The cohomology ring of weight varieties and polygon spaces

We use a theorem of Tolman and Weitsman to find explicit formul\ae for the rational cohomology rings of the symplectic reduction of flag varieties in C^n, or generic coadjoint orbits of SU(n), by (maximal) torus actions. We also calculate the cohomology ring of the moduli space of $n$ points in CP^k, which is isomorphic to the Grassmannian of k-planes in C^n, by realizing it as a degenerate coadjoint orbit.Comment: 31 pages, 1 figur

Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points

Manifolds associated with (Z2)n(Z_2)^n-colored regular graphs

In this article we describe a canonical way to expand a certain kind of $(\mathbb Z_2)^{n+1}$-colored regular graphs into closed $n$-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial $n$-manifold can be obtained in this way. When $n\leq 3$, we give simple equivalent conditions for a colored graph to admit an expansion. In addition, we show that if a $(\mathbb Z_2)^{n+1}$-colored regular graph admits an $n$-skeletal expansion, then it is realizable as the moment graph of an $(n+1)$-dimensional closed $(\mathbb Z_2)^{n+1}$-manifold.Comment: 20 pages with 9 figures, in AMS-LaTex, v4 added a new section on reconstructing a space with a $(Z_2)^n$-action for which its moment graph is a given colored grap

Thrombin and factor Xa link the coagulation system with Liver fibrosis

Background: Thrombin activates hepatic stellate cells via protease-activated receptor-1. The role of Factor Xa (FXa) in hepatic fibrosis has not been elucidated. We aimed to evaluate the impact of FXa and thrombin in vitro on stellate cells and their respective inhibition in vivo using a rodent model of hepatic fibrosis. Methods: HSC-LX2 cells were incubated with FXa and/or thrombin in cell culture, stained for αSMA and relative gene expression and gel contraction calculated. C57BL/6 J mice were administered thioacetamide (TAA) for 8 weeks with Rivaroxaban (n = 15) or Dabigatran (n = 15). Control animals received TAA alone (n = 15). Fibrosis was scored and quantified using digital image analysis and hepatic tissue hydroxyproline estimated. Results Stellate cells treated with FXa and thrombin demonstrated upregulation of procollagen, TGF-beta, αSMA and significant cell contraction (43.48%+/− 4.12) compared to culturing with FXa or thrombin alone (26.90%+/− 8.90, p = 0.02; 13.1%+/− 9.84, p < 0.001). Mean fibrosis score, percentage area of fibrosis and hepatic hydroxyproline content (2.46 vs 4.08, p = 0.008; 2.02% vs 3.76%, p = 0.012; 276.0 vs 651.3, p = 0.0001) were significantly reduced in mice treated with the FXa inhibitor compared to control mice. FXa inhibition was significantly more effective than thrombin inhibition in reducing percentage area of fibrosis and hepatic hydroxyproline content (2.02% vs 3.70%,p = 0.031; 276.0 vs 413.1,p = 0.001). Conclusions: FXa promotes stellate cell contractility and activation. Early inhibition of coagulation using a FXa inhibitor significantly reduces TAA induced murine liver fibrosis and may be a viable treatment for liver fibrosis in patients

Oscillatory instabilities in d.c. biased quantum dots

We consider a `quantum dot' in the Coulomb blockade regime, subject to an arbitrarily large source-drain voltage V. When V is small, quantum dots with odd electron occupation display the Kondo effect, giving rise to enhanced conductance. Here we investigate the regime where V is increased beyond the Kondo temperature and the Kondo resonance splits into two components. It is shown that interference between them results in spontaneous oscillations of the current through the dot. The theory predicts the appearance of ``Shapiro steps'' in the current-voltage characteristics of an irradiated quantum dot; these would constitute an experimental signature of the predicted effect.Comment: Four pages with embedded figure