R. Vilela Mendes

Carlos Aguirre, R. Vilela Mendes

Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are robust in the presence of noise. Tomograms based on the time-frequency operator pair, were used in the past for component separation and denoising. Here we show how, by the construction of an operator pair adapted to the signal, meaningful information with good time resolution is extracted even in very noisy situations.

João P. S. Bizarro, L. Venâncio, R. Vilela Mendes

When the singular values of the evolution operator are all smaller or all greater than one, stable integration algorithms are obtained either by explicit or implicit methods. When the singular spectrum mixes greater and smaller than one values, neither explicit nor implicit methods insure stabilty. The problem is solved by using a splitting of the evolution operator and a semi-implicit scheme. The method is illustrated in the study of a two-field model of the tokamak scrape-off layer.

Rui Ligeiro, R. Vilela Mendes

It is not, in general, possible to have access to all variables that determine the behavior of a system. Having identified a number of variables whose values can be accessed, there may still be hidden variables which influence the dynamics of the system. The result is model ambiguity in the sense that, for the same (or very similar) input values, different objective outputs should have been obtained. In addition, the degree of ambiguity may vary widely across the whole range of input values. Thus, to evaluate the accuracy of a model it is of utmost importance to create a method to obtain the degree of reliability of each output result. In this paper we present such a scheme composed of two coupled artificial neural networks: the first one being responsible for outputting the predicted value, whereas the other evaluates the reliability of the output, which is learned from the error values of the first one. As an illustration, the scheme is applied to a model for tracking slopes in a straw chamber and to a credit scoring model.