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Sep 20, 2013
09/13

by
M. Virgilio; P. Grigolini

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The aim of this paper is to shed light on the analysis of non-stationary time series by means of the method of diffusion entropy. For this purpose, we first study the case when infinitely many time series, as different realizations of the same dynamic process, are available, so as to adopt the Gibbs ensemble perspective. We solve the problem of establishing under which conditions scaling emerges from within this perspective. Then, we study the more challenging problem of creating a diffusion...

Source: http://arxiv.org/abs/cond-mat/0204223v2

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Sep 23, 2013
09/13

by
M. Annunziato; P. Grigolini

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We study the influence of a dissipation process on diffusion dynamics triggered by slow fluctuations. We study both strong- and weak-friction regime. When the latter regime applies, the system is attracted by the basin of either Gauss or Levy statistics according to whether the fluctuation correlation function is integrable or not. We analyze with a numerical calculation the border between the two basins of attraction.

Source: http://arxiv.org/abs/cond-mat/9909456v1

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Sep 23, 2013
09/13

by
A. Rocco; P. Grigolini

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We revisit the Markov approximation necessary to derive ordinary Brownian motion from a model widely adopted in literature for this specific purpose. We show that this leads to internal inconsistencies, thereby implying that further search for a more satisfactory model is required.

Source: http://arxiv.org/abs/quant-ph/9909051v1

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Sep 22, 2013
09/13

by
M. Ignaccolo; P. Grigolini; G. Gross

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We address the problem of enhancing the sensitivity of biosensors to the influence of toxicants, with an entropy method of analysis, denoted as CASSANDRA, recently invented for the specific purpose of studying non-stationary time series. We study the specific case where the toxicant is tetrodotoxin. This is a very poisonous substance that yields an abrupt drop of the rate of spike production at t approximatively 170 minutes when the concentration of toxicant is 4 nanomoles. The CASSANDRA...

Source: http://arxiv.org/abs/cond-mat/0307451v2

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Sep 23, 2013
09/13

by
M. Annunziato; P. Grigolini; J. Riccardi

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We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied numerically and theoretically, with a good agreement between theory and numerical treatment. As a result of this assumption the equilibrium distribution departs from the ordinary canonical distribution. The distribution tails are truncated, the distribution border...

Source: http://arxiv.org/abs/cond-mat/9908445v1

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Sep 19, 2013
09/13

by
S. Montangero; L. Fronzoni; P. Grigolini

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We address the problem of applying the Kolmogorov-Sinai method of entropic analysis, expressed in a generalized non-extensive form, to the dynamics of the logistic map at the chaotic threshold, which is known to be characterized by a power law rather than exponential sensitivity to initial conditions. The computer treatment is made difficult, if not impossible, by the multifractal nature of the natural invariant distribution: Thus the statistical average is carried out on the power index. The...

Source: http://arxiv.org/abs/cond-mat/9911412v1

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Sep 19, 2013
09/13

by
R. Cakir; P. Grigolini; M. Ignaccolo

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We use the model of ballistic deposition as a simple way to establish cooperation among the columns of a growing surface, \emph{the single individual of the same society}. We show that cooperation generates memory properties and at same time non-Poisson renewal events. The variable generating memory can be regarded as the velocity of a particle driven by a bath with the same time scale, and the variable generating renewal processes is the corresponding diffusional coordinate.

Source: http://arxiv.org/abs/cond-mat/0610245v1

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Sep 20, 2013
09/13

by
R Mannella; P Grigolini; BJ West

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Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is applicable, we establish a connection between diffusion (either standard or anomalous) and the dynamical indicator known as the Hurst coefficient. We argue on the basis of numerical simulations that although we have been able to prove scaling only for...

Source: http://arxiv.org/abs/chao-dyn/9308004v1

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Sep 19, 2013
09/13

by
M. Annunziato; P. Grigolini; B. J. West

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We address the problem of the dynamical foundation of non-canonical equilibrium. We consider, as a source of divergence from ordinary statistical mechanics, the breakdown of the condition of time scale separation between microscopic and macroscopic dynamics. We show that this breakdown has the effect of producing a significant deviation from the canonical prescription. We also show that, while the canonical equilibrium can be reached with no apparent dependence on dynamics, the specific form of...

Source: http://arxiv.org/abs/cond-mat/0010363v1

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Sep 18, 2013
09/13

by
P. Grigolini; A. Rocco; B. J. West

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We generalize the method of Van Hove so as to deal with the case of non-ordinary statistical mechanics, that being phenomena with no time-scale separation. We show that in the case of ordinary statistical mechanics, even if the adoption of the Van Hove method imposes randomness upon Hamiltonian dynamics, the resulting statistical process is described using normal calculus techniques. On the other hand, in the case where there is no time-scale separation, this generalized version of Van Hove's...

Source: http://arxiv.org/abs/cond-mat/9809075v3

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Sep 22, 2013
09/13

by
M. Ignaccolo; P. Grigolini; B. J. West

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We introduce a new method for detecting scaling in time series. The method uses the properties of the probability flux for stochastic self-affine processes and is called the probability flux analysis (PFA). The advantages of this method are: 1) it is independent of the finiteness of the moments of the self-affine process; 2) it does not require a binning procedure for numerical evaluation of the the probability density function. These properties make the method particularly efficient for heavy...

Source: http://arxiv.org/abs/1004.0372v1

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Sep 21, 2013
09/13

by
R. Failla; P. Grigolini; M. Ignaccolo; A. Schwettmann

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We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y(t)= h(t)- < h(t)>, which is depicted as being subordinated to a standard fluctuation-dissipation process with friction gamma. We argue that the main properties of Kardar-Parisi-Zhang theory, in one dimension, are derived by identifying the distribution of return times to y(0) = 0, which is a truncated inverse power law, with the...

Source: http://arxiv.org/abs/nlin/0407010v1

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Sep 22, 2013
09/13

by
N. Scafetta; P. Grigolini; P. Hamilton; B. J. West

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A complex process is often a balance between non-stationary and stationary components. We show how the non-extensive Tsallis q-entropy indicator may be interpreted as a measure of non-stationarity in time series. This is done by applying the non-extensive entropy formalism to the Diffusion Entropy Analysis (DEA). We apply the analysis to the study of the teen birth phenomenon. We find that the unmarried teen births are strongly influenced by social processes with memory. This memory is related...

Source: http://arxiv.org/abs/cond-mat/0205524v1

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Sep 21, 2013
09/13

by
P. Allegrini; P. Grigolini; L. Palatella; B. J. West

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We study a two-state symmetric noise, with a given waiting time distribution $\psi (\tau)$, and focus our attention on the connection between the four-time and the two-time correlation functions. The transition of $\psi (\tau)$ from the exponential to the non-exponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties, and establish the...

Source: http://arxiv.org/abs/cond-mat/0402494v1

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Jul 20, 2013
07/13

by
P. Allegrini; P. Grigolini; P. Hamilton; L. Palatella; G. Raffaelli

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We study the long-range correlations of heartbeat fluctuations with the method of diffusion entropy. We show that this method of analysis yields a scaling parameter $\delta$ that apparently conflicts with the direct evaluation of the distribution of times of sojourn in states with a given heartbeat frequency. The strength of the memory responsible for this discrepancy is given by a parameter $\epsilon^{2}$, which is derived from real data. The distribution of patients in the ($\delta$,...

Source: http://arxiv.org/abs/cond-mat/0107597v1

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Sep 21, 2013
09/13

by
M. Ignaccolo; M. Latka; W. Jernajczyk; P. Grigolini; B. J. West

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EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a phenomenological Langevin equation interpreted within a neural network context. Detrended fluctuation analysis of the EEG data is compared with diffusion entropy analysis and is found to suppress certain important properties of the EEG time series.

Source: http://arxiv.org/abs/0902.1113v1

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Jul 20, 2013
07/13

by
P. Allegrini; P. Grigolini; L. Palatella; A. Rosa; B. J. West

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We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To accomodate the equilibrium condition behind the stationary correlation function, we study the time evolution of the anti-symmetric component, while keeping the symmetric component at equilibrium. For any realistic form of...

Source: http://arxiv.org/abs/cond-mat/0406120v1

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Sep 20, 2013
09/13

by
M. Ignaccolo; P. Allegrini; P. Grigolini; P. Hamilton; B. J. West

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Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of analysis resting on the stationary assumption can produce a wrong information on the scaling, and so on the complexity of the process under study. Herein, we test and compare two techniques for removing the non-stationary influences from computer generated time...

Source: http://arxiv.org/abs/physics/0301057v1

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Sep 23, 2013
09/13

by
M. Ignaccolo; M. Latka; W. Jernajczyk; P. Grigolini; B. J. West

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EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a phenomenological Langevin equation interpreted within a neural network context.

Source: http://arxiv.org/abs/0903.1078v1

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Sep 20, 2013
09/13

by
M. Ignaccolo; P. Allegrini; P. Grigolini; P. Hamilton; B. J. West

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This paper is devoted to the problem of statistical mechanics raised by the analysis of an issue of sociological interest: the teen birth phenomenon. It is expected that these data are characterized by correlated fluctuations, reflecting the cooperative properties of the process. However, the assessment of the anomalous scaling generated by these correlations is made difficult, and ambiguous as well, by the non-stationary nature of the data that show a clear dependence on seasonal periodicity...

Source: http://arxiv.org/abs/physics/0301058v1

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Sep 22, 2013
09/13

by
M. Ignaccolo; A. Schwettmann; R. Failla; M. C. Storrie-Lombardi; P. Grigolini

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We apply the method of Diffusion Entropy (DE) to the study of stromatolites by means of a two-dimensional procedure that makes it possible for us to compare the DE analysis to the results of a compression method. As done with the compression method, we analyze two pairs of samples, one biotic and the other a-biotic. Each pair consists of a target, the putative stromatolite sample, and of its surrounding matrix. We use two different procedures, referring to single colors and to a color...

Source: http://arxiv.org/abs/cond-mat/0307485v1

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Sep 22, 2013
09/13

by
P. Allegrini; P. Grigolini; P. Hamilton; L. Palatella; G. Raffaelli; M. Virgilio

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We address the problem of detecting non-stationary effects in time series (in particular fractal time series) by means of the Diffusion Entropy Method (DEM). This means that the experimental sequence under study, of size $N$, is explored with a window of size $L < < N$. The DEM makes a wise use of the statistical information available and, consequently, in spite of the modest size of the window used, does succeed in revealing local statistical properties, and it shows how they change upon...

Source: http://arxiv.org/abs/cond-mat/0111246v1

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Sep 22, 2013
09/13

by
P. Allegrini; J. Bellazzini; G. Bramanti; M. Ignaccolo; P. Grigolini; J. Yang

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We show that the dynamic approach to L\'{e}vy statistics is characterized by aging and multifractality, induced by an ultra-slow transition to anomalous scaling. We argue that these aspects make it a protoptype of complex systems.

Source: http://arxiv.org/abs/cond-mat/0111517v1

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Sep 18, 2013
09/13

by
L. Palatella; P. Allegrini; P. Grigolini; V. Latora; M. S. Mega; A. Rapisarda; S. Vinciguerra

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With the help of the Diffusion Entropy technique we show the non-Poisson statistics of the distances between consecutive Omori's swarms of earthquakes. We give an analytical proof of the numerical results of an earlier paper [cond-mat/0212529, Mega et al., Phys. Rev. Lett. 90 (2003) 188501]

Source: http://arxiv.org/abs/cond-mat/0401382v1

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Sep 19, 2013
09/13

by
P. Allegrini; R. Balocchi; S. Chillemi; P. Grigolini; P. Hamilton; R. Maestri; L. Palatella; G. Raffaelli

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Using a method of entropic analysis of time series we establish the correlation between heartbeat long-range memory and mortality risk in patients with congestive heart failure.

Source: http://arxiv.org/abs/cond-mat/0209038v1

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Sep 18, 2013
09/13

by
P. Allegrini; V. Benci; P. Grigolini; P. Hamilton; M. Ignaccolo; G. Menconi; L. Palatella; G. Raffaelli; N. Scafetta; M. Virgilio; J. Jang

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The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here we present a plan of action based on the joint action...

Source: http://arxiv.org/abs/cond-mat/0202123v1