Tractability in Constraint Satisfaction Problems: A Survey

International audienceEven though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

B-L Cosmic Strings in Heterotic Standard Models

E_{8} X E_{8} heterotic string and M-theory, when compactified on smooth Calabi-Yau manifolds with SU(4) vector bundles, can give rise to softly broken N=1 supersymmetric theories with the exact matter spectrum of the MSSM, including three right-handed neutrinos and one Higgs-Higgs conjugate pair of supermultiplets. These vacua have the SU(3)_{C} X SU(2)_{L} X U(1)_{Y} gauge group of the standard model augmented by an additional gauged U(1)_{B-L}. Their minimal content requires that the B-L symmetry be spontaneously broken by a vacuum expectation value of at least one right-handed sneutrino. The soft supersymmetry breaking operators can induce radiative breaking of the B-L gauge symmetry with an acceptable B-L/electroweak hierarchy. In this paper, it is shown that U(1)_{B-L} cosmic strings occur in this context, potentially with both bosonic and fermionic superconductivity. We present a numerical analysis that demonstrates that boson condensates can, in principle, form for theories of this type. However, the weak Yukawa and gauge couplings of the right-handed sneutrino suggests that bosonic superconductivity will not occur in the simplest vacua in this context. The electroweak phase transition also disallows fermion superconductivity, although substantial bound state fermion currents can exist.Comment: 41 pages, 5 figure

Endothelin-1 Inhibits Prolyl Hydroxylase Domain 2 to Activate Hypoxia-Inducible Factor-1α in Melanoma Cells

The endothelin B receptor (ET(B)R) promotes tumorigenesis and melanoma progression through activation by endothelin (ET)-1, thus representing a promising therapeutic target. The stability of hypoxia-inducible factor (HIF)-1alpha is essential for melanomagenesis and progression, and is controlled by site-specific hydroxylation carried out by HIF-prolyl hydroxylase domain (PHD) and subsequent proteosomal degradation.Here we found that in melanoma cells ET-1, ET-2, and ET-3 through ET(B)R, enhance the expression and activity of HIF-1alpha and HIF-2alpha that in turn regulate the expression of vascular endothelial growth factor (VEGF) in response to ETs or hypoxia. Under normoxic conditions, ET-1 controls HIF-alpha stability by inhibiting its degradation, as determined by impaired degradation of a reporter gene containing the HIF-1alpha oxygen-dependent degradation domain encompassing the PHD-targeted prolines. In particular, ETs through ET(B)R markedly decrease PHD2 mRNA and protein levels and promoter activity. In addition, activation of phosphatidylinositol 3-kinase (PI3K)-dependent integrin linked kinase (ILK)-AKT-mammalian target of rapamycin (mTOR) pathway is required for ET(B)R-mediated PHD2 inhibition, HIF-1alpha, HIF-2alpha, and VEGF expression. At functional level, PHD2 knockdown does not further increase ETs-induced in vitro tube formation of endothelial cells and melanoma cell invasiveness, demonstrating that these processes are regulated in a PHD2-dependent manner. In human primary and metastatic melanoma tissues as well as in cell lines, that express high levels of HIF-1alpha, ET(B)R expression is associated with low PHD2 levels. In melanoma xenografts, ET(B)R blockade by ET(B)R antagonist results in a concomitant reduction of tumor growth, angiogenesis, HIF-1alpha, and HIF-2alpha expression, and an increase in PHD2 levels.In this study we identified the underlying mechanism by which ET-1, through the regulation of PHD2, controls HIF-1alpha stability and thereby regulates angiogenesis and melanoma cell invasion. These results further indicate that targeting ET(B)R may represent a potential therapeutic treatment of melanoma by impairing HIF-1alpha stability