generalized information entropy analysis of financial time series abstract generalized information entropy has been widely applied to analyzing complex systems in this paper we propose the weighted multiscale renyi permutation entropy mswrpe based on the weight assigned to each vector as a novel technique to consider the amplitude information renyi permutation entropy rpe has a parameter q for non extensivity compared to shannon permutation entropy pe hence we speculate that rpe has a better sensitivity to patterns extracted from signals containing amplitude information and a better robustness to noise compared to pe firstly we perform the multiscale renyi permutation entropy msrpe and mswrpe methods on synthetic data we find that mswrpe suits better signals containing considerable amplitude information and is successful to consider the multiple time scales inherent in the financial systems the finding is also verified in four different stock markets then we make a comparison between mswrpe and weighted multiscale permutation entropy mswpe on different stock markets the conclusion is that the mswrpe method has a better characterization than mswpe for q 1 different markets have the same law on mswrpe while hsi can be distinguished from the other markets for q 1 which is more obvious when m 7

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

distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach in this paper we introduce a multiscale symbolic information theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems more precisely we show that the multiscale complexity entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system s dynamics numerical simulations obtained from the well known and widely used mackey glass oscillator operating in a high dimensional chaotic regime were used as test beds the effect of an increased amount of observational white noise was carefully examined the results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles finally several experimental and natural time series were analyzed in order to show the applicability of this scale dependent symbolic approach in practical situations

upper bound covariance control of discrete perturbed systems abstract the purpose of this paper is to develop a methodology which is based on the state covariance assignment theory to design feedback controllers such that a specified state covariance upper bound will be achieved furthermore an example is given to illustrate the effectiveness of the present approach

generalized system of trial equation methods and their applications to biological systems abstract it is shown that many systems of nonlinear differential equations of interest in various fields are naturally embedded in a new family of differential equations in this paper we improve new and effective methods for nonautonomous systems and they produce new exact solutions to some important biological systems the exact solution of predator and prey population for different particular cases has been derived the numerical examples show that new exact solutions can be obtained for many biological systems such as sir model lotka volterra model the methods perform extremely well in terms of efficiency and simplicity to solve this historical biological models the lotka volterra nonlinear differential equations for two competing species namely x and y contain six independent parameters their general analytic solutions valid for arbitrary values of the parameters are at present unknown however when two or more of these parameters are interrelated it is possible to obtain the exact solutions in the x y phase plane and six cases of solvability are given in this paper the dependence of the solutions on the parameters and the initial conditions can thus be readily investigated

quantifying long range correlations with a multiscale ordinal pattern approach abstract in this paper we use the ordinal patterns probabilities associated with fractional brownian motions for estimating the hurst exponent of artificially generated and experimentally measured data numerical analysis show a reliable estimation of this scaling parameter even when data with low resolution are analysed robustness to observational noise is also obtained several experimental applications allow us to confirm the practical utility of the proposed approach we contrast results obtained by implementing this multiscale symbolic tool with those obtained from the classical detrended fluctuation analysis

a path integral approach to the hodgkin huxley model abstract to understand how single neurons process sensory information it is necessary to develop suitable stochastic models to describe the response variability of the recorded spike trains spikes in a given neuron are produced by the synergistic action of sodium and potassium of the voltage dependent channels that open or close the gates hodgkin and huxley hh equations describe the ionic mechanisms underlying the initiation and propagation of action potentials through a set of nonlinear ordinary differential equations that approximate the electrical characteristics of the excitable cell path integral provides an adequate approach to compute quantities such as transition probabilities and any stochastic system can be expressed in terms of this methodology we use the technique of path integrals to determine the analytical solution driven by a non gaussian colored noise when considering the hh equations as a stochastic system the different neuronal dynamics are investigated by estimating the path integral solutions driven by a non gaussian colored noise q more specifically we take into account the correlational structures of the complex neuronal signals not just by estimating the transition probability associated to the gaussian approach of the stochastic hh equations but instead considering much more subtle processes accounting for the non gaussian noise that could be induced by the surrounding neural network and by feedforward correlations this allows us to investigate the underlying dynamics of the neural system when different scenarios of noise correlations are considered

simple measure for complexity a measure of complexity is proposed based on appropriately defined notions of order and disorder which has a considerable degree of flexibility in its dependence on these concepts the possible functional dependencies which result encompass those of many earlier definitions of complexity the proposed measure is in principle easy to calculate and has the property of an intensive thermodynamic quantity with appropriate choices of parameters it behaves similarly to effective measure complexity for the logistic map it is also a generalization of the normalized complexity of lopez ruiz et al but does not suffer from over universality

characterization of electric load with information theory quantifiers abstract this paper presents a study of the electric load behavior based on the causality complexity entropy plane we use a public data set namely redd which contains detailed power usage information from several domestic appliances in our characterization we use the available power data of the circuit devices of all houses the bandt pompe methodology combined with the causality complexity entropy plane was used to identify and characterize regimes and behaviors over these data the results showed that this characterization provides a useful insight into the underlying dynamics that govern the electric load

upper and lower covariance bounds for perturbed linear systems both upper and lower bounds are established for state covariance matrices under parameter perturbations of the plant the motivation for this study lies in the fact that many robustness properties of linear systems are given explicitly in terms of the state covariance matrix moreover there exists a theory for control by covariance assignment the results provide robustness properties of these covariance controllers

evaluation of the status of rotary machines by time causal information theory quantifiers abstract in this paper several causal information theory quantifiers i e shannon entropy statistical complexity and fisher information using the bandt and pompe permutation probability distribution measure are applied to describe the behavior of a rotating machine an experiment was conducted where a rotating machine runs balanced and then after a misalignment runs unbalanced all the causal information theory quantifiers applied are capable to distinguish between both states and grasp the corresponding transition between them

characterizing time series via complexity entropy curves the search for patterns in time series is a very common task when dealing with complex systems this is usually accomplished by employing a complexity measure such as entropies and fractal dimensions however such measures usually only capture a single aspect of the system dynamics here we propose a family of complexity measures for time series based on a generalization of the complexity entropy causality plane by replacing the shannon entropy by a monoparametric entropy tsallis q entropy and after considering the proper generalization of the statistical complexity q complexity we build up a parametric curve the q complexity entropy curve that is used for characterizing and classifying time series based on simple exact results and numerical simulations of stochastic processes we show that these curves can distinguish among different long range short range and oscillating correlated behaviors also we verify that simulated chaotic and stochastic time series can be distinguished based on whether these curves are open or closed we further test this technique in experimental scenarios related to chaotic laser intensity stock price sunspot and geomagnetic dynamics confirming its usefulness finally we prove that these curves enhance the automatic classification of time series with long range correlations and interbeat intervals of healthy subjects and patients with heart disease

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

complexity analysis of the turbulent environmental fluid flow time series abstract we have used the kolmogorov complexities sample and permutation entropies to quantify the randomness degree in river flow time series of two mountain rivers in bosnia and herzegovina representing the turbulent environmental fluid for the period 1926 1990 in particular we have examined the monthly river flow time series from two rivers the miljacka and the bosnia in the mountain part of their flow and then calculated the kolmogorov complexity kl based on the lempel ziv algorithm lza lower kll and upper klu sample entropy se and permutation entropy pe values for each time series the results indicate that the kll klu se and pe values in two rivers are close to each other regardless of the amplitude differences in their monthly flow rates we have illustrated the changes in mountain river flow complexity by experiments using i the data set for the bosnia river and ii anticipated human activities and projected climate changes we have explored the sensitivity of considered measures in dependence on the length of time series in addition we have divided the period 1926 1990 into three subintervals a 1926 1945 b 1946 1965 c 1966 1990 and calculated the kll klu se pe values for the various time series in these subintervals it is found that during the period 1946 1965 there is a decrease in their complexities and corresponding changes in the se and pe in comparison to the period 1926 1990 this complexity loss may be primarily attributed to i human interventions after the second world war on these two rivers because of their use for water consumption and ii climate change in recent times

revisiting the decay of missing ordinal patterns in long term correlated time series abstract we revisit the decay of missing ordinal patterns in long term correlated time series more precisely a stretched exponential model is proposed to describe more appropriately how the number of missing ordinal patterns decreases as a function of the time series length in the case of correlated stochastic data numerical analysis and experimental applications confirm that this generalized model allows a more accurate characterization of the underlying dynamics and a reliable quantification of the long range temporal correlations

weighted permutation entropy based on different symbolic approaches for financial time series abstract in this paper we introduce weighted permutation entropy wpe and three different symbolic approaches to investigate the complexities of stock time series containing amplitude coded information and explore the influence of using different symbolic approaches on obtained wpe results we employ wpe based on symbolic approaches to the us and chinese stock markets and make a comparison between the results of us and chinese stock markets three symbolic approaches are able to help the complexity containing in the stock time series by wpe method drop whatever the embedding dimension is the similarity between these stock markets can be detected by the wpe based on binary coding method while the difference between them can be revealed by the wpe based on method max min method the combinations of the symbolic approaches method and max min method and wpe method are capable of reflecting the multiscale structure of complexity by different time delay and analyze the differences between complexities of stock time series in more detail and more accurately furthermore the correlations between stock markets in the same region and the similarities hidden in the s p500 and dji shangzheng and shencheng are uncovered by the comparison of the wpe based on binary coding method of six stock markets

a theory of state covariance assignment for discrete systems in many regulation control problems it is desired to design the controller so that various system states have acceptable root mean squared values this is a multiple objective problem one way to satisfy these objectives is to assign a specified state covariance to the system this paper introduces and solves the following problem 1 characterize the entire set of state covariances which may be assigned to a linear discrete time system by state feedback and 2 find the set of all state feedback gains which will assign an admissible state covariance to the system extensions are also presented for state estimate feedback

extended trial equation method to generalized nonlinear partial differential equations in this article we give the extended trial equation method for solving nonlinear partial differential equations with higher order nonlinearity by use of this method the exact traveling wave solutions including soliton solution singular soliton solutions rational function solution and elliptic integral function solution to one dimensional general improved kdv gikdv equation and r m n equation are obtained also a more general trial equation method is proposed

modified permutation entropy analysis of heartbeat dynamics heart rate variability hrv contains important information about the modulation of the cardiovascular system various methods of nonlinear dynamics e g estimating lyapunov exponents and complexity measures e g correlation dimension or entropies have been applied to hrv analysis permutation entropy which was proposed recently has been widely used in many fields due to its conceptual and computational simplicity it maps a time series onto a symbolic sequence of permutation ranks the original permutation entropy assumes the time series under study has a continuous distribution thus equal values are rare and can be ignored by ranking them according to their order of emergence or broken by adding small random perturbations to ensure every symbol in a sequence is different however when the observed time series is digitized with lower resolution leading to a greater number of equal values or the equalities represent certain characteristic sequential patterns of the system it may not be rational to simply ignore or break them in the present paper a modified permutation entropy is proposed that by mapping the equal value onto the same symbol rank allows for a more accurate characterization of system states the application of the modified permutation entropy to the analysis of hrv is investigated using clinically collected data results show that modified permutation entropy can greatly improve the ability to distinguish the hrv signals under different physiological and pathological conditions it can characterize the complexity of hrv more effectively than the original permutation entropy

characterization of autoregressive processes using entropic quantifiers abstract the aim of the contribution is to introduce a novel information plane the causal amplitude informational plane as previous works seems to indicate bandt and pompe methodology for estimating entropy does not allow to distinguish between probability distributions which could be fundamental for simulation or for probability analysis purposes once a time series is identified as stochastic by the causal complexity entropy informational plane the novel causal amplitude gives a deeper understanding of the time series quantifying both the autocorrelation strength and the probability distribution of the data extracted from the generating processes two examples are presented one from climate change model and the other from financial markets

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

solution of the epidemic model by adomian decomposition method in this article the problem of the spread of a non fatal disease in a population which is assumed to have constant size over the period of the epidemic is considered mathematical modeling of the problem leads to a system of non linear ordinary differential equations adomian decomposition method is employed to solve this system of non linear ordinary differential equations the problem of convergence has been addressed

generalized statistical complexity measures geometrical and analytical properties abstract we discuss bounds on the values adopted by the generalized statistical complexity measures m t martin et al phys lett a 311 2003 126 p w lamberti et al physica a 334 2004 119 introduced by lopez ruiz et al phys lett a 209 1995 321 and shiner et al phys rev e 59 1999 1459 several new theorems are proved and illustrated with reference to the celebrated logistic map

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

signatures of chaotic and stochastic dynamics uncovered with recurrence networks an old and important problem in the field of nonlinear time series analysis entails the distinction between chaotic and stochastic dynamics recently recurrence networks have been proposed as a t

the theory of individual based discrete time processes a general theory is developed to study individual based models which are discrete in time we begin by constructing a markov chain model that converges to a one dimensional map in the infinite population limit stochastic fluctuations are hence intrinsic to the system and can induce qualitative changes to the dynamics predicted from the deterministic map from the chapman kolmogorov equation for the discrete time markov process we derive the analogues of the fokker planck equation and the langevin equation which are routinely employed for continuous time processes in particular a stochastic difference equation is derived which accurately reproduces the results found from the markov chain model stochastic corrections to the deterministic map can be quantified by linearizing the fluctuations around the attractor of the map the proposed scheme is tested on stochastic models which have the logistic and ricker maps as their deterministic limits

approximate analytical solutions of general lotka volterra equations on presente une solution analytique approchee des equations de lotka volterra generales en utilisant des transformations de laplace et une methode de perturbation

efficiency characterization of a large neuronal network a causal information approach abstract when inhibitory neurons constitute about 40 of neurons they could have an important antinociceptive role as they would easily regulate the level of activity of other neurons we consider a simple network of cortical spiking neurons with axonal conduction delays and spike timing dependent plasticity representative of a cortical column or hypercolumn with a large proportion of inhibitory neurons each neuron fires following a hodgkin huxley like dynamics and it is interconnected randomly to other neurons the network dynamics is investigated estimating bandt and pompe probability distribution function associated to the interspike intervals and taking different degrees of interconnectivity across neurons more specifically we take into account the fine temporal structures of the complex neuronal signals not just by using the probability distributions associated to the interspike intervals but instead considering much more subtle measures accounting for their causal information the shannon permutation entropy fisher permutation information and permutation statistical complexity this allows us to investigate how the information of the system might saturate to a finite value as the degree of interconnectivity across neurons grows inferring the emergent dynamical properties of the system

contrasting stochasticity with chaos in a permutation lempel ziv complexity shannon entropy plane abstract this paper aims at introducing the lempel ziv permutation complexity vs permutation entropy plane ec plane as a tool to analyze time series with diverse dynamical nature these two quantities use the bandt and pompe representation to quantify a continuous state time series the main strength of this approach lies in the fact that this plane combines two different perspectives to study a signal one being purely statistic the permutation entropy and the other being algorithmic the lempel ziv complexity the results allow us to conclude that the ec plane constitutes an appropriate framework for i characterizing non linear chaotic maps ii distinguishing deterministic from stochastic processes and iii to discriminate between fractional brownian motion fractional gaussian noise and k noise

unraveling the decay of the number of unobserved ordinal patterns in noisy chaotic dynamics in this paper we introduce a model to describe the decay of the number of unobserved ordinal patterns as a function of the time series length in noisy chaotic dynamics more precisely we show that a stretched exponential model fits the decay of the number of unobserved ordinal patterns for both discrete and continuous chaotic systems contaminated with observational noise independently of the noise level and the sampling time numerical simulations obtained from the logistic map and the x coordinate of the lorenz system both operating in a totally chaotic dynamics were used as test beds in addition we contrast our results with those obtained from pure stochastic dynamics the fitting parameters namely the stretching exponent and the characteristic decay rate are used to distinguish whether the dynamical nature of the data sequence is stochastic or chaotic finally the analysis of experimental records associated with the hyperchaotic pulsations of an optoelectronic oscillator allows us to illustrate the applicability of the proposed approach in a practical context

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