Characterization of Vehicle Behavior with Information Theory

This work proposes the use of Information Theory for the characterization of vehicles behavior through their velocities. Three public data sets were used: i.Mobile Century data set collected on Highway I-880, near Union City, California; ii.Borl\"ange GPS data set collected in the Swedish city of Borl\"ange; and iii.Beijing taxicabs data set collected in Beijing, China, where each vehicle speed is stored as a time series. The Bandt-Pompe methodology combined with the Complexity-Entropy plane were used to identify different regimes and behaviors. The global velocity is compatible with a correlated noise with f^{-k} Power Spectrum with k >= 0. With this we identify traffic behaviors as, for instance, random velocities (k aprox. 0) when there is congestion, and more correlated velocities (k aprox. 3) in the presence of free traffic flow

Bandt-Pompe symbolization dynamics for time series with tied values: A data-driven approach

In 2002, Bandt and Pompe [Phys. Rev. Lett. 88, 174102 (2002)] introduced a successfully symbolic encoding scheme based on the ordinal relation between the amplitude of neighboring values of a given data sequence, from which the permutation entropy can be evaluated. Equalities in the analyzed sequence, for example, repeated equal values, deserve special attention and treatment as was shown recently by Zunino and co-workers [Phys. Lett. A 381, 1883 (2017)]. A significant number of equal values can give rise to false conclusions regarding the underlying temporal structures in practical contexts. In the present contribution, we review the different existing methodologies for treating time series with tied values by classifying them according to their different strategies. In addition, a novel data-driven imputation is presented that proves to outperform the existing methodologies and avoid the false conclusions pointed by Zunino and co-workers.Fil: Traversaro Varela, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Lanús; ArgentinaFil: Redelico, Francisco Oscar. Hospital Italiano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; ArgentinaFil: Risk, Marcelo. Hospital Italiano; Argentina. Instituto Tecnológico de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Frery, Alejandro César. Universidade Federal de Alagoas; BrasilFil: Rosso, Osvaldo Aníbal. Hospital Italiano; Argentina. Universidade Federal de Alagoas; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Los Andes; Chil