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Thesis (M.S. in Resource Planning and Management for International Defense) Naval Postgraduate School, June 1997. / Thesis advisor(s): Jansen, Erik ; Evered, Roger D. "June 1997." DTIC Descriptors: Colombia, Coast Guard, Matrix Theory, Stability, United States Government, Environments, Organizations, Strategy, Management, Models, Dynamics, Parameters, Navy, Theory, Theses, Surveys, Naval Operations, Culture. DTIC Identifiers: Maritime Operations, Strategic Management. Includes bibliographical references (p. 95-96).

For beta > 0, the beta-ensemble corresponds to the joint probability density on the real line proportional to prod_{n > m}^N abs{x_n - x_m}^beta prod_{n = 1}^N w(x_n) where w is the weight of the system. It has the application of being the Boltzmann factor for the configuration of N charge-one particles interacting logarithmically on an infinite wire inside an external field Q = -log w at inverse temperature beta. Similarly, the circular beta-ensemble has joint probability density proportional to prod_{n > m}^N abs{e^{itheta_n} - e^{itheta_m}}^beta prod_{n = 1}^N w(x_n) quad for theta_n in [- pi, pi) and can be interpreted as N charge-one particles on the unit circle interacting logarithmically with no external field. When beta = 1, 2, and 4, both ensembles are said to be solvable in that their correlation functions can be expressed in a form which allows for asymptotic calculations. It is not known, however, whether the general beta-ensemble is solvable. We present four families of particle models which are solvable point processes related to the beta-ensemble. Two of the examples interpolate between the circular beta-ensembles for beta = 1, 2, and 4. These give alternate ways of connecting the classical beta-ensembles besides simply changing the values of beta. The other two examples are "mirrored" particle models, where each particle has a paired particle reflected about some point or axis of symmetry.

Ng Sheung Wah = 米氏散射--以形態關聯共振分析之 / 伍尚華. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves [112]-114). / Text in English; abstracts in English and Chinese. / Ng Sheung Wah = Mi shi san she--yi xing tai guan lian gong zhen fen xi zhi / Wu Shanghua. / Abstract --- p.i / Acknowledgements --- p.iii / Contents --- p.iv / List of Figures --- p.vii / List of Tables --- p.xii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- MDR Expansion of Scattering Matrix --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Definition of Scattering Matrix --- p.8 / Chapter 2.3 --- Expansion of St with MDR's --- p.9 / Chapter 2.4 --- The Scattering Matrix in Mie's Theory for Uniform Dielectric Spheres --- p.12 / Chapter 2.5 --- Convergence of the Series --- p.15 / Chapter 2.6 --- Contributions of Different MDR's in Cross Section --- p.19 / Chapter Chapter 3. --- Numerical Method for MDR's --- p.27 / Chapter 3.1 --- Multipole Expansion --- p.27 / Chapter 3.2 --- Green's Theorem --- p.29 / Chapter 3.3 --- Translational Matrix --- p.31 / Chapter 3.4 --- Rotational Matrix --- p.36 / Chapter 3.5 --- Transfer Matrix to the Outside --- p.39 / Chapter 3.6 --- Diagonalization --- p.40 / Chapter Chapter 4. --- Degenerate Perturbation for MDR --- p.44 / Chapter 4.1 --- Introduction --- p.44 / Chapter 4.2 --- Perturbation Theory for Degenerate Systems --- p.44 / Chapter Chapter 5. --- Microdroplets with multiple inclusions: Experiments --- p.52 / Chapter 5.1 --- Introduction --- p.52 / Chapter 5.2 --- Method --- p.52 / Chapter Chapter 6. --- Formalism for Scattering from Inhomogeneous Spheres --- p.61 / Chapter 6.1 --- The Green's Function Formalism --- p.61 / Chapter 6.2 --- MDR Expansion of Dyadic Green's Function --- p.62 / Chapter 6.3 --- Cross Section Calculation --- p.64 / Chapter Chapter 7. --- Simulation of the Multiple Scattering Experiment --- p.66 / Chapter 7.1 --- Introduction --- p.66 / Chapter 7.2 --- Method --- p.67 / Chapter Chapter 8. --- Numerical Results of Multiple Scattering --- p.69 / Chapter 8.1 --- Introduction --- p.69 / Chapter 8.2 --- Comparisons of the Experimental and Simulation Result --- p.69 / Chapter 8.2.1 --- General Trend --- p.69 / Chapter 8.2.2 --- Position of the Resonance --- p.70 / Chapter 8.2.3 --- Width of the Resonance --- p.71 / Chapter Chapter 9. --- Scaling Behaviours of the Perturbation in MDR's --- p.83 / Chapter 9.1 --- Introduction --- p.83 / Chapter 9.2 --- Scaling Behaviours of MDR's shifts --- p.84 / Chapter 9.3 --- Analytical Approach to the Scaling Behaviours --- p.84 / Chapter 9.3.1 --- Average Shifts --- p.85 / Chapter 9.3.2 --- """slope"" of the Shifts" --- p.87 / Chapter 9.3.3 --- Spreading of the shifts --- p.87 / Chapter Chapter 10. --- Conclusion --- p.96 / Appendix A. Transverse Dyadic Green's Function Expansion --- p.98 / Appendix B. Calculation of the Self-Energy Matrix to First Order --- p.101 / Appendix C. Computer Code for Diagonalization of Δmm --- p.103 / Bibliography --- p.112

In this thesis, we focus on studying the performance of general regularized discriminant analysis (RDA) classifiers. The data used for analysis is assumed to follow Gaussian mixture model with different means and covariances. RDA offers a rich class of regularization options, covering as special cases the regularized linear discriminant analysis (RLDA) and the regularized quadratic discriminant analysis (RQDA) classi ers. We analyze RDA under the double asymptotic regime where the data dimension and the training size both increase in a proportional way. This double asymptotic regime allows for application of fundamental results from random matrix theory. Under the double asymptotic regime and some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that only depends on the data statistical parameters and dimensions. This result not only implicates some mathematical relations between the misclassification error and the class statistics, but also can be leveraged to select the optimal parameters that minimize the classification error, thus yielding the optimal classifier. Validation results on the synthetic data show a good accuracy of our theoretical findings. We also construct a general consistent estimator to approximate the true classification error in consideration of the unknown previous statistics. We benchmark the performance of our proposed consistent estimator against classical estimator on synthetic data. The observations demonstrate that the general estimator outperforms others in terms of mean squared error (MSE).

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 75-81). Available also in a digital version from Dissertation Abstracts.

Thesis--University of California, Berkeley, 1963. / "UC-34 Physics Distributions" -t.p. "TID-4500 (19th Ed.)" -t.p. Includes bibliographical references (p. 67-70).

The covariance estimation is one of the most critical tasks in multivariate statistical analysis. In many applications, reliable estimation of the covariance matrix, or scatter matrix in general, is required. The performance of the classical maximum likelihood method relies a great deal on the validity of the model assumption. Since the assumptions are often approximately correct, many robust statistical methods have been proposed to be robust against the deviation from the model assumptions. M-estimator is an important class of robust estimator of the scatter matrix. The properties of these robust estimators under high dimensional setting, which means the number of dimensions has the same order of magnitude as the number of observations, is desirable. To study these, random matrix theory is a very important tool. With high dimensional properties of robust estimators, we introduced a new method for blind spectrum sensing in cognitive radio networks.

This work utilizes zero-beta CAPM to derive an alternative form dubbed the ZCAPM. The ZCAPM posits that asset prices are a function of market risk composed of two components: average market returns and cross-sectional market volatility. Market risk associated with average market returns in the CAPM market model is known as beta risk. We refer to market risk related to cross-sectional market volatility as zeta risk. Using U.S. stock returns from January 1965 to December 2010, out-of-sample cross-sectional asset pricing tests show that the ZCAPM better predicts stock returns than popular three- and four-factor models. These and other empirical tests lead us to conclude that the ZCAPM holds promise as a robust asset pricing model.

Thesis (M.S.)--Oregon State University, 2008. / Printout. Includes bibliographical references (leaves 44-46). Also available on the World Wide Web.