## FG Angewandte Funktionalanalysis

3 Items

**Solving parametric PDEs with neural networks: unfavorable structure vs. expressive power**

*Raslan, Mones Konstantin* (2021)

This cumulative dissertation extends the theory of neural networks (NNs). In the first part of this thesis, [PRV20] in Appendix A, we provide a general analysis of the hypothesis class of NNs from a structural point of view. Here, we examine the algebraic and topological properties of the set of NNs with fixed architecture. We establish that this set is never convex, hardly ever closed in class...

**Approximation of signals and functions in high dimensions with low dimensional structure: finite-valued sparse signals and generalized ridge functions**

*Keiper, Sandra* (2020)

In this thesis, we consider the class of high dimensional functions which contains functions which are defined in high-dimensional spaces but are known to be constant along some unknown manifolds. We study different reconstruction problems under additional assumptions. In the papers [54, 41, 56] (see Appendix A – C), we consider this problem in the context of compressed sensing and study the...

**Sparse Proteomics Analysis – a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data**

*Conrad, Tim O. F. ; Genzel, Martin ; Cvetkovic, Nada ; Wulkow, Niklas ; Leichtle, Alexander ; Vybiral, Jan ; Kutyniok, Gitta ; Schütte, Christof* (2017)

Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) i...