Canonical decompositions of 3-manifolds

We describe a new approach to the canonical decompositions of 3-manifolds along tori and annuli due to Jaco-Shalen and Johannson (with ideas from Waldhausen) - the so-called JSJ-decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus-torus theorems, and the theory of Seifert fibrations does not need to be developed in advance.Comment: 20 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper3.abs.htm

Oscillating bound states for a giant atom

We investigate the relaxation dynamics of a single artificial atom interacting, via multiple coupling points, with a continuum of bosonic modes (photons or phonons) in a one-dimensional waveguide. In the non-Markovian regime, where the traveling time of a photon or phonon between the coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the atom, we find that a boson can be trapped and form a stable bound state. As a key discovery, we further find that a persistently oscillating bound state can appear inside the continuous spectrum of the waveguide if the number of coupling points is more than two since such a setup enables multiple bound modes to coexist. This opens up prospects for storing and manipulating quantum information in larger Hilbert spaces than available in previously known bound states

Flood Risk Management Policy in the Upper Tisza Basin: A System Analytical Approach. Simulation and Analysis of Three Flood Management Strategies

This report describes an integrated flood catastrophe model as well as some results of a case study made in the upper Tisza region in northeastern Hungary: the Palad-Csecsei basin (the pilot basin). The background data was provided through the Hungarian Academy of Sciences and complemented by interviews with different stakeholders in the region. Based upon these data, where a large degree of uncertainty is prevailing, we demonstrate how an implementation of a simulation and decision analytical model can provide insights into the effects of imposing different policy options for a flood risk management program in the region. We focus herein primarily on general options for designing a public-private insurance and reinsurance system for Hungary. Obviously, this is a multi-criteria and multi-stakeholder problem and cannot be solved using standard approaches. It should however be emphasized that the main purpose of this report is not to provide any definite recommendations, but rather to explore a set of policy packages that could gain a consensus among the stakeholders

Knot Floer homology detects fibred knots

Ozsv\'ath and Szab\'o conjectured that knot Floer homology detects fibred knots in $S^3$. We will prove this conjecture for null-homologous knots in arbitrary closed 3--manifolds. Namely, if $K$ is a knot in a closed 3--manifold $Y$, $Y-K$ is irreducible, and $\hat{HFK}(Y,K)$ is monic, then $K$ is fibred. The proof relies on previous works due to Gabai, Ozsv\'ath--Szab\'o, Ghiggini and the author. A corollary is that if a knot in $S^3$ admits a lens space surgery, then the knot is fibred.Comment: version 4: incorporates referee's suggestions, to appear in Inventiones Mathematica

Social Media Content of Idiopathic Pulmonary Fibrosis Groups and Pages on Facebook: Cross-sectional Analysis.

BACKGROUND Patients use Facebook as a resource for medical information. We analyzed posts on idiopathic pulmonary fibrosis (IPF)-related Facebook groups and pages for the presence of guideline content, user engagement, and usefulness. OBJECTIVE The objective of this study was to describe and analyze posts from Facebook groups and pages that primarily focus on IPF-related content. METHODS Cross-sectional analysis was performed on a single date, identifying Facebook groups and pages resulting from separately searching "IPF" and "idiopathic pulmonary fibrosis." For inclusion, groups and pages needed to meet either search term and be in English, publicly available, and relevant to IPF. Every 10th post was assessed for general characteristics, source, focus, and user engagement metrics. Posts were analyzed for presence of IPF guideline content, useful scientific information (eg, scientific publications), useful support information (eg, information about support groups), and potentially harmful information. RESULTS Eligibility criteria were met by 12 groups and 27 pages, leading to analysis of 523 posts. Of these, 42% contained guideline content, 24% provided useful support, 20% provided useful scientific information, and 5% contained potentially harmful information. The most common post source was nonmedical users (85%). Posts most frequently focused on IPF-related news (29%). Posts containing any guideline content had fewer likes or comments and a higher likelihood of containing potentially harmful content. Posts containing useful supportive information had more likes, shares, and comments. CONCLUSIONS Facebook contains useful information about IPF, but posts with misinformation and less guideline content have higher user engagement, making them more visible. Identifying ways to help patients with IPF discriminate between useful and harmful information on Facebook and other social media platforms is an important task for health care professionals

Expected length of the longest common subsequence for large alphabets

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.Comment: 14 pages, 1 figure, LaTe

Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity

This review contains a summary of work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables -the Liouville exponentials and the Liouville field itself - and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.Comment: 38 pages, LaTex file. Proceedings of the Vth International Conference on Mathematical Physics, Strings and Quantum gravity, Alushta, Ukraine 199

Incidence and prognostic significance of hypoxemia in fibrotic interstitial lung disease: an international cohort study.

BACKGROUND Hypoxemia is a cardinal feature of fibrotic interstitial lung disease (ILD). The incidence, progression, and prognostic significance of hypoxemia in patients with fibrotic ILD is currently unknown. RESEARCH QUESTION What are the epidemiology of hypoxemia and its additive prognostic value in current risk prediction model in fibrotic ILD? METHODS We identified 848 patients with fibrotic ILD (258 with idiopathic pulmonary fibrosis (IPF)) in five prospective ILD registries from Australia, Canada, and Switzerland. Cumulative incidence of exertional and resting hypoxemia from the time of diagnosis was estimated at 1-year intervals in patients with baseline 6-minute walk tests, adjusted for competing risks of death and lung transplantation. Likelihood ratio tests were used to determine the prognostic significance of exertional and resting hypoxemia for 1-year mortality/transplantation when added to the ILD-GAP model. The cohort was divided into derivation and validation subsets to evaluate performance characteristics of the extended model (the "ILD-GAP-O2" model), which included oxygenation status as a predictor. RESULTS The 1-, 2-, and 5-year overall cumulative incidence was 6.1%, 17.3%, and 40.1% for exertional hypoxemia, and 2.4%, 5.6%, and 16.5% for resting hypoxemia, which were significantly higher in IPF patients compared to non-IPF patients (p<0.001 for both). Addition of exertional or resting hypoxemia to the ILD-GAP model improved 1-year mortality/transplantation prediction (p<0.001 for both). The ILD-GAP-O2 model had improved discrimination (C-index of 0.80 vs 0.75) and model fit (Akaike information criteria of 400 vs 422) in the validation cohort, with comparable calibration. INTERPRETATION IPF patients have higher cumulative incidence of exertional and resting hypoxemia than non-IPF patients. The extended ILD-GAP-O2 model provides additional risk stratification for 1-year prognosis in fibrotic ILD

Exposure to ambient particulate matter is associated with accelerated functional decline in idiopathic pulmonary fibrosis

BACKGROUND: Idiopathic pulmonary fibrosis (IPF), a progressive disease with an unknown pathogenesis, may be due in part to an abnormal response to injurious stimuli by alveolar epithelial cells. Air pollution and particulate inhalation of matter evoke a wide variety of pulmonary and systemic inflammatory diseases. We therefore hypothesized that increased average ambient particulate matter (PM) concentrations would be associated with an accelerated rate of decline in FVC in IPF. METHODS: We identified a cohort of subjects seen at a single university referral center from 2007 to 2013. Average concentrations of particulate matter < 10 and < 2.5 μg/m3 (PM10 and PM2.5, respectively) were assigned to each patient based on geocoded residential addresses. A linear multivariable mixed-effects model determined the association between the rate of decline in FVC and average PM concentration, controlling for baseline FVC at first measurement and other covariates. RESULTS: One hundred thirty-five subjects were included in the final analysis after exclusion of subjects missing repeated spirometry measurements and those for whom exposure data were not available. There was a significant association between PM10 levels and the rate of decline in FVC during the study period, with each μg/m3 increase in PM10 corresponding with an additional 46 cc/y decline in FVC (P = .008). CONCLUSIONS: Ambient air pollution, as measured by average PM10 concentration, is associated with an increase in the rate of decline of FVC in IPF, suggesting a potential mechanistic role for air pollution in the progression of disease