Approaching complex networks for time series analysis

Abstract

Time series analysis is an important topic in physics, as well as a powerful method to characterize data in Biology, Medicine and Economics, and to understand their underlying dynamical origin. In the last decades, the topic has received input from different disciplines such as nonlinear dynamics, Statistical Physics, Computer Science and, as a result, new approaches have emerged. Among these approaches, the so called visibility algorithms have been shown to be simple, computationally efficient and analytically tractable methods, able to extract nontrivial information about the original signal, classify different dynamical origins and provide a clean description of low dimensional dynamics. As a consequence, this particular methodology has been used in different domains including earth and planetary sciences, finance or biomedical fields. This project will be focused on (but not limited to) the analysis of time series that come from three disciplines, using the Visibility Graph (VG). First; using epidemiological data from vector borne diseases (Malaria, Dengue, Chikungunya, Zika) from target countries of South America (Colombia and Venezuela, among others) we will study the temporal and stationary features of these diseases. In general, the objective is to use weekly reports data to understand the dynamical attributes of vector-borne diseases, as well as to propose methods with a feasible implementation for forecasting. Second; making use of the recently proposed extension of VGs to analyze multidimensional time series (Multiplex VG) we will transform the time series of magnitude an depth of seismic activity for state-level data from Venezuela (and other countries if available) into networks and multiplex networks. The data corresponds to the seismic activity (magnitude of 2.5 MW and stronger) registered by the Fundacion Venezolana de Investigaciones Sismologicas (Funvisis) for the time interval 2008 to 2016. It is of interest compare the dynamical similarities/differences between these data and other studies already reported using VGs and the new intuition introduced by the multilayer formulation. Third; it is been noticed that in the past years, many countries have shown a strong polarization when deciding which party they will vote for in presidential elections; examples of these countries are Venezuela, Colombia, Ecuador, Spain and most recently USA, among others. Generally speaking, this polarization can be divided into "socialist" and "capitalist" parties. One aspect that characterizes these two diametrically ideologies is their speech. The objective of this study is to develop a tool to analyze quantitatively speeches and/or written text, using statistical and complex network approaches (VG). In particular, we are interested in comparing quantitatively speeches given by two extremist parties in Latin America. We are using as base examples the speeches given by former Venezuelan president Hugo Chavez Frias and former Colombian president Alvaro Uribe Velez. In conclusion; we propose to apply this methodology to study three different contexts. The general objective is to evaluate the applicability of this methodology and to propose (if possible) an appropriate formulation to be used for forecasting where suitable. (AU)