Some Remarks on {g\mathfrak g}-invariant Fedosov Star Products and Quantum Momentum Mappings

In these notes we consider the usual Fedosov star product on a symplectic manifold $(M,\omega)$ emanating from the fibrewise Weyl product $\circ$, a symplectic torsion free connection $\nabla$ on M, a formal series $\Omega \in \nu Z^2_{\rm\tiny dR}(M)[[\nu]]$ of closed two-forms on M and a certain formal series s of symmetric contravariant tensor fields on M. For a given symplectic vector field X on M we derive necessary and sufficient conditions for the triple $(\nabla,\Omega,s)$ determining the star product * on which the Lie derivative \Lie_X with respect to X is a derivation of *. Moreover, we also give additional conditions on which \Lie_X is even a quasi-inner derivation. Using these results we find necessary and sufficient criteria for a Fedosov star product to be $\mathfrak g$-invariant and to admit a quantum Hamiltonian. Finally, supposing the existence of a quantum Hamiltonian, we present a cohomological condition on $\Omega$ that is equivalent to the existence of a quantum momentum mapping. In particular, our results show that the existence of a classical momentum mapping in general does not imply the existence of a quantum momentum mapping.Comment: 15 pages, one corollary and one definition added to Section 4, typos remove

Loss of expression of the tumor suppressor CEACAM1 links different hereditary colorectal carcinoma sub-types to the genesis of sporadic colorectal carcinoma

According to their carcinogenesis, colorectal cancer (CRC) subtypes show distinct molecular parameters. Hereditary non-polypous colorectal cancer (HNPCC) is the most common inherited CRC characterized by clinical criteria and confirmed microsatellite instability (MSI). Interestingly, a recently identified subtype, familial colorectal cancer type X (FCC-X), shows the same clinical criteria but microsatellite stability (MSS). CEACAM1 is a known tumor suppressor that regulates apoptosis in colon cells, and its loss is one of the most frequent events in early tumorigenesis of CRC. Therefore its loss may characterize precursor colon cells prior to neoplastic transformation. We analyzed tumor specimens of HNPCC and FCC-X patients in order to investigate whether there is a loss of CEACAM1 expression analogous to sporadic CRC and whether the expression of CEACAM1 would distinguish between these tumor entities. No differences in CEACAM1 expression were noted between HNPPC (n = 38) and FCC-X (n = 30) tumors. CEACAM1 was reduced in near-identical frequencies in 36/38 (95%) HNPCC and 29/30 (97%) FCC-X. This is the first report to demonstrate the loss of CEACAM1 expression in hereditary CRC. There was no difference between HNPCC and FCC-X. The frequency of expression loss was comparable to sporadic CRC, indicating that loss of CEACAM1 is an early event in colorectal tumorigenesis linking the genesis of sporadic and hereditary CRC

Invariant Star Products of Wick Type : Classification and Quantum Momentum Mappings

We extend our investigations on g-invariant Fedosov star products and quantum momentum mappings [22] to star products of Wick type on pseudo-Kähler manifolds. Star products of Wick type can be completely characterized by a local description as given by Karabegov in [16] for star products with separation of variables. We separately treat the action of a Lie group G on C∞(M)[[v]] by (pull-backs with) diffeomorphisms and the action of a Lie algebra g on C∞(M)[[v]] by (Lie derivatives with respect to) vector fields. Within Karabegov's framework, we prove necessary and sufficient conditions for a given star product of Wick type to be invariant in the respective sense. Moreover, our results yield a complete classification of invariant star products of Wick type. We also prove a necessary and sufficient condition for (the Lie derivative with respect to) a vector field to be even a quasi-inner derivation of a given star product of Wick type. We then transfer our former results about quantum momentum mappings for g-invariant Fedosov star products to the case of invariant star products of Wick type

External quality assessment of molecular biology-based methods used in laboratories of clinical chemistry and human genetics

The Reference Institute of Bioanalysis of the German Society of Clinical Chemistry has performed the first external assessment of molecular genetics methods used in medical diagnosis. The following procedures were tested: (I) DNA preparation from whole blood, (II) PCR amplification using "standard" primers, and (III) submarine agarose gel electrophoresis. Out of 50 participants, 45 returned samples for evaluation

Controlled generation of a pn-junction in a waveguide integrated graphene photodetector

With its electrically tunable light absorption and ultrafast photoresponse, graphene is a promising candidate for high-speed chip-integrated photonics. The generation mechanisms of photosignals in graphene photodetectors have been studied extensively in the past years. However, the knowledge about efficient light conversion at graphene pn-junctions has not yet been translated into high-performance devices. Here, we present a graphene photodetector integrated on a silicon slot-waveguide, acting as a dual-gate to create a pn-junction in the optical absorption region of the device. While at zero bias the photo-thermoelectric effect is the dominant conversion process, an additional photoconductive contribution is identified in a biased configuration. Extrinsic responsivities of 35 mA/W, or 3.5 V/W, at zero bias and 76 mA/W at 300 mV bias voltage are achieved. The device exhibits a 3 dB-bandwidth of 65 GHz, which is the highest value reported for a graphene-based photodetector.Comment: 19 pages, 16 figure

CGM2, a Member of the Carcinoembryonic Antigen Gene Family is Down- Regulated in Colorectal Carcinomas

We have determined the precise chromosomal location, the exon structure, and the expression pattern of CGM2, a member of the carcinoembryonic antigen (CEA) gene family. CGM2 cDNA was amplified by reverse transcription-polymerase chain reaction (RT/PCR) from the colon adenocarcinoma cell line, LS174T. A defective exon is missing from this cDNA clone, leading to a novel domain organization for the human CEA family with two immunoglobulin-like domains. The derived C-terminal domain predicts that the CGM2 protein is membrane-bound through a glycosyl phosphatidylinositol anchor. RT/PCR analyses identified CGM2 transcripts in mucinous ovarian and colonic adenocarcinomas as well as in adjacent colonic tissue, but not in other tumors including leukocytes from six chronic myeloid leukemia patients. Thus, unlike several other family members, CGM2 is not expressed in granulocytes but reveals a more CEA-like expression pattern. Northern blot analyses identified a 2.5-kilobase CGM2 mRNA that is strongly down-regulated in colonic adenocarcinomas compared with adjacent colonic mucosa, suggesting a possible tumor suppressor function. In addition, a 3.2- kilobase transcript was observed in a number of colon tumors that is not detectable in normal colonic tissue. This mRNA species could represent a tumor-specific CGM2 splice variant

Mice Transgenic for the Human Carcinoembryonic Antigen Gene Maintain Its Spatiotemporal Expression Pattern

The tumor marker carcinoembryonic antigen (CEA) is predominantly expressed in epithelial cells along the gastrointestinal tract and in a variety of adenocarcinomas. As a basis for investigating its in vivo regulation and for establishing an animal model for tumor immunotherapy, transgenic mice were generated with a 33-kilobase cosmid clone insert containing the complete human CEA gene and flanking sequences. CEA was found in the tongue, esophagus, stomach, small intestine, cecum, colon, and trachea and at low levels in the lung, testis, and uterus of adult mice of independent transgenic strains. CEA was first detected at day 10.5 of embryonic development (embryonic day 10.5) in primary trophoblast giant cells and was found in the developing gut, urethra, trachea, lung, and nucleus pulposus of the vertebral column from embryonic day 14.5 onwards. From embryonic day 16.5 CEA was also visible in the nasal mucosa and tongue. Because this spatiotemporal expression pattern correlates well with that known for humans, it follows that the transferred genomic region contains all of the regulatory elements required for the correct expression of CEA. Furthermore, although mice apparently lack an endogenous CEA gene, the entire repertoire of transcription factors necessary for correct expression of the CEA transgene is conserved between mice and humans. After tumor induction, these immunocompetent mice will serve as a model for optimizing various forms of immunotherapy, using CEA as a target antigen