A feed forward architecture is suggested that increases the complexity of conventional neural network components through the implementation of a more complex scheme of interconnection. This is done with a view to increasing the range of application of the feed forward paradigm. The uniqueness of this new network design is illustrated by developing an extended taxonomy of accepted published constructs specific and similar to the higher order, product kernel approximations achievable using "parallel paths". Network topologies from this taxonomy are then compared to each other and the architectures containing parallel paths. In attempting this comparison, the context of the term "network topology" is reconsidered. The output of "channels" in these parallel paths are the products of a conventional connection as observed facilitating interconnection between two layers in a multilayered perceptron and the output of a network processing unit, a "control element", that can assume the identity of a number of pre-existing processing paradigms. The inherent property of universal approximation is tested by existence proof and the method found to be inconclusive. In so doing an argument is suggested to indicate that the parametric nature of the functions as determined by conditions upon initialization may only lead to conditional approximations. The property of universal approximation is neither, confirmed or denied. Universal approximation cannot be conclusively determined by the application of Stone Weierstrass Theorem, as adopted from real analysis. This novel implementation requires modifications to component concepts and the training algorithm. The inspiration for these modifications is related back to previously published work that also provides the basis of "proof of concept". By achieving proof of concept the appropriateness of considering network topology without assessing the impact of the method of training on this topology is considered and discussed in some detail. Results of limited testing are discussed with an emphasis on visualising component contributions to the global network output.

In many digital signal processing applications, we often need some special function units which can compute complicated arithmetic functions such as reciprocal and logarithm. Conventionally, table-based arithmetic design strategy uses lookup tables to implement these kinds of function units. However, the table size will increase exponentially with respect to the required precision. In this thesis, we propose two methods to reduce the table size: bottom-up non-uniform segmentation and the approach which merges uniform piecewise interpolation and Newton-Raphson method. Experimental results show that we obtain significant table sizes reduction in most cases.

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[pt] Métodos de aprendizagem de variedades assumem que um conjunto de dados de alta dimensão possuem uma representação de baixa dimensionalidade. Tais métodos podem ser empregados para simplificar os dados e obter um melhor entendimento da estrutura da qual os dados fazem parte. Nesta tese, utiliza-se o método de aprendizagem de variedades chamado votação por tensores para obter informação da dimensionalidade intrínseca dos dados, bem como estimativas confiáveis da orientação dos vetores normais e tangentes em cada ponto da variedade. Em seguida, propõe-se um método construtivo para aproximar a variedade implícita e realizar uma regressão. O método e chamado de Regressão Construtiva em Variedades Implícitas (RCVI). Com os resultados obtidos no método de votação por tensores, busca-se uma aproximação da variedade através de uma participação do domínio, controlada pelo erro, baseada em malhas 2n-adicas (n denota o numero de características dos dados de entrada) e em arvore binaria com funções de transição suave. A construção consiste em dividir os dados em vários subconjuntos, de maneira a aproximar cada subconjunto de dados com funções implícitas simples. Nesse trabalho empregamos funções polinomiais multivariadas. A forma global pode ser obtida combinando essas estruturas simples. A cada dado de entrada esta associada uma saída e a partir de uma boa aproximação da variedade, utilizando esses dados de entrada, busca-se obter uma boa estimativa da saída. Dessa forma, os critérios de parada da subdivisão do domínio incluem uma precisão, definida pelo usuário, na aproximação da variedade, bem como um critério envolvendo a dispersão das saídas em cada subdomínio. Para avaliar o desempenho do método proposto, realiza-se uma regressão com dados reais, compara-se com métodos de aprendizagem supervisionada e efetua-se ainda uma aplicação na área de dados de poucos de petróleo. / [en] Manifold Learning Methods assume that a high-dimensional data set has a low-dimensional representation. These methods can be employed in order to simplify data, and to obtain a better understanding of the structure of which the data belong. In this thesis, a tensor voting approach is employed as a technique of manifold learning, to obtain information about the intrinsic dimensionality of the data and reliable estimates of the orientation of normal and tangent vectors at each data point in the manifold. Next, a constructive method is proposed to approximate an implicit manifold and perform a regression. The method is called Constructive Regression on Implicit Manifold (RCVI). With the obtained results, search is made in order to obtain a manifold approximation, which consists in a domain partition, error-controlled, based on 2n-trees (n means the number of features of the input data set) and binary partition trees with smooth transition functions. The construction implies in partition the data set into several subsets in order to approximate each subset with a simple implicit function. In this work, it is used multivariate polynomial functions. The global shape can be obtained by combining these simple structures. Each input data set is associated with an output data, then, from a good manifold approximation using those input data set, it is hoped that occurs a good estimate of the output data. Therefore, the stop criteria of the domain subdivision include a precision, deffined by the user, on the manifold approximation, as well as a criterion that involves the output dispersion on each subdomain. To evaluate the performance of the proposed method, a regression on real data is computed, and compared with some supervised learning algorithms and also an application on well data is performed.

O jitter de fase é um fenômeno inerente nos sistemas elétricos. O crescente interesse pelo jitter deve-se à degradação que causa em sistemas de transmissão de alta velocidade. Seus efeitos fazem-se sentir ao afetar o processo de recuperação de dados, causando aumento na taxa de erros por bit. Neste trabalho, o jitter é modelado como uma perturbação periódica e seu efeito na operação de PLLs é analisado. Deduzimos uma fórmula para o cálculo da amplitude do jitter envolvendo somente os parâmetros do PLL e do jitter e identificamos as regiões do espaço de parâmetros com os comportamentos dinâmicos do PLL. / Phase jitter or timing jitter is an inherent phenomenum on electrical systems. Jitter growing interest is due to degradation it causes in high-speed transmission systems. It affects the data recovering process and it causes an increase in the bit error rate. In this work, jitter is modelled as a periodic perturbation and its effects in the operation of a PLL are analysed. We deduce a formula that measures jitter amplitude by PLL and jitter parameters and we identify the regions of parameter space according to the system dynamical behaviour.

Title: A construction of minimum DNF representations of 2-interval functions Author: Jakub Dubovský Department: Dep. of Theoretical Computer Science and Mathematical Logic Supervisor: doc.RNDr.Ondřej Čepek, Ph.D. Abstract: The thesis is devoted to interval boolean functions. It is focused on construction of their representation by disjunctive normal forms with minimum number of terms. Summary of known results in this field for 1-interval functions is presented. It shows that method used to prove those results cannot be in general used for two or more interval functions. It tries to extend those results to 2-interval functions. An optimization algorithm for special subclass of them is constructed. Exact error estimation for approximation algorithm is proven. A command line software for experimentation with interval function is part of the thesis. Keywords: boolean function, interval function, representation construction, ap- proximation 1

<p>The field of reinforcement learning concerns the question of automated action selection given past experiences. As an agent moves through the state space, it must recognize which state choices are best in terms of allowing it to reach its goal. This is quantified with value functions, which evaluate a state and return the sum of rewards the agent can expect to receive from that state. Given a good value function, the agent can choose the actions which maximize this sum of rewards. Value functions are often chosen from a linear space defined by a set of features; this method offers a concise structure, low computational effort, and resistance to overfitting. However, because the number of features is small, this method depends heavily on these few features being expressive and useful, making the selection of these features a core problem. This document discusses this selection.</p><p>Aside from a review of the field, contributions include a new understanding of the role approximate models play in value function approximation, leading to new methods for analyzing feature sets in an intuitive way, both using the linear and the related kernelized approximation architectures. Additionally, we present a new method for automatically choosing features during value function approximation which has a bounded approximation error and produces superior policies, even in extremely noisy domains.</p> / Dissertation

This thesis develops approximate dynamic programming (ADP) strategies suitable for process control problems aimed at overcoming the limitations of MPC, which are the potentially exorbitant on-line computational requirement and the inability to consider the future interplay between uncertainty and estimation in the optimal control calculation. The suggested approach solves the DP only for the state points visited by closed-loop simulations with judiciously chosen control policies. The approach helps us combat a well-known problem of the traditional DP called 'curse-of-dimensionality,' while it allows the user to derive an improved control policy from the initial ones. The critical issue of the suggested method is a proper choice and design of function approximator. A local averager with a penalty term is proposed to guarantee a stably learned control policy as well as acceptable on-line performance. The thesis also demonstrates versatility of the proposed ADP strategy with difficult process control problems. First, a stochastic adaptive control problem is presented. In this application an ADP-based control policy shows an "active" probing property to reduce uncertainties, leading to a better control performance. The second example is a dual-mode controller, which is a supervisory scheme that actively prevents the progression of abnormal situations under a local controller at their onset. Finally, two ADP strategies for controlling nonlinear processes based on input-output data are suggested. They are model-based and model-free approaches, and have the advantage of conveniently incorporating the knowledge of identification data distribution into the control calculation with performance improvement.

The example based processing problem can be expressed as: "Given an example of an image or video before and after processing, apply a similar processing to a new image or video". Our thesis is that there are some problems where a single general algorithm can be used to create varieties of outputs, solely by presenting examples of what is desired to the algorithm. This is valuable if the algorithm to produce the output is non-obvious, e.g. an algorithm to emulate an example painting's style. We limit our investigations to example based processing of images, video, and 3D models as these data types are easy to acquire and experiment with. We represent this problem first as a texture synthesis influenced sampling problem, where the idea is to form feature vectors representative of the data and then sample them coherently to synthesize a plausible output for the new image or video. Grounding the problem in this manner is useful as both problems involve learning the structure of training data under some assumptions to sample it properly. We then reduce the problem to a labeling problem to perform example based processing in a more generalized and principled manner than earlier techniques. This allows us to perform a different estimation of what the output should be by approximating the optimal (and possibly not known) solution through a different approach.

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