Corrigendum to "Knot Floer homology detects fibred knots"

We correct a mistake on the citation of JSJ theory in \cite{Ni}. Some arguments in \cite{Ni} are also slightly modified accordingly.Comment: 3 page

Spatial Graphs with Local Knots

It is shown that for any locally knotted edge of a 3-connected graph in $S^3$, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in $S^3$.Comment: 20 pages, 3 figures; in v. 2 the proof of Theorem 1 has been clarified, and other minor revisions have been mad

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

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

Palliative care in interstitial lung disease: living well

Progressive fibrotic interstitial lung diseases (ILDs) are characterised by major reductions in quality of life and survival and have similarities to certain malignancies. However, palliative care expertise is conspicuously inaccessible to many patients with ILD. Unmet patient and caregiver needs include effective pharmacological and psychosocial interventions to improve quality of life throughout the disease course, sensitive advanced care planning, and timely patient-centred end-of-life care. The incorrect perception that palliative care is synonymous with end-of-life care, with no role earlier in the course of ILD, has created a culture of neglect. Interventions that aim to improve life expectancy are often prioritised without rigorous assessment of the individual's health and psychosocial needs, thereby inadvertently reducing quality of life. As in malignant disorders, radical interventions to slow disease progression and palliative measures to improve quality of life should both be prioritised. Efficient patient-centred models of palliative care must be validated, taking into account religious and cultural differences, as well as variability of resources. Effective implementation of palliative care for ILD will require multidisciplinary participation from clinicians, specialist nurses, psychologists, social workers, and, in some countries, non-governmental faith and community-based organisations with access to palliative care expertise

Genome-Wide Analysis of Subependymomas Shows Underlying Chromosomal Copy Number Changes Involving Chromosomes 6, 7, 8 and 14 in a Proportion of Cases

Subependymomas (SE) are slow-growing brain tumors that tend to occur within the ventricles of middle-aged and elderly adults. The World Health Organization classifies these tumors within the ependymoma group. Previous limited analysis of this tumor type had not revealed significant underlying cytogenetic abnormalities

In Vivo Carbon-13 Dynamic MRS and MRSI of Normal and Fasted Rat Liver with Hyperpolarized 13C-Pyruvate

BACKGROUND: The use of in vivo (13)C nuclear magnetic resonance spectroscopy in probing metabolic pathways to study normal metabolism and characterize disease physiology has been limited by its low sensitivity. However, recent technological advances have enabled greater than 50,000-fold enhancement of liquid-state polarization of metabolically active (13)C substrates, allowing for rapid assessment of (13)C metabolism in vivo. The present study applied hyperpolarized (13)C magnetic resonance spectroscopy to the investigation of liver metabolism, demonstrating for the first time the feasibility of applying this technology to detect differences in liver metabolic states. PROCEDURES: [1-(13)C]pyruvate was hyperpolarized with a dynamic nuclear polarization instrument and injected into normal and fasted rats. The uptake of pyruvate and its conversion to the metabolic products lactate and alanine were observed with slice-localized dynamic magnetic resonance spectroscopy and 3D magnetic resonance spectroscopic imaging (3D-MRSI). RESULTS: Significant differences in lactate to alanine ratio (P < 0.01) between normal and fasted rat liver slice dynamic spectra were observed. 3D-MRSI localized to the fasted livers demonstrated significantly decreased (13)C-alanine levels (P < 0.01) compared to normal. CONCLUSIONS: This study presents the initial demonstration of characterizing metabolic state differences in the liver with hyperpolarized (13)C spectroscopy and shows the ability to detect physiological perturbations in alanine aminotransferase activity, which is an encouraging result for future liver disease investigations with hyperpolarized magnetic resonance technology