Neurofuzzy network model construction using Bézier-Bernstein polynomial functions

Neurofuzzy modelling systems combine fuzzy logic with quantitative artificial neural networks via a concept of fuzzification by using a fuzzy membership function usually based on B-splines and algebraic operators for inference, etc. The paper introduces a neurofuzzy model construction algorithm using Bezier-Bernstein polynomial functions as basis functions. The new network maintains most of the properties of the B-spline expansion based neurofuzzy system, such as the non-negativity of the basis functions, and unity of support but with the additional advantages of structural parsimony and Delaunay input space partitioning, avoiding the inherent computational problems of lattice networks. This new modelling network is based on the idea that an input vector can be mapped into barycentric co-ordinates with respect to a set of predetermined knots as vertices of a polygon (a set of tiled Delaunay triangles) over the input space. The network is expressed as the Bezier-Bernstein polynomial function of barycentric co-ordinates of the input vector. An inverse de Casteljau procedure using backpropagation is developed to obtain the input vector's barycentric co-ordinates that form the basis functions. Extension of the Bezier-Bernstein neurofuzzy algorithm to n-dimensional inputs is discussed followed by numerical examples to demonstrate the effectiveness of this new data based modelling approach.

Des liaisons dangereuses? Réseaux donnés, réseaux supposés et réseaux déguisés d’une nonne vénitienne au XVIIe siècle

This article deals with Tarabotti's own family, her religious family within her nunnery and her ideal family, the so-called "République des lettres". Despite her permanent denial about her parents and siblings, she has ties with them all: she benifitted from her sister Camilla's and her mother's wills, she had a friendly relationship with one of her brothers-in-law, she took pity of her two sisters who remained spinsters. The same occurred with her religious family, where she developed close friendships with at least two of them. Moreover, her sisters in religion often belonged to patrician, well-off families and it is possible to argue that Tarabotti managed to expand her relationships with very important people via her sisters in religion. But the family she truly cherished, was her family d'election, the one she had been free to choose and to pursue: her literary family. However, this latter one was not a very recomandable family for a nun: therefore she kept silent with the most relevant elements of it, namely with the French priest and astronomer Ismael Boulliau who acted as the go-between for her last book, published abroad two years after her death. The article provides evidence to such connections, ties and knots, explaining at least in part Tarabotti's extraordinary success in life as a proto-feminist and political writer.