Dissertations / Theses on the topic 'Quantization'
To see the other types of publications on this topic, follow the link: Quantization.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Quantization.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Misra, Vinith. "Functional quantization." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/46021.
Full textAbstract:
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 119-121).
Data is rarely obtained for its own sake; oftentimes, it is a function of the data that we care about. Traditional data compression and quantization techniques, designed to recreate or approximate the data itself, gloss over this point. Are performance gains possible if source coding accounts for the user's function? How about when the encoders cannot themselves compute the function? We introduce the notion of functional quantization and use the tools of high-resolution analysis to get to the bottom of this question. Specifically, we consider real-valued raw data Xn/1 and scalar quantization of each component Xi of this data. First, under the constraints of fixed-rate quantization and variable-rate quantization, we obtain asymptotically optimal quantizer point densities and bit allocations. Introducing the notions of functional typicality and functional entropy, we then obtain asymptotically optimal block quantization schemes for each component. Next, we address the issue of non-monotonic functions by developing a model for high-resolution non-regular quantization. When these results are applied to several examples we observe striking improvements in performance.Finally, we answer three questions by means of the functional quantization framework: (1) Is there any benefit to allowing encoders to communicate with one another? (2) If transform coding is to be performed, how does a functional distortion measure influence the optimal transform? (3) What is the rate loss associated with a suboptimal quantizer design? In the process, we demonstrate how functional quantization can be a useful and intuitive alternative to more general information-theoretic techniques.
by Vinith Misra.
M.Eng.
2
Gardell, Fredrik. "Geometric Quantization." Thesis, Uppsala universitet, Teoretisk fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-296618.
Full textAbstract:
In this project we introduce the general idea of geometric quantization and demonstratehow to apply the process on a few examples. We discuss how to construct a line bundleover the symplectic manifold with Dirac’s quantization conditions and how to determine if we are able to quantize a system with the help of Weil’s integrability condition. To reducethe prequantum line bundle we employ real polarization such that the system does notbreak Heisenberg’s uncertainty principle anymore. From the prequantum bundle and thepolarization we construct the sought after Hilbert space.
3
Hedlund, William. "Geometric Quantization." Thesis, Uppsala universitet, Teoretisk fysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-325649.
Full textAbstract:
We formulate a process of quantization of classical mechanics, from a symplecticperspective. The Dirac quantization axioms are stated, and a satisfactory prequantizationmap is constructed using a complex line bundle. Using polarization, it isdetermined which prequantum states and observables can be fully quantized. Themathematical concepts of symplectic geometry, fibre bundles, and distributions are exposedto the degree to which they occur in the quantization process. Quantizationsof a cotangent bundle and a sphere are described, using real and K¨ahler polarizations,respectively.
4
Tangboondouangjit, Aram. "Sigma-Delta quantization number theoretic aspects of refining quantization error /." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3793.
Full textAbstract:
Thesis (Ph. D.) -- University of Maryland, College Park, 2006.Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
5
Li, Minyue. "Distribution Preserving Quantization." Doctoral thesis, KTH, Skolan för elektro- och systemteknik (EES), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-38482.
Full textAbstract:
In the lossy coding of perceptually relevant signals, such as sound and images, the ultimate goal is to achieve good perceived quality of the reconstructed signal, under a constraint on the bit-rate. Conventional methodologies focus either on a rate-distortion optimization or on the preservation of signal features. Technologies resulting from these two perspectives are efficient only for high-rate or low-rate scenarios. In this dissertation, a new objective is proposed: to seek the optimal rate-distortion trade-off under a constraint that statistical properties of the reconstruction are similar to those of the source. The new objective leads to a new quantization concept: distribution preserving quantization (DPQ). DPQ preserves the probability distribution of the source by stochastically switching among an ensemble of quantizers. At low rates, DPQ exhibits a synthesis nature, resembling existing coding methods that preserve signal features. Compared with rate-distortion optimized quantization, DPQ yields some rate-distortion performance for perceptual benefits. The rate-distortion optimization for DPQ facilitates mathematical analysis. The dissertation defines a distribution preserving rate-distortion function (DP-RDF), which serves as a lower bound on the rate of any DPQ method for a given distortion. For a large range of sources and distortion measures, the DP-RDF approaches the classic rate-distortion function with increasing rate. This suggests that, at high rates, an optimal DPQ can approach conventional quantization in terms of rate-distortion characteristics. After verifying the perceptual advantages of DPQ with a relatively simple realization, this dissertation focuses on a method called transformation-based DPQ, which is based on dithered quantization and a non-linear transformation. Asymptotically, with increasing dimensionality, a transformation-based DPQ achieves the DP-RDF for i.i.d. Gaussian sources and the mean squared error (MSE). This dissertation further proposes a DPQ scheme that asymptotically achieves the DP-RDF for stationary Gaussian processes and the MSE. For practical applications, this scheme can be reduced to dithered quantization with pre- and post-filtering. The simplified scheme preserves the power spectral density (PSD) of the source. The use of dithered quantization and non-linear transformations to construct DPQ is extended to multiple description coding, which leads to a multiple description DPQ (MD-DPQ) scheme. MD-DPQ preserves the source probability distribution for any packet loss scenario. The proposed schemes generally require efficient entropy coding. The dissertation also includes an entropy coding algorithm for lossy coding systems, which is referred to as sequential entropy coding of quantization indices with update recursion on probability (SECURE). The proposed lossy coding methods were subjected to evaluations in the context of audio coding. The experimental results confirm the benefits of the methods and, therewith, the effectiveness of the proposed new lossy coding objective.QC 20110829
6
Brown, Jonathan D. "N-Symplectic Quantization." NCSU, 2008. http://www.lib.ncsu.edu/theses/available/etd-02282008-135847/.
Full textAbstract:
A quantization scheme based on n-symplectic geometry is defined. Using this new definition a generalized Van Hove prequantization is given for the frame bundle of R^n, LR^n. The full set of operators of the generalized Van Hove prequantization is irreducible and essentially self adjoint. However, this prequantization is reducible when it is restricted to the Heisenberg algebra. Several full quantizations are also given for LR^n proving there is no Groenwold Van Hove type obstruction for quantizing LR^n. Using the covering theory of n-symplectic geometry we analyse why this quantization fails under symplectic quantization. Throughout the paper, emphasis is placed on comparison to the symplectic theory.
7
Matschkal, Bernd. "Spherical logarithmic quantization." Aachen Shaker, 2007. http://d-nb.info/988124009/04.
Full text
8
Dunne, G. V. "Methods of quantization." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47039.
Full text
9
Nazaikinskii, Vladimir E., Bert-Wolfgang Schulze, and Boris Sternin. "Quantization methods in differential equations : Chapter 2: Quantization of Lagrangian modules." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2558/.
Full textAbstract:
In this chapter we use the wave packet transform described in Chapter 1 to quantize extended classical states represented by so-called Lagrangian sumbanifolds of the phase space. Functions on a Lagrangian manifold form a module over the ring of classical Hamiltonian functions on the phase space (with respect to pointwise multiplication). The quantization procedure intertwines this multiplication with the action of the corresponding quantum Hamiltonians; hence we speak of quantization of Lagrangian modules. The semiclassical states obtained by this quantization procedure provide asymptotic solutions to differential equations with a small parameter. Locally, such solutions can be represented by WKB elements. Global solutions are given by
Maslov's canonical operator [2]; also see, e.g., [3] and the references therein. Here the canonical operator is obtained in the framework of the universal quantization procedure provided by the wave packet transform. This procedure was suggested in [4] (see also the references there) and further developed in [5]; our exposition is in the spirit of these papers. Some further bibliographical remarks can be found in the beginning of Chapter 1.
10
Polastri, Costanza. "Quantization of angular momentum." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14610/.
Full textAbstract:
La tesi tratta una breve esposizione della teoria del momento angolare, con particolare enfasi sui costrutti matematici che sono necessari a comprenderla.
Dapprima, nel Capitolo 1 si vede una panoramica dei concetti principali di geometria differenziale. Nel Capitolo 2 si approfondisce la teoria dei gruppi di Lie, con particolare attenzione alla mappa esponenziale e alle rappresentazioni matriciali dei gruppi SU(2) e
SO(3). Il Capitolo 3 è dedicato alla parte di fisica: si espongono i concetti di operatore e osservabile, dopodiche' si analizza il gruppo di Galileo di trasformazioni spazio-temporali e si usano le simmetrie dello spazio-tempo per ricavare l'operatore momento angolare.
11
Zhu, Sanguo. "Quantization for probability measures." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=979725658.
Full text
12
Cardinal, Jean. "Quantization with multple constraints." Doctoral thesis, Universite Libre de Bruxelles, 2001. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211618.
Full text
13
Pratt, Alan Edward. "Quantization of nonholonomic systems." Thesis, University of Bristol, 1996. http://hdl.handle.net/1983/71bd9b91-d990-443d-958f-691cf5763495.
Full text
14
Du, Toit Benjamin David. "Data Compression and Quantization." Diss., University of Pretoria, 2014. http://hdl.handle.net/2263/79233.
Full textAbstract:
Data Compression
Due to limitations in data storage and bandwidth, data of all types has often required compression. This need has spawned many different methods of compressing data. In certain situations the fidelity of the data can be compromised and unnecessary information can be discarded, while in other situations, the fidelity of the data is necessary for the data to be useful thereby requiring methods of reducing the data storage requirements without discarding any information.
The theory of data compression has received much attention over the past half century, with some of the most important work done by Claude E. Shannon in the 1940’s and 1950’s and at present topics such as Information and Coding Theory, which encompass a wide variety of sciences, continue to make headway into the interesting and highly applicable topic of data compression.
Quantization
Quantization is a broad notion used in several fields especially in the sciences, including signal processing, quantum physics, computer science, geometry, music and others. The concept of quantization is related to the idea of grouping, dividing or approximating some physical quantity by a set of small discrete measurements.
Data Quantization involves the discretization of data, or the approximation of large data sets by smaller data sets.
This mini dissertation is a research dissertation that considers how data, which is of a statistical nature, can be quantized and compressed.Dissertation (MSc)--University of Pretoria, 2014.
Statistics
MSc
Unrestricted
15
Englis, Miroslav, and englis@math cas cz. "Weighted Bergman Kernels and Quantization." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi932.ps.
Full text
16
Wannamaker, Robert Alexander. "The theory of dithered quantization." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq22246.pdf.
Full text
17
Kleeman, R. "Generalized quantization and colour algebras /." Title page, table of contents and abstract only, 1985. http://web4.library.adelaide.edu.au/theses/09PH/09phk635.pdf.
Full text
18
Saab, Rayan. "Compressed sensing : decoding and quantization." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/24696.
Full textAbstract:
Recently, great strides in sparse approximation theory and its application have been made. Many of these developments were spurred by the emerging area of compressed sensing. Compressed sensing is a signal acquisition paradigm that entails recovering estimates of sparse and compressible signals from n linear measurements, many fewer than the signal ambient dimension N. In general, these measurements are assumed to be imperfect. For example, they may be noisy or quantized (or both). Thus, the associated sparse recovery problem requires the existence of stable and robust “decoders” to reconstruct the signal. In this thesis, we first address the theoretical properties of ∆p, a class of compressed sensing decoders that rely on ℓp minimization with p ∈ (0, 1). In particular, we extend the known results regarding the decoder ∆₁, based on ℓ₁ minimization, to ∆p with p ∈ (0, 1). Our results are two-fold. We show that under sufficient conditions that are weaker than the analogous sufficient conditions for ∆₁, the decoders ∆p are robust to noise and stable. In particular, they are (2, p) instance optimal. We also show that, like ∆₁, the decoders ∆p are (2, 2) instance optimal in probability provided the measurement matrix is drawn from an appropriate distribution. Second, we address quantization of compressed sensing measurements. Typically, the most commonly assumed approach (called PCM) entails quantizing each measurement independently, using a quantization alphabet with step-size d. Subsequently, by using a stable and robust decoder one can guarantee that the estimate produced by the decoder is within O(d) of the signal. As a more effective alternative, we propose using sigma-delta schemes to quantize compressed sensing measurements of a k-sparse signal. We show that there is an associated two-stage recovery method which guarantees a reduction of the approximation error by a factor of (n/k){α(r−¹/²)}, for any α < 1 if n ≳ k(log N)¹{¹−α)} (with high probability on the initial draw of the measurement matrix). In particular, the first recovery stage employs a stable decoder to estimate the support of the signal, while the second stage employs Sobolev dual frames to approximate the signal.
19
Khan, Mohammad Asmat Ullah. "Trellis-coded residual vector quantization." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/13734.
Full text
20
Robson, Mark Andrew. "Geometric quantization of constrained systems." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.363252.
Full text
21
Pötzelberger, Klaus. "The Quantization Dimension of Distributions." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/1430/1/document.pdf.
Full textAbstract:
We show that the asymptotic behavior of the quantization error allows the definition of dimensions for probability distributions, the upper and the lower quantization dimension. These concepts fit into standard geometric measure theory, as the upper quantization dimension is always between the packing and the upper box-counting dimension, whereas the lower quantization dimension is between the Hausdorff and the lower box-counting dimension. (author's abstract)Series: Forschungsberichte / Institut für Statistik
22
Ali, Khan Syed Irteza. "Classification using residual vector quantization." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50300.
Full textAbstract:
Residual vector quantization (RVQ) is a 1-nearest neighbor (1-NN) type of technique. RVQ is a multi-stage implementation of regular vector quantization. An input is successively quantized to the nearest codevector in each stage codebook. In classification, nearest neighbor techniques are very attractive since these techniques very accurately model the ideal Bayes class boundaries. However, nearest neighbor classification techniques require a large size of representative dataset. Since in such techniques a test input is assigned a class membership after an exhaustive search the entire training set, a reasonably large training set can make the implementation cost of the nearest neighbor classifier unfeasibly costly. Although, the k-d tree structure offers a far more efficient implementation of 1-NN search, however, the cost of storing the data points can become prohibitive, especially in higher dimensionality.
RVQ also offers a nice solution to a cost-effective implementation of 1-NN-based classification. Because of the direct-sum structure of the RVQ codebook, the memory and computational of cost 1-NN-based system is greatly reduced. Although, as compared to an equivalent 1-NN system, the multi-stage implementation of the RVQ codebook compromises the accuracy of the class boundaries, yet the classification error has been empirically shown to be within 3% to 4% of the performance of an equivalent 1-NN-based classifier.
23
Lares, Santos Asin. "Deformation quantization on poisson manifolds." Thesis, University of Warwick, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340626.
Full text
24
Mihov, Diko. "Quantization of nilpotent coadjoint orbits." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38410.
Full text
25
Kravchenko, Olga. "Deformation quantization of symplectic fibrations." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38405.
Full text
26
Platts, Alexander. "Functional quantization-based stratified sampling." Master's thesis, University of Cape Town, 2017. http://hdl.handle.net/11427/27105.
Full textAbstract:
Functional quantization-based stratified sampling is a method for variance reduction proposed by Corlay and Pagès (2015). This method requires the ability to both create functional quantizers and to sample Brownian paths from the strata defined by the quantizers. We show that product quantizers are a suitable approximation of an optimal quantizer for the formation of functional quantizers. The notion of functional stratification is then extended to options written on multiple stocks and American options priced using the Longstaff-Schwartz method. To illustrate the gains in performance we focus on geometric brownian motion (GBM), constant elasticity of variance (CEV) and constant elasticity of variance with stochastic volatility (CEV-SV) models. The pricing algorithm is used to price knock-in, knockout, autocall, call on the max and path dependent call on the max options.
27
Lunin, Oleg. "Supersymmetry and light cone quantization /." The Ohio State University, 2000. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488202171197003.
Full text
28
Lindsay, Larry J. "Quantization Dimension for Probability Definitions." Thesis, University of North Texas, 2001. https://digital.library.unt.edu/ark:/67531/metadc3008/.
Full textAbstract:
The term quantization refers to the process of estimating a given probability by a discrete probability supported on a finite set. The quantization dimension Dr of a probability is related to the asymptotic rate at which the expected distance (raised to the rth power) to the support of the quantized version of the probability goes to zero as the size of the support is allowed to go to infinity. This assumes that the quantized versions are in some sense ``optimal'' in that the expected distances have been minimized. In this dissertation we give a short history of quantization as well as some basic facts. We develop a generalized framework for the quantization dimension which extends the current theory to include a wider range of probability measures. This framework uses the theory of thermodynamic formalism and the multifractal spectrum. It is shown that at least in certain cases the quantization dimension function D(r)=Dr is a transform of the temperature function b(q), which is already known to be the Legendre transform of the multifractal spectrum f(a). Hence, these ideas are all closely related and it would be expected that progress in one area could lead to new results in another. It would also be expected that the results in this dissertation would extend to all probabilities for which a quantization dimension function exists. The cases considered here include probabilities generated by conformal iterated function systems (and include self-similar probabilities) and also probabilities generated by graph directed systems, which further generalize the idea of an iterated function system.
29
Lin, Yuzhang, and Yuzhang Lin. "Measurement Quantization in Compressive Imaging." Thesis, The University of Arizona, 2016. http://hdl.handle.net/10150/622858.
Full textAbstract:
In compressive imaging the measurement quantization and its impact on the overall system performance is an important problem. This work considers several challenges that derive from quantization of compressive measurements. We investigate the design of scalar quantizer (SQ), vector quantizer (VQ), and tree-structured vector quantizer (TSVQ) for information-optimal compressive imaging. The performance of these quantizer designs is quantified for a variety of compression rates and measurement signal-to-noise-ratio (SNR) using simulation studies. Our simulation results show that in the low SNR regime a low bit-depth (3 bit per measurement) SQ is sufficient to minimize the degradation due to measurement quantization. However, in mid-to-high SNR regime, quantizer design requires higher bit-depth to preserve the information in the measurements. Simulation results also confirm the superior performance of VQ over SQ. As expected, TSVQ provides a good tradeoff between complexity and performance, bounded by VQ and SQ designs on either side of performance/complexity limits. In compressive image the size of final measurement data (i.e. in bits) is also an important system design metric. In this work, we also optimize the compressive imaging system using this design metric, and investigate how to optimally allocate the number of measurement and bits per measurement, i.e. the rate allocation problem. This problem is solved using both an empirical data driven approach and a model-based approach. As a function of compression rate (bits per pixel), our simulation results show that compressive imaging can outperform traditional (non-compressive) imaging followed by image compression (JPEG 2000) in low-to-mid SNR regime. However, in high SNR regime traditional imaging (with image compression) offers a higher image fidelity compare to compressive imaging for a given data rate. Compressive imaging using blockwise measurements is partly limited due to its inability to perform global rate allocation. We also develop an optimal minimum mean-square error (MMSE) reconstruction algorithm for quantized compressed measurements. The algorithm employs Monte-Carlo Markov Chain (MCMC) sampling technique to estimate the posterior mean. Simulation results show significant improvement over approximate MMSE algorithms.
30
Maeser, Anna Marie. "Time-frequency dual and quantization." View electronic thesis (PDF), 2009. http://dl.uncw.edu/etd/2009-1/maesera/annamaeser.pdf.
Full text
31
Panchapakesan, Kannan. "Image processing through vector quantization." Diss., The University of Arizona, 2000. http://hdl.handle.net/10150/289118.
Full textAbstract:
Vector quantization (VQ) is an established data compression technique. It has been successfully used to compress signals such as speech, imagery, and video. In recent years, it has been employed to perform various image processing tasks such as edge detection, classification, and volume rendering. The advantage of using VQ depends on the specific task but usually includes memory gain, computational gain, or the inherent compression it offers. Nonlinear interpolative vector quantization (NLIVQ) was introduced as an approach to overcome the curse of dimensionality incurred by an unconstrained, exhaustive-search VQ, especially, at high rates. In this dissertation, it is modified to accomplish specific image processing tasks. VQ-based techniques are introduced to achieve the following image processing tasks. (1) Blur identification: VQ encoder distortion is used to identify image blur. The blur is estimated by choosing from a finite set of candidate blur functions. A VQ codebook is trained on images corresponding to each candidate blur. The blur in an image is then identified by choosing from the candidates, the one corresponding to the codebook that provides the lowest encoder distortion. (2) Superresolution: Images obtained through a diffraction-limited optical system do not possess any information beyond a certain cut-off frequency and are therefore limited in their resolution. Superresolution refers to the endeavor of improving the resolution of such images. Superresolution is achieved through an NLIVQ trained on pairs of original and blurred images. (3) Joint compression and restoration: Combining compression and restoration in one step is useful from the standpoints of memory and computing needs. An NLIVQ is suggested for this purpose that performs the restoration entirely in the wavelet transform domain. The training set for VQ design consists of pairs of original and blurred images. (4) Combined compression and denoising: Compression of a noisy source is a classic problem that involves the combined efforts of compression and denoising (estimation). A robust NLIVQ technique is presented that first identifies the variance of the noise in an image and subsequently performs simultaneous compression and denoising.
32
Rivezzi, Andrea. "Lie bialgebras and Etingof-Kazhdan quantization." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21784/.
Full textAbstract:
In questa tesi viene presentata la soluzione data da Pavel Etingof e David Kazhdan al problema della quantizzazione delle bialgebre di Lie, formulato da Vladimir Drinfeld nel 1992.
Il problema consiste nel trovare un funtore che, data una bialgebra di Lie, costruisca una algebra di Hopf che la quantizzi.
Nel primo capitolo vengono presentati gli aspetti di teoria delle categorie necessarie per la lettura.
Nel secondo capitolo, introduciamo le nozioni di algebra, coalgebra, bialgebra e algebra di Hopf, con particolare attenzione alla loro teoria delle rappresentazioni.
Nel terzo capitolo, presentiamo le nozioni base della teoria delle algebre di Lie, per poi definire le nozioni di coalgebra di Lie e di bialgebra di Lie. Vengono quindi definite le triple di Manin e il doppio di Drinfeld di una bialgebra di Lie.
Nel quarto capitolo definiamo la nozione di quantizzazione di una bialgebra di Lie, e presentiamo i quantum groups di Drinfeld e Jimbo, che ne sono un esempio nel caso delle algebre di Kac-Moody simmetrizzabili.
Infine, nel quinto ed ultimo capitolo presentiamo la costruzione della quantizzazione di Etingof e Kazhdan. Tale tecnica di quantizzazione si suddivide in diversi passi, ed è basata sulla dualità di Tannaka-Krein. In un primo momento, analizziamo il caso in cui la bialgebra di Lie è di dimensione finita. In seguito, adattiamo la costruzione del caso finito dimensionale al caso infinito dimensionale.
33
Basu, Sayandeb. "Perturbation theory in covariant canonical quantization /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2005. http://uclibs.org/PID/11984.
Full text
34
Aslam, Salman Muhammad. "Target tracking using residual vector quantization." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42883.
Full textAbstract:
In this work, our goal is to track visual targets using residual vector quantization (RVQ). We compare our results with principal components analysis (PCA) and tree structured vector quantization (TSVQ) based tracking.
This work is significant since PCA is commonly used in the Pattern Recognition, Machine Learning and Computer Vision communities. On the other hand, TSVQ is commonly used in the Signal Processing and data compression communities. RVQ with more than two stages has not received much attention due to the difficulty in producing stable designs. In this work, we bring together these different approaches into an integrated tracking framework and show that RVQ tracking performs best according to multiple criteria on publicly available datasets. Moreover, an advantage of our approach is a learning-based tracker that builds the target model while it tracks, thus avoiding the costly step of building target models prior to tracking.
35
Fedosov, Boris. "Non-Abelian reduction in deformation quantization." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2510/.
Full textAbstract:
We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B. In other words, we show that the reduction commutes with the canonical G-invariant
deformation quantization. A similar statement in the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now completely proved).
36
Nazaikinskii, Vladimir, Bert-Wolfgang Schulze, and Boris Sternin. "Quantization and the wave packet transform." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2544/.
Full text
37
Fedosov, Boris. "Pseudo-differential operators and deformation quantization." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2565/.
Full textAbstract:
Using the Riemannian connection on a compact manifold X, we show that the algebra of classical pseudo-differential operators on X generates a canonical deformation quantization on the cotangent manifold T*X. The corresponding Abelian connection is calculated explicitly in terms of the of the exponential mapping. We prove also that the index theorem for elliptic operators may be obtained as a consequence of the index theorem for deformation quantization.
38
Schiefele, Jürgen. "Casimir-Polder interaction in second quantization." Phd thesis, Universität Potsdam, 2011. http://opus.kobv.de/ubp/volltexte/2011/5417/.
Full textAbstract:
The Casimir-Polder interaction between a single neutral atom and a nearby surface, arising from the (quantum and thermal) fluctuations of the electromagnetic field, is a cornerstone of cavity quantum electrodynamics (cQED), and theoretically well established. Recently, Bose-Einstein condensates (BECs) of ultracold atoms have been used to test the predictions of cQED. The purpose of the present thesis is to upgrade single-atom cQED with the many-body theory needed to describe trapped atomic BECs. Tools and methods are developed in a second-quantized picture that treats atom and photon fields on the same footing. We formulate a diagrammatic expansion using correlation functions for both the electromagnetic field and the atomic system.
The formalism is applied to investigate, for BECs trapped near surfaces, dispersion interactions of the van der Waals-Casimir-Polder type, and the Bosonic stimulation in spontaneous decay of excited atomic states. We also discuss a phononic Casimir effect, which arises from the quantum fluctuations in
an interacting BEC.Die durch (quantenmechanische und thermische) Fluktuationen des elektromagnetischen Feldes hervorgerufene Casimir-Polder-Wechselwirkung zwischen einem elektrisch neutralen Atom und einer benachbarten Oberfläche stellt einen theoretisch gut untersuchten Aspekt der Resonator-Quantenelektrodynamik (cavity quantum electrodynamics, cQED) dar. Seit kurzem werden atomare Bose-Einstein-Kondensate (BECs) verwendet, um die theoretischen Vorhersagen der cQED zu überprüfen. Das Ziel der vorliegenden Arbeit ist es, die bestehende cQED Theorie für einzelne Atome mit den Techniken der Vielteilchenphysik zur Beschreibung von BECs zu verbinden. Es werden Werkzeuge und Methoden entwickelt, um sowohl Photon- als auch Atom-Felder gleichwertig in zweiter Quantisierung zu beschreiben. Wir formulieren eine diagrammatische Störungstheorie, die Korrelationsfunktionen des elektromagnetischen Feldes und des Atomsystems benutzt. Der Formalismus wird anschließend verwendet, um für in Fallen nahe einer Oberfläche gehaltene BECs Atom-Oberflächen-Wechselwirkungen vom Casimir-Polder-Typ und die bosonische Stimulation des spontanen Zerfalls angeregter Atome zu untersuchen. Außerdem untersuchen wir einen phononischen Casimir-Effekt, der durch die quantenmechanischen Fluktuationen in einem wechselwirkenden BEC entsteht.
39
Charlier, Isabelle. "Conditional quantile estimation through optimal quantization." Thesis, Universite Libre de Bruxelles, 2015. http://www.theses.fr/2015BORD0274/document.
Full textAbstract:
Les applications les plus courantes des méthodes non paramétriques concernent l’estimation d’une fonction de régression (i.e. de l’espérance conditionnelle). Cependant, il est souvent intéressant de modéliser les quantiles conditionnels, en particulier lorsque la moyenne conditionnelle ne permet pas de représenter convenablement l’impact des covariables sur la variable dépendante. De plus, ils permettent d’obtenir des graphiques plus compréhensibles de la distribution conditionnelle de la variable dépendante que ceux obtenus avec la moyenne conditionnelle. À l’origine, la « quantification » était utilisée en ingénierie du signal et de l’information. Elle permet de discrétiser un signal continu en un nombre fini de quantifieurs. En mathématique, le problème de la quantification optimale consiste à trouver la meilleure approximation d’une distribution continue d’une variable aléatoire par une loi discrète avec un nombre fixé de quantifieurs. Initialement utilisée pour des signaux univariés, la méthode a été étendue au cadre multivarié et est devenue un outil pour résoudre certains problèmes en probabilités numériques. Le but de cette thèse est d’appliquer la quantification optimale en norme Lp à l’estimation des quantiles conditionnels. Différents cas sont abordés : covariable uni- ou multidimensionnelle, variable dépendante uni- ou multivariée. La convergence des estimateurs proposés est étudiée d’un point de vue théorique. Ces estimateurs ont été implémentés et un package R, nommé QuantifQuantile, a été développé. Leur comportement numérique est évalué sur des simulations et des données réellesOne of the most common applications of nonparametric techniques has been the estimation of a regression function (i.e. a conditional mean). However it is often of interest to model conditional quantiles, particularly when it is felt that the conditional mean is not representative of the impact of the covariates on the dependent variable. Moreover, the quantile regression function provides a much more comprehensive picture of the conditional distribution of a dependent variable than the conditional mean function. Originally, the “quantization” was used in signal and information theories since the fifties. Quantization was devoted to the discretization of a continuous signal by a finite number of “quantizers”. In mathematics, the problem of optimal quantization is to find the best approximation of the continuous distribution of a random variable by a discrete law with a fixed number of charged points. Firstly used for a one-dimensional signal, the method has then been developed in the multi-dimensional case and extensively used as a tool to solve problems arising in numerical probability. The goal of this thesis is to study how to apply optimal quantization in Lp-norm to conditional quantile estimation. Various cases are studied: one-dimensional or multidimensional covariate, univariate or multivariate dependent variable. The convergence of the proposed estimators is studied from a theoretical point of view. The proposed estimators were implemented and a R package, called QuantifQuantile, was developed. Numerical behavior of the estimators is evaluated through simulation studies and real data applications
40
Ramirez, Daniel Alonso. "Semiclassical quantization and classical chaotic systems." Doctoral thesis, Universite Libre de Bruxelles, 1995. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212531.
Full text
41
Posthuma, Hessel Bouke. "Quantization of Hamiltonian loop group actions." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2003. http://dare.uva.nl/document/70151.
Full text
42
Matschkal, Bernd. "Spherical logarithmic quantization = Sphärisch logarithmische Quantisierung /." Aachen : Shaker, 2008. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=016432314&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
Full text
43
Ayaz, Ulaş. "Sigma-delta quantization and Sturmian words." Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/14203.
Full textAbstract:
In this thesis, our main focus is Sigma-Delta quantization schemes. These are commonly used in state-of-art Analog-to-digital conversion technology. Their main advantage is the ease of implementation and more importantly their insensitivity to certain circuit imperfections. When we compare sigma-delta scheme with pulse-code modulation (PCM), sigma-delta is inferior in
terms of rate distortion because an N-bit kth order sigma-delta quantizer produces an approximation with the error of order O(N-k) whereas the corresponding N-bit PCM scheme has accuracy of O(2−N)). However, this is a raw estimate of the actual rate-distortion characteristic of sigma-delta as one can further compress the bitstreams obtained via sigma-delta quantization. Even though this observation was made earlier in [10] under certain assumptions, to our knowledge, it was not investigated fully. In this thesis,
such an investigation is made for first-order sigma-delta quantizers by using some results from symbolic dynamics literature on “Sturmian words”. Surprisingly, it turns out that the approximation error is a function of the
“actual bit-rate”, i.e., the bit-rate after compressing an N-bit first-order sigma-delta encoding.
In addition, in this thesis, we will introduce a new setup for sampling a bandlimited function and then quantizing these samples via first-order sigma-delta scheme. This simple but surprisingly efficient technique will allow us to get a better bound for the approximation rate of sigma-delta schemes and it will allow us to apply the derived results for compression of
the bitstreams.
44
Al-Yatama, Anwar. "Quantization and routing in broadband networks." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/15374.
Full text
45
Quesnel, Ronny. "Image compression using subjective vector quantization." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60714.
Full textAbstract:
The goal of this research is to improve the subjective quality of real world imagery encoded with spatial vector quantization (VQ). Improved subjective quality implies that a human perceives less visually objectionable distortion when looking at the coded images. Through study of several basic VQ schemes, the issues fundamental to achieving good subjective quality are uncovered and addressed in this work. Vector quantization is very good at reproducing quasi-uniform textures in an image, but has difficulty in reproducing abrupt changes in textures (edges) and fine detail and can cause a block effect which is subjectively annoying. A second generation coding scheme is developed which takes certain properties of the human visual system into account. A promising method which is developed utilizes omniscient finite state VQ, a new quadratic distortion measure which penalizes the misrepresentation of edges, and brightness compensation based on Steven's power law. The proposed subjective VQ is compared with several classical, first generation VQ methods.
46
Bowes, David. "Weyl quantization, reduction, and star products." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358585.
Full text
47
Goatcher, J. K. "Adaptive speech recognition using vector quantization." Thesis, Swansea University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.637065.
Full textAbstract:
Adaptation to the voice characteristics of different people is performed automatically by human listeners. If a machine is to achieve the performance approaching that of a human then it too must adapt to the individual talker. One such adaptation scheme is proposed and investigated in this thesis. A review of template-based speech recognition systems is presented. The spectral estimation technique of LPC and vector quantization are examined in some detail. The development of a speech recognition system is described including performance measurements and comparisons with other published results. The effect of vector quantization upon the system's performance is presented for a range of vector codebook sizes from 2 to 128. The hardware for the generation of a database of speech utterances is described. This database is used for all recognition and adaptation experiments and consists of the numeric and alpha-numeric vocabulary sets along with two phonetically representative sentences. The proposed adaptation scheme is based upon the assumption that a mapping may be made from the codebook entries of speaker-independent templates to the codebook entries of a particular speaker. A conventional dynamic time warping algorithm gives a trace of the correspondence between the codebook entries of a particular speaker and the speaker-independent templates. A map is created with the scores of this matching process and characterises the differences. These maps improve the performance of the speaker-independent templates, an error rate of 7.5% is reduced to 2.2% for the numeric vocabulary and from 28.4% to 19.2% for the alpha-numeric vocabulary. A number of variations on the method for generating the maps are presented. The most succesful of which is the simplest, using the whole vocabulary to form the maps.
48
Sampson, Demetrios G. "Lattice vector quantization for image coding." Thesis, University of Essex, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282525.
Full text
49
Sun, John Zheng. "Quantization in acquisition and computation networks." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/82366.
Full textAbstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 151-165).
In modern systems, it is often desirable to extract relevant information from large amounts of data collected at different spatial locations. Applications include sensor networks, wearable health-monitoring devices and a variety of other systems for inference. Several existing source coding techniques, such as Slepian-Wolf and Wyner-Ziv coding, achieve asymptotic compression optimality in distributed systems. However, these techniques are rarely used in sensor networks because of decoding complexity and prohibitively long code length. Moreover, the fundamental limits that arise from existing techniques are intractable to describe for a complicated network topology or when the objective of the system is to perform some computation on the data rather than to reproduce the data. This thesis bridges the technological gap between the needs of real-world systems and the optimistic bounds derived from asymptotic analysis. Specifically, we characterize fundamental trade-offs when the desired computation is incorporated into the compression design and the code length is one. To obtain both performance guarantees and achievable schemes, we use high-resolution quantization theory, which is complementary to the Shannon-theoretic analyses previously used to study distributed systems. We account for varied network topologies, such as those where sensors are allowed to collaborate or the communication links are heterogeneous. In these settings, a small amount of intersensor communication can provide a significant improvement in compression performance. As a result, this work suggests new compression principles and network design for modern distributed systems. Although the ideas in the thesis are motivated by current and future sensor network implementations, the framework applies to a wide range of signal processing questions. We draw connections between the fidelity criteria studied in the thesis and distortion measures used in perceptual coding. As a consequence, we determine the optimal quantizer for expected relative error (ERE), a measure that is widely useful but is often neglected in the source coding community. We further demonstrate that applying the ERE criterion to psychophysical models can explain the Weber-Fechner law, a longstanding hypothesis of how humans perceive the external world. Our results are consistent with the hypothesis that human perception is Bayesian optimal for information acquisition conditioned on limited cognitive resources, thereby supporting the notion that the brain is efficient at acquisition and adaptation.
by John Z. Sun.
Ph.D.
50
Boufounos, Petros T. 1977. "Quantization and erasures in frame representations." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/35288.
Full textAbstract:
Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 123-126).
Frame representations, which correspond to overcomplete generalizations to basis expansions, are often used in signal processing to provide robustness to errors. In this thesis robustness is provided through the use of projections to compensate for errors in the representation coefficients, with specific focus on quantization and erasure errors. The projections are implemented by modifying the unaffected coefficients using an additive term, which is linear in the error. This low-complexity implementation only assumes linear reconstruction using a pre-determined synthesis frame, and makes no assumption on how the representation coefficients are generated. In the context of quantization, the limits of scalar quantization of frame representations are first examined, assuming the analysis is using inner products with the frame vectors. Bounds on the error and the bit-efficiency are derived, demonstrating that scalar quantization of the coefficients is suboptimal. As an alternative to scalar quantization, a generalization of Sigma-Delta noise shaping to arbitrary frame representations is developed by reformulating noise shaping as a sequence of compensations for the quantization error using projections.
(cont.) The total error is quantified using both the additive noise model of quantization, and a deterministic upper bound based on the triangle inequality. It is thus shown that the average and the worst-case error is reduced compared to scalar quantization of the coefficients. The projection principle is also used to provide robustness to erasures. Specifically, the case of a transmitter that is aware of the erasure occurrence is considered, which compensates for the erasure error by projecting it to the subsequent frame vectors. It is further demonstrated that the transmitter can be split to a transmitter/receiver combination that performs the same compensation, but in which only the receiver is aware of the erasure occurrence. Furthermore, an algorithm to puncture dense representations in order to produce sparse approximate ones is introduced. In this algorithm the error due to the puncturing is also projected to the span of the remaining coefficients. The algorithm can be combined with quantization to produce quantized sparse representations approximating the original dense representation.
by Petros T. Boufounos.
Sc.D.