Osvaldo A. Rosso

Bio: Osvaldo A. Rosso is an academic researcher from Federal University of Alagoas. The author has contributed to research in topics: Probability distribution & Entropy (information theory). The author has an hindex of 49, co-authored 241 publications receiving 8770 citations. Previous affiliations of Osvaldo A. Rosso include University of Los Andes & Universidade Federal de Minas Gerais.

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

Abstract: Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.

Distinguishing noise from chaos.

Abstract: Chaotic systems share with stochastic processes several properties that make them almost undistinguishable. In this communication we introduce a representation space, to be called the complexity-entropy causality plane. Its horizontal and vertical axis are suitable functionals of the pertinent probability distribution, namely, the entropy of the system and an appropriate statistical complexity measure, respectively. These two functionals are evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the system. Several well-known model-generated time series, usually regarded as being of either stochastic or chaotic nature, are analyzed so as to illustrate the approach. The main achievement of this communication is the possibility of clearly distinguishing between them in our representation space, something that is rather difficult otherwise.

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.

Intensive entropic non-triviality measure

Abstract: We discuss a way of characterizing probability distributions, complementing that provided by the celebrated notion of information measure, with reference to a measure of complexity that we call a “nontriviality measure”. Our starting point is the “LMC” measure of complexity advanced by Lopez-Ruiz et al. (Phys. Lett. A 209 (1995) 321) and its analysis by Anteneodo and Plastino (Phys. Lett. A 223 (1997) 348). An improvement of some of their troublesome characteristics is thereby achieved. Basically, we replace the Euclidean distance to equilibrium by the Jensen–Shannon divergence. The resulting measure turns out to be (i) an intensive quantity and (ii) allows one to distinguish between different degrees of periodicity. We apply the “cured” measure to the logistic map so as to clearly exhibit its advantages.

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Proceedings of the National Academy of Sciences

Abstract: where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Clinical Diagnosis of Alzheimer's Disease

Abstract: There are a number of ways in which a clinical diagnosis of dementia of the Alzheimer type can be made – the application of clinical criteria is the commonest but ancillary techniques such as neuroima