Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities

Let X be a surface with an isolated singularity at the origin, given by the equation Q(x,y,z)=0, where Q is a weighted-homogeneous polynomial. In particular, this includes the Kleinian surfaces X = C^2/G for G < SL(2,C) finite. Let Y be the n-th symmetric power of X. We compute the zeroth Poisson homology of Y, as a graded vector space with respect to the weight grading. In the Kleinian case, this confirms a conjecture of Alev, that the zeroth Poisson homology of the n-th symmetric power of C^2/G is isomorphic to the zeroth Hochschild homology of the n-th symmetric power of the algebra of G-invariant differential operators on C. That is, the Brylinski spectral sequence degenerates in this case. In the elliptic case, this yields the zeroth Hochschild homology of symmetric powers of the elliptic algebras with three generators modulo their center, for the parameter equal to all but countably many points of the elliptic curve.Comment: 17 page

Liposomal amphotericin B twice weekly as antifungal prophylaxis in paediatric haematological malignancy patients

AbstractData on antifungal prophylaxis in paediatric cancer patients at high risk for invasive fungal disease (IFD) are scant. Intermittent administration of liposomal amphotericin B (LAMB) has been shown to be safe and effective in adult patients with haematological malignancies. We prospectively evaluated the safety and efficacy of prophylactic LAMB at a dosage of 2.5 mg/kg twice weekly in children at high risk for IFD. Efficacy was compared with that in a historical control group of patients with similar demographic characteristics not receiving LAMB prophylaxis. A total of 46 high-risk patients (24 boys; mean age, 7.7 years) with 187 episodes of antifungal prophylaxis were analysed. The median duration of neutropenia (<500/µL) was 10 days. LAMB was discontinued in four patients because of acute allergic reactions. Median values for creatinine and liver enzymes at end of treatment did not differ significantly from those at baseline. Hypokalaemia (<3.0 mmol/L) occurred with 13.5% of the prophylactic episodes, but was usually mild and always reversible. No proven/probable IFD occurred in patients receiving LAMB prophylaxis. In comparison, five proven and two probable IFDs were observed in 45 historical controls not receiving LAMB prophylaxis (p 0.01). LAMB prophylaxis had no impact on the use of empirical antifungal therapy. Systemic antifungal prophylaxis with LAMB 2.5 mg/kg twice weekly is feasible and safe, and seems to be an effective approach for antifungal prophylaxis in high-risk paediatric cancer patients

Magnetism and superconductivity driven by identical 4ff states in a heavy-fermion metal

The apparently inimical relationship between magnetism and superconductivity has come under increasing scrutiny in a wide range of material classes, where the free energy landscape conspires to bring them in close proximity to each other. This is particularly the case when these phases microscopically interpenetrate, though the manner in which this can be accomplished remains to be fully comprehended. Here, we present combined measurements of elastic neutron scattering, magnetotransport, and heat capacity on a prototypical heavy fermion system, in which antiferromagnetism and superconductivity are observed. Monitoring the response of these states to the presence of the other, as well as to external thermal and magnetic perturbations, points to the possibility that they emerge from different parts of the Fermi surface. This enables a single 4$f$ state to be both localized and itinerant, thus accounting for the coexistence of magnetism and superconductivity.Comment: 4 pages, 4 figure

Classes on compactifications of the moduli space of curves through solutions to the quantum master equation

In this paper we describe a construction which produces classes in a compactification of the moduli space of curves. This construction extends a construction of Kontsevich which produces classes in the open moduli space from the initial data of a cyclic A-infinity algebra. The initial data for our construction is what we call a `quantum A-infinity algebra', which arises as a type of deformation of a cyclic A-infinity algebra. The deformation theory for these structures is described explicitly. We construct a family of examples of quantum A-infinity algebras which extend a family of cyclic A-infinity algebras, introduced by Kontsevich, which are known to produce all the Miller-Morita-Mumford classes using his construction.Comment: This version includes an updated list of reference