Bounding the dimensions of rational cohomology groups

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple simply-connected algebraic group over $k$ that is defined and split over the prime field $\mathbb{F}_p$. In this paper we investigate situations where the dimension of a rational cohomology group for $G$ can be bounded by a constant times the dimension of the coefficient module. We then demonstrate how our results can be applied to obtain effective bounds on the first cohomology of the symmetric group. We also show how, for finite Chevalley groups, our methods permit significant improvements over previous estimates for the dimensions of second cohomology groups.Comment: 13 page

Quantum Double-Torus

A symmetry extending the $T^2$-symmetry of the noncommutative torus $T^2_q$ is studied in the category of quantum groups. This extended symmetry is given by the quantum double-torus defined as a compact matrix quantum group consisting of the disjoint union of $T^2$ and $T^2_{q^2}$. The bicross-product structure of the polynomial Hopf algebra of the quantum double-torus is computed. The Haar measure and the complete list of unitary irreducible representations of the quantum double-torus are determined explicitly.Comment: 6 pages, no figures, amslatex, reformatted for Comptes Rendus, references added, typos and French correcte

Spin Excitations in BaFe1.84Co0.16As2 Superconductor Observed by Inelastic Neutron Scattering

Superconductivity appears to compete against the spin-density-wave in Fe pnictides. However, optimally cobalt doped samples show a quasi-two-dimensional spin excitation centered at the (0.5, 0.5, L) wavevector, "the spin resonance peak", that is strongly tied to the onset of superconductivity. By inelastic neutron scattering on single crystals we show the similarities and differences of the spin excitations in BaFe1.84Co0.16As2, with respect to the spin excitations in the high-temperature superconducting cuprates. As in the cuprates the resonance occurs as an enhancement to a part of the spin excitation spectrum which extends to higher energy transfer and higher temperature. However, unlike in the cuprates, the resonance peak in this compound is asymmetric in energy.Comment: 12 pages, 6 figures; PACS # 74.70.-b, 74.20.Mn, 78.70.Nx, 74.25.Ha; corrected discussion of figures in tex

On dual canonical bases

The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type $A$. The construction of a basis for the coordinate algebra of the $n\times n$ quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a basis of quantum SL(n) is obtained by setting the quantum determinant to one. This basis turns out to be equivalent to the dual canonical basis

Test–retest reliability of multidimensional dyspnea profile recall ratings in the emergency department: a prospective, longitudinal study

BACKGROUND: Dyspnea is among the most common reasons for emergency department (ED) visits by patients with cardiopulmonary disease who are commonly asked to recall the symptoms that prompted them to come to the ED. The reliability of recalled dyspnea has not been systematically investigated in ED patients. METHODS: Patients with chronic or acute cardiopulmonary conditions who came to the ED with dyspnea (N = 154) completed the Multidimensional Dyspnea Profile (MDP) several times during the visit and in a follow-up visit 4 to 6 weeks later (n = 68). The MDP has 12 items with numerical ratings of intensity, unpleasantness, sensory qualities, and emotions associated with how breathing felt when participants decided to come to the ED (recall MDP) or at the time of administration (“now” MDP). The recall MDP was administered twice in the ED and once during the follow-up visit. Principal components analysis (PCA) with varimax rotation was used to assess domain structure of the recall MDP. Internal consistency reliability was assessed with Cronbach’s alpha. Test–retest reliability was assessed with intraclass correlation coefficients (ICCs) for absolute agreement for individual items and domains. RESULTS: PCA of the recall MDP was consistent with two domains (Immediate Perception, 7 items, Cronbach’s alpha = .89 to .94; Emotional Response, 5 items; Cronbach’s alpha = .81 to .85). Test–retest ICCs for the recall MDP during the ED visit ranged from .70 to .87 for individual items and were .93 and .94 for the Immediate Perception and Emotional Response domains. ICCs were much lower for the interval between the ED visit and follow-up, both for individual items (.28 to .66) and for the Immediate Perception and Emotional Response domains (.72 and .78, respectively). CONCLUSIONS: During an ED visit, recall MDP ratings of dyspnea at the time participants decided to seek care in the ED are reliable and sufficiently stable, both for individual items and the two domains, that a time lag between arrival and questionnaire administration does not critically affect recall of perceptual and emotional characteristics immediately prior to the visit. However, test–retest reliability of recall over a 4- to 6-week interval is poor for individual items and significantly attenuated for the two domains

Automated prediction of catalytic mechanism and rate law using graph-based reaction-path sampling

In a recent article [J. Chem. Phys., 143, 094106 (2015)], we have introduced a novel graph-based sampling scheme which can be used to generate chemical reaction paths in many-atom systems in an efficient and highly-automated manner. The main goal of this work is to demonstrate how this approach, when combined with direct kinetic modelling, can be used to determine the mechanism and phenomenological rate law of a complex catalytic cycle, namely cobalt-catalyzed hydroformylation of ethene. Our graph-based sampling scheme generates 31 unique chemical products and 32 unique chemical reaction pathways; these sampled structures and reaction paths en- able automated construction of a kinetic network model of the catalytic system when combined with density functional theory (DFT) calculations of free energies and resul- tant transition-state theory rate constants. Direct simulations of this kinetic network across a range of initial reactant concentrations enables determination of both the re- action mechanism and the associated rate law in an automated fashion, without the need for either pre-supposing a mechanism or making steady-state approximations in kinetic analysis. Most importantly, we find that the reaction mechanism which emerges from these simulations is exactly that originally proposed by Heck and Breslow; fur- thermore, the simulated rate law is also consistent with previous experimental and computational studies, exhibiting a complex dependence on carbon monoxide pres- sure. While the inherent errors of using DFT simulations to model chemical reactivity limit the quantitative accuracy of our calculated rates, this work confirms that our automated simulation strategy enables direct analysis of catalytic mechanisms from first principles