Features combination for art authentication studies: brushstroke and materials analysis of Amadeo de Souza-Cardoso

This work presents a tool to support authentication studies of paintings attributed to the modernist Portuguese artist Amadeo de Souza-Cardoso (1887-1918). The strategy adopted was to quantify and combine the information extracted from the analysis of the brushstroke with information on the pigments present in the paintings. The brushstroke analysis was performed combining Gabor filter and Scale Invariant Feature Transform. Hyperspectral imaging and elemental analysis were used to compare the materials in the painting with those present in a database of oil paint tubes used by the artist. The outputs of the tool are a quantitative indicator for authenticity, and a mapping image that indicates the areas where materials not coherent with Amadeo's palette were detected, if any. This output is a simple and effective way of assessing the results of the system. The method was tested in twelve paintings obtaining promising results.

Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.