On Quasiconvex Conditional Maps Duality Results And Applications To Finance

On Quasiconvex Conditional Maps. Duality Results and Applications to Finance

Stochastic Methods in Cancer Research. Applications to Genomics and Angiogenesis

In this thesis, I study three stochastic methods that can be applied for the analysis of data in cancer research and, in particular, to cancer genomic data and to images of angiogenic processes. Cancer is a multistep process where the accumulation of genomic lesions alters cell biology. The latter is under control of several pathways and thus, cancer can arise via different mechanisms affecting different pathways. Due to the general complexity of this disease and the different types of tumors, the efforts of cancer research cover several research areas such as, for example, immunology, genetics, cell biology, angiogenesis.

Non-overlapping Domain Decomposition Methods for Three-dimensional Cardiac Reaction-diffusion Models and Applications

Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of life sciences, in particular of cardiac electrophysiology. Multiscale modeling of the bioelectric activity of the heart, taking into account macroscopic (fiber architecture and anisotropy) and microscopic (cellular) features of the tissue, aim to develop predictive tools for future drug design and patient-specific therapies, using detailed and efficient three-dimensional solvers for the governing equations of tissue electrophysiology.