A Census Of Highly Symmetric Combinatorial Designs

As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t > 2 most of these characterizations have remained longstanding challenging problems. Especially, the determination of all flag-transitive Steiner t-designs with 2 < t < 7 is of particular interest and has been open for about 40 years (cf. [11, p. 147] and [12, p. 273], but presumably dating back to 1965). The present paper continues the author's work [20, 21, 22] of classifying all flag-transitive Steiner 3-designs and 4-designs. We give a complete classification of all flag-transitive Steiner 5-designs and prove furthermore that there are no non-trivial flag-transitive Steiner 6-designs. Both results rely on the classification of the finite 3-homogeneous permutation groups. Moreover, we survey some of the most general results on highly symmetric Steiner t-designs.Comment: 26 pages; to appear in: "Journal of Algebraic Combinatorics

On the Inverse Problem of Binocular 3D Motion Perception

It is shown that existing processing schemes of 3D motion perception such as interocular velocity difference, changing disparity over time, as well as joint encoding of motion and disparity, do not offer a general solution to the inverse optics problem of local binocular 3D motion. Instead we suggest that local velocity constraints in combination with binocular disparity and other depth cues provide a more flexible framework for the solution of the inverse problem. In the context of the aperture problem we derive predictions from two plausible default strategies: (1) the vector normal prefers slow motion in 3D whereas (2) the cyclopean average is based on slow motion in 2D. Predicting perceived motion directions for ambiguous line motion provides an opportunity to distinguish between these strategies of 3D motion processing. Our theoretical results suggest that velocity constraints and disparity from feature tracking are needed to solve the inverse problem of 3D motion perception. It seems plausible that motion and disparity input is processed in parallel and integrated late in the visual processing hierarchy

Microelectrode for energy and current control of nanotip field electron emitters

Emerging experiments and applications in electron microscopy, holography, and diffraction benefit from miniaturized electron guns for compact experimental setups. We present a highly compact microelectrode integrated field emitter that consists of a tungsten nanotip coated with a few micrometers thick polyimide film followed by a several nanometers thick gold film, both positioned behind the exposed emitter apex by approximately 10–30 μm. The control of the electric field strength at the nanometer scale tip apex allows suppression, extraction, and energy tuning of field-emitted electrons. The performance of the microelectrode is demonstrated experimentally and supported by numerical simulations