The Computational Complexity of Knot and Link Problems

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, {\sc unknotting problem} is in {\bf NP}. We also consider the problem, {\sc unknotting problem} of determining whether two or more such polygons can be split, or continuously deformed without self-intersection so that they occupy both sides of a plane without intersecting it. We show that it also is in NP. Finally, we show that the problem of determining the genus of a polygonal knot (a generalization of the problem of determining whether it is unknotted) is in {\bf PSPACE}. We also give exponential worst-case running time bounds for deterministic algorithms to solve each of these problems. These algorithms are based on the use of normal surfaces and decision procedures due to W. Haken, with recent extensions by W. Jaco and J. L. Tollefson.Comment: 32 pages, 1 figur

Factors affecting residency rank-listing: A Maxdiff survey of graduating Canadian medical students

<p>Abstract</p> <p>Background</p> <p>In Canada, graduating medical students consider many factors, including geographic, social, and academic, when ranking residency programs through the Canadian Residency Matching Service (CaRMS). The relative significance of these factors is poorly studied in Canada. It is also unknown how students differentiate between their top program choices. This survey study addresses the influence of various factors on applicant decision making.</p> <p>Methods</p> <p>Graduating medical students from all six Ontario medical schools were invited to participate in an online survey available for three weeks prior to the CaRMS match day in 2010. Max-Diff discrete choice scaling, multiple choice, and drop-list style questions were employed. The Max-Diff data was analyzed using a scaled simple count method. Data for how students distinguish between top programs was analyzed as percentages. Comparisons were made between male and female applicants as well as between family medicine and specialist applicants; statistical significance was determined by the Mann-Whitney test.</p> <p>Results</p> <p>In total, 339 of 819 (41.4%) eligible students responded. The variety of clinical experiences and resident morale were weighed heavily in choosing a residency program; whereas financial incentives and parental leave attitudes had low influence. Major reasons that applicants selected their first choice program over their second choice included the distance to relatives and desirability of the city. Both genders had similar priorities when selecting programs. Family medicine applicants rated the variety of clinical experiences more importantly; whereas specialty applicants emphasized academic factors more.</p> <p>Conclusions</p> <p>Graduating medical students consider program characteristics such as the variety of clinical experiences and resident morale heavily in terms of overall priority. However, differentiation between their top two choice programs is often dependent on social/geographic factors. The results of this survey will contribute to a better understanding of the CaRMS decision making process for both junior medical students and residency program directors.</p

Crystalline silicates and dust processing in the protoplanetary disks of the Taurus young cluster

We characterize the crystalline silicate content and spatial distribution of small dust grains in a large sample of protoplanetary disks in the Taurus-Auriga young cluster, using Spitzer Space Telescope mid-infrared spectra. In turn we use the results to analyze the evolution of structure and composition of these 1-2 Myr-old disks around Solar- and later-type young stars, and test the standard models of dust processing which result in the conversion of originally amorphous dust into minerals. We find strong evidence of evolution of the dust crystalline mass fraction in parallel with that of the structure of the disks, in the sense that increasing crystalline mass fraction is strongly linked to dust settling to the disk midplane. We also confirm that the crystalline silicates are confined to small radii, r < 10 AU. However, we see no significant correlation of crystalline mass fraction with stellar mass or luminosity, stellar accretion rate, disk mass, or disk/star mass ratio, as would be expected in the standard models of dust processing based upon photo-evaporation and condensation close to the central star, accretion-heating-driven annealing at r < 1 AU, or spiral-shock heating at r < 10 AU, with or without effective radial mixing mechanisms. Either another grain-crystallizing mechanism dominates over these, or another process must be at work within the disks to erase the correlations they produce. We propose one of each sort that seem to be worth further investigation, namely X-ray heating and annealing of dust grains, and modulation of disk structure by giant-planetary formation and migration.Comment: 116 pages, including 11 figures and 4 table

Crowdsourcing hypothesis tests: Making transparent how design choices shape research results

To what extent are research results influenced by subjective decisions that scientists make as they design studies? Fifteen research teams independently designed studies to answer fiveoriginal research questions related to moral judgments, negotiations, and implicit cognition. Participants from two separate large samples (total N > 15,000) were then randomly assigned to complete one version of each study. Effect sizes varied dramatically across different sets of materials designed to test the same hypothesis: materials from different teams renderedstatistically significant effects in opposite directions for four out of five hypotheses, with the narrowest range in estimates being d = -0.37 to +0.26. Meta-analysis and a Bayesian perspective on the results revealed overall support for two hypotheses, and a lack of support for three hypotheses. Overall, practically none of the variability in effect sizes was attributable to the skill of the research team in designing materials, while considerable variability was attributable to the hypothesis being tested. In a forecasting survey, predictions of other scientists were significantly correlated with study results, both across and within hypotheses. Crowdsourced testing of research hypotheses helps reveal the true consistency of empirical support for a scientific claim.</div

Les droits disciplinaires des fonctions publiques : « unification », « harmonisation » ou « distanciation ». A propos de la loi du 26 avril 2016 relative à la déontologie et aux droits et obligations des fonctionnaires

The production of tt‾ , W+bb‾ and W+cc‾ is studied in the forward region of proton–proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98±0.02 fb−1 . The W bosons are reconstructed in the decays W→ℓν , where ℓ denotes muon or electron, while the b and c quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions.The production of $t\overline{t}$, $W+b\overline{b}$ and $W+c\overline{c}$ is studied in the forward region of proton-proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98 $\pm$ 0.02 \mbox{fb}^{-1}. The $W$ bosons are reconstructed in the decays $W\rightarrow\ell\nu$, where $\ell$ denotes muon or electron, while the $b$ and $c$ quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions