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 $N_F=2$ Schwinger model on the lattice by adding a charged scalar field. In this so-called $\chi U\phi_2$ 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 $\chi U\phi_2$ 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

Arabidopsis AtVPS15 is essential for pollen development and germination through modulating phosphatidylinositol 3-phosphate formation

Arabidopsis thaliana phosphatidylinositol 3-kinase (AtVPS34) functions in the development and germination of pollen by catalyzing the biosynthesis of phosphatidylinositol 3-phosphate (PI3P). In yeast, Vps15p is required for the membrane targeting and activity of Vps34. The expression of Arabidopsis thaliana VPS15 (AtVPS15), an ortholog of yeast Vps15, is mainly detected in pollen grains and pollen tubes. To determine its role in pollen development and pollen tube growth, we attempted to isolate the T-DNA insertion mutants of AtVPS15; however, homozygous lines of atvps15 were not obtained from the progeny of atvps15/+ heterozygotes. Genetic analysis revealed that the abnormal segregation is due to the failure of transmission of the atvps15 allele through pollen. Most pollen grains from the atvps15/+ genotype are viable, with normal exine structure and nuclei, but some mature pollen grains are characterized with unusual large vacuoles that are not observed in pollen grains from the wild AtVPS15 genotype. The germination ratio of pollen from the atvps15/+ genotype is about half when compared to that from the wild AtVPS15 genotype. When supplied with PI3P, in vitro pollen germination of the atvps15/+ genotype is greatly improved. Presumably, AtVPS15 functions in pollen development and germination by regulating PI3P biosynthesis in Arabidopsis