Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space

We construct holomorphic families of proper holomorphic embeddings of \mathbb {C}^{k} into \mathbb {C}^{n} (0\textless k\textless n-1), so that for any two different parameters in the family, no holomorphic automorphism of \mathbb {C}^{n} can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of \mathbb {C}^{n}, we derive the existence of families of holomorphic \mathbb {C}^{*}-actions on \mathbb {C}^{n} (n\ge5) so that different actions in the family are not conjugate. This result is surprising in view of the long-standing holomorphic linearization problem, which, in particular, asked whether there would be more than one conjugacy class of \mathbb {C}^{*}-actions on \mathbb {C}^{n} (with prescribed linear part at a fixed point).

Survey estimation and marginal effects in Stata

Stata is a general purpose software package that has become popular among various disciplines such as epidemiology, economics, or social sciences. Users like Stata for its scientific approach, its robustness and reliability, and the ease with which its functionality can be extended by user written programs. In this talk I will first give a brief overview of the functionality of Stata and then discuss two specific features: survey estimation and predictive margins/marginal effects. Most surveys are based on complex samples that contain multiple sampling stages, are stratified or clustered, and feature unequal selection probabilities. Standard estimators can produce misleading results in such samples unless the peculiarities of the sampling plan are taken into account. Stata offers survey statistics for complex samples for a wide variety of estimators and supports several variance estimation procedures such as linearization, jackknife, and balanced repeated replication (see Kreuter and Valliant, 2007, Stata Journal 7: 1-21). In the talk I will illustrate these features using applied examples and I will also show how user written commands can be adapted to support complex samples. Complex can also be the models we fit to our data, making it difficult to interpret them, especially in case of nonlinear or non-additive models (Mood, 2010, European Sociological Review 26: 67-82). Stata provides a number of highly useful commands to make results of such models accessible by computing and displaying predictive margins and marginal effects. In my talk I will discuss these commands provide various examples demonstrating their use.

Macular atrophy in patients with long-term anti-VEGF treatment for neovascular age-related macular degeneration.

PURPOSE To identify the prevalence and progression of macular atrophy (MA) in neovascular age-related macular degeneration (AMD) patients under long-term anti-vascular endothelial growth factor (VEGF) therapy and to determine risk factors. METHOD This retrospective study included patients with neovascular AMD and ≥30 anti-VEGF injections. Macular atrophy (MA) was measured using near infrared and spectral-domain optical coherence tomography (SD-OCT). Yearly growth rate was estimated using square-root transformation to adjust for baseline area and allow for linearization of growth rate. Multiple regression with Akaike information criterion (AIC) as model selection criterion was used to estimate the influence of various parameters on MA area. RESULTS Forty-nine eyes (47 patients, mean age 77 ± 14) were included with a mean of 48 ± 13 intravitreal anti-VEGF injections (ranibizumab:37 ± 11, aflibercept:11 ± 6, mean number of injections/year 8 ± 2.1) over a mean treatment period of 6.2 ± 1.3 years (range 4-8.5). Mean best-corrected visual acuity improved from 57 ± 17 letters at baseline (= treatment start) to 60 ± 16 letters at last follow-up. The MA prevalence within and outside the choroidal neovascularization (CNV) border at initial measurement was 45% and increased to 74%. Mean MA area increased from 1.8 ± 2.7 mm(2) within and 0.5 ± 0.98 mm(2) outside the CNV boundary to 2.7 ± 3.4 mm(2) and 1.7 ± 1.8 mm(2) , respectively. Multivariate regression determined posterior vitreous detachment (PVD) and presence/development of intraretinal cysts (IRCs) as significant factors for total MA size (R(2) = 0.16, p = 0.02). Macular atrophy (MA) area outside the CNV border was best explained by the presence of reticular pseudodrusen (RPD) and IRC (R(2) = 0.24, p = 0.02). CONCLUSION A majority of patients show MA after long-term anti-VEGF treatment. Reticular pseudodrusen (RPD), IRC and PVD but not number of injections or treatment duration seem to be associated with the MA size.