On the number of higher order Delaunay triangulations

Higher order Delaunay triangulations are a generalization of the Delaunay triangulation that provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-k Delaunay if the circumcircle of each triangle of the triangulation contains at most k points. In this paper we study lower and upper bounds on the number of higher order Delaunay triangulations, as well as their expected number for randomly distributed points. We show that arbitrarily large point sets can have a single higher order Delaunay triangulation, even for large orders, whereas for first order Delaunay triangulations, the maximum number is 2ⁿ⁻³. Next we show that uniformly distributed points have an expected number of at least 2^{ρ₁n(1+o(1))} first order Delaunay triangulations, where ρ₁ is an analytically defined constant (ρ₁≈0.525785), and for k>1, the expected number of order-k Delaunay triangulations (which are not order-i for any i<k) is at least 2^{ρ_kn(1+o(1))}, where ρ_k can be calculated numerically.     

In vivo interactive visualization of four-dimensional blood flow patterns

In this paper we give an overview over a series of experiments to visualize and measure flow fields in the human vascular system with respect to their diagnostic capabilities. The experiments utilize a selection of GPU-based sparse and dense flow visualization algorithms to show the diagnostic opportunities for volumetric cardiovascular phase contrast magnetic resonance imaging data sets. Besides classical hardware accelerated particle and line-based approaches, an extensible tublet-based visualization, a four-dimensional volumetric line integral convolution and a new two-dimensional cutting plane tool for three-dimensional velocity data sets have been implemented. To evaluate the results, several hearts of human subjects have been investigated and a flow phantom was built to artificially simulate distinctive flow features. Our results demonstrate that we are able to provide an interactive tool for cardiovascular diagnostics with complementary hardware accelerated visualizations. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.

On packing shortest cycles in graphs

We study the problems to find a maximum packing of shortest edge-disjoint cycles in a graph of given girth g (g-ESCP) and its vertex-disjoint analogue g-VSCP. In the case g=3, Caprara and Rizzi (2001) have shown that g-ESCP can be solved in polynomial time for graphs with maximum degree 4, but is APX-hard for graphs with maximum degree 5, while g-VSCP can be solved in polynomial time for graphs with maximum degree 3, but is APX-hard for graphs with maximum degree 4. For g∈{4,5}, we show that both problems allow polynomial time algorithms for instances with maximum degree 3, but are APX-hard for instances with maximum degree 4. For each g?6, both problems are APX-hard already for graphs with maximum degree 3.     

Contact type dependency of texture classification in a whiskered mobile robot

Actuated artificial whiskers modeled on rat macrovibrissae can provide effective tactile sensor systems for autonomous robots. This article focuses on texture classification using artificial whiskers and addresses a limitation of previous studies, namely, their use of whisker deflection signals obtained under relatively constrained experimental conditions. Here we consider the classification of signals obtained from a whiskered robot required to explore different surface textures from a range of orientations and distances. This procedure resulted in a variety of deflection signals for any given texture. Using a standard Gaussian classifier we show, using both hand-picked features and ones derived from studies of rat vibrissal processing, that a robust rough-smooth discrimination is achievable without any knowledge of how the whisker interacts with the investigated object. On the other hand, finer discriminations appear to require knowledge of the target’s relative position and/or of the manner in which the whisker contact its surface. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.

Exact Algorithms for <Emphasis Type="Italic">L</Emphasis>(2,1)-Labeling of Graphs

The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph G=(V,E) into an interval of integers {0,…,k} is an L(2,1)-labeling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbor are mapped onto distinct integers. It is known that for any fixed k≥4, deciding the existence of such a labeling is an NP-complete problem. We present exact exponential time algorithms that are faster than the naive O ^*((k+1) ⁿ ) algorithm that would try all possible mappings. The improvement is best seen in the first NP-complete case of k=4, where the running time of our algorithm is O(1.3006 ⁿ ). Furthermore we show that dynamic programming can be used to establish an O(3.8730 ⁿ ) algorithm to compute an optimal L(2,1)-labeling.     

Bandwidth on AT-free graphs

We study the classical Bandwidth problem from the viewpoint of parametrised algorithms. Given a graph G=(V,E) and a positive integer k, the Bandwidth problem asks whether there exists a bijective function β:{1,…,∣V∣}→V such that for every edge uv∈E, ∣β⁻¹(u)−β⁻¹(v)∣≤k. It is known that under standard complexity assumptions, no algorithm for Bandwidth with running time of the form f(k)n^O(1) exists, even when the input is restricted to trees. We initiate the search for classes of graphs where such algorithms do exist. We present an algorithm with running time n⋅2^O(klogk) for Bandwidth on AT-free graphs, a well-studied graph class that contains interval, permutation, and cocomparability graphs. Our result is the first non-trivial algorithm that shows fixed-parameter tractability of Bandwidth on a graph class on which the problem remains NP-complete.     

A Pragmatic Approach to Reuse in Tactical Theorem Proving

In interactive theorem proving, tactics and tacticals have been introduced to automate proof search. In this scenario, user interaction traditionally is restricted to the mode in which the user decides which tactic to apply on the top-level, without being able to interact with the tactic once it has begun running.We propose a technique to allow the implementation of derivational analogy in tactical theorem proving. Instead of replaying tactics including backtracked dead ends our framework makes choice points in tactics explicit and thus avoids dead ends when reusing tactics. Additionally users can override choices a tactic has made or add additional steps to a derivation without terminating the tactic. The technique depends on an efficient replay of tactic executions without repeating search that the original computation may have involved.     

Die Mifare-Attacke

Zusammenfassung  Eine Kryptoanalyse des verbreiteten Mifare-Chips, der in ca. 85% aller kontaktlosen Chipkarten zum Einsatz kommt, wurde erstmalig auf dem CCC-Jahreskongress am 28.12.2007 vorgestellt. Inzwischen wurden weitere Details bekannt — und der Angriff erheblich verbessert. Mitte April 2008 stellten Forscher der Radboud Universiteit Nijmegen einen Kurzfilm in You-Tube ein, in dem sie den erfolgreichen Angriff auf eine Campus-Zugangskarte zeigen. Dirk Fox Gesch?ftsführer der Secorvo Security Consulting GmbH und Herausgeber der DuD.     

Stroboscopic image capture: reducing the dose per frame by a factor of 30 does not prevent beam-induced specimen movement in paraffin

Beam-induced specimen movement may be the major factor that limits the quality of high-resolution images of organic specimens. One of the possible measures to improve the situation that was proposed by Henderson and Glaeser [Ultramicroscopy 16 (1985) 139-150], which we refer to here as "stroboscopic image capture", is to divide the normal exposure into many successive frames, thus reducing the amount of electron exposure--and possibly the amount of beam-induced movement--per frame. The frames would then be aligned and summed. We have performed preliminary experiments on stroboscopic imaging using a 200-kV electron microscope that was equipped with a high dynamic range Charge-coupled device (CCD) camera for image recording and a liquid N2-cooled cryoholder. Single-layer paraffin crystals on carbon film were used as a test specimen. The ratio F(g)/F(0) of paraffin reflections, calculated from the images, serves as our criterion for the image quality. In the series that were evaluated, no significant improvement of the F(image)(g)/F(image)(0) ratio was found, even though the electron exposure per frame was reduced by a factor of 30. A frame-to-frame analysis of image distortions showed that considerable beam-induced movement had still occurred during each frame. In addition, the paraffin crystal lattice was observed to move relative to the supporting carbon film, a fact that cannot be explained as being an electron-optical effect caused by specimen charging. We conclude that a significant further reduction of the dose per frame (than was possible with this CCD detector) will be needed in order to test whether the frame-to-frame changes ultimately become small enough for stroboscopic image capture to show its potential.