Splitting Proofs for Interpolation

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refuta- tion into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201

Distances and parallax bias in Gaia DR2

We derive Bayesian distances for all stars in the radial velocity sample of Gaia DR2, and use the statistical method of Schönrich, Binney & Asplund to validate the distances and test the Gaia parallaxes. In contrast to other methods, which rely on special sources, our method directly tests the distances to all stars in our sample. We find clear evidence for a near-linear trend of distance bias f with distance s, proving a parallax offset δp. On average, we find δp=−0.054mas (parallaxes in Gaia DR2 need to be increased) when accounting for the parallax uncertainty underestimate in the Gaia set (compared to δp=−0.048mas on the raw parallax errors), with negligible formal error and a systematic uncertainty of about 0.006mas⁠. The value is in concordance with results from asteroseismic measurements, but differs from the much lower bias found on quasar samples. We further use our method to compile a comprehensive set of quality cuts in colour, apparent magnitude, and astrometric parameters. Lastly, we find that for this sample δp appears to strongly depend on σp (when including the additional 0.043mas⁠) with a statistical confidence far in excess of 10σ and a proportionality factor close to 1, though the dependence varies somewhat with σp. Correcting for the σp dependence also resolves otherwise unexplained correlations of the offset with the number of observation periods nvis and ecliptic latitude. Every study using Gaia DR2 parallaxes/distances should investigate the sensitivity of its results on the parallax biases described here and – for fainter samples – in the DR2 astrometry paper

Two-Band-Type Superconducting Instability in MgB2

Using the tight-binding method for the $\pi$-bands in MgB$_2$, the Hubbard on-site Coulomb interaction on two inequivalent boron $p_z$-orbitals is transformed into expressions in terms of $\pi$-band operators. For scattering processes relevant to the problemin which a wave vector {\bf q} is parallel to $\hat{z}$, it is found to take a relatively simple form consisting of intra-band Coulomb scattering, interband pair scattering etc. with large constant coupling constants. This allows to get a simple expression for the amplitude of interband pair scattering between two $\pi$-bands, which diverges if the interband polarization function in it becomes large enough.The latter was approximately evaluated and found to be largely enhanced in the band structure in MgB$_2$. These results lead to a divergent interband pair scattering, meaning two-band-type superconducting instability with enhanced $T_c$. Adding a subsidiary BCS attractive interaction in each band into consideration, a semi-quantitative gap equation is given, and $T_c$ and isotope exponent $\alpha$ are derived. The present instability is asserted to be the origin of high $T_c$ in MgB$_2$.Comment: 4 pages, to be published in J. Phys. Soc. Jpn. vol. 70, No.

Preoperative systemic inflammation predicts postoperative infectious complications in patients undergoing curative resection for colorectal cancer

The presence of systemic inflammation before surgery, as evidenced by the glasgow prognostic score (mGPS), predicts poor long-term survival in colorectal cancer. The aim was to examine the relationship between the preoperative mGPS and the development of postoperative complications in patients undergoing potentially curative resection for colorectal cancer. Patients (n=455) who underwent potentially curative resections between 2003 and 2007 were assessed consecutively, and details were recorded in a database. The majority of patients presented for elective surgery (85%) were over the age of 65 years (70%), were male (58%), were deprived (53%), and had TNM stage I/II disease (61%), had preoperative haemoglobin (56%), white cell count (87%) and mGPS 0 (58%) in the normal range. After surgery, 86 (19%) patients developed a postoperative complication; 70 (81%) of which were infectious complications. On multivariate analysis, peritoneal soiling (P<0.01), elevated preoperative white cell count (P<0.05) and mGPS (P<0.01) were independently associated with increased risk of developing a postoperative infection. In elective patients, only the mGPS (OR=1.75, 95% CI=1.17-2.63, P=0.007) was significantly associated with increased risk of developing a postoperative infection. Preoperative elevated mGPS predicts increased postoperative infectious complications in patients undergoing potentially curative resection for colorectal cancer

Planets in triple star systems--the case of HD188753

We consider the formation of the recently discovered ``hot Jupiter'' planet orbiting the primary component of the triple star system HD188753. Although the current outer orbit of the triple is too tight for a Jupiter-like planet to have formed and migrated to its current location, the binary may have been much wider in the past. We assume here that the planetary system formed in an open star cluster, the dynamical evolution of which subsequently led to changes in the system's orbital parameters and binary configuration. We calculate cross sections for various scenarios that could have led to the multiple system currently observed, and conclude that component A of HD188753 with its planet were most likely formed in isolation to be swapped in a triple star system by a dynamical encounter in an open star cluster. We estimate that within 500pc of the Sun there are about 1200 planetary systems which, like Hd188753, have orbital parameters unfavorable for forming planets but still having a planet, making it quite possible that the HD188753 system was indeed formed by a dynamical encounter in an open star cluster.Comment: ApJ Letters in pres

A comparison of incompressible limits for resistive plasmas

The constraint of incompressibility is often used to simplify the magnetohydrodynamic (MHD) description of linearized plasma dynamics because it does not affect the ideal MHD marginal stability point. In this paper two methods for introducing incompressibility are compared in a cylindrical plasma model: In the first method, the limit $\gamma \to \infty$ is taken, where $\gamma$ is the ratio of specific heats; in the second, an anisotropic mass tensor $\mathbf{\rho}$ is used, with the component parallel to the magnetic field taken to vanish, $\rho_{\parallel} \to 0$. Use of resistive MHD reveals the nature of these two limits because the Alfv\'en and slow magnetosonic continua of ideal MHD are converted to point spectra and moved into the complex plane. Both limits profoundly change the slow-magnetosonic spectrum, but only the second limit faithfully reproduces the resistive Alfv\'en spectrum and its wavemodes. In ideal MHD, the slow magnetosonic continuum degenerates to the Alfv\'en continuum in the first method, while it is moved to infinity by the second. The degeneracy in the first is broken by finite resistivity. For numerical and semi-analytical study of these models, we choose plasma equilibria which cast light on puzzling aspects of results found in earlier literature.Comment: 14 pages, 10 figure

Tunneling spectra of strongly coupled superconductors: Role of dimensionality

We investigate numerically the signatures of collective modes in the tunneling spectra of superconductors. The larger strength of the signatures observed in the high-Tc superconductors, as compared to classical low-Tc materials, is explained by the low dimensionality of these layered compounds. We also show that the strong-coupling structures are dips (zeros in the d2I/dV2 spectrum) in d-wave superconductors, rather than the steps (peaks in d2I/dV2) observed in classical s-wave superconductors. Finally we question the usefulness of effective density of states models for the analysis of tunneling data in d-wave superconductors.Comment: 8 pages, 6 figure

The impact of biological invasion and genomic local adaptation on the geographical distribution of Aedes aegypti in Panama

Local adaptation is an important consideration when predicting arthropod-borne disease risk because it can impact on vector population fitness and persistence. However, the extent that vector populations are adapted to local environmental conditions and whether this can impact on species distributions generally remains unknown. Here we find that the geographic distribution of Ae. aegypti across Panama is rapidly changing as a consequence of the recent invasion by its ecological competitor, Aedes albopictus. Although Ae. albopictus has displaced Ae. aegypti in some areas, species coexist across many areas, raising the question: What biological and environmental factors permit population persistence?. Despite low population structure and high gene flow in Ae. aegypti across Panama, excepting the province of Bocas del Toro, we identify 128 candidate SNPs, clustered within 17 genes, which show a strong genetic signal of local adaptation. This putatively adaptive variation occurs across relatively fine geographic scales with the composition and frequency of candidate adaptive loci differing between populations in wet tropical environments along the Caribbean coast and the dry tropical conditions typical of the Pacific coast of Panama. Temperature and vegetation were important predictors of adaptive genomic variation in Ae. aegypti with potential areas of local adaptation occurring within the Caribbean region of Bocas del Toro, the Pacific coastal areas of Herrera and Panama City and the eastern Azuero Peninsula. Interestingly, several of these locations coincide with areas where Ae. aegypti and Ae. albopictus co-exist, suggesting that Ae. aegypti could have an adaptive edge under local environmental conditions that impacts on inter-specific competition with Ae. albopictus. Our results guide future experimental work by suggesting that locally adapted Ae. aegypti are able to persist on invasion by Ae. albopictus and, as a consequence, may fundamentally alter future arborviral disease risk and efforts to control mosquito populations.Local adaptation is an important consideration when predicting arthropod-borne disease risk because it can impact on vector population fitness and persistence. However, the extent that vector populations are adapted to local environmental conditions and whether this can impact on species distributions generally remains unknown. Here we find that the geographic distribution of Ae. aegypti across Panama is rapidly changing as a consequence of the recent invasion by its ecological competitor, Aedes albopictus. Although Ae. albopictus has displaced Ae. aegypti in some areas, species coexist across many areas, raising the question: What biological and environmental factors permit population persistence?. Despite low population structure and high gene flow in Ae. aegypti across Panama, excepting the province of Bocas del Toro, we identify 128 candidate SNPs, clustered within 17 genes, which show a strong genetic signal of local adaptation. This putatively adaptive variation occurs across relatively fine geographic scales with the composition and frequency of candidate adaptive loci differing between populations in wet tropical environments along the Caribbean coast and the dry tropical conditions typical of the Pacific coast of Panama. Temperature and vegetation were important predictors of adaptive genomic variation in Ae. aegypti with potential areas of local adaptation occurring within the Caribbean region of Bocas del Toro, the Pacific coastal areas of Herrera and Panama City and the eastern Azuero Peninsula. Interestingly, several of these locations coincide with areas where Ae. aegypti and Ae. albopictus co-exist, suggesting that Ae. aegypti could have an adaptive edge under local environmental conditions that impacts on inter-specific competition with Ae. albopictus. Our results guide future experimental work by suggesting that locally adapted Ae. aegypti are able to persist on invasion by Ae. albopictus and, as a consequence, may fundamentally alter future arborviral disease risk and efforts to control mosquito populations

Direct perturbation theory on the shift of Electron Spin Resonance

We formulate a direct and systematic perturbation theory on the shift of the main paramagnetic peak in Electron Spin Resonance, and derive a general expression up to second order. It is applied to one-dimensional XXZ and transverse Ising models in the high field limit, to obtain explicit results including the polarization dependence for arbitrary temperature.Comment: 5 pages (no figures) in REVTE

Academic literacy diagnostic assessment in the first semester of first year at university

One vital aspect of the first semester of the first year at university is how academic literacy expectations are made explicit though teaching and assessment practices at the disciplinary level. This paper describes how an academic literacy diagnostic process, and the MASUS tool, was used to ascertain the academic literacy profile of a cohort of undergraduate nursing students [N=569] at the beginning and end of their first semester. Key findings of this quantitative descriptive case study were that only just over half of commencing students possessed appropriate academic literacy skills in all four aspects of the diagnostic and nearly 20% scored in the lowest band—suggesting difficulty with multiple aspects of academic literacy. By the end of semester, 77% of the students who had scored in the lowest band of the MASUS at the beginning of the semester had improved their scores to the middle or highest band, and 73% of them eventually attained a pass or higher grade for the course. The findings of this study suggest that large-scale academic literacy diagnostic assessment, when embedded and contextualized within a course of study, is an effective means of providing the early feedback and targeted support that many commencing university students need