Stationary and Time-Dependent Optimization of the Casino Floor Slot Machine Mix

Modeling and optimizing the performance of a mix of slot machines on a gaming floor can be addressed at various levels of coarseness, and may or may not consider time-dependent trends. For example, a model might consider only time-averaged, aggregate data for all machines of a given type; time-dependent aggregate data; time-averaged data for individual machines; or fully time dependent data for individual machines. Fine-grained, time-dependent data for individual machines offers the most potential for detailed analysis and improvements to the casino floor performance, but also suffers the greatest amount of statistical noise. We present a theoretical analysis of single and multi-objective optimization methods that address the casino floor optimization problem at all levels of coarseness, considering both linear and non-linear formulations of the problem. We also address the impact of statistical noise and time-dependent trends on solutions, using both Gaussian and non-Gaussian distributions to model the performance of individual machines. We show that advanced methods from evolutionary computing can track trends in performance and continually adjust the optimal mix of machines, potentially allowing an operator to respond rapidly to customer preferences, and allowing a property to operate continuously near the optimal mix

Helical Fields and Filamentary Molecular Clouds II - Axisymmetric Stability and Fragmentation

In Paper I (Fiege & Pudritz, 1999), we constructed models of filamentary molecular clouds that are truncated by a realistic external pressure and contain a rather general helical magnetic field. We address the stability of our models to gravitational fragmentation and axisymmetric MHD-driven instabilities. By calculating the dominant modes of axisymmetric instability, we determine the dominant length scales and growth rates for fragmentation. We find that the role of pressure truncation is to decrease the growth rate of gravitational instabilities by decreasing the self-gravitating mass per unit length. Purely poloidal and toroidal fields also help to stabilize filamentary clouds against fragmentation. The overall effect of helical fields is to stabilize gravity-driven modes, so that the growth rates are significantly reduced below what is expected for unmagnetized clouds. However, MHD ``sausage'' instabilities are triggered in models whose toroidal flux to mass ratio exceeds the poloidal flux to mass ratio by more than a factor of $\sim 2$. We find that observed filaments appear to lie in a physical regime where the growth rates of both gravitational fragmentation and axisymmetric MHD-driven modes are at a minimum.Comment: 16 pages with 18 eps figures. Submitted to MNRA

Helical Fields and Filamentary Molecular Clouds

We study the equilibrium of pressure truncated, filamentary molecular clouds that are threaded by rather general helical magnetic fields. We first derive a new virial equation appropriate for magnetized filamentary clouds, which includes the effects of non-thermal motions and the turbulent pressure of the surrounding ISM. When compared with the data, we find that many filamentary clouds have a mass per unit length that is significantly reduced by the effects of external pressure, and that toroidal fields play a significant role in squeezing such clouds. We also develop exact numerical MHD models of filamentary molecular clouds with more general helical field configurations than have previously been considered. We also examine the effects of the equation of state by comparing ``isothermal'' filaments, with constant total (thermal plus turbulent) velocity dispersion, with equilibria constructed using a logatropic equation of state. We perform a Monte Carlo exploration of our parameter space to determine which choices of parameters result in models that agree with the available observational constraints. We find that both equations of state result in equilibria that agree with the observational results. Moreover, we find that models with helical fields have more realistic density profiles than either unmagnetized models or those with purely poloidal fields; we find that most isothermal models have density distributions that fall off as r^{-1.8} to r^{-2}, while logatropes have density profiles that range from r^{-1} to r^{-1.8}. We find that purely poloidal fields produce filaments with steep density gradients that not allowed by the observations.Comment: 21 pages, 8 eps figures, submitted to MNRAS. Significant streamlining of tex