On Colorful Bin Packing Games

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 $m\geq 2$ 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 $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. 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

Stimulation of Nicotiana tabacum pollen tube growth by γ-irradiation

Irradiation of pollen grains from Nicotiana tabacum with 60Co-γ-irradiation in the dose range of 1–6Gy stimulates growth of the pollen tube up to 50% above control level. Further increase of the irradiation dose to 12Gy reduces pollen growth approximately to control level. Pollen tube growth was measured photometrically by determination of the turbidity of a suspension of the fragmented pollen tubes. The sensitivity of Nicotiana tabacum pollen to γ-irradiation is higher than that of pollen from pine and Douglas-fir. The biological and environmental implications are discussed

Small-scale swirl events in the quiet Sun chromosphere

Recent progress in instrumentation enables solar observations with high resolution simultaneously in the spatial, temporal, and spectral domains. We use such high-resolution observations to study small-scale structures and dynamics in the chromosphere of the quiet Sun. We analyze time series of spectral scans through the Ca II 854.2nm spectral line obtained with the CRISP instrument at the Swedish 1-m Solar Telescope. The targets are quiet Sun regions inside coronal holes close to disc-centre. The line core maps exhibit relatively few fibrils compared to what is normally observed in quiet Sun regions outside coronal holes. The time series show a chaotic and dynamic scene that includes spatially confined "swirl" events. These events feature dark and bright rotating patches, which can consist of arcs, spiral arms, rings or ring fragments. The width of the fragments typically appears to be on the order of only 0.2", which is close to the effective spatial resolution. They exhibit Doppler shifts of -2 to -4 km/s but sometimes up to -7 km/s, indicating fast upflows. The diameter of a swirl is usually of the order of 2". At the location of these swirls, the line wing and wide-band maps show close groups of photospheric bright points that move with respect to each other. A likely explanation is that the relative motion of the bright points twists the associated magnetic field in the chromosphere above. Plasma or propagating waves may then spiral upwards guided by the magnetic flux structure, thereby producing the observed intensity signature of Doppler-shifted ring fragments.Comment: 4 pages, 3 figures, A&A Letter, accepted (final version

Thermodynamic Consistency of Two-mechanism Models in the Non-isothermal Case

This note investigates two-mechanism models (= 2M models) in the case of plastic behavior. 2M models (or, generally, multi-mechanism models) are a useful tool for modelling of complex material behavior. They have been studied and applied for the last twenty years. We prove thermodynamic consistency for some classes of 2M models, and we derive new coupled evolution equations for the back stresses. Moreover, a coupling in the evolution equations of the internal variables is presented. Finally, a comparison between a 2M model and a modified Chabochemodel is presented in order to illustrate the possibilities and problems in modelling of complex material behavior like ratcheting

New data on Austroalpine Liassic Ammonites from the Adnet Quarries and adjacent areas (Salzburg, Northern Calcareous Alps)

The biostratigraphic studies of ammonites from the Adnet quarries allow to propose a set of 11 horizons or levels for the Upper Austroalpine Late Hettangian–Sinemurian. The originality of the faunal assemblages [e.g. Adnethiceras adnethicus (HAUER), Gleviceras doris sensu PIA] and the discontinuity of the biostratigraphical sequence make local comparisons and correlations with NW Europe, the Middle Austroalpine and the Apennines rather difficult. By contrast, the Pliensbachian fauna from Wetzsteingraben presents a clear faunal homogeneity with the other studied regions of the Upper Austroalpine. Moreover, they well integrate with the Euroboreal and Tethyan standard biostratigraphical framework