Square root and division elimination in PVS

International audienceIn this paper we present a new strategy for PVS that imple- ments a square root and division elimination in order to use automatic arithmetic strategies that were not able to deal with these operations in the ﰁrst place. This strategy relies on a PVS formalization of the square root and division elimination and deep embedding of PVS expressions inside PVS. Therefore using computational reﰂection and symbolic com- putation we are able to automatically transform expressions into division and square root free ones before using these decision procedures

Is tidal heating sufficient to explain bloated exoplanets? Consistent calculations accounting for finite initial eccentricity

In this paper, we present the consistent evolution of short-period exoplanets coupling the tidal and gravothermal evolution of the planet. Contrarily to previous similar studies, our calculations are based on the complete tidal evolution equations of the Hut model, valid at any order in eccentricity, obliquity and spin. We demonstrate, both analytically and numerically, that, except if the system was formed with a nearly circular orbit (e<0.2), solving consistently the complete tidal equations is mandatory to derive correct tidal evolution histories. We show that calculations based on tidal models truncated at second order in eccentricity, as done in all previous studies, lead to erroneous tidal evolutions. As a consequence, tidal energy dissipation rates are severely underestimated in all these calculations and the characteristic timescales for the various orbital parameters evolutions can be wrong by up to three orders in magnitude. Based on these complete, consistent calculations, we revisit the viability of the tidal heating hypothesis to explain the anomalously large radius of transiting giant planets. We show that, even though tidal dissipation does provide a substantial contribution to the planet's heat budget and can explain some of the moderately bloated hot-Jupiters, this mechanism can not explain alone the properties of the most inflated objects, including HD 209458b. Indeed, solving the complete tidal equations shows that enhanced tidal dissipation and thus orbit circularization occur too early during the planet's evolution to provide enough extra energy at the present epoch. In that case another mechanisms, such as stellar irradiation induced surface winds dissipating in the planet's tidal bulges, or inefficient convection in the planet's interior must be invoked, together with tidal dissipation, to provide all the pieces of the abnormally large exoplanet puzzle.Comment: 14 pages, 10 figures, Accepted for publication in Astronomy and Astrophysics

Tidal effects on brown dwarfs: Application to the eclipsing binary 2MASSJ05352184-0546085 - The anomalous temperature reversal in the context of tidal heating

2MASSJ05352184-0546085 (2M0535-05) is the only known eclipsing brown dwarf (BD) binary, and so may serve as an important benchmark for models of BD formation and evolution. However, theoretical predictions of the system's properties seem inconsistent with observations: i. The more massive (primary) component is observed to be cooler than the less massive (secondary) one. ii. The secondary is more luminous (by roughly 10^{24} W) than expected. We study the impact of tidal heating to the energy budget of both components. We also compare various plausible tidal models to determine a range of predicted properties. We apply two versions of two different, well-known models for tidal interaction, respectively, (i.) the 'constant-phase-lag' model and (ii.) the 'constant-time-lag' model, and incorporate the predicted tidal heating into a model of BD structure. We find that the contribution of heat from tides in 2M0535-05 alone may only be large enough to account for the discrepancies between observation and theory in an unlikely region of the parameter space. The tidal quality factor of BDs, Q_{BD}, would have to be 10^{3.5} and the secondary needs a spin-orbit misalignment greater than 50 degrees. However, tidal synchronization time scales for 2M0535-05 restrict the tidal dissipation function Q_{BD} to values greater than 10^{4.5} and rule out intense tidal heating in 2M0535-05. We provide the first constraint on Q_{BD}. Tidal heating alone is unlikely to be responsible for the surprising temperature reversal within 2M0535-05. But an evolutionary embedment of tidal effects and a coupled treatment with the structural evolution of the BDs is necessary to corroborate or refute this result.Comment: accepted by AandA January 2010, 18 pages, 13 figures, 1 tabl

The role of chaotic resonances in the solar system

Our understanding of the Solar System has been revolutionized over the past decade by the finding that the orbits of the planets are inherently chaotic. In extreme cases, chaotic motions can change the relative positions of the planets around stars, and even eject a planet from a system. Moreover, the spin axis of a planet-Earth's spin axis regulates our seasons-may evolve chaotically, with adverse effects on the climates of otherwise biologically interesting planets. Some of the recently discovered extrasolar planetary systems contain multiple planets, and it is likely that some of these are chaotic as well.Comment: 28 pages, 9 figure

Needle & knot : binder boilerplate tied up

To lighten the burden of programming language mechanization, many approaches have been developed that tackle the substantial boilerplate which arises from variable binders. Unfortunately, the existing approaches are limited in scope. They typically do not support complex binding forms (such as multi-binders) that arise in more advanced languages, or they do not tackle the boilerplate due to mentioning variables and binders in relations. As a consequence, the human mechanizer is still unnecessarily burdened with binder boilerplate and discouraged from taking on richer languages. This paper presents Knot, a new approach that substantially extends the support for binder boilerplate. Knot is a highly expressive language for natural and concise specification of syntax with binders. Its meta-theory constructively guarantees the coverage of a considerable amount of binder boilerplate for well-formed specifications, including that for well-scoping of terms and context lookups. Knot also comes with a code generator, Needle, that specializes the generic boilerplate for convenient embedding in COQ and provides a tactic library for automatically discharging proof obligations that frequently come up in proofs of weakening and substitution lemmas of type-systems. Our evaluation shows, that Needle & Knot significantly reduce the size of language mechanizations (by 40% in our case study). Moreover, as far as we know, Knot enables the most concise mechanization of the POPLmark Challenge (1a + 2a) and is two-thirds the size of the next smallest. Finally, Knot allows us to mechanize for instance dependentlytyped languages, which is notoriously challenging because of dependent contexts and mutually-recursive sorts with variables

Molecular Evolution of the Neuropeptide S Receptor

The neuropeptide S receptor (NPSR) is a recently deorphanized member of the G protein-coupled receptor (GPCR) superfamily and is activated by the neuropeptide S (NPS). NPSR and NPS are widely expressed in central nervous system and are known to have crucial roles in asthma pathogenesis, locomotor activity, wakefulness, anxiety and food intake. The NPS-NPSR system was previously thought to have first evolved in the tetrapods. Here we examine the origin and the molecular evolution of the NPSR using in-silico comparative analyses and document the molecular basis of divergence of the NPSR from its closest vertebrate paralogs. In this study, NPSR-like sequences have been identified in a hemichordate and a cephalochordate, suggesting an earlier emergence of a NPSR-like sequence in the metazoan lineage. Phylogenetic analyses revealed that the NPSR is most closely related to the invertebrate cardioacceleratory peptide receptor (CCAPR) and the group of vasopressin-like receptors. Gene structure features were congruent with the phylogenetic clustering and supported the orthology of NPSR to the invertebrate NPSR-like and CCAPR. A site-specific analysis between the vertebrate NPSR and the well studied paralogous vasopressin-like receptor subtypes revealed several putative amino acid sites that may account for the observed functional divergence between them. The data can facilitate experimental studies aiming at deciphering the common features as well as those related to ligand binding and signal transduction processes specific to the NPSR

A seven-planet resonant chain in TRAPPIST-1

The TRAPPIST-1 system is the first transiting planet system found orbiting an ultra-cool dwarf star1. At least seven planets similar to Earth in radius were previously found to transit this host star2. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 d orbital period for the outermost transiting planet, TRAPPIST-1h, which was unconstrained until now. This value matches our theoretical expectations based on Laplace relations3 and places TRAPPIST-1h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1h has a radius of 0.727 R⊕ and an equilibrium temperature of 169 K. We have also measured the rotational period of the star at 3.3 d and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf

Crystal Structure of an Integron Gene Cassette-Associated Protein from Vibrio cholerae Identifies a Cationic Drug-Binding Module

Background The direct isolation of integron gene cassettes from cultivated and environmental microbial sources allows an assessment of the impact of the integron/gene cassette system on the emergence of new phenotypes, such as drug resistance or virulence. A structural approach is being exploited to investigate the modularity and function of novel integron gene cassettes. Methodology/Principal Findings We report the 1.8 A crystal structure of Cass2, an integron-associated protein derived from an environmental V. cholerae. The structure defines a monomeric beta-barrel protein with a fold related to the effector-binding portion of AraC/XylS transcription activators. The closest homologs of Cass2 are multi-drug binding proteins, such as BmrR. Consistent with this, a binding pocket made up of hydrophobic residues and a single glutamate side chain is evident in Cass2, occupied in the crystal form by polyethylene glycol. Fluorescence assays demonstrate that Cass2 is capable of binding cationic drug compounds with submicromolar affinity. The Cass2 module possesses a protein interaction surface proximal to its drug-binding cavity with features homologous to those seen in multi-domain transcriptional regulators. Conclusions/Significance Genetic analysis identifies Cass2 to be representative of a larger family of independent effector-binding proteins associated with lateral gene transfer within Vibrio and closely-related species. We propose that the Cass2 family not only has capacity to form functional transcription regulator complexes, but represents possible evolutionary precursors to multi-domain regulators associated with cationic drug compounds.National Health and Medical Research Council (Australia) (NHMRC grant 488502)National Institutes of Health (U.S.) (Grant GM62414-0 )Ontario. Ministry of Revenue (Challenge Fund

Multinationals’ Accountability on Sustainability: The Evolution of Third-party Assurance of Sustainability Reports

In this article we explore how multinational corporations (MNCs) adopt assurance practices to develop and sustain organizational accountability for sustainability. Using a panel of Fortune Global 250 firms over a period of 10 years, we document the diffusion patterns of third-party assurance of sustainability reports. We specifically investigate how evolving auditing practices, namely diversity of assurance standards and type of assurance providers, shape the quality of sustainability assurance statements. The results illustrate great variability in the adoption of assurance practices in the formative stages of this novel market. Our descriptive analysis indicates the relevance of external institutional pressures as well as internal resources and capabilities as underlying factors driving the adoption of assurance. Our evidence also suggests that several MNCs project a decoupled or symbolic image of accountability through assurance, thereby undermining the credibility of these verification practices. The paper contributes to the emerging literature on international accountability standards and emphasizes the need to enhance theory-based, cross-disciplinary knowledge related to auditing and accountability processes for sustainability