On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form

Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) \bigwedge V and an ordering, guarantees a multi-vector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomorphism theorem cannot be generalized to algebras if the Z_n-grading or other structures are added, e.g., a linear form. We work with pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford algebras'. It turns out, that in this sense, all multi-vector Clifford algebras of the same quadratic but different bilinear forms are non-isomorphic. The usefulness of such algebras in quantum field theory and superconductivity was shown elsewhere. Allowing for arbitrary bilinear forms however spoils their diagonalizability which has a considerable effect on the tensor decomposition of the Clifford algebras governed by the periodicity theorems, including the Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which can be decomposed in the symmetric case into a tensor product Cl_{p-1,q-1} \otimes Cl_{1,1}. The general case used in quantum field theory lacks this feature. Theories with non-symmetric bilinear forms are however needed in the analysis of multi-particle states in interacting theories. A connection to q-deformed structures through nontrivial vacuum states in quantum theories is outlined.Comment: 25 pages, 1 figure, LaTeX, {Paper presented at the 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa, Mexico, June 27 - July 4, 199

Outcomes of abdominoperineal resection for management of anal cancer in HIV-positive patients: a national case review

BACKGROUND: The incidence of anal cancer in human immunodeficiency virus (HIV)-positive individuals is increasing, and how co-infection affects outcomes is not fully understood. This study sought to describe the current outcome disparities between anal cancer patients with and without HIV undergoing abdominoperineal resection (APR). METHODS: A retrospective review of all US patients diagnosed with anal squamous cell carcinoma, undergoing an APR, was performed. Cases were identified using a weighted derivative of the Healthcare Utilization Project’s National Inpatient Sample (2000–2011). Patients greater than 60 years old were excluded after finding a skewed population distribution between those with and without HIV infection. Multivariable logistic regression and generalized linear modeling analysis examined factors associated with postoperative outcomes and cost. Perioperative complications, in-hospital mortality, length of hospital stay, and hospital costs were compared for those undergoing APR with and without HIV infection. RESULTS: A total of 1725 patients diagnosed with anal squamous cell cancer undergoing APR were identified, of whom 308 (17.9 %) were HIV-positive. HIV-positive patients were younger than HIV-negative patients undergoing APR for anal cancer (median age 47 years old versus 51 years old, p < 0.001) and were more likely to be male (95.1 versus 30.6 %, p < 0.001). Postoperative hemorrhage was more frequent in the HIV-positive group (5.1 versus 1.5 %, p = 0.05). Mortality was low in both groups (0 % in HIV-positive versus 1.49 % in HIV-negative, p = 0.355), and length of stay (LOS) (10+ days; 75th percentile of patient data) was similar (36.9 % with HIV versus 29.8 % without HIV, p = 0.262). Greater hospitalization costs were associated with patients who experienced a complication. However, there was no difference in hospitalization costs seen between HIV-positive and HIV-negative patients (p = 0.66). CONCLUSIONS: HIV status is not associated with worse postoperative recovery after APR for anal cancer as measured by length of stay or hospitalization cost. Further study may support APRs to be used more aggressively in HIV-positive patients with anal cancer. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12957-016-0970-x) contains supplementary material, which is available to authorized users

Precise measurement of the W-boson mass with the CDF II detector

We have measured the W-boson mass MW using data corresponding to 2.2/fb of integrated luminosity collected in proton-antiproton collisions at 1.96 TeV with the CDF II detector at the Fermilab Tevatron collider. Samples consisting of 470126 W->enu candidates and 624708 W->munu candidates yield the measurement MW = 80387 +- 12 (stat) +- 15 (syst) = 80387 +- 19 MeV. This is the most precise measurement of the W-boson mass to date and significantly exceeds the precision of all previous measurements combined

Metal-organic frameworks as kinetic modulators for branched selectivity in hydroformylation.

Finding heterogeneous catalysts that are superior to homogeneous ones for selective catalytic transformations is a major challenge in catalysis. Here, we show how micropores in metal-organic frameworks (MOFs) push homogeneous catalytic reactions into kinetic regimes inaccessible under standard conditions. Such property allows branched selectivity up to 90% in the Co-catalysed hydroformylation of olefins without directing groups, not achievable with existing catalysts. This finding has a big potential in the production of aldehydes for the fine chemical industry. Monte Carlo and density functional theory simulations combined with kinetic models show that the micropores of MOFs with UMCM-1 and MOF-74 topologies increase the olefins density beyond neat conditions while partially preventing the adsorption of syngas leading to high branched selectivity. The easy experimental protocol and the chemical and structural flexibility of MOFs will attract the interest of the fine chemical industries towards the design of heterogeneous processes with exceptional selectivity