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  • Quantile Function Modeling and Analysis for Multivariate Functional Data

    Agarwal, Gaurav (2020-11-25) [Dissertation]
    Advisor: Sun, Ying
    Committee members: Ombao, Hernando; Tester, Mark A.; He, Xuming
    Quantile function modeling is a more robust, comprehensive, and flexible method of statistical analysis than the commonly used mean-based methods. More and more data are collected in the form of multivariate, functional, and multivariate functional data, for which many aspects of quantile analysis remain unexplored and challenging. This thesis presents a set of quantile analysis methods for multivariate data and multivariate functional data, with an emphasis on environmental applications, and consists of four significant contributions. Firstly, it proposes bivariate quantile analysis methods that can predict the joint distribution of bivariate response and improve on conventional univariate quantile regression. The proposed robust statistical techniques are applied to examine barley plants grown in saltwater and freshwater conditions providing interesting insights into barley’s responses, informing future crop decisions. Secondly, it proposes modeling and visualization of bivariate functional data to characterize the distribution and detect outliers. The proposed methods provide an informative visualization tool for bivariate functional data and can characterize non-Gaussian, skewed, and heavy-tailed distributions using directional quantile envelopes. The radiosonde wind data application illustrates our proposed quantile analysis methods for visualization, outlier detection, and prediction. However, the directional quantile envelopes are convex by definition. This feature is shared by most existing methods, which is not desirable in nonconvex and multimodal distributions. Thirdly, this challenge is addressed by modeling multivariate functional data for flexible quantile contour estimation and prediction. The estimated contours are flexible in the sense that they can characterize non-Gaussian and nonconvex marginal distributions. The proposed multivariate quantile function enjoys the theoretical properties of monotonicity, uniqueness, and the consistency of its contours. The proposed methods are applied to air pollution data. Finally, we perform quantile spatial prediction for non-Gaussian spatial data, which often emerges in environmental applications. We introduce a copula-based multiple indicator kriging model, which makes no distributional assumptions on the marginal distribution, thus offers more flexibility. The method performs better than the commonly used variogram approach and Gaussian kriging for spatial prediction in simulations and application to precipitation data.
  • The equations of polyconvex thermoelasticity

    Galanopoulou, Myrto Maria (2020-11-25) [Dissertation]
    Advisor: Tzavaras, Athanasios
    Committee members: Hoteit, Ibrahim; Markowich, Peter A.; Christoforou, Cleopatra; Dafermos Constantine, M.
    In my Dissertation, I consider the system of thermoelasticity endowed with poly- convex energy. I will present the equations in their mathematical and physical con- text, and I will explain the relevant research in the area and the contributions of my work. First, I embed the equations of polyconvex thermoviscoelasticity into an aug- mented, symmetrizable, hyperbolic system which possesses a convex entropy. Using the relative entropy method in the extended variables, I show convergence from ther- moviscoelasticity with Newtonian viscosity and Fourier heat conduction to smooth solutions of the system of adiabatic thermoelasticity as both parameters tend to zero and convergence from thermoviscoelasticity to smooth solutions of thermoelasticity in the zero-viscosity limit. In addition, I establish a weak-strong uniqueness result for the equations of adiabatic thermoelasticity in the class of entropy weak solutions. Then, I prove a measure-valued versus strong uniqueness result for adiabatic poly- convex thermoelasticity in a suitable class of measure-valued solutions, de ned by means of generalized Young measures that describe both oscillatory and concentra- tion e ects. Instead of working directly with the extended variables, I will look at the parent system in the original variables utilizing the weak stability properties of certain transport-stretching identities, which allow to carry out the calculations by placing minimal regularity assumptions in the energy framework. Next, I construct a variational scheme for isentropic processes of adiabatic polyconvex thermoelasticity. I establish existence of minimizers which converge to a measure-valued solution that dissipates the total energy. Also, I prove that the scheme converges when the limit- ing solution is smooth. Finally, for completeness and for the reader's convenience, I present the well-established theory for local existence of classical solutions and how it applies to the equations at hand.
  • Multiple wheat genomes reveal global variation in modern breeding

    Walkowiak, Sean; Gao, Liangliang; Monat, Cecile; Haberer, Georg; Kassa, Mulualem T.; Brinton, Jemima; Ramirez-Gonzalez, Ricardo H.; Kolodziej, Markus C.; Delorean, Emily; Thambugala, Dinushika; Klymiuk, Valentyna; Byrns, Brook; Gundlach, Heidrun; Bandi, Venkat; Siri, Jorge Nunez; Nilsen, Kirby; Aquino, Catharine; Himmelbach, Axel; Copetti, Dario; Ban, Tomohiro; Venturini, Luca; Bevan, Michael; Clavijo, Bernardo; Koo, Dal-Hoe; Ens, Jennifer; Wiebe, Krystalee; N’Diaye, Amidou; Fritz, Allen K.; Gutwin, Carl; Fiebig, Anne; Fosker, Christine; Fu, Bin Xiao; Accinelli, Gonzalo Garcia; Gardner, Keith A.; Fradgley, Nick; Gutierrez-Gonzalez, Juan; Halstead-Nussloch, Gwyneth; Hatakeyama, Masaomi; Koh, Chu Shin; Deek, Jasline; Costamagna, Alejandro C.; Fobert, Pierre; Heavens, Darren; Kanamori, Hiroyuki; Kawaura, Kanako; Kobayashi, Fuminori; Krasileva, Ksenia; Kuo, Tony; McKenzie, Neil; Murata, Kazuki; Nabeka, Yusuke; Paape, Timothy; Padmarasu, Sudharsan; Percival-Alwyn, Lawrence; Kagale, Sateesh; Scholz, Uwe; Sese, Jun; Juliana, Philomin; Singh, Ravi; Shimizu-Inatsugi, Rie; Swarbreck, David; Cockram, James; Budak, Hikmet; Tameshige, Toshiaki; Tanaka, Tsuyoshi; Tsuji, Hiroyuki; Wright, Jonathan; Wu, Jianzhong; Steuernagel, Burkhard; Small, Ian; Cloutier, Sylvie; Keeble-Gagnère, Gabriel; Muehlbauer, Gary; Tibbets, Josquin; Nasuda, Shuhei; Melonek, Joanna; Hucl, Pierre J.; Sharpe, Andrew G.; Clark, Matthew; Legg, Erik; Bharti, Arvind; Langridge, Peter; Hall, Anthony; Uauy, Cristobal; Mascher, Martin; Krattinger, Simon G.; Handa, Hirokazu; Shimizu, Kentaro K.; Distelfeld, Assaf; Chalmers, Ken; Keller, Beat; Mayer, Klaus F. X.; Poland, Jesse; Stein, Nils; McCartney, Curt A.; Spannagl, Manuel; Wicker, Thomas; Pozniak, Curtis J. (Nature, Springer Science and Business Media LLC, 2020-11-25) [Article]
    AbstractAdvances in genomics have expedited the improvement of several agriculturally important crops but similar efforts in wheat (Triticum spp.) have been more challenging. This is largely owing to the size and complexity of the wheat genome$^{1}$, and the lack of genome-assembly data for multiple wheat lines$^{2,3}$. Here we generated ten chromosome pseudomolecule and five scaffold assemblies of hexaploid wheat to explore the genomic diversity among wheat lines from global breeding programs. Comparative analysis revealed extensive structural rearrangements, introgressions from wild relatives and differences in gene content resulting from complex breeding histories aimed at improving adaptation to diverse environments, grain yield and quality, and resistance to stresses$^{4,5}$. We provide examples outlining the utility of these genomes, including a detailed multi-genome-derived nucleotide-binding leucine-rich repeat protein repertoire involved in disease resistance and the characterization of Sm1$^{6}$, a gene associated with insect resistance. These genome assemblies will provide a basis for functional gene discovery and breeding to deliver the next generation of modern wheat cultivars.
  • Imitation Learning based on Generative Adversarial Networks for Robot Path Planning

    Yi, Xianyong (2020-11-24) [Thesis]
    Advisor: Michels, Dominik L.
    Committee members: Wonka, Peter; Moshkov, Mikhail
    Robot path planning and dynamic obstacle avoidance are defined as a problem that robots plan a feasible path from a given starting point to a destination point in a nonlinear dynamic environment, and safely bypass dynamic obstacles to the destination with minimal deviation from the trajectory. Path planning is a typical sequential decision-making problem. Dynamic local observable environment requires real-time and adaptive decision-making systems. It is an innovation for the robot to learn the policy directly from demonstration trajectories to adapt to similar state spaces that may appear in the future. We aim to develop a method for directly learning navigation behavior from demonstration trajectories without defining the environment and attention models, by using the concepts of Generative Adversarial Imitation Learning (GAIL) and Sequence Generative Adversarial Network (SeqGAN). The proposed SeqGAIL model in this thesis allows the robot to reproduce the desired behavior in different situations. In which, an adversarial net is established, and the Feature Counts Errors reduction is utilized as the forcing objective for the Generator. The refinement measure is taken to solve the instability problem. In addition, we proposed to use the Rapidly-exploring Random Tree* (RRT*) with pre-trained weights to generate adequate demonstration trajectories in dynamic environment as the training data, and this idea can effectively overcome the difficulty of acquiring huge training data.
  • A Multilayer Nonlinear Elimination Preconditioned Inexact Newton Method for Steady-State Incompressible Flow Problems in Three Dimensions

    Luo, Li; Cai, Xiao Chuan; Yan, Zhengzheng; Xu, Lei; Keyes, David E. (SIAM Journal on Scientific Computing, Society for Industrial & Applied Mathematics (SIAM), 2020-11-24) [Article]
    We develop a multilayer nonlinear elimination preconditioned inexact Newton method for a nonlinear algebraic system of equations, and a target application is the three-dimensional steady-state incompressible Navier--Stokes equations at high Reynolds numbers. Nonlinear steadystate problems are often more difficult to solve than time-dependent problems because the Jacobian matrix is less diagonally dominant, and a good initial guess from the previous time step is not available. For such problems, Newton-like methods may suffer from slow convergence or stagnation even with globalization techniques such as line search. In this paper, we introduce a cascadic multilayer nonlinear elimination approach based on feedback from intermediate solutions to improve the convergence of Newton iteration. Numerical experiments show that the proposed algorithm is superior to the classical inexact Newton method and other single layer nonlinear elimination approaches in terms of the robustness and efficiency. Using the proposed nonlinear preconditioner with a highly parallel domain decomposition framework, we demonstrate that steady solutions of the Navier--Stokes equations with Reynolds numbers as large as 7,500 can be obtained for the lid-driven cavity flow problem in three dimensions without the use of any continuation methods.

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