Learn While You Earn: Two Approaches to Learning Auction Parameters in Take-it-or-leave-it Auctions

Much of the research in auction theory assumes that the auctioneer knows the distribution of participants ’ valuations with complete certainty. However, this is unrealistic. Thus, we analyse cases in which the auctioneer is uncertain about the valuation distributions; specifically, we consider a repeated auction setting in which the auctioneer can learn these distributions. Using take-it-or-leave-it auctions (Sandholm and Gilpin, 2006) as an exemplar auction format, we consider two auction design criteria. Firstly, an auctioneer could maximise expected revenue each time the auction is held. Secondly, an auctioneer could maximise the information gained in earlier auctions (as measured by the Kullback-Liebler divergence between its posterior and prior) to develop good estimates of the unknowns, which are later exploited to improve the revenue earned in the long-run. Simulation results comparing the two criteria indicate that setting offers to maximise revenue does not significantly detract from learning performance, but optimising offers for information gain substantially reduces expected revenue while not producing significantly better parameter estimates

On the accretion origin of a vast extended stellar disk around the Andromeda galaxy

We present the discovery of an inhomogenous, low-surface brightness, extended disk-like structure around the Andromeda galaxy (M31) based on a large kinematic survey of more than 2800 stars with the Keck/DEIMOS spectrograph. The stellar structure spans radii from 15 kpc out to ~40 kpc, with detections out to R ~ 70 kpc. The constituent stars lag the expected velocity of circular orbits in the plane of the M31 disk by ~40 kms and have a velocity dispersion of ~30 kms. The color range on the upper RGB shows a large spread indicative of a population with a significant range of metallicity. The mean metallicity of the population, measured from Ca II equivalent widths, is [Fe/H] = -0.9 +/- 0.2. The morphology of the structure is irregular at large radii, and shows a wealth of substructures which must be transitory in nature, and are almost certainly tidal debris. The presence of these substructures indicates that the global entity was formed by accretion. This extended disk follows smoothly on from the central parts of M31 disk with an exponential density law of scale-length of 5.1 +/- 0.1 kpc, similar to that of the bright inner disk. The population possesses similar kinematic and abundance properties over the entire region where it is detected in the survey. We estimate that the structure accounts for approximately 10% of the total luminosity of the M31 disk, and given the huge scale, contains ~30% of the total disk angular momentum. This finding indicates that at least some galactic stellar disks are vastly larger than previously thought and are formed, at least in their outer regions, primarily by accretion. [abridged]Comment: 20 pages, 30 figures, ApJ submitte

A near zero velocity dispersion stellar component in the Canes Venatici dwarf spheroidal galaxy

We present a spectroscopic survey of the newly-discovered Canes Venatici dwarf galaxy using the Keck/DEIMOS spectrograph. Two stellar populations of distinct kinematics are found to be present in this galaxy: an extended, metal-poor component, of half-light radius 7'.8(+2.4/-2.1), which has a velocity dispersion of 13.9(+3.2/-2.5) km/s, and a more concentrated (half-light radius 3'.6(+1.1/-0.8) metal-rich component of extremely low velocity dispersion. At 99% confidence, the upper limit to the central velocity dispersion of the metal-rich population is 1.9 km/s. This is the lowest velocity dispersion ever measured in a galaxy. We perform a Jeans analysis on the two components, and find that the dynamics of the structures can only be consistent if we adopt extreme (and unlikely) values for the scale length and velocity dispersion of the metal-poor population. With a larger radial velocity sample and improved measurements of the density profile of the two populations, we anticipate that it will be possible to place strong constraints on the central distribution of the dark matter in this galaxy.Comment: 5 pages, 7 figures, accepted by MNRA

Nonequilibrium Response from the dissipative Liouville Equation

The problem of response of nonequilibrium systems is currently under intense investigation. We propose a general method of solution of the Liouville Equation for thermostatted particle systems subjected to external forces which retains only the slow degrees of freedom, by projecting out the majority of fast variables. Response formulae, extending the Green-Kubo relations to dissipative dynamics are provided, and comparison with numerical data is presented

Macroscopic control parameter for avalanche models for bursty transport

Similarity analysis is used to identify the control parameter RA for the subset of avalanching systems that can exhibit self-organized criticality (SOC). This parameter expresses the ratio of driving to dissipation. The transition to SOC, when the number of excited degrees of freedom is maximal, is found to occur when RA-->0. This is in the opposite sense to (Kolmogorov) turbulence, thus identifying a deep distinction between turbulence and SOC and suggesting an observable property that could distinguish them. A corollary of this similarity analysis is that SOC phenomenology, that is, power law scaling of avalanches, can persist for finite RA with the same RA-->0 exponent if the system supports a sufficiently large range of lengthscales, necessary for SOC to be a candidate for physical (RA finite) systems

An investigation for the development of an integrated optical data preprocessor

A laboratory model of a 16 channel integrated optical data preprocessor was fabricated and tested in response to a need for a device to evaluate the outputs of a set of remote sensors. It does this by accepting the outputs of these sensors, in parallel, as the components of a multidimensional vector descriptive of the data and comparing this vector to one or more reference vectors which are used to classify the data set. The comparison is performed by taking the difference between the signal and reference vectors. The preprocessor is wholly integrated upon the surface of a LiNbO3 single crystal with the exceptions of the source and the detector. He-Ne laser light is coupled in and out of the waveguide by prism couplers. The integrated optical circuit consists of a titanium infused waveguide pattern, electrode structures and grating beam splitters. The waveguide and electrode patterns, by virtue of their complexity, make the vector subtraction device the most complex integrated optical structure fabricated to date

Flexible high-voltage supply for experimental electron microscope

Scanning microscope uses a field-emission tip for the electron source, an electron gun that simultaneously accelerates and focuses electrons from the source, and one auxiliary lens to produce a final probe size at the specimen on the order of angstroms