The Elliptic curves in gauge theory, string theory, and cohomology

Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, thes elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the reduction of M-theory to) type IIA and as the elliptic fiber leading to F-theory for type IIB. In this paper we elaborate on the physical setting for various generalized cohomology theories, including elliptic cohomology, and we note that the above two seemingly unrelated descriptions can be unified using Sen's picture of the orientifold limit of F-theory compactification on K3, which unifies the Seiberg-Witten curve with the F-theory curve, and through which we naturally explain the constancy of the modulus that emerges from elliptic cohomology. This also clarifies the orbifolding performed in the previous work and justifies the appearance of the w_4 condition in the elliptic refinement of the mod 2 part of the partition function. We comment on the cohomology theory needed for the case when the modular parameter varies in the base of the elliptic fibration.Comment: 23 pages, typos corrected, minor clarification

Quantum discontinuity between zero and infinitesimal graviton mass with a Lambda term

We show that the recently demonstrated absence of the usual discontinuity for massive spin 2 with a Lambda term is an artifact of the tree approximation, and that the discontinuity reappears at one loop.Comment: 8 pages, revtex 3.1, title changed (version to appear in Phys. Rev. Lett.

Duality symmetry and the form fields of M-theory

In previous work we derived the topological terms in the M-theory action in terms of certain characters that we defined. In this paper, we propose the extention of these characters to include the dual fields. The unified treatment of the M-theory four-form field strength and its dual leads to several observations. In particular we elaborate on the possibility of a twisted cohomology theory with a twist given by degrees greater than three.Comment: 12 pages, modified material on the differentia

Twisted topological structures related to M-branes II: Twisted Wu and Wu^c structures

Studying the topological aspects of M-branes in M-theory leads to various structures related to Wu classes. First we interpret Wu classes themselves as twisted classes and then define twisted notions of Wu structures. These generalize many known structures, including Pin^- structures, twisted Spin structures in the sense of Distler-Freed-Moore, Wu-twisted differential cocycles appearing in the work of Belov-Moore, as well as ones introduced by the author, such as twisted Membrane and twisted String^c structures. In addition, we introduce Wu^c structures, which generalize Pin^c structures, as well as their twisted versions. We show how these structures generalize and encode the usual structures defined via Stiefel-Whitney classes.Comment: 20 page

Principal infinity-bundles - General theory

The theory of principal bundles makes sense in any infinity-topos, such as that of topological, of smooth, or of otherwise geometric infinity-groupoids/infinity-stacks, and more generally in slices of these. It provides a natural geometric model for structured higher nonabelian cohomology and controls general fiber bundles in terms of associated bundles. For suitable choices of structure infinity-group G these G-principal infinity-bundles reproduce the theories of ordinary principal bundles, of bundle gerbes/principal 2-bundles and of bundle 2-gerbes and generalize these to their further higher and equivariant analogs. The induced associated infinity-bundles subsume the notions of gerbes and higher gerbes in the literature. We discuss here this general theory of principal infinity-bundles, intimately related to the axioms of Giraud, Toen-Vezzosi, Rezk and Lurie that characterize infinity-toposes. We show a natural equivalence between principal infinity-bundles and intrinsic nonabelian cocycles, implying the classification of principal infinity-bundles by nonabelian sheaf hyper-cohomology. We observe that the theory of geometric fiber infinity-bundles associated to principal infinity-bundles subsumes a theory of infinity-gerbes and of twisted infinity-bundles, with twists deriving from local coefficient infinity-bundles, which we define, relate to extensions of principal infinity-bundles and show to be classified by a corresponding notion of twisted cohomology, identified with the cohomology of a corresponding slice infinity-topos. In a companion article [NSSb] we discuss explicit presentations of this theory in categories of simplicial (pre)sheaves by hyper-Cech cohomology and by simplicial weakly-principal bundles; and in [NSSc] we discuss various examples and applications of the theory.Comment: 46 pages, published versio

The Loop Group of E8 and Targets for Spacetime

The dimensional reduction of the E8 gauge theory in eleven dimensions leads to a loop bundle in ten dimensional type IA string theory. We show that the restriction to the Neveu-Schwarz sector leads naturally to a sigma model with target space E8 with the ten-dimensional spacetime as the source. The corresponding bundle has a structure group the group of based loops, whose classifying space we study. We explore some consequences of this proposal such as possible Lagrangians and existence of flat connections.Comment: 17 pages, main section improved, change in title, reference and acknowledgement adde

LIPID PEROXIDE LEVELS AND ANTIOXIDANT STATUS IN HEALTHY AND ALCOHOLIC HEPATITIS PATIENTS

Background: Alcohol remains the single most significant cause of liver disease throughout the Western world, responsible for between 40 and 80% of cases of cirrhosis in different countries. Material & Methods:The study was conducted in Department of Biochemistry, Santosh medical college & Hospital, Ghaziabad and Veer Chandra Singh Garhwali Govt. Institute of Medical Sciences & Research, 164 alcoholic hepatitis patients were subjected to detailed clinical examination and laboratory investigations and the results were compared with 82controls. Blood samples were collected for oxidative stress parameters. It was observed that there was a significant increase in activities of Catalase, SOD, MDA, GPX and GR activity in patients with alcoholic hepatitis when compared to controls. Results: Results of our study show higher oxygen free radical production, evidenced by elevated levels of MDA and decreased levels of Catalase, SOD, GPx, GR, and TAS activity, supporting the evidence of oxidative stress in alcoholic hepatitis patients. Decreased concentrations of antioxidant support the hypothesis that alcoholic hepatitis is an important causative factor in pathogenesis of lipid peroxidation. Conclusion: Theantioxidant defense mechanisms might be impaired in patients with alcoholic hepatitis. These findings also provide a theoretical basis for development of novel therapeutic strategies, such as antioxidant supplementation. Keywords: Alcoholic Hepatitis; Catalase; Glutathione Peroxidase; Glutathione Reductase; Malondialdehyde; Superoxide dismutase; Total antioxidant status

LIPID PEROXIDE LEVELS AND ANTIOXIDANT STATUS IN HEALTHY AND ALCOHOLIC HEPATITIS PATIENTS

Background: Alcohol remains the single most significant cause of liver disease throughout the Western world, responsible for between 40 and 80% of cases of cirrhosis in different countries. Material & Methods:The study was conducted in Department of Biochemistry, Santosh medical college & Hospital, Ghaziabad and Veer Chandra Singh Garhwali Govt. Institute of Medical Sciences & Research, 164 alcoholic hepatitis patients were subjected to detailed clinical examination and laboratory investigations and the results were compared with 82controls. Blood samples were collected for oxidative stress parameters. It was observed that there was a significant increase in activities of Catalase, SOD, MDA, GPX and GR activity in patients with alcoholic hepatitis when compared to controls. Results: Results of our study show higher oxygen free radical production, evidenced by elevated levels of MDA and decreased levels of Catalase, SOD, GPx, GR, and TAS activity, supporting the evidence of oxidative stress in alcoholic hepatitis patients. Decreased concentrations of antioxidant support the hypothesis that alcoholic hepatitis is an important causative factor in pathogenesis of lipid peroxidation. Conclusion: Theantioxidant defense mechanisms might be impaired in patients with alcoholic hepatitis. These findings also provide a theoretical basis for development of novel therapeutic strategies, such as antioxidant supplementation. Keywords: Alcoholic Hepatitis; Catalase; Glutathione Peroxidase; Glutathione Reductase; Malondialdehyde; Superoxide dismutase; Total antioxidant status

Twisted topological structures related to M-branes

Studying the M-branes leads us naturally to new structures that we call Membrane-, Membrane^c-, String^K(Z,3)- and Fivebrane^K(Z,4)-structures, which we show can also have twisted counterparts. We study some of their basic properties, highlight analogies with structures associated with lower levels of the Whitehead tower of the orthogonal group, and demonstrate the relations to M-branes.Comment: 17 pages, title changed on referee's request, minor changes to improve presentation, typos correcte

Bayesian model averaging approach in health effects studies: Sensitivity analyses using PM10 and cardiopulmonary hospital admissions in Allegheny County, Pennsylvania and simulated data

AbstractGeneralized Additive Models (GAMs) with natural cubic splines (NS) as smoothing functions have become a standard analytical tool in time series studies of health effects of air pollution. However, standard model selection procedures ignore the model uncertainty that may lead to biased estimates, in particular those of the lagged effects. We addressed this issue by Bayesian model averaging (BMA) approach which accounts for model uncertainty by combining information from all possible models where GAMs and NS were used. Firstly, we conducted a sensitivity analysis with simulation studies for Bayesian model averaging with different calibrated hyperparameters contained in the posterior model probabilities. Our results indicated the importance of selecting the optimum degree of lagging for variables, based not only on maximizing the likelihood, but also by considering the possible effects of concurvity, consistency of degree of lagging, and biological plausibility. This was illustrated by analyses of the Allegheny County Air Pollution Study (ACAPS) where the quantity of interest was the relative risk of cardiopulmonary hospital admissions for a 20 μg/m3 increase in PM10 values for the current day. Results showed that the posterior means of the relative risk and 95% posterior probability intervals were close to each other under different choices of the prior distributions. Simulation results were consistent with these findings. It was also found that using lag variables in the model when there is only same day effect, may underestimate the relative risk attributed to the same day effect