This thesis analyzes the complexity of the urban system, being described with multiple variables that represent the environmental, economic, and social characters of the city. The portrayal of the urban diversity and its relationship with a better response of the city to disturbances, hence to its sustainability, is the main motivation of the study. Certainly, this thesis aims to provide theoretical knowledge through the application of statistical and computational methodologies that are developed progressively in its chapters. Beginning with the introduction, which draws the city as an abstract urban system and reviews the concepts and measures of diversity within the theoretical frameworks of sustainability, urban ecology, and complex systems theory. Afterward, the city of Barcelona is introduced as the case study: it is constituted by a set of districts and represented by an information system that contains temporal measurements of multiple environmental, economic, and social variables. A first approach to the sustainability of the city is made with the entropy of information as a measure of the urban system's diversity. But the fundamental contribution of the thesis focuses on the application of loratory Multivariate Analysis (EMA) to the urban system: Principal Component Analysis (PCA), Multiple Factorial Analysis (MFA), and Hierarchical Cluster Analysis (HCA). From this EMA approach, diversity is analyzed by identifying the similarity -or dissimilarity- between the different parts that make up the urban system. Some other techniques based on computer science and physics are proposed to evaluate the temporal transformation of the urban system, understood as a three-dimensional data cloud that gradually deforms. Differentiated characters and distinctive functions of districts are identifiable in the EMA application to the case study. Moreover, the temporal dependency of the dataset reveals information about the district's differentiation or homogenization trends. Finally, the conclusions of the most relevant results are presented and some future lines of research are proposed.
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