K-orbit closures on G/B as universal degeneracy loci for flagged vector bundles with symmetric or skew-symmetric bilinear form

We use equivariant localization and divided difference operators to determine formulas for the torus-equivariant fundamental cohomology classes of $K$-orbit closures on the flag variety $G/B$, where G = GL(n,\C), and where $K$ is one of the symmetric subgroups O(n,\C) or Sp(n,\C). We realize these orbit closures as universal degeneracy loci for a vector bundle over a variety equipped with a single flag of subbundles and a nondegenerate symmetric or skew-symmetric bilinear form taking values in the trivial bundle. We describe how our equivariant formulas can be interpreted as giving formulas for the classes of such loci in terms of the Chern classes of the various bundles.Comment: Minor revisions and corrections suggested by referees. Final version, to appear in Transformation Group

Calibration of <i>Herschel</i> SPIRE FTS observations at different spectral resolutions

The SPIRE Fourier Transform Spectrometer on-board the Herschel Space Observatory had two standard spectral resolution modes for science observations: high resolution (HR) and low resolution (LR), which could also be performed in sequence (H+LR). A comparison of the HR and LR resolution spectra taken in this sequential mode revealed a systematic discrepancy in the continuum level. Analysing the data at different stages during standard pipeline processing demonstrates that the telescope and instrument emission affect HR and H+LR observations in a systematically different way. The origin of this difference is found to lie in the variation of both the telescope and instrument response functions, while it is triggered by fast variation of the instrument temperatures. As it is not possible to trace the evolution of the response functions using housekeeping data from the instrument subsystems, the calibration cannot be corrected analytically. Therefore, an empirical correction for LR spectra has been developed, which removes the systematic noise introduced by the variation of the response functions

Schur Q-functions and degeneracy locus formulas for morphisms with symmetries

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle, and is based on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear in the Proceedings of Intersection Theory Conference in Bologna, "Progress in Mathematics", Birkhause

Box ball system associated with antisymmetric tensor crystals

A new box ball system associated with an antisymmetric tensor crystal of the quantum affine algebra of type A is considered. This includes the so-called colored box ball system with capacity 1 as the simplest case. Infinite number of conserved quantities are constructed and the scattering rule of two olitons are given explicitly.Comment: 15 page

Radiation from a Charge Uniformly Accelerated for All Time

A recent paper of Singal [Gen. Rel. Grav. 27 (1995), 953-967] argues that a uniformly accelerated particle does not radiate, in contradiction to the consensus of the research literature over the past 30 years. This note points out some questionable aspects of Singal's argument and shows how similar calculations can lead to the opposite conclusion.Comment: LaTeX, 9 pages, to appear in General Relativity and Gravitatio

Entanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond

This paper concentrates on a particular example of a constraint imposed by superselection rules (SSRs): that which applies when the parties (Alice and Bob) cannot distinguish among certain quantum objects they have. This arises naturally in the context of ensemble quantum information processing such as in liquid NMR. We discuss how a SSR for the symmetric group can be applied, and show how the extractable entanglement can be calculated analytically in certain cases, with a maximum bipartite entanglement in an ensemble of N Bell-state pairs scaling as log(N) as N goes to infinity . We discuss the apparent disparity with the asymptotic (N >> 1) recovery of unconstrained entanglement for other sorts of superselection rules, and show that the disparity disappears when the correct notion of applying the symmetric group SSR to multiple copies is used. Next we discuss reference frames in the context of this SSR, showing the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502 (2004)]. The action of a reference frame can be regarded as the analog of activation in mixed-state entanglement. We also discuss the analog of distillation: there exist states such that one copy can act as an imperfect reference frame for another copy. Finally we present an example of a stronger operational constraint, that operations must be non-collective as well as symmetric. Even under this stronger constraint we nevertheless show that Bell-nonlocality (and hence entanglement) can be demonstrated for an ensemble of N Bell-state pairs no matter how large N is. This last work is a generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)].Comment: 16 pages, 6 figures. v2 updated version published in Phys Rev

Lie group weight multiplicities from conformal field theory

Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of Wess-Zumino-Witten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new relations are strong enough to completely fix all multiplicities.Comment: 12 pages, Plain TeX, no figure

Hyperinsulinism-hyperammonaemia syndrome: novel mutations in the GLUD1 gene and genotype-phenotype correlations

Background: Activating mutations in the GLUD1 gene (which encodes for the intra-mitochondrial enzyme glutamate dehydrogenase, GDH) cause the hyperinsulinism–hyperammonaemia (HI/HA) syndrome. Patients present with HA and leucine-sensitive hypoglycaemia. GDH is regulated by another intra-mitochondrial enzyme sirtuin 4 (SIRT4). Sirt4 knockout mice demonstrate activation of GDH with increased amino acid-stimulated insulin secretion. Objectives: To study the genotype–phenotype correlations in patients with GLUD1 mutations. To report the phenotype and functional analysis of a novel mutation (P436L) in the GLUD1 gene associated with the absence of HA. Patients and methods: Twenty patients with HI from 16 families had mutational analysis of the GLUD1 gene in view of HA (n=19) or leucine sensitivity (n=1). Patients negative for a GLUD1 mutation had sequence analysis of the SIRT4 gene. Functional analysis of the novel P436L GLUD1 mutation was performed. Results: Heterozygous missense mutations were detected in 15 patients with HI/HA, 2 of which are novel (N410D and D451V). In addition, a patient with a normal serum ammonia concentration (21 µmol/l) was heterozygous for a novel missense mutation P436L. Functional analysis of this mutation confirms that it is associated with a loss of GTP inhibition. Seizure disorder was common (43%) in our cohort of patients with a GLUD1 mutation. No mutations in the SIRT4 gene were identified. Conclusion: Patients with HI due to mutations in the GLUD1 gene may have normal serum ammonia concentrations. Hence, GLUD1 mutational analysis may be indicated in patients with leucine sensitivity; even in the absence of HA. A high frequency of epilepsy (43%) was observed in our patients with GLUD1 mutations