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Approved for public release; distribution is unlimited. / The use of higher-order statistics provides insight into signals which is not always available at lower orders. Additionally, Gaussian-distributed signals have the interesting characteristic of disappearing at higher orders. Because so much of the noise and inter- ference environment is Gaussian-distributed, higher-order statistics thus offer the promise of an additional method of noise reduction and interference mitigation. As communica- tions signals become more and more complex, any additional ability to reduce the effects of noise and interference will have a profound impact on communications, surveillance, and intelligence systems. / US Department of Defense author (civilian).

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Kevin B. Lease / Xiao J. Xin / Peridynamics is a non-local continuum theory that formulates problems in terms of integration of interactions between the material points. Because the governing equation of motion in the peridynamic theory involves only integrals of displacements, rather than derivatives of displacements, this new theory offers great advantages in dealing with problems that contain discontinuities. Integration of the interaction force plays an important role in the formulation and numerical implementation of the peridynamic theory. In this study two enhanced methods of integration for peridynamics have been developed. In the first method, the continuum is discretized into cubic cells, and different geometric configurations over the cell and the horizon of interaction are categorized in detail. Integration of the peridynamic force over different intersection volumes are calculated accurately using an adaptive trapezoidal integration scheme with a combined relative-absolute error control. Numerical test examples are provided to demonstrate the accuracy of this new adaptive integration method. The bond-based peridynamic constitutive model is used in the calculation but this new method is also applicable to state-based peridynamics. In the second method, an integration method with fixed Gaussian points is employed to accurately calculate the integration of the peridynamic force. The moving least square approximation method is incorporated for interpolating the displacement field from the Gaussian points. A compensation factor is introduced to correct the soft boundary effect on the nodes near the boundaries. This work also uses linear viscous damping to minimize the dynamic effect in the solution process. Numerical results show the accuracy and effectiveness of this Gaussian integration method. Finally current research progress and prospective directions for several topics are discussed.

A quantum/semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested and applied to simulate and interpret ultrafast optical signals. Linear wave-packet interferometry and time-resolved coherent anti-Stokes Raman scattering signals for a model of molecular iodine in a 2D krypton lattice are calculated and used to study the vibrational decoherence and energy dissipation of iodine molecules in condensed media. The total wave function of the whole model is approximately obtained instead of a reduced system density matrix, and therefore the theory enables us to analyze the behavior and the role of the host matrix in quantum dynamics. This dissertation includes previously published co-authored material.

Cette thèse étudie l'inférence de modèles graphiques Gaussiens en grande dimension à partir de données du transcriptome non indépendamment et identiquement distribuées dans l'objectif d'estimer des réseaux de régulation génétique. Dans ce contexte de données en grande dimension, l'hétérogénéité des données peut être mise à profit pour définir des méthodes de régularisation structurées améliorant la qualité des estimateurs. Nous considérons tout d'abord l'hétérogénéité apparaissant au niveau du réseau, fondée sur l'hypothèse que les réseaux biologiques sont organisés, ce qui nous conduit à définir une régularisation l1 pondérée. Modélisant l'hétérogénéité au niveau des données, nous étudions les propriétés théoriques d'une méthode de régularisation par bloc appelée coopérative-Lasso, définie dans le but de lier l'inférence sur des jeux de données distincts mais proches en un certain sens. Pour finir, nous nous intéressons au problème central de l'incertitude des estimations, définissant un test d'homogénéité pour modèle linéaire en grande dimension. / This thesis investigates the inference of high-dimensional Gaussian graphical models from non identically and independently distributed transcriptomic data in the objective of recovering gene regulatory networks. In the context of high-dimensional statistics, data heterogeneity paves the way to the definition of structured regularizers in order to improve the quality of the estimator. We first consider heterogeneity at the network level, building upon the assumption that biological networks are organized, which leads to the definition of a weighted l1 regularization. Modelling heterogeneity at the observation level, we provide a consistency analysis of a recent block-sparse regularizer called the cooperative-Lasso designed to combine observations from distinct but close datasets. Finally we address the crucial question of uncertainty, deriving homonegeity tests for high-dimensional linear regression.

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One of the fundamental tasks in science is to find explainable relationships between observed phenomena. Recent work has addressed this problem by attempting to learn the structure of graphical models - especially Gaussian models - by the imposition of sparsity constraints. The graphical lasso is a popular method for learning the structure of a Gaussian model. It uses regularisation to impose sparsity. In real-world problems, there may be latent variables that confound the relationships between the observed variables. Ignoring these latents, and imposing sparsity in the space of the visibles, may lead to the pruning of important structural relationships. We address this problem by introducing an expectation maximisation (EM) method for learning a Gaussian model that is sparse in the joint space of visible and latent variables. By extending this to a conditional mixture, we introduce multiple structures, and allow side information to be used to predict which structure is most appropriate for each data point. Finally, we handle non-Gaussian data by extending each sparse latent Gaussian to a Gaussian copula. We train these models on a financial data set; we find the structures to be interpretable, and the new models to perform better than their existing competitors. A potential problem with the mixture model is that it does not require the structure to persist in time, whereas this may be expected in practice. So we construct an input-output HMM with sparse Gaussian emissions. But the main result is that, provided the side information is rich enough, the temporal component of the model provides little benefit, and reduces efficiency considerably. The GWishart distribution may be used as the basis for a Bayesian approach to learning a sparse Gaussian. However, sampling from this distribution often limits the efficiency of inference in these models. We make a small change to the state-of-the-art block Gibbs sampler to improve its efficiency. We then introduce a Hamiltonian Monte Carlo sampler that is much more efficient than block Gibbs, especially in high dimensions. We use these samplers to compare a Bayesian approach to learning a sparse Gaussian with the (non-Bayesian) graphical lasso. We find that, even when limited to the same time budget, the Bayesian method can perform better. In summary, this thesis introduces practically useful advances in structure learning for Gaussian graphical models and their extensions. The contributions include the addition of latent variables, a non-Gaussian extension, (temporal) conditional mixtures, and methods for efficient inference in a Bayesian formulation.

by Su, Shi Chun = 宇宙微波背景各向異性的非高斯特性與旋轉宇宙的規範 / by 蘇士俊. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 78-83). / Abstracts in English and Chinese. / by Su, Shi Chun = Yu zhou wei bo bei jing ge xiang yi xing de fei Gaosi te xing yu xuan zhuan yu zhou de gui fan / by Su Shijun. / Chapter 1 --- Review of Cosmic Microwave Background Anisotropies --- p.1 / Chapter 1.1 --- Robertson-Walker metric --- p.1 / Chapter 1.2 --- Cosmological Perturbation --- p.4 / Chapter 1.2.1 --- Scalar-Vector-Tensor Decomposition --- p.6 / Chapter 1.2.2 --- Gauge Transformations --- p.8 / Chapter 1.2.3 --- Scalar Perturbation --- p.8 / Chapter 1.3 --- Sachs-Wolfe Effect --- p.9 / Chapter 1.4 --- Spectrum of CMB Anisotropies --- p.11 / Chapter 1.4.1 --- Rotation Transformation of Spherical Harmonics --- p.14 / Chapter 1.5 --- Contaminations of the CMBA --- p.16 / Chapter 1.5.1 --- The Internal Linear Combination Method --- p.17 / Chapter 2 --- Review of Models of Rotating Universe --- p.22 / Chapter 2.1 --- Godel's Model of a Rotating Universe --- p.23 / Chapter 2.2 --- Bianchi Models of a Rotating Universe --- p.24 / Chapter 2.3 --- Constraints on the Rotation of our Universe --- p.26 / Chapter 3 --- Study of Non-Gaussian Properties of the CMB Anisotropies --- p.31 / Chapter 3.1 --- Methodology --- p.32 / Chapter 3.2 --- Suspicious Anomalies against the IGH --- p.33 / Chapter 3.3 --- Verifications of the Suspicious Anomalies --- p.37 / Chapter 3.3.1 --- Different Cleaning Methods --- p.37 / Chapter 3.3.2 --- Effects of the Foreground Contaminations --- p.39 / Chapter 3.4 --- Further Study and Discussion --- p.52 / Chapter 3.5 --- Conclusions --- p.56 / Chapter 4 --- CMB Constraint on the Rotation of the Universe --- p.57 / Chapter 4.1 --- The Einstein Field Equations with Rotational Perturbations --- p.58 / Chapter 4.2 --- Analytic Solutions of the EFEs for the Rotating Universe --- p.63 / Chapter 4.3 --- The Sachs-Wolfe Effects up to Second-Order due to the Rotation --- p.65 / Chapter 4.4 --- Constraints on Our Model --- p.69 / Chapter 4.5 --- Discussion --- p.72 / Chapter 4.6 --- Conclusions --- p.75 / Chapter 5 --- Summary of the Thesis --- p.76 / Bibliography --- p.78

Detection of biological and chemical threats is an important consideration in the modern national defense policy. Much of the testing and evaluation of threat detection technologies is performed without appropriate uncertainty quantification. This paper proposes an approach to analyzing the effect of threat concentration on the probability of detecting chemical and biological threats. The approach uses a probit semi-parametric formulation between threat concentration level and the probability of instrument detection. It also utilizes a bayesian adaptive design to determine at which threat concentrations the tests should be performed. The approach offers unique advantages, namely, the flexibility to model non-monotone curves and the ability to test in a more informative way. We compare the performance of this approach to current threat detection models and designs via a simulation study.