The purpose of this thesis is to study methods by which conformal vector fields on pseudo-Riemannian manifolds can be simplified. A vector field on a manifold M with metric g is conformal if its local flows preserve the metric g up to a scaling and unlike Killing vector fields, which preserve g exactly, it cannot in general be linearised in a neighbourhood of any given point. The difference is that a Killing vector field is affine, that is it preserves a connection on the manifold. In this case the connection is the canonical (Levi-Civita) connection associated with g, but affine vector fields with respect to any connection are linearisable. The task is to find new connections with respect to which the set of conformal vector fields, or some subset of them, are affine. Suppose that we have a manifold M with a pseudo-Riemannian conformal structure and an orthogonal splitting of the tangent bundle. We construct, for a natural choice of torsion, a unique connection in the principal bundle of frames adapted to the splitting. Moreover this connection is preserved by any transformations which preserve the splitting of the tangent bundle. Thus any conformal vector field which preserves the splitting is affine. The splitting can be chosen to reflect the tangent to the orbits of a subalgebra of conformal vector fields, the principal null directions of the Weyl tensor or the flow of a perfect fluid. We also give a study of conformal vector fields in three-dimensional Lorentzian manifolds. An equivalent of the Cotton-York tensor is used to investigate the behaviour of these vector fields at their fixed points in the same spirit as the Weyl tensor is used in four dimensions.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg in ful lment of the requirements for the degree of Master of Science. June 29, 2017. / In this dissertation we explore the connection between entanglement and geometry. Recent work in the AdS/CFT correspondence has uncovered fascinating connections between quantum information and geometry, suggesting that entanglement in the CFT results in the emergence of spacetime in the bulk . We work in the 1/2 BPS sector of the duality between N = 4 super Yang Mills on R x S3 and IIB string theory on AdS5 S5. We aim to test this connection by calculating the Renyi entropies in the presence of 1/2 BPS operators heavy enough to deform the background geometry. This allows us to calculate the entanglement of these operators via the replica trick. The Ryu-Takayanagi formula relates this calculation to a minimal surface in the dual supergravity geometry, thus allowing us to observe how the boundary entanglement affects the bulk spacetime. We build a formula to calculate correlation functions of 1/2 BPS operators on the Riemann sheet that arises from the replica trick. This is a recursive formula based on group theory techniques. We demonstrate how the formula works for light operators and discuss how it can be generalised to include heavy operators by considering symmetric groups of higher order. / LG2018

Setup time reduction Is an essential activity used to prepare the facility for just-in-time (JIT) manufacturing; the aim oZ which Is to assist In meeting the desirable manufacturing requirements of delivering low cost quality products on time. (20) The Japanese have shown that setup reduction eliminates the need for setup skills and producing In large or "economic" lot sizes. (1 ) It is usually the case that preparation and adjustments, which usually account for 95% of the setup time, can be externalised or eliminated. (1) The overall production process should be examined before setup times are reduced on existing equipment. (2) Considerations Include group technology, setup sequencing, dedicated machines identifying bottlenecks (stated by OPT) and the 80/20 rule. A training programme should be initiated where setup reduction teams, consisting of production operators, setters, foremen line supervisors and production engineers, are educated in JIT manufacturing, the changing business environment and recording and analysis methods. (31) A theoretical approach to setup reduction has been formulated by Shlgeo Shlngo. (1) During the preliminary stage Internal and external setup are not distinguished, therefore this stage involves a work/time study of the existing setup and activity categorisation. From this, potential externallsatlon or elimination of setup operations can be determined. The first stage of setup reduction involves separating internal and external operations. During this stage tooling organisation and pre-preperation activities are converted to external operations. The second stage of setup reduction involves converting internal to external setup. A simple Pareto analysis is conducted to determine time consuming activities, which are then tackled first. This stage includes equipment modification, standardisation of procedures, parallel operations and elimination of adjustments. The third stage involves streamlining setup operations by improving operations and initiating setup practise sessions. All ideas should be documented and implemented immediately. Setups should be kept in mind when buying new equipment, however it is usually more beneficial to modify existing equipment in-house. (4) Setup reduction costs are low at first for large time reductions, but costs become high yielding small returns during the final stages of the programme. (31) It may be beneficial to introduce an incentive scheme where members of setup teams receive recognition and a financial reward for implemented ideas. (34) A setup reduction programme was implemented at Viro Looks, the aim of which was to illustrate the theoretical approach to setup reduction. Setups were reduced here on a transfer machine by 67%, 60% time savings being achieved at low/no cost. A survey was performed involving 18 leading JIT companies, where it was found that the majority (14 companies) have initiated a setup reduction programme. However many of these companies have only limited experience in setup reduction and, according to the survey, require 4-6 years to reach the final stages of setup reduction.

by Man-Cheung Hau. / Bibliography: leaves 110-112 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1984

by Chan, Kin Pong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 100-105). / Abstracts in English and Chinese. / Acknowledgments --- p.ii / Abstract --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Wavelet Transform --- p.4 / Chapter 1.2 --- Time Warping --- p.5 / Chapter 1.3 --- Outline of the Thesis --- p.6 / Chapter 2 --- Related Work --- p.8 / Chapter 2.1 --- Similarity Models for Time Series --- p.8 / Chapter 2.2 --- Dimensionality Reduction --- p.11 / Chapter 2.3 --- Wavelet Transform --- p.15 / Chapter 2.4 --- Similarity Search under Time Warping --- p.16 / Chapter 3 --- Dimension Reduction by Wavelets --- p.21 / Chapter 3.1 --- The Proposed Approach --- p.21 / Chapter 3.1.1 --- Haar Wavelets --- p.23 / Chapter 3.1.2 --- DFT versus Haar Transform --- p.27 / Chapter 3.1.3 --- Guarantee of no False Dismissal --- p.29 / Chapter 3.2 --- The Overall Strategy --- p.34 / Chapter 3.2.1 --- Pre-processing --- p.35 / Chapter 3.2.2 --- Range Query --- p.35 / Chapter 3.2.3 --- Nearest Neighbor Query --- p.36 / Chapter 3.3 --- Performance Evaluation --- p.39 / Chapter 3.3.1 --- Stock Data --- p.39 / Chapter 3.3.2 --- Synthetic Random Walk Data --- p.45 / Chapter 3.3.3 --- Scalability Test --- p.51 / Chapter 3.3.4 --- Other Wavelets --- p.52 / Chapter 4 --- Time Warping --- p.55 / Chapter 4.1 --- Similarity Search based on K-L Transform --- p.60 / Chapter 4.2 --- Low Resolution Time Warping --- p.63 / Chapter 4.2.1 --- Resolution Reduction of Sequences --- p.63 / Chapter 4.2.2 --- Distance Compensation --- p.67 / Chapter 4.2.3 --- Time Complexity --- p.73 / Chapter 4.3 --- Adaptive Time Warping --- p.77 / Chapter 4.3.1 --- Time Complexity --- p.79 / Chapter 4.4 --- Performance Evaluation --- p.80 / Chapter 4.4.1 --- Accuracy versus Runtime --- p.80 / Chapter 4.4.2 --- Precision versus Recall --- p.85 / Chapter 4.4.3 --- Overall Runtime --- p.91 / Chapter 4.4.4 --- Starting Up Evaluation --- p.93 / Chapter 5 --- Conclusion and Future Work --- p.95 / Chapter 5.1 --- Conclusion --- p.95 / Chapter 5.2 --- Future Work --- p.96 / Chapter 5.2.1 --- Application of Wavelets on Biomedical Signals --- p.96 / Chapter 5.2.2 --- Moving Average Similarity --- p.98 / Chapter 5.2.3 --- Clusters-based Matching in Time Warping --- p.98 / Bibliography --- p.99

Leung Tat Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 94-98). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Unusual Pattern Discovery --- p.3 / Chapter 1.2 --- Trend Prediction --- p.4 / Chapter 1.3 --- Thesis Organization --- p.5 / Chapter 2 --- Unusual Pattern Discovery --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Related Work --- p.7 / Chapter 2.2.1 --- Time Series Discords --- p.7 / Chapter 2.2.2 --- Brute Force Algorithm --- p.8 / Chapter 2.2.3 --- Keogh et al.'s Algorithm --- p.10 / Chapter 2.2.4 --- Performance Analysis --- p.14 / Chapter 2.3 --- Proposed Approach --- p.18 / Chapter 2.3.1 --- Haar Transform --- p.20 / Chapter 2.3.2 --- Discretization --- p.22 / Chapter 2.3.3 --- Augmented Trie --- p.24 / Chapter 2.3.4 --- Approximating the Magic Outer Loop --- p.27 / Chapter 2.3.5 --- Approximating the Magic Inner Loop --- p.28 / Chapter 2.3.6 --- Experimental Result --- p.28 / Chapter 2.4 --- More on discord length --- p.42 / Chapter 2.4.1 --- Modified Haar Transform --- p.42 / Chapter 2.4.2 --- Fast Haar Transform Algorithm --- p.43 / Chapter 2.4.3 --- Relation between discord length and discord location --- p.45 / Chapter 2.5 --- Further Optimization --- p.47 / Chapter 2.5.1 --- Improved Inner Loop Heuristic --- p.50 / Chapter 2.5.2 --- Experimental Result --- p.52 / Chapter 2.6 --- Top K discords --- p.53 / Chapter 2.6.1 --- Utility of top K discords --- p.53 / Chapter 2.6.2 --- Algorithm --- p.58 / Chapter 2.6.3 --- Experimental Result --- p.62 / Chapter 2.7 --- Conclusion --- p.64 / Chapter 3 --- Trend Prediction --- p.69 / Chapter 3.1 --- Introduction --- p.69 / Chapter 3.2 --- Technical Analysis --- p.70 / Chapter 3.2.1 --- Relative Strength Index --- p.70 / Chapter 3.2.2 --- Chart Analysis --- p.70 / Chapter 3.2.3 --- Dow Theory --- p.71 / Chapter 3.2.4 --- Moving Average --- p.72 / Chapter 3.3 --- Proposed Algorithm --- p.79 / Chapter 3.3.1 --- Piecewise Linear Representation --- p.80 / Chapter 3.3.2 --- Prediction Tree --- p.82 / Chapter 3.3.3 --- Trend Prediction --- p.84 / Chapter 3.4 --- Experimental Results --- p.86 / Chapter 3.4.1 --- Experimental setup --- p.86 / Chapter 3.4.2 --- Experiment on accuracy --- p.87 / Chapter 3.4.3 --- Experiment on performance --- p.88 / Chapter 3.5 --- Conclusion --- p.90 / Chapter 4 --- Conclusion --- p.92 / Bibliography --- p.94

This dissertation was conducted as part of the efforts related to WPI's Precision Personnel Location (PPL) project, the purpose of which is to locate emergency personnel in hazardous indoor environments using radio location techniques. The current PPL system prototype uses a radio transmitter worn by the personnel, indoors, and receivers on reference units, outdoors. This dissertation proposes a new system architecture with bidirectional radio transmissions to replace the current unidirectional system architecture. This allows the development of a synchronization scheme that can extract additional Time of Arrival (TOA) information for estimating the location of personnel. This dissertation also describes an extension of the multi-signal fusion technique previously used that incorporates this TOA information. At the cost of a more complicated mobile unit design, resultant benefits of this approach include rejection of signal reflectors as solutions, improved accuracy with limited reference unit geometries, improved noise rejection and significant computation reduction. In this dissertation the mathematical underpinnings of this approach are presented, a performance analysis is developed and the results are evaluated in the context of experimental data.

Photocopy of typescript. / Digitized by Kansas Correctional Industries

Thesis (M. Arch.)--Massachusetts Institute of Technology, Dept. of Architecture, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH. / Includes bibliographical references. / Physical manifestations of time occur in natural forms of all sizes. Architectural form serves as shelter while providing a built envelope of human life, simultaneously influencing and influenced by energetic activities which occur within the containment. Change is either progressive or cyclic, apparently linear or circular. Similarly built form is either discontinuous or continuous, angular or curved. All physical presences, energetic configurations, are fleeting. Physical forms are shaped by time and so reflect the movement of the energy flows through time and space. Specific parts of time-space signify future forms while others revel in the past. / by Martha Jane McInnis. / M.Arch.

Ip Ching-Tak. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 68-70). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Importance of Time Series Analysis with Outliers --- p.1 / Chapter 2 --- Outlier Analysis in Time Series --- p.4 / Chapter 2.1 --- Basic Idea --- p.4 / Chapter 2.2 --- Outliers in Time Series --- p.6 / Chapter 2.2.1 --- One Outlier Case --- p.6 / Chapter 2.2.2 --- Multiple Outliers Case --- p.8 / Chapter 2.3 --- Outlier Identification --- p.9 / Chapter 2.3.1 --- Outlier Detection of One Outlier Case --- p.9 / Chapter 2.3.2 --- Case of Unknown Model Parameters --- p.10 / Chapter 2.3.3 --- Iterative Identification Procedure --- p.10 / Chapter 3 --- ARMA Model Forecasting --- p.13 / Chapter 3.1 --- Unknown Model Problem --- p.13 / Chapter 3.1.1 --- AR Approximation --- p.14 / Chapter 3.1.2 --- ARMA Approximation --- p.15 / Chapter 3.1.3 --- "Comparison of AIC, AICC and BIC" --- p.16 / Chapter 3.2 --- A Simulation Study --- p.19 / Chapter 3.2.1 --- Results for One-Step-Ahead Forecast --- p.20 / Chapter 3.2.2 --- Results for the Mean of Multiple Forecasts --- p.22 / Chapter 4 --- ARIMA Model Forecasting --- p.24 / Chapter 4.1 --- Effect of Differencing on Time Series --- p.24 / Chapter 4.1.1 --- Outlier Free Model --- p.24 / Chapter 4.1.2 --- Outlier Model --- p.25 / Chapter 4.2 --- Unknown Model Problem --- p.28 / Chapter 4.2.1 --- AR Approximation --- p.28 / Chapter 4.2.2 --- ARMA Approximation --- p.28 / Chapter 4.3 --- Unknown Differencing Case --- p.29 / Chapter 4.4 --- A Simulation Study --- p.29 / Chapter 4.4.1 --- Results for One-Step-Ahead Forecast --- p.30 / Chapter 4.4.2 --- Results for the Mean of Multiple Forecasts --- p.32 / Chapter 5 --- Illustrative Examples --- p.34 / Chapter 5.1 --- Examples of Stationary Time Series --- p.34 / Chapter 5.1.1 --- Example 1 --- p.34 / Chapter 5.1.2 --- Example 2 --- p.36 / Chapter 5.2 --- Examples of Nonstationary Time Series --- p.37 / Chapter 5.2.1 --- Example 3 --- p.37 / Chapter 5.2.2 --- Example 4 --- p.38 / Chapter 6 --- Conclusion --- p.40 / Chapter A --- "Comparison of AIC, AICC and BIC" --- p.42 / Chapter A.1 --- AR Approximation Results --- p.42 / Chapter A.2 --- ARMA Approximation Results --- p.45 / Chapter B --- Simulation Results for ARMA Models --- p.47 / Chapter C --- Simulation Results for ARIMA Models --- p.56 / Chapter D --- SACF and SPACF of Examples --- p.65 / Bibliography --- p.68