Convergence of random zeros on complex manifolds

We show that the zeros of random sequences of Gaussian systems of polynomials of increasing degree almost surely converge to the expected limit distribution under very general hypotheses. In particular, the normalized distribution of zeros of systems of m polynomials of degree N, orthonormalized on a regular compact subset K of C^m, almost surely converge to the equilibrium measure on K as the degree N goes to infinity.Comment: 16 page

Scaling asymptotics for quantized Hamiltonian flows

In recent years, the near diagonal asymptotics of the equivariant components of the Szeg\"{o} kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map

Semiclassical almost isometry

Let M be a complex projective manifold, and L an Hermitian ample line bundle on it. A fundamental theorem of Gang Tian, reproved and strengthened by Zelditch, implies that the Khaeler form of L can be recovered from the asymptotics of the projective embeddings associated to large tensor powers of L. More precisely, with the natural choice of metrics the projective embeddings associated to the full linear series |kL| are asymptotically symplectic, in the appropriate rescaled sense. In this article, we ask whether and how this result extends to the semiclassical setting. Specifically, we relate the Weinstein symplectic structure on a given isodrastic leaf of half-weighted Bohr-Sommerfeld Lagrangian submanifolds of M to the asymptotics of the the pull-back of the Fubini-Study form under the semiclassical projective maps constructed by Borthwick, Paul and Uribe.Comment: exposition improve

Local trace formulae and scaling asymptotics in Toeplitz quantization

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of symmetries on quantizable compact symplectic manifolds. The local trace formula involves certain scaling asymptotics along the clean fixed locus of the Hamiltonian flow of the symbol, reminiscent of the scaling asymptotics of the equivariant components of the Szeg\"o kernel along the diagonal

Community-based control of a neglected tropical disease: the mossy foot treatment and prevention association

Podoconiosis (endemic non-filarial elephantiasis, also known as mossy foot) is a non-communicable disease now found exclusively in the tropics, caused by the conjunction of environmental, genetic, and economic factors. Silicate particles formed by the disintegration of lava in areas of high altitude (over 1,000 m) and seasonal rainfall (over 1,000 mm per annum) penetrate the skin of barefoot subsistence farmers, and in susceptible individuals cause lymphatic blockage and subsequent elephantiasis [1]. Although an estimated one million Ethiopians (of a total population of 77 million) are afflicted with podoconiosis [2], which creates a huge economic burden in endemic areas [3], no national policy has yet been developed to control or prevent the condition, and most affected communities remain unaware of treatment options

Meta-analysis: re-treatment of genotype I hepatitis C nonresponders and relapsers after failing interferon and ribavirin combination therapy

Aliment Pharmacol Ther 2010; 32: 969–983The efficacy of re-treating genotype I hepatitis C virus (HCV) patients who failed combination therapy with interferon/pegylated interferon (PEG-IFN) and ribavirin remains unclear.To quantify sustained virological response (SVR) rates with different re-treatment regimens through meta-analysis of randomized controlled trials (RCTs).Randomized controlled trials of genotype I HCV treatment failure patients that compared currently available re-treatment regimens were selected. Two investigators independently extracted data on patient population, methods and results. The pooled relative risk of SVR for treatment regimens was computed using a random effects model.Eighteen RCTs were included. In nonresponders to standard interferon/ribavirin, re-treatment with high-dose PEG-IFN combination therapy improved SVR compared with standard PEG-IFN combination therapy (RR = 1.49; 95% CI: 1.09–2.04), but SVR rates did not exceed 18% in most studies. In relapsers to standard interferon/ribavirin, re-treatment with high-dose PEG-IFN or prolonged CIFN improved SVR (RR = 1.57; 95% CI: 1.16–2.14) and achieved SVR rates of 43–69%.In genotype I HCV treatment failure patients who received combination therapy, re-treatment with high-dose PEG-IFN combination therapy is superior to re-treatment with standard combination therapy, although SVR rates are variable for nonresponders (≤18%) and relapsers (43–69%). Re-treatment may be appropriate for select patients, especially relapsers and individuals with bridging fibrosis or compensated cirrhosis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79170/1/j.1365-2036.2010.04427.x.pd