N=4 Multi-Particle Mechanics, WDVV Equation and Roots

We review the relation of N=4 superconformal multi-particle models on the real line to the WDVV equation and an associated linear equation for two prepotentials, F and U. The superspace treatment gives another variant of the integrability problem, which we also reformulate as a search for closed flat Yang-Mills connections. Three- and four-particle solutions are presented. The covector ansatz turns the WDVV equation into an algebraic condition, for which we give a formulation in terms of partial isometries. Three ideas for classifying WDVV solutions are developed: ortho-polytopes, hypergraphs, and matroids. Various examples and counterexamples are displayed

Development of a Procedure for Genome-wide Expression Profiling from Minute Tissue Samples and Application in Mammary Carcinoma:Gene Activity Patterns Unveiling Molecular Pathways and Predicting Clinical Response

In this thesis, a novel procedure for linear amplification of messenger RNA (mRNA) molecules and labeling with fluorescently modified nucleotides was developed, that can be used to perform genome-wide expression analysis from minute tissue samples using microarrays of long gene-specific oligonucleotide DNA probes. The procedure was then applied to analyze core needle biopsies taken at time of diagnosis from tumors of female primary breast carcinoma patients. Upon receiving chemotherapy consisting of gemcitabine, epirubicin and docetaxel, the patients were classified according to their response to the chemotherapy into responders, defined as patients with a pathological complete remission of the tumor, and non-responders, defined as patients with no change or pathological partial remission. The gene expression profiles of the tumors from these patients were then bioinformatically processed and analyzed to identify a gene expression signature, which could be used to predict the response of the patients. Additionally, this gene signature was inspected for the significantly enriched pathways and biological processes, and a subset of genes was analyzed in the patient's biopsies with respect to RNA expression as validated by real-time quantitative polymerase chain reaction and protein expression as measured by immuno-histochemistry. The gene expression signature contained 512 genes, which allow a prediction of the patient response with an overall accuracy of 88%, a sensitivity of 78% and a specificity of 90%. Signaling pathways and biological processes identified with significant enrichment in the gene set were the Ras pathway, TGF β signaling, DNA damage response and apoptosis. From these pathways, the genes DAPK2, BAMBI, LMO4 and SMAD3 could be validated by RQ-PCR, but not SRC. In protein analysis by IHC, BAMBI was strongly associated with the patient's outcome, while BMP4, LMO4, SMAD3 and SRC were not directly associated. Additionally, BAMBI protein expression showed strong relationship with BRCA1 expression in the primary female breast carcinoma. Taken together, these results show the applicability of the novel developed procedure for amplification and labeling of mRNA for genome-wide gene expression analysis with the long oligonucleotide microarray technique and the successful use in biological and clinical investigations. The analysis of gene expression profiles of the primary breast tumors revealed an association of the Ras pathway, TGF β signaling, DNA damage response and apoptosis with the outcome of the patients after chemotherapy, as well as associations of several genes within these pathways and biological processes