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Many optimization problems for a smooth cost function f on a manifold M can be solved by determining the zeros of a vector field F; such as e.g. the gradient F of the cost function f. If F does not depend on additional parameters, numerous zero-finding techniques are available for this purpose. It is a natural generalization however, to consider time-dependent optimization problems that require the computation of time-varying zeros of time-dependent vector fields F(x,t). Such parametric optimization problems arise in many fields of applied mathematics, in particular path-following problems in robotics, recursive eigenvalue and singular value estimation in signal processing, as well as numerical linear algebra and inverse eigenvalue problems in control theory. In the literature, there are already some tracking algorithms for these tasks, but these do not always adequately respect the manifold structure. Hence, available tracking results can often be improved by implementing methods working directly on the manifold. Thus, intrinsic methods are of interests that evolve during the entire computation on the manifold. It is the task of this thesis, to develop such intrinsic zero finding methods. The main results of this thesis are as follows: - A new class of continuous and discrete tracking algorithms is proposed for computing zeros of time-varying vector fields on Riemannian manifolds. This was achieved by studying the newly introduced time-varying Newton Flow and the time-varying Newton Algorithm on Riemannian manifolds. - Convergence analysis is performed on arbitrary Riemannian manifolds. - Concretization of these results on submanifolds, including for a new class of algorithms via local parameterizations. - More specific results in Euclidean space are obtained by considering inexact and underdetermined time-varying Newton Flows. - Illustration of these newly introduced algorithms by examining time-varying tracking tasks in three application areas: Subspace analysis, matrix decompositions (in particular EVD and SVD) and computer vision.
Introduction: The German PID-NET registry was founded in 2009, serving as the first national registry of patients with primary immunodeficiencies (PID) in Germany. It is part of the European Society for Immunodeficiencies (ESID) registry. The primary purpose of the registry is to gather data on the epidemiology, diagnostic delay, diagnosis, and treatment of PIDs.
Methods: Clinical and laboratory data was collected from 2,453 patients from 36 German PID centres in an online registry. Data was analysed with the software Stata® and Excel.
Results: The minimum prevalence of PID in Germany is 2.72 per 100,000 inhabitants. Among patients aged 1-25, there was a clear predominance of males. The median age of living patients ranged between 7 and 40 years, depending on the respective PID. Predominantly antibody disorders were the most prevalent group with 57% of all 2,453 PID patients (including 728 CVID patients). A gene defect was identified in 36% of patients. Familial cases were observed in 21% of patients. The age of onset for presenting symptoms ranged from birth to late adulthood (range 0-88 years). Presenting symptoms comprised infections (74%) and immune dysregulation (22%). Ninety-three patients were diagnosed without prior clinical symptoms. Regarding the general and clinical diagnostic delay, no PID had undergone a slight decrease within the last decade. However, both, SCID and hyper IgE-syndrome showed a substantial improvement in shortening the time between onset of symptoms and genetic diagnosis. Regarding treatment, 49% of all patients received immunoglobulin G (IgG) substitution (70%-subcutaneous; 29%-intravenous; 1%-unknown). Three-hundred patients underwent at least one hematopoietic stem cell transplantation (HSCT). Five patients had gene therapy.
Conclusion: The German PID-NET registry is a precious tool for physicians, researchers, the pharmaceutical industry, politicians, and ultimately the patients, for whom the outcomes will eventually lead to a more timely diagnosis and better treatment.
Objectives: The aim of this study was to evaluate the efficiency of cetuximab-based anti-EGFR treatment and Aurora kinase A / B knockdown as a function of Aurora kinase polymorphism in HNSCC cell lines.
Materials and methods: First, protein expression of Aurora kinase A / B and EGFR and Aurora kinase A polymorphism were studied in tumour samples.
The survival and proliferation of Aurora kinase A homo- (Cal27) and heterozygous (HN) HNSCC cell lines was evaluated using a colony formation assay and a flow cytometric assay. Also, aneuploidy was determined. EGFR signalling pathway were visualised by western blotting.
Results: Immunohistochemistry revealed the overexpression of Aurora kinase A / B in HNSCC. The knockdown of each kinase caused a significant decrease in clonogenic survival, independent of Aurora kinase A polymorphism. In contrast, cetuximab treatment impaired clonogenic survival only in the Aurora kinase A-homozygous cell line (Cal27).
Conclusion: This study provides in vitro evidence for the predictive value of Aurora kinase A polymorphism in the efficiency of cetuximab treatment. Resistance to cetuximab treatment can be overcome by simultaneous Aurora kinase A/B knockdown.