The objective of the proposed research is to compress data such as speech, audio, and images using a new re-ordering vector quantization approach that exploits the transition probability between consecutive code vectors in a signal. Vector quantization is the process of encoding blocks of samples from a data sequence by replacing every input vector from a dictionary of reproduction vectors. Shannon’s rate-distortion theory states that signals encoded as blocks of samples have a better rate-distortion performance relative to when encoded on a sample-to-sample basis. As such, vector quantization achieves a lower coding rate for a given distortion relative to scalar quantization for any given signal. Vector quantization does not take advantage of the inter-vector correlation between successive input vectors in data sequences. It has been demonstrated that real signals have significant inter-vector correlation. This correlation has led to vector quantization approaches that encode input vectors based on previously encoded vectors. Some methods have been proposed in literature to exploit the dependence between successive code vectors. Predictive vector quantization, dynamic codebook re-ordering, and finite-state vector quantization are examples of vector quantization schemes that use intervector correlation. Predictive vector quantization and finite-state vector quantization predict the reproduction vector for a given input vector by using past input vectors. Dynamic codebook re-ordering vector quantization has the same reproduction vectors as standard vector quantization. The dynamic codebook re-ordering algorithm is based on the concept of re-ordering indices whereby existing reproduction vectors are assigned new channel indices according a structure that orders the reproduction vectors in an order of increasing dissimilarity. Hence, an input vector encoded in the standard vector quantization method is transmitted through a channel with new indices such that 0 is assigned to the closest reproduction vector to the past reproduction vector. Larger index values are assigned to reproduction vectors that have larger distances from the previous reproduction vector. Dynamic codebook re-ordering assumes that the reproduction vectors of two successive vectors of real signals are typically close to each other according to a distance metric. Sometimes, two successively encoded vectors may have relatively larger distances from each other. Our likelihood codebook re-ordering vector quantization algorithm exploits the structure within a signal by exploiting the non-uniformity in the reproduction vector transition probability in a data sequence. Input vectors that have higher probability of transition from prior reproduction vectors are assigned indices of smaller values. The code vectors that are more likely to follow a given vector are assigned indices closer to 0 while the less likely are given assigned indices of higher value. This re-ordering provides the reproduction dictionary a structure suitable for entropy coding such as Huffman and arithmetic coding. Since such transitions are common in real signals, it is expected that our proposed algorithm when combined with entropy coding algorithms such binary arithmetic and Huffman coding, will result in lower bit rates for the same distortion as a standard vector quantization algorithm. The re-ordering vector quantization approach on quantized indices can be useful in speech, images, audio transmission. By applying our re-ordering approach to these data types, we expect to achieve lower coding rates for a given distortion or perceptual quality. This reduced coding rate makes our proposed algorithm useful for transmission and storage of larger image, speech streams for their respective communication channels. The use of truncation on the likelihood codebook re-ordering scheme results in much lower compression rates without significantly distorting the perceptual quality of the signals. Today, texts and other multimedia signals may be benefit from this additional layer of likelihood re-ordering compression.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The experimental observation of the quantum Hall effect in a two-dimensional electron gas posed an intriguing question to theorists: Why is the quantization of conductance so precise, given the imperfections of the measured samples? The question was answered a few years later, when a connection was uncovered between the quantum Hall effect and topological quantities associated with the band structure of the material in which it is observed. The Hall conductance was revealed to be an integer topological invariant, implying its robustness to certain perturbations. The topological theory went further than explaining only the usual integer quantum Hall effect in a perpendicular magnetic field. Soon it was realized that it also applies to certain systems in which the total magnetic flux is zero. Thus it is possible to have a quantized Hall effect without Landau levels. We study a carbon nanotube in a magnetic field perpendicular to its axial direction. Recent studies suggest that the application of an electric field parallel to the magnetic field would induce a gap in the electronic spectrum of a previously metallic carbon nanotube. Despite the quasi onedimensional nature of the carbon nanotube, the gapped state supports a quantum Hall effect and is associated with a non zero topological invariant. This result is revealed when an additional magnetic field is applied parallel to the axis of the carbon nanotube. If the flux due to this magnetic field is varied by one flux quantum, exactly one electron is transported between the ends of the carbon nanotube. / AFRIKAANSE OPSOMMING: Die eksperimentele waarneming van die kwantum Hall effek in ’n twee-dimensionele elektron gas laat ’n interessante vraag aan teoretiese fisikuste: Waarom sou die kwantisasie van die geleiding so presies wees al bevat die monsters, waarop die meetings gedoen word, onsuiwerhede? Hierdie vraag word ’n paar jaar later geantwoord toe ’n konneksie tussen die kwantum Hall effek en topologiese waardes, wat verband hou met die bandstruktuur van die monster, gemaak is. Dit is aan die lig gebring dat die Hall geleiding ’n heeltallige topologiese invariante is wat die robuustheid teen sekere steurings impliseer. Die topologiese teorie verduidelik nie net die gewone kwantum Hall effek wat in ’n loodregte magneetveld waargeneem word nie. Dit is ook moontlik om ’n kwantum Hall effek waar te neem in sekere sisteme waar die totale magneetvloed nul is. Dit is dus moontlik om ’n gekwantiseerde Hall effek sonder Landau levels te hˆe. Ons bestudeer ’n koolstofnanobuis in ’n magneetveld loodreg tot die aksiale rigting. Onlangse studies dui daarop dat die toepassing van ’n elektriese veld parallel aan die magneetveld ’n gaping in die elektroniese spektrum van ’n metaliese koolstofnanobuis induseer. Ten spyte van die een-dimensionele aard van die koolstofnanobuis ondersteun die gapings-toestand steeds ’n kwantum Hall effek en hou dit verband met ’n nie-nul topologiese invariante. Hierdie resultaat word openbaar wanneer ’n bykomende magneetveld parallel tot die as van die koolstofnanobuis toegedien word. Indien die vloed as gevolg van hierdie magneetveld met een vloedkwantum verander word, word presies een elektron tussen die twee kante van die koolstofnanobuis vervoer.

The main theme of this thesis is higher algebraic structures that come from operads and props. The first chapter is an introduction to the mathematical framework needed for the content of this thesis. The chapter does not contain any new results. The second chapter is concerned with the construction of a configuration space model for a particular 2-colored differential graded operad encoding the structure of two A∞ algebras with two A∞ morphisms and a homotopy between the morphisms. The cohomology of this operad is shown to be the well-known 2-colored operad encoding the structure of two associative algebras and of an associative algebra morphism between them. The third chapter is concerned with deformation quantization of (potentially) infinite dimensional (quasi-)Poisson manifolds. Our proof employs a variation on the transcendental methods pioneered by M. Kontsevich for the finite dimensional case. The first proof of the infinite dimensional case is due to B. Shoikhet. A key feature of the first proof is the construction of a universal L∞ structure on formal polyvector fields. Our contribution is a simplification of B. Shoikhet proof by considering a more natural configuration space and a simpler choice of propagator. The result is also put into a natural context of the dg Lie algebras coming from graph complexes; the L∞ structure is proved to come from a Maurer-Cartan element in the oriented graph complex. The fourth chapter also deals with deformation quantization of (quasi-)Poisson structures in the infinite dimensional setting. Unlike the previous chapter, the methods used here are purely algebraic. Our main theorem is the possibility to deformation quantize quasi-Poisson structures by only using perturbative methods; in contrast to the transcendental methods employed in the previous chapter. We give two proofs of the theorem via the theory of dg operads, dg properads and dg props. We show that there is a dg prop morphism from a prop governing star-products to a dg prop(erad) governing (quasi-)Poisson structures. This morphism gives a theorem about the existence of a deformation quantization of (quasi-)Poisson structure. The proof proceeds by giving an explicit deformation quantization of super-involutive Lie bialgebras and then lifting that to the dg properad governing quasi-Poisson structures. The prop governing star-products was first considered by S.A. Merkulov, but the properad governing quasi-Poisson structures is a new construction. The second proof of the theorem employs the Merkulov-Willwacher polydifferential functor to transfer the problem of finding a morphism of dg props to that of finding a morphism of dg operads.We construct an extension of the well known operad of A∞ algebras such that the representations of it in V are equivalent to an A∞ structure on V[[ħ]]. This new operad is also a minimal model of an operad that can be seen as the extension of the operad of associative algebras by a unary operation. We give an explicit map of operads from the extended associative operad to the operad we get when applying the Merkulov-Willwacher polydifferential functor to the properad of super-involutive Lie bialgebras. Lifting this map so as to go between their respective models gives a new proof of the main theorem.

Now a days the conditions at which the image taken may lead to near zero visibility for the human eye. They may usually due to lack of clarity, just like effects enclosed on earth’s atmosphere which have effects upon the images due to haze, fog and other day light effects. The effects on such images may exists, so useful information taken under those scenarios should be enhanced and made clear to recognize the objects and other useful information. To deal with such issues caused by low light or through the imaging devices experience haze effect many image processing algorithms were implemented. These algorithms also provide nonlinear contrast enhancement to some extent. We took pre-existed algorithms like SMQT (Successive mean Quantization Transform), V Transform, histogram equalization algorithms to improve the visual quality of digital picture with large range scenes and with irregular lighting conditions. These algorithms were performed in two different method and tested using different image facing low light and color change and succeeded in obtaining the enhanced image. These algorithms helps in various enhancements like color, contrast and very accurate results of images with low light. Histogram equalization technique is implemented by interpreting histogram of image as probability density function. To an image cumulative distribution function is applied so that accumulated histogram values are obtained. Then the values of the pixels are changed based on their probability and spread over the histogram. From these algorithms we choose histogram equalization, MATLAB code is taken as reference and made changes to implement in API (Application Program Interface) using JAVA and confirms that the application works properly with reduction of execution time.

Topics in source and channel coding for audiovisual communication systems are studied. The goal of source coding is to represent a source with the lowest possible rate to achieve a particular distortion, or with the lowest possible distortion at a given rate. Channel coding adds redundancy to quantized source information to recover channel errors. This thesis consists of four topics. Firstly, based on high-rate theory, we propose Karhunen-Loéve transform (KLT)-based classified vector quantization (VQ) to efficiently utilize optimal VQ advantages over scalar quantization (SQ). Compared with code-excited linear predictive (CELP) speech coding, KLT-based classified VQ provides not only a higher SNR and perceptual quality, but also lower computational complexity. Further improvement is obtained by companding. Secondly, we compare various transmitter-based packet-loss recovery techniques from a rate-distortion viewpoint for real-time audiovisual communication systems over the Internet. We conclude that, in most circumstances, multiple description coding (MDC) is the best packet-loss recovery technique. If channel conditions are informed, channel-optimized MDC yields better performance. Compared with resolution-constrained quantization (RCQ), entropy-constrained quantization (ECQ) produces a smaller number of distortion outliers but is more sensitive to channel errors. We apply a generalized γ-th power distortion measure to design a new RCQ algorithm that has less distortion outliers and is more robust against source mismatch than conventional RCQ methods. Finally, designing quantizers to effectively remove irrelevancy as well as redundancy is considered. Taking into account the just noticeable difference (JND) of human perception, we design a new RCQ method that has improved performance in terms of mean distortion and distortion outliers. Based on high-rate theory, optimal centroid density and its corresponding mean distortion are also accurately predicted. The latter two quantization methods can be combined with practical source coding systems such as KLT-based classified VQ and with joint source-channel coding paradigms such as MDC.

Neste trabalho, fazemos um estudo dos campos tensoriais antissimétricos em geral e, em particular, do campo tensorial antissimétrico de ordem dois. Utilizando o método de quantização BRST-BFV para teorias redutíveis no formalismo hamiltoniano, mostramos a equivalência quântica do campo tensorial antissimétrico de ordem dois não-massivo ao campo escalar em 4 dimensões e ao campo vetorial no gauge de Lorentz em 5 dimensões. Também é mostrada a equivalência entre as formulações de 1ª e 2ª ordem do campo tensorial antissimétrico de ordem dois. Por fim, é efetuada a quantização BRST-BFV de um modelo de partícula relativística com spin com duas supersimetrias acrescido de um termo Chern-Simons, mostrando que a amplitude de transição obtida equivale à amplitude de transição do \"rotacional\" de um campo tensorial antissimétrico de ordem qualquer. O caso massivo também é tratado brevemente. / In this work, we make a study of anti symmetric tensor fields in general, and, in particular, of the anti symmetric tensor fields of order two. Using the BRST-BFV quantization method for reducible theories in the Hamiltonian formalism, we show the quantum equivalence of the massless anti symmetric tensor field of order two to the scalar field in 4 dimensions, and to the vector field in the Lorentz gauge in 5 dimensions. It is also shown the quantum equivalence between the 1st and 2nd order formulations for the anti symmetric tensor field of order two. Finally, it is made the BRST-BFV quantization of a model of relativistic spinning particle with two super symmetries with a Chern-Simons term, showing that the transition amplitude obtained is equivalent to the transition amplitude for the field strength of an anti symmetric tensor field of any order. The massive case is also treated in breaf.

Recent experimental and theoretical studies have found evidence of coupled interactions between magnons and phonons. The aim of this study is to construct a model of coupled magnons and phonons, as well as analysing their frequency spectrum. The model is derived by quantizing spin and lattice degrees of freedom, and the frequency spectrum is derived by solving the equations of motion. We found that both the strength and the composition of the coupled interactions affect the frequencies of magnons and phonons, with emphasis on the magnons. Their frequencies are imaginary close to the center of the Brillouin zone, which opens questions for future research.

Na presente dissertação fazemos um resumo das idéias fundamentais do método de Quantização Estocástica de Parisi e Wu, com aplicações a teorias de campo Escalares, de Gauge e Fermiônicas. Em particular, nós utilizamos o esquema de Regularização Analítica Estocástica no cálculo do tensor de polarização para a Eletrodinâmica Quântica com Bósons ou Fêrmions de Dirac. A influência da regularização na invariância de Gauge e estudada para ambas as teorias, e é sugerida uma extensão do método para alguns modelos supersimétricos. / In the present dissertation, we made a survey of the fundamental ideas about Parisi-Wu\'s Stochastic Quantization Method, with applications to Scalar, Gauge and Fermionic theories. In particular, we use the Analytic Stochastic Regularization Scheme to calculate the polarization tensor for Quantum Electrodynamics with bosons or Dirac Fermions. The regularization influence is studied for both theories and an extension of this method for some supersymmetrical models is suggested.

Neste trabalho, fazemos um estudo dos campos tensoriais antissimétricos em geral e, em particular, do campo tensorial antissimétrico de ordem dois. Utilizando o método de quantização BRST-BFV para teorias redutíveis no formalismo hamiltoniano, mostramos a equivalência quântica do campo tensorial antissimétrico de ordem dois não-massivo ao campo escalar em 4 dimensões e ao campo vetorial no gauge de Lorentz em 5 dimensões. Também é mostrada a equivalência entre as formulações de 1ª e 2ª ordem do campo tensorial antissimétrico de ordem dois. Por fim, é efetuada a quantização BRST-BFV de um modelo de partícula relativística com spin com duas supersimetrias acrescido de um termo Chern-Simons, mostrando que a amplitude de transição obtida equivale à amplitude de transição do \"rotacional\" de um campo tensorial antissimétrico de ordem qualquer. O caso massivo também é tratado brevemente. / In this work, we make a study of anti symmetric tensor fields in general, and, in particular, of the anti symmetric tensor fields of order two. Using the BRST-BFV quantization method for reducible theories in the Hamiltonian formalism, we show the quantum equivalence of the massless anti symmetric tensor field of order two to the scalar field in 4 dimensions, and to the vector field in the Lorentz gauge in 5 dimensions. It is also shown the quantum equivalence between the 1st and 2nd order formulations for the anti symmetric tensor field of order two. Finally, it is made the BRST-BFV quantization of a model of relativistic spinning particle with two super symmetries with a Chern-Simons term, showing that the transition amplitude obtained is equivalent to the transition amplitude for the field strength of an anti symmetric tensor field of any order. The massive case is also treated in breaf.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-07-18T17:58:49Z No. of bitstreams: 1 JoseRibamarFonseca.pdf: 2069580 bytes, checksum: 26f5e4becf41e81d4359f2bc5df171fa (MD5) / Made available in DSpace on 2017-07-18T17:58:49Z (GMT). No. of bitstreams: 1 JoseRibamarFonseca.pdf: 2069580 bytes, checksum: 26f5e4becf41e81d4359f2bc5df171fa (MD5) Previous issue date: 2017-02-16 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ) / The adaptive filtering is currently an important tool in the statistical processing of signals, especially when it is necessary to process signals from environments with unknown statistics varying with time. The adaptive filtering study was driven by the development of the Least Mean Square algorithm (LMS) in 1960. Since then other adaptive algorithms have come up with a better performance than LMS algorithm with respect to misadjustment and convergence rate. Among them, the Sigmoidal algorithm (SA) which showed superior to the LMS, for the convergence rate and the mismatch in their implementations infinite precision. In hardware devices such as DSPs, microcontrollers and FPGAs, adaptive algorithms are implemented in finite precision, in general, fixed point arithmetic. When the adaptive filters are implemented in finite precision some effects can affect their performance. Ultimately lead to divergence due to quantization errors specified in the approximation process of the variables involved in the adaptive processing of their original values. Thus, this article aims to analyze the performance of the adaptive algorithm Sigmoidal (SA) in finite precision when implemented using fixed-point arithmetic. In particular, the analysis of its performance curve and mismatch, comparing them in different word lengths (number of bits). The results presented in this article proposes a series of Taylor Ln gradient of cost function (cosh αe) algorithm SA for implementation in finite precision. We analyze its performance curve for different lengths of words. It shows that the algorithm is stable in its performance compared to convergence to different lengths of words, and that the increase in mismatch level at steady state is sensitive or afected by the quantization of the variables involved in the calculations of this algorithm. / A filtragem adaptativa constitui atualmente uma ferramenta importante no processamento estatístico de sinais, especialmente quando é necessário processar sinais provenientes de ambientes com estatísticas desconhecidas que variam com o tempo. O estudo de filtragem adaptativa foi impulsionado com o desenvolvimento do algoritmo Least Mean Square (LMS) em 1960. Desde então outros algoritmos adaptativos têm surgido com um desempenho superior ao algoritmo LMS em relação ao desajuste e à taxa de convergência. Entre eles, o algoritmo Sigmoidal (SA) que se apresentou superior ao LMS, em relação a taxa de convergência e o desajuste em suas implementações na forma analógica. Nos dispositivos de hardware, tais como DSPs, Microcontroladores e FPGAs, os algoritmos adaptativos são implementados na forma digital, onde a precisão é finita, em geral, com aritmética de ponto fixo. Quando os filtros adaptativos são implementados em precisão finita alguns efeitos podem afetar o seu desempenho. Em última análise, levar à divergência devido aos erros de quantização especificados no processo de aproximação dos valores das variáveis envolvidas no processamento adaptativo de seus valores originais. Assim, este trabalho propõe analisar o desempenho do algoritmo adaptativo Sigmoidal (SA) em precisão nita, quando implementado utilizando aritmética de ponto xo. Em particular, a análise de sua curva de desempenho e o desajuste, comparando-os em diferentes comprimentos de palavras (número de bits). Os resultados apresentados neste trabalho propõe uma aproximação em série de Taylor do gradiente da função de custo Ln(cosh αe) do algoritmo SA para implementação em precisão finita. Analisamos a sua curva de desempenho para diferentes comprimentos de palavras. Mostra-se que o algoritmo apresenta estabilidade em seu desempenho em relação à convergência, para diferentes comprimentos de palavras, e que o aumento no nível do desajuste em estado estacionário é sensível ou influenciado pela quantização dos valores das variáveis envolvidas nos cálculos desse algoritmo.