Local Index Formula on the Equatorial Podles Sphere

We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the `degenerate' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one. After the identification of the smooth pre-$C^*$-algebra we compute the dimension spectrum and residues. We check the nontriviality of the (noncommutative) Chern character of the associated Fredholm modules by computing the pairing with the fundamental projector of the $C^*$-algebra (the nontrivial generator of the $K_0$-group) as well as the pairing with the $q$-analogue of the Bott projector. Finally, we show that the local index formula is trivially satisfied.Comment: 18 pages, no figures; minor correction

An Obstruction to Quantization of the Sphere

In the standard example of strict deformation quantization of the symplectic sphere $S^2$, the set of allowed values of the quantization parameter $\hbar$ is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including $S^2$) in which $\hbar$ can take any value in an interval, but these examples are badly behaved. Here, I identify a natural additional axiom for strict deformation quantization and prove that it implies that the parameter set for quantizing $S^2$ is never connected.Comment: 23 page. v2: changed sign conventio

Quantum teardrops

Algebras of functions on quantum weighted projective spaces are introduced, and the structure of quantum weighted projective lines or quantum teardrops are described in detail. In particular the presentation of the coordinate algebra of the quantum teardrop in terms of generators and relations and classification of irreducible *-representations are derived. The algebras are then analysed from the point of view of Hopf-Galois theory or the theory of quantum principal bundles. Fredholm modules and associated traces are constructed. C*-algebras of continuous functions on quantum weighted projective lines are described and their K-groups computed.Comment: 18 page

Dexamethasone intravitreal implant in previously treated patients with diabetic macular edema : Subgroup analysis of the MEAD study

Background: Dexamethasone intravitreal implant 0.7 mg (DEX 0.7) was approved for treatment of diabetic macular edema (DME) after demonstration of its efficacy and safety in the MEAD registration trials. We performed subgroup analysis of MEAD study results to evaluate the efficacy and safety of DEX 0.7 treatment in patients with previously treated DME. Methods: Three-year, randomized, sham-controlled phase 3 study in patients with DME, best-corrected visual acuity (BCVA) of 34.68 Early Treatment Diabetic Retinopathy Study letters (20/200.20/50 Snellen equivalent), and central retinal thickness (CRT) 65300 \u3bcm measured by time-domain optical coherence tomography. Patients were randomized to 1 of 2 doses of DEX (0.7 mg or 0.35 mg), or to sham procedure, with retreatment no more than every 6 months. The primary endpoint was 6515-letter gain in BCVA at study end. Average change in BCVA and CRT from baseline during the study (area-under-the-curve approach) and adverse events were also evaluated. The present subgroup analysis evaluated outcomes in patients randomized to DEX 0.7 (marketed dose) or sham based on prior treatment for DME at study entry. Results: Baseline characteristics of previously treated DEX 0.7 (n = 247) and sham (n=261) patients were similar. In the previously treated subgroup, mean number of treatments over 3 years was 4.1 for DEX 0.7 and 3.2 for sham, 21.5 % of DEX 0.7 patients versus 11.1 % of sham had 6515-letter BCVA gain from baseline at study end (P = 0.002), mean average BCVA change from baseline was +3.2 letters with DEX 0.7 versus +1.5 letters with sham (P = 0.024), and mean average CRT change from baseline was -126.1 \u3bcm with DEX 0.7 versus -39.0 \u3bcm with sham(P < 0.001). Cataract-related adverse events were reported in 70.3 % of baseline phakic patients in the previously treated DEX 0.7 subgroup; vision gains were restored following cataract surgery. Conclusions: DEX 0.7 significantly improved visual and anatomic outcomes in patients with DME previously treated with laser, intravitreal anti-vascular endothelial growth factor, intravitreal triamcinolone acetonide, or a combination of these therapies. The safety profile of DEX 0.7 in previously treated patients was similar to its safety profile in the total study population

Associations of autozygosity with a broad range of human phenotypes

In many species, the offspring of related parents suffer reduced reproductive success, a phenomenon known as inbreeding depression. In humans, the importance of this effect has remained unclear, partly because reproduction between close relatives is both rare and frequently associated with confounding social factors. Here, using genomic inbreeding coefficients (FROH) for >1.4 million individuals, we show that FROH is significantly associated (p < 0.0005) with apparently deleterious changes in 32 out of 100 traits analysed. These changes are associated with runs of homozygosity (ROH), but not with common variant homozygosity, suggesting that genetic variants associated with inbreeding depression are predominantly rare. The effect on fertility is striking: FROH equivalent to the offspring of first cousins is associated with a 55% decrease [95% CI 44–66%] in the odds of having children. Finally, the effects of FROH are confirmed within full-sibling pairs, where the variation in FROH is independent of all environmental confounding