Equivariant quantization of orbifolds

Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of singular spaces, orbifolds, stratified spaces... In this work, we prove existence of an equivariant quantization for orbifolds. Our construction combines an appropriate desingularization of any Riemannian orbifold by a foliated smooth manifold, with the foliated equivariant quantization that we built in \cite{PoRaWo}. Further, we suggest definitions of the common geometric objects on orbifolds, which capture the nature of these spaces and guarantee, together with the properties of the mentioned foliated resolution, the needed correspondences between singular objects of the orbifold and the respective foliated objects of its desingularization.Comment: 13 page

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

Abundance and Characteristics of Microplastics in Commercially sold fishes from Cebu Island, Philippines

This study documents microplastics (MPs) in the top three commercially sold fishes viz. Auxis rochei, Rastrelliger kanagurta and Chanos chanos in major public markets of Cebu Island, Philippines. MPs were found in the gastrointestinal tracts (FGIT) and quantified and characterized according to size, type, and color. In general, nine (97.3%) of 81 FGIT samples contained 635 total pieces of MPs with size ranging 0.01 to 0.50 and 1.00 to 2.00 mm. Transparent microfibers (91%) were the most predominant MPs, with blue (48%) as the most common MP color observed, followed by red (39%), black (8%) and white (5%). Chanos chanos proved to be the most susceptible fish to MP ingestion with a mean average of 11.6 pieces per individual fish, followed by A. rochei with 6.6 pieces, and R. kanagurta with 5.3 pieces. The results indicated that MPs were ubiquitous and high in commercially sold fishes in major public wet markets of Cebu Island, Philippines. The ingestion of fishes is of primary concern as a route of human exposure to MPs because they filter a large volume of seawater and are typically eaten whole without gut removal. Further study is needed on the potential consequences of MPs to aquatic populations to assess comprehensive exposure integrating multiple sources and routes.

A Novel WAC Loss of Function Mutation in an Individual Presenting with Encephalopathy Related to Status Epilepticus during Sleep (ESES)

WAC (WW Domain Containing Adaptor With Coiled-Coil) mutations have been reported in only 20 individuals presenting a neurodevelopmental disorder characterized by intellectual disability, neonatal hypotonia, behavioral problems, and mildly dysmorphic features. Using targeted deep sequencing, we screened a cohort of 630 individuals with variable degrees of intellectual disability and identified five WAC rare variants: two variants were inherited from healthy parents; two previously reported de novo mutations, c.1661_1664del (p.Ser554*) and c.374C>A (p.Ser125*); and a novel c.381+2T>C variant causing the skipping of exon 4 of the gene, inherited from a reportedly asymptomatic father with somatic mosaicism. A phenotypic evaluation of this individual evidenced areas of cognitive and behavioral deficits. The patient carrying the novel splicing mutation had a clinical history of encephalopathy related to status epilepticus during slow sleep (ESES), recently reported in another WAC individual. This first report of a WAC somatic mosaic remarks the contribution of mosaicism in the etiology of neurodevelopmental and neuropsychiatric disorders. We summarized the clinical data of reported individuals with WAC pathogenic mutations, which together with our findings, allowed for the expansion of the phenotypic spectrum of WAC-related disorders

Association of intronic variants of the KCNAB1 gene with lateral temporal epilepsy.

The KCNAB1 gene is a candidate susceptibility factor for lateral temporal epilepsy (LTE) because of its functional interaction with LGI1, the gene responsible for the autosomal dominant form of LTE. We investigated association between polymorphic variants across the KCNAB1 gene and LTE. The allele and genotype frequencies of 14 KCNAB1 intronic SNPs were determined in 142 Italian LTE patients and 104 healthy controls and statistically evaluated. Single SNP analysis revealed one SNP (rs992353) located near the 3'end of KCNAB1 slightly associated with LTE after multiple testing correction (odds ratio=2.25; 95% confidence interval 1.26-4.04; P=0.0058). Haplotype analysis revealed two haplotypes with frequencies higher in cases than in controls, and these differences were statistically significant after permutation tests (Psim=0.047 and 0.034). One of these haplotypes was shown to confer a high risk for the syndrome (odds ratio=12.24; 95% confidence interval 1.32-113.05) by logistic regression analysis. These results support KCNAB1 as a susceptibility gene for LTE, in agreement with previous studies showing that this gene may alter susceptibility to focal epilepsy

The ternary invariant differential operators acting on the spaces of weighted densities

Over n-dimensional manifolds, I classify ternary differential operators acting on the spaces of weighted densities and invariant with respect to the Lie algebra of vector fields. For n=1, some of these operators can be expressed in terms of the de Rham exterior differential, the Poisson bracket, the Grozman operator and the Feigin-Fuchs anti-symmetric operators; four of the operators are new, up to dualizations and permutations. For n>1, I list multidimensional conformal tranvectors, i.e.,operators acting on the spaces of weighted densities and invariant with respect to o(p+1,q+1), where p+q=n. Except for the scalar operator, these conformally invariant operators are not invariant with respect to the whole Lie algebra of vector fields.Comment: 13 pages, no figures, to appear in Theor. Math. Phy

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

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

peer reviewe

Distribution of Lyt antigens on the surface of thymocytes associated with thymic macrophages and dendritic cells.

peer reviewedThymocyte subpopulations that are associated with macrophages and dendritic cells of the thymus in vivo were isolated from the thymuses of C57B1/6 mice, and their Lyt phenotypes were analyzed. Electron-microscopic examination of immunogold-labeled cells revealed that the thymic complexes formed by macrophages mainly contained Lyt-2-positive thymocytes, while Lyt-1-positive thymocytes were more frequently associated with dendritic cells. The characteristic distributions of Lyt antigens on the surface of thymocytes in regions of reciprocal contact with macrophages (Lyt-2-positive cells) and dendritic cells (Lyt-1-positive cells) suggest that these antigens play a role in specific interactions between thymocytes and stroma cells