The standard deviation of surface EMG (EMGσ) is often related to muscle force; the accuracy of EMGσ estimation is valuable for many application areas such as clinical biomechanics, prostheses control and sports medicine. Numerous researchers have developed methods to optimize EMGσ estimation. Whitening the EMG signal has been proved to improve the statistical efficiency of EMGσ estimation, but conventional linear whitening filters fail at low contraction level. An adaptive whitening filter was proposed by Clancy and Farry[14]. This technique has a better performance than prior whitening methods, however, the adaptive whitening filter needs to be calibrated each time electrodes are applied, which increase the complexity of the implementation. We designed a universal whitening filter which can omit most calibration steps for the adaptive whitening filter in future use. We used the ensemble mean of the power spectrum of 512 EMG recordings to form a general shape of a fixed whitening filter that can applied on any EMG signal. The test error on an EMG-torque task based on universal whitening over 512 subjects had a mean error of 4.80% maximum voluntary contraction (MVC) and standard deviation (std) of 2.03% MVC, compared with an original adaptive whitening filter error of 4.84±1.98% MVC. Additionally, the rest contraction modeling hasn’t received enough attention. Existing RMS estimates of EMGσ subtract noise in either the amplitude or power domain. These procedures have never been modeled analytically. We show that power domain noise subtraction is optimal. But rest contractions which are processed using power domain noise subtraction only estimate a zero-valued EMGσ approximately 50% of the time, which is undesirable in prosthesis-control. The prosthesis has a 50% possibility to slowly drift based on the current RMS estimator. We propose a new estimator to improve the zero-amplitude estimation probability during rest. We used 512 rest contraction recordings to validate the probability distribution of rest EMG signal showing that it only has 1.6% difference compared with Gaussian distribution. We also evaluated the percent of zero-valued EMGσ estimates using power domain noise subtraction and our new estimator, matching experimental findings to the theoretic predictions.

Lattice-based cryptography has generated considerable interest in the last two decades due toattractive features, including conjectured security against quantum attacks, strong securityguarantees from worst-case hardness assumptions and constructions of fully homomorphicencryption schemes. On the other hand, even though it is a crucial part of many lattice-basedschemes, Gaussian sampling is still lagging and continues to limit the effectiveness of this newcryptography. The first goal of this thesis is to improve the efficiency of Gaussian sampling forlattice-based hash-and-sign signature schemes. We propose a non-centered algorithm, with aflexible time-memory tradeoff, as fast as its centered variant for practicable size of precomputedtables. We also use the Rényi divergence to bound the precision requirement to the standarddouble precision. Our second objective is to construct Falcon, a new hash-and-sign signaturescheme, based on the theoretical framework of Gentry, Peikert and Vaikuntanathan for latticebasedsignatures. We instantiate that framework over NTRU lattices with a new trapdoor sampler.

by Chong-kan Chiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 97-103). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Related Work --- p.2 / Chapter 1.2 --- Organizations of the Dissertation --- p.4 / Chapter 1.3 --- Notations --- p.4 / Chapter 2 --- Overview of ICLP(R) --- p.6 / Chapter 2.1 --- Basics of Interval Arithmetic --- p.6 / Chapter 2.2 --- Relational Interval Arithmetic --- p.8 / Chapter 2.2.1 --- Interval Reduction --- p.8 / Chapter 2.2.2 --- Arithmetic Primitives --- p.10 / Chapter 2.2.3 --- Interval Narrowing and Interval Splitting --- p.13 / Chapter 2.3 --- Syntax and Semantics --- p.16 / Chapter 3 --- Limitations of Interval Narrowing --- p.18 / Chapter 3.1 --- Computation Inefficiency --- p.18 / Chapter 3.2 --- Inability to Detect Inconsistency --- p.23 / Chapter 3.3 --- The Newton Language --- p.27 / Chapter 4 --- Design of CIAL --- p.30 / Chapter 4.1 --- The CIAL Architecture --- p.30 / Chapter 4.2 --- The Inference Engine --- p.31 / Chapter 4.2.1 --- Interval Variables --- p.31 / Chapter 4.2.2 --- Extended Unification Algorithm --- p.33 / Chapter 4.3 --- The Solver Interface and Constraint Decomposition --- p.34 / Chapter 4.4 --- The Linear and the Non-linear Solvers --- p.37 / Chapter 5 --- The Linear Solver --- p.40 / Chapter 5.1 --- An Interval Gaussian Elimination Solver --- p.41 / Chapter 5.1.1 --- Naive Interval Gaussian Elimination --- p.41 / Chapter 5.1.2 --- Generalized Interval Gaussian Elimination --- p.43 / Chapter 5.1.3 --- Incrementality of Generalized Gaussian Elimination --- p.47 / Chapter 5.1.4 --- Solvers Interaction --- p.50 / Chapter 5.2 --- An Interval Gauss-Seidel Solver --- p.52 / Chapter 5.2.1 --- Interval Gauss-Seidel Method --- p.52 / Chapter 5.2.2 --- Preconditioning --- p.55 / Chapter 5.2.3 --- Increment ality of Preconditioned Gauss-Seidel Method --- p.58 / Chapter 5.2.4 --- Solver Interaction --- p.71 / Chapter 5.3 --- Comparisons --- p.72 / Chapter 5.3.1 --- Time Complexity --- p.72 / Chapter 5.3.2 --- Storage Complexity --- p.73 / Chapter 5.3.3 --- Others --- p.74 / Chapter 6 --- Benchmarkings --- p.76 / Chapter 6.1 --- Mortgage --- p.78 / Chapter 6.2 --- Simple Linear Simultaneous Equations --- p.79 / Chapter 6.3 --- Analysis of DC Circuit --- p.80 / Chapter 6.4 --- Inconsistent Simultaneous Equations --- p.82 / Chapter 6.5 --- Collision Problem --- p.82 / Chapter 6.6 --- Wilkinson Polynomial --- p.85 / Chapter 6.7 --- Summary and Discussion --- p.86 / Chapter 6.8 --- Large System of Simultaneous Equations --- p.87 / Chapter 6.9 --- Comparisons Between the Incremental and the Non-Incremental Preconditioning --- p.89 / Chapter 7 --- Concluding Remarks --- p.93 / Chapter 7.1 --- Summary and Contributions --- p.93 / Chapter 7.2 --- Future Work --- p.95 / Bibliography --- p.97

by Wong Kwok Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 50-52). / Chapter 1. --- Introduction --- p.1 / Chapter 2. --- Taguchi's methodology in design of experiments --- p.3 / Chapter 2.1 --- System design / Chapter 2.2 --- Parameter design / Chapter 2.3 --- Tolerance design / Chapter 3. --- Inverse Gaussian distribution --- p.8 / Chapter 3.1 --- Genesis / Chapter 3.2 --- Probability density function / Chapter 3.3 --- Estimation of parameters / Chapter 3.4 --- Applications / Chapter 4. --- Iterative procedures and Derivation of the GLIM 4 macros --- p.21 / Chapter 4.1 --- Generalized linear models with varying dispersion / Chapter 4.2 --- Mean and dispersion models for inverse Gaussian distribution / Chapter 4.3 --- Devising the GLIM 4 macro / Chapter 4.4 --- Model fitting / Chapter 5. --- Simulation Study --- p.34 / Chapter 5.1 --- Generating random variates from the inverse Gaussian distribution / Chapter 5.2 --- Simulation model / Chapter 5.3 --- Results / Chapter 5.4 --- Discussion / Appendix --- p.46 / References --- p.50

by Jones Chui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 62-[66]). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Fundamentals of Artificial Neural Networks --- p.2 / Chapter 1.1.1 --- Processing Unit --- p.2 / Chapter 1.1.2 --- Topology --- p.3 / Chapter 1.1.3 --- Learning Rules --- p.4 / Chapter 1.2 --- Overview of Various Neural Network Models --- p.6 / Chapter 1.3 --- Introduction to the Radial Basis Function Networks (RBFs) --- p.8 / Chapter 1.3.1 --- Historical Development --- p.9 / Chapter 1.3.2 --- Some Intrinsic Problems --- p.9 / Chapter 1.4 --- Objective of the Thesis --- p.10 / Chapter 2 --- Low-dimensional Gaussian RBF networks (LowD RBFs) --- p.13 / Chapter 2.1 --- Architecture of LowD RBF Networks --- p.13 / Chapter 2.1.1 --- Network Structure --- p.13 / Chapter 2.1.2 --- Learning Rules --- p.17 / Chapter 2.2 --- Construction of LowD RBF Networks --- p.19 / Chapter 2.2.1 --- Growing Heuristic --- p.19 / Chapter 2.2.2 --- Pruning Heuristic --- p.27 / Chapter 2.2.3 --- Summary --- p.31 / Chapter 3 --- Application examples --- p.34 / Chapter 3.1 --- Chaotic Time Series Prediction --- p.35 / Chapter 3.1.1 --- Performance Comparison --- p.39 / Chapter 3.1.2 --- Sensitivity Analysis of MSE THRESHOLDS --- p.41 / Chapter 3.1.3 --- Effects of Increased Embedding Dimension --- p.41 / Chapter 3.1.4 --- Comparison with Tree-Structured Network --- p.46 / Chapter 3.1.5 --- Overfitting Problem --- p.46 / Chapter 3.2 --- Nonlinear prediction of speech signal --- p.49 / Chapter 3.2.1 --- Comparison with Linear Predictive Coding (LPC) --- p.54 / Chapter 3.2.2 --- Performance Test in Noisy Conditions --- p.55 / Chapter 3.2.3 --- Iterated Prediction of Speech --- p.59 / Chapter 4 --- Conclusion --- p.60 / Chapter 4.1 --- Discussions --- p.60 / Chapter 4.2 --- Limitations and Suggestions for Further Research --- p.61 / Bibliography --- p.62

by Sze Tsz-leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 91). / Chapter Chapter 1 --- Introduction / Chapter 1.1 --- Basic concepts of Monte Carlo integration --- p.1 / Chapter 1.1.1 --- Importance sampling --- p.4 / Chapter 1.1.2 --- Control variate --- p.5 / Chapter 1.1.3 --- Antithetic variate --- p.6 / Chapter 1.1.4 --- Stratified sampling --- p.7 / Chapter 1.1.5 --- Biased Estimator --- p.10 / Chapter 1.2 --- Some special methods in Monte Carlo integration --- p.11 / Chapter 1.2.1 --- Haber´ةs modified Monte Carlo quadrature I --- p.11 / Chapter 1.2.2 --- Haber's modified Monte Carlo quadrature II --- p.11 / Chapter 1.2.3 --- Weighted Monte Carlo integration --- p.12 / Chapter 1.2.4 --- Adaptive importance sampling --- p.13 / Chapter Chapter 2 --- New methods / Chapter 2.1 --- The use of Newton Cotes quadrature formulae in stage one --- p.17 / Chapter 2.1.1 --- Using one-dimensional trapezoidal rule --- p.17 / Chapter 2.1.2 --- Using two-dimensional or higher dimensional product trapezoidal rule --- p.21 / Chapter 2.1.3 --- Extension to higher order one-dimensional Newton Cotes formulae --- p.32 / Chapter 2.2 --- The use of Guass quadrature rule in stage one --- p.45 / Chapter 2.3 --- Some variations of the new methods --- p.56 / Chapter 2.3.1 --- Using probability points in both stages --- p.56 / Chapter 2.3.2 --- Importance sampling --- p.59 / Chapter 2.3.2.1 --- Triangular distribution --- p.60 / Chapter 2.3.2.2 --- Beta distribution --- p.64 / Chapter Chapter 3 --- Examples / Chapter 3.1 --- Example one: using trapezoidal rule as basic rule --- p.73 / Chapter 3.1.1 --- One-dimensional case --- p.73 / Chapter 3.1.2 --- Two-dimensional case --- p.80 / Chapter 3.2 --- Example two: Using Simpson's 3/8 rule as basic rule --- p.85 / Chapter 3.3 --- Example three： Using Guass rule as basic rule --- p.86 / Chapter Chapter 4 --- Conclusion and discussions --- p.88 / Reference --- p.91

Chien Siu-Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references. / Abstracts in English and Chinese. / Abstract (English) / Abstract (Chinese) / Acknowledgements / Table of Contents / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Gaussian-2 Method / Chapter 1.2 --- The Gaussian-3 Method / Chapter 1.3 --- The G3 Method with Reduced Moller-Plesset Order and Basis Set / Chapter 1.4 --- Calculated Thermochemical Data / Chapter 1.5 --- Remark on the Location of Transition State / Chapter 1.6 --- Scope of the Thesis / Chapter 1.7 --- References / Chapter Chapter 2 --- "Energetics and Structures of the Carbonyl Chloride Radical, Oxalyl Chloride, and Their Cations" --- p.6 / Chapter 2.1 --- Introduction / Chapter 2.2 --- Computational Methods / Chapter 2.3 --- Results and Discussion / Chapter 2.3.1 --- Carbonyl Chloride and Its Cation / Chapter 2.3.2 --- The anti and syn Conformers of Oxalyl Chloride and Oxalyl Chloride Cation / Chapter 3.3.3 --- The anti and gauche Conformers of (ClCO) 2 and the TS Linking Them / Chapter 2.4 --- Conclusions / Chapter 2.5 --- Publication Note / Chapter 2.6 --- References / Chapter Chapter 3 --- "An Isomeric Study of N5, N5+，and N5- : A Gaussian-3 Investigation" --- p.17 / Chapter 3.1 --- Introduction / Chapter 3.2 --- Computational Methods / Chapter 3.3 --- Results and Discussion / Chapter 3.3.1 --- "The N5 Isomers """ / Chapter 3.3.2 --- The N5+ Isomers / Chapter 3.3.3 --- The N5- Isomers / Chapter 3.3.4 --- Comparison of the G3 and G3(MP2) Results / Chapter 3.4 --- Conclusions / Chapter 3.5 --- Publication Note / Chapter 3.6 --- References / Chapter Chapter 4 --- Thermochemistry of Hydrochlorofluorosilanes : An Ab Initio Gaussian-3 Study --- p.28 / Chapter 4.1 --- Introduction / Chapter 4.2 --- Computational Methods / Chapter 4.3 --- Results and Discussion / Chapter 4.3.1 --- Heats of Formation for Neutral HCFSis / Chapter 4.3.2 --- Ionization Energies / Chapter 4.3.3 --- Electron Affinities / Chapter 4.3.4 --- Proton Affinities / Chapter 4.3.5 --- Acidities / Chapter 4.3.6 --- G3 versus G3(MP2) / Chapter 4.4 --- Conclusions / Chapter 4.5 --- Publication Note / Chapter 4.6 --- References / Chapter Chapter 5 --- A Gaussian-3 Study of the Photodissociation Channels of Thiirane --- p.48 / Chapter 5.1 --- Introduction / Chapter 5.2 --- Computational Methods / Chapter 5.3 --- Results and Discussion / Chapter 5.3.1 --- The Heats of Reactions / Chapter 5.3.2 --- The Dissociation Channels Taking Place at the Ground State / Chapter 5.3.3 --- The Dissociation Channels Taking Place at Excited States / Chapter 5.4 --- Conclusions / Chapter 5.5 --- References / Chapter Chapter 6 --- A Gaussian-3 Study of the VUV Photoionization and Photodissociation of Chloropropylene Oxide --- p.59 / Chapter 6.1 --- Introduction / Chapter 6.2 --- Computational Methods / Chapter 6.3 --- Results and Discussion / Chapter 6.3.1 --- Ionization Energy / Chapter 6.3.2 --- Dissociation Channels / Chapter 6.4 --- Conclusions / Chapter 6.5 --- Publication Note / Chapter 6.6 --- References / Chapter Chapter 7 --- Conclusions --- p.69 / Appendix A The Gaussian-n (n=l-3) Theoretical Models --- p.71 / Chapter A.1 --- The G1 and G2 Theories / Chapter A.2 --- The G3 Theory / Chapter A.3 --- The G3(MP2) Theory / "Appendix B Calculation of Enthalpy at 298 K,H298" --- p.74

Li Chi-Lun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references. / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Table of Contents --- p.iv / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Remark on the Location of Transition Structures --- p.1 / Chapter 1.2 --- Scope of the Thesis --- p.1 / Chapter 1.3 --- References --- p.2 / Chapter Chapter 2 --- "A Gaussian-3 Study on the Photodissociation of Phenylacetylene and Formation of 1,3,5-Hexatriyne" --- p.5 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Computational Method --- p.7 / Chapter 2.3 --- Results and Discussion --- p.8 / Chapter 2.3.1 --- Phenylacetylene → Acetylene + Benzyne --- p.8 / Chapter 2.3.2 --- "Phenylacetylene → Acetylene + (Z)-3 -Hexene- 1,5-diyne" --- p.9 / Chapter 2.3.3 --- "(Z)-3-Hexene-l,5-diyne / (E)-3 -Hexene-1,5-diyne → 1,3,5-Hexatriyne and Molecular Hydrogen" --- p.9 / Chapter 2.3.4 --- Evaluation of Thermochemical Data --- p.10 / Chapter 2.3.5 --- Evaluation of Ion Energetics Data --- p.10 / Chapter 2.4 --- Conclusions --- p.10 / Chapter 2.5 --- References --- p.11 / Chapter Chapter 3 --- A Gaussian-3 Study of the Photoionization and Dissociative Photoionization Channels of Cyanoethylene --- p.21 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Computational Method --- p.22 / Chapter 3.3 --- Results and Discussion --- p.23 / Chapter 3.3.1 --- Bond Cleavage Reactions --- p.23 / Chapter 3.3.2 --- Dissociation Channels Involving Transition Structures --- p.25 / Chapter 3.4 --- Conclusions --- p.25 / Chapter 3.5 --- References --- p.26 / Chapter Chapter 4 --- "A Gaussian´ؤ2 Study of Structures, Energetics, and Reactions of C2H3S- Anions" --- p.34 / Chapter 4.1 --- Introduction --- p.35 / Chapter 4.2 --- Computational Method --- p.35 / Chapter 4.3 --- Results and Discussion --- p.36 / Chapter 4.3.1 --- Thioformylmethyl Anion --- p.37 / Chapter 4.3.2 --- Thioacetyl Anion --- p.37 / Chapter 4.3.3 --- Cyclic C2H3S- Ions --- p.37 / Chapter 4.3.4 --- CH2SCH- --- p.38 / Chapter 4.3.5 --- 2-Thiovinyl Anion --- p.38 / Chapter 4.3.6 --- 1-Thiovinyl Anion --- p.39 / Chapter 4.3.7 --- Intramolecular Rearrangements of 1- --- p.39 / Chapter 4.3.8 --- Intramolecular Rearrangements of Cyclic C2H3S- ions and 1´ؤThiovinyl Anion --- p.39 / Chapter 4.4 --- Conclusions --- p.40 / Chapter 4.5 --- References --- p.40 / Chapter Chapter 5 --- "Theoretical Studies of Transition Metal Complexes: Bond Energies for Fe+-D, Fe+-H2O, and Fe+-CO" --- p.51 / Chapter 5.1 --- Introduction --- p.52 / Chapter 5.2 --- Computational Method --- p.53 / Chapter 5.3 --- Results and Discussion --- p.54 / Chapter 5.3.1 --- Fe+-D --- p.54 / Chapter 5.3.2 --- Fe+-CO --- p.54 / Chapter 5.3.3 --- Fe+-H2O --- p.55 / Chapter 5.4 --- Conclusions --- p.56 / Chapter 5.5 --- References --- p.57 / Chapter Chapter 6 --- Ab Initio Study of the Charge-Delocalized and -Localized Form of the Rhodizonate Dianion --- p.61 / Chapter 6.1 --- Introduction --- p.62 / Chapter 6.2 --- Computational Method --- p.63 / Chapter 6.3 --- Results and Discussion --- p.64 / Chapter 6.3.1 --- Charge-Localized C6062- --- p.64 / Chapter 6.3.2 --- Charge-Delocalized C6062- --- p.64 / Chapter 6.4 --- Conclusions --- p.65 / Chapter 6.5 --- References --- p.66 / Chapter Chapter 7 --- "Franck-Condon Factor Simulated Spectra of the Cations of cis-2-Butene,trans-2-Butene, Isobutene, cis-Dichloroethene, and trans-Dichloroethene" --- p.71 / Chapter 7.1 --- Introduction --- p.72 / Chapter 7.2 --- Computational Method --- p.72 / Chapter 7.3 --- Results and Discussion --- p.73 / Chapter 7.3.1 --- cis-2-Butene Cation --- p.73 / Chapter 7.3.2 --- trans-2-Butene Cation --- p.74 / Chapter 7.3.3 --- cis-Dichloroethene Cation --- p.75 / Chapter 7.3.4 --- trans-Dichloroethene Cation --- p.76 / Chapter 7.3.5 --- Isobutene --- p.76 / Chapter 7.4 --- Conclusions --- p.77 / Chapter 7.5 --- References --- p.77 / Chapter Chapter 8 --- Conclusions --- p.88 / Appendix A --- p.89 / Appendix B --- p.91 / Appendix C --- p.92

This thesis describes the work undertaken in producing the passive radio-frequency section of a heterodyne receiver for use on the United Kingdom Infra-Red Telescope at signal frequencies in the 200-300 GHz range. This is a Quasi-Optical system, comprised of a Martin-Puplet polarising interferometer employed as a diplexer and the lenses and feed horns by which the diplexer was coupled to the telescope, local oscillator, and mixer. The Gaussian beam-mode approach was employed to develop a theoretical basis for understanding the operation of such a system upon coherent paraxial beams. Quasi-Optical systems were then designed and their performance predicted by the application of this extension of Gaussian optics. Two such systems were constructed and their performance determined by laboratory measurements to be as predicted. One of these systems was then installed on the telescope where it was shown to function as designed. As part of the calibration and test routine on the telescope a number of astronomical measurements were made, including a determination of the apparent temperatures of the planets Jupiter and Saturn by a method different to that employed for results previously published. The Quasi-Optical receiver was successfully calibrated and commissioned as a common-user instrument. As such it will continue to be used in a variety of astronomical research programs undertaken by various groups.

Although the Maxwell equations govern the propagation of EM waves at all frequencies, the methods required to generate, direct, analyse and detect radiation differ from band to band. This thesis is concerned with the development and demonstration of 'Quasi-optical' techniques for millimetre wavelengths, which involve the propagation of Gaussian profiled beams a few wavelengths across, and the realization of a general circuit approach to mm-wave measurement. Gaussian beam-mode analysis, which is used in later chapters to understand propagation of quasi-optical beams, is reviewed in chapter 1. Chapter 2 outlines the design, manufacture and testing of corrugated feed horns which generate fundamental Gaussian beam-modes. The design and manufacture of lenses which control the spreading of the beams and directional couplers which provide desirable signal processing functions in quasi-optical circuits is discussed in chapter 3. Chapter 4 traces the development of a Faraday isolator which operates in free-space and can suppress unwanted reflections in quasi-optical circuits. Chapter 5 discusses a reusable circuit board upon which systems can be easily and quickly constructed. A null reflectometer built using quasi-optical components is outlined in chapter 6 and reflection measurements from lenses and horns presented. Chapter 7 describes a corrugated feed horn/lens antenna used in a balloon-borne nw-wave cosmic background experiment. Finally, Chapter 8 demonstrates the use of quasi-optical components in a 115 GHz receiver circuit.