Certification of Bounds of Non-linear Functions: the Templates Method

The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of inequalities. We introduce an approximation algorithm, which combines ideas of the max-plus basis method (in optimal control) and of the linear templates method developed by Manna et al. (in static analysis). This algorithm consists in bounding some of the constituents of the function by suprema of quadratic forms with a well chosen curvature. This leads to semialgebraic optimization problems, solved by sum-of-squares relaxations. Templates limit the blow up of these relaxations at the price of coarsening the approximation. We illustrate the efficiency of our framework with various examples from the literature and discuss the interfacing with Coq.Comment: 16 pages, 3 figures, 2 table

Platelet adhesion and degranulation induce pro-survival and pro-angiogenic signalling in ovarian cancer cells

Thrombosis is common in ovarian cancer. However, the interaction of platelets with ovarian cancer cells has not been critically examined. To address this, we investigated platelet interactions in a range of ovarian cancer cell lines with different metastatic potentials [HIO-80, 59M, SK-OV-3, A2780, A2780cis]. Platelets adhered to ovarian cancer cells with the most significant adhesion to the 59M cell line. Ovarian cancer cells induced platelet activation [P-selectin expression] in a dose dependent manner, with the most significant activation seen in response to the 59M cell line. The platelet antagonists [cangrelor, MRS2179, and apyrase] inhibited 59M cell induced activation suggesting a P2Y12 and P2Y1 receptor mediated mechanism of platelet activation dependent on the release of ADP by 59M cells. A2780 and 59M cells potentiated PAR-1, PAR-4, and TxA2 receptor mediated platelet activation, but had no effect on ADP, epinephrine, or collagen induced activation. Analysis of gene expression changes in ovarian cancer cells following treatment with washed platelets or platelet releasate showed a subtle but valid upregulation of anti-apoptotic, anti-autophagy pro-angiogenic, pro-cell cycle and metabolic genes. Thus, ovarian cancer cells with different metastatic potential adhere and activate platelets differentially while both platelets and platelet releasate mediate pro-survival and pro-angiogenic signals in ovarian cancer cells

Platelet adhesion and degranulation induce pro-survival and pro-angiogenic signalling in ovarian cancer cells

Thrombosis is common in ovarian cancer. However, the interaction of platelets with ovarian cancer cells has not been critically examined. To address this, we investigated platelet interactions in a range of ovarian cancer cell lines with different metastatic potentials [HIO-80, 59M, SK-OV-3, A2780, A2780cis]. Platelets adhered to ovarian cancer cells with the most significant adhesion to the 59M cell line. Ovarian cancer cells induced platelet activation [P-selectin expression] in a dose dependent manner, with the most significant activation seen in response to the 59M cell line. The platelet antagonists [cangrelor, MRS2179, and apyrase] inhibited 59M cell induced activation suggesting a P2Y12 and P2Y1 receptor mediated mechanism of platelet activation dependent on the release of ADP by 59M cells. A2780 and 59M cells potentiated PAR-1, PAR-4, and TxA2 receptor mediated platelet activation, but had no effect on ADP, epinephrine, or collagen induced activation. Analysis of gene expression changes in ovarian cancer cells following treatment with washed platelets or platelet releasate showed a subtle but valid upregulation of anti-apoptotic, anti-autophagy pro-angiogenic, pro-cell cycle and metabolic genes. Thus, ovarian cancer cells with different metastatic potential adhere and activate platelets differentially while both platelets and platelet releasate mediate pro-survival and pro-angiogenic signals in ovarian cancer cells