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.     

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.     

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.     

Micromechanics of solvent crazes in polystyrene

Double exposure holographic interferometry (DEHI) is used to determine the strain energy release rate, craze opening displacement profile, and craze stress profile ofn-heptane and methanol crazes growing from cracks in polystyrene.n-heptane crazes have strain energy release rates (SERRs) close to those of cracks and their stress profile is almost crack-like in that the tensile stress across the craze falls almost to zero. On the other hand, the SERRs of methanol crazes are only 30 to 55% the SERR of a crack depending on stress intensity factorK _I of the precrack from which they are grown. The stress profile of the methanol craze shows it to be strongly load-bearing away from the craze tip, apparently as a result of the strain hardening of the craze fibrils. The stress concentration in front of the methanol craze tip is only 40% of that in front of then-heptane craze tip. The opening displacements of the methanol craze are almost as large as those of a crack very near its tip but are much less than those of a crack at large distances behind the tip. The Dugdale model of a strip yielding zone provides a poor representation of the craze opening displacements of the growing methanol craze. Dry (static) methanol crazes have larger opening displacements in response to an incremental tensile strain at moderate prestrains than at either low or high prestrains, suggesting that the craze fibrils undergo a yielding/strain-hardening process as the strain is increased similar to that observed in polycarbonate crazes by Kopp and Kambour. Dryn-heptane crazes do not show this response but rather open linearly with increasing prestrain. The opening displacement for long (dry)n-heptane crazes is almost crack-like whereas the largest opening of a dry methanol craze is only 20% of that of a crack. Dry methanol crazes break at aK _IC that is 40% of theK _IC of precracked but uncrazed specimens. The strongest (shortest) dryn-heptane crazes fail at only 7% ofK _IC of uncrazed specimens and theK _IC of the dryn-heptane crazes decreases markedly with increasing craze length.