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.     

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.     

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.     

Sampling from binomial and poisson distributions: A method with bounded computation times

An accurate acceptance-rejection algorithm is devised and tested. The procedure requires an average of less than 3 uniform deviates whenever the standard deviation of the distribution is at least 4, and this number decreases monotonically to 2.63 as . Variable parameters are permitted, and no subroutines for sampling from other statistical distributions are needed.This research was supported by the Austrian Research Council (Fonds zur Förderung der wissenschaftlichen Forschung).     

Information systems for enhancing social experience in a conference context: A sensor based approach

We combine Auto Identification and Web technologies in an extensible on-site event support system for enhancing experience of conference organizers as well as participants. Our system enables users to authenticate themselves using RFID badges and to access interactive, Web-based services via a touchscreen PC. The developed services aim at supporting social interactions of participants, and thus validate the promising usage directions of the combination of offline social networks and the online social Web. The main hypothesis of our work is that: ??A sensor based information system can truly enhance social conference experience.?? Technically, we have investigated employment of Web 2.0 technologies in social, sensor and mobile technologies enabled systems at conferences and events. This article gives an overview of the overall system and its evaluation via a user survey and usage log data collected during the Extended Semantic Web Conference (ESWC) 2010 and similar international conferences, altogether with several hundred participants.     

Phase diagram for the helical texture in 3He-A

The stability region of the helical textures in³He-A in thev _s-H phase diagram is theoretically determined. Herev _sis the superflow velocity andH (v _s) is the external magnetic field. The pitch of the helixk ^–1 that minimizes the Gibbs free energy and the corresponding inclination angles ofl andd are determined numerically as functions ofv _sandH. The NMR frequencies (two longitudinal and four transverse frequencies) associated with the helical texture are obtained.Work supported by the National Science Foundation under Grant No. DMR 76-21032.     

Thermochemische Kennwerte für die Reaktion,Mo + O2 ⇌ MoO2 sowie in Eisenschmelzen

Zusammenstellung von Schrifttumsangaben für die Änderung der freien Standardenthalpien der Reaktionen , Mo + O₂ ? MoO₂ und in Eisenschmelzen. Neubestimmung der Temperaturabhängigkeiten der Größen ΔG^oCr₂O₃, ΔG^oMoO₂ und ΔG^o_O im Eisen bei Temperaturen zwischen 1460 bzw. 1530 und 1725 °C. Nachweis der Anwendbarkeit der neu ermittelten thermodynamischen Funktionen durch EMK-Parallelmessungen an ThO₂ (Y₂O₃)- und ZrO₂ (MgO)-Festelektrolytzellen mit Cr-Cr₂O₃- und Mo-MoO₂-Referenzelektroden in Reineisenschmelzen bei 1600 °C. Ermittlung des Parameters p_e′ der Elektronenteilleitfähigkeit für einen teilstabilisierten ZrO₂-Festelektrolyten mit einem Stoffmengengehalt von 5% MgO.