Proving and Computing: Applying Automated Reasoning to the Verification of Symbolic Computation Systems

The application of automated reasoning to the formal verification of symbolic computation systems is motivated by the need of ensuring the correctness of the results computed by the system, beyond the classical approach of testing. Formal verification of properties of the implemented algorithms require not only to formalize the properties of the algorithm, but also of the underlying (usually rich) mathematical theory. We show how we can use ACL2, a first-order interactive theorem prover, to reason about properties of algorithms that are typically implemented as part of symbolic computation systems. We emphasize two aspects. First, how we can override the apparent lack of expressiveness we have using a first-order approach (at least compared to higher-order logics). Second, how we can execute the algorithms (efficiently, if possible) in the same setting where we formally reason about their correctness. Three examples of formal verification of symbolic computation algorithms are presented to illustrate the main issues one has to face in this task: a Gr¨obner basis algorithm, a first-order unification algorithm based on directed acyclic graphs, and the Eilenberg-Zilber algorithm, one of the central components of a symbolic computation system in algebraic topology

Spread of a SARS-CoV-2 variant through Europe in the summer of 2020.

Following its emergence in late 2019, the spread of SARS-CoV-21,2 has been tracked by phylogenetic analysis of viral genome sequences in unprecedented detail3–5. Although the virus spread globally in early 2020 before borders closed, intercontinental travel has since been greatly reduced. However, travel within Europe resumed in the summer of 2020. Here we report on a SARS-CoV-2 variant, 20E (EU1), that was identified in Spain in early summer 2020 and subsequently spread across Europe. We find no evidence that this variant has increased transmissibility, but instead demonstrate how rising incidence in Spain, resumption of travel, and lack of effective screening and containment may explain the variant’s success. Despite travel restrictions, we estimate that 20E (EU1) was introduced hundreds of times to European countries by summertime travellers, which is likely to have undermined local efforts to minimize infection with SARS-CoV-2. Our results illustrate how a variant can rapidly become dominant even in the absence of a substantial transmission advantage in favourable epidemiological settings. Genomic surveillance is critical for understanding how travel can affect transmission of SARS-CoV-2, and thus for informing future containment strategies as travel resumes. © 2021, The Author(s), under exclusive licence to Springer Nature Limited

Dust environment and dynamical history of a sample of short-period comets: II. 81P/Wild 2 and 103P/Hartley 2

Aims. This paper is a continuation of the first paper in this series, where we presented an extended study of the dust environment of a sample of short-period comets and their dynamical history. On this occasion, we focus on comets 81P/Wild 2 and 103P/Hartley 2, which are of special interest as targets of the spacecraft missions Stardust and EPOXI. Methods. As in the previous study, we used two sets of observational data: a set of images, acquired at Sierra Nevada and Lulin observatories, and the Afρ data as a function of the heliocentric distance provided by the amateur astronomical association Cometas-Obs. The dust environment of comets (dust loss rate, ejection velocities, and size distribution of the particles) was derived from our Monte Carlo dust tail code. To determine their dynamical history we used the numerical integrator Mercury 6.2 to ascertain the time spent by these objects in the Jupiter family Comet region. Results. From the dust analysis, we conclude that both 81P/Wild 2 and 103P/Hartley 2 are dusty comets, with an annual dust production rate of 2.8 × 109 kg yr-1 and (0.4-1.5) × 109 kg yr-1, respectively. From the dynamical analysis, we determined their time spent in the Jupiter family Comet region as ~40 yr in the case of 81P/Wild 2 and ~1000 yr for comet 103P/Hartley 2. These results imply that 81P/Wild 2 is the youngest and the most active comet of the eleven short-period comets studied so far, which tends to favor the correlation between the time spent in JFCs region and the comet activity previously discussed

Search for H→γγ produced in association with top quarks and constraints on the Yukawa coupling between the top quark and the Higgs boson using data taken at 7 TeV and 8 TeV with the ATLAS detector

A search is performed for Higgs bosons produced in association with top quarks using the diphoton decay mode of the Higgs boson. Selection requirements are optimized separately for leptonic and fully hadronic final states from the top quark decays. The dataset used corresponds to an integrated luminosity of 4.5 fb−14.5 fb−1 of proton–proton collisions at a center-of-mass energy of 7 TeV and 20.3 fb−1 at 8 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. No significant excess over the background prediction is observed and upper limits are set on the tt¯H production cross section. The observed exclusion upper limit at 95% confidence level is 6.7 times the predicted Standard Model cross section value. In addition, limits are set on the strength of the Yukawa coupling between the top quark and the Higgs boson, taking into account the dependence of the tt¯H and tH cross sections as well as the H→γγ branching fraction on the Yukawa coupling. Lower and upper limits at 95% confidence level are set at −1.3 and +8.0 times the Yukawa coupling strength in the Standard Model

The forward physics facility at the high-luminosity LHC

High energy collisions at the High-Luminosity Large Hadron Collider (LHC) produce a large number of particles along the beam collision axis, outside of the acceptance of existing LHC experiments. The proposed Forward Physics Facility (FPF), to be located several hundred meters from the ATLAS interaction point and shielded by concrete and rock, will host a suite of experiments to probe standard model (SM) processes and search for physics beyond the standard model (BSM). In this report, we review the status of the civil engineering plans and the experiments to explore the diverse physics signals that can be uniquely probed in the forward region. FPF experiments will be sensitive to a broad range of BSM physics through searches for new particle scattering or decay signatures and deviations from SM expectations in high statistics analyses with TeV neutrinos in this low-background environment. High statistics neutrino detection will also provide valuable data for fundamental topics in perturbative and non-perturbative QCD and in weak interactions. Experiments at the FPF will enable synergies between forward particle production at the LHC and astroparticle physics to be exploited. We report here on these physics topics, on infrastructure, detector, and simulation studies, and on future directions to realize the FPF's physics potential