ramsey theorems for knots links and spatial graphs an embedding f g r of a graph g into r is said to be linear if each edge f e e g e g is a straight line segment it will be shown that for any knot or link type k there is a finite number r k such that every linear embedding of the complete graph kn with at least r k vertices n r k in r contains a knot or link equivalent to k

on multiscale entropy analysis for physiological data abstract we perform an analysis of cardiac data using multiscale entropy as proposed in costa et al multiscale entropy analysis of complex physiological time series phys rev lett 89 2002 068102 we reproduce the signatures of the multiscale entropy for the three cases of young healthy hearts atrial fibrillation and congestive heart failure we show that one has to be cautious how to interpret these signatures in terms of the underlying dynamics in particular we show that different dynamical systems can exhibit the same signatures depending on the sampling time and that similar systems may have different signatures depending on the time scales involved besides the total amount of data we identify the sampling time the correlation time and the period of possible nonlinear oscillations as important time scales which have to be involved in a detailed analysis of the signatures of multiscale entropies we illustrate our ideas with the lorenz equation as a simple deterministic chaotic system

correlations and variability in electrical signals related to earthquake activity abstract evaluating complex fluctuations in geoelectric time series is an important task not only for earthquake prediction but also for understanding complex processes related to earthquake preparation previous studies have reported alterations such as the emergence of correlated dynamics in geoelectric potentials prior to an important earthquake eq however the presence of correlations and its relation with variability has not been widely explored in this work we apply the detrended fluctuation analysis and the multiscale entropy methods to analyze the fluctuations of geoelectric time series monitored in two sites located in mexico we systematically calculate the correlation exponents and the sample entropy s e of geoelectric time series important differences in the scaling exponents and entropy profiles for several time scales are observed in particular a complex behavior characterized by a high entropy across several scales and crossover in the correlation exponents is observed in the vicinity of an m 7 4 eq that occurred on sept 14 1995 moreover we compare the changes in the entropy of the original data with their corresponding shuffled version to see whether correlations in the original data are related to variability

modified multiscale cross sample entropy for complex time series we introduce the cmcse and further propose the rcmcse method mcse cmcse and rcmcse methods are employed to artificial and financial time series rcmcse reduces standard deviation and the probability of inducing undefined entropy rcmcse can provide better robustness and more accurate entropies rcmcse is more applicable for the study between us and chinese stock markets in this paper we introduce the composite multiscale cross sample entropy cmcse which may induce undefined entropies and then further propose the refined composite multiscale cross sample entropy rcmcse which modifies cmcse first we apply multiscale cross sample entropy mcse cmcse and rcmcse methods to three types of artificial time series in order to test the validity and accuracy of these methods results show that rcmcse reduces not only standard deviation but also the probability of inducing undefined entropy effectively which can provide better robustness and more accurate entropies then these three methods are employed to investigate financial time series including us and chinese stock indices for the study between stock indices in the same region some conclusions which are consistent with previous study are drawn by the rcmcse results meanwhile it can be found that undefined entropies are induced and the numbers of inducing undefined entropy by three methods for investigation between three us stock indices and two chinese mainland stock indices are given compared with mcse and cmcse rcmcse method is capable of reducing the number of undefined entropy and providing more accurate entropies moreover the differences on inducing undefined entropy between results for us stock indices two chinese mainland stock indices and results for us stock indices hsi demonstrate a much closer relation between us stock markets and hsi than between us stock markets and two chinese mainland stock markets hence it can be concluded that rcmcse is more applicable for the study between us and chinese stock markets

refined composite multivariate generalized multiscale fuzzy entropy a tool for complexity analysis of multichannel signals abstract multiscale entropy mse is an appealing tool to characterize the complexity of time series over multiple temporal scales recent developments in the field have tried to extend the mse technique in different ways building on these trends we propose the so called refined composite multivariate multiscale fuzzy entropy rcmvmfe whose coarse graining step uses variance rcmvmfe 2 or mean rcmvmfe we investigate the behavior of these multivariate methods on multichannel white gaussian and 1 f noise signals and two publicly available biomedical recordings our simulations demonstrate that rcmvmfe 2 and rcmvmfe lead to more stable results and are less sensitive to the signals length in comparison with the other existing multivariate multiscale entropy based methods the classification results also show that using both the variance and mean in the coarse graining step offers complexity profiles with complementary information for biomedical signal analysis we also made freely available all the matlab codes used in this paper

solution of the crow kimura and eigen models for alphabets of arbitrary size by schwinger spin coherent states to represent the evolution of nucleic acid and protein sequence we express the parallel and eigen models for molecular evolution in terms of a functional integral representation with an h letter alphabet lifting the two state purine pyrimidine assumption often made in quasi species theory for arbitrary h and a general mutation scheme we obtain the solution of this model in terms of a maximum principle euler s theorem for homogeneous functions is used to derive this thermodynamic formulation of evolution the general result for the parallel model reduces to known results for the purine pyrimidine h 2 alphabet and the nucleic acid h 4 alphabet for the kimura 3 st mutation scheme examples are presented for the h 4 and h 20 cases we also derive the maximum principle for the eigen model for general h the general result for the eigen model reduces to a known result for h 2 examples are presented for the nucleic acid h 4 and the amino acid h 20 alphabet an error catastrophe phase transition occurs in these models and the order of the phase transition changes from second to first order for smooth fitness functions when the alphabet size is increased beyond two letters to the generic case as examples we analyze the general analytic solution for sharp peak linear quadratic and quartic fitness functions

multiscale statistical behaviors for ising financial dynamics with continuum percolation jump abstract a financial dynamics of interaction and jump is developed and investigated by two statistical physics systems ising model and continuum percolation this proposed model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price in an attempt to describe interacting micromechanism and sudden jump for stock price changes further the corresponding fluctuation behaviors and various complexity properties of logarithmic returns for the financial model are investigated by some statistical and complex analyses then p order multiscale autocorrelation function and q order multiscale entropy are also introduced to study the financial model with scaled analysis methods moreover the real stock market indexes are used to compare with the simulation returns from the financial model the empirical research shows that the simulation time series exhibits the similar fluctuation patterns with real time series

emd based refined composite multiscale entropy analysis of complex signals abstract multiscale entropy mse is an effective method to measure the complexity of signals from complex systems which has been applied to various fields successfully however mse may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse graining procedure reduces the length of data considerably at large scales refined composite multiscale entropy rcmse is then developed to solve this problem however trends superimposed in signals may significantly affect the complexity measurement thus we introduce an empirical mode decomposition based rcmse called emd rcmse to first eliminate such effects of trends and then measure the complexity of signals it is validated from simulated signals and has good estimation in addition this method is also applied to study the complexity of traffic signals and we obtain some interesting results 1 traffic signals are more complex than the results showing from rcmse mse 2 weekday and weekend patterns different combination of trends greatly affect the results 3 complexity indices change with time at each day due to the degree of human activities

possibilistic nonlinear dynamical analysis for pattern recognition a nonlinear dynamical system can be defined as a study of any system that implies motion change or evolution in time where a change in one variable is not proportional to a change in a related variable the mathematical operations underlying such a system are very useful for pattern recognition with time series data one of the most recent developments in nonlinear dynamical analysis is the so called approximate entropy family however its algorithms are deterministic and do not consider uncertainty where the modeling of possibility can be appropriate and advantageous in many practical situations thus possibilistic entropy algorithms are proposed in this paper as a new methodology for nonlinear dynamical analysis the proposed approach is based on the notions of the approximate entropy family geostatistics and the theory of fuzzy sets furthermore for the first time nonlinear dynamical analysis of mass spectrometry data is presented for computer based recognition of potential protein biomarkers and classification which can be utilized for early disease prediction experimental results using proteomic and genetic data have shown the potential application of the proposed possibilistic nonlinear dynamical analysis to the study of complex biosignals

refined generalized multiscale entropy analysis for physiological signals abstract multiscale entropy analysis has become a prevalent complexity measurement and been successfully applied in various fields however it only takes into account the information of mean values first moment in coarse graining procedure then generalized multiscale entropy mse n considering higher moments to coarse grain a time series was proposed and mse 2 has been implemented however the mse 2 sometimes may yield an imprecise estimation of entropy or undefined entropy and reduce statistical reliability of sample entropy estimation as scale factor increases for this purpose we developed the refined model rmse 2 to improve mse 2 simulations on both white noise and 1 f noise show that rmse 2 provides higher entropy reliability and reduces the occurrence of undefined entropy especially suitable for short time series besides we discuss the effect on rmse 2 analysis from outliers data loss and other concepts in signal processing we apply the proposed model to evaluate the complexity of heartbeat interval time series derived from healthy young and elderly subjects patients with congestive heart failure and patients with atrial fibrillation respectively compared to several popular complexity metrics the results demonstrate that rmse 2 measured complexity a decreases with aging and diseases and b gives significant discrimination between different physiological pathological states which may facilitate clinical application

structure of principal eigenvectors and genetic diversity abstract the main concern of this paper is long term genotypic diversity genotypes are represented as finite sequences s 1 s 2 s n where the entries s i are drawn from a finite alphabet the mutation matrix is given in terms of hamming distances it is proved that the long time behavior of solutions for a class of genotype evolution models is governed by the principal eigenvectors of the sum of the mutation and fitness matrices it is proved that the components of principal eigenvectors are symmetric and monotonely decreasing in terms of hamming distances whenever the fitness matrix has those properties

multivariate multiscale entropy analysis of horizontal oil water two phase flow abstract characterizing flow behavior underlying horizontal oil water flows from experimental measurements is a challenging problem in the fields of time series analysis and fluid mechanics we systematically conduct a horizontal oil water two phase flow experiment and use our designed distributed conductance sensor to measure multivariate signals from five different flow patterns taking two coupled lorenz systems as examples we first demonstrate that the multivariate multiscale entropy mmse enables to uncover the one way both way coupling structure of dynamic systems then we use mmse method to analyze the experimental measurements and extract the slopes and mean values from low scales of mmse to quantitatively characterize the flow behavior the results suggest that the mmse enables to quantitatively distinguish different horizontal oil water flow patterns and further allows deeply uncovering dynamic flow behavior in the transitions of different flow patterns

weighted multiscale renyi permutation entropy of nonlinear time series abstract in this paper based on renyi permutation entropy rpe which has been recently suggested as a relative measure of complexity in nonlinear systems we propose multiscale renyi permutation entropy mrpe and weighted multiscale renyi permutation entropy wmrpe to quantify the complexity of nonlinear time series over multiple time scales first we apply mpre and wmpre to the synthetic data and make a comparison of modified methods and rpe meanwhile the influence of the change of parameters is discussed besides we interpret the necessity of considering not only multiscale but also weight by taking the amplitude into account then mrpe and wmrpe methods are employed to the closing prices of financial stock markets from different areas by observing the curves of wmrpe and analyzing the common statistics stock markets are divided into 4 groups 1 dji s p500 and hsi 2 nasdaq and ftse100 3 dax40 and cac40 and 4 shangzheng and shencheng results show that the standard deviations of weighted methods are smaller showing wmrpe is able to ensure the results more robust besides wmpre can provide abundant dynamical properties of complex systems and demonstrate the intrinsic mechanism

cumulative tsallis entropy based on multi scale permuted distribution of financial time series abstract a method based on multi scale permuted distribution cumulative tsallis entropy mpdcte is proposed in this paper to measure the complexity and dissimilarity between sequences it avoids the influence of permutation on spatial distribution and uses the calculation of spatial distance matrix in distributed entropy to effectively measure the complexity of time series we apply the mpdcte method to the simulation data verify the effectiveness of the method discuss the influence of the parameters and compare it with the traditional entropy metric the results show that this method is insensitive to parameter changes and has a low dependence on data length the dependencies all show superiority finally it was applied to the real financial market and we selected 9 stocks in the world to analyze the mpdcte method clearly divided the stocks by analyzing the sequence which is consistent with the phenomenon of the financial market

how random is your heart beat we measure the content of random uncorrelated noise in heart rate variability using a general method of noise level estimation using a coarse grained entropy we show that usually except for atrial fibrillation the level of such noise is within 5 15 of the variance of the data and that the variability due to the linearly correlated processes is dominant in all cases analyzed but atrial fibrillation the nonlinear deterministic content of heart rate variability remains significant and may not be ignored

entropy analysis of stochastic processes at finite resolution abstract the time evolution of complex systems usually can be described through stochastic processes these processes are measured at finite resolution which necessarily reduces them to finite sequences of real numbers in order to relate these data sets to realizations of the original stochastic processes to any functions indeed it is obligatory to choose an interpolation space for example the space of band limited functions clearly this choice is crucial if the intent is to approximate optimally the original processes inside the interval of measurement here we argue that discrete wavelets are suitable to this end the wavelet approximations of stochastic processes allow us to define an entropy measure for the order disorder balance of evolution regimes of complex systems where order is understood as confinement of energy in simple local modes we calculate exact results for the fractional brownian motion fbm with application to kolmogorov k41 theory for fully developed turbulence

comment on multiscale entropy analysis of complex physiologic time series a comment on the letter by madalena costa ary l goldberger and c k peng phys rev lett 89 068102 2002 the authors of the letter offer a reply

refined composite multiscale weighted permutation entropy of financial time series abstract for quantifying the complexity of nonlinear systems multiscale weighted permutation entropy mwpe has recently been proposed mwpe has incorporated amplitude information and been applied to account for the multiple inherent dynamics of time series however mwpe may be unreliable because its estimated values show large fluctuation for slight variation of the data locations and a significant distinction only for the different length of time series therefore we propose the refined composite multiscale weighted permutation entropy rcmwpe by comparing the rcmwpe results with other methods results on both synthetic data and financial time series rcmwpe method shows not only the advantages inherited from mwpe but also lower sensitivity to the data locations more stable and much less dependent on the length of time series moreover we present and discuss the results of rcmwpe method on the daily price return series from asian and european stock markets there are significant differences between asian markets and european markets and the entropy values of hang seng index hsi are close to but higher than those of european markets the reliability of the proposed rcmwpe method has been supported by simulations on generated and real data it could be applied to a variety of fields to quantify the complexity of the systems over multiple scales more accurately

binary indices of time series complexity measures and entropy plane abstract complexity of time series is an important feature of dynamical systems such as financial systems in order to bring out the complete non linear behavior of financial time series non linear tools of complexity measurement like entropy measures are indispensable sample entropy sampen and distribution entropy disten are popular methods of assessing the complexity in various fields however both sample entropy and distribution entropy show some limitations in detecting the complexity of stock markets therefore we use two entropies as binary indices to analyze the complexity of time series and structure the entropy plane in order to further improve the accuracy of the research results we take the embedding dimension m as the variable expand the entropy point into the entropy curve for further research furthermore considering the shortcomings of sample entropy and distribution entropy in practical application we generalize them by i replacing sample entropy and distribution entropy with multi scale sample entropy and multi scale distribution entropy ii generalizing shannon entropy as tsallis entropy also scale factor and entropic index q are taken respectively as variables to get the entropy curves by using the artificial data we confirm the rationality of using entropy points and entropy curves to study the complexity of time series finally we apply this method to measure the complexity of real world financial time series the results show that the entropy curves plotted by the financial time series obtained from different areas have significant differences

a statistical complexity measure with nonextensive entropy and quasi multiplicativity the properties of a statistical complexity measure that are characterized by nonextensivity in entropy have been investigated which is of so called disequilibrium type considering the composition law for two systems with different nonextensivities quasi multiplicativity a nontrivial relation between the nonextensive parameters and the fluctuating bit number in information theory has been mentioned to see the time evolution of the nonextensive complexity measure we examine systems having a lognormal distribution the underlying dynamics for which is known to obey a random multiplicative process in the presence of a boundary constraint

chaos based nonlinear analysis to study cardiovascular responses to changes in posture abstract cardiovascular responses to changes in posture have been the focus of numerous investigations in the past analysis of ecg and arterial blood pressure abp data for different postures obtained from physionet was done from a new perspective of analyzing nonlinear time series having multifractal features multifractal detrended fluctuation analysis mfdfa and also the cross correlation between ecg and bp with another technique multifractal detrended cross correlation analysis mfdxa reveals ecg and abp time series of different subjects to be multifractal in nature with different degree of complexity different degree of auto and cross correlation for both ecg and abp signals is also observed for all subjects further significant information obtained from the cross correlation parameters obtained from mfdxa analysis is very important and relevant particularly for understanding the dynamics of orthostatic stress

symbolic diffusion entropy rate of chaotic time series as a surrogate measure for the largest lyapunov exponent existing methods for estimating the largest lyapunov exponent from a time series rely on the rate of separation of initially nearby trajectories reconstructed from the time series in phase space according to ueda chaotic dynamical behavior is viewed as a manifestation of random transitions between unstable periodic orbits in a chaotic attractor which are triggered by perturbations due to experimental observation or the roundoff error characteristic of the computing machine and consequently consists of a sequence of piecewise deterministic processes instead of an entirely deterministic process chaotic trajectories might have no physical reality here we propose a mathematical method for estimating a surrogate measure for the largest lyapunov exponent on the basis of the random diffusion of the symbols generated from a time series in a chaotic attractor without resorting to initially nearby trajectories we apply the proposed method to numerical time series generated by chaotic flow models and verify its validity

maximum minimum and optimal mutation rates in dynamic environments we analyze the dynamics of the parallel mutation selection quasispecies model with a changing environment for an environment with the sharp peak fitness function in which the most fit sequence changes by k spin flips every period t we find analytical expressions for the minimum and maximum mutation rates for which a quasispecies can survive valid in the limit of large sequence size we find an asymptotic solution in which the quasispecies population changes periodically according to the periodic environmental change in this state we compute the mutation rate that gives the optimal mean fitness over a period we find that the optimal mutation rate per genome k t is independent of genome size a relationship which is observed across broad groups of real organisms

long range dependencies in heart rate signals revisited abstract the arguments are given that local exponents obtained in multifractal analysis by two methods wavelet transform modulus maxima wtmm and multifractal detrended fluctuation analysis mdfa allow to separate statistically hearts of healthy people and subjects suffering from reduced left ventricle systolic function nyha i iii class proposed indices of fractality suggest that a signal of human heart rate is a mixture of two processes monofractal and multifractal ones

solvable biological evolution models with general fitness functions and multiple mutations in parallel mutation selection scheme in a recent paper phys rev e 69 046121 2004 we used the suzuki trottere formalism to study a quasispecies biological evolution model in a parallel mutation selection scheme with a single peak fitness function and a point mutation in the present paper we extend such a study to evolution models with more general fitness functions or multiple mutations in the parallel mutation selection scheme we give some analytical equations to define the error thresholds for some general cases of mean field like or symmetric mutation schemes and fitness functions we derive some equations for the dynamics in the case of a point mutation and polynomial fitness functions we derive exact dynamics for two point mutations asymmetric mutations and the four value spin model with a single peak fitness function the same method is applied for the model with a royal road fitness function we derive the steady state distribution for the single peak fitness function

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

model for the respiratory modulation of the heart beat to beat time interval series abstract in this study we present a model for the respiratory modulation of the heart beat to beat interval series the model consists of a set of differential equations used to simulate the membrane potential of a single rabbit sinoatrial node cell excited with a periodic input signal with added correlated noise this signal which simulates the input from the autonomous nervous system to the sinoatrial node was included in the pacemaker equations as a modulation of the i nak current pump and the potassium current i k we focus at modeling the heart beat to beat time interval series from normal subjects during meditation of the kundalini yoga and chi techniques the analysis of the experimental data indicates that while the embedding of pre meditation and control cases have a roughly circular shape it acquires a polygonal shape during meditation triangular for the kundalini yoga data and quadrangular in the case of chi data the model was used to assess the waveshape of the respiratory signals needed to reproduce the trajectory of the experimental data in the phase space the embedding of the chi data could be reproduced using a periodic signal obtained by smoothing a square wave in the case of kundalini yoga data the embedding was reproduced with a periodic signal obtained by smoothing a triangular wave having a rising branch of longer duration than the decreasing branch our study provides an estimation of the respiratory signal using only the heart beat to beat time interval series

quasispecies theory for multiple peak fitness landscapes we use a path integral representation to solve the eigen and crow kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions in the general case we find that the solution to these molecular evolution models can be written as the optimum of a fitness function with constraints enforced by lagrange multipliers and with a term accounting for the entropy of the spreading population in sequence space the results for the eigen model are applied to consider virus or cancer proliferation under the control of drugs or the immune system

an investigation of oil water two phase flow instability using multivariate multi scale weighted permutation entropy abstract the present study is devoted to the investigation of oil water two phase flow instability using multivariate multi scale weighted permutation entropy mwmpe four typical multivariate multi scale entropies namely mwmpe multivariate multi scale permutation entropy mmpe multivariate multi scale sample entropy mmse and multivariate multi scale approximate entropy mmae are applied in lorenz system with the addition of different kinds of noises the comparison results indicate that mwmpe presents the superiorities of being sensitive to the variation in scale showing a monotonous increasing trend as well as the best anti noise ability accordingly with the fluctuating signals from an eight electrode rotating electrical field conductance sensor used for the measurement of oil water flows we extract mwmpe for the whole experimental flow conditions in terms of which the effects of mixture velocity and water cut on oil water two phase flow instability are illuminated our research provides an effective method for uncovering the underlying evolution instability of the flow structures in oil water flows

model for the heart beat to beat time series during meditation abstract we present a model for the respiratory modulation of the heart beat to beat interval series the model consists of a pacemaker that simulates the membrane potential of the sinoatrial node modulated by a periodic input signal plus correlated noise that simulates the respiratory input the model was used to assess the waveshape of the respiratory signals needed to reproduce in the phase space the trajectory of experimental heart beat to beat interval data the data sets were recorded during meditation practices of the chi and kundalini yoga techniques our study indicates that in the first case the respiratory signal has the shape of a smoothed square wave and in the second case it has the shape of a smoothed triangular wave

point process nonlinear models with laguerre and volterra expansions instantaneous assessment of heartbeat dynamics in the last decades mathematical modeling and signal processing techniques have played an important role in the study of cardiovascular control physiology and heartbeat nonlinear dynamics in particular nonlinear models have been devised for the assessment of the cardiovascular system by accounting for short memory second order nonlinearities in this paper we introduce a novel inverse gaussian point process model with laguerre expansion of the nonlinear volterra kernels within the model the second order nonlinearities also account for the long term information given by the past events of the nonstationary non gaussian time series in addition the mathematical link to an equivalent cubic input output wiener volterra model allows for a novel instantaneous estimation of the dynamic spectrum bispectrum and trispectrum of the considered inter event intervals the proposed framework is tested with synthetic simulations and two experimental heartbeat interval datasets applications on further heterogeneous datasets such as milling inserts neural spikes gait from short walks and geyser geologic events are also reported results show that our model improves on previously developed models and at the same time it is able to provide a novel instantaneous characterization and tracking of the inherent nonlinearity of heartbeat dynamics

average entropy measurement of disorder for cardiac rr interval signals abstract we introduce average entropy ae as a disorder measure of heart rate time series the ae measurement reflects both the probability distribution of all discrete values in a time series and the randomness of the series the ae analysis is able to differentiate the congestive heart failure chf the healthy and the atrial fibrillation af subjects for both short and long heart rate time series the differentiation accuracy of ae is higher than 90 in addition since the meaning of disorder is easily confused with complexity we explore the relation between them by analyzing heart rate time series specifically we demonstrate that the complexity measured by entropy of entropy eoe versus the disorder measured by ae plot of heart rate time series exhibits a distinct inverted u relation

link lengths and their growth powers for a certain infinite family of knots or links we study the growth power ratios of their stick number lattice stick number minimum lattice length and minimum ropelength compared with their minimum crossing number c k for every it is known that the stick number and lattice stick number grow between the and linear power of the crossing number and minimum lattice length and minimum ropelength grow with at least the power of crossing number which is called the four thirds power law furthermore the minimal lattice length and minimum ropelength grow at most as o but it is unknown whether any family exhibits superlinear growth for any real number r between and 1 we give an infinite family of non splittable prime links in which the stick number and lattice stick number grow exactly as the rth power of crossing number furthermore for any real number r between and 1 we give another infinite family of non splittable prime links in which the minimum lattice length and minimum ropelength grow exactly as the rth power of crossing number

enhancing poincare plot information via sampling rates poincare plots of a continuous solution of the logistic equation at different sampling rates are studied the study uses the continuous solution obtained for the parameter a 4 in the logistic equation this solution of the logistic equation used in this study provides a useful handle to study sampling effects and at the same time look at a system which exhibits complex correlations the results of this study show that the poincare plots of a continuous function at different sampling rates provide valuable information about the complex correlations present in the system this additional information provided by the poincare plots of data from a continuous system sampled at different rates will be a useful and simple way of studying correlations present in a real system with applications in biomedicine

solvable biological evolution model with a parallel mutation selection scheme based on the connection between a quantum spin model and an asexual biological evolution model with a single peak fitness function in parallel mutation selection scheme we solve exactly both static and dynamics of the evolution model we find that relaxation in such a parallel scheme is faster than that in a connected scheme of eigen model our method can also be extended to other fitness functions

quasispecies model of evolution with migration we consider the model of asexual evolution with migration which was proposed by waclaw et al phys rev lett 105 268101 2010 prltao0031 900710 1103 physrevlett 105 268101 this model setting is based on the standard mutation scheme from the quasispecies theory but with replicators moving from one habitat to another the primary goal is to solve exactly the infinite population genome length version of the model for the independent random distribution of fitnesses considered in the original paper moreover we propose the analytical solution for the single peak and the symmetric fitness landscape our analytical solution is exact at the limit of large n we found two phases the correlated phase with the identical distributions of mutations in both habitats and the uncorrelated phase where the second habitat is choosing another peak of distribution in sequence space compared to the peak in the first habitat

generalized entropy plane based on large deviations theory for financial time series abstract complexity entropy causality plane analysis and large deviations spectrums theory are proposed to study time series the entropy plane analysis depicts the complexity of a system in two dimensional plane while large deviations theory shows the spectral structure of time series in the way of multifractal in this paper we combine the characteristics of these two popular methods and propose a generalized entropy plane model based on the large deviation theory the methodology is applied to both synthetic data and financial markets we discuss the impact of the parameters on the results in detail besides the modified model can distinguish different time series meanwhile we compare our results with the original complexity entropy causality plane and large deviations spectrums and the consistency of these results is confirmed the method can provide abundant dynamical properties of complex systems

dispersive graded entropy on computing dynamical complexity abstract we propose a phase space based statistical disorder to investigate the dynamical complexity of chaotic models the statistical disorder is defined by introducing a grade function inversely maps the mean dispersion of the trajectories in the phase space we denote the associate entropy by the dispersive graded entropy dge numerical investigation shows that dge can quantify the dynamical complexity of discrete as well as continuous chaotic systems a comparative study is also made with the other phase space based entropy measures finally the proposed measure has been applied on three types of heart rate variability hrv signals the results support the clinical observations related to the dynamics of healthy and congestive hearts

measuring randomness by leave one out prediction error analysis of eeg after painful stimulation abstract a parametric approach to measure randomness in time series is presented time series are modelled by a kernel machine performing regularized least squares and the leave one out loo error is used to quantify unpredictability on analyzing simulated data sets we find that structure in data leads to a minimum of the loo error as the regularizing parameter is varied we consider electroencephalographic signals from migraineurs and healthy humans after painful stimulation and use the proposed approach to detect changes of physiological state and to find differences between the response from patients and healthy subjects as painful stimulus causes organization of the local activity in the cortex eeg series become more predictable after stimulation this phenomenon is less evident in patients the inadequate cortical response to pain in migraineurs separates patients from controls with a probability close to 0 005

links with small lattice stick numbers knots and links have been considered to be useful models for structural analysis of molecular chains such as dna and proteins one quantity that we are interested in for molecular links is the minimum number of monomers necessary for realizing them in this paper we consider every link in the cubic lattice the lattice stick number sl l of a link l is defined to be the minimum number of sticks required to construct a polygonal representation of the link in the cubic lattice huh and oh found all knots whose lattice stick numbers are at most 14 they proved that only the trefoil knot 31 and the figure eight knot 41 have lattice stick numbers of 12 and 14 respectively in this paper we find all links with more than one component whose lattice stick numbers are at most 14 indeed we prove combinatorically that and any other non split links have stick numbers of at least 15

modified multiscale entropy for short term time series analysis abstract multiscale entropy mse is a prevalent algorithm used to measure the complexity of a time series because the coarse graining procedure reduces the length of a time series the conventional mse algorithm applied to a short term time series may yield an imprecise estimation of entropy or induce undefined entropy to overcome this obstacle the modified multiscale entropy mmse was developed the coarse graining procedure was replaced with a moving average procedure and a time delay was incorporated for constructing template vectors in calculating sample entropy for conducting short term time series analysis this study shows that the mmse algorithm is more reliable than the conventional mse

volatility behavior of visibility graph emd financial time series from ising interacting system abstract a financial market dynamics model is developed and investigated by stochastic ising system where the ising model is the most popular ferromagnetic model in statistical physics systems applying two graph based analysis and multiscale entropy method we investigate and compare the statistical volatility behavior of return time series and the corresponding imf series derived from the empirical mode decomposition emd method and the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further we find that the degree distribution of visibility graph for the simulation series has the power law tails and the assortative network exhibits the mixing pattern property all these features are in agreement with the real market data the research confirms that the financial model established by the ising system is reasonable

complexity and multifractal behaviors of multiscale continuum percolation financial system for chinese stock markets abstract a new financial agent based time series model is developed and investigated by multiscale continuum percolation system which can be viewed as an extended version of continuum percolation system in this financial model for different parameters of proportion and density two poisson point processes where the radii of points represent the ability of receiving or transmitting information among investors are applied to model a random stock price process in an attempt to investigate the fluctuation dynamics of the financial market to validate its effectiveness and rationality we compare the statistical behaviors and the multifractal behaviors of the simulated data derived from the proposed model with those of the real stock markets further the multiscale sample entropy analysis is employed to study the complexity of the returns and the cross sample entropy analysis is applied to measure the degree of asynchrony of return autocorrelation time series the empirical results indicate that the proposed financial model can simulate and reproduce some significant characteristics of the real stock markets to a certain extent

monofractal and multifractal analysis of simulated heat release fluctuations in a spark ignition heat engine abstract we study data from cycle by cycle variations in heat release for a simulated spark ignited engine our analyses are based on nonlinear scaling properties of heat release fluctuations obtained from a turbulent combustion model we apply monofractal and multifractal methods to characterize the fluctuations for several fuel air ratio values from lean mixtures to stoichiometric situations the monofractal approach reveals that for lean and stoichiometric conditions the fluctuations are characterized by the presence of weak anticorrelations whereas for intermediate mixtures we observe complex dynamics characterized by a crossover in the scaling exponents for short scales the variations display positive correlations while for large scales the fluctuations are close to white noise moreover a broad multifractal spectrum is observed for intermediate fuel ratio values while for low and high the fluctuations lead to a narrow spectrum finally we explore the origin of correlations by using the surrogate data method to compare the findings of multifractality and scaling exponents between original simulated and randomized data

geoentropy a measure of complexity and similarity measuring the complexity of a pattern expressed either in time or space has been introduced to quantify the information content of the pattern which can then be applied for classification such information measures are particularly useful for the understanding of systems complexity in many fields of sciences business and engineering the novel concept of geostatistical entropy geoentropy as a measure of pattern complexity and similarity is addressed in this paper it has been experimentally shown that geoentropy is an effective algorithm for studying signal predictability and has superior capability of classifying complex bio patterns

multi scale symbolic transfer entropy analysis of eeg abstract from both global and local perspectives we symbolize two kinds of eeg and analyze their dynamic and asymmetrical information using multi scale transfer entropy multi scale process with scale factor from 1 to 199 and step size of 2 is applied to eeg of healthy people and epileptic patients and then the permutation with embedding dimension of 3 and global approach are used to symbolize the sequences the forward and reverse symbol sequences are taken as the inputs of transfer entropy scale factor intervals of permutation and global way are 37 57 and 65 85 where the two kinds of eeg have satisfied entropy distinctions when scale factor is 67 transfer entropy of the healthy and epileptic subjects of permutation 0 1137 and 0 1028 have biggest difference and the corresponding values of the global symbolization is 0 0641 and 0 0601 which lies in the scale factor of 165 research results show that permutation which takes contribution of local information has better distinction and is more effectively applied to our multi scale transfer entropy analysis of eeg

approximate entropy analysis of short term hfecg based on wave mode abstract an improved approximate entropy apen algorithm based on wave mode is proposed by analyzing and modifying apen so that the irregular analysis can be applied to analyze the short term series which contain a great deal of detailed information and fluctuate slowly but in a wide range such as high frequency electrocardiogram hfecg by analyzing the complexity of hfecg a conclusion can be drawn that apen algorithm based on wave mode can obviously distinguish heart diseases from the healthy group therefore it is of significance for diagnosing myocardial infarction in time

schwinger boson formulation and solution of the crow kimura and eigen models of quasispecies theory we express the crow kimura and eigen models of quasispecies theory in a functional integral representation we formulate the spin coherent state functional integrals using the schwinger boson method in this formulation we are able to deduce the long time behavior of these models for arbitrary replication and degradation functions we discuss the phase transitions that occur in these models as a function of mutation rate we derive for these models the leading order corrections to the infinite genome length limit

gas liquid two phase flow structure in the multi scale weighted complexity entropy causality plane abstract the multi scale weighted complexity entropy causality plane ms wcecp is proposed for characterizing the physical structure of complex system firstly we use the method to investigate typical nonlinear time series compared with the multi scale complexity entropy causality plane ms cecp the ms wcecp can not only uncover the dynamic information loss of complex system with the increase of scale but also can characterize the complexity of nonlinear dynamic system in particular the algorithm of ms wcecp performs strong anti noise ability then we calculate the ms wcecp for the conductance fluctuating signals measured from vertical upward gas liquid two phase flow experiments in a small diameter pipe the results demonstrate that the ms wcecp is a useful approach for exploring the stability and complexity in gas liquid two phase flows

reshape scale method a novel multi scale entropic analysis approach abstract the reshape scale rs method was introduced in this article as a novel approach to perform multi scale transition of sample entropy this method was able to quantify the orderliness in the signal by determining the distance over which the subsequent data points can remain affiliated to one another entropic half life enhl was introduced to characterize such an affiliation the method was tested for 1 f processes for different values furthermore the dependency of the multi scale entropy analysis developed by costa et al 2002 6 to the probability density function and the standard deviation of autoregressive signals was studied and discussed

multiscale permutation entropy analysis of electrocardiogram abstract to make a comprehensive nonlinear analysis to ecg multiscale permutation entropy mpe was applied to ecg characteristics extraction to make a comprehensive nonlinear analysis of ecg three kinds of ecg from physionet database congestive heart failure chf patients healthy young and elderly subjects are applied in this paper we set embedding dimension to 4 and adjust scale factor from 2 to 100 with a step size of 2 and compare mpe with multiscale entropy mse as increase of scale factor mpe complexity of the three ecg signals are showing first decrease and last increase trends when scale factor is between 10 and 32 complexities of the three ecg had biggest difference entropy of the elderly is 0 146 less than the chf patients and 0 025 larger than the healthy young in average in line with normal physiological characteristics test results showed that mpe can effectively apply in ecg nonlinear analysis and can effectively distinguish different ecg signals

nonadditive tsallis entropy applied to the earth s climate a b s t r a c t the concepts of nonextensive statistics which has been applied in the study of complex systems are used to analyze past records of the earth s climate the fluctuations within the record of deuterium content hence temperature in the last glacial period appear to follow a q gaussian distribution analyses of the time dependent nonadditive entropy indicate transitions between different complexity levels in the data prior to the abrupt change in the system dynamics at the end of the last glaciation different fluctuation regimens are evidenced through wavelets analysis it is also suggested that time dependent entropy analysis could be useful for indicating the approach to a critical transition of the earth s climate for which theoretical models are in many cases not available

the experimental signals analysis for bubbly oil in water flow using multi scale weighted permutation entropy abstract we firstly combine multi scale method ms and weighted permutation entropy wpe to analyze chaotic noisy and fractal time series and find that mswpe can distinguish different nonlinear time series and exhibit a better robustness in the presence of higher levels of noise a task that multi scale permutation entropy mspe fails to work we then apply mswpe to analyze the signals from vertical upward oil in water two phase flow experiments our results suggest that the change rate of mswpe enables to characterize the transition of flow patterns and multi scale weighted permutation entropy allows indicating the discrepancy of complexity of oil in water two phase flow

anderson localization non linearity and stable genetic diversity in many models of genotypic evolution the vector of genotype populations satisfies a system of linear ordinary differential equations this system of equations models a competition between differential replication rates fitness and mutation mutation operates as a generalized diffusion process on genotype space in the large time asymptotics the replication term tends to produce a single dominant quasi species unless the mutation rate is too high in which case the asymptotic population becomes de localized we introduce a more macroscopic picture of genotypic evolution wherein a random fitness term in the linear model produces features analogous to anderson localization when coupled with density dependent non linearities which limit the population of any given genotype we obtain a model whose large time asymptotics display stable genotypic diversity

generalized multivariate multiscale sample entropy for detecting the complexity in complex systems abstract using the first moment in coarse graining the original time series in different time scales will lose some important information of the complexity in this paper we propose the generalized multivariate multiscale sample entropy gmmse to analyze the complexity for multivariate time series before empirical analysis numerical simulation is conducted by applying g m m s e 1 mean g m m s e 2 variance g m m s e 3 skewness to the autoregressive fractionally integrated moving average arfima processes the simulated results illustrate that g m m s e 2 is more appropriate to analyze the complexity of arfima time series then we apply gmmse method to traffic multivariate time series and discuss their complexities over different time scales comparing the g m m s e 1 g m m s e 2 and g m m s e 3 results for different detectors g m m s e 2 and g m m s e 3 can clearly differentiate the detectors with different complexity and reflect the characteristics and similarities of the complexity of traffic data between different locations besides both the effect of traffic accident and the effect of the weekday and weekend patterns containing in traffic signals on the complexity can be detected by g m m s e 2 and g m m s e 3 methods g m m s e 2 and g m m s e 3 are capable of providing more important information and knowledge concerning the complexity of traffic time series and will bring enhanced understanding of the properties of traffic system

inhomogeneous point process entropy an instantaneous measure of complexity in discrete systems measures of entropy have been widely used to characterize complexity particularly in physiological dynamical systems modeled in discrete time current approaches associate these measures to finite single values within an observation window thus not being able to characterize the system evolution at each moment in time here we propose a new definition of approximate and sample entropy based on the inhomogeneous point process theory the discrete time series is modeled through probability density functions which characterize and predict the time until the next event occurs as a function of the past history laguerre expansions of the wiener volterra autoregressive terms account for the long term nonlinear information as the proposed measures of entropy are instantaneously defined through probability functions the novel indices are able to provide instantaneous tracking of the system complexity the new measures are tested on synthetic data as well as on real data gathered from heartbeat dynamics of healthy subjects and patients with cardiac heart failure and gait recordings from short walks of young and elderly subjects results show that instantaneous complexity is able to effectively track the system dynamics and is not affected by statistical noise properties

finite genome length corrections for the mean fitness and gene probabilities in evolution models using the hamilton jacobi equation approach to study genomes of length l we obtain 1 l corrections for the steady state population distributions and mean fitness functions for horizontal gene transfer model as well as for the diploid evolution model with general fitness landscapes our numerical solutions confirm the obtained analytic equations our method could be applied to the general case of nonlinear markov models

spin coherent state representation of the crow kimura and eigen models of quasispecies theory we present a spin coherent state representation of the crow kimura and eigen models of biological evolution we deal with quasispecies models where the fitness is a function of hamming distances from one or more reference sequences in the limit of large sequence length n we find exact expressions for the mean fitness and magnetization of the asymptotic quasispecies distribution in symmetric fitness landscapes the results are obtained by constructing a path integral for the propagator on the coset su 2 u 1 and taking the classical limit the classical limit gives a hamiltonian function on a circle for one reference sequence and on the product of 2m 1 circles for m reference sequences we apply our representation to study the schuster swetina phenomena where a wide lower peak is selected over a narrow higher peak the quadratic landscape with two reference sequences is also analyzed specifically and we present the phase diagram on the mutation fitness parameter phase space furthermore we use our method to investigate more biologically relevant system a model of escape from adaptive conflict through gene duplication and find three different phases for the asymptotic population distribution

event and time scale characteristics of heart rate dynamics the cardiac system shows various scale dynamic activities from secondly to yearly therefore multiple time scale characteristics of heart dynamics have received much attention for understanding and distinguishing healthy and pathological cardiac systems in this paper we expand the multiple time scale analysis into event and time scales to investigate scale characteristics in healthy and pathologic cardiac systems to do this we define a measure based on symbolic dynamics which calculates complexity at each time and event scale called the unit time block entropy utbe this measure allows a reliable comparison of experimental data through matching the number of words and the total measurement time at the same time for all rr interval sequences which are composed of the time durations between consecutive r waves of electrocardiograms we apply the utbe to the healthy heart rate hr group and pathological hr groups and find that the rr interval acceleration is more effective than the rr interval in distinguishing each group and we also find that the normal and pathological hr groups are clearly distinguished in some specific event and time scale regions

weighted multiscale cumulative residual renyi permutation entropy of financial time series abstract in this paper based on cumulative residual entropy cre and renyi permutation entropy rpe multiscale cumulative residual renyi permutation entropy mcrrrpe and weighted multiscale cumulative residual renyi permutation entropy wmcrrpe are proposed as novelty measures to quantify the uncertainty of the nonlinear time series first the mcrrpe and wmcrrpe methods are performed on the synthetic data and the impact of the changes to parameters is discussed then the mcrrpe and wmcrrpe methods are applied to the closing prices of the us european and chinese stock markets we analyze the statistics and draw some conclusions from the comparison the stock markets can be divided into four categories 1 nasdaq and ftse100 2 s p500 dji and hsi 3 dax30 and cac40 and 4 sse and szse the standard deviation has a certain relationship with wmcrrpe compared with the mcrrpe method the wmcrrpe method can distinguish these financial stock markets effectively and better estimate the complexity of the time series containing amplitude information

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

time dependent limited penetrable visibility graph analysis of nonstationary time series abstract recent years have witnessed the development of visibility graph theory which allows us to analyze a time series from the perspective of complex network we in this paper develop a novel time dependent limited penetrable visibility graph tdlpvg two examples using nonstationary time series from rr intervals and gas liquid flows are provided to demonstrate the effectiveness of our approach the results of the first example suggest that our tdlpvg method allows characterizing the time varying behaviors and classifying heart states of healthy congestive heart failure and atrial fibrillation from rr interval time series for the second example we infer tdlpvgs from gas liquid flow signals and interestingly find that the deviation of node degree of tdlpvgs enables to effectively uncover the time varying dynamical flow behaviors of gas liquid slug and bubble flow patterns all these results render our tdlpvg method particularly powerful for characterizing the time varying features underlying realistic complex systems from time series

revisiting sample entropy analysis abstract we modify the definition of sample entropy saen by incorporating a time delay between the components of the block from which the densities are estimated and show that the modified method characterizes the complexity of the system better than the original version we apply the modified saen to the standard deterministic systems and stochastic processes uncorrelated and long range correlated lrc processes and show that the underlying complexity of the system is better quantified by the modified method we extend this analysis to the rr intervals of the normal and congestive heart failure chf subjects available via www physionet org and show that there is a good degree of separation between the two groups

optimal mutation rates in dynamic environments the eigen model we consider the eigen quasispecies model with a dynamic environment for an environment with sharp peak fitness in which the most fit sequence moves by k spin flips each period t we find an asymptotic stationary state in which the quasispecies population changes regularly according to the regular environmental change from this stationary state we estimate the maximum and the minimum mutation rates for a quasispecies to survive under the changing environment and calculate the optimum mutation rate that maximizes the population growth interestingly we find that the optimum mutation rate in the eigen model is lower than that in the crow kimura model and at their optimum mutation rates the corresponding mean fitness in the eigen model is lower than that in the crow kimura model suggesting that the mutation process which occurs in parallel to the replication process as in the crow kimura model gives an adaptive advantage under changing environment

hierarchical entropy analysis for biological signals we develop a hierarchical entropy he method to quantify the complexity of a time series based on hierarchical decomposition and entropy analysis the proposed method is applied to the gaussian white noise and the 1 f noise we prove that the difference frequency components of the gaussian white noise with the same scale factor have the same value of entropies and the values decline as the scale factor increases we also apply the he method to the 1 f noise and prove mathematically that a lower frequency component of a 1 f noise is also a 1 f noise and verify numerically that a higher frequency component of a 1 f random vector is approximately equal to a gaussian random vector the theoretical results are confirmed by numerical results moreover we show that the he method is an efficient method to analyze heartbeat signals by applying it to the cardiac interbeat interval time series of healthy young and elderly subjects congestive heart failure chf subjects and atrial fibrillation af subjects

entropy of electromyography time series abstract a nonlinear analysis based on renyi entropy is applied to electromyography emg time series from back muscles the time dependence of the entropy of the emg signal exhibits a crossover from a subdiffusive regime at short times to a plateau at longer times we argue that this behavior characterizes complex biological systems the plateau value of the entropy can be used to differentiate between healthy and low back pain individuals

eigen model as a quantum spin chain exact dynamics we map the eigen model of biological evolution naturwissenschaften 58 465 1971 into a quantum spin model with non hermitian hamiltonian based on such a connection we derive exact relaxation periods for the eigen model to approach static energy landscape from various initial conditions we also study a simple case of dynamic fitness function

a complexity measure for heart rate signals abstract in this paper we present an adaptive measurement to quantify the complexity of time series called q sample entropy difference mean q sediffave and apply this method to heart rate time series it quantifies the structural information of the signals and helps identify different conditions of the heart systems experiments show that compared with the traditional sample entropy sampen q sediffave has significant advantages in reflecting the inherent information of sequences it also reveals that the q sediffave curves of healthy subjects are significantly different from the atrial fibrillation af and congestive heart failure chf groups because the chf signals tend to fluctuate between narrow ranges while the atrial fibrillation af signals are random and the signals of healthy subjects are usually mixed by signals with different dynamic characteristics showing higher complexity in addition the most important parameter in the model q can enlarge the differences between q sediffave curves of healthy and pathological states

multi scale entropy analysis and hurst exponent abstract several methods exist for measuring the complexity in a system through analysis of its associated time series multi scale entropy appears as a successful method on this matter it has been applied in many disciplines with great achievements for example by analysis of the bio signals we are able to diagnose various diseases however in most versions for the multi scale entropy the examined time series is analyzed qualitatively in this study we try to present a quantitative picture for the multi scale entropy analysis particularly we focus on finding relation between the result of the multi scale analysis and the hurst exponent which quantifies the persistence in time series for this purpose the fractional gaussian noise time series with different hurst exponents are analyzed by the multi scale entropy method and the results are fitted to a decreasing q exponential function we observe remarkable relation between the function parameters and hurst exponent this function can simulate the result of analysis for the white noise to the 1 f noise

an information based tool for inferring the nature of deterministic sources in real data the scope of the paper is to find signatures of the forces controlling complex systems modeled by langevin equations by recourse to information theory quantifiers we evaluate in detail the permutation entropy pe and the permutation statistical complexity psc measures for two similarity classes of stochastic models characterized by either drifting or reversion properties and employ them as a reference basis for the inspection of real series new relevant model parameters arise as compared to standard entropy measures we determine the normalized pe and psc curves according to them over a range of permutation orders n and infer the limiting measures for arbitrary large order we found that the psc measure is strongly scale dependent with systems of the drifting class showing crossovers as n increases this result gives warning signs about the proper interpretation of finite scale analysis of complexity in general processes conversely a key n invariant outcome arises that is the normalized pe values for both classes of models keep complementary for any n we argue that both pe and psc measures enable one to unravel the nature drifting or restoring of the deterministic sources underlying complexity we conclude by investigating the presence of local trends in stock price series

dynamical complexity changes during two forms of meditation abstract detection of dynamical complexity changes in natural and man made systems has deep scientific and practical meaning we use the base scale entropy method to analyze dynamical complexity changes for heart rate variability hrv series during specific traditional forms of chinese chi and kundalini yoga meditation techniques in healthy young adults the results show that dynamical complexity decreases in meditation states for two forms of meditation meanwhile we detected changes in probability distribution of m words during meditation and explained this changes using probability distribution of sine function the base scale entropy method may be used on a wider range of physiologic signals