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After 25 years, the microscopic mechanism of High-Tc superconductivity is still an open problem. In particular, the role of lattice vibrations is not yet clear. Many of the proposed models invoke unusual vibrational properties, such as nonlinearity in the interatomic potentials. In this thesis we present a combined experimental and theoretical study of lattice anharmonicities in cuprates. We first introduce and describe our Extended X-Ray Absorption Spectroscopy (EXAFS) experiments. We then develop a novel data analysis technique, which enables us to measure directly the nonlinearity in the...

System identification in nonstationary environment represents a challenging problem and an advaned neural architecture namely Time-Varying Neural Net- works (TV-NN) has shown remarkable identification properties in nonlinear and nonstationary conditions. Time-varying weights, each being a linear com- bination of a certain set of basis functions, are used in such kind of networks instead of stable ones, which inevitalbly increases the number of free parame- ters. Therefore, an Extreme Learning Machine (ELM) approach is developed to accelerate the training procedure for TV-NN. What is more, in...