A Continuation Method for Nash Equilibria in Structured Games

Structured game representations have recently attracted interest as models for multi-agent artificial intelligence scenarios, with rational behavior most commonly characterized by Nash equilibria. This paper presents efficient, exact algorithms for computing Nash equilibria in structured game representations, including both graphical games and multi-agent influence diagrams (MAIDs). The algorithms are derived from a continuation method for normal-form and extensive-form games due to Govindan and Wilson; they follow a trajectory through a space of perturbed games and their equilibria, exploiting game structure through fast computation of the Jacobian of the payoff function. They are theoretically guaranteed to find at least one equilibrium of the game, and may find more. Our approach provides the first efficient algorithm for computing exact equilibria in graphical games with arbitrary topology, and the first algorithm to exploit fine-grained structural properties of MAIDs. Experimental results are presented demonstrating the effectiveness of the algorithms and comparing them to predecessors. The running time of the graphical game algorithm is similar to, and often better than, the running time of previous approximate algorithms. The algorithm for MAIDs can effectively solve games that are much larger than those solvable by previous methods

The Stellar Content of Obscured Galactic Giant H II Regions: II. W42

We present near infrared J, H, and K images and K-band spectroscopy in the giant HII region W42. A massive star cluster is revealed; the color-color plot and K-band spectroscopic morphology of two of the brighter objects suggest the presence of young stellar objects. The spectrum of the bright central star is similar to unobscured stars with MK spectral types of O5-O6.5. If this star is on the zero age main sequence, then the derived spectrophotometric distance is considerably smaller than previous estimates. The Lyman continuum luminosity of the cluster is a few times that of the Trapezium. The slope of the K-band luminosity function is similar to that for the Trapezium cluster and significantly steeper than that for the massive star cluster in M17 or the Arches cluster near the Galactic center.Comment: 30 pages, 11 figures, late

Submillimetre-sized dust aggregate collision and growth properties

The collisional and sticking properties of sub-mm-sized aggregates composed of protoplanetary dust analogue material are measured, including the statistical threshold velocity between sticking and bouncing, their surface energy and tensile strength within aggregate clusters. We performed an experiment on the REXUS 12 suborbital rocket. The protoplanetary dust analogue materials were micrometre-sized monodisperse and polydisperse SiO2 particles prepared into aggregates with sizes around 120 $\mu$m and 330 $\mu$m, respectively and volume filling factors around 0.37. During the experimental run of 150 s under reduced gravity conditions, the sticking of aggregates and the formation and fragmentation of clusters of up to a few millimetres in size was observed. The sticking probability of the sub-mm-sized dust aggregates could be derived for velocities decreasing from 22 to 3 cm/s. The transition from bouncing to sticking collisions happened at 12.7 cm/s for the smaller aggregates composed of monodisperse particles and at 11.5 and 11.7 cm/s for the larger aggregates composed of mono- and polydisperse dust particles, respectively. Using the pull-off force of sub-mm-sized dust aggregates from the clusters, the surface energy of the aggregates composed of monodisperse dust was derived to be 1.6x10-5 J/m2, which can be scaled down to 1.7x10-2 J/m2 for the micrometre-sized monomer particles and is in good agreement with previous measurements for silica particles. The tensile strengths of these aggregates within the clusters were derived to be 1.9 Pa and 1.6 Pa for the small and large dust aggregates, respectively. These values are in good agreement with recent tensile strength measurements for mm-sized silica aggregates. Using our data on the sticking-bouncing threshold, estimates of the maximum aggregate size can be given. For a minimum mass solar nebula model, aggregates can reach sizes of 1 cm.Comment: 21 pages (incl. 6 pages of appendix), 23 figure

Low-velocity collision behaviour of clusters composed of sub-mm sized dust aggregates

The experiments presented aim to measure the outcome of collisions between sub-mm sized protoplanetary dust aggregate analogues. We also observed the clusters formed from these aggregates and their collision behaviour. The experiments were performed at the drop tower in Bremen. The protoplanetary dust analogue materials were micrometre-sized monodisperse and polydisperse SiO$_2$ particles prepared into aggregates with sizes between 120~$\mu$m and 250~$\mu$m. One of the dust samples contained aggregates that were previously compacted through repeated bouncing. During three flights of 9~s of microgravity each, individual collisions between aggregates and the formation of clusters of up to a few millimetres in size were observed. In addition, the collisions of clusters with the experiment cell walls leading to compaction or fragmentation were recorded. We observed collisions amongst dust aggregates and collisions between dust clusters and the cell aluminium walls at speeds ranging from about 0.1 cm/s to 20 cm/s. The velocities at which sticking occurred ranged from 0.18 to 5.0 cm/s for aggregates composed of monodisperse dust, with an average value of 2.1 cm/s for reduced masses ranging from 1.2x10-6 to 1.8x10-3 g with an average value of 2.2x10-4 g. From the restructuring and fragmentation of clusters composed of dust aggregates colliding with the aluminium cell walls, we derived a collision recipe for dust aggregates ($\sim$100 $\mu$m) following the model of Dominik \& Thielens (1997) developed for microscopic particles. We measured a critical rolling energy of 1.8x10-13 J and a critical breaking energy of 3.5x10-13 J for 100 $\mu$m-sized non-compacted aggregates.Comment: 12 pages, 13 figure

Really Cool Stars and the Star Formation History at the Galactic Center

We present R=550 to 1200 near infrared H and K spectra for a magnitude limited sample of 79 asymptotic giant branch and cool supergiant stars in the central ~ 5 pc (diameter) of the Galaxy. We use a set of similar spectra obtained for solar neighborhood stars with known Teff and Mbol that is in the same range as the Galactic center (GC) sample to derive Teff and Mbol for the GC sample. We then construct the Hertzsprung--Russell (HRD) diagram for the GC sample. Using an automated maximum likelihood routine, we derive a coarse star formation history of the GC. We find (1) roughly 75% of the stars formed in the central few pc are older than 5 Gyr; (2) the star formation rate (SFR) is variable over time, with a roughly 4 times higher star formation rate in the last 100 Myr compared to the average SFR; (3) our model can only match dynamical limits on the total mass of stars formed by limiting the IMF to masses above 0.7 M$_\odot$. This could be a signature of mass segregation or of the bias toward massive star formation from the unique star formation conditions in the GC; (4) blue supergiants account for 12 % of the total sample observed, and the ratio of red to blue supergiants is roughly 1.5; (5) models with isochrones with [Fe/H] = 0.0 over all ages fit the stars in our HRD better than models with lower [Fe/H] in the oldest age bins, consistent with the finding of Ramirez et al. (2000) that stars with ages between 10 Myr and 1 Gyr have solar [Fe/H].Comment: ApJ, accepted. Latex, 65 pages including 19 figure

Collisions of small ice particles under microgravity conditions (II): Does the chemical composition of the ice change the collisional properties?

Context: Understanding the collisional properties of ice is important for understanding both the early stages of planet formation and the evolution of planetary ring systems. Simple chemicals such as methanol and formic acid are known to be present in cold protostellar regions alongside the dominant water ice; they are also likely to be incorporated into planets which form in protoplanetary disks, and planetary ring systems. However, the effect of the chemical composition of the ice on its collisional properties has not yet been studied. Aims: Collisions of 1.5 cm ice spheres composed of pure crystalline water ice, water with 5% methanol, and water with 5% formic acid were investigated to determine the effect of the ice composition on the collisional outcomes. Methods: The collisions were conducted in a dedicated experimental instrument, operated under microgravity conditions, at relative particle impact velocities between 0.01 and 0.19 m s^-1, temperatures between 131 and 160 K and a pressure of around 10^-5 mbar. Results: A range of coefficients of restitution were found, with no correlation between this and the chemical composition, relative impact velocity, or temperature. Conclusions: We conclude that the chemical composition of the ice (at the level of 95% water ice and 5% methanol or formic acid) does not affect the collisional properties at these temperatures and pressures due to the inability of surface wetting to take place. At a level of 5% methanol or formic acid, the structure is likely to be dominated by crystalline water ice, leading to no change in collisional properties. The surface roughness of the particles is the dominant factor in explaining the range of coefficients of restitution

H-Band Spectroscopic Classification of OB Stars

We present a new spectroscopic classification for OB stars based on H-band (1.5 micron to 1.8 micron) observations of a sample of stars with optical spectral types. Our initial sample of nine stars demonstrates that the combination of He I 1.7002 micron and H Brackett series absorption can be used to determine spectral types for stars between about O4 and B7 (to within about +/- 2 sub-types). We find that the Brackett series exhibits luminosity effects similar to the Balmer series for the B stars. This classification scheme will be useful in studies of optically obscured high mass star forming regions. In addition, we present spectra for the OB stars near 1.1 micron and 1.3 micron which may be of use in analyzing their atmospheres and winds.Comment: Accepted by AJ, 16 pages Latex (aastex4.0) including 4 figures and 2 tables. A complete PostScript copy is available at ftp://degobah.colorado.edu/pub/rblum/Hband