Complementarity in classical dynamical systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.Comment: 18 pages, no figure

Detecting event-related recurrences by symbolic analysis: Applications to human language processing

Quasistationarity is ubiquitous in complex dynamical systems. In brain dynamics there is ample evidence that event-related potentials reflect such quasistationary states. In order to detect them from time series, several segmentation techniques have been proposed. In this study we elaborate a recent approach for detecting quasistationary states as recurrence domains by means of recurrence analysis and subsequent symbolisation methods. As a result, recurrence domains are obtained as partition cells that can be further aligned and unified for different realisations. We address two pertinent problems of contemporary recurrence analysis and present possible solutions for them.Comment: 24 pages, 6 figures. Draft version to appear in Proc Royal Soc

Permutation entropy and its main biomedical and econophysics applications: a review

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.Facultad de Ingenierí

Estructura jerárquica y dinámica en los mercados cambiarios latinoamericanos

En este trabajo estudiamos la estructura jerárquica y la dinámica de las relaciones existentes entre los tipos de cambio reales en los principales mercados latinoamericanos. Con este fin, introducimos una metodología que combina el análisis de series temporales simbólicas (STSA) de Daw et al. (2003) con el algoritmo de agrupación de asociación al vecino más cercano (nearest neighbor single linkage clustering algorithm, NSLCA; véase Mantegna y Stanley, 2000). A partir de la simbolización de los datos podemos obtener distancias métricas entre series temporales que pueden ser usadas para construir un árbol de expansión mínima (MST), y distancias ultramétricas que permiten construir un árbol jerárquico (HT). Estos árboles permiten detectar conexiones dinámicas y organización jerárquica de los mercados cambiarios de Latinoamerica a partir de la construcción de distintos grupos de acuerdo a su proximidad.</p

Changes in EEG Permutation Entropy in the evening and in the transition from wake to sleep

Peer reviewe