Quantization

We show how changes in unitarity-preserving boundary conditions allow continuous interpolation among the Hilbert spaces of quantum mechanics on topologically distinct manifolds. We present several examples, including a computation of entanglement entropy production. We discuss approximate realization of boundary conditions through appropriate interactions, thus suggesting a route to possible experimental realization. We give a theoretical application to quantization of singular Hamiltonians, and give tangible form to the "many worlds" interpretation of wave functions.

Multiple description (MD) coding is source coding in which several descriptions of the source are produced such that various reconstruction qualities are obtained from different subsets of the descriptions. Unlike multiresolution or layered source coding, there is no hierarchy of descriptions; thus, MD coding is suitable for packet erasure channels or networks without priority provisions. Generalizing work by Orchard, Wang, Vaishampayan, and Reibman, a transform-based approach is developed for producing descriptions of an -tuple source, . The descriptions are sets of transform coefficients, and the transform coefficients of different descriptions are correlated so that missing coefficients can be estimated. Several transform optimization results are presented for memoryless Gaussian sources, including a complete solution of the = 2, = 2 case with arbitrary weighting of the descriptions. The technique is effective only when independent components of the source have differing variances. Numerical studies show that this method performs well at low redundancies, as compared to uniform MD scalar quantization.

Adaptive space-frequency quantization scheme in scalar fashion applied to wavelet-based compression is presented. Because of strong demands due to detail preserving in lossy image archiving and transmission, as it is for example in medical applications, different modifications of uniform threshold quantization are considered. The main features of elaborated procedure are as follows: fitting threshold value to local data characteristics in backward way and quantization step size estimation for each subband as forward and backward framework in optimization procedure. Many tests conducted in real wavelet compression scheme c o n f i i significant efficiency of presented quantization procedures. Achieved total compression effectiveness is promising in spite of simple coding algorithm.

The increased need of content based image retrieval technique can be found in a number of different domains such as Data Mining, Education, Medical Imaging, Crime Prevention, Weather forecasting, Remote Sensing and Management of Earth Resources. This paper presents the content based image retrieval, using features like texture and color, called WBCHIR (Wavelet Based Color Histogram Image Retrieval).The texture and color features are extracted through wavelet transformation and color histogram and the combination of these features is robust to scaling and translation of objects in an image. The proposed system has demonstrated a promising and faster retrieval method on a WANG image database containing 1000 general-purpose color images. The performance has been evaluated by comparing with the existing systems in the literature.

In video coding, it is commonly accepted that the encoding parameters such as the quantization step-size have an influence on the perceived quality. It is also sometimes accepted that using given encoding parameters, the perceived quality does not change significantly according to the encoded source content. In this paper, we present the outcomes of two video subjective quality assessment experiments in the context of Scalable Video Coding. We encoded a large set of video sequences under a group of constant quality scenarios based on two spatially scalable layers. One first experiment explores of the relation between a wide range of quantization parameters for each layer and the perceived quality, while the second experiment uses a subset of the encoding scenarios on a large number of video sequences. The two experiments are aligned on a common scale using a set of shared processed video sequences, resulting in a database containing the subjective scores for 60 different sources combined with 20 SVC scenarios. We propose a detailed analysis of the experimental results of the two experiments, bringing a clear insight of the relation between the encoding parameters combination of the scalable layers and the perceived quality, as well as spreading light on the differences in terms of quality depending on the encoded source content. As an endeavour to analyse these differences, we propose a classification of the sources with regards to their relative behaviour when compared to the average of other source contents. We use this classification to identify potential factors to explain the differences between source contents.

This paper presents an ECG compressor based on optimized quantization of Discrete Cosine Transform (DCT) coefficients. The ECG to be compressed is partitioned in blocks of fixed size, and each DCT block is quantized using a quantization vector and a threshold vector that are specifically defined for each signal. These vectors are defined, via Lagrange multipliers, so that the estimated entropy is minimized for a given distortion in the reconstructed signal. The optimization method presented in this paper is an adaptation for ECG of a technique previously used for image compression. In the last step of the compressor here proposed, the quantized coefficients are coded by an arithmetic coder. The Percent Root-Mean-Square Difference (PRD) was adopted as a measure of the distortion introduced by the compressor. To assess the performance of the proposed compressor, 2-minute sections of all 96 records of the MIT-BIH Arrhythmia Database were compressed at different PRD values, and the corresponding compression ratios were computed. We also present traces of test signals before and after the compression/decompression process. The results show that the proposed method achieves good compression ratios (CR) with excellent reconstruction quality. An average CR of 9.3:1 is achieved for PRD equal to 2.5%. Experiments with ECG records used in other results from the literature revealed that the proposed method compares favorably with various classical and state-of-the-art ECG compressors. 

This letter studies the effect of quantized channel state information (CSI) feedback on the average rate of correlated channels. Demonstrating the general rate optimization problem, the results are obtained for both delayed and delay-free feedback conditions under different short-and long-term power allocation strategies. We also evaluate the effect of adaptive CSI quantization on the channel average rate. Analytical and numerical results show that exploiting the channel memory not only increases the forward channel data transmission efficiency but also can lead to dramatic feedback rate reduction.

Two new fast algorithms for computing the inverse modified discrete cosine transform (IMDCT) as used in the adaptive spectral entropy coder (ASPEC) [2] are proposed. A fixed-point error analysis is presented to determine the number of significant bits required for fixed-point implementations.

A simple dynamic element matching (DEM) scheme for sampled data systems is presented. The scheme is suitable for Switch-Capacitor (SC) or Switch-Current circuits. The DEM scheme eliminates the mirror spectral image around +/-Fs/4, where Fs is the sampling frequency, while generally introducing a more benign self-image. The scheme is suitable for quadrature SC Band-Pass (BP) Σ∆ modulators with a centre frequency at Fs/4 or -Fs/4, where it can minimize the quantization noise mirror image and where the signal mirror image can be suppressed. Furthermore, a quadrature mismatch noise shaping method that can be used with this DEM scheme is introduced.

Aims To prospectively evaluate by ultrasound biomicroscopy (UBM) and gonioscopy the anterior chamber angle widening following laser peripheral iridotomy (LPI) in eyes with early chronic primary angle closure glaucoma (CACG). Methods A total of 55 eyes of 55 patients with CACG presenting with less than 1801 peripheral anterior synechiae (PAS) were enrolled in the study. Angles were assessed by gonioscopy (Shaffer's grading) and UBM, before and 4 weeks after LPI. The angle opening distance at 250 and 500 lm from the scleral spur (AOD 250 and AOD 500) was computed. Results were analysed using the Wilcoxon signed-rank test. Results In the quadrant with LPI, the mean gonioscopy grade increased significantly from 0.45 to 1.45 (Po0.001) and the mean AOD 250 and AOD 500 increased from 38.5725.9 to 83.5748.4 lm (Po0.001) and 110.2780.9 to 170.6783.4 lm (Po0.001), respectively. The angles widened significantly in the opposite quadrant on UBM (AOD 250: 48.8731.5-82.7743.9 lm, Po0.001; AOD 500:117.27 65.5-172.2781.7 lm; Po0.001), but the median gonioscopy grade remained unchanged.

Abstracr-Predictive coding is a promising approach for speech coding. In this paper, we review the recent work on adaptive predictive coding of speech signals, with particular emphasis on achieving high speech quality at low bit rates (less than 10 kbits/s). Efficient prediction of the redundant structure in speech signals is obviously important for proper functioning of a predictive coder. It is equally important to ensure that the distortion in the coded speech signal be perceptually small. The subjective loudness of quantization noise depends both on the short-time spectrum of the noise and its relation to the short-time spectrum of the speech signal. The noise in the formant regions is partially masked by the speech signal itself. This masking of quantization noise by speech signal allows one to use low bit rates while maintaining high speech quality. This paper will present generalizations of predictive coding for minimizing subjective distortion in the reconstructed speech signal at the receiver. The quantizer in predictive coders quantizes its input on a sample-by-sample basis. Such sample-by-sample (instantaneous) quantization creates difficulty in realizing an arbitrary noise spectrum, particularly at low bit rates. We will describe a new class of speech coders in this paper which could be considered to be a generalization of the predictive coder. These new coders not only allow one to realize the precise optimum noise spectrum which is crucial to achieving very low bit rates, but also represent the important first step in bridging the gap between waveform coders and vocoders without suffering from their limitations.

Critical steps in electronic volume quantification of gingival crevicular fluid: the potential impact of evaporation, fluid retention, local conditions and repeated measurements. J Periodont Res 2004; 39; 344-357. Ó Blackwell Munksgaard 2004

We present a hybrid neural-network for human face recognition which compares favourably with other methods. The system combines local image sampling, a self-organizing map (SOM) neural network, and a convolutional neural network. The SOM provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space, thereby providing dimensionality reduction and invariance to minor changes in the image sample, and the convolutional neural network provides partial invariance to translation, rotation, scale, and deformation. The convolutional network extracts successively larger features in a hierarchical set of layers. We present results using the Karhunen-Loeve transform in place of the SOM, and a multilayer perceptron (MLP) in place of the convolutional network for comparison. We use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression, pose, and facial details. We analyze the computational complexity and discuss how new classes could be added to the trained recognizer

In this work, we investigate the electrical properties of the Double-Gate MOSFET (DG-MOSFET), which turn out to be very promising for device miniaturization below 0.1 m. A compact model which accounts for charge quantization within the channel, Fermi statistics, and nonstatic effects in the transport model is worked out. The main results of this investigation are: 1) the ideality factor in subthreshold is equal to unity, i.e., the slope of the turn-on characteristic is 60 mV/decade at room temperature; 2) the drain-induced barrier lowering is minimized by the shielding effect of the double gate, which allows us to reduce the channel length below 30 nm; and 3) the device transconductance per unit width is maximized by the combination of the double gate and by a strong velocity overshoot which occurs in response to the sudden variation of the electric field at the source end of the channel, and which can be further strengthened near the drain in view of the short device length. As a result, a sustained electron velocity of nearly twice the saturation velocity is achievable. The above results prove that the potential performance advantages of the double-gate device architecture may be worth the development effort.

The design and implementation of lossless audio signal processing using Finite Field Transforms is discussed. Finite field signal processing techniques are described. The effects of filter length and coefficient accuracy are also discussed. Finite field transform algorithms which would be suitable for lossless signal processing are presented

To develop a method for assessing absolute renal function (as well as morphology) in children, using gamma camera imaging of intravenously injected technetium-99m (99mTc) dimercaptosuccinic acid (DMSA). Forty-five children (ages 1 week to 10 years; mean, 2.0 years) were imaged using a planar technique in which not only the appearance but the absolute amount of intravenously administered 99mTc DMSA taken up by the kidneys was calculated for each child and compared with contemporaneous determinations of creatinine clearance. There was a close correlation between the absolute DMSA uptake and creatinine clearance (r = 0.752). Renal function in children, expressed as creatinine clearance, can be accurately estimated by measuring absolute DMSA uptake with planar gamma camera imaging using 99mTc DMSA.

Gas chromatography-mass spectrometry (GC-MS) and multidimensional gas chromatography olfactometry (GC/GC-O) were utilized to study the aroma profile and the aroma active components of commercial kiwi essence and the initial fresh fruit puree. Totals of 29 and 33 components were identified and quantified in the essence and the puree, respectively. Ten components were quantified for the first time as constituents of the kiwi fruit including 3-penten-2-ol, 3-hydroxy-2-butanone, 3-methyl-2-butenal, 2-hexanol, nonanal, 3-methyl-1-butanol, 2-methyl-1-butanol, 3-methyl-2-butanone, 3-methyl 3-buten-2-one, and octane. Analysis of these samples by multidimensional gas chromatography-olfactometry (GC-O) allowed for the identification of >80% of the aroma active components present at level traces in this fruit. A total of 35 components appear to contribute to the aroma of kiwi fresh puree and its aqueous essence. Components described for the first time as constituents of the aroma profile in this fruit were 2-ethylfuran, 3-methyl-1-butanol, 2-cyclohexen-1-one, (E,E)-2,6nonadienal, diethyl succinate, and hexyl hexanoate.

The JPEG baseline standard for image compression employs a block Discrete Cosine Transform (DCT) and uniform quantization. For a monochrome image, a single quantization matrix is allowed, while for a color image, distinct matrices are allowed for each color channel.. Here we describe a method, called DCTune, for design of color quantization matrices that is based on a model of the visibility of quantization artifacts. The model describes artifact visibility as a function of DCT frequency, color channel, and display resolution and brightness. The model also describes summation of artifacts over space and frequency, and masking of artifacts by the image itself. The DCTune matrices are different from the de facto JPEG matrices, and appear to provide superior visual quality at equal bit-rates.

this paper reports a PFD/CP linearization technique and a new charge pump circuit to enhance the performance of a delta-sigma (∆Σ) fractional-N PLL. The proposed method improves the PLL linearity by forcing the PFD/CP to operate in a linear part of its transfer characteristic; while the CP circuit minimizes the current mismatch between the up and down currents by feedback. These circuit techniques are employed in the design of a 2.4-GHz ∆Σ fractional-N PLL. This chip has been fabricated in the TSMC 0.18-µm CMOS process. The experimental results demonstrate that the proposed techniques considerably improve the fractional-N PLL performance. This fully-integrated PLL dissipate 22 mW under a 1.8-V supply.

A compressão de dados é um dos factores que mais contribuiu para o grande crescimento das tecnologias da informação e da comunicação. Sem compressão, a maioria dos produtos tecnológicos de consumo e entretenimento, que são hoje banais, nunca teria chegado a existir, destacando-se, entre muitos outros, o DVD, as câmaras fotográficas digitais, os leitores de MP3, o YouTube e o streaming de vídeo, as redes sem fios e a televisão digital. De facto, as tecnologias de compressão multimédia permitem representar a informação de uma forma mais eficiente, reduzindo os grandes volumes de espaço de armazenamento que ocupa e, portanto, a largura de banda que consome para se transmitir nas redes e na Internet. Este livro tem como objectivo principal apresentar uma introdução fundamentada, clara, acessível e abrangente aos conceitos e tecnologias relacionadas com métodos, algoritmos e normas internacionais de compressão de informação multimédia. Ao longo do livro são abordados, entre outros, os seguintes temas: Conceitos e normas sobre compressão de informação multimédia, incluindo texto, imagens, áudio e vídeo; Entropia e algoritmos de compressão sem perdas: Shannon-Fano, Huffman, Aritmética e LZW; Psicoacústica, métodos e normas de compressão de áudio, incluindo voz (ADPCM, vocoders) e áudio de alta-fidelidade (transformadas, MP3, AAC, MP4 e Dolby AC-3); Teoria rate-distortion, métodos de compressão de imagem (DPCM, transformadas DCT, waveletet Haar, quantificadores lineares e não-lineares); Normas internacionais JPEG e JPEG2000; Compressão de vídeo, redundância espacial e temporal, quantificação de vídeo para aplicações multimédia e de videoconferência; Normas MPEG.

An efficient,and intuitive algorithm is presented for the design of vector quantizers based either on a known prohabitistic model or on a long training sequence of data. The basic properties of the algorithm are discussed mid demonstrated by examples. Quite general distoriion measures and long blocklengths are allowed, as exemplified by the design of parameter vector quantizers of tendiensional vectors arising in Linear Predictive Coded (LE) speech compression with a complicated distortion measure arisiig in LPC analysis that does not depend only on the error vector.

This paper presents the architecture and VHDL design of a Two Dimensional Discrete Cosine Transform (2D-DCT) with Quantization and zigzag arrangement. This architecture is used as the core and path in JPEG image compression hardware. The 2D- DCT calculation is made using the 2D- DCT Separability property, such that the whole architecture is divided into two 1D-DCT calculations by using a transpose buffer. Architecture for Quantization and zigzag process is also described in this paper. The quantization process is done using division operation. This design aimed to be implemented in Spartan-3E XC3S500 FPGA. The 2D- DCT architecture uses 1891 Slices, 51I/O pins, and 8 multipliers of one Xilinx Spartan-3E XC3S500E FPGA reaches an operating frequency of 101.35 MHz One input block with 8 x 8 elements of 8 bits each is processed in 6604 ns and pipeline latency is 140 clock cycles.

Burst transmission of digital data and voice has become commonplace, particularly in satellite communication systems employing time-division multiple-access (TDMA) and packet demand-assignment mnltiple-access (DAMA) techniques. In TDMA systems particularly, phase estimation on each successive burst is a requirement, while bit timing and carrier frequency can be accurately tracked between bursts. A class of nonlinear estimation algorithms is described to estimate the unknown phase of a carrier which is fully modulated by m-ary PSK modulation. Performance of the method is determined in closed form and compared to the Cramer-Rao lower bound for the variance of the estimation error in the phase of an unmodulated carrier. Results are also obtained when the carrier frequency is imprecisely known. Finally, the effect of quantization and finite read-only-memory (ROM) implementation of the nonlinearity are determined by computer simulation.

After a brief summary of the mathematical problems of the main stream quantum field
theory, a way out of this difficulties is presented. This proposal implies a revolution of
mathematics, i.e. the mathematics based on the quantum set theory of G. Takeuti and offers a new framework to understand the visible and invisible (dark) components of the Universe.

This paper provides a survey on modeling and theories of networked control systems (NCS). In the first part, modeling of the different types of imperfections that affect NCS is discussed. These imperfections are quantization errors, packet dropouts, variable sampling/transmission intervals, variable transmission delays, and communication constraints. Then follows in the second part a presentation of several theories that have been applied for controlling networked systems. These theories include: input delay system approach, Markovian system approach, switched system approach, stochastic system approach, impulsive system approach, and predictive control approach. In the last part, some advanced issues in NCS including decentralized and distributed NCS, cloud control system, and co-design of NCS are reviewed.

Geometry and physics have a long history of mutual interactions. Among those coming from quantum mechanics, the early “Weyl quantization” of the phase space observables paved the way for the understanding of some deep relations between Poisson geometry and quantum algebras. As two outgrowths, of prime importance in the last decades were the Moyal and Weyl products, respectively in formal and non-formal deformation quantization. The notion of a midpoint of two given points appears naturally in the Weyl quantization and product, suggesting to consider symplectic symmetric spaces with midpoint map.

A conjecture of Weinstein in this context relates the associativity of non-formal products of functions with the symplectic area of so-called “double triangles”. The aim of this thesis is to improve the understanding of the structure of solvable symplectic symmetric spaces and to provide the necessary tools for an inductive construction of quantizations of these spaces satisfying the above conjecture.

For a general symmetric space, we relate the existence of a midpoint map to the existence and uniqueness of geodesics joining two points, and characterize the symmetric spaces for which each triangle has a unique double triangle. We introduce symplectic reduction and double extension for symplectic symmetric spaces, and uncover a “primitive structure” canonically attached to any such space, allowing the construction of T-star extensions à la Bordemann. We then study the behaviour of the main ingredient in our proposed quantization procedure, the Severa projection, under the above-mentioned operations. We end the thesis by providing explicit computations for a new class of examples yielding in particular new universal deformation formulas for the actions of some symplectic Lie groups on Fréchet algebras.

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This are some notes on mathematical physics.

Contents:
- Introduction and basics in differential geometry
-Symplectic geometry
          -Symplectic vector space
          -Symplectic mfd
          -Symplectic structure of cotangent bundle
          -Symplectomorphism and canonical transformation
          -Darboux Theorem                                                               
-Newtonian Mechanics
          -Poisson brackets
          -Physical interpretation
        -Integrability                                             
        -Co-adjoint orbits                                         
-Poisson Manifold
        -Poisson fields
        -Poisson cohomology
        -Classical R-matrix
        -Lax Representation
-Deformation quantization (with Kontsevich's thm)

We study four dimensional N = 2 supersymmetric gauge theory in the Ωbackground with the two dimensional N = 2 super-Poincare invariance. We explain how this gauge theory provides the quantization of the classical integrable system underlying the moduli space of vacua of the ordinary four dimensional N = 2 theory. The ε-parameter of the Ω-background is identified with the Planck constant, the twisted chiral ring maps to quantum Hamiltonians, the supersymmetric vacua are identified with Bethe states of quantum integrable systems. This four dimensional gauge theory in its low energy description has two dimensional twisted superpotential which becomes the Yang-Yang function of the integrable system. We present the thermodynamic-Bethe-ansatz like formulae for these functions and for the spectra of commuting Hamiltonians following the direct computation in gauge theory. The general construction is illustrated at the examples of the many-body systems, such as the periodic Toda chain, the elliptic Calogero-Moser system, and their relativistic versions, for which we present a complete characterization of the L 2 -spectrum. We very briefly discuss the quantization of Hitchin system.

Formal deformation or rather symbolic calculus? To which extent do these approaches complete each other in the study of symmetry-preserving quantization procedures for homogeneous spaces? The representation theory of underlying Lie groups shows that the answer is much more delicate than initially thought and that it cannot be always reduced to asymptotic expansions with respect to some Planck's constant. The main goal of this survey is to give hints regarding the aims of each approach and, on the domain where these intersect, to compare the answers they lead to.