Integral Invariants of 3-Manifolds

This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.Comment: 39 pages, AMS-LaTeX, to appear in J. Diff. Geo

Wilson surfaces and higher dimensional knot invariants

An observable for nonabelian, higher-dimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higher-dimensional knots.Comment: 31 pages, 9 figure

Evaluating detection limits of next-generation sequencing for the surveillance and monitoring of international marine pests

Most surveillance programmes for marine invasive species (MIS) require considerable taxonomic expertise, are laborious, and are unable to identify species at larval or juvenile stages. Therefore, marine pests may go undetected at the initial stages of incursions when population densities are low. In this study, we evaluated the ability of the benchtop GS Junior™ 454 pyrosequencing system to detect the presence of MIS in complex sample matrices. An initial in-silico evaluation of the mitochondrial cytochrome c oxidase subunit I (COI) and the nuclear small subunit ribosomal DNA (SSU) genes, found that multiple primer sets (targeting a ca. 400 base pair region) would be required to obtain species level identification within the COI gene. In contrast a single universal primer set was designed to target the V1–V3 region of SSU, allowing simultaneous PCR amplification of a wide taxonomic range of MIS. To evaluate the limits of detection of this method, artificial contrived communities (10 species from 5 taxonomic groups) were created using varying concentrations of known DNA samples and PCR products. Environmental samples (water and sediment) spiked with one or five 160 hr old Asterias amurensis larvae were also examined. Pyrosequencing was able to recover DNA/PCR products of individual species present at greater than 0.64% abundance from all tested contrived communities. Additionally, single A. amurensis larvae were detected from both water and sediment samples despite the co-occurrence of a large array of environmental eukaryotes, indicating an equivalent sensitivity to quantitative PCR. NGS technology has tremendous potential for the early detection of marine invasive species worldwide

A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models

The algebraic definition of charges for symmetry-preserving D-branes in Wess-Zumino-Witten models is shown to coincide with the geometric definition, for all simple Lie groups. The charge group for such branes is computed from the ambiguities inherent in the geometric definition.Comment: 12 pages, fixed typos, added references and a couple of remark

Elastic-plastic analysis of frames- including axial force effect on moment capacity

A method is presented for analyzing the elastic-plastic behavior of frames which account for the reduction of plastic moment capacity due to the presence of axial force

Inner topological structure of Hopf invariant

In light of $\phi$-mapping topological current theory, the inner topological structure of Hopf invariant is investigated. It is revealed that Hopf invariant is just the winding number of Gauss mapping. According to the inner structure of topological current, a precise expression for Hopf invariant is also presented. It is the total sum of all the self-linking and all the linking numbers of the knot family.Comment: 13pages, no figure. Accepted by J.Math.Phy

The Standard Model Fermion Spectrum From Complex Projective spaces

It is shown that the quarks and leptons of the standard model, including a right-handed neutrino, can be obtained by gauging the holonomy groups of complex projective spaces of complex dimensions two and three. The spectrum emerges as chiral zero modes of the Dirac operator coupled to gauge fields and the demonstration involves an index theorem analysis on a general complex projective space in the presence of topologically non-trivial SU(n)xU(1) gauge fields. The construction may have applications in type IIA string theory and non-commutative geometry.Comment: 13 pages. Typset using LaTeX and JHEP3 style files. Minor typos correcte

Noncommutative generalization of SU(n)-principal fiber bundles: a review

This is an extended version of a communication made at the international conference ``Noncommutative Geometry and Physics'' held at Orsay in april 2007. In this proceeding, we make a review of some noncommutative constructions connected to the ordinary fiber bundle theory. The noncommutative algebra is the endomorphism algebra of a SU(n)-vector bundle, and its differential calculus is based on its Lie algebra of derivations. It is shown that this noncommutative geometry contains some of the most important constructions introduced and used in the theory of connections on vector bundles, in particular, what is needed to introduce gauge models in physics, and it also contains naturally the essential aspects of the Higgs fields and its associated mechanics of mass generation. It permits one also to extend some previous constructions, as for instance symmetric reduction of (here noncommutative) connections. From a mathematical point of view, these geometrico-algebraic considerations highlight some new point on view, in particular we introduce a new construction of the Chern characteristic classes