Tverberg's theorem with constraints

The topological Tverberg theorem claims that for any continuous map of the (q-1)(d+1)-simplex to R^d there are q disjoint faces such that their images have a non-empty intersection. This has been proved for affine maps, and if $q$ is a prime power, but not in general. We extend the topological Tverberg theorem in the following way: Pairs of vertices are forced to end up in different faces. This leads to the concept of constraint graphs. In Tverberg's theorem with constraints, we come up with a list of constraints graphs for the topological Tverberg theorem. The proof is based on connectivity results of chessboard-type complexes. Moreover, Tverberg's theorem with constraints implies new lower bounds for the number of Tverberg partitions. As a consequence, we prove Sierksma's conjecture for $d=2$, and $q=3$.Comment: 16 pages, 12 figures. Accepted for publication in JCTA. Substantial revision due to the referee

Cluster-Based Autoencoders for Volumetric Point Clouds

Autoencoders allow to reconstruct a given input from a small set of parameters. However, the input size is often limited due to computational costs. We therefore propose a clustering and reassembling method for volumetric point clouds, in order to allow high resolution data as input. We furthermore present an autoencoder based on the well-known FoldingNet for volumetric point clouds and discuss how our approach can be utilized for blending between high resolution point clouds as well as for transferring a volumetric design/style onto a pointcloud while maintaining its shape

Optimizing Apparent Display Resolution Enhancement for Arbitrary Videos

Display resolution is frequently exceeded by available image resolution. Recently, apparent display resolution enhancement techniques (ADRE) have demonstrated how characteristics of the human visual system can be exploited to provide super-resolution on high refresh rate displays. In this paper we address the problem of generalizing the apparent display resolution enhancement technique to conventional videos of arbitrary content. We propose an optimization-based approach to continuously translate the video frames in such a way that the added motion enables apparent resolution enhancement for the salient image region. The optimization takes the optimal velocity, smoothness and similarity into account to compute an appropriate trajectory. Additionally, we provide an intuitive user interface which allows to guide the algorithm interactively and preserve important compositions within the video. We present a user study evaluating apparent rendering quality and demonstrate versatility of our method on a variety of general test scenes.Aktuelle Kameras sind in der Lage, Videos mit sehr hoher Auflösung aufzunehmen (> 4K Pixel). Monitore, Fernseher und Projektoren haben jedoch meist eine deutlich niedrigere Auflösung (FullHD). Bei der Darstellung hochaufgelöster Videos auf diesen Geräten gehen durch das nötige Herrunterrechnen der Videodaten feine Details verloren, z.B. Haare oder die Pigmentierung von Oberflächenmaterialien. Es wird ein Verfahren präsentiert, welches die Darstellung eines beliebigen Videos mit einer Auflösung ermöglicht, die perzeptuell höher ist als die Auflösung des Ausgabegerätes

Optimal precision and accuracy in 4Pi-STORM using dynamic spline PSF models

Coherent fluorescence imaging with two objective lenses (4Pi detection) enables single-molecule localization microscopy with sub-10 nm spatial resolution in three dimensions. Despite its outstanding sensitivity, wider application of this technique has been hindered by complex instrumentation and the challenging nature of the data analysis. Here we report the development of a 4Pi-STORM microscope, which obtains optimal resolution and accuracy by modeling the 4Pi point spread function (PSF) dynamically while also using a simpler optical design. Dynamic spline PSF models incorporate fluctuations in the modulation phase of the experimentally determined PSF, capturing the temporal evolution of the optical system. Our method reaches the theoretical limits for precision and minimizes phase-wrapping artifacts by making full use of the information content of the data. 4Pi-STORM achieves a near-isotropic three-dimensional localization precision of 2–3 nm, and we demonstrate its capa-bilities by investigating protein and nucleic acid organization in primary neurons and mammalian mitochondria

A high affinity RIM-binding protein/Aplip1 interaction prevents the formation of ectopic axonal active zones

Synaptic vesicles (SVs) fuse at active zones (AZs) covered by a protein scaffold, at Drosophila synapses comprised of ELKS family member Bruchpilot (BRP) and RIM-binding protein (RBP). We here demonstrate axonal co-transport of BRP and RBP using intravital live imaging, with both proteins co- accumulating in axonal aggregates of several transport mutants. RBP, via its C-terminal Src-homology 3 (SH3) domains, binds Aplip1/JIP1, a transport adaptor involved in kinesin-dependent SV transport. We show in atomic detail that RBP C-terminal SH3 domains bind a proline-rich (PxxP) motif of Aplip1/JIP1 with submicromolar affinity. Pointmutating this PxxP motif provoked formation of ectopic AZ-like structures at axonal membranes. Direct interactions between AZ proteins and transport adaptors seem to provide complex avidity and shield synaptic interaction surfaces of pre-assembled scaffold protein transport complexes, thus, favouring physiological synaptic AZ assembly over premature assembly at axonal membranes. - See more at: http://elifesciences.org/content/4/e06935#sthash.oVGZ8cdi.dpu