Punctured polygons and polyominoes on the square lattice

We use the finite lattice method to count the number of punctured staircase and self-avoiding polygons with up to three holes on the square lattice. New or radically extended series have been derived for both the perimeter and area generating functions. We show that the critical point is unchanged by a finite number of punctures, and that the critical exponent increases by a fixed amount for each puncture. The increase is 1.5 per puncture when enumerating by perimeter and 1.0 when enumerating by area. A refined estimate of the connective constant for polygons by area is given. A similar set of results is obtained for finitely punctured polyominoes. The exponent increase is proved to be 1.0 per puncture for polyominoes.Comment: 36 pages, 11 figure

Andreev scattering and Josephson current in a one-dimensional electron liquid

Andreev scattering and the Josephson current through a one-dimensional interacting electron liquid sandwiched between two superconductors are re-examined. We first present some apparently new results on the non-interacting case by studying an exactly solvable tight-binding model rather than the usual continuum model. We show that perfect Andreev scattering (i.e. zero normal scattering) at the Fermi energy can only be achieved by fine-tuning junction parameters. We also obtain exact results for the Josephson current, which is generally a smooth function of the superconducting phase difference except when the junction parameters are adjusted to give perfect Andreev scattering, in which case it becomes a sawtooth function. We then observe that, even when interactions are included, all low energy properties of a junction (E<<\Delta, the superconducting gap) can be obtained by "integrating out" the superconducting electrons to obtain an effective Hamiltonian describing the metallic electrons only with a boundary pairing interaction. This boundary model provides a suitable starting point for bosonization/renormalization group/boundary conformal field theory analysis. We argue that total normal reflection and total Andreev reflection correspond to two fixed points of the boundary renormalization group. For repulsive bulk interactions the Andreev fixed point is unstable and the normal one stable. However, the reverse is true for attractive interactions. This implies that a generic junction Hamiltonian (without fine-tuned junction parameters) will renormalize to the normal fixed point for repulsive interactions but to the Andreev one for attractive interactions. An exact mapping of our tight-binding model to the Hubbard model with a transverse magnetic field is used to help understand this behavior.Comment: revtex, 17 pages, 5 postscript figure

Moderate D/H Ratios in Methane Ice on Eris and Makemake as Evidence of Hydrothermal or Metamorphic Processes in Their Interiors: Geochemical Analysis

Dwarf planets Eris and Makemake have surfaces bearing methane ice of unknown origin. D/H ratios were recently determined from James Webb Space Telescope (JWST) observations of Eris and Makemake (Grundy et al., submitted), giving us new clues to decipher the origin of methane. Here, we develop geochemical models to test if the origin of methane could be primordial, derived from CO$_2$ or CO ("abiotic"), or sourced by organics ("thermogenic"). We find that primordial methane is inconsistent with the observational data, whereas both abiotic and thermogenic methane can have D/H ratios that overlap the observed ranges. This suggests that Eris and Makemake either never acquired a significant amount of methane during their formation, or their original inventories were removed and then replaced by a source of internally produced methane. Because producing abiotic or thermogenic methane likely requires temperatures in excess of ~150{\deg}C, we infer that Eris and Makemake have rocky cores that underwent substantial radiogenic heating. Their cores may still be warm/hot enough to produce methane. This heating could have driven hydrothermal circulation at the bottom of an ice-covered ocean to generate abiotic methane, and/or metamorphic reactions involving accreted organic matter could have occurred in response to heating in the deeper interior, generating thermogenic methane. Additional analyses of thermal evolution model results and predictions from modeling of D-H exchange in the solar nebula support our findings of elevated subsurface temperatures and a lack of primordial methane on Eris and Makemake. It remains an open question whether their D/H ratios may have evolved subsequent to methane outgassing. Recommendations are given for future activities to further test proposed scenarios of abiotic and thermogenic methane production on Eris and Makemake, and to explore these worlds up close.Comment: Submitted to Icarus, 29 pages, 5 figures, 1 tabl

Diagnostic Accuracy of Adenosine Stress Cardiovascular Magnetic Resonance Following Acute ST-segment Elevation Myocardial Infarction Post Primary Angioplasty

Extent: 8p.Background: Adenosine stress cardiovascular magnetic resonance (CMR) has been proven an effective tool in detection of reversible ischemia. Limited evidence is available regarding its accuracy in the setting of acute coronary syndromes, particularly in evaluating the significance of non-culprit vessel ischaemia. Adenosine stress CMR and recent advances in semi-quantitative image analysis may prove effective in this area. We sought to determine the diagnostic accuracy of semi-quantitative versus visual assessment of adenosine stress CMR in detecting ischemia in non-culprit territory vessels early after primary percutaneous coronary intervention (PCI) for ST-segment elevation myocardial infarction (STEMI). Methods: Patients were prospectively enrolled in a CMR imaging protocol with rest and adenosine stress perfusion, viability and cardiac functional assessment 3 days after successful primary-PCI for STEMI. Three short axis slices each divided into 6 segments on first pass adenosine perfusion were visually and semi-quantitatively analysed. Diagnostic accuracy of both methods was compared with non-culprit territory vessels utilising quantitative coronary angiography (QCA) with significant stenosis defined as ≥70%. Results: Fifty patients (age 59 ± 12 years) admitted with STEMI were evaluated. All subjects tolerated the adenosine stress CMR imaging protocol with no significant complications. The cohort consisted of 41% anterior and 59% non anterior infarctions. There were a total of 100 non-culprit territory vessels, identified on QCA. The diagnostic accuracy of semi-quantitative analysis was 96% with sensitivity of 99%, specificity of 67%, positive predictive value (PPV) of 97% and negative predictive value (NPV) of 86%. Visual analysis had a diagnostic accuracy of 93% with sensitivity of 96%, specificity of 50%, PPV of 97% and NPV of 43%. Conclusion: Adenosine stress CMR allows accurate detection of non-culprit territory stenosis in patients successfully treated with primary-PCI post STEMI. Semi-quantitative analysis may be required for improved accuracy. Larger studies are however required to demonstrate that early detection of non-culprit vessel ischemia in the post STEMI setting provides a meaningful test to guide clinical decision making and ultimately improved patient outcomes.Dennis TL Wong, Michael CH Leung, Rajiv Das, Gary YH Liew, Kerry Williams, Benjamin K Dundon, Payman Molaee, Karen SL Teo, Ian T Meredith, Matthew I Worthley and Stephen G Worthle

Effectiveness of BNT162b2 and CoronaVac vaccinations against SARS-CoV-2 omicron infection in people aged 60 years or above: a case–control study

BACKGROUND: In view of limited evidence that specifically addresses vaccine effectiveness (VE) in the older population, this study aims to evaluate the real-world effectiveness of BNT162b2 and CoronaVac in older adults during the Omicron BA.2 outbreak. METHODS: This case-control study analyzed data available between January and March 2022 from the electronic health databases in Hong Kong and enrolled individuals aged 60 or above. Each case was matched with up to 10 controls by age, sex, index date and Charlson Comorbidity Index for the four outcomes (COVID-19 infection, COVID-19-related hospitalization, severe complications, and all-cause mortality) independently. Conditional logistic regression was conducted to evaluate VE of BNT162b2 and CoronaVac against COVID-19-related outcomes within 28 days after COVID-19 infection among participants stratified by age groups (60-79, ≥80 years old). RESULTS: A dose-response relationship between the number of vaccine doses received and protection against severe or fatal disease was observed. Highest VE (95% CI) against COVID-19 infection was observed in individuals aged ≥80 who received three doses of BNT162b2 [75.5% (73.1-77.7%)] or three doses of CoronaVac [53.9% (51.0-56.5%)] compared to those in the younger age group who received three doses of BNT162b2 [51.1% (49.9-52.4%)] or three doses of CoronaVac [2.0% (-0.1-4.1%)]. VE (95% CI) was higher for other outcomes, reaching 91.9% (89.4-93.8%) and 86.7% (84.3-88.8%) against COVID-19-related hospitalization; 85.8% (61.2-94.8%) and 89.8% (72.4-96.3%) against COVID-19-related severe complications; and 96.4% (92.9-98.2%) and 95.0% (92.1-96.8%) against COVID-19-related mortality after three doses of BNT162b2 and CoronaVac in older vaccine recipients, respectively. A similar dose-response relationship was established in younger vaccine recipients and after stratification by sex and Charlson Comorbidity Index. CONCLUSION: Both BNT162b2 and CoronaVac vaccination were effective in protecting older adults against COVID-19 infection and COVID-19-related severe outcomes amidst the Omicron BA.2 pandemic, and VE increased further with the third dose

A sub-Neptune exoplanet with a low-metallicity methane-depleted atmosphere and Mie-scattering clouds

With no analogues in the Solar System, the discovery of thousands of exoplanets with masses and radii intermediate between Earth and Neptune was one of the big surprises of exoplanet science. These super-Earths and sub-Neptunes probably represent the most common outcome of planet formation. Mass and radius measurements indicate a diversity in bulk composition much wider than for gas giants; however, direct spectroscopic detections of molecular absorption and constraints on the gas mixing ratios have largely remained limited to planets more massive than Neptune. Here we analyse a combined Hubble/Spitzer Space Telescope dataset of 12 transits and 20 eclipses of the sub-Neptune exoplanet GJ 3470 b, whose mass of 12.6 M⊕ places it near the halfway point between previously studied Neptune-like exoplanets (22–23 M⊕) and exoplanets known to have rocky densities (7 M⊕). Obtained over many years, our dataset provides a robust detection of water absorption (>5σ) and a thermal emission detection from the lowest irradiated planet to date. We reveal a low-metallicity, hydrogen-dominated atmosphere similar to that of a gas giant, but strongly depleted in methane gas. The low metallicity (O/H = 0.2–18.0) sets important constraints on the potential planet formation processes at low masses as well as the subsequent accretion of solids. The low methane abundance indicates that methane is destroyed much more efficiently than previously predicted, suggesting that the CH_4/CO transition curve has to be revisited for close-in planets. Finally, we also find a sharp drop in the cloud opacity at 2–3 µm, characteristic of Mie scattering, which enables narrow constraints on the cloud particle size and makes GJ 3470 b a key target for mid-infrared characterization with the James Webb Space Telescope

Exoplanet phase curves: observations and theory

Phase curves are the best technique to probe the three dimensional structure of exoplanets' atmospheres. In this chapter we first review current exoplanets phase curve observations and the particular challenges they face. We then describe the different physical mechanisms shaping the atmospheric phase curves of highly irradiated tidally locked exoplanets. Finally, we discuss the potential for future missions to further advance our understanding of these new worlds.Comment: Fig.5 has been updated. Table 1 and corresponding figures have been updated with new values for WASP-103b and WASP-18b. Contains a table sumarizing phase curve observation

Accurate reconstruction of insertion-deletion histories by statistical phylogenetics

The Multiple Sequence Alignment (MSA) is a computational abstraction that represents a partial summary either of indel history, or of structural similarity. Taking the former view (indel history), it is possible to use formal automata theory to generalize the phylogenetic likelihood framework for finite substitution models (Dayhoff's probability matrices and Felsenstein's pruning algorithm) to arbitrary-length sequences. In this paper, we report results of a simulation-based benchmark of several methods for reconstruction of indel history. The methods tested include a relatively new algorithm for statistical marginalization of MSAs that sums over a stochastically-sampled ensemble of the most probable evolutionary histories. For mammalian evolutionary parameters on several different trees, the single most likely history sampled by our algorithm appears less biased than histories reconstructed by other MSA methods. The algorithm can also be used for alignment-free inference, where the MSA is explicitly summed out of the analysis. As an illustration of our method, we discuss reconstruction of the evolutionary histories of human protein-coding genes.Comment: 28 pages, 15 figures. arXiv admin note: text overlap with arXiv:1103.434