and random bond two dimensional triangular ising ferromagnet we investigate the effects of quenched bond randomness on the critical properties of the two dimensional ferromagnetic ising model embedded in a triangular lattice the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method in the first part of our study we present the finite size scaling behavior of the pure model for which we calculate the critical amplitude of the specific heat s logarithmic expansion for the disordered system the numerical data and the relevant detailed finite size scaling analysis along the lines of the two well known scenarios logarithmic corrections versus weak universality strongly support the field theoretically predicted scenario of logarithmic corrections a particular interest is paid to the sample to sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality

a stochastic model of human gait dynamics abstract we present a stochastic model of gait rhythm dynamics based on transitions between different neural centers that reproduces distinctive statistical properties of normal human walking by tuning one model parameter the transition hopping range the model can describe alterations in gait dynamics from childhood to adulthood including a decrease in the correlation and volatility exponents with maturation the model also generates time series with multifractal spectra whose broadness depends only on this parameter moreover we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum suggesting the possibility of a change in multifractality with maturation

effects of coarse graining on the scaling behavior of long range correlated and anti correlated signals abstract we investigate how various coarse graining signal quantization methods affect the scaling properties of long range power law correlated and anti correlated signals quantified by the detrended fluctuation analysis specifically for coarse graining in the magnitude of a signal we consider i the floor ii the symmetry and iii the centro symmetry coarse graining methods we find that for anti correlated signals coarse graining in the magnitude leads to a crossover to random behavior at large scales and that with increasing the width of the coarse graining partition interval this crossover moves to intermediate and small scales in contrast the scaling of positively correlated signals is less affected by the coarse graining with no observable changes when 1 while for 1 a crossover appears at small scales and moves to intermediate and large scales with increasing for very rough coarse graining 3 based on the floor and symmetry methods the position of the crossover stabilizes in contrast to the centro symmetry method where the crossover continuously moves across scales and leads to a random behavior at all scales thus indicating a much stronger effect of the centro symmetry compared to the floor and the symmetry method for coarse graining in time where data points are averaged in non overlapping time windows we find that the scaling for both anti correlated and positively correlated signals is practically preserved the results of our simulations are useful for the correct interpretation of the correlation and scaling properties of symbolic sequences

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

broad histogram method extension and efficiency test compared to standard histogram techniques the broad histogram method allows us to increase the efficiency of monte carlo simulations by a tremendous amount this gain of efficiency is achieved by measuring simulation averages of particular system observables different from those used in standard histogram techniques while the algorithm of the simulation can be left unchanged in this paper the broad histogram method is reformulated in a more mathematical and precise way furthermore the method is extended to estimate the density of states as a function of more than one parameter a quantitative investigation of the gain of efficiency of monte carlo simulations is performed for the broad histogram method we find a gain of efficiency which amounts to orders of magnitude in comparison to the standard histogram method

magnitude and sign scaling in power law correlated time series a time series can be decomposed into two sub series a magnitude series and a sign series here we analyze separately the scaling properties of the magnitude series and the sign series using the increment time series of cardiac interbeat intervals as an example we 6nd that time series having identical distributions and long range correlation properties can exhibit quite di8erent temporal organizations of the magnitude and sign sub series from the cases we study it follows that the long range correlations in the magnitude series indicate nonlinear behavior speci6cally our results suggest that the correlation exponent of the magnitude series is a monotonically increasing function of the multifractal spectrum width of the original series on the other hand the sign series mainly relates to linear properties of the original series we also show that the magnitude and sign series of the heart interbeat interval series can be used for diagnosis purposes c

levels of complexity in turbulent time series for weakly and high reynolds number abstract we use the detrended fluctuation analysis dfa the detrended cross correlation analysis dcca and the magnitude and sign decomposition analysis to study the fluctuations in the turbulent time series and to probe long term nonlinear levels of complexity in weakly and high turbulent flow the dfa analysis indicate that there is a time scaling region in the fluctuation function segregating regimes with different scaling exponents we discuss that this time scaling region is related to inertial range in turbulent flows the dcca exponent implies the presence of power law cross correlations in addition we conclude its multifractality for high reynold s number in inertial range further we find that turbulent time series exhibit complex features by magnitude and sign scaling exponents

estimation of critical behavior from the density of states in classical statistical models we present a simple and efficient approximation scheme which greatly facilitates the extension of wang landau sampling or similar techniques in large systems for the estimation of critical behavior the method presented in an algorithmic approach is based on a very simple idea familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem it is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters it is proposed that the extensions of the finite size critical part of the energy space determining the specific heat satisfy a scaling law involving the thermal critical exponent the method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic ising lattices the proposed scaling law is verified by estimating the thermal critical exponent from the finite size behavior of the critical part of the energy space the density of states of the zero field ising model on these lattices is obtained via a multirange wang landau sampling

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

baxter wu model in the presence of an external magnetic field abstract in this work we study an unusual phase transition of the baxter wu model in the presence of an external magnetic field the model is pure baxter wu which means that only three spin interactions are taken into account we construct a phase diagram on the temperature field plane based mainly on the singularities of the specific heat these singularities are more clearly observed than those of the magnetic susceptibility which are used in existing works we establish a discontinuity in the critical exponents when the field is changed from zero to negative

entropic sampling via wang landau random walks in dominant energy subspaces dominant energy subspaces of statistical systems are defined with the help of restrictive conditions on various characteristics of the energy distribution such as the probability density and the fourth order binder s cumulant our analysis generalizes the ideas of the critical minimum energy subspace crmes technique applied previously to study the specific heat s finite size scaling here we illustrate alternatives that are useful for the analysis of further finite size anomalies and the behavior of the corresponding dominant subspaces is presented for the two dimensional 2d baxter wu and the 2d and 3d ising models in order to show that a crmes technique is adequate for the study of magnetic anomalies we study and test simple methods which provide the means for an accurate determination of the energy order parameter e m histograms via wang landau random walks the 2d ising model is used as a test case and it is shown that high level wang landau sampling schemes yield excellent estimates for all magnetic properties our estimates compare very well with those of the traditional metropolis method the relevant dominant energy subspaces and dominant magnetization subspaces scale as expected with exponents alpha nu and gamma nu respectively using the metropolis method we examine the time evolution of the corresponding dominant magnetization subspaces and we uncover the reasons behind the inadequacy of the metropolis method to produce a reliable estimation scheme for the tail regime of the order parameter distribution

critical endpoint behavior in an asymmetric ising model application of wang landau sampling to calculate the density of states using the wang landau sampling method with a two dimensional random walk we determine the density of states for an asymmetric ising model with two and three body interactions on a triangular lattice in the presence of an external field with an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite size analyses at and away from the critical endpoint we observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint and the exponents for both divergences agree well with previous theoretical predictions

multifractal formalism for fractal signals the structure function approach versus the wavelet transform modulus maxima method several attempts have been made recently to generalize the multifractal formalism originally introduced for singular measures to fractal signals we report on a systematic comparison between the structure function approach pioneered by parisi and frisch in 2 proceedings of the international school on turbulence and predictability in geophysical fluid dynamics and climate dynamics edited by m ghil r benzi and g parisi north holland amsterdam 1985 p 84 to account for the multifractal nature of fully developed turbulent signals and an alternative method we have developed within the framework of the wavelet transform analysis we comment on the intrinsic limitations of the structure function approach this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases we demonstrate that our method based on the wavelet transform modulus maxima representation works in most situations and is likely to be the ground of a unified multifractal description of self affine distributions our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations

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

invariant in cellular automata for a subclass of the set of reversible cellular automata the author gives the form of an exact time invariant quantity which can be seen as a kind of energy with the ergodic assumption this is a model of two interacting ising spin systems

criticality in the randomness induced second order phase transition of the triangular ising antiferromagnet with nearest and next nearest neighbor interactions abstract using a wang landau entropic sampling scheme we investigate the effects of quenched bond randomness on a particular case of a triangular ising model with nearest j n n and next nearest neighbor j n n n antiferromagnetic interactions we consider the case r j n n n j n n 1 for which the pure model is known to have a columnar ground state where rows of nearest neighbor spins up and down alternate and undergo a weak first order phase transition from the ordered to the paramagnetic state with the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first order phase transition to a second order phase transition and using the lee kosterlitz method we quantitatively verify this conversion the emerging under random bonds continuous transition shows a strongly saturating specific heat behavior corresponding to a negative exponent and belongs to a new distinctive universality class with 1 135 11 1 744 9 and 0 124 8 thus our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent but a different thermal critical exponent as a wide variety of two dimensional 2d systems without and with quenched disorder

critical energy distribution function of the baxter wu model abstract in this work we examine the critical finite size scaling behavior of the energy probability distribution function and its corresponding binder cumulant at critical point based on the results of monte carlo simulations at zero external magnetic field using the recently developed triangle cluster algorithm we calculate the energy distribution function s exponents and we derive the scaling relations for the energy binder cumulant finally we predict the exact form of the scaled energy distribution function most of our conclusions seem applicable not only to the baxter wu model but also to other ising like models

investigation on gait time series by means of factorial moments abstract by means of factorial moments fm the fractal structures embedded in gait time series are investigated intermittency is found in records for healthy objects and this kind of intermittency is much sensitive to disease or outside influences it is found that fm is an effective tool to deal with this kind of time series

holder exponent spectra for human gait abstract the stride interval time series in normal human gait is not strictly constant but fluctuates from step to step in a complex manner more precisely it has been shown that the control process for human gait is a fractal random phenomenon that is one with a long term memory herein we study the holder exponent spectra for the slow normal and fast gaits of 10 young healthy men in both free and metronomically triggered conditions and establish that the stride interval time series is more complex than a monofractal phenomenon a slightly multifractal and non stationary time series under the three different gait conditions emerges

correlation differences in heartbeat fluctuations during rest and exercise we study the heartbeat activity of healthy individuals at rest and during exercise we focus on correlation properties of the intervals formed by successive peaks in the pulse wave and find significant scaling differences between rest and exercise for exercise the interval series is anticorrelated at short time scales and correlated at intermediate time scales while for rest we observe the opposite crossover pattern from strong correlations in the short time regime to weaker correlations at larger scales we also suggest a physiologically motivated stochastic scenario to provide an intuitive explanation of the scaling differences between rest and exercise

first order transition features of the triangular ising model with nearest and next nearest neighbor antiferromagnetic interactions abstract we implement a new and accurate numerical entropic scheme to investigate the first order transition features of the triangular ising model with nearest neighbor j nn and next nearest neighbor j nnn antiferromagnetic interactions in ratio r j nn j nnn 1 important aspects of the existing theories of first order transitions are briefly reviewed tested on this model and compared with previous work on the potts model using lattices with linear sizes l 30 40 100 120 140 160 200 240 360 and 480 we estimate the thermal characteristics of the present weak first order transition our results improve the original estimates of rastelli et al and verify all the generally accepted predictions of the finite size scaling theory of first order transitions including transition point shifts thermal and magnetic anomalies however two of our findings are not compatible with current phenomenological expectations the behavior of transition points derived from the number of phases parameter is not in accordance with the theoretically conjectured exponentially small shift behavior and the well known double gaussian approximation does not correctly describe higher correction terms of the energy cumulants it is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections

multiresolution wavelet analysis of heartbeat intervals discriminates healthy patients from those with cardiac pathology we applied multiresolution wavelet analysis to the sequence of times between human heartbeats r ensuremath r intervals and have found a scale window between 16 and 32 heartbeat intervals over which the widths of the r ensuremath r wavelet coefficients fall into disjoint sets for normal and heart failure patients this has enabled us to correctly classify every patient in a standard data set as belonging either to the heart failure or normal group with 100 accuracy thereby providing a clinically significant measure of the presence of heart failure from the r ensuremath r intervals alone comparison is made with previous approaches which have provided only statistically significant measures

multi affine model for the velocity distribution in fully turbulent flows a simple multi affine model for the velocity distribution in fully developed turbulent flows is introduced to capture the essential features of the underlying geometry of the velocity field the authors show that in this model the various relevant quantities characterizing different aspects of turbulence can be readily calculated a simultaneous good agreement is found with the available experimental data for the velocity structure functions the dq spectra obtained from studies of the velocity derivatives and the exponent describing the scaling of the spectrum of the kinetic energy fluctuations their results are obtained analytically assuming a single free parameter the fractal dimension of the region where the dominating contribution to dissipation comes from is estimated to be d approximately 2 88

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

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

statistical properties of share volume traded in financial markets we quantitatively investigate the ideas behind the often expressed adage it takes volume to move stock prices and study the statistical properties of the number of shares traded q deltat for a given stock in a fixed time interval deltat we analyze transaction data for the largest 1000 stocks for the two year period 1994 95 using a database that records every transaction for all securities in three major us stock markets we find that the distribution p q deltat displays a power law decay and that the time correlations in q deltat display long range persistence further we investigate the relation between q deltat and the number of transactions n deltat in a time interval deltat and find that the long range correlations in q deltat are largely due to those of n deltat our results are consistent with the interpretation that the large equal time correlation previously found between q deltat and the absolute value of price change g deltat related to volatility are largely due to n deltat

a comparison between broad histogram and multicanonical methods we discuss the conceptual differences between the broad histogram bhm and reweighting methods in general and particularly the so called multicanonical muca approaches the main difference is that bhm is based on microcanonical fixed energy averages which depend only on the good statistics taken inside each energy level the detailed distribution of visits among different energy levels determined by the particular dynamic rule one adopts is irrelevant contrary to muca where the results are extracted from the dynamic rule itself within bhm any microcanonical dynamics could be adopted as a numerical test we have used both bhm and muca in order to obtain the spectral energy degeneracy of the ising model in 4 4 4 and 32 32 lattices for which exact results are known we discuss why bhm gives more accurate results than muca even using the same markovian sequence of states in addition such an advantage increases for larger systems

scaling and universality in heart rate variability distributions we find that a universal homogeneous scaling form describes the distribution of cardiac variations for a group of healthy subjects which is stable over a wide range of time scales however a similar scaling function does not exist for a group with a common cardiopulmonary instability associated with sleep apnea subtle differences in the distributions for the day and night phase dynamics for healthy subjects are detected

static critical behavior of the q states potts model high resolution entropic study abstract here we report a precise computer simulation study of the static critical properties of the two dimensional q states potts model using very accurate data obtained from a modified wang landau wl scheme proposed by caparica and cunha netto 2012 this algorithm is an extension of the conventional wl sampling but the authors changed the criterion to update the density of states during the random walk and established a new procedure to windup the simulation run these few changes have allowed a more precise microcanonical averaging which is essential to a reliable finite size scaling analysis in this work we used this new technique to determine the static critical exponents and in an unambiguous fashion the static critical exponents were determined as 0 10811 77 1 4459 31 and 0 8197 17 for the q 3 case and 0 0877 37 1 3161 69 and 0 7076 10 for the q 4 potts model a comparison of the present results with conjectured values and with those obtained from other well established approaches strengthens this new way of performing wl simulations