Strategic Project - UI 144 - 2011-2012

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Publications

Shades of hyperbolicity for hamiltonians

Publication . Bessa, Mário; Rocha, Jorge; Torres, Maria Joana

We prove that a Hamiltonian system H ∈ C2(M,R) is globally hyperbolic if any of the following statements hold: H is robustly topologically stable; H is stably shadowable; H is stably expansive; and H has the stable weak specification property. Moreover, we prove that, for a C2-generic Hamiltonian H , the union of the partially hyperbolic regular energy hypersurfaces and the closed elliptic orbits, forms a dense subset of M. As a consequence, any robustly transitive regular energy hypersurface of a C2-Hamiltonian is partially hyperbolic. Finally, we prove that stable weakly-shadowable regular energy hypersurfaces are partially hyperbolic.

2013Journal article

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Contributions to the geometric and ergodic theory of conservative flows

Publication . Bessa, Mário; Rocha, Jorge

We prove the following dichotomy for vector fields in a C1-residual subset of volume-preserving flows: for Lebesgue-almost every point, either all of its Lyapunov exponents are equal to zero or its orbit has a dominated splitting. Moreover, we prove that a volume-preserving and C1-stably ergodic flow can be C1-approximated by another volume-preserving flow which is non-uniformly hyperbolic.

2012Journal article

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Fuzzy logic model to describe anesthetic effect and muscular influence on EEG Cerebral State Index

Publication . Brás, S.; Gouveia, S.; Ribeiro, L.; Ferreira, David A.; Antunes, L.; Nunes, Catarina S.

The well-known Cerebral State Index (CSI) quantifies depth of anesthesia and is traditionally modeled with Hill equation and propofol effect-site concentration (Ce). This work brings out two novelties: introduction of electromyogram (EMG) and use of fuzzy logic models with ANFIS optimized parameters. The data were collected from dogs (n = 27) during routine surgery considering two propofol administration protocols: constant infusion (G1, n = 14) and bolus (G2, n = 13). The median modeling error of the fuzzy logic model with Ce and EMG was lower or similar than that of the Hill with Ce (p = 0.012-G1, p = 0.522-G2). Furthermore, there was no significant performance impact due to model structure alteration (p = 0.288-G1, p = 0.330-G2) and EMG introduction increased or maintained the performance (p = 0.036-G1, p = 0.798-G2). Therefore, the new model can achieve higher performance than Hill model, mostly due to EMG information and not due to changes in the model structure. In conclusion, the fuzzy models adequately describe CSI data with advantages over traditional Hill models.

2013Journal article

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