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Neural interfaces are devices that are implanted into the body and interface electrically with the central (CNS) or peripheral nervous system. They are inserted surgically for short periods of time or chronically to diagnose or treat several neural disease ...
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 ...
Hydrogels are among the first materials expressly designed for their use in biomedicine. However, state-of-the-art applications of hydrogels are severely limited because they are typically either too soft or too brittle such that they cannot bear significa ...
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 ...
The drive to develop cartilage implants for the treatment of major defects in the musculoskeletal sys-tem has resulted in a major research thrust towards developing biomaterial devices for cartilage repair. Investigational devices for the restoration of ar ...
We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...
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 ...
Jet injection devices have been studied and developed for transdermal drug delivery to avoid the use of needles. Such contact-less devices provide several advantages such as better dose control, lateral and depth localisation, lower collateral damage than ...
This article presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. The roles of Riemannian manifolds, geodesics and parallel transport in robotic ...
We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With hig ...
