Products, coproducts and singular value decomposition

Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, ie generalized eigenvalues, to these maps. We show, for the case of Grassmann and Clifford products, that twist maps significantly alter these data reducing degeneracies. Since non group like coproducts give rise to non classical behavior of the algebra of functions, ie make them noncommutative, we hope to be able to learn more about such geometries. Remarkably the coproduct for positive singular values of eigenvectors in $A$ yields directly corresponding eigenvectors in A\otimes A.Comment: 17 pages, three eps-figure

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

Z_2-gradings of Clifford algebras and multivector structures

Let Cl(V,g) be the real Clifford algebra associated to the real vector space V, endowed with a nondegenerate metric g. In this paper, we study the class of Z_2-gradings of Cl(V,g) which are somehow compatible with the multivector structure of the Grassmann algebra over V. A complete characterization for such Z_2-gradings is obtained by classifying all the even subalgebras coming from them. An expression relating such subalgebras to the usual even part of Cl(V,g) is also obtained. Finally, we employ this framework to define spinor spaces, and to parametrize all the possible signature changes on Cl(V,g) by Z_2-gradings of this algebra.Comment: 10 pages, LaTeX; v2 accepted for publication in J. Phys.

A Hopf laboratory for symmetric functions

An analysis of symmetric function theory is given from the perspective of the underlying Hopf and bi-algebraic structures. These are presented explicitly in terms of standard symmetric function operations. Particular attention is focussed on Laplace pairing, Sweedler cohomology for 1- and 2-cochains, and twisted products (Rota cliffordizations) induced by branching operators in the symmetric function context. The latter are shown to include the algebras of symmetric functions of orthogonal and symplectic type. A commentary on related issues in the combinatorial approach to quantum field theory is given.Comment: 29 pages, LaTeX, uses amsmat

The structure of Green functions in quantum field theory with a general state

In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are required. The corresponding Green functions are essentially more complex than in the vacuum, because they cannot be written in terms of standard Feynman diagrams. Here, a method is proposed to determine the structure of these Green functions and to derive nonperturbative equations for them. The main idea is to transform the cumulants describing correlations into interaction terms.Comment: 13 pages, 6 figure

Long-term outcome of patients with newly diagnosed chronic myeloid leukemia: a randomized comparison of stem cell transplantation with drug treatment.

Tyrosine kinase inhibitors represent today's treatment of choice in chronic myeloid leukemia (CML). Allogeneic hematopoietic stem cell transplantation (HSCT) is regarded as salvage therapy. This prospective randomized CML-study IIIA recruited 669 patients with newly diagnosed CML between July 1997 and January 2004 from 143 centers. Of these, 427 patients were considered eligible for HSCT and were randomized by availability of a matched family donor between primary HSCT (group A; N=166 patients) and best available drug treatment (group B; N=261). Primary end point was long-term survival. Survival probabilities were not different between groups A and B (10-year survival: 0.76 (95% confidence interval (CI): 0.69-0.82) vs 0.69 (95% CI: 0.61-0.76)), but influenced by disease and transplant risk. Patients with a low transplant risk showed superior survival compared with patients with high- (P<0.001) and non-high-risk disease (P=0.047) in group B; after entering blast crisis, survival was not different with or without HSCT. Significantly more patients in group A were in molecular remission (56% vs 39%; P=0.005) and free of drug treatment (56% vs 6%; P<0.001). Differences in symptoms and Karnofsky score were not significant. In the era of tyrosine kinase inhibitors, HSCT remains a valid option when both disease and transplant risk are considered

Cidofovir for BK Virus-Associated Hemorrhagic Cystitis: A Retrospective Study

Background.BK virus-associated hemorrhagic cystitis (BKV-HC) is a severe complication after allogeneic hematopoietic stem cell transplantation (HSCT), but antiviral treatment for this condition has not been evaluated. Methods.We conducted a retrospective survey on the safety and outcome of cidofovir treatment for patients with BKV-HC in centers affiliated with the European Group for Blood and Marrow Transplantation. Results.From 1 April 2004 to 31 December 2007, 62 patients received a diagnosis of BKV-HC after a median interval of 35 days after HSCT (range, 3-577 days). Fifty-seven patients (92%) received intravenous cidofovir, whereas 5 patients received cidofovir intravesically. Complete response (CR) was recorded in 38 (67%) of 57 patients with HC treated with intravenous cidofovir, whereas partial response (PR) was documented in 7 patients (12%). CR was documented in 3 patients and PR in 1 patient with HC treated with intravesical cidofovir. A reduction of 1-3 logs in BKV load was documented in 8 of the 10 patients achieving CR. Mild-to-moderate toxic effects were recorded in 18 of 57 patients who received intravenous cidofovir administration. In a multivariate analysis, the factors significantly associated with response to cidofovir were the stem cell source (P=.01) and the use of total body irradiation (P=.03). After a median follow-up of 287 days, overall survival and total treatment-related mortality rates were 63% and 40% for patients achieving CR, compared with 14% and 72% for patients with PR or no response to cidofovir, respectively (P<.001 and P=.001, respectively). Conclusions.Cidofovir may be a potentially effective therapy for BKV-HC, but evidence supporting its use requires randomized controlled trial

Neonicotinoid Insecticides and Their Impacts on Bees: A Systematic Review of Research Approaches and Identification of Knowledge Gaps

It has been suggested that the widespread use of neonicotinoid insecticides threatens bees, but research on this topic has been surrounded by controversy. In order to synthesize which research approaches have been used to examine the effect of neonicotinoids on bees and to identify knowledge gaps, we systematically reviewed research on this subject that was available on the Web of Science and PubMed in June 2015. Most of the 216 primary research studies were conducted in Europe or North America (82%), involved the neonicotinoid imidacloprid (78%), and concerned the western honey bee Apis mellifera (75%). Thus, little seems to be known about neonicotinoids and bees in areas outside Europe and North America. Furthermore, because there is considerable variation in ecological traits among bee taxa, studies on honey bees are not likely to fully predict impacts of neonicotinoids on other species. Studies on crops were dominated by seed-treated maize, oilseed rape (canola) and sunflower, whereas less is known about potential side effects on bees from the use of other application methods on insect pollinated fruit and vegetable crops, or on lawns and ornamental plants. Laboratory approaches were most common, and we suggest that their capability to infer real-world consequences are improved when combined with information from field studies about realistic exposures to neonicotinoids. Studies using field approaches often examined only bee exposure to neonicotinoids and more field studies are needed that measure impacts of exposure. Most studies measured effects on individual bees. We suggest that effects on the individual bee should be linked to both mechanisms at the sub-individual level and also to the consequences for the colony and wider bee populations. As bees are increasingly facing multiple interacting pressures future research needs to clarify the role of neonicotinoids in relative to other drivers of bee declines

Bumble bee parasite strains vary in resistance to phytochemicals

Nectar and pollen contain diverse phytochemicals that can reduce disease in pollinators. However, prior studies showed variable effects of nectar chemicals on infection, which could reflect variable phytochemical resistance among parasite strains. Inter-strain variation in resistance could influence evolutionary interactions between plants, pollinators, and pollinator disease, but testing direct effects of phytochemicals on parasites requires elimination of variation between bees. Using cell cultures of the bumble bee parasite Crithidia bombi, we determined (1) growth-inhibiting effects of nine floral phytochemicals and (2) variation in phytochemical resistance among four parasite strains. C. bombi growth was unaffected by naturally occurring concentrations of the known antitrypanosomal phenolics gallic acid, caffeic acid, and chlorogenic acid. However, C. bombi growth was inhibited by anabasine, eugenol, and thymol. Strains varied >3-fold in phytochemical resistance, suggesting that selection for phytochemical resistance could drive parasite evolution. Inhibitory concentrations of thymol (4.53-22.2 ppm) were similar to concentrations in Thymus vulgaris nectar (mean 5.2 ppm). Exposure of C. bombi to naturally occurring levels of phytochemicals—either within bees or during parasite transmission via flowers—could influence infection in nature. Flowers that produce antiparasitic phytochemical, including thymol, could potentially reduce infection in Bombus populations, thereby counteracting a possible contributor to pollinator decline