This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework based on a single g ...
We prove that the real cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective sp ...
We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in [23] to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we look at the class of gro ...
Determining the relationship between the cause of damage and the subsequent structural behavior of infrastructure systems requires an accurate characterization of the propagation of cracks, which represents the evolution of the damage state. When no inform ...
Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...
Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, ...
In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...
In this paper we study Weingarten surfaces and explore their potential for fabrication-aware design in freeform architecture. Weingarten surfaces are characterized by a functional relation between their principal curvatures that implicitly defines approxim ...
We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage t ...
While over fields of characteristic at least 5, a normal, projective and Gorenstein del Pezzo surface is geometrically normal, this does not hold for characteristic 2 and 3. There is no characterization of all such non-geometrically normal surfaces, but th ...
This thesis is centered on questions coming from Machine Learning (ML) and Statistical Field Theory (SFT).
In Machine Learning, we consider the subfield of Supervised Learning (SL), and in particular regression tasks where one tries to find a regressor tha ...
