1,368 research outputs found

    Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras

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    Darboux coordinates are constructed on rational coadjoint orbits of the positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by the values of the spectral parameters at the divisors corresponding to eigenvector line bundles over the associated spectral curves, defined within a given matrix representation. A Liouville generating function is obtained in completely separated form and shown, through the Liouville-Arnold integration method, to lead to the Abel map linearization of all Hamiltonian flows induced by the spectral invariants. Serre duality is used to define a natural symplectic structure on the space of line bundles of suitable degree over a permissible class of spectral curves, and this is shown to be equivalent to the Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general construction is given for g=gl(r)\frak{g}=\frak{gl}(r) or sl(r)\frak{sl}(r), with reductions to orbits of subalgebras determined as invariant fixed point sets under involutive automorphisms. The case g=sl(2)\frak{g=sl}(2) is shown to reproduce the classical integration methods for finite dimensional systems defined on quadrics, as well as the quasi-periodic solutions of the cubically nonlinear Schr\"odinger equation. For g=sl(3)\frak{g=sl}(3), the method is applied to the computation of quasi-periodic solutions of the two component coupled nonlinear Schr\"odinger equation.Comment: 61 pg

    Resistance to autosomal dominant Alzheimer's disease in an APOE3 Christchurch homozygote: a case report.

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    We identified a PSEN1 (presenilin 1) mutation carrier from the world's largest autosomal dominant Alzheimer's disease kindred, who did not develop mild cognitive impairment until her seventies, three decades after the expected age of clinical onset. The individual had two copies of the APOE3 Christchurch (R136S) mutation, unusually high brain amyloid levels and limited tau and neurodegenerative measurements. Our findings have implications for the role of APOE in the pathogenesis, treatment and prevention of Alzheimer's disease

    Singularities of bi-Hamiltonian systems

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    We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of linearization of a Poisson pencil. From the algebraic viewpoint, a linearized Poisson pencil can be understood as a Lie algebra with a fixed 2-cocycle. In terms of such linearizations, we give a criterion for non-degeneracy of singular points of bi-Hamiltonian systems and describe their types

    Folliculin interacts with p0071 (plakophilin-4) and deficiency is associated with disordered rhoa signalling, epithelial polarization and cytokinesis

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    Inherited mutations in the folliculin (FLCN) gene cause the Birt-Hogg-Dubé syndrome of familial hair follicle tumours (fibrofolliculomas), lung cysts and kidney tumours. Though folliculin has features of a tumour suppressor, the precise function of the FLCN gene product is not well characterized. We identified plakophilin-4 (p0071) as a potential novel folliculin interacting protein by yeast two-hybrid analysis. We confirmed the interaction of folliculin with p0071 by co-immunoprecipitation studies and, in view of previous studies linking p0071 to the regulation of rho-signalling, cytokinesis and intercellular junction formation, we investigated the effect of cell folliculin status on p0071-related functions. Folliculin and p0071 partially co-localized at cell junctions and in mitotic cells, at the midbody during cytokinesis. Previously, p0071 has been reported to regulate RhoA signalling during cytokinesis and we found that folliculin deficiency was associated with increased expression and activity of RhoA and evidence of disordered cytokinesis. Treatment of folliculin-deficient cells with a downstream inhibitor of RhoA signalling (the ROCK inhibitor Y-27632) reversed the increased cell migration phenotype observed in folliculin-deficient cells. Deficiency of folliculin and of p0071 resulted in tight junction defects and mislocalization of E-cadherin in mouse inner medullary collecting duct-3 renal tubular cells. These findings suggest that aspects of folliculin tumour suppressor function are linked to interaction with p0071 and the regulation of RhoA signalling

    Intratumoral macrophages contribute to epithelial-mesenchymal transition in solid tumors

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    <p>Abstract</p> <p>Background</p> <p>Several stromal cell subtypes including macrophages contribute to tumor progression by inducing epithelial-mesenchymal transition (EMT) at the invasive front, a mechanism also linked to metastasis. Tumor associated macrophages (TAM) reside mainly at the invasive front but they also infiltrate tumors and in this process they mainly assume a tumor promoting phenotype. In this study, we asked if TAMs also regulate EMT intratumorally. We found that TAMs through TGF-β signaling and activation of the β-catenin pathway can induce EMT in intratumoral cancer cells.</p> <p>Methods</p> <p>We depleted macrophages in F9-teratocarcinoma bearing mice using clodronate-liposomes and analyzed the tumors for correlations between gene and protein expression of EMT-associated and macrophage markers. The functional relationship between TAMs and EMT was characterized <it>in vitro </it>in the murine F9 and mammary gland NMuMG cells, using a conditioned medium culture approach. The clinical relevance of our findings was evaluated on a tissue microarray cohort representing 491 patients with non-small cell lung cancer (NSCLC).</p> <p>Results</p> <p>Gene expression analysis of F9-teratocarcinomas revealed a positive correlation between TAM-densities and mesenchymal marker expression. Moreover, immunohistochemistry showed that TAMs cluster with EMT phenotype cells in the tumors. <it>In vitro</it>, long term exposure of F9-and NMuMG-cells to macrophage-conditioned medium led to decreased expression of the epithelial adhesion protein E-cadherin, activation of the EMT-mediating β-catenin pathway, increased expression of mesenchymal markers and an invasive phenotype. In a candidate based screen, macrophage-derived TGF-β was identified as the main inducer of this EMT-associated phenotype. Lastly, immunohistochemical analysis of NSCLC patient samples identified a positive correlation between intratumoral macrophage densities, EMT markers, intraepithelial TGF-β levels and tumor grade.</p> <p>Conclusions</p> <p>Data presented here identify a novel role for macrophages in EMT-promoted tumor progression. The observation that TAMs cluster with intra-epithelial fibroblastoid cells suggests that the role of macrophages in tumor-EMT extends beyond the invasive front. As macrophage infiltration and pronounced EMT tumor phenotype correlate with increased grade in NSCLC patients, we propose that TAMs also promote tumor progression by inducing EMT locally in tumors.</p

    The history of degenerate (bipartite) extremal graph problems

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    This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete
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