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

Projectively equivariant quantizations over the superspace Rp∣q\R^{p|q}

We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra pgl(p+1|q) is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of pgl(n|n)\not\cong sl(n|n)), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms of a generalized divergence operator acting on supersymmetric tensor fields.Comment: 19 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

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

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

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

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

The human epidermal growth factor receptor (EGFR) gene in European patients with advanced colorectal cancer harbors infrequent mutations in its tyrosine kinase domain

ABSTRACT: BACKGROUND: The epidermal growth factor receptor (EGFR), a member of the ErbB family of receptors, is a transmembrane tyrosine kinase (TK) activated by the binding of extracellular ligands of the EGF-family and involved in triggering the MAPK signaling pathway, which leads to cell proliferation. Mutations in the EGFR tyrosine kinase domain are frequent in non-small-cell lung cancer (NSCLC). However, to date, only very few, mainly non-European, studies have reported rare EGFR mutations in colorectal cancer (CRC). METHODS: We screened 236 clinical tumor samples from European patients with advanced CRC by direct DNA sequencing to detect potential, as yet unknown mutations, in the EGFR gene exons 18 to 21, mainly covering the EGFR TK catalytic domain. RESULTS: EGFR sequences showed somatic missense mutations in exons 18 and 20 at a frequency of 2.1% and 0.4% respectively. Somatic SNPs were also found in exons 20 and 21 at a frequency of about 3.1% and 0.4% respectively. Of these mutations, four have not yet been described elsewhere. CONCLUSIONS: These mutation frequencies are higher than in a similarly sized population characterized by Barber and colleagues, but still too low to account for a major role played by the EGFR gene in CRC.Peer reviewe