The Discrete Wavelet Transform (DWT) is a popular tool in the field of image and video compression applications. Because of its multi-resolution representation capability, the DWT has been used effectively in applications such as transient signal analysis, computer vision, texture analysis, cell detection, and image compression. Daubechies wavelets are one of the popular transforms in the wavelet family. Daubechies filters provide excellent spatial and spectral locality-properties which make them useful in image compression.<p> In this thesis, we present an efficient implementation of a shared hardware core to compute two 8-point Daubechies wavelet transforms. The architecture is based on a new two-level folded mapping technique, an improved version of the Algebraic Integer Quantization (AIQ). The scheme is developed on the factorization and decomposition of the transform coefficients that exploits the symmetrical and wrapping structure of the matrices. The proposed architecture is parallel, pipelined, and multiplexed. Compared to existing designs, the proposed scheme reduces significantly the hardware cost, critical path delay and power consumption with a higher throughput rate.<p> Later, we have briefly presented a new mapping scheme to error-freely compute the Daubechies-8 tap wavelet transform, which is the next transform of Daubechies-6 in the Daubechies wavelet series. The multidimensional technique maps the irrational transformation basis coefficients with integers and results in considerable reduction in hardware and power consumption, and significant improvement in image reconstruction quality.

Let $M$ be a smooth compact manifold equipped with a co-oriented subbundle $E\subset TM$. We suppose that a compact Lie group $G$ acts on $M$ preserving $E$, such that the $G$-orbits are transverse to $E$. If the fibres of $E$ are equipped with a complex structure then it is possible to construct a $G$-invariant Dirac operator $\dirac$ in terms of the resulting almost CR structure. We show that there is a canonical equivariant differential form with generalized coefficients $\mathcal{J}(E,X)$ defined on $M$ that depends only on the $G$-action and the co-oriented subbundle $E$. Moreover, the group action is such that $\dirac$ is a $G$-transversally elliptic operator in the sense of Atiyah \cite{AT}. Its index is thus defined as a generalized function on $G$. Beginning with the equivariant index formula of Paradan and Vergne \cite{PV3}, we obtain an index formula for $\dirac$ computed as an integral over $M$ that is free of choices and growth conditions. This formula necessarily involves equivariant differential forms with generalized coefficients and we show that the only such form required is the canonical form $\mathcal{J}(E,X)$. In certain cases the index of $\dirac$ can be interpreted in terms of a CR analogue of the space of holomorphic sections, allowing us to view our index formula as a character formula for the $G$-equivariant quantization of the almost CR manifold $(M,E)$. In particular, we obtain the ``almost CR'' quantization of a contact manifold, in a manner directly analogous to the almost complex quantization of a symplectic manifold.

We study the effects of loop quantum gravity motivated corrections in classical systems. Computational methods are used to simulate black hole formation from the gravitational collapse of a massless scalar field in Painleve-Gullstrand coordinates. Singularities present in the classical case are resolved by a radiation-like phase in the quantum collapse. The evaporation is not complete but leaves behind an outward moving shell of mass that disperses to infinity. We reproduce Choptuik scaling showing the usual behaviour for the curvature scaling, while observing previously unseen behaviour in the mass scaling. The quantum corrections are found to impose a lower limit on black hole mass and generate a new universal power law scaling relationship. In a parallel study, we quantize the Hamiltonian for a particle in the singular $1/r^2$ potential, a form that appears frequently in black hole physics. In addition to conventional Schrodinger methods, the quantization is performed using full and semiclassical polymerization. The various quantization schemes are in excellent agreement for the highly excited states but differ for the low-lying states, and the polymer spectrum is bounded below even when the Schrodinger spectrum is not. / May 2009

Cette thèse décrit des méthodes de construction de martingales avec marginales spécifiées. La première collection de méthodes procède par quantization. C'est-à-dire en approximant une mesure par une autre mesure dont le support consiste en un nombre fini de points. Nous introduisons une méthode de quantization qui préserve l'ordre convexe. L'ordre convexe est un ordre partiel sur l'espace des mesures qui les compare en termes de leur dispertion relative. Cette nouvelle méthode de quantization présente l'avantage que si deux mesures admettent une transition de martingale alors les mesures quantisées en admettent aussi. Ceci n'est pas le cas pour la méthode de quantization habituellement utilisée en probabilités (la méthode de quantization L2). Pour les mesures quantifiés nous présentons plusieurs méthodes de construction de transition de martingale. La première méthode procède par programmation linéaire. La deuxième méthode procède par construction de matrices avec diagonale et spectre données. La troisième méthode procède par l'algorithme de Chacon et Walsh. Dans une seconde partie la thèse présente une nouvelle solution au problème du plongement de Skorokhod. Dans une troisième partie la thèse étudie la construction de martingales à temps continu avec marginales données. Des constructions sont données à l'aide du draps Brownien. D'autres constructions sont données en modifiant une méthode développée par Albin, les martingales construites ainsi possèdent une propriété de scaling.. Dans une partie annexe, certaines conséquences de cette théorie concernant le management du risque des options asiatiques, par rapport à leur sensibilité à la volatilité et à la maturité sont établies.

In digital watermarking, one embeds a watermark into a covertext, in such a way that the resulting watermarked signal is robust to a certain distortion caused by either standard data processing in a friendly environment or malicious attacks in an unfriendly environment. In addition to the robustness, there are two other conflicting requirements a good watermarking system should meet: one is referred as perceptual quality, that is, the distortion incurred to the original signal should be small; and the other is payload, the amount of information embedded (embedding rate) should be as high as possible. To a large extent, digital watermarking is a science and/or art aiming to design watermarking systems meeting these three conflicting requirements. As watermarked signals are highly desired to be compressed in real world applications, we have looked into the design and analysis of joint watermarking and compression (JWC) systems to achieve efficient tradeoffs among the embedding rate, compression rate, distortion and robustness. Using variable-rate scalar quantization, an optimum encoding and decoding scheme for JWC systems is designed and analyzed to maximize the robustness in the presence of additive Gaussian attacks under constraints on both compression distortion and composite rate. Simulation results show that in comparison with the previous work of designing JWC systems using fixed-rate scalar quantization, optimum JWC systems using variable-rate scalar quantization can achieve better performance in the distortion-to-noise ratio region of practical interest. Inspired by the good performance of JWC systems, we then investigate its applications in image compression. We look into the design of a joint image compression and blind watermarking system to maximize the compression rate-distortion performance while maintaining baseline JPEG decoder compatibility and satisfying the additional constraints imposed by watermarking. Two watermarking embedding schemes, odd-even watermarking (OEW) and zero-nonzero watermarking (ZNW), have been proposed for the robustness to a class of standard JPEG recompression attacks. To maximize the compression performance, two corresponding alternating algorithms have been developed to jointly optimize run-length coding, Huffman coding and quantization table selection subject to the additional constraints imposed by OEW and ZNW respectively. Both of two algorithms have been demonstrated to have better compression performance than the DQW and DEW algorithms developed in the recent literature. Compared with OEW scheme, the ZNW embedding method sacrifices some payload but earns more robustness against other types of attacks. In particular, the zero-nonzero watermarking scheme can survive a class of valumetric distortion attacks including additive noise, amplitude changes and recompression for everyday usage.

The thesis demonstrates a low-cost, low-bandwidth and low-resolution Analog-to- Digital Converter(ADC) in 0.35 um CMOS Process. A second-order Sigma-Delta modulator is used as the basis of the A/D Converter. A Semi-Uniform quantizer is used with the modulator to take advantage of input distributions that are dominated by smaller-amplitude signals e.g. Audio, Voice and Image-sensor signals. A Single-bit feedback topology is used with a multi-bit quantizer in the modulator. This topology avoids the use of a multi-bit DAC in the feedback loop – hence the system does not need to use digital correction techniques to compensate for a multi-bit DAC nonlinearity. High-Level Simulations of the second-order Sigma-Delta modulator single-bit feedback topology along with a Semi-Uniform quantizer are performed in Cadence. Results indicate that a 5-bit Semi-Uniform quantizer with a Over-Sampling Ratio of 32, can achieve a resolution of 10 bits, in addition, a semi-uniform quantizer exhibits a 5-6 dB gain in SNR over its uniform counterpart for input amplitudes smaller than –10 dB. Finally, this system is designed in 0.35um CMOS process.

Given the recent abundance of brand choice data from scanner panels market researchers have neglected the measurement and analysis of perceptions. Heterogeneity of perceptions is still a largely unexplored issue in market structure and segmentation studies. Over the last decade various parametric approaches toward modelling segmented perception-preference structures such as combined MDS and Latent Class procedures have been introduced. These methods, however, are not taylored for qualitative data describing consumers' redundant and fuzzy perceptions of brand images. A completely different method is based on topology-sensitive vector quantization (VQ) for consumers-by-brands-by-attributes data. It maps the segment-specific perceptual structures into bubble-pie-bar charts with multiple brand positions demonstrating perceptual distinctiveness or similarity. Though the analysis proceeds without any distributional assumptions it allows for significance testing. The application of exploratory and inferential data processing steps to the same data base is statistically sound and particularly attractive for market structure analysts. A brief outline of the VQ method is followed by a sample study with travel market data which proved to be particularly troublesome for conventional processing tools. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

In digital watermarking, one embeds a watermark into a covertext, in such a way that the resulting watermarked signal is robust to a certain distortion caused by either standard data processing in a friendly environment or malicious attacks in an unfriendly environment. In addition to the robustness, there are two other conflicting requirements a good watermarking system should meet: one is referred as perceptual quality, that is, the distortion incurred to the original signal should be small; and the other is payload, the amount of information embedded (embedding rate) should be as high as possible. To a large extent, digital watermarking is a science and/or art aiming to design watermarking systems meeting these three conflicting requirements. As watermarked signals are highly desired to be compressed in real world applications, we have looked into the design and analysis of joint watermarking and compression (JWC) systems to achieve efficient tradeoffs among the embedding rate, compression rate, distortion and robustness. Using variable-rate scalar quantization, an optimum encoding and decoding scheme for JWC systems is designed and analyzed to maximize the robustness in the presence of additive Gaussian attacks under constraints on both compression distortion and composite rate. Simulation results show that in comparison with the previous work of designing JWC systems using fixed-rate scalar quantization, optimum JWC systems using variable-rate scalar quantization can achieve better performance in the distortion-to-noise ratio region of practical interest. Inspired by the good performance of JWC systems, we then investigate its applications in image compression. We look into the design of a joint image compression and blind watermarking system to maximize the compression rate-distortion performance while maintaining baseline JPEG decoder compatibility and satisfying the additional constraints imposed by watermarking. Two watermarking embedding schemes, odd-even watermarking (OEW) and zero-nonzero watermarking (ZNW), have been proposed for the robustness to a class of standard JPEG recompression attacks. To maximize the compression performance, two corresponding alternating algorithms have been developed to jointly optimize run-length coding, Huffman coding and quantization table selection subject to the additional constraints imposed by OEW and ZNW respectively. Both of two algorithms have been demonstrated to have better compression performance than the DQW and DEW algorithms developed in the recent literature. Compared with OEW scheme, the ZNW embedding method sacrifices some payload but earns more robustness against other types of attacks. In particular, the zero-nonzero watermarking scheme can survive a class of valumetric distortion attacks including additive noise, amplitude changes and recompression for everyday usage.

The Discrete Wavelet Transform (DWT) is a popular tool in the field of image and video compression applications. Because of its multi-resolution representation capability, the DWT has been used effectively in applications such as transient signal analysis, computer vision, texture analysis, cell detection, and image compression. Daubechies wavelets are one of the popular transforms in the wavelet family. Daubechies filters provide excellent spatial and spectral locality-properties which make them useful in image compression.<p> In this thesis, we present an efficient implementation of a shared hardware core to compute two 8-point Daubechies wavelet transforms. The architecture is based on a new two-level folded mapping technique, an improved version of the Algebraic Integer Quantization (AIQ). The scheme is developed on the factorization and decomposition of the transform coefficients that exploits the symmetrical and wrapping structure of the matrices. The proposed architecture is parallel, pipelined, and multiplexed. Compared to existing designs, the proposed scheme reduces significantly the hardware cost, critical path delay and power consumption with a higher throughput rate.<p> Later, we have briefly presented a new mapping scheme to error-freely compute the Daubechies-8 tap wavelet transform, which is the next transform of Daubechies-6 in the Daubechies wavelet series. The multidimensional technique maps the irrational transformation basis coefficients with integers and results in considerable reduction in hardware and power consumption, and significant improvement in image reconstruction quality.

This thesis describes advanced modeling of nanoscale bulk MOSFETs incorporating critical quantum mechanical effects such as gate direct tunneling and energy quantization of carriers. An explicit expression of gate direct tunneling for thin gate oxides has been developed by solving the Schroinger equation analytically. In addition, the impact of different gate electrode as well as gate insulation materials on the gate direct tunneling is explored. This results in an analytical estimation of the potential solutions to excessive gate leakage current. The energy quantization analysis involves the derivation of a quantum mechanical charge distribution model by solving the coupled Poisson and Schroinger equations. Based on the newly developed charge distribution model, threshold voltage and subthreshold swing models are obtained. A transregional drain current model which takes into account the quantum mechanical correction on device parameters is derived. Results from this model show good agreement with numeric simulation results of both long-channel and short-channel MOSFETs.The models derived here are used to project MOSFET scaling limits. Tunneling and quantization effects cause large power dissipation, low drive current, and strong sensitivities to process variation, which greatly limit CMOS scaling. Developing new materials and structures is imminent to extend the scaling process.