5,137 research outputs found

    On Colorful Bin Packing Games

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    We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of m2m\geq 2 colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when m3m\geq 3 while they are equal to 3 for black and white games, where m=2m=2. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

    Zum locus desperatus des Hellum Hispaniense

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    Radiation-hydrodynamics simulations of surface convection in low-mass stars: connections to stellar structure and asteroseismology

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    Radiation-hydrodynamical simulations of surface convection in low-mass stars can be exploited to derive estimates of i) the efficiency of the convective energy transport in the stellar surface layers; ii) the convection-related photometric micro-variability. We comment on the universality of the mixing-length parameter, and point out potential pitfalls in the process of its calibration which may be in part responsible for the contradictory findings about its variability across the Hertzsprung-Russell digramme. We further comment on the modelling of the photometric micro-variability in HD49933 - one of the first main COROT targets.Comment: 6 pages, 5 figures, Proceedings paper of IAU Symposium 25

    Is the Sun Lighter than the Earth? Isotopic CO in the Photosphere, Viewed through the Lens of 3D Spectrum Synthesis

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    We consider the formation of solar infrared (2-6 micron) rovibrational bands of carbon monoxide (CO) in CO5BOLD 3D convection models, with the aim to refine abundances of the heavy isotopes of carbon (13C) and oxygen (18O,17O), to compare with direct capture measurements of solar wind light ions by the Genesis Discovery Mission. We find that previous, mainly 1D, analyses were systematically biased toward lower isotopic ratios (e.g., R23= 12C/13C), suggesting an isotopically "heavy" Sun contrary to accepted fractionation processes thought to have operated in the primitive solar nebula. The new 3D ratios for 13C and 18O are: R23= 91.4 +/- 1.3 (Rsun= 89.2); and R68= 511 +/- 10 (Rsun= 499), where the uncertainties are 1 sigma and "optimistic." We also obtained R67= 2738 +/- 118 (Rsun= 2632), but we caution that the observed 12C17O features are extremely weak. The new solar ratios for the oxygen isotopes fall between the terrestrial values and those reported by Genesis (R68= 530, R6= 2798), although including both within 2 sigma error flags, and go in the direction favoring recent theories for the oxygen isotope composition of Ca-Al inclusions (CAI) in primitive meteorites. While not a major focus of this work, we derive an oxygen abundance of 603 +/- 9 ppm (relative to hydrogen; 8.78 on the logarithmic H= 12 scale). That the Sun likely is lighter than the Earth, isotopically speaking, removes the necessity to invoke exotic fractionation processes during the early construction of the inner solar system

    Hopf Categories

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    We introduce Hopf categories enriched over braided monoidal categories. The notion is linked to several recently developed notions in Hopf algebra theory, such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We generalize the fundamental theorem for Hopf modules and some of its applications to Hopf categories.Comment: 47 pages; final version to appear in Algebras and Representation Theor

    Etablierung ausgewählter Arten zur Nachsaat in ökologisch bewirtschafteten Grünlandbeständen in Abhängigkeit von Nachsaattechnik und Standort

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    Die Artenzusammensetzung des Grünlandes verändert sich in Abhängigkeit der Nutzungsdauer, des Nutzungsregimes und von Bewirtschaftungsmaßnahmen. Daher ist eine regelmäßige Bewertung der Grünlandnarbe und der Artenzusammensetzung notwendig. Eine Grünlandverbesserung kann durch Nachsaaten erreicht werden. Hierfür stehen verschiedene Nachsaattechniken und Arten zur Verfügung. Der Nachsaaterfolg von ausgewählten Futterpflanzenarten, die für den Ökologischen Landbau von besonderer Bedeutung sein können, wurde mit zwei unterschiedlichen Nachsaattechniken auf insgesamt 8 Standorten in Nordwestdeutschland geprüft
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