The Uncertainty of Fluxes

In the ordinary quantum Maxwell theory of a free electromagnetic field, formulated on a curved 3-manifold, we observe that magnetic and electric fluxes cannot be simultaneously measured. This uncertainty principle reflects torsion: fluxes modulo torsion can be simultaneously measured. We also develop the Hamilton theory of self-dual fields, noting that they are quantized by Pontrjagin self-dual cohomology theories and that the quantum Hilbert space is Z/2-graded, so typically contains both bosonic and fermionic states. Significantly, these ideas apply to the Ramond-Ramond field in string theory, showing that its K-theory class cannot be measured.Comment: 33 pages; minor modifications for publication in Commun. Math. Phy

Galois theory and Lubin-Tate cochains on classifying spaces

We consider brave new cochain extensions F(BG +,R) → F(EG +,R), where R is either a Lubin-Tate spectrum E n or the related 2-periodic Morava K-theory K n , and G is a finite group. When R is an Eilenberg-Mac Lane spectrum, in some good cases such an extension is a G-Galois extension in the sense of John Rognes, but not always faithful. We prove that for E n and K n these extensions are always faithful in the K n local category. However, for a cyclic p-group C p r, the cochain extension F(BC p r +,E n ) → F(EC p r +, E n ) is not a Galois extension because it ramifies. As a consequence, it follows that the E n -theory Eilenberg-Moore spectral sequence for G and BG does not always converge to its expected target

A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra

We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq(gln). We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weight, Drinfeld polynomials and the Gelfand-Tsetlin character (or q-character). We also apply the quantum Sylvester theorem to construct a q-analogue of the Olshanski algebra as a projective limit of certain centralizers in Uq(gln) and show that this limit algebra contains the q-Yangian as a subalgebra

M-theory and Characteristic Classes

In this note we show that the Chern-Simons and the one-loop terms in the M-theory action can be written in terms of new characters involving the M-theory four-form and the string classes. This sheds a new light on the topological structure behind M-theory and suggests the construction of a theory of `higher' characteristic classes.Comment: 8 pages. Error in gravitational term fixed; minor corrections; reference and acknowledgement adde

ASSESSING CHEMICAL HAZARDS AT THE PLUTONIUM FINISHING PLANT (PFP) FOR PLANNING FUTURE D&D

This paper documents the fiscal year (FY) 2006 assessment to evaluate potential chemical and radiological hazards associated with vessels and piping in the former plutonium process areas at Hanford's Plutonium Finishing Plant (PFP). Evaluations by PFP engineers as design authorities for specific systems and other subject-matter experts were conducted to identify the chemical hazards associated with transitioning the process areas for the long-term layup of PFP before its eventual final decontamination and decommissioning (D and D). D and D activities in the main process facilities were suspended in September 2005 for a period of between 5 and 10 years. A previous assessment conducted in FY 2003 found that certain activities to mitigate chemical hazards could be deferred safely until the D and D of PFP, which had been scheduled to result in a slab-on-grade condition by 2009. As a result of necessary planning changes, however, D and D activities at PFP will be delayed until after the 2009 time frame. Given the extended project and plant life, it was determined that a review of the plant chemical hazards should be conducted. This review to determine the extended life impact of chemicals is called the ''Plutonium Finishing Plant Chemical Hazards Assessment, FY 2006''. This FY 2006 assessment addresses potential chemical and radiological hazard areas identified by facility personnel and subject-matter experts who reevaluated all the chemical systems (items) from the FY 2003 assessment. This paper provides the results of the FY 2006 chemical hazards assessment and describes the methodology used to assign a hazard ranking to the items reviewed

LDRD final report: Physical simulation of nonisothermal multiphase multicomponent flow in porous media

This document reports on the accomplishments of a laboratory-directed research and development (LDRD) project whose objective was to initiate a research program for developing a fundamental understanding of multiphase multicomponent subsurface transport in heterogeneous porous media and to develop parallel processing computational tools for numerical simulation of such problems. The main achievement of this project was the successful development of a general-purpose, unstructured grid, multiphase thermal simulator for subsurface transport in heterogeneous porous media implemented for use on massively parallel (MP) computers via message-passing and domain decomposition techniques. The numerical platform provides an excellent base for new and continuing project development in areas of current interest to SNL and the DOE complex including, subsurface nuclear waste disposal and cleanup, groundwater availability and contamination studies, fuel-spill transport for accident analysis, and DNAPL transport and remediation

Stratifying derived categories of cochains on certain spaces

In recent years, Benson, Iyengar and Krause have developed a theory of stratification for compactly generated triangulated categories with an action of a graded commutative Noetherian ring. Stratification implies a classification of localizing and thick subcategories in terms of subsets of the prime ideal spectrum of the given ring. In this paper two stratification results are presented: one for the derived category of a commutative ring-spectrum with polynomial homotopy and another for the derived category of cochains on certain spaces. We also give the stratification of cochains on a space a topological content.Comment: 27 page

A genome-wide linkage and association scan reveals novel loci for autism

Member of the Autism Genome Project Consortium: Astrid M. VicenteAlthough autism is a highly heritable neurodevelopmental disorder, attempts to identify specific susceptibility genes have thus far met with limited success. Genome-wide association studies using half a million or more markers, particularly those with very large sample sizes achieved through meta-analysis, have shown great success in mapping genes for other complex genetic traits. Consequently, we initiated a linkage and association mapping study using half a million genome-wide single nucleotide polymorphisms (SNPs) in a common set of 1,031 multiplex autism families (1,553 affected offspring). We identified regions of suggestive and significant linkage on chromosomes 6q27 and 20p13, respectively. Initial analysis did not yield genome-wide significant associations; however, genotyping of top hits in additional families revealed an SNP on chromosome 5p15 (between SEMA5A and TAS2R1) that was significantly associated with autism (P = 2 x 10(-7)). We also demonstrated that expression of SEMA5A is reduced in brains from autistic patients, further implicating SEMA5A as an autism susceptibility gene. The linkage regions reported here provide targets for rare variation screening whereas the discovery of a single novel association demonstrates the action of common variants

On a Conjecture of Rapoport and Zink

In their book Rapoport and Zink constructed rigid analytic period spaces $F^{wa}$ for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of $p$-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism $F^a \to F^{wa}$ of rigid analytic spaces and of a universal local system of $Q_p$-vector spaces on $F^a$. For Hodge-Tate weights $n-1$ and $n$ we construct in this article an intrinsic Berkovich open subspace $F^0$ of $F^{wa}$ and the universal local system on $F^0$. We conjecture that the rigid-analytic space associated with $F^0$ is the maximal possible $F^a$, and that $F^0$ is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, $F^0$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal $p$-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases $F^0$ equals all of $F^{wa}$ and when the Shimura group is $GL_n$ we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

The anomaly line bundle of the self-dual field theory

In this work, we determine explicitly the anomaly line bundle of the abelian self-dual field theory over the space of metrics modulo diffeomorphisms, including its torsion part. Inspired by the work of Belov and Moore, we propose a non-covariant action principle for a pair of Euclidean self-dual fields on a generic oriented Riemannian manifold. The corresponding path integral allows to study the global properties of the partition function over the space of metrics modulo diffeomorphisms. We show that the anomaly bundle for a pair of self-dual fields differs from the determinant bundle of the Dirac operator coupled to chiral spinors by a flat bundle that is not trivial if the underlying manifold has middle-degree cohomology, and whose holonomies are determined explicitly. We briefly sketch the relevance of this result for the computation of the global gravitational anomaly of the self-dual field theory, that will appear in another paper.Comment: 41 pages. v2: A few typos corrected. Version accepted for publication in CM