AC-KBO Revisited

Equational theories that contain axioms expressing associativity and commutativity (AC) of certain operators are ubiquitous. Theorem proving methods in such theories rely on well-founded orders that are compatible with the AC axioms. In this paper we consider various definitions of AC-compatible Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are revisited. The former is enhanced to a more powerful version, and we modify the latter to amend its lack of monotonicity on non-ground terms. We further present new complexity results. An extension reflecting the recent proposal of subterm coefficients in standard Knuth-Bendix orders is also given. The various orders are compared on problems in termination and completion.Comment: 31 pages, To appear in Theory and Practice of Logic Programming (TPLP) special issue for the 12th International Symposium on Functional and Logic Programming (FLOPS 2014

Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity

Unravelings are transformations from a conditional term rewriting system (CTRS, for short) over an original signature into an unconditional term rewriting systems (TRS, for short) over an extended signature. They are not sound w.r.t. reduction for every CTRS, while they are complete w.r.t. reduction. Here, soundness w.r.t. reduction means that every reduction sequence of the corresponding unraveled TRS, of which the initial and end terms are over the original signature, can be simulated by the reduction of the original CTRS. In this paper, we show that an optimized variant of Ohlebusch's unraveling for a deterministic CTRS is sound w.r.t. reduction if the corresponding unraveled TRS is left-linear or both right-linear and non-erasing. We also show that soundness of the variant implies that of Ohlebusch's unraveling. Finally, we show that soundness of Ohlebusch's unraveling is the weakest in soundness of the other unravelings and a transformation, proposed by Serbanuta and Rosu, for (normal) deterministic CTRSs, i.e., soundness of them respectively implies that of Ohlebusch's unraveling.Comment: 49 pages, 1 table, publication in Special Issue: Selected papers of the "22nd International Conference on Rewriting Techniques and Applications (RTA'11)

A Formally Verified Floating-Point Implementation of the Compact Position Reporting Algorithm

The Automatic Dependent Surveillance-Broadcast (ADS-B) system allows aircraft to communicate their current state, including position and velocity information, to other aircraft in their vicinity and to ground stations. The Compact Position Reporting (CPR) algorithm is the ADS-B module responsible for the encoding and decoding of aircraft positions. CPR is highly sensitive to computer arithmetic since it heavily relies on functions that are intrinsically unstable such as floor and modulo. In this paper, a formally-verified double-precision floating-point implementation of the CPR algorithm is presented. The verification proceeds in three steps. First, an alternative version of CPR, which reduces the floating-point rounding error is proposed. Then, the Prototype Verification System (PVS) is used to formally prove that the ideal real-number counterpart of the improved algorithm is mathematically equivalent to the standard CPR definition. Finally, the static analyzer Frama-C is used to verify that the double-precision implementation of the improved algorithm is correct with respect to its operational requirement. The alternative algorithm is currently being considered for inclusion in the revised version of the ADS-B standards document as the reference implementation of the CPR algorithm

Generating Functions for Coherent Intertwiners

We study generating functions for the scalar products of SU(2) coherent intertwiners, which can be interpreted as coherent spin network evaluations on a 2-vertex graph. We show that these generating functions are exactly summable for different choices of combinatorial weights. Moreover, we identify one choice of weight distinguished thanks to its geometric interpretation. As an example of dynamics, we consider the simple case of SU(2) flatness and describe the corresponding Hamiltonian constraint whose quantization on coherent intertwiners leads to partial differential equations that we solve. Furthermore, we generalize explicitly these Wheeler-DeWitt equations for SU(2) flatness on coherent spin networks for arbitrary graphs.Comment: 31 page

Wave Equation Numerical Resolution: a Comprehensive Mechanized Proof of a C Program

We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and floating-point computations lead to round-off errors. We annotate this C program to specify both method error and round-off error. We use Frama-C to generate theorems that guarantee the soundness of the code. We discharge these theorems using SMT solvers, Gappa, and Coq. This involves a large Coq development to prove the adequacy of the C program to the numerical scheme and to bound errors. To our knowledge, this is the first time such a numerical analysis program is fully machine-checked.Comment: No. RR-7826 (2011

Effects of halogens on European air-quality

Halogens (Cl, Br) have a profound influence on stratospheric ozone (O3). They (Cl, Br and I) have recently also been shown to impact the troposphere, notably by reducing the mixing ratios of O3 and OH. Their potential for impacting regional air-quality is less well understood. We explore the impact of halogens on regional pollutants (focussing on O3) with the European grid of the GEOS-Chem model (0.25° × 0.3125°). It has recently been updated to include a representation of halogen chemistry. We focus on the summer of 2015 during the ICOZA campaign at the Weybourne Atmospheric Observatory on the North Sea coast of the UK. Comparisons between these observations together with those from the UK air-quality network show that the model has some skill in representing the mixing ratios/concentration of pollutants during this period. Although the model has some success in simulating the Weybourne ClNO2 observations, it significantly underestimates ClNO2 observations reported at inland locations. It also underestimates mixing ratios of IO, OIO, I2 and BrO, but this may reflect the coastal nature of these observations. Model simulations, with and without halogens, highlight the processes by which halogens can impact O3. Throughout the domain O3 mixing ratios are reduced by halogens. In northern Europe this is due to a change in the background O3 advected into the region, whereas in southern Europe this is due to local chemistry driven by Mediterranean emissions. The proportion of hourly O3 above 50 nmol mol-1 in Europe is reduced from 46% to 18% by halogens. ClNO2 from N2O5 uptake onto sea-salt leads to increases in O3 mixing ratio, but these are smaller than the decreases caused by the bromine and iodine. 12% of ethane and 16% of acetone within the boundary layer is oxidised by Cl. Aerosol response to halogens is complex with small (∼10%) reductions in PM2.5 in most locations. A lack of observational constraints coupled to large uncertainties in emissions and chemical processing of halogens make these conclusions tentative at best. However, the results here point to the potential for halogen chemistry to influence air quality policy in Europe and other parts of the world

Evaluation of rapid antigen detection kits for the diagnosis of highly pathogenic avian influenza H5N1 infection.

&lt;p&gt;Early detection of highly pathogenic (HP) strains of avian influenza, especially the HP H5N1, is important in terms of controlling and minimizing the spread of the virus. Several rapid antigen detection kits that are able to detect influenza A viruses in less than 1 hr are commercially available, but only a few of them have been evaluated. In this study, four commercially available rapid tests for veterinary usage and two tests for human usage were evaluated and compared. The evaluation of the detection limits of the different tests established with serial dilution of HP H5N1 indicated that most of them have a detection limit of about 10(5) to 10(6) 50% tissue culture infectious dose/ml. None of the tests was able to detect virus in oral and cloacal swabs 24 hr post-experimental infection of specific-pathogen-free chickens with HP H5N1. However, 48 hr postinfection, almost all of the rapid tests were able to detect infected birds (dead or alive). Moreover, organs were also successful samples for detection of H5N1 with the rapid tests. Unexpectedly, the specificity was not very high for some tests. However, in general in this study, the tests for veterinary usage showed better sensitivity. To conclude, these tests offer good indicative value in the event of an outbreak, but as a result of their low sensitivity and some aspecific reactions, test results always need to be confirmed by other methods.&lt;/p&gt;</p

Evaluation of different strategies for the use of ELISA tests as first screening tools for serologic surveillance of low pathogenic avian influenza in the Belgian poultry sector.

&lt;p&gt;Since the emergence of the highly pathogenic avian influenza H5N1, avian influenza surveillance has been expanded in Europe. The serologic monitoring of domestic poultry is usually accomplished using the reference hemagglutination inhibition (HI) test for the detection of H5 and H7 subtypes. However, as the number of tested sera has been increasing, there is a need for another serologic method that could be used as a preliminary screening test. A comparison of four enzyme-linked immunosorbent assay (ELISA) tests (two indirect and two competitive) was conducted, and they showed good specificity and higher sensitivity than the HI test. The selected ELISA tests were then tested using approximately 800 field sera representative of different poultry species, and a simulation was done to determine the best strategy for screening. The first strategy was testing both gallinaceous and nongallinaceous sera with a competitive ELISA and using the HI test for H5 and H7 as a confirmatory test. The second strategy was testing only gallinaceous bird sera with the indirect ELISA with confirmatory H5 and H7 HI and all nongallinaceous sera by the H5 and H7 HI test. In the Belgian poultry context, the best strategy seems to be the use of a blocking ELISA as the primary screening tool to test all the poultry sera, followed by confirmation by H5 and H7 HI test subtyping.&lt;/p&gt;</p

Comparative study of Leishmania mexicana and Trypanosoma brucei NAD-dependent glycerol-3-phosphate dehydrogenase.

The NAD-dependent glycerol-3-phosphate dehydrogenases (G3PDH, EC 1.1.1.8) of Trypanosoma brucei and Leishmania mexicana are thought to have different roles in carbohydrate metabolism. Here the physicochemical and kinetic properties of natural G3PDH from T. brucei with the recombinant homologue of L. mexicana which share 63% positional identity are compared. Despite their supposed different functions in energy metabolism of the parasites the two G3PDHs have remarkably similar properties, including pH optima and K(m) value for dihydroxyacetone phosphate (DHAP) and NADH in the formation of glycerol 3-phosphate (G3P) and for NAD+ and G3P in the reverse reaction. Both enzymes are subject inhibition by dihydroxyacetone phosphate at concentrations above 0.2 mM and are inhibited by the trypanocidal drugs suramin and melarsen oxide at sub-micromolar concentrations

Termination Modulo Combinations of Equational Theories

Rewriting with rules R modulo axioms E is a widely used technique in both rule-based programming languages and in automated deduction. Termination methods for rewriting systems modulo specific axioms E (e.g., associativity-commutativity) are known. However, much less seems to be known about termination methods that can be modular in the set E of axioms. In fact, current termination tools and proof methods cannot be applied to commonly occurring combinations of axioms that fall outside their scope. This work proposes a modular termination proof method based on semantics- and termination-preserving transformations that can reduce the proof of termination of rules R modulo E to an equivalent proof of termination of the transformed rules modulo a typically much simpler set B of axioms. Our method is based on the notion of variants of a term recently proposed by Comon and Delaune. We illustrate its practical usefulness by considering the very common case in which E is an arbitrary combination of associativity, commutativity, left- and right-identity axioms for various function symbols.F. Dur ??an and S. Lucas were partially supported by Spanish MEC under grants TIN 2008-03107 and TIN 2007-68093-C02, respectively. J. Meseguer was partially supported by NSF Grants CNS 07-16638 and CNS 08-31064.unpublishednot peer reviewe