Towards Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give n^{O(1)} size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result

Residential Radon and Brain Tumour Incidence in a Danish Cohort

BACKGROUND: Increased brain tumour incidence over recent decades may reflect improved diagnostic methods and clinical practice, but remain unexplained. Although estimated doses are low a relationship between radon and brain tumours may exist. OBJECTIVE: To investigate the long-term effect of exposure to residential radon on the risk of primary brain tumour in a prospective Danish cohort. METHODS: During 1993-1997 we recruited 57,053 persons. We followed each cohort member for cancer occurrence from enrolment until 31 December 2009, identifying 121 primary brain tumour cases. We traced residential addresses from 1 January 1971 until 31 December 2009 and calculated radon concentrations at each address using information from central databases regarding geology and house construction. Cox proportional hazards models were used to estimate incidence rate-ratios (IRR) and 95% confidence intervals (CI) for the risk of primary brain tumours associated with residential radon exposure with adjustment for age, sex, occupation, fruit and vegetable consumption and traffic-related air pollution. Effect modification by air pollution was assessed. RESULTS: Median estimated radon was 40.5 Bq/m(3). The adjusted IRR for primary brain tumour associated with each 100 Bq/m(3) increment in average residential radon levels was 1.96 (95% CI: 1.07; 3.58) and this was exposure-dependently higher over the four radon exposure quartiles. This association was not modified by air pollution. CONCLUSIONS: We found significant associations and exposure-response patterns between long-term residential radon exposure radon in a general population and risk of primary brain tumours, adding new knowledge to this field. This finding could be chance and needs to be challenged in future studies

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente

Measurement of the t¯tZ and t¯tW cross sections in proton-proton collisions at √s=13 TeV with the ATLAS detector

A measurement of the associated production of a top-quark pair (t¯t) with a vector boson (W, Z) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented, using 36.1  fb−1 of integrated luminosity collected by the ATLAS detector at the Large Hadron Collider. Events are selected in channels with two same- or opposite-sign leptons (electrons or muons), three leptons or four leptons, and each channel is further divided into multiple regions to maximize the sensitivity of the measurement. The t¯tZ and t¯tW production cross sections are simultaneously measured using a combined fit to all regions. The best-fit values of the production cross sections are σt¯tZ=0.95±0.08stat±0.10syst pb and σt¯tW=0.87±0.13stat±0.14syst pb in agreement with the Standard Model predictions. The measurement of the t¯tZ cross section is used to set constraints on effective field theory operators which modify the t¯tZ vertex

Measurement of the inclusive and fiducial tt ¯ production cross-sections in the lepton+jets channel in pp collisions at s √ =8 TeV with the ATLAS detector

The inclusive and fiducial tt ¯ production cross-sections are measured in the lepton+jets channel using 20.2 fb −1 of proton-proton collision data at a centre-of-mass energy of 8 TeV recorded with the ATLAS detector at the LHC. Major systematic uncertainties due to the modelling of the jet energy scale and b -tagging efficiency are constrained by separating selected events into three disjoint regions. In order to reduce systematic uncertainties in the most important background, the W+jets process is modelled using Z+jets events in a data-driven approach. The inclusive tt ¯ cross-section is measured with a precision of 5.7% to be σ inc (tt ¯ ) = 248.3 ± 0.7 (stat.) ± 13.4 (syst.) ± 4.7 (lumi.) pb, assuming a top-quark mass of 172.5 GeV. The result is in agreement with the Standard Model prediction. The cross-section is also measured in a phase space close to that of the selected data. The fiducial cross-section is σ fid (tt ¯ ) = 48.8 ± 0.1 (stat.) ± 2.0 (syst.) ± 0.9 (lumi.) pb with a precision of 4.5%

Conservation Genetics of a Critically Endangered Limpet Genus and Rediscovery of an Extinct Species

A third of all known freshwater mollusk extinctions worldwide have occurred within a single medium-sized American drainage. The Mobile River Basin (MRB) of Alabama, a global hotspot of temperate freshwater biodiversity, was intensively industrialized during the 20(th) century, driving 47 of its 139 endemic mollusk species to extinction. These include the ancylinid limpet Rhodacmea filosa, currently classified as extinct (IUCN Red List), a member of a critically endangered southeastern North American genus reduced to a single known extant population (of R. elatior) in the MRB.We document here the tripling of known extant populations of this North American limpet genus with the rediscovery of enduring Rhodacmea filosa in a MRB tributary and of R. elatior in its type locality: the Green River, Kentucky, an Ohio River Basin (ORB) tributary. Rhodacmea species are diagnosed using untested conchological traits and we reassessed their systematic and conservation status across both basins using morphometric and genetic characters. Our data corroborated the taxonomic validity of Rhodacmea filosa and we inferred a within-MRB cladogenic origin from a common ancestor bearing the R. elatior shell phenotype. The geographically-isolated MRB and ORB R. elatior populations formed a cryptic species complex: although overlapping morphometrically, they exhibited a pronounced phylogenetic disjunction that greatly exceeded that of within-MRB R. elatior and R. filosa sister species.Rhodacmea filosa, the type species of the genus, is not extinct. It persists in a Coosa River tributary and morphometric and phylogenetic analyses confirm its taxonomic validity. All three surviving populations of the genus Rhodacmea merit specific status. They collectively contain all known survivors of a phylogenetically highly distinctive North American endemic genus and therefore represent a concentrated fraction of continental freshwater gastropod biodiversity. We recommend the establishment of a proactive targeted conservation program that may include their captive propagation and reintroduction