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 ...
Objective: Structure-function coupling remains largely unknown in brain disorders. We studied this coupling during interictal epileptic discharges (IEDs), using graph signal processing in temporal lobe epilepsy (TLE). ...
We consider the problem of sampling from a density of the form p(x) ? exp(-f (x) - g(x)), where f : Rd-+ R is a smooth function and g : R-d-+ R is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Hastings framework. Under ...
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 ...
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 ...
For compact, isometrically embedded Riemannian manifolds N -> R-L, we introduce a fourth-order version of the wave maps equation. By energy estimates, we prove an a priori estimate for smooth local solutions in the energy subcritical dimension n = 1, 2. Th ...
We discuss criteria for a stable map of genus two and degree 4 to the projective plane to be smoothable, as an application of our modular desingularisation of (M) over bar (2,n)(P-r, d)(main) via logarithmic geometry and Gorenstein singularities. ...
This paper presents a comparative study of the geometrical optimization of mechanical wedge-barrel anchors for prestressed carbon fiber-reinforced polymer (CFRP) rods. Various anchor configurations were simulated using three-dimensional finite-element (FE) ...
In an open, bounded subset Omega of R-N such that 0 is an element of Omega we consider the nonlinear eigenvalue problem -Sigma(N)(i,j,=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + V(x)u + n(x,del u)+ g(x, u) = lambda u in Omega integral(Omega ...
