30 research outputs found
The uniqueness of the SDPS-set of the symplectic dual polar space ,
SDPS-sets are very nice sets of points in dual polar spaces which themselves carry the structure of dual polar spaces. They were introduced in \cite{DB-V:2} because they gave rise to new valuations and hyperplanes of dual polar spaces. In the present paper, we show that the symplectic dual polar space (4n-1,q), has up to isomorphisms a unique SDPS-set
Non-classical hyperplanes of finite thick dual polar spaces
We obtain a classification of the non-classical hyperplanes of all finite thick dual polar spaces of rank at least 3 under the assumption that there are no ovoidal and semi-singular hex intersections. In view of the absence of known examples of ovoids and semi-singular hyperplanes in finite thick dual polar spaces of rank 3, the condition on the nonexistence of these hex intersections can be regarded as not very restrictive. As a corollary, we also obtain a classification of the non-classical hyperplanes of DW(2n - 1, q), q even. In particular, we obtain a complete classification of all non-classical hyperplanes of DW(2n - 1, q) if q is an element of {8, 32}
Maximal violation of steering inequalities and the matrix cube
In this work, we characterize the amount of steerability present in quantum
theory by connecting the maximal violation of a steering inequality to an
inclusion problem of free spectrahedra. In particular, we show that the maximal
violation of an arbitrary unbiased dichotomic steering inequality is given by
the inclusion constants of the matrix cube, which is a well-studied object in
convex optimization theory. This allows us to find new upper bounds on the
maximal violation of steering inequalities and to show that previously obtained
violations are optimal. In order to do this, we prove lower bounds on the
inclusion constants of the complex matrix cube, which might be of independent
interest. Finally, we show that the inclusion constants of the matrix cube and
the matrix diamond are the same. This allows us to derive new bounds on the
amount of incompatibility available in dichotomic quantum measurements in fixed
dimension.Comment: Slightly generalized Lemma 2.3 and Theorem 3.
Localization of the 17q breakpoint of a constitutional 1;17 translocation in a patient with neuroblastoma within a 25-kb segment located between the ACCN1 and TLK2 genes and near the distal breakpoints of two microdeletions in neurofibromatosis type I patients.
We have constructed a 1.4-Mb P1 artificial chromosome/bacterial artificial chromosome (PAC/BAC) contig spanning the 17q breakpoint of a constitutional translocation t(1;17)(p36.2;q11.2) in a patient with neuroblastoma. Three 17q breakpoint-overlapping cosmids were identified and sequenced. No coding sequences were found in the immediate proximity of the 17q breakpoint. The PAC/BAC contig covers the region between the proximally located ACCN1 gene and the distally located TLK2 gene and SCYA chemokine gene cluster. The observation that the 17q breakpoint region could not be detected in any of the screened yeast artificial chromosome libraries and the localization of the 17q breakpoint in the vicinity of the distal breakpoints of two microdeletions in patients with neurofibromatosis type 1 suggest that this chromosomal region is genetically unstable and prone to rearrangement