This work treats dual-plane automatic ball balancing of elastically-mounted cylindrical rotors. The application is primarily to systems with a vertically-oriented single-bearing support, but extension is also made to horizontally-oriented single-bearing support as typically found in a vehicle wheel. The rotor elastic mounting includes three translational degrees of freedom for the body geometric center and three rotational degrees of freedom. Damping is included for each of these six degrees of freedom. The model for the automatic ball balancer consists of up to two arbitrarily-located hollow circumferential races, each of which contains up to two sliding particles. The friction model for the particles includes both viscous and Coulomb friction forces. Of considerable complexity is the logic path for the individual particles being either in motion or stationary relative to the rotor. The exact equations of motion for the overall system are derived via a Newtonian approach. Numerical-integration results show that the balancer performance depends strongly on the friction levels as well as the operating speed of the body. Simulations conducted with a pure static imbalance show that ideal automatic balancing is possible only for vertical-axis rotors that have zero Coulomb friction levels between the balancing particles and the races. Simulations with a horizontal-axis statically-imbalanced rotor show that an automatic balancer can improve performance for certain operating speeds and non-zero Coulomb friction levels in the presence of gravitational forces. Simulations conducted with a pure dynamic imbalance show that there is no inherent mechanism to counteract rotational displacements of the rotor about its geometric center. As a result, the balancing particles exhibit several phenomena described in previous works such as synchronous motion and oscillatory behaviors within their respective races. Simulations for an arbitrarily located imbalance show that rotor performance can be improved using dual-plane balancing techniques for certain operating speeds and Coulomb friction levels. Due to the inherent complexity in eliminating an arbitrarily located mass imbalance, the system is generally unable to reach a perfectly balanced configuration, but performance can be improved for carefully-selected initial conditions. / Ph. D.

Collectible Card Games (CCG) are one of the most popular types of games in both digital and physical space. Despite their popularity, there is a great deal of room for exploration into the application of artificial intelligence in order to enhance CCG gameplay and development. This paper presents Fifth Aeon a novel and open source CCG built to run in browsers and two A.I applications built upon Fifth Aeon. The first application is an artificial intelligence competition run on the Fifth Aeon game. The second is an automatic balancing system capable of helping a designer create new cards that do not upset the balance of an existing collectible card game. The submissions to the A.I competition include one that plays substantially better than the existing Fifth Aeon A.I with a higher winrate across multiple game formats. The balancer system also demonstrates an ability to automatically balance several types of cards against a wide variety of parameters. These results help pave the way to cheaper CCG development with more compelling A.I opponents.

This thesis examines stabilizing mechanisms in social security retirement systems (“SSRS”), especially those purporting to be automatic balancing mechanisms (“ABM”). It develops a consistent approach to identifying whether an ABM is robust, partial or transitory and establishes a terminology to classify balancing mechanisms. Both financial and equitable balances are considered in assessing whether an ABM achieves balance. Families of definitions of equity are presented and a benchmark by which to measure equitable balance is defined and applied. The balancing mechanisms of Canada, Germany, Japan and Sweden are described, evaluated and classified. None of these mechanisms are found to be robust. This thesis provides a critical analysis of an approach referred to as integration to financial markets and the approach is found to be deficient. In analyzing the Swedish SSRS a critical error in the way assets are calculated is identified and a suitable correction is proposed. A further weakness in the application of the Swedish ABM is identified that means that once an imbalance occurs, balance is unlikely to be restored. The thesis also discusses some of the unusual characteristics of the steady-state contribution rate calculation for the Canadian SSRS and shows that although it has limited application and does not appear to depend on any actuarial principle, the steady-state contribution rate calculation creates a tension between the near and distant future, which is a factor in achieving financial balance over a seventy-five year horizon. With respect to the balancing mechanism in the Canadian SSRS, the thesis proposes a change in how the mechanism is defined so that the mechanism would be robust, within certain ranges.

This thesis examines stabilizing mechanisms in social security retirement systems (“SSRS”), especially those purporting to be automatic balancing mechanisms (“ABM”). It develops a consistent approach to identifying whether an ABM is robust, partial or transitory and establishes a terminology to classify balancing mechanisms. Both financial and equitable balances are considered in assessing whether an ABM achieves balance. Families of definitions of equity are presented and a benchmark by which to measure equitable balance is defined and applied. The balancing mechanisms of Canada, Germany, Japan and Sweden are described, evaluated and classified. None of these mechanisms are found to be robust. This thesis provides a critical analysis of an approach referred to as integration to financial markets and the approach is found to be deficient. In analyzing the Swedish SSRS a critical error in the way assets are calculated is identified and a suitable correction is proposed. A further weakness in the application of the Swedish ABM is identified that means that once an imbalance occurs, balance is unlikely to be restored. The thesis also discusses some of the unusual characteristics of the steady-state contribution rate calculation for the Canadian SSRS and shows that although it has limited application and does not appear to depend on any actuarial principle, the steady-state contribution rate calculation creates a tension between the near and distant future, which is a factor in achieving financial balance over a seventy-five year horizon. With respect to the balancing mechanism in the Canadian SSRS, the thesis proposes a change in how the mechanism is defined so that the mechanism would be robust, within certain ranges.