Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Local Stereology of Tensors of Convex Bodies

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝ d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ℝ3, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.

A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method

We present a novel approach to the reconstruction of depth from light field data. Our method uses dictionary representations and group sparsity constraints to derive a convex formulation. Although our solution results in an increase of the problem dimensionality, we keep numerical complexity at bay by restricting the space of solutions and by exploiting an efficient Primal-Dual formulation. Comparisons with state of the art techniques, on both synthetic and real data, show promising performances.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Prevention of increased abnormal fundus autofluorescence with blue light-filtering intraocular lenses

PURPOSE To observe changes in fundus autofluorescence 2 years after implantation of blue light-filtering (yellow-tinted) and ultraviolet light-filtering (colorless) intraocular lenses (IOLs). SETTING Department of Ophthalmology and Visual Science, Nagoya City University Graduate School of Medical Sciences, Nagoya, Japan, and the Department of Ophthalmology, University of Bern, Bern, Switzerland. DESIGN Prospective comparative observational study. METHODS Patients were enrolled who had cataract surgery with implantation of a yellow-tinted or colorless IOL and for whom images were obtained on which the fundus autofluorescence was measurable using the Heidelberg Retina Angiogram 2 postoperatively. The fundus autofluorescence in the images was classified into 8 abnormal patterns based on the classification of the International Fundus Autofluorescence Classification Group, The presence of normal fundus autofluorescence, geographic atrophy, and wet age-related macular degeneration (AMD) also was recorded. The fundus findings at baseline and 2 years postoperatively were compared. RESULTS Fifty-two eyes with a yellow-tinted IOL and 79 eyes with a colorless IOL were included. Abnormal fundus autofluorescence did not develop or increase in the yellow-tinted IOL group; however, progressive abnormal fundus autofluorescence developed or increased in 12 eyes (15.2%) in the colorless IOL group (P = .0016). New drusen, geographic atrophy, and choroidal neovascularization were observed mainly in the colorless IOL group. The incidence of AMD was statistically significantly higher in the colorless IOL group (P = .042). CONCLUSIONS Two years after cataract surgery, significant differences were seen in the progression of abnormal fundus autofluorescence between the 2 groups. The incidence of AMD was lower in eyes with a yellow-tinted IOL. FINANCIAL DISCLOSURE No author has a financial or proprietary interest in any material or method mentioned.

Reduced foveal vision enhances peripheral monitoring and peripheral event detection

Introduction: Although it seems plausible that sports performance relies on high-acuity foveal vision, it could be empirically shown that myoptic blur (up to +2 diopters) does not harm performance in sport tasks that require foveal information pick-up like golf putting (Bulson, Ciuffreda, & Hung, 2008). How myoptic blur affects peripheral performance is yet unknown. Attention might be less needed for processing visual cues foveally and lead to better performance because peripheral cues are better processed as a function of reduced foveal vision, which will be tested in the current experiment. Methods: 18 sport science students with self-reported myopia volunteered as participants, all of them regularly wearing contact lenses. Exclusion criteria comprised visual correction other than myopic, correction of astigmatism and use of contact lenses out of Swiss delivery area. For each of the participants, three pairs of additional contact lenses (besides their regular lenses; used in the “plano” condition) were manufactured with an individual overcorrection to a retinal defocus of +1 to +3 diopters (referred to as “+1.00 D”, “+2.00 D”, and “+3.00 D” condition, respectively). Gaze data were acquired while participants had to perform a multiple object tracking (MOT) task that required to track 4 out of 10 moving stimuli. In addition, in 66.7 % of all trials, one of the 4 targets suddenly stopped during the motion phase for a period of 0.5 s. Stimuli moved in front of a picture of a sports hall to allow for foveal processing. Due to the directional hypotheses, the level of significance for one-tailed tests on differences was set at α = .05 and posteriori effect sizes were computed as partial eta squares (ηρ2). Results: Due to problems with the gaze-data collection, 3 participants had to be excluded from further analyses. The expectation of a centroid strategy was confirmed because gaze was closer to the centroid than the target (all p < .01). In comparison to the plano baseline, participants more often recalled all 4 targets under defocus conditions, F(1,14) = 26.13, p < .01, ηρ2 = .65. The three defocus conditions differed significantly, F(2,28) = 2.56, p = .05, ηρ2 = .16, with a higher accuracy as a function of a defocus increase and significant contrasts between conditions +1.00 D and +2.00 D (p = .03) and +1.00 D and +3.00 D (p = .03). For stop trials, significant differences could neither be found between plano baseline and defocus conditions, F(1,14) = .19, p = .67, ηρ2 = .01, nor between the three defocus conditions, F(2,28) = 1.09, p = .18, ηρ2 = .07. Participants reacted faster in “4 correct+button” trials under defocus than under plano-baseline conditions, F(1,14) = 10.77, p < .01, ηρ2 = .44. The defocus conditions differed significantly, F(2,28) = 6.16, p < .01, ηρ2 = .31, with shorter response times as a function of a defocus increase and significant contrasts between +1.00 D and +2.00 D (p = .01) and +1.00 D and +3.00 D (p < .01). Discussion: The results show that gaze behaviour in MOT is not affected to a relevant degree by a visual overcorrection up to +3 diopters. Hence, it can be taken for granted that peripheral event detection was investigated in the present study. This overcorrection, however, does not harm the capability to peripherally track objects. Moreover, if an event has to be detected peripherally, neither response accuracy nor response time is negatively affected. Findings could claim considerable relevance for all sport situations in which peripheral vision is required which now needs applied studies on this topic. References: Bulson, R. C., Ciuffreda, K. J., & Hung, G. K. (2008). The effect of retinal defocus on golf putting. Ophthalmic and Physiological Optics, 28, 334-344.