The parabolic Anderson model (PAM), which is the Cauchy problem for the heat equation with random potential. The PAM is a mathematical model that describes how mass (i.e. matter or energy) flows in... Show moreThe parabolic Anderson model (PAM), which is the Cauchy problem for the heat equation with random potential. The PAM is a mathematical model that describes how mass (i.e. matter or energy) flows in a medium in the presence of a field of sources and sinks.The PAM has been extensively studied on regular lattices and is well understood there. However, the lattice is not always a suitable model and we look for extensions to random graphs. Very little is known for general graphs and the literature is extremely sparse. The present thesis is a contribution to this developing area. Because sparse random graphs can often be approximated by trees, the natural first step is to consider the PAM on a tree. In particular, this thesis is devoted to studying the PAM on random trees. Show less
Glycosylation is a widely occurring and complex modification found on lipids and proteins and is involved in the recognition, signaling and interaction events within the cell and between cells.... Show moreGlycosylation is a widely occurring and complex modification found on lipids and proteins and is involved in the recognition, signaling and interaction events within the cell and between cells. These events based on glycan structures result in adhesion, cell-matrix interaction and immune recognition. Alterations in the glycomic profile are considered a hallmark of various diseases, including cancer where it contributes to the development and progression of cancer, affecting cell-cell communication, cell-matrix interactions, tumor angiogenesis, invasion and metastasis. These functions are governed by different glycans and their terminal structures. In order to further explore these structures with regard to their potential as biomarkers and specific targets for diagnostic applications and therapeutical strategies for various diseases, in-depth glycomic analysis is needed. It is further noted that aberrant glycosylation not only results from the altered expression of glycosyltransferases (GTs) but also from the changed activity of GTs and glycosidases as well as the availability and abundance of sugar nucleotide donors. The aim of the research described in this thesis was to explore the glycomic signatures of colorectal cancer (CRC) in cell lines and tissues as well as of acute myeloid leukemia (AML) cell lines. Show less
