A 2D DWT architecture suitable for the Embedded Zerotree Wavelet Algorithm

Digital Imaging has had an enormous impact on industrial applications such as the Internet and video-phone systems. However, demand for industrial applications is growing enormously. In particular, internet application users are, growing at a near exponential rate. The sharp increase in applications using digital images has caused much emphasis on the fields of image coding, storage, processing and communications. New techniques are continuously developed with the main aim of increasing efficiency. Image coding is in particular a field of great commercial interest. A digital image requires a large amount of data to be created. This large amount of data causes many problems when storing, transmitting or processing the image. Reducing the amount of data that can be used to represent an image is the main objective of image coding. Since the main objective is to reduce the amount of data that represents an image, various techniques have been developed and are continuously developed to increase efficiency. The JPEG image coding standard has enjoyed widespread acceptance, and the industry continues to explore its various implementation issues. However, recent research indicates multiresolution based image coding is a far superior alternative. A recent development in the field of image coding is the use of Embedded Zerotree Wavelet (EZW) as the technique to achieve image compression. One of The aims of this theses is to explain how this technique is superior to other current coding standards. It will be seen that an essential part orthis method of image coding is the use of multi resolution analysis, a subband system whereby the subbands arc logarithmically spaced in frequency and represent an octave band decomposition. The block structure that implements this function is termed the two dimensional Discrete Wavelet Transform (2D-DWT). The 20 DWT is achieved by several architectures and these are analysed in order to choose the best suitable architecture for the EZW coder. Finally, this architecture is implemented and verified using the Synopsys Behavioural Compiler and recommendations are made based on experimental findings

Phenomenology of the Standard Model, and beyond, at high-energy colliders

I review planned searches for the so far unobserved Higgs boson of the Standard Model of High Energy Physics. In particular a light 'intermediate' mass Higgs with mass in the range 80 GeV ≤ M(_H) ≤130 GeV will be hard to detect. I suggest several methods at planned future high energy particle colliders for observing this Higgs boson. At LEP I we have reasonable numbers of Higgs produced in association with a Z boson up to the limit imposed by phase space M(_H) ˂ √s - 100 GeV. Unfortunately if the Higgs is degenerate in mass with the Z boson we have large numbers of background events from double Z production. I investigate possible methods round this background. Firstly in polarizing the initial e+e- beams, and secondly in studying the differing topologies of the ZH signal, and ZZ background events. Moving on to the hadron super colliders the LHC and the SSC. These colliders typically produce very clean signals for 'heavy' Higgs. However for a light "'intermediate* mass Higgs all Higgs decays are either dominated by huge QCD backgrounds; or put very strong constraints upon our experimental apparatus. I investigate the signals and backgrounds for an alternative approach where rather than looking for the Higgs in isolation, we look for it produced in association with other heavy particles. Despite these production mechanisms having a far lower rate than isolated Higgs production they have far better signal to background ratios, which makes them look promising. Two modes in particular appear to give encouraging signals; WH production, and tiH production. Both these production modes can be detected in the isolated lepton and two photon channel

B Physics

I introduce and define Quantum Chromodynamics. I describe various well-known nonperturbative techniques for calculating quantities from the theory and discuss their merits and deficiencies. I then motivate and define a non-relativistic formulation (NRQCD) of the theory. I discuss the mechanics of the extraction of numbers from numerical simulations, and present general arguments as to the expected form of these data. I present results and details of their extraction from simulations of heavy-heavy and heavy-light mesons using NRQCD. I compare these results with those from other calculations and with experimental data, where they exist. I make suggestions for further work. An appendix contains details of the code used in the simulation together with the input parameters of the simulation

Feature Extraction Methods for Character Recognition

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The combinatorics of adinkras

Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 67-69).Adinkras are graphical tools created to study representations of supersymmetry algebras. Besides having inherent interest for physicists, the study of adinkras has already shown nontrivial connections with coding theory and Clifford algebras. Furthermore, adinkras offer many easy-to-state and accessible mathematical problems of algebraic, combinatorial, and computational nature. In this work, we make a self-contained treatment of the mathematical foundations of adinkras that slightly generalizes the existing literature. Then, we make new connections to other areas including homological algebra, theory of polytopes, Pfaffian orientations, graph coloring, and poset theory. Selected results include the enumeration of odd dashings for all adinkraizable chromotopologies, the notion of Stiefel-Whitney classes for codes and their vanishing conditions, and the enumeration of all Hamming cube adinkras up through dimension 5.by Yan Zhang.Ph.D

Meson distribution amplitudes: applications to weak radiative B decays and в transition form factors

This thesis examines the applications and determinations of meson light-cone distribution amplitudes, which enter the theoretical description of exclusive processes at large moment urn transfer. The investigation of such processes, in the context of в physics, provides one with a rich and extensive way of determining the Standard Model parameters of the CKM matrix, which are essential in describing CP violation, and searching for tell-tale signs of new physics beyond the Standard Model. We investigate the twist-2 and twist-3 distribution amplitudes of vector mesons and fully examine SU(3)(_F)-breaking effects and include leading G-parity violating terms. We use the conformal expansion allowing the distribution amplitudes to be described by a set of non-perturbative hadronic parameters which is reduced by invoking the QCD equation of motion to find various interrelations between the distribution amplitudes. Numerical values of the leading non-perturbative hadronie parameters are determined from QCD sum rules. The new distribution amplitude results find direct application in the radiative B decays to light vector mesons B → Vγ. We examine the phenomenologically most important observables in this decay mode using the formalism of QCD factorisation in which the distribution amplitudes play a vital role. We also include long-distance photon emission and soft quark loop effects, which formally lie outside the QCD factorisation formalism. The analysis encompasses all the relevant modes, that is B(_u),(_d)→(_p),(_w),K* and B(_s) → φ,K*.We also calculate the B → n(^1) transition form factor using QCD sum rules on the light- cone. The method relies on the collinear factorisation of the QCD dynamics into a pertur- batively calculable hard-scattering kernel and the non-perturbative universal distribution amplitudes. We include the singlet contribution originating from the U(1)a anomaly and bring the calculation consistently within the n-n(^1) mixing framework

Limit linear series in positive characteristic and Frobenius-unstable vector bundles on curves

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.Includes bibliographical references (p. 243-248).(cont.) yield a new proof of a result of Mochizuki yield a new proof of a result of Mochizuki Frobenius-unstable bundles for C general, and hence obtaining a self-contained proof of the resulting formula for the degree of V₂.Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of self-maps of P¹ with ramification to order e[sub]i at general points P[sub]i the case that all e[sub]i are less than the characteristic. We also develop a new, more functorial construction for the basic theory of limit linear series, which works transparently in positive and mixed characteristics, yielding a result on lifting linear series from characteristic p to characteristic 0, and even showing promise for generalization to higher-dimensional varieties. Now, let C be a curve of genus 2 over a field k of positive characteristic, and V₂ the Verschiebung rational map induced by pullback under Frobenius on moduli spaces of semistable vector bundles of rank two and trivial determinant. We show that if the Frobenius-unstable vector bundles are deformation-free in a suitable sense, then they are precisely the undefined points of V₂, and may each be resolved by a single blow-up; in this setting, we are able to calculate the degree of V₂ in terms of the number of Frobenius-unstable bundles, and describe the image of the exceptional divisors. We finally examine the Frobenius-unstable bundles on C by studying connections with vanishing p-curvature on certain unstable bundles on C. Using explicit formulas for p-curvature, we completely describe the Frobenius-unstable bundles in characteristics 3, 5, 7. We classify logarithmic connections with vanishing p-curvature on vector bundles of rank 2 on P¹ in terms of self-maps of P¹ with prescribed ramification. Using our knowledge of such maps, we then glue the connections to a nodal curve and deform to a smooth curve toby Brian Osserman.Ph.D

The Common Link: An Exploration of the Social Cognitive Dimensions of Meaning-Making in Algebra and the Visual Arts Using a Case Study Approach

It is commonplace to hold that algebra and the visual arts are mutually exclusive activities. In this thesis, an attempt was made to connect how we learn in algebra and the visual arts from the social cognitive perspective proposed by Bandura (1986, 1997). That is, the personal, social, and behavioural dimensions of learning in algebra and the visual arts were considered. Also, the issue of a connection between algebra and the visual arts was tackled by taking into account the most recent advances in cognitive science, like the situated movement, the notion, in a nutshell, that cognition is extended throughout our social relations and practices. Making the connection between, what Snow (1959) called generally the two cultures (cited in Stent, 2001, p. 31) of art and science, has precedence. There have been attempts, as interpreted in this thesis, to consider what learning in the arts and sciences have in common from various quarters, be they philosophical, psychological, or historical. Identifying the link between algebra and the visual arts involved several things. First, the historical context for the schism between our understanding of learning in algebra and the visual arts was considered. Second, a detailed review-cum-analysis of the literature was undertaken, and this yielded the themes upon which the connections between algebra and the visual arts were made. Turning to the fieldwork, four probing case studies were utilized to explore how those in algebra or the visual arts learn in their fields. By analyzing the data from the case studies, pattern regularities between learning in algebra and the visual arts were extracted. Finally, the theoretical and pedagogical consequences of having made the common link between algebra and the visual arts were addressed. Theoretically, by considering the role of, for instance, aesthetics and identity as reasons to pursue algebra or the visual arts, Bandura\u27s (1986, 1997) social cognitive theory was corroborated and enlarged. Practically, recommendations were offered for the pedagogy of algebra and the visual arts

Towards an integrated understanding of neural networks

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 123-136).Neural networks underpin both biological intelligence and modern Al systems, yet there is relatively little theory for how the observed behavior of these networks arises. Even the connectivity of neurons within the brain remains largely unknown, and popular deep learning algorithms lack theoretical justification or reliability guarantees. This thesis aims towards a more rigorous understanding of neural networks. We characterize and, where possible, prove essential properties of neural algorithms: expressivity, learning, and robustness. We show how observed emergent behavior can arise from network dynamics, and we develop algorithms for learning more about the network structure of the brain.by David Rolnick.Ph. D