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) Borlange GPS data set collected in the Swedish city of Borlange; 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 ≃ 0) when there is congestion, and more correlated velocities (k ≃ 3) in the presence of free traffic flow. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015
Many works employed the Complexity-Entropy plane for the characterization of time series in a diversity of applications: stock market evolution @cite_10 , brain behavior @cite_10 , climate change @cite_16 , and vehicles velocities variation @cite_18 .
@cite_18 @cite_16 @cite_10
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In this paper, the complexity-entropy causality plane approach is applied to analyze traffic data. The R S analysis and detrended fluctuation analysis (DFA) methods are also used to compare with this approach. Moreover, based on the concept of entropy, we propose to use permutation to calculate the probability distribution of the time series when applying the representation plane. The empirical results indicate that traffic dynamics exhibit different levels of traffic congestion and demonstrate that this statistical method can give a more refined classification of traffic states than the R S analysis and DFA. We study the entropy landscape of solutions for the bicoloring problem in random graphs, a representative difficult constraint satisfaction problem. Our goal is to classify which types of clusters of solutions are addressed by different algorithms. In the first part of the study we use the cavity method to obtain the number of clusters with a given internal entropy and determine the phase diagram of the problem--e.g., dynamical, rigidity, and satisfiability-unsatisfiability (SAT-UNSAT) transitions. In the second part of the paper we analyze different algorithms and locate their behavior in the entropy landscape of the problem. For instance, we show that a smoothed version of a decimation strategy based on belief propagation is able to find solutions belonging to subdominant clusters even beyond the so-called rigidity transition where the thermodynamically relevant clusters become frozen. These nonequilibrium solutions belong to the most probable unfrozen clusters. In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous environment consists of a sequence of macroscopic time intervals, in each of which the law of reproduction remains constant. We prove that the asymptotic behaviour of the maximal displacement in this process consists of a first ballistic order, given by the solution of an optimization problem under constraints, a negative logarithmic correction, plus stochastically bounded fluctuations. We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence homology to detect and quantify topological patterns that appear in multidimensional time series. Using a sliding window, we extract time-dependent point cloud data sets, to which we associate a topological space. We detect transient loops that appear in this space, and we measure their persistence. This is encoded in real-valued functions referred to as a 'persistence landscapes'. We quantify the temporal changes in persistence landscapes via their @math -norms. We test this procedure on multidimensional time series generated by various non-linear and non-equilibrium models. We find that, in the vicinity of financial meltdowns, the @math -norms exhibit strong growth prior to the primary peak, which ascends during a crash. Remarkably, the average spectral density at low frequencies of the time series of @math -norms of the persistence landscapes demonstrates a strong rising trend for 250 trading days prior to either dotcom crash on 03 10 2000, or to the Lehman bankruptcy on 09 15 2008. Our study suggests that TDA provides a new type of econometric analysis, which goes beyond the standard statistical measures. The method can be used to detect early warning signals of imminent market crashes. We believe that this approach can be used beyond the analysis of financial time series presented here.