Topological types of real regular jacobian elliptic surfaces

We present the topological classification of real parts of real regular elliptic surfaces with a real section.Comment: 17 pages, 7 figures, to appear in Geometriae Dedicat

Right-handed Hopf algebras and the preLie forest formula

Three equivalent methods allow to compute the antipode of the Hopf algebras of Feynman diagrams in perturbative quantum field theory (QFT): the Dyson-Salam formula, the Bogoliubov formula, and the Zimmermann forest formula. Whereas the first two hold generally for arbitrary connected graded Hopf algebras, the third one requires extra structure properties of the underlying Hopf algebra but has the nice property to reduce drastically the number of terms in the expression of the antipode (it is optimal in that sense).The present article is concerned with the forest formula: we show that it generalizes to arbitrary right-handed polynomial Hopf algebras. These Hopf algebras are dual to the enveloping algebras of preLie algebras -a structure common to many combinatorial Hopf algebras which is carried in particular by the Hopf algebras of Feynman diagrams

Quality-improving alliances in differentiated oligopoly

We study rival firms' incentives in quality-improving Research and Development (R&D) networks. The analysis stresses the role of free riding associated to collaboration and three major consequences emerge: R&D efforts decrease with the number of partners, networks of alliances are over-connected as compared to the social optimum and the profitmaximizing number of alliances is possibly non monotonic (decreasing then increasing) with respect to inverse measure of product differentiation.Vertically and horizontally Differentiated Oligopoly, Product Innovation, R&D, Alliance

Standardization versus Preference for Variety in Linear Cournot Oligopoly

We consider a Cournot oligopoly setting in which consumers have an intrinsic preference for variety, while unit production costs of firms increase with the number of goods they produce. This environment exhibits a general under-provision of variety with respect to social welfare.Standardization; Preference for Variety; Oligopoly

Nonlinear Dimension Reduction for Microarray Data

[Biomedical imaging

Inverse spectral problem for singular AKNS operator on [0,1]

We consider an inverse spectral problem for a class of singular AKNS operators $H\_a, a\in\N$ with an explicit singularity. We construct for each $a\in\N$, a standard map $\lambda^a\times\kappa^a$ with spectral data $\lambda^a$ and some norming constant $\kappa^a$. For $a=0$, $\lambda^a\times\kappa^a$ was known to be a local coordinate system on \lr\times\lr. Using adapted transformation operators, we extend this result to any non-negative integer $a$, give a description of isospectral sets and we obtain a Borg-Levinson type theorem.Comment: 31 page

Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line

We present a proof of Minami type estimates for one dimensional random Schr\"odinger operators valid at all energies in the localization regime provided a Wegner estimate is known to hold. The Minami type estimates are then applied to various models to obtain results on their spectral statistics. The heuristics underlying our proof of Minami type estimates is that close by eigenvalues of a one-dimensional Schr\"odinger operator correspond either to eigenfunctions that live far away from each other in space or they come from some tunneling phenomena. In the second case, one can undo the tunneling and thus construct quasi-modes that live far away from each other in space.Comment: In section 5, a proof of localization at the bottom of the spectrum for the displacement model in dimension 1 was added. This required a study of Lifshitz type asymptotics in the same energy region. The main theorem was improve and some assumptions weakene

Tree-width of hypergraphs and surface duality

In Graph Minors III, Robertson and Seymour write: "It seems that the tree-width of a planar graph and the tree-width of its geometric dual are approximately equal - indeed, we have convinced ourselves that they differ by at most one". They never gave a proof of this. In this paper, we prove a generalisation of this statement to embedding of hypergraphs on general surfaces, and we prove that our bound is tight