303 research outputs found
Menelaus relation and Fay's trisecant formula are associativity equations
It is shown that the celebrated Menelaus relation and Fay's trisecant formula
similar to the WDVV equation are associativity conditions for structure
constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons
and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte
Determinantal Characterization of Canonical Curves and Combinatorial Theta Identities
We characterize genus g canonical curves by the vanishing of combinatorial
products of g+1 determinants of Brill-Noether matrices. This also implies the
characterization of canonical curves in terms of (g-2)(g-3)/2 theta identities.
A remarkable mechanism, based on a basis of H^0(K_C) expressed in terms of
Szego kernels, reduces such identities to a simple rank condition for matrices
whose entries are logarithmic derivatives of theta functions. Such a basis,
together with the Fay trisecant identity, also leads to the solution of the
question of expressing the determinant of Brill-Noether matrices in terms of
theta functions, without using the problematic Klein-Fay section sigma.Comment: 35 pages. New results, presentation improved, clarifications added.
Accepted for publication in Math. An
Quartic double solids with ordinary singularities
We study the mixed Hodge structure on the third homology group of a threefold
which is the double cover of projective three-space ramified over a quartic
surface with a double conic. We deal with the Torelli problem for such
threefolds.Comment: 14 pages, presented at the Conference Arnol'd 7
Two-dimensional model of dynamical fermion mass generation in strongly coupled gauge theories
We generalize the Schwinger model on the lattice by adding a charged
scalar field. In this so-called model the scalar field shields
the fermion charge, and a neutral fermion, acquiring mass dynamically, is
present in the spectrum. We study numerically the mass of this fermion at
various large fixed values of the gauge coupling by varying the effective
four-fermion coupling, and find an indication that its scaling behavior is the
same as that of the fermion mass in the chiral Gross-Neveu model. This suggests
that the model is in the same universality class as the
Gross-Neveu model, and thus renormalizable and asymptotic free at arbitrary
strong gauge coupling.Comment: 18 pages, LaTeX2e, requires packages rotating.sty and curves.sty from
CTA
Research priorities for managing the impacts and dependencies of business upon food, energy, water and the environment
Delivering access to sufficient food, energy and water resources to ensure human wellbeing is a major concern for governments worldwide. However, it is crucial to account for the ‘nexus’ of interactions between these natural resources and the consequent implications for human wellbeing. The private sector has a critical role in driving positive change towards more sustainable nexus management and could reap considerable benefits from collaboration with researchers to devise solutions to some of the foremost sustainability challenges of today. Yet opportunities are missed because the private sector is rarely involved in the formulation of deliverable research priorities. We convened senior research scientists and influential business leaders to collaboratively identify the top forty questions that, if answered, would best help companies understand and manage their food-energy-water-environment nexus dependencies and impacts. Codification of the top order nexus themes highlighted research priorities around development of pragmatic yet credible tools that allow businesses to incorporate nexus interactions into their decision-making; demonstration of the business case for more sustainable nexus management; identification of the most effective levers for behaviour change; and understanding incentives or circumstances that allow individuals and businesses to take a leadership stance. Greater investment in the complex but productive relations between the private sector and research community will create deeper and more meaningful collaboration and cooperation.This work was supportedby the Economic and Social Research Council [Grant Number ES/L01632X/1] and is part of the Nexus Network Initiative. WJS is funded by Arcadia
Modulation of β-Catenin Signaling by Glucagon Receptor Activation
The glucagon receptor (GCGR) is a member of the class B G protein–coupled receptor family. Activation of GCGR by glucagon leads to increased glucose production by the liver. Thus, glucagon is a key component of glucose homeostasis by counteracting the effect of insulin. In this report, we found that in addition to activation of the classic cAMP/protein kinase A (PKA) pathway, activation of GCGR also induced β-catenin stabilization and activated β-catenin–mediated transcription. Activation of β-catenin signaling was PKA-dependent, consistent with previous reports on the parathyroid hormone receptor type 1 (PTH1R) and glucagon-like peptide 1 (GLP-1R) receptors. Since low-density-lipoprotein receptor–related protein 5 (Lrp5) is an essential co-receptor required for Wnt protein mediated β-catenin signaling, we examined the role of Lrp5 in glucagon-induced β-catenin signaling. Cotransfection with Lrp5 enhanced the glucagon-induced β-catenin stabilization and TCF promoter–mediated transcription. Inhibiting Lrp5/6 function using Dickkopf-1(DKK1) or by expression of the Lrp5 extracellular domain blocked glucagon-induced β-catenin signaling. Furthermore, we showed that Lrp5 physically interacted with GCGR by immunoprecipitation and bioluminescence resonance energy transfer assays. Together, these results reveal an unexpected crosstalk between glucagon and β-catenin signaling, and may help to explain the metabolic phenotypes of Lrp5/6 mutations
Cisplatin-DNA adduct formation in patients treated with cisplatin-based chemoradiation: lack of correlation between normal tissues and primary tumor
Contains fulltext :
69595.pdf (publisher's version ) (Closed access)PURPOSE: In this study, the formation of cisplatin-DNA adducts after concurrent cisplatin-radiation and the relationship between adduct-formation in primary tumor tissue and normal tissue were investigated. METHODS: Three intravenous cisplatin-regimens, given concurrently with radiation, were studied: daily low-dose (6 mg/m(2)) cisplatin, weekly 40 mg/m(2), three-weekly 100 mg/m(2). A (32)P-postlabeling technique was used to quantify adducts in normal tissue [white blood cells (WBC) and buccal cells] and tumor. RESULTS: Normal tissue samples for adduct determination were obtained from 63 patients and tumor biopsies from 23 of these patients. Linear relationships and high correlations were observed between the levels of two guanosine- and adenosine-guanosine-adducts in normal and tumor tissue. Adduct levels in tumors were two to five times higher than those in WBC (P<0.001). No significant correlations were found between adduct levels in normal tissues and primary tumor biopsies, nor between WBC and buccal cells. CONCLUSIONS: In concurrent chemoradiotherapy schedules, cisplatin adduct levels in tumors were significantly higher than in normal tissues (WBC). No evidence of a correlation was found between adduct levels in normal tissues and primary tumor biopsies. This lack of correlation may, to some extent, explain the inconsistencies in the literature regarding whether or not cisplatin-DNA adducts can be used as a predictive test in anticancer platinum therapy
COUP-TFII Controls Mouse Pancreatic β-Cell Mass through GLP-1-β-Catenin Signaling Pathways
Background: The control of the functional pancreatic beta-cell mass serves the key homeostatic function of releasing the right amount of insulin to keep blood sugar in the normal range. It is not fully understood though how beta-cell mass is determined
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