Shrinking targets and eventually always hitting points for interval maps

We study shrinking target problems and the set $\mathcal{E}_{\text{ah}}$ of eventually always hitting points. These are the points whose first $n$ iterates will never have empty intersection with the $n$-th target for sufficiently large $n$. We derive necessary and sufficient conditions on the shrinking rate of the targets for $\mathcal{E}_{\text{ah}}$ to be of full or zero measure especially for some interval maps including the doubling map, some quadratic maps and the Manneville-Pomeau map. We also obtain results for the Gauss map and correspondingly for the maximal digits in continued fractions expansions. In the case of the doubling map we also compute the packing dimension of $\mathcal{E}_{\text{ah}}$ complementing already known results on the Hausdorff dimension of $\mathcal{E}_{\text{ah}}$.Comment: 21 pages, 1 figure, comments welcome

Selective retina therapy (SRT) in patients with geographic atrophy due to age-related macular degeneration

For geographic atrophy (GA) due to age-related macular degeneration (AMD) there is so far no approved treatment option. Usually, increased autofluorescence (AF) levels of different patterns adjacent to the atrophic area indicate lipofuscin-laden retinal pigment epithelium (RPE) cells at a high risk for apoptosis. Herein, SRT was used to selectively treat these cells to stimulate RPE proliferation, in order to reduce or ideally stop further growth of the atrophic area

Optical coherence tomography controlled selective retina therapy with a novel microsecond laser

Selective retina therapy (SRT) is a short pulse (μs-regime) alternative to conventional laser photocoagulation (LPC) for treatment of retinal diseases. LPC leads to collateral damage of retinal layers adjacent to the retinal pigment epithelium (RPE), including healthy, non-regenerative photoreceptors due to the high thermal load, whereas in SRT, RPE cells are destroyed by microbubbles without damaging the neuronal retina. A novel experimental SRT laser operating at 532 nm wavelength can deliver 2 – 20 μs pulse sequences. Its tight integration into an upgraded diagnostic SPECTRALIS system combines beam control for treatment planning with real-time optical coherence tomography (OCT) overexposure protection of the photoreceptors. This “Spectralis Centaurus” system, was built and preliminary tested on porcine ex-vivo samples, reaching an unprecedented accuracy with unique planning and follow-up capabilities for upcoming clinical cellular level micro-surgery. The combination of OCT with SRT selectively limits cell death to the RPE by precisely controlling energy deposition while optically monitoring tissue response