QUANDO OS ESPÍRITOS SAEM DO ABISMO: O ESTABELECIMENTO NARRATIVO DO TERROR ESCATOLÓGICO EM APOCALIPSE 9,1-21

O Apocalipse de João é uma obra instigante. Sua linguagem cheia de violência, com monstros aterrorizantes, pessoas clamando por justiça, anúncios de mortes e desespero, em um quadro de espetáculos celestes, fascina os que gostam de ficção e alimenta a esperança dos que esperam um dia entrar na Nova Jerusalém, onde não haverá mar nem morte, quando as lágrimas serão enxugadas. Contudo, o livro do Apocalipse será lido como uma narração da realidade. Nesse sentido, o texto não é visto como reflexo de qualquer opressão, mas construção discursiva a respeito do sistema que, para o visionário, é a negação da ordem. Neste trabalho, a partir dos conceitos de texto e memória cultural, à luz das pesquisas de I. Lótman, da escola russa de semiótica da cultura e das pesquisas dos Assmann, observar-se-á como as memórias de seres celestes caídos e aprisionados da tradição enoquita estão presentes na literatura judaico-cristã e servem para a construção narrativa do cenário de terror escatológico na quinta e sexta trombetas de Ap 9,1-21. Assim sendo, a tese defende o terror como instrumento de persuasão, o qual serviu, na estratégia do visionário, para descrever o seu contexto como realidade caótica. Por meio de estratégias narrativas, o narrador deseja que sua visão seja levada a sério e que seus interlocutores aceitem a sua interpretação da realidade, deixando a associação com a vida e sistema romanos, pois se assim procederem serão comparados aos selados e receberão as mesmas recompensas. Dessa maneira, sua descrição com linguagem escatológica joga com o futuro e com o presente; prevê o caos, mas o vive em nível narrativo. Por isso o livro do Apocalipse, com um dualismo extremamente radical, não dá espaços para dúvidas. A tese defende, portanto, que essa obra pode ser lida como instrumento retórico de terror e medo que leva seus leitores implícitos a não flertarem com Roma, a não aceitarem seus discursos ou os que com ela se associam.

IGREJA SEM FRONTEIRAS, FRONTEIRAS SEM IGREJA: Análise das Práticas Pastorais nas Igrejas Batistas da Região Leste da Cidade de São Paulo, num Contexto Urbano de Contrastes, de 1990 a 2000, na Perspectiva da Teologia Prática

A cidade se desenvolve a partir de um núcleo denominado centro, na direção de círculos periféricos. As populações instaladas nestas zonas de fronteiras vivenciam e estabelecem relações próprias com o espaço que ocupam e com o núcleo denominado centro. Em São Paulo, é plausível que se reconheça não há uma uniformidade na população urbana, mas populações urbanas, marcadas por características plurais e significativos contrastes entre si, inclusive nas manifestações de fenômenos religiosos.A zona leste da cidade de São Paulo é objeto da análise desta pesquisa apresentada em quatro capítulos, observada em seus diferentes aspectos, identificando-se inclusive, que há na própria região geográfica marcada como ZL, duas disposições, a saber: ZL 1 e ZL 2, que por si só evidenciam o contraste na zona de fronteira. O olhar específico para este espaço é delimitado pelo tempo, entre 1990-2000 e pela referência da pesquisa que se propõe identificar e analisar as Práticas Pastorais das Igrejas Batistas residentes nesta Zona. Na análise das Práticas Pastorais no viés da evangelização e expansão missionária, elabora-se a pesquisa especificamente sobre três comunidades, a saber: Primeira Igreja Batista da Penha, Igreja Batista em Vila Salete e Primeira Igreja Evangélica Batista em Guaianases.Parte-se não de um referencial externo à comunidade como instrumental de análise, mas suas respectivas propostas de Práticas Pastorais registradas em seus documentos oficiais como atas, anuários e informativos dominicais, os quais serviram como fonte documental. As fronteiras urbanas são, por natureza, inovadoras e caóticas, sendo exatamente por isso o espaço mais adequado para igrejas criarem e desenvolverem Práticas Pastorais próprias e conseqüentes, sem delimitadores à inovação de toda a ordem, configurando-se como Igreja sem Fronteiras. Em caso contrário à motivação inovadora, rompendo-se o diálogo e a vivência com o meio urbano fronteiriço, excluindo-se o ambiente de contraste que se oferece à igreja, dá-se a gênese ao vazio, à desesperança, a Fronteiras sem Igreja.(AU)

INDIFERENÇA OU INJUSTIÇA DIVINA? EM BUSCA DE UMA COMPREENSÃO DO SOFRIMENTO HUMANO: UMA EXEGESE DE JÓ 24,7-12

O livro de Jó, cujo tema principal é a dor humana, mostra que as provações que Jó foi obrigado a suportar são absurdas e cruéis. Diante da realidade de sua existência, Jó percebe o universo como uma ausência do Deus em quem crê. A vida humana aparece caótica e as desigualdades sociais não encontram solução, a não ser na morte. Na obra, a explicação a cerca do sofrimento do inocente continuou arbitrária e permaneceu irrespondida. Contudo, a aflição gerada pela miséria total, pelo abandono e pela solidão fez Jó compreender a aflição das pessoas com as quais ele se identificou: o pobre, a viúva, o órfão, o faminto, todos aqueles que de alguma forma sofriam injustamente. Foi a partir dessa identificação que Jó lançou seu grito de protesto e denunciou os crimes cometidos pelos poderosos aos trabalhadores do campo e da cidade na sociedade de sua época, como mostra o capítulo 24,7-12. Jó não desprezou o próximo, nem se omitiu diante da violência contra seres humanos, mas engajou-se no combate do mal. Mal que pode ser entendido como tudo aquilo que contraria o dom mais preciso de Deus, o dom da vida.(AU)

Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

A new entropy measure based on the Renyi entropy rate using Gaussian kernels

The concept of entropy rate is well defined in dynamical systems theory but is impossible to apply it directly to finite real world data sets. With this in mind, Pincus developed Approximate Entropy (ApEn), which uses ideas from Eckmann and Ruelle to create a regularity measure based on entropy rate that can be used to determine the influence of chaotic behaviour in a real world signal. However, this measure was found not to be robust and so an improved formulation known as the Sample Entropy (SampEn) was created by Richman and Moorman to address these issues. We have developed a new, related, regularity measure which is not based on the theory provided by Eckmann and Ruelle and proves a more well-behaved measure of complexity than the previous measures whilst still retaining a low computational cost.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Emulation of dynamic computer models with multivariate output

This preliminary report describes work carried out as part of work package 1.2 of the MUCM research project. The report is split in two parts: the ?rst part (Sections 1 and 2) summarises the state of the art in emulation of computer models, while the second presents some initial work on the emulation of dynamic models. In the ?rst part, we describe the basics of emulation, introduce the notation and put together the key results for the emulation of models with single and multiple outputs, with or without the use of mean function. In the second part, we present preliminary results on the chaotic Lorenz 63 model. We look at emulation of a single time step, and repeated application of the emulator for sequential predic- tion. After some design considerations, the emulator is compared with the exact simulator on a number of runs to assess its performance. Several general issues related to emulating dynamic models are raised and discussed. Current work on the larger Lorenz 96 model (40 variables) is presented in the context of dimension reduction, with results to be provided in a follow-up report. The notation used in this report are summarised in appendix.

Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1?:?1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.

Chemical modification of polymers

Based on the knowledge of PVC degradation and stabilisation, chemical modifications were imposed on degraded PVC and raw PVC with the aim of obtaining non-migrating additives. The modifications were carried out mainly in the presence of dibutyl maleate (DBM), and the resulting polymer contained dibutyl maleic residues. Such modifications result in a polymer which contain substantive additives which resist migration under aggressive environments. Previous studies have shown that stable nitroxyl radicals function as stabilisers in polymer during processing (e.g. PP, PVC) by deactivating a large number of kinetic chains via a redox process whereby the concentrations of the nitroxyl and its reduced form, the hydroxylamine, fluctuate reciprocally and rhythmically. In order to understand the major reactions involved in such systems, a simulation method was used which resulted in a mathematical model and some rate constants, explaining the kinetic behaviour exhibited by such system. In the process of forming a suitable model, two nonlinear oscillators were proposed, which could be of interest in the study of nonlinear phenomenon because of their chaotic behaviour.

Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

Synchronization processes in nonlinear systems and their relation to cortical oscillatory dynamics

This thesis was focused on theoretical models of synchronization to cortical dynamics as measured by magnetoencephalography (MEG). Dynamical systems theory was used in both identifying relevant variables for brain coordination and also in devising methods for their quantification. We presented a method for studying interactions of linear and chaotic neuronal sources using MEG beamforming techniques. We showed that such sources can be accurately reconstructed in terms of their location, temporal dynamics and possible interactions. Synchronization in low-dimensional nonlinear systems was studied to explore specific correlates of functional integration and segregation. In the case of interacting dissimilar systems, relevant coordination phenomena involved generalized and phase synchronization, which were often intermittent. Spatially-extended systems were then studied. For locally-coupled dissimilar systems, as in the case of cortical columns, clustering behaviour occurred. Synchronized clusters emerged at different frequencies and their boundaries were marked through oscillation death. The macroscopic mean field revealed sharp spectral peaks at the frequencies of the clusters and broader spectral drops at their boundaries. These results question existing models of Event Related Synchronization and Desynchronization. We re-examined the concept of the steady-state evoked response following an AM stimulus. We showed that very little variability in the AM following response could be accounted by system noise. We presented a methodology for detecting local and global nonlinear interactions from MEG data in order to account for residual variability. We found crosshemispheric nonlinear interactions of ongoing cortical rhythms concurrent with the stimulus and interactions of these rhythms with the following AM responses. Finally, we hypothesized that holistic spatial stimuli would be accompanied by the emergence of clusters in primary visual cortex resulting in frequency-specific MEG oscillations. Indeed, we found different frequency distributions in induced gamma oscillations for different spatial stimuli, which was suggestive of temporal coding of these spatial stimuli. Further, we addressed the bursting character of these oscillations, which was suggestive of intermittent nonlinear dynamics. However, we did not observe the characteristic-3/2 power-law scaling in the distribution of interburst intervals. Further, this distribution was only seldom significantly different to the one obtained in surrogate data, where nonlinear structure was destroyed. In conclusion, the work presented in this thesis suggests that advances in dynamical systems theory in conjunction with developments in magnetoencephalography may facilitate a mapping between levels of description int he brain. this may potentially represent a major advancement in neuroscience.

Incoherent fibre supercontinuum generation for all-optical random number generation

Random number generation is a central component of modern information technology, with crucial applications in ensuring communications and information security. The development of new physical mechanisms suitable to directly generate random bit sequences is thus a subject of intense current research, with particular interest in alloptical techniques suitable for the generation of data sequences with high bit rate. One such promising technique that has received much recent attention is the chaotic semiconductor laser systems producing high quality random output as a result of the intrinsic nonlinear dynamics of its architecture [1]. Here we propose a novel complementary concept of all-optical technique that might dramatically increase the generation rate of random bits by using simultaneously multiple spectral channels with uncorrelated signals - somewhat similar to use of wave-division-multiplexing in communications. We propose to exploit the intrinsic nonlinear dynamics of extreme spectral broadening and supercontinuum (SC) generation in optical fibre, a process known to be often associated with non-deterministic fluctuations [2]. In this paper, we report proof-of concept results indicating that the fluctuations in highly nonlinear fibre SC generation can potentially be used for random number generation.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.