Biodegradable Implantable Microsystems

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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 ...

Encoding quantum information onto bosonic systems is a promising route to quantum error correc-tion. In a cat code, this encoding relies on the confinement of the dynamics of the system onto the two-dimensional manifold spanned by Schrodinger cats of oppos ...

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 ...

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 ...

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 ...

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 native tissues, the interaction between cells and the surrounding extracellular matrix (ECM) is reciprocal, as cells not only receive signals from the ECM but also actively remodel it through secretion of cell-derived ECM. However, very little is known ...

Mechanical stimuli are ubiquitous in the human body. In contrast to biochemical stimuli such as pH, redox, hypoxia or enzymes as well as exogenous stimuli such as magnetic fields, temperature or ultrasound, endogenous biomechanical stimuli have only receiv ...

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...

Inspired from additive manufacturing's success, the structuring of biocompatible materials through bioprinting has become a growing field of research in the past fifteen years. It opened the door to a plethora of applications ranging from the fabrication o ...

We study the evolution equation where is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary . We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the res ...

The invention relates to a scaffold material comprising a plurality of particles of a highly porous polymeric material, characterized in that said scaffold material becomes a shapeable paste once hydrated. The specific features of the particle material imp ...

Many signal processing problems involve data whose underlying structure is non-Euclidean, but may be modeled as a manifold or (combinatorial) graph. For instance, in social networks, the characteristics of users can be modeled as signals on the vertices of ...

The recapitulation of tissue organization and function in vitro is one of the main objectives of tissue engineering. Proper tissue function depends on the spatial assembly and interactions between key components such as cells, growth factors, signaling cue ...

The aim of this paper is to derive convergence results for projected line-search methods on the real-algebraic variety M-

We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with l(p) -type data terms in the manifold case. These algorithms are ba ...

Biodegradable Implantable Microsystems

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From low-rank retractions to dynamical low-rank approximation and back

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Critical Schrodinger Cat Qubit

Controlling the Microstructure and Composition of 3D Printed Soft Load-Bearing Hydrogels

Continuous-variable neural network quantum states and the quantum rotor model

A guide to preclinical evaluation of hydrogel-based devices for treatment of cartilage lesions

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Laser-induced liquid micro-jets for drug delivery

Integration of hybrid material systems in conformable neural interfaces

Extracellular Matrix Production by Mesenchymal Stromal Cells in Hydrogels Facilitates Cell Spreading and Is Inhibited by FGF-2

Mechanoresponsive Micro- and Nanoparticles

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Implementation of Functional Microfluidic Dispensing Tools Enabling Enhanced Control in Extrusion Bioprinting

Detecting Anisotropic Inclusions Through EIT

Shapeable scaffold material and uses thereof

Geometric deep learning: going beyond Euclidean data

Tunable and cell-responsive 3D poly(ethylene glycol) microenvironments for the development of tissue models

Convergence Results For Projected Line-Search Methods On Varieties Of Low-Rank Matrices Via Lojasiewicz Inequality

Total Variation Regularization for Manifold-Valued Data