Khovanov Homology, Lee Homology and a Rasmussen Invariant for Virtual Knots

The paper contains an essentially self-contained treatment of Khovanov homology, Khovanov-Lee homology as well as the Rasmussen invariant for virtual knots and virtual knot cobordisms which directly applies to classical knot and classical knot cobordisms. To do so, we give an alternate formulation for the Manturov definition of Khovanov homology for virtual knots and links with arbitrary coefficients. This approach uses cut loci on the knot diagram to induce a conjugation operator in the Frobenius algebra. We then discuss the implications of the maps induced in the aforementioned theory to the universal Frobenius algebra for virtual knots. Next we show how one can apply the Karoubi envelope approach of Bar-Natan and Morrison on abstract link diagrams with cross cuts to construct the canonical generators of the Khovanov-Lee homology. Using these canonical generators we derive a generalization of the Rasmussen invariant for virtual knot cobordisms and furthermore generalize Rasmussen's result on the slice genus for positive knots to the case of positive virtual knots. It should also be noted that this generalization of the Rasmussen invariant provides an easy to compute obstruction to knot cobordisms in $S_g \times I \times I$ in the sense of Turaev

Minimal surface representations of virtual knots and links

Kuperberg [Algebr. Geom. Topol. 3 (2003) 587-591] has shown that a virtual knot corresponds (up to generalized Reidemeister moves) to a unique embedding in a thichened surface of minimal genus. If a virtual knot diagram is equivalent to a classical knot diagram then this minimal surface is a sphere. Using this result and a generalised bracket polynomial, we develop methods that may determine whether a virtual knot diagram is non-classical (and hence non-trivial). As examples we show that, except for special cases, link diagrams with a single virtualization and link diagrams with a single virtual crossing are non-classical.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-22.abs.html Version 5: a minor correction and a citation adde

Infection of human primary renal epithelial cells with HIV-1 from children with HIV-associated nephropathy

Infection of human primary renal epithelial cells with HIV-1 from children with HIV-associated nephropathy. Children affected with human immunodefficiency virus (HIV)-associated nephropathy (HIVAN) usually develop significant renal glomerular and tubular epithelial cell injury. The pathogenesis of these changes is not clearly understood. Human renal tubular epithelial cells (RTEc) do not express CD4 surface receptors, and it is not clear whether these cells can be infected by HIV-1. Certain strains of HIV-1, however, have been shown capable of infecting CD4-negative epithelial cell lines. We hypothesized that the inability of laboratory strains of HIV-1 to infect renal epithelial cells may be due to a limited tropism, as opposed to wild-type viruses derived from children with HIVAN, and that viruses derived from these children are capable of infecting RTEc from the same patient. Here, we have demonstrated that HIV-1 isolates from children with HIVAN can productively infect RTEc through a CD4 independent pathway, and that infected mononuclear cells can transfer the virus to human RTEc. Human RTEc sustained low levels of viral replication and HIV-1 inhibited the growth and survival of cultured human RTEc. Thus, HIV-1 may directly induce degenerative changes in RTEc of children with HIVAN. Infected macrophages may play a relevant role in this process by transferring viruses to RTEc

Human condensin function is essential for centromeric chromatin assembly and proper sister kinetochore orientation.

Condensins I and II in vertebrates are essential ATP-dependent complexes necessary for chromosome condensation in mitosis. Condensins depletion is known to perturb structure and function of centromeres, however the mechanism of this functional link remains elusive. Depletion of condensin activity is now shown to result in a significant loss of loading of CENP-A, the histone H3 variant found at active centromeres and the proposed epigenetic mark of centromere identity. Absence of condensins and/or CENP-A insufficiency produced a specific kinetochore defect, such that a functional mitotic checkpoint cannot prevent chromosome missegregation resulting from improper attachment of sister kinetochores to spindle microtubules. Spindle microtubule-dependent deformation of both inner kinetochores and the HEC1/Ndc80 microtubule-capturing module, then results in kinetochore separation from the Aurora B pool and ensuing reduced kinase activity at centromeres. Moreover, recovery from mitosis-inhibition by monastrol revealed a high incidence of merotelic attachment that was nearly identical with condensin depletion, Aurora B inactivation, or both, indicating that the Aurora B dysfunction is the key defect leading to chromosome missegregation in condensin-depleted cells. Thus, beyond a requirement for global chromosome condensation, condensins play a pivotal role in centromere assembly, proper spatial positioning of microtubule-capturing modules and positioning complexes of the inner centromere versus kinetochore plates

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

The preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess.Comment: Major update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figure