https://repositorio.ufba.br/handle/ri/2093 2026-05-03T07:09:36Z 2026-05-03T07:09:36Z Molitor, Mathieu https://repositorio.ufba.br/handle/ri/17184 2022-08-26T14:03:14Z 2014-01-01T00:00:00Z

Título: Gaussian distributions, Jacobi group, and Siegel-Jacobi space Autor(es): Molitor, Mathieu Abstract: Let N be the space of Gaussian distribution functions over ℝ, regarded as a 2-dimensional statistical manifold parameterized by the mean μ and the deviation σ. In this paper, we show that the tangent bundle of N , endowed with its natural Kähler structure, is the Siegel-Jacobi space appearing in the context of Number Theory and Jacobi forms. Geometrical aspects of the Siegel-Jacobi space are discussed in detail (completeness, curvature, group of holomorphic isometries, space of Kähler functions, and relationship to the Jacobi group), and are related to the quantum formalism in its geometrical form, i.e., based on the Kähler structure of the complex projective space. This paper is a continuation of our previous work [M. Molitor, “Remarks on the statistical origin of the geometrical formulation of quantum mechanics,” Int. J. Geom. Methods Mod. Phys. 9(3), 1220001, 9 (2012); M. Molitor, “Information geometry and the hydrodynamical formulation of quantum mechanics,” e-print arXiv (2012); M. Molitor, “Exponential families, Kähler geometry and quantum mechanics,” J. Geom. Phys. 70, 54–80 (2013)], where we studied the quantum formalism from a geometric and information-theoretical point of view. Tipo: Artigo de Periódico

2014-01-01T00:00:00Z Varandas, Paulo César Rodrigues Pinto https://repositorio.ufba.br/handle/ri/15724 2022-08-26T14:03:46Z 2012-01-01T00:00:00Z

Título: Non-uniform Specification and Large Deviations for Weak Gibbs Measures Autor(es): Varandas, Paulo César Rodrigues Pinto Abstract: We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of deviation sets of some non-uniformly expanding maps, including quadratic maps and robust multidimensional non-uniformly expanding local diffeomorphisms. For that purpose, a measure theoretical weak form of specification is introduced and proved to hold for the robust classes of multidimensional non-uniformly expanding local diffeomorphisms and Viana maps. Tipo: Artigo de Periódico

2012-01-01T00:00:00Z Araujo, Vitor Varandas, Paulo César Rodrigues Pinto https://repositorio.ufba.br/handle/ri/15600 2022-08-26T14:02:33Z 2012-01-01T00:00:00Z

Título: Robust Exponential Decay of Correlations for Singular-Flows Autor(es): Araujo, Vitor; Varandas, Paulo César Rodrigues Pinto Abstract: We construct open sets of C k (k ≥ 2) vector fields with singularities that have robust exponential decay of correlations with respect to the unique physical measure. In particular we prove that the geometric Lorenz attractor has exponential decay of correlations with respect to the unique physical measure. Tipo: Artigo de Periódico

2012-01-01T00:00:00Z Gomes, Gecynalda S. da S. Ludermir, Teresa B. https://repositorio.ufba.br/handle/ri/15001 2022-08-26T14:02:59Z 2013-01-01T00:00:00Z

Título: Optimization of the weights and asymmetric activation function family of neural network for time series forecasting Autor(es): Gomes, Gecynalda S. da S.; Ludermir, Teresa B. Abstract: The use of neural network models for time series forecasting has been motivated by experimental results that indicate high capacity for function approximation with good accuracy. Generally, these models use activation functions with fixed parameters. However, it is known that the choice of activation function strongly influences the complexity and neural network performance and that a limited number of activation functions has been used in general. We describe the use of an asymmetric activation functions family with free parameter for neural networks. We prove that the activation functions family defined, satisfies the requirements of the universal approximation theorem We present a methodology for global optimization of the activation functions family with free parameter and the connections between the processing units of the neural network. The main idea is to optimize, simultaneously, the weights and activation function used in a Multilayer Perceptron (MLP), through an approach that combines the advantages of simulated annealing, tabu search and a local learning algorithm. We have chosen two local learning algorithms: the backpropagation with momentum (BPM) and Levenberg–Marquardt (LM). The overall purpose is to improve performance in time series forecasting. Tipo: Artigo de Periódico

2013-01-01T00:00:00Z