Submitted by (lucia.rodrigues@ufrpe.br) on 2016-06-09T14:34:56Z No. of bitstreams: 1 Renato Barros Moraes.pdf: 1461731 bytes, checksum: 72fe61b249cbff251455227ca064db5a (MD5) / Made available in DSpace on 2016-06-09T14:34:56Z (GMT). No. of bitstreams: 1 Renato Barros Moraes.pdf: 1461731 bytes, checksum: 72fe61b249cbff251455227ca064db5a (MD5) Previous issue date: 2010-02-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Over the last 25 years, major advances have occurred in the techniques of nonlinear analysis applied to time series. These techniques have helped us to understand how dynamic systems behave over time. The brain is considered the most complex dynamic system known for man, and as such, it presents great challenges to the understanding of their processes, both physiological and pathological. In this work, we try to better understand epilepsy, a brain disease that affects millions of individuals around the world. The records of electroencephalogram (EEG) and electrocorticogram (ECoG) are widely used in the clinic for diagnosis and monitoring of epilepsy, but the information contained in these records are underutilized, since they are generally analyzed by the clinical eye. It is known that is contained in the EEG and ECoG, some specific frequencies such as alpha (α), beta (β), theta (θ), delta (δ) and gamma (γ) and they have interesting properties for the diagnosis of some brain pathologies. Through the DFA (Detrended fluctuation Analysis) technique used to verify long-range correlation in time series, and a derivation of this, the Parabolicity index (b), we observed some differences in EEG and ECoG signals, to normal and epileptic conditions between different brain rhythms, both in an animal model and in human records. / Nos últimos 25 anos, grandes avanços têm ocorrido nas técnicas de análise não-linear aplicadas a séries temporais. Essas técnicas têm nos ajudado a entender como sistemas dinâmicos se comportam com o passar do tempo. O cérebro é considerado o sistema dinâmico mais complexo conhecido pelo homem, e como tal apresenta grandes desafios para a compreensão de seus processos, tanto fisiológicos quanto patológicos. Nesse trabalho, tentamos compreender melhor a epilepsia, uma patologia cerebral que afeta milhões de indivíduos em todo o mundo. Os registros de eletroencefalograma (EEG) e eletrocorticograma (ECoG) são bastante utilizados na clínica para o diagnóstico e acompanhamento da epilepsia, porém as informações contidas nestes registros são subutilizadas, uma vez que são analisadas geralmente pelo olho clínico. Sabe-se que estão contidas no EEG e ECoG, algumas freqüências específicas tais como alfa(α), beta(β), teta(θ), delta(δ) e gama(γ), e que elas possuem propriedades interessantes para diagnóstico de algumas patologias cerebrais. Através da DFA (Análise de Flutuação sem Tendência), técnica usada para verificar correlação de longo alcance em séries temporais, e de uma derivação dessa, o Índice de parabolicidade (b), conseguimos verificar algumas diferenças nos sinais de ECoG e EEG, para uma condição normal e epiléptico, entre as diferentes ondas cerebrais, tanto num modelo animal quanto em registros de humanos.

We consider linear and semilinear stochastic partial differential equations that in some sense can be viewed as being at the "endpoints" of the classical variational theory by Krylov and Rozovskii [25]. In terms of regularity of the coeffcients, the minimal assumption is boundedness and measurability, and a unique L2- valued solution is then readily available. We investigate its further properties, such as higher order integrability, boundedness, and continuity. The other class of equations considered here are the ones whose leading operators do not satisfy the strong coercivity condition, but only a degenerate version of it, and therefore are not covered by the classical theory. We derive solvability in Wmp spaces and also discuss their numerical approximation through finite different schemes.