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 ß-decay of 71Kr: Precise measurement of the half-life

4 pags., 6 figs. --European Nuclear Physics Conference (EuNPC 2022), Section: P2 Nuclear Structure, Spectroscopy and DynamicsThe very proton-rich 71Kr isotope was produced through the in-flight fragmentation of 78Kr on a beryllium target at RIKEN ¿ Nishina Center in order to study its ß-decay properties. A stack of double-sided silicon strip detectors, called WAS3ABi, was used as the decay station, where the detection of ion implants, ß-decays and ß-delayed protons took place. Beta-delayed ¿-rays were measured using a system of 84 HPGe detectors, called EURICA, surrounding the decay station. The main goal of the present study was the precise measurement of the half-life of 71Kr, as in the literature there is an almost 10 ¿ difference between the most precise independent results. Implant¿ß time correlations, implant¿proton time correlations and implant¿ß¿¿ time correlations were all used to derive the half-life value, followed by a thorough investigation of systematic uncertainties for each method. As these values were found to be consistent, the weighted average t1/2 = 94.40+19ms is reported as a new half-life value in this work. Furthermore a total of 26 previously unreported ¿ following the ß-decay of 71Kr were also identified in the analysis.This work was carried out at the RIBF operated by RIKEN Nishina Center and CNS, University of Tokyo. We acknowledge the EUROBALL Owners Committee for the loan of germanium detectors and the PreSpec Collaboration for the readout electronics of the cluster detectors. This work was supported by the Spanish MICINN grants FPA2014-52823-C2-1-P, FPA2017-83946-C2-1-P (MCIU/AEI/FEDER); Ministerio de Ciencia e Innovacion grant PID2019-104714GB-C21; Centro de Excelencia Severo Ochoa del IFIC SEV - 2014 - 0398; Junta para la Ampliacion de E studios ´ Programme (CSIC JAEDoc contract) co-financed by FSE, by NKFIH (NN128072), the National Research, Development, and Innovation Fund of Hungary Project No. K 128729 the STFC (UK) through Grant No. ST/P005314/, the PROMETEO/2019/007 project and by the ÚNKP-20-5-DE-02 New National Excellence Program of the Ministry of Human Capacities of Hungary and by the JSPS KAKENHI of Japan (Grant No. 25247045). G. G. Kiss acknowledges support from the János Bolyai research fellowship of the Hungarian Academy of Sciences. A. A. acknowledges partial support of the JSPS Invitational Fellowships for Research in Japan (ID: L1955) P. S. acknowledges support from MCI/AEI/FEDER,UE (Spain) under grant PGC2018-093636-BI00. F. M. acknowledges support from ANID FONDECYT Regular Project 1221364 and ANID - Millennium Science Initiative Program - ICN2019-044. Supported by the ÚNKP-22-3 New National Excellence Program of the Ministry for Culture and Innovation from the source of the National Research, Development and Innovation Fund (Project No. ÚNKP-22-3-II-DE-132)

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