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

Versatile Coordination of Cyclopentadienyl-Arene Ligands and Its Role in Titanium-Catalyzed Ethylene Trimerization

Cationic titanium(IV) complexes with ansa-(η5-cyclopentadienyl,η6-arene) ligands were synthesized and characterized by X-ray crystallography. The strength of the metal-arene interaction in these systems was studied by variable-temperature NMR spectroscopy. Complexes with a C1 bridge between the cyclopentadienyl and arene moieties feature hemilabile coordination behavior of the ligand and consequently are active ethylene trimerization catalysts. Reaction of the titanium(IV) dimethyl cations with CO results in conversion to the analogous cationic titanium(II) dicarbonyl species. Metal-to-ligand backdonation in these formally low-valent complexes gives rise to a strongly bonded, partially reduced arene moiety. In contrast to the η6-arene coordination mode observed for titanium, the more electron-rich vanadium(V) cations [cyclopentadienyl-arene]V(NiPr2)(NC6H4-4-Me)+ feature η1-arene binding, as determined by a crystallographic study. The three different metal-arene coordination modes that we experimentally observed model intermediates in the cycle for titanium-catalyzed ethylene trimerization. The nature of the metal-arene interaction in these systems was studied by DFT calculations.

Comparative Evaluation of Three Automated Systems for DNA Extraction in Conjunction with Three Commercially Available Real-Time PCR Assays for Quantitation of Plasma Cytomegalovirus DNAemia in Allogeneic Stem Cell Transplant Recipients▿

Limited data are available on the performance of different automated extraction platforms and commercially available quantitative real-time PCR (QRT-PCR) methods for the quantitation of cytomegalovirus (CMV) DNA in plasma. We compared the performance characteristics of the Abbott mSample preparation system DNA kit on the m24 SP instrument (Abbott), the High Pure viral nucleic acid kit on the COBAS AmpliPrep system (Roche), and the EZ1 Virus 2.0 kit on the BioRobot EZ1 extraction platform (Qiagen) coupled with the Abbott CMV PCR kit, the LightCycler CMV Quant kit (Roche), and the Q-CMV complete kit (Nanogen), for both plasma specimens from allogeneic stem cell transplant (Allo-SCT) recipients (n = 42) and the OptiQuant CMV DNA panel (AcroMetrix). The EZ1 system displayed the highest extraction efficiency over a wide range of CMV plasma DNA loads, followed by the m24 and the AmpliPrep methods. The Nanogen PCR assay yielded higher mean CMV plasma DNA values than the Abbott and the Roche PCR assays, regardless of the platform used for DNA extraction. Overall, the effects of the extraction method and the QRT-PCR used on CMV plasma DNA load measurements were less pronounced for specimens with high CMV DNA content (>10,000 copies/ml). The performance characteristics of the extraction methods and QRT-PCR assays evaluated herein for clinical samples were extensible at cell-based standards from AcroMetrix. In conclusion, different automated systems are not equally efficient for CMV DNA extraction from plasma specimens, and the plasma CMV DNA loads measured by commercially available QRT-PCRs can differ significantly. The above findings should be taken into consideration for the establishment of cutoff values for the initiation or cessation of preemptive antiviral therapies and for the interpretation of data from clinical studies in the Allo-SCT setting

Panel 4 : Report of the Microbiology Panel

Objective. To perform a comprehensive review of the literature from July 2011 until June 2015 on the virology and bacteriology of otitis media in children. Data Sources. PubMed database of the National Library of Medicine. Review Methods. Two subpanels comprising experts in the virology and bacteriology of otitis media were created. Each panel reviewed the relevant literature in the fields of virology and bacteriology and generated draft reviews. These initial reviews were distributed to all panel members prior to meeting together at the Post-symposium Research Conference of the 18th International Symposium on Recent Advances in Otitis Media, National Harbor, Maryland, in June 2015. A final draft was created, circulated, and approved by all panel members. Conclusions. Excellent progress has been made in the past 4 years in advancing our understanding of the microbiology of otitis media. Numerous advances were made in basic laboratory studies, in animal models of otitis media, in better understanding the epidemiology of disease, and in clinical practice. Implications for Practice. (1) Many viruses cause acute otitis media without bacterial coinfection, and such cases do not require antibiotic treatment. (2) When respiratory syncytial virus, metapneumovirus, and influenza virus peak in the community, practitioners can expect to see an increase in clinical otitis media cases. (3) Biomarkers that predict which children with upper respiratory tract infections will develop otitis media may be available in the future. (4) Compounds that target newly identified bacterial virulence determinants may be available as future treatment options for children with otitis media.Peer reviewe

Using relict rockglaciers in GIS-based modelling to reconstruct Younger Dryas permafrost distribution patterns in the Err-Julier area, Swiss Alp

Differences in mean annual air temperature between the Younger Dryas period and today were estimated at the fronts of 32 relict rockglaciers in the Err-Julier area, eastern Swiss Alps. The analyses were based on a case-by-case calculation of direct incoming solar radiation and mean annual air temperature using a digital elevation model (DEM) and meteo data of recent years. Our results suggest that mean annual air temperature during the Younger Dryas was lowered by c. 3°C to 4°C, and that the lower limit of permafrost occurrence was depressed considerably more than glacier equilibrium lines. This indicates strongly reduced precipitation (30% to 40% reduction) and much larger abundance of mountain permafrost at that time. A model simulation of the corresponding spatial permafrost distribution during the Younger Dryas indicates that glaciers in the study area were mostly surrounded by permafrost at that time and probably had a polythermal structure of englacial temperatures

The 10Be deglaciation chronology of the Göschenertal, central Swiss Alps, and new insights into the Göschenen Cold Phases

The Göschenertal (Göschenen valley) is the type locality of the so‐called Göschenen Cold Phases I (~3–2.3 ka) and II (~1.8–1.1 ka). According to earlier studies, these Late Holocene climatic cooling periods were characterized by changes in vegetation and pronounced glacier advances. As a peculiarity, the Göschenen Cold Phase I was thought to be connected to a local surge‐type advance of the Chelengletscher (Chelen glacier) – an exceptional event of unparalleled dimension in the European Alps. Based on cosmogenic 10Be exposure ages from moraine boulders, we investigated the local glacier chronology. In contrast to former research, moraines at different positions within the Göschenen valley (central Swiss Alps) have been dated to the Younger Dryas and the Early Holocene. This questions the applicability of palaeo‐Equilibrium Line Altitude (ELA) calculations for stadial attributions without additional numerical age constraints. Furthermore, we have found compelling evidence that the proposed non‐climatic glacier advance attributed to the Göschenen Cold Phase I did not occur. The present results, along with a reappraisal of the original study, question the scientific reliability and the glaciological definition of the Göschenen Cold Phases as glacier advances that clearly exceeded the Little Ice Age positions. While our data do not exclude potential changes in climate and vegetation, we nonetheless show that the Göschenen Cold Phases are not suitable as reference stadials in the system of Alpine Holocene glacier fluctuations

Cosmogenic ¹⁰Be and ²⁶Al ages of Holocene moraines in southern Norway I: testing the method and confirmation of the date of the Erdalen Event (<i>c</i>. 10 ka) at its type-site

Cosmogenic nuclide dating (10Be and 26Al) is applied to boulders on two moraine ridges at the type-site of the early-Holocene Erdalen Event, southern Norway, dated previously using radiocarbon. Quartz-rich rock samples yielded 10Be age estimates between 9.8 ± 1.2 and 10.1 ± 1.1ka (external uncertainties, ±1σ), with an average of 9.95 ka. These age estimates are statistically indistinguishable from the independent radiocarbon age estimate. 26Al age estimates, which ranged from 9.4 ± 1.1 to 11.2 ± 1.3 ka, provided useful corroboration of the 10Be results. Although current levels of precision and accuracy are insufficient to distinguish between the ages of younger inner and older outer moraines, the results demonstrate the potential of the method at suitable sites where radiocarbon dating is not possible. Several environmental factors, including effective glacial erosion, stability of moraine sloes, snow cover of sufficiently shallow depth and short duration, and the absence of colluvial contamination, appear to have been instrumental in the success of applying the method at this site. The results confirm the timing and extent of the Erdalen Event in southern Norway with implications for Holocene glacier chronology and millennial-scale climatic variability