Avoiding the Curse of Dimensionality in Dynamic Stochastic Games

Continuous-time stochastic games with a finite number of states have substantial computational and conceptual advantages over the more common discrete-time model. In particular, continuous time avoids a curse of dimensionality and speeds up computations by orders of magnitude in games with more than a few state variables. The continuous-time approach opens the way to analyze more complex and realistic stochastic games than is feasible in discrete-time models.

Influence of friction on granular segregation

Vertical shaking of a mixture of small and large beads can lead to segregation where the large beads either accumulate at the top of the sample, the so called Brazil Nut effect (BNE), or at the bottom, the Reverse Brazil Nut effect (RBNE). Here we demonstrate experimentally a sharp transition from the RBNE to the BNE when the particle coefficient of friction increases due to aging of the particles. This result can be explained by the two competing mechanisms of buoyancy and sidewall-driven convection, where the latter is assumed to grow in strength with increasing friction.Comment: 3 pages, 2 figure

Inflation after WMAP3

I discuss the current status of inflationary cosmology in light of the recent WMAP 3-year data release. The basic predictions of inflation are all supported by the data. Inflation also makes predictions which have not been well tested by current data but can be by future experiments, most notably a deviation from a scale-invariant power spectrum and the production of primordial gravitational waves. A scale-invariant spectrum is disfavored by current data, but not conclusively. Tensor modes are currently poorly constrained, and slow-roll inflation does not make an unambiguous prediction of the expected amplitude of primordial gravitational waves. A tensor/scalar ratio of $r \simeq 0.01$ is within reach of near-future measurements.Comment: To appear in the proceedings of Colliders to Cosmic Rays 2007. 8 pages, 2 figures. (V2: Minor typo corrected

Avoiding the Curse of Dimensionality in Dynamic Stochastic Games

Discrete-time stochastic games with a finite number of states have been widely ap- plied to study the strategic interactions among forward-looking players in dynamic en- vironments. However, these games suffer from a "curse of dimensionality" since the cost of computing players' expectations over all possible future states increases exponentially in the number of state variables. We explore the alternative of continuous-time stochas- tic games with a finite number of states, and show that continuous time has substantial computational and conceptual advantages. Most important, continuous time avoids the curse of dimensionality, thereby speeding up the computations by orders of magnitude in games with more than a few state variables. Overall, the continuous-time approach opens the way to analyze more complex and realistic stochastic games than currently feasible.

Interpretation of Solar Magnetic Field Strength Observations

This study based on longitudinal Zeeman effect magnetograms and spectral line scans investigates the dependence of solar surface magnetic fields on the spectral line used and the way the line is sampled in order to estimate the magnetic flux emerging above the solar atmosphere and penetrating to the corona from magnetograms of the Mt. Wilson 150-foot tower synoptic program (MWO). We have compared the synoptic program \lambda5250\AA line of Fe I to the line of Fe I at \lambda5233\AA since this latter line has a broad shape with a profile that is nearly linear over a large portion of its wings. The present study uses five pairs of sampling points on the $\lambda5233$\AA line. We recommend adoption of the field determined with a line bisector method with a sampling point as close as possible to the line core as the best estimate of the emergent photospheric flux. The combination of the line profile measurements and the cross-correlation of fields measured simultaneously with \lambda5250\AA and \lambda5233\AA yields a formula for the scale factor 1/\delta that multiplies the MWO synoptic magnetic fields. The new calibration shows that magnetic fields measured by the MDI system on the SOHO spacecraft are equal to 0.619+/-0.018 times the true value at a center-to-limb position 30 deg. Berger and Lites (2003) found this factor to be 0.64+/-0.013 based on a comparison the the Advanced Stokes Polarimeter.Comment: Accepted by Solar Physic

National Space Transportation System (NSTS) technology needs

The National Space Transportation System (NSTS) is one of the Nation's most valuable resources, providing manned transportation to and from space in support of payloads and scientific research. The NSTS program is currently faced with the problem of hardware obsolescence, which could result in unacceptable schedule and cost impacts to the flight program. Obsolescence problems occur because certain components are no longer being manufactured or repair turnaround time is excessive. In order to achieve a long-term, reliable transportation system that can support manned access to space through 2010 and beyond, NASA must develop a strategic plan for a phased implementation of enhancements which will satisfy this long-term goal. The NSTS program has initiated the Assured Shuttle Availability (ASA) project with the following objectives: eliminate hardware obsolescence in critical areas, increase reliability and safety of the vehicle, decrease operational costs and turnaround time, and improve operational capability. The strategy for ASA will be to first meet the mandatory needs - keep the Shuttle flying. Non-mandatory changes that will improve operational capability and enhance performance will then be considered if funding is adequate. Upgrade packages should be developed to install within designated inspection periods, grouped in a systematic approach to reduce cost and schedule impacts, and allow the capability to provide a Block 2 Shuttle (Phase 3)

PROFITABILITY OF CONVENIENCE MARKET DAIRY DEPARTMENTS

Examines return on investment to dairy departments in a sample of convenience markets and makes recommendations for profit improvement.Agribusiness,