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Title: Multifractal Analysis of Closed Contour Fluctuations Speaker: Paulo Duarte-Neto Affiliation: Departamento de Estatística e Informática - UFRPE Abstract In recent decades multifractal analysis has been successfully applied to characterize the complex temporal and spatial organization of diverse natural phenomena such as heartbeat dynamics, the dendritic shape of neurons, retinal vessels, rock fractures, etc. However, common methods of multifractal analysis do not seem appropriate for analyzing quasi-onedimensional structures, with complexity far from filling two dimensional space, but more complex than a line, such as the contours of objects. For this reason, the characterization of multifractal properties of closed contours has up to date remained rather elusive. A new, robust, technique, “The Traveling Observer” Multifractal Detrended Fluctuation Analysis is presented, which bridges the gap between the methods used for geometrical fractals and those used for temporal series, reducing the limitations present in existing multifractal techniques to analyze contours. The procedure first maps the contour onto a “time series” of distances from the central path (defined by harmonic term zero), as observed by a virtual observer traveling along this path at constant angular speed. The fluctuations from the central path of the contour perimeter are registered as a “time series”, and the MF-DFA is then implemented to quantify the “temporal” correlations of this series. The relevance of studying the fractal properties of the contour fluctuations is demonstrated through several applications to natural and simulated data, highlighting the advantages of this new approach.