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- 7Frei, Christoph (Mathematical and Statistical Sciences)
- 7Kong, Linglong (Mathematical and Statistical Sciences)
- 7Lewis, Mark (Mathematical and Statistical Sciences)
- 6Han, Bin (Mathematical and Statistical Sciences)
- 6Hillen, Thomas (Mathematical and Statistical Sciences)
- 6Mizera, Ivan (Mathematical and Statistical Sciences)
This dissertation first introduces the concepts of robust active learning (also called optimal experimental design in statistics), and the possible advantages of it over the traditional passive learning method. Then a general regression problem with possibly misspecified models is presented, and...
This thesis is based on three papers on selected topics in Asymptotic Geometric Analysis. The first paper is about the volume of high-dimensional random polytopes; in particular, on polytopes generated by Gaussian random vectors. We consider the question of how many random vertices (or ...
Regularized Tensor Quantile Regression for Functional Data Analysis with Applications to NeuroimagingDownload
With accelerating technological advancements, functional data analysis is of ever-growing importance in statistics, engineering, and medicine as the collection, storage, and analysis of data becomes ingrained in every aspect of modern life beyond any one field of study. From continuous biometric...
The formalism of variations of local systems is applied in a geometric setting to define a notion of geometric variation of local systems; this provides a natural framework with which to study families of fibrations of Kahler manifolds. We apply this formalism in various contexts, starting with...
This thesis is dedicated to the study of topological degree for different classes of monotone maps and applications to nonlinear problems in mathematical analysis and the applied mathematics. Employing topological methods for nonlinear problems in mathematics goes back to the pioneering work of...
The aim of my thesis consists of characterizing explicitly the optimal consumption and investment strategy for an investor, when her habit level process is incorporated in the utility formulation. For a continuous-time market model, I maximize the expected utility from terminal wealth and/or...
Mathematical models are used to simulate the behavior of the electrical activity of a single cell or multiple cells of the heart. Single cell models contain a system of ODEs (ordinary differential equations) while multi-cell models consist of a coupled system of ODEs and PDEs (partial...
We address several related problems from convex geometry and geometric tomography, which separate along two main themes. The content of this thesis is based on five papers, either published or submitted. The first theme concerns the origin-symmetry and unique determination of convex bodies. A...
This study focuses on the motion of a hollow flexible tube conveying a flowing fluid, also known as the garden-hose instability. This system becomes unstable when the fluid moving through the pipe exceeds a critical flow rate. This non-linear dynamical system involves complex fluid-structure...
One of the main aims in this thesis is to establish analogues of the classical Hardy-Littlewood-Sobolev (HLS) inequality for weighted orthogonal polynomial expansions (WOPEs) on the unit sphere, the unit ball and the simplex. An optimal condition for which this inequality holds is obtained....