Homogeneous Riemannian Structures on Berger 3-Spheres

13 pages.-- MSC2000 codes: 53C30, 53C25.The homogeneous Riemannian structures on the 3-dimensional Berger spheres, their corresponding reductive decompositions and the associated groups of isometries are obtained. The Berger 3-spheres are also considered as homogeneous almost contact metric manifolds.Partially supported by DGICYT, Spain, under grant BFM2002-00141 and by Xunta de Galicia under grant PGIDT01PXI20704PR.Peer reviewe

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AbstractWe discuss the reduction and reconstruction problem for ordinary differential equations that admit a linear symmetry group. The goal is to prove that modulo reduction there remain only linear differential equations, and to construct these explicitly. Extending previous work on one-parameter groups, we show this for certain unipotent and solvable groups, and for all semisimple groups. Some applications to relative equilibria are given

Discrete Routh Reduction

This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical $J_2$ correction, as well as the double spherical pendulum. The $J_2$ problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a nontrivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the noncanonical nature of the symplectic structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added, fixed typo

A transcriptome anatomy of human colorectal cancers

BACKGROUND: Accumulating databases in human genome research have enabled integrated genome-wide study on complicated diseases such as cancers. A practical approach is to mine a global transcriptome profile of disease from public database. New concepts of these diseases might emerge by landscaping this profile. METHODS: In this study, we clustered human colorectal normal mucosa (N), inflammatory bowel disease (IBD), adenoma (A) and cancer (T) related expression sequence tags (EST) into UniGenes via an in-house GetUni software package and analyzed the transcriptome overview of these libraries by GOTree Machine (GOTM). Additionally, we downloaded UniGene based cDNA libraries of colon and analyzed them by Xprofiler to cross validate the efficiency of GetUni. Semi-quantitative RT-PCR was used to validate the expression of β-catenin and. 7 novel genes in colorectal cancers. RESULTS: The efficiency of GetUni was successfully validated by Xprofiler and RT-PCR. Genes in library N, IBD and A were all found in library T. A total of 14,879 genes were identified with 2,355 of them having at least 2 transcripts. Differences in gene enrichment among these libraries were statistically significant in 50 signal transduction pathways and Pfam protein domains by GOTM analysis P < 0.01 Hypergeometric Test). Genes in two metabolic pathways, ribosome and glycolysis, were more enriched in the expression profiles of A and IBD than in N and T. Seven transmembrane receptor superfamily genes were typically abundant in cancers. CONCLUSION: Colorectal cancers are genetically heterogeneous. Transcription variants are common in them. Aberrations of ribosome and glycolysis pathway might be early indicators of precursor lesions in colon cancers. The electronic gene expression profile could be used to highlight the integral molecular events in colorectal cancers

Prostate-Specific Ets (PSE) factor: a novel marker for detection of metastatic breast cancer in axillary lymph nodes

Prostate Specific Ets factor is a recently identified transcriptional activator that is overexpressed in prostate cancer. To determine whether this gene is overexpressed in breast cancer, we performed a virtual Northern blot using data available online at the Cancer Genome Anatomy Project website. Ninety-five SAGE libraries were probed with a unique sequence tag to the Prostate Specific Ets gene. The results indicate that Prostate Specific Ets is expressed in 14 out of 15 breast cancer libraries (93%), nine out of 10 prostate cancer libraries (90%), three out of 40 libraries from other cancers (7.5%), and four out of 30 normal tissue libraries (13%). To determine the possibility that the Prostate Specific Ets gene is a novel marker for detection of metastatic breast cancer in axillary lymph nodes, quantitative real-time RT–PCR analyses were performed. The mean level of Prostate Specific Ets expression in lymph nodes containing metastatic breast cancer (n=22) was 410-fold higher than in normal lymph node (n=51). A receiver operator characteristic curve analysis indicated that Prostate Specific Ets was overexpressed in 18 out of 22 lymph nodes containing metastatic breast cancer (82%). The receiver operator characteristic curve analysis also indicated that the diagnostic accuracy of the Prostate Specific Ets gene for detection of metastatic breast cancer in axillary lymph nodes was 0.949. These results provide evidence that Prostate Specific Ets is a potentially informative novel marker for detection of metastatic breast cancer in axillary lymph nodes, and should be included in any study that involves molecular profiling of breast cancer

ErbB2 and bone sialoprotein as markers for metastatic osteosarcoma cells

Osteosarcoma is the most common malignant bone neoplasia occurring in young patients in the first two decades of life, and represents 20% of all primitive malignant bone tumours. At present, treatment of metastatic osteosarcoma is unsatisfactory. High-dose chemotherapy followed by CD34+ leukapheresis rescue may improve these poor results. Neoplastic cells contaminating the apheresis may, however, contribute to relapse. To identify markers suitable for detecting osteosarcoma cells in aphereses we analysed the expression of bone-specific genes (Bone Sialoprotein (BSP) and Osteocalcin) and oncogenes (Met and ErbB2) in 22 patients with metastatic osteosarcoma and six healthy stem cell donors. The expression of these genes in aphereses of patients affected by metastatic osteosarcoma was assessed by RT–PCR and Southern blot analysis. Met and Osteocalcin proved to be not useful markers since they are positive in aphereses of both patients with metastatic osteosarcoma and healthy stem cell donors. On the contrary, BSP was expressed at significant levels in 85% of patients. Moreover, 18% of patients showed a strong and significantly positive (seven to 16 times higher than healthy stem cell donors) ErbB2 expression. In all positive cases, neoplastic tissue also expressed ErbB2. Our data show that ErbB2 can be a useful marker for tumour contamination in aphereses of patients affected by ErbB2-expressing osteosarcomas and that analysis of Bone Sialoprotein expression can be an alternative useful marker