S. Tim Hatamian | Searcharxiv

arXiv2005

Alliance Prediction by Energy Minimization: Neutrality

We extend the method of Axelrod and Bennetts for alliance prediction, based very loosely on the Spin-Glass theory of magnetism, to include the possibility of a neutral camp. We also explore the effect of physical separation between players. Using the second European war data, we demonstrate that either one of these extensions is sufficient to move Portugal out of the Axis camp, where it was previously found. If neutrality is allowed, then Portugal is found in that camp by itself. Without a neutral camp, Portugal is placed in the Allied camp if affinities decay with characteristic lengths of about 2000km. Most importantly, the consistency of results under such non-trivial alterations, provides incremental evidence for the robustness of the model as an empirical tool.

physics.soc-ph↗

arXiv2004

Diagrammar For Random Flight Motion

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The series for the exact moments, if not the distribution itself, for many important cases can be summed for arbitrary times. As expected, the behavior at early time regime, for the sample processes considered, deviate significantly from diffusion theory; a fact with important consequences in various applications such as financial physics. A half dozen sample problems are solved starting with one posed by Feynman who originally solved it only to first order. Another illustrative case is found to be a physically more plausible substitute for both the Uhlenbeck-Ornstein and the Wiener processes. The remaining cases we've solved are useful for applications in regime-switching and isotropic scattering of light in turbid media. It is demonstrated that under isotropic random flight with invariant-speed, the description of motion in higher dimensions is recursively related to either the one or two dimensional movement. Also for this motion, we show that the solution heretofore presumed correct in one dimension, applies only to the case we've named the "Shooting Gallery" problem; a special case of the full problem. A new class of functions dubbed "Damped-exponential-integrals" are also identified.

physics.class-ph↗