Decomposition of symmetric tensor fields in the presence of a flat contact projective structure

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we consider symmetric tensor fields with coefficients in tensor densities, the vertical cotangent lift of contact form $\alpha$ is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued tensor fields. This generalized Hamiltonian operator on the symbol space is invariant with respect to the action of the projective contact algebra $sp(2n+2)$. The preceding invariant operators lead to a decomposition of the symbol space (expect for some critical density weights), which generalizes a splitting proposed by V. Ovsienko

Natural and projectively equivariant quantizations by means of Cartan Connections

The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant quantization exists in the flat situation in the sense of [18], thus solving one of the problems left open by M. Bordemann.Comment: 13 page

On sl(2)-equivariant quantizations

By computing certain cohomology of Vect(M) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-projective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear Mathematical Physic

Impact of medical specialists' locus of control on communication skills in oncological interviews

SCOPUS: ar.jinfo:eu-repo/semantics/publishe

The combined immunodetection of AP-2α and YY1 transcription factors is associated with ERBB2 gene overexpression in primary breast tumors

INTRODUCTION: Overexpression of the ERBB2 oncogene is observed in about 20% of human breast tumors and is the consequence of increased transcription rates frequently associated with gene amplification. Several studies have shown a link between activator protein 2 (AP-2) transcription factors and ERBB2 gene expression in breast cancer cell lines. Moreover, the Yin Yang 1 (YY1) transcription factor has been shown to stimulate AP-2 transcriptional activity on the ERBB2 promoter in vitro. In this report, we examined the relationships between ERBB2, AP-2alpha, and YY1 both in breast cancer tissue specimens and in a mammary cancer cell line. METHODS: ERBB2, AP-2alpha, and YY1 protein levels were analyzed by immunohistochemistry in a panel of 55 primary breast tumors. ERBB2 gene amplification status was determined by fluorescent in situ hybridization. Correlations were evaluated by a chi2 test at a p value of less than 0.05. The functional role of AP-2alpha and YY1 on ERBB2 gene expression was analyzed by small interfering RNA (siRNA) transfection in the BT-474 mammary cancer cell line followed by real-time reverse transcription-polymerase chain reaction and Western blotting. RESULTS: We observed a statistically significant correlation between ERBB2 and AP-2alpha levels in the tumors (p < 0.01). Moreover, associations were found between ERBB2 protein level and the combined high expression of AP-2alpha and YY1 (p < 0.02) as well as between the expression of AP-2alpha and YY1 (p < 0.001). Furthermore, the levels of both AP-2alpha and YY1 proteins were inversely correlated to ERBB2 gene amplification status in the tumors (p < 0.01). Transfection of siRNAs targeting AP-2alpha and AP-2gamma mRNAs in the BT-474 breast cancer cell line repressed the expression of the endogenous ERBB2 gene at both the mRNA and protein levels. Moreover, the additional transfection of an siRNA directed against the YY1 transcript further reduced the ERBB2 protein level, suggesting that AP-2 and YY1 transcription factors cooperate to stimulate the transcription of the ERBB2 gene. CONCLUSION: This study highlights the role of both AP-2alpha and YY1 transcription factors in ERBB2 oncogene overexpression in breast tumors. Our results also suggest that high ERBB2 expression may result either from gene amplification or from increased transcription factor levels

Characterization of Spontaneous Bone Marrow Recovery after Sublethal Total Body Irradiation: Importance of the Osteoblastic/Adipocytic Balance

Many studies have already examined the hematopoietic recovery after irradiation but paid with very little attention to the bone marrow microenvironment. Nonetheless previous studies in a murine model of reversible radio-induced bone marrow aplasia have shown a significant increase in alkaline phosphatase activity (ALP) prior to hematopoietic regeneration. This increase in ALP activity was not due to cell proliferation but could be attributed to modifications of the properties of mesenchymal stem cells (MSC). We thus undertook a study to assess the kinetics of the evolution of MSC correlated to their hematopoietic supportive capacities in mice treated with sub lethal total body irradiation. In our study, colony-forming units – fibroblasts (CFU-Fs) assay showed a significant MSC rate increase in irradiated bone marrows. CFU-Fs colonies still possessed differentiation capacities of MSC but colonies from mice sacrificed 3 days after irradiation displayed high rates of ALP activity and a transient increase in osteoblastic markers expression while pparγ and neuropilin-1 decreased. Hematopoietic supportive capacities of CFU-Fs were also modified: as compared to controls, irradiated CFU-Fs significantly increased the proliferation rate of hematopoietic precursors and accelerated the differentiation toward the granulocytic lineage. Our data provide the first evidence of the key role exerted by the balance between osteoblasts and adipocytes in spontaneous bone marrow regeneration. First, (pre)osteoblast differentiation from MSC stimulated hematopoietic precursor's proliferation and granulopoietic regeneration. Then, in a second time (pre)osteoblasts progressively disappeared in favour of adipocytic cells which down regulated the proliferation and granulocytic differentiation and then contributed to a return to pre-irradiation conditions

“Thymic Nurse Cells” Contain the First Virus Producing Cells after Inoculation of the Radiation Leukemia Virus in C57BL/Ka Mice

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