Angelo Plastino

Early universe test of nonextensive statistics

Within an early Universe scenario, nonextensive thermostatistics is investigated on the basis of data concerning primordial helium abundance. We obtain first order corrections to the energy densities and weak interaction rates, and use them to compute the deviation in the primordial helium abundance. After comparing with observational results, we get

Central limit theorem and deformed exponentials

|q\ensuremath{-}1|l2.08\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}

Causality and the entropy–complexity plane: Robustness and missing ordinal patterns

as a bound for the nonextensive parameter.

Cortical dynamics and subcortical signatures of motor-language coupling in Parkinson’s disease

The central limit theorem (CLT) can be ranked among the most important ones in probability theory and statistics and plays an essential role in several basic and applied disciplines, notably in statistical thermodynamics. We show that there exists a natural extension of the CLT from exponentials to so-called deformed exponentials (also denoted as q-Gaussians). Our proposal applies exactly in the usual conditions in which the classical CLT is used.

Distances in Probability Space and the Statistical Complexity Setup

We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative weights in a given time series. Two different tools have been advanced in the literature to such effect, namely, (i) the “causal” entropy–complexity plane [O.A. Rosso, H.A. Larrondo, M.T. Martin, A. Plastino, M.A. Fuentes, Distinguishing noise from chaos, Phys. Rev. Lett. 99 (2007) 154102] and (ii) the estimation of the decay rate of missing ordinal patterns [J.M. Amigo, S. Zambrano, M.A.F. Sanjuan, True and false forbidden patterns in deterministic and random dynamics, Europhys. Lett. 79 (2007) 50001; L.C. Carpi, P.M. Saco, O.A. Rosso, Missing ordinal patterns in correlated noises. Physica A 389 (2010) 2020–2029]. In this work we extend the use of these techniques to address the analysis of deterministic finite time series contaminated with additive noises of different degree of correlation. The chaotic series studied here was via the logistic map (r=4) to which we added correlated noise (colored noise with f−k Power Spectrum, 0≤k≤2) of varying amplitudes. In such a fashion important insights pertaining to the deterministic component of the original time series can be gained. We find that in the entropy–complexity plane this goal can be achieved without additional computations.

On extracting probability distribution information from time series

Impairments of action language have been documented in early stage Parkinson’s disease (EPD). The action-sentence compatibility effect (ACE) paradigm has revealed that EPD involves deficits to integrate action-verb processing and ongoing motor actions. Recent studies suggest that an abolished ACE in EPD reflects a cortico-subcortical disruption, and recent neurocognitive models highlight the role of the basal ganglia (BG) in motor-language coupling. Building on such breakthroughs, we report the first exploration of convergent cortical and subcortical signatures of ACE in EPD patients and matched controls. Specifically, we combined cortical recordings of the motor potential, functional connectivity measures, and structural analysis of the BG through voxel-based morphometry. Relative to controls, EPD patients exhibited an impaired ACE, a reduced motor potential, and aberrant frontotemporal connectivity. Furthermore, motor potential abnormalities during the ACE task were predicted by overall BG volume and atrophy. These results corroborate that motor-language coupling is mainly subserved by a cortico-subcortical network including the BG as a key hub. They also evince that action-verb processing may constitute a neurocognitive marker of EPD. Our findings suggest that research on the relationship between language and motor domains is crucial to develop models of motor cognition as well as diagnostic and intervention strategies.

Information and Thermal Physics

Statistical complexity measures (SCM) are the composition of two ingredients: (i) entropies and (ii) distances in probability-space. In consequence, SCMs provide a simultaneous quantification of the randomness and the correlational structures present in the system under study. We address in this review important topics underlying the SCM structure, viz., (a) a good choice of probability metric space and (b) how to assess the best distance-choice, which in this context is called a “disequilibrium” and is denoted with the letter Q. Q, indeed the crucial SCM ingredient, is cast in terms of an associated distance D. Since out input data consists of time-series, we also discuss the best way of extracting from the time series a probability distribution P. As an illustration, we show just how these issues affect the description of the classical limit of quantum mechanics.

A Maximum Entropy Approach for Predicting Epileptic Tonic-Clonic Seizure

Time-series (TS) are employed in a variety of academic disciplines. In this paper we focus on extracting probability density functions (PDFs) from TS to gain an insight into the underlying dynamic processes. On discussing this “extraction” problem, we consider two popular approaches that we identify as histograms and Bandt–Pompe. We use an information-theoretic method to objectively compare the information content of the concomitant PDFs.

Interplay of information quantifiers and the modified Jaynes-Cummings model

Thermal physics constitutes a fundamental part of our understanding of nature. In this chapter we will be concerned with the connection