Satisfiability Modulo Transcendental Functions via Incremental Linearization

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted in the abstract space, which is described in terms of the combined theory of linear arithmetic on the rationals with uninterpreted functions, and are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear functions. Suitable numerical techniques are used to ensure that the abstractions of the transcendental functions are sound even in presence of irrationals. Our experimental evaluation on benchmarks from verification and mathematics demonstrates the potential of our approach, showing that it compares favorably with delta-satisfiability /interval propagation and methods based on theorem proving

A formal proof of the Kepler conjecture

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project

Beta decay of the Tz=-2 nucleus 64Se and its descendants

International audience; The beta decay of the Tz=-2 nucleus 64Se has been studied in a fragmentation reaction at RIKEN-Nishina Center. 64Se is the heavies Tz=-2 nucleus that decays to bound states in the daughter nucleus and the heaviest case where the mirror reaction 64Zn(3He,t)64Ga on the Tz=+2 64Zn stable target exists and can be compared. Beta-delayed gamma and proton radiation is reported for the 64Se and 64As cases. New levels have been observed in 64As, 64Ge (N=Z), 63Ge and 63Ga. The associated T1/2 values have been obtained

The Fanconi anemia group C protein interacts with uncoordinated 5A and delays apoptosis.

The Fanconi anemia group C protein (FANCC) is one of the several proteins that comprise the Fanconi anemia (FA) network involved in genomic surveillance. FANCC is mainly cytoplasmic and has many functions, including apoptosis suppression through caspase-mediated proteolytic processing. Here, we examined the role of FANCC proteolytic fragments by identifying their binding partners. We performed a yeast two-hybrid screen with caspase-mediated FANCC cleavage products and identified the dependence receptor uncoordinated-5A (UNC5A) protein. Here, we show that FANCC physically interacts with UNC5A, a pro-apoptotic dependence receptor. FANCC interaction occurs through the UNC5A intracellular domain, specifically via its death domain. FANCC modulates cell sensitivity to UNC5A-mediated apoptosis; we observed reduced UNC5A-mediated apoptosis in the presence of FANCC and increased apoptosis in FANCC-depleted cells. Our results show that FANCC interferes with UNC5A's functions in apoptosis and suggest that FANCC may participate in developmental processes through association with the dependence receptor UNC5A

On Exact Polya and Putinar's Representations

19 pages, 4 algorithms, 3 tablesInternational audienceWe consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers. We start by providing a hybrid numeric-symbolic algorithm computing exact rational SOS decompositions for polynomials lying in the interior of the SOS cone. It computes an approximate SOS decomposition for a perturbation of the input polynomial with an arbitrary-precision SDP solver. An exact SOS decomposition is obtained thanks to the perturbation terms. We prove that bit complexity estimates on output size and runtime are both polynomial in the degree of the input polynomial and simply exponential in the number of variables. Next, we apply this algorithm to compute exact Polya and Putinar's representations respectively for positive definite forms and positive polynomials over basic compact semi-algebraic sets. We also compare the implementation of our algorithms with existing methods in computer algebra including cylindrical algebraic decomposition and critical point method

EPISCIENCES – an overlay publication platform

This paper delineates the main characteristics of the Episciences platform, an environment for overlay peer-reviewing that complements existing publication repositories, designed by the Centre pour la Communication Scientifique directe (CCSD is a joint service unit between the CNRS, Inria and the University of Lyon) service unit. We describe the main characteristics of the platform and present the first experiment of launching two journals in the computer science domain onto it. Finally, we address a series of open questions related to the actual changes in editorial models (open submission, open peer-review, augmented publication) that such a platform is likely to raise, as well as some hints as to the underlying business model

A FORMAL PROOF OF THE KEPLER CONJECTURE

Contains fulltext : 176365.pdf (publisher's version ) (Open Access