Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds

The notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles are adapted for canonically polarized framed manifolds, i. e. compact complex manifolds together with a smooth divisor admitting a certain projective embedding. The main tool is the Poincaré metric, a special complete Kähler-Einstein metric on the complement of the divisor, whose asymptotic behaviour near the divisor is well-known due to results by Schumacher. The existence and uniqueness of Hermitian-Einstein connections in stable holomorphic vector bundles (Kobayashi-Hitchin correspondence) is proved in the setting of framed manifolds

Existence of approximate Hermitian-Einstein structures on semistable principal bundles

Let E_G be a principal G-bundle over a compact connected K\"ahler manifold, where G is a connected reductive complex linear algebraic group. We show that E_G is semistable if and only if it admits approximate Hermitian-Einstein structures.Comment: 7 pages, Bulletin des Sciences Math\'ematiques (to appear

Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds

We adapt the notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles for canonically polarized framed manifolds, i.e. compact complex manifolds X together with a smooth divisor D such that K_X \otimes [D] is ample. It turns out that the degree of a torsion-free coherent sheaf on X with respect to the polarization K_X \otimes [D] coincides with the degree with respect to the complete K\"ahler-Einstein metric g_{X \setminus D} on X \setminus D. For stable holomorphic vector bundles, we prove the existence of a Hermitian-Einstein metric with respect to g_{X \setminus D} and also the uniqueness in an adapted sense.Comment: 21 pages, International Journal of Mathematics (to appear

The Epithelial Cell Adhesion Molecule EpCAM Is Required for Epithelial Morphogenesis and Integrity during Zebrafish Epiboly and Skin Development

The aberrant expression of the transmembrane protein EpCAM is associated with tumor progression, affecting different cellular processes such as cell–cell adhesion, migration, proliferation, differentiation, signaling, and invasion. However, the in vivo function of EpCAM still remains elusive due to the lack of genetic loss-of-function studies. Here, we describe epcam (tacstd) null mutants in zebrafish. Maternal-zygotic mutants display compromised basal protrusive activity and epithelial morphogenesis in cells of the enveloping layer (EVL) during epiboly. In partial redundancy with E-cadherin (Ecad), EpCAM made by EVL cells is further required for cell–cell adhesion within the EVL and, possibly, for proper attachment of underlying deep cells to the inner surface of the EVL, thereby also affecting deep cell epiboly movements. During later development, EpCAM per se becomes indispensable for epithelial integrity within the periderm of the skin, secondarily leading to disrupted morphology of the underlying basal epidermis and moderate hyper-proliferation of skin cells. On the molecular level, EVL cells of epcam mutant embryos display reduced levels of membranous Ecad, accompanied by an enrichment of tight junction proteins and a basal extension of apical junction complexes (AJCs). Our data suggest that EpCAM acts as a partner of E-cadherin to control adhesiveness and integrity as well as plasticity and morphogenesis within simple epithelia. In addition, EpCAM is required for the interaction of the epithelia with underlying cell layers

Follow-up for breast cancer - the patients' view

Background: International and national guidelines (S3 guideline) for the surveillance of post-treatment breast cancer patients recommend a clinical follow-up including routine history and physical examination and regular mammograms. The practice of a clinical follow-up has been often discussed, but has been proven not to be inferior when compared to an intensified follow-up in randomized trials. Patients and Methods: The present manuscript reports the patients' view on the basis of a survey including 2000 patients with a history of breast cancer. Results: A total of 452 patients (22.6%) answered the questionnaire. The median age was 62 years (range 23-85 years). More than 80% of the patients were disease-free at the time of the survey. The need for surveillance was affirmed by the majority of patients (>95%), and one third stated that there was a need for more technical efforts during follow-up. In contrast to the follow-up guidelines, the results of the present survey indicated that most of the regularly scheduled follow-up visits were expanded using extensive laboratory and imaging procedures. Conclusion: This survey shows that the majority of physicians obviously do not accept the present follow-up guidelines. A new surveillance study investigating the efficacy of an intensified surveillance based on the improved possibilities of modern diagnostics and endocrine, immunotherapeutic, chemotherapeutic and interventional treatment options is warranted

Association between TAS2R38 gene polymorphisms and colorectal cancer risk

Molecular sensing in the lingual mucosa and in the gastro-intestinal tract play a role in the detection of ingested harmful drugs and toxins. Therefore, genetic polymorphisms affecting the capability of initiating these responses may be critical for the subsequent efficiency of avoiding and/or eliminating possible threats to the organism. By using a tagging approach in the region of Taste Receptor 2R38 (TAS2R38) gene, we investigated all the common genetic variation of this gene region in relation to colorectal cancer risk with a case-control study in a German population (709 controls and 602 cases) and in a Czech population (623 controls and 601 cases). We found that there were no significant associations between individual SNPs of the TAS2R38 gene and colorectal cancer in the Czech or in the German population, nor in the joint analysis. However, when we analyzed the diplotypes and the phenotypes we found that the non-taster group had an increased risk of colorectal cancer in comparison to the taster group. This association was borderline significant in the Czech population, (OR = 1.28, 95% CI 0.99-1.67; P(value) = 0.058) and statistically significant in the German population (OR = 1.36, 95% CI 1.06-1.75; P(value) = 0.016) and in the joint analysis (OR = 1.34, 95% CI 1.12-1.61; P(value) = 0.001). In conclusion, we found a suggestive association between the human bitter tasting phenotype and the risk of CRC in two different populations of Caucasian origin