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In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...
The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...
We initiate the study of neural network quantum state algorithms for analyzing continuous-variable quantum systems in which the quantum degrees of freedom correspond to coordinates on a smooth manifold. A simple family of continuous-variable trial wavefunc ...
In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...
Programming intelligent robots requires robust controllers that can achieve desired tasks while adapting to the changes in the task and the environment. In this thesis, we address the challenges in designing such adaptive and anticipatory feedback controll ...
Epsilon-near-zero (ENZ) materialshave attracted great interestdue to their exotic linear and nonlinear responses, which makes itsignificant to tune ENZ wavelengths for wavelength-dependent applications.However, studies to achieve tunability in a wide spect ...
Limited data and low dose constraints are common problems in a variety of tomographic reconstruction paradigms which lead to noisy and incomplete data. Over the past few years sinogram denoising has become an essential pre-processing step for low dose Comp ...
Graph sparsification has been studied extensively over the past two decades, culminating in spectral sparsifiers of optimal size (up to constant factors). Spectral hypergraph sparsification is a natural analogue of this problem, for which optimal bounds on ...
Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time; this problem is further emph ...
