Using Sifting for k-Layer Straightline Crossing Minimization

We present a new algorithm for k-layer straightline crossing minimization which is based on sifting that is a heuristic for dynamic reordering of decision diagrams used during logic synthesis and formal verification of logic circuits. The experiments prove sifting to be very efficient. In particular it outperforms the traditional layer by layer sweep based heuristics known from literature by far when applied to k-layered graphs with k \ge 3

Systematic study of the decay rates of antiprotonic helium states

A systematic study of the decay rates of antiprotonic helium (\pbhef and \pbhet) at CERN AD (Antiproton Decelerator) has been made by a laser spectroscopic method. The decay rates of some of its short-lived states, namely those for which the Auger rates $\gamma_{\mathrm{A}}$ are much larger than their radiative decay rates ($\gamma_{\mathrm{rad}} \sim 1$ $\mu$s$^{-1}$), were determined from the time distributions of the antiproton annihilation signals induced by laser beams, and the widths of the atomic resonance lines. The magnitude of the decay rates, especially their relation with the transition multipolarity, is discussed and compared with theoretical calculations.Comment: 6 pages, 5 figures, and 1 tabl

On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

Hyperfine structure of antiprotonic helium revealed by a laser-microwave-laser resonance method

Using a newly developed laser-microwave-laser resonance method, we observed a pair of microwave transitions between hyperfine levels of the $(n,L)=(37,35)$ state of antiprotonic helium. This experiment confirms the quadruplet hyperfine structure due to the interaction of the antiproton orbital angular momentum, the electron spin and the antiproton spin as predicted by Bakalov and Korobov. The measured frequencies of $\nu_{\text HF}^+ =12.89596 \pm 0.00034$ GHz and $\nu_{\text HF}^- =12.92467 \pm 0.00029$ GHz agree with recent theoretical calculations on a level of $6 \times10^{-5}$.Comment: 4 pages, 4 figures, 1 tabl

A Book of Generations – Writing at the Frontier

We address the problem of finding viewpoints that preserve the relational structure of a three-dimensional graph drawing under orthographic parallel projection. Previously, algorithms for finding the best viewpoints under two natural models of viewpoint “goodness” were proposed. Unfortunately, the inherent combinatorial complexity of the problem makes finding exact solutions is impractical. In this paper, we propose two approximation algorithms for the problem, commenting on their design, and presenting results on their performance

Morte celular nas lâminas epidermais de equinos com laminite

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Drawing Trees with Perfect Angular Resolution and Polynomial Area

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2{\pi}/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.Comment: 30 pages, 17 figure