Fuchsian bispectral operators

The aim of this paper is to classify the bispectral operators of any rank with regular singular points (the infinite point is the most important one). We characterise them in several ways. Probably the most important result is that they are all Darboux transformations of powers of generalised Bessel operators (in the terminology of q-alg/9602011). For this reason they can be effectively parametrised by the points of a certain (infinite) family of algebraic manifolds as pointed out in q-alg/9602011.Comment: 32 pages, late

On the Genus Two Free Energies for Semisimple Frobenius Manifolds

We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called "genus two G-function". Conjecturally the genus two G-function vanishes for a series of important examples of Frobenius manifolds associated with simple singularities as well as for ${\bf P}^1$-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases.Comment: 37 pages, 3 figures, V2: the published versio

The Extended Bigraded Toda hierarchy

We generalize the Toda lattice hierarchy by considering N+M dependent variables. We construct roots and logarithms of the Lax operator which are uniquely defined operators with coefficients that are $\epsilon$-series of differential polynomials in the dependent variables, and we use them to provide a Lax pair definition of the extended bigraded Toda hierarchy. Using R-matrix theory we give the bihamiltonian formulation of this hierarchy and we prove the existence of a tau function for its solutions. Finally we study the dispersionless limit and its connection with a class of Frobenius manifolds on the orbit space of the extended affine Weyl groups of the $A$ series.Comment: 32 pages, corrected typo

The local Gromov-Witten theory of CP^1 and integrable hierarchies

In this paper we begin the study of the relationship between the local Gromov-Witten theory of Calabi-Yau rank two bundles over the projective line and the theory of integrable hierarchies. We first of all construct explicitly, in a large number of cases, the Hamiltonian dispersionless hierarchies that govern the full descendent genus zero theory. Our main tool is the application of Dubrovin's formalism, based on associativity equations, to the known results on the genus zero theory from local mirror symmetry and localization. The hierarchies we find are apparently new, with the exception of the resolved conifold O(-1) + O(-1) -> P1 in the equivariantly Calabi-Yau case. For this example the relevant dispersionless system turns out to be related to the long-wave limit of the Ablowitz-Ladik lattice. This identification provides us with a complete procedure to reconstruct the dispersive hierarchy which should conjecturally be related to the higher genus theory of the resolved conifold. We give a complete proof of this conjecture for genus g<=1; our methods are based on establishing, analogously to the case of KdV, a "quasi-triviality" property for the Ablowitz-Ladik hierarchy at the leading order of the dispersive expansion. We furthermore provide compelling evidence in favour of the resolved conifold/Ablowitz-Ladik correspondence at higher genus by testing it successfully in the primary sector for g=2.Comment: 30 pages; v2: an issue involving constant maps contributions is pointed out in Sec. 3.3-3.4 and is now taken into account in the proofs of Thm 1.3-1.4, whose statements are unchanged. Several typos, formulae, notational inconsistencies have been fixed. v3: typos fixed, minor textual changes, version to appear on Comm. Math. Phy

Double Ramification Cycles and Integrable Hierarchies

In this paper we present a new construction of a hamiltonian hierarchy associated to a cohomological field theory. We conjecture that in the semisimple case our hierarchy is related to the Dubrovin–Zhang hierarchy by a Miura transformation, and we check it in several examples

Rifapentine access in Europe: growing concerns over key tuberculosis treatment component

[No abstract available]Support statement: C. Lange is supported by the German Center of Infection Research (DZIF). All other authors have no funding to declare for this study. Funding information for this article has been deposited with the Crossref Funder Registry

Sex- and age-related differences in the management and outcomes of chronic heart failure: an analysis of patients from the ESC HFA EORP Heart Failure Long-Term Registry

Aims: This study aimed to assess age- and sex-related differences in management and 1-year risk for all-cause mortality and hospitalization in chronic heart failure (HF) patients. Methods and results: Of 16 354 patients included in the European Society of Cardiology Heart Failure Long-Term Registry, 9428 chronic HF patients were analysed [median age: 66 years; 28.5% women; mean left ventricular ejection fraction (LVEF) 37%]. Rates of use of guideline-directed medical therapy (GDMT) were high (angiotensin-converting enzyme inhibitors/angiotensin receptor blockers, beta-blockers and mineralocorticoid receptor antagonists: 85.7%, 88.7% and 58.8%, respectively). Crude GDMT utilization rates were lower in women than in men (all differences: P\ua0 64 0.001), and GDMT use became lower with ageing in both sexes, at baseline and at 1-year follow-up. Sex was not an independent predictor of GDMT prescription; however, age >75 years was a significant predictor of GDMT underutilization. Rates of all-cause mortality were lower in women than in men (7.1% vs. 8.7%; P\ua0=\ua00.015), as were rates of all-cause hospitalization (21.9% vs. 27.3%; P\ua075 years. Conclusions: There was a decline in GDMT use with advanced age in both sexes. Sex was not an independent predictor of GDMT or adverse outcomes. However, age >75 years independently predicted lower GDMT use and higher all-cause mortality in patients with LVEF 6445%

Tau-Structure for the Double Ramification Hierarchies

In this paper we continue the study of the double ramification hierarchy of Buryak (Commun Math Phys 336(3):1085–1107, 2015). After showing that the DR hierarchy satisfies tau-symmetry we define its partition function as the (logarithm of the) tau-function of the string solution and show that it satisfies various properties (string, dilaton, and divisor equations plus some important degree constraints). We then formulate a stronger version of the conjecture from Buryak (2015): for any semisimple cohomological field theory, the Dubrovin–Zhang and double ramification hierarchies are related by a normal [i.e. preserving the tau-structure (Dubrovin et al. in Adv Math 293:382–435, 2016)] Miura transformation which we completely identify in terms of the partition function of the CohFT. In fact, using only the partition functions, the conjecture can be formulated even in the non-semisimple case (where the Dubrovin–Zhang hierarchy is not defined). We then prove this conjecture for various CohFTs (trivial CohFT, Hodge class, Gromov–Witten theory of CP¹, 3-, 4- and 5-spin classes) and in genus 1 for any semisimple CohFT. Finally we prove that the higher genus part of the DR hierarchy is basically trivial for the Gromov–Witten theory of smooth varieties with non-positive first Chern class and their analogue in Fan–Jarvis–Ruan–Witten quantum singularity theory (Fan et al. in Ann Math 178(1):1–106, 2013)

Impact of renal impairment on atrial fibrillation: ESC-EHRA EORP-AF Long-Term General Registry

Background: Atrial fibrillation (AF) and renal impairment share a bidirectional relationship with important pathophysiological interactions. We evaluated the impact of renal impairment in a contemporary cohort of patients with AF. Methods: We utilised the ESC-EHRA EORP-AF Long-Term General Registry. Outcomes were analysed according to renal function by CKD-EPI equation. The primary endpoint was a composite of thromboembolism, major bleeding, acute coronary syndrome and all-cause death. Secondary endpoints were each of these separately including ischaemic stroke, haemorrhagic event, intracranial haemorrhage, cardiovascular death and hospital admission. Results: A total of 9306 patients were included. The distribution of patients with no, mild, moderate and severe renal impairment at baseline were 16.9%, 49.3%, 30% and 3.8%, respectively. AF patients with impaired renal function were older, more likely to be females, had worse cardiac imaging parameters and multiple comorbidities. Among patients with an indication for anticoagulation, prescription of these agents was reduced in those with severe renal impairment, p&nbsp;&lt;.001. Over 24&nbsp;months, impaired renal function was associated with significantly greater incidence of the primary composite outcome and all secondary outcomes. Multivariable Cox regression analysis demonstrated an inverse relationship between eGFR and the primary outcome (HR 1.07 [95% CI, 1.01–1.14] per 10&nbsp;ml/min/1.73&nbsp;m2 decrease), that was most notable in patients with eGFR &lt;30&nbsp;ml/min/1.73&nbsp;m2 (HR 2.21 [95% CI, 1.23–3.99] compared to eGFR ≥90&nbsp;ml/min/1.73&nbsp;m2). Conclusion: A significant proportion of patients with AF suffer from concomitant renal impairment which impacts their overall management. Furthermore, renal impairment is an independent predictor of major adverse events including thromboembolism, major bleeding, acute coronary syndrome and all-cause death in patients with AF