arXiv subjects

B. J. West

Publications and source records attributed to B. J. West.

13 recordsLinked to original sources

arXiv2010

Probability flux as a method for detecting scaling

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 tailed distributions in which the variance is not finite, for example, in Levy alpha-stable processes. This utility is established using a comparison with the diffusion entropy (DE) method.

physics.data-an↗

arXiv2010

The Failure of the Ergodic Assumption

The well established procedure of constructing phenomenological ensemble from a single long time series is investigated. It is determined that a time series generated by a simple Uhlenbeck-Ornstein Langevin equation is mean ergodic. However the probability ensemble average yields a variance that is different from that determined using the phenomenological ensemble (time average). We conclude that the latter ensemble is often neither stationary nor ergodic and consequently the probability ensemble averages can misrepresent the underlying dynamic process.

physics.data-an↗

arXiv2009

The Dynamics of EEG Entropy

physics.data-an↗

arXiv2009

Dynamics of EEG Entropy: beyond signal plus noise

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.

physics.data-an↗

arXiv2004

Non-Poisson processes: regression to equilibrium versus equilibrium correlation functions

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 the perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order correlation functions, an unsettled problem, which has been addressed in the past by means of approximations yielding quite different physical effects.

cond-mat.stat-mech↗

arXiv2004

Non-Poisson dichotomous noise: higher-order correlation functions and aging

We study a two-state symmetric noise, with a given waiting time distribution $ψ(τ)$, and focus our attention on the connection between the four-time and the two-time correlation functions. The transition of $ψ(τ)$ 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 condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process.

cond-mat.stat-mech↗

arXiv2003

Scaling in Non-stationary Time Series II: Teen Birth Phenomenon

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 (periodic component) and an average changing slowly in time (slow component), as well. We use the detrending techniques described in the companion paper \cite{paper1}, to safely remove all the biases and to derive the genuine scaling of the teen birth phenomenon.

physics.data-an↗

arXiv2003

Scaling in Non-stationary time series I

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 series, consisting of the superposition of a slow signal and a random fluctuation. The former is based on the method of wavelet decomposition, and the latter is a proposal of this paper, denoted by us as step detrending technique. We focus our attention on two cases, when the slow signal is a periodic function mimicking the influence of seasons, and when it is an aperiodic signal mimicking the influence of a population change (increase or decrease). For the purpose of computational simplicity the random fluctuation is taken to be uncorrelated. However, the detrending techniques here illustrated work also in the case when the random component is correlated. This expectation is fully confirmed by the sociological applications made in the companion paper. We also illustrate a new procedure to assess the existence of a genuine scaling, based on the adoption of diffusion entropy, multiscaling analysis and the direct assessment of scaling. Using artificial sequences, we show that the joint use of all these techniques yield the detection of the real scaling, and that this is independent of the technique used to detrend the original signal.

physics.data-an↗

arXiv2002

Holder exponent spectra for human gait

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

cond-mat.stat-mech↗

arXiv2002

Non-extensive diffusion entropy analysis: non-stationarity in teen birth phenomena

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 to the strength of the non-stationary component of the signal and is more intense than that in the married teen time series. By using the wavelet multiresolution analysis we attempt to give a social interpretation of this effect.

cond-mat.stat-mech↗

arXiv2001

Strange kinetics: conflict between density and trajectory description

We study a process of anomalous diffusion, based on intermittent velocity fluctuations, and we show that its scaling depends on whether we observe the motion of many independent trajectories or that of a Liouville-like equation driven density. The reason for this discrepancy seems to be that the Liouville-like equation is unable to reproduce the multi-scaling properties emerging from trajectory dynamics. We argue that this conflict between density and trajectory might help us to define the uncertain border between dynamics and thermodynamics, and that between quantum and classical physics as well.

cond-mat.stat-mech↗

arXiv2000

Canonical and non-canonical equilibrium distribution

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 non-canonical equilibrium is, in fact, determined by dynamics. We consider the special case where the thermal reservoir driving the system of interest to equilibrium is a generator of intermittent fluctuations. We assess the form of the non-canonical equilibrium reached by the system in this case. Using both theoretical and numerical arguments we demonstrate that Levy statistics are the best description of the dynamics and that the Levy distribution is the correct basin of attraction. We also show that the correct path to non-canonical equilibrium by means of strictly thermodynamic arguments has not yet been found, and that further research has to be done to establish a connection between dynamics and thermodynamics.

cond-mat.stat-mech↗

arXiv1998

Fractional Calculus as a Macroscopic Manifestation of Randomness

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 method not only imposes randomness upon the microscopic dynamics, but it also transmits randomness to the macroscopic level. As a result, the correct description of macroscopic dynamics has to be expressed in terms of the fractional calculus.

cond-mat↗