A new proof of the Herman-Avila-Bochi formula for Lyapunov exponents of SL(2,R)-cocycles

We study the geometry of the action of SL(2,R) on the projective line in order to present a new and simpler proof of the Herman-Avila-Bochi formula. This formula gives the average Lyapunov exponent of a class of 1-families of SL(2,R)-cocycles.Comment: 13 pages, 2 figure

Convexity properties of the condition number II

In our previous paper [SIMAX 31 n.3 1491-1506(2010)], we studied the condition metric in the space of maximal rank matrices. Here, we show that this condition metric induces a Lipschitz-Riemann structure on that space. After investigating geodesics in such a nonsmooth structure, we show that the inverse of the smallest singular value of a matrix is a log-convex function along geodesics (Theorem 1). We also show that a similar result holds for the solution variety of linear systems (Theorem 31). Some of our intermediate results, such as Theorem 12, on the second covariant derivative or Hessian of a function with symmetries on a manifold, and Theorem 29 on piecewise self-convex functions, are of independent interest. Those results were motivated by our investigations on the com- plexity of path-following algorithms for solving polynomial systems.Comment: Revised versio

Restauration des terrains en montagne (RTM) et défense des forêts contre les incendies (DFCI)

Les grandes tendances pesant sur les perspectives d'aménagement du territoire régional peuvent être résumées ainsi : le maintien du pastoralisme ovin, la politique européenne du développement rural, la poursuite de la déprise agricole, les bons résultats de la prévention des feux de forêt

Punctual Hilbert Schemes and Certified Approximate Singularities

In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a polynomial system f $=(f\_1, \ldots, f\_N)\in C[x\_1, \ldots, x\_n]^N$, we present a Newton iteration on an extended deflated system that locally converges, under regularity conditions, to a small deformation of $f$ such that this deformed system has an exact singular root. The iteration simultaneously converges to the coordinates of the singular root and the coefficients of the so called inverse system that describes the multiplicity structure at the root. We use $$\alpha$$-theory test to certify the quadratic convergence, and togive bounds on the size of the deformation and on the approximation error. The approach relies on an analysis of the punctual Hilbert scheme, for which we provide a new description. We show in particular that some of its strata can be rationally parametrized and exploit these parametrizations in the certification. We show in numerical experimentation how the approximate inverse system can be computed as a starting point of the Newton iterations and the fast numerical convergence to the singular root with its multiplicity structure, certified by our criteria.Comment: International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Franc

Living bioethics, theories and children’s consent to heart surgery

Background: This analysis is about practical living bioethics and how law, ethics and sociology understand and respect children’s consent to, or refusal of, elective heart surgery. Analysis of underlying theories and influences will contrast legalistic bioethics with living bioethics. In-depth philosophical analysis compares social science traditions of positivism, interpretivism, critical theory and functionalism and applies them to bioethics and childhood, to examine how living bioethics may be encouraged or discouraged. Illustrative examples are drawn from research interviews and observations in two London paediatric cardiac units. This paper is one of a series on how the multidisciplinary cardiac team members all contribute to the complex mosaic of care when preparing and supporting families’ informed consent to surgery. Results: The living bioethics of justice, care and respect for children and their consent depends on theories and practices, contexts and relationships. These can all be undermined by unseen influences: the history of adult-centric ethics; developmental psychology theories; legal and financial pressures that require consent to be defined as an adult contract; management systems and daily routines in healthcare that can intimidate families and staff; social inequalities. Mainstream theories in the clinical ethics literature markedly differ from the living bioethics in clinical practices. Conclusion: We aim to contribute to raising standards of respectful paediatric bioethics and to showing the relevance of virtue and feminist ethics, childhood studies and children’s rights

Ethanol application at veraison decreases acidity in Cabernet Sauvignon grapes

Research NoteSpraying ethanol (5 % v/v in water) onto grape clusters at mid-veraison led to a 30 % drop in the malic acid concentration at harvest. As a consequence, titratable acidity also dropped by 10 %. The concentration of tartaric acid did not change significantly. The mode of action of ethanol on malic acid metabolism is discussed.

Resonant X-ray emission spectroscopy reveals d–d ligand-field states involved in the self-assembly of a square-planar platinum complex

Resonant X-ray Emission Spectroscopy (RXES) is used to characterize the ligand field states of the prototypic self-assembled square-planar complex, [Pt(tpy)Cl]Cl (tpy=2,2′:6′,2′′-terpyridine), and determine the effect of weak metal-metal and π-π interactions on their energy. © 2012 the Owner Societies