Francisco J. Esquivel

Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information

Entropy-based tools are commonly used to describe the dynamics of complex systems. In the last few decades, non-extensive statistics, based on Tsallis entropy, and multifractal techniques have shown to be useful to characterize long-range interaction and scaling behavior. In this paper, an approach based on generalized Tsallis dimensions is used for the formulation of mutual-information-related dependence coefficients in the multifractal domain. Different versions according to the normalizing factor, as well as to the inclusion of the non-extensivity correction term are considered and discussed. An application to the assessment of dimensional interaction in the structural dynamics of a seismic real series is carried out to illustrate the usefulness and comparative performance of the measures introduced.

Structural complexity in space–time seismic event data

Different approaches and tools have been adopted for the analysis and characterization of regional seismicity based on spatio–temporal series of event occurrences. Two main aspects of interest in this context concern scaling properties and dimensional interaction. This paper is focused on the statistical use of information-theoretic concepts and measures in the analysis of structural complexity of seismic distributional patterns. First, contextual significance is motivated, and preliminary elements related to informational entropy, complexity and multifractal analysis are introduced. Next, several technical and methodological extensions are proposed. Specifically, limiting behaviour of some complexity measures in connection with generalized dimensions is established, justifying a concept of multifractal complexity. Under scaling behaviour, a mutual-information-related dependence coefficient for assessing spatio–temporal interaction is defined in terms of generalized dimensions. Also, an alternative form of generalized dimensions based on Tsallis entropy convergence rates is formulated. Further, possible incorporation of effects, such as earthquake magnitude, is achieved in terms of weighted box-counting distributions. Different aspects in relation to the above elements are analyzed and illustrated using two well-known series of seismic event data of an underlying different nature, occurred in the areas of Agrón (Granada, Spain) and El Hierro (Canary Islands, Spain). Finally, various related directions for continuing research are indicated.

Statistical Complexity Analysis of Spatiotemporal Dynamics

Knowledge about structural aspects of spatiotemporal dynamics can be obtained, among other approaches, in terms of a variety of information-theoretic related measures. In this context, multifractal analysis tools such as generalized dimensions and multifractal spectrum are useful to study different aspects of scaling behaviour. Recent research has been focused on statistical complexity measures. Conceptual connections between multifractality and complexity, generally understood from intuitive interpretation, can be established based on limiting behaviour according to scale, in terms of variational properties of generalized dimension curves. Complexity and multifractality analysis, in combination with suitable transformations of the data space-time coordinates, allows to identify and assess dimensional interaction and evolutionary changes, two important issues in structural analysis of dependence and heterogeneity. These aspects are investigated and illustrated with application to seismic data.

Statistical Analysis of Attitude and Behavior of Youths on the "Other" in Granada City (Andalusia, Spain)

The recent process of immigration, mainly since 2001, represents a serious integration problem for the society of Granada (Spain) due to the great increase of immigrants in the last years. The viewpoint of the young people in the city of Granada (from 14 to 25 years) is key with regard to future trends. These youths need to learn how to share and compete for the new economic niches inside the society of Granada, a situation aggravated by the economic crisis. This scenario presents increasing levels of racism and xenophobia at the moment. In this paper, using a statistical analysis of opinion polls, we examine the influence of the human diversity, i.e. migrants living in Granada, holding jobs and studying, etc. These analyses enable us to outline the way in which youths regard for- eigners, in order to understand and characterize how the phenomenon of the immigration will be perceived over the long term within the society Granada.