Hierarchical Economic Agents and their Interactions

We present a new type of spin market model, populated by hierarchical agents, represented as configurations of sites and arcs in an evolving network. We describe two analytic techniques for investigating the asymptotic behavior of this model: one based on the spectral theory of Markov chains and another exploiting contingent submartingales to construct a deterministic cellular automaton that approximates the stochastic dynamics. Our study of this system documents a phase transition between a sub-critical and a super-critical regime based on the values of a coupling constant that modulates the tradeoff between local majority and global minority forces. In conclusion, we offer a speculative socioeconomic interpretation of the resulting distributional properties of the system.Comment: 38 pages, 13 figures, presented at the 2013 WEHIA conference; to appear in Journal of Economic Interaction and Coordination, to appear in Journal of Economic Interaction and Coordinatio

Periodic attractors of random truncator maps

This paper introduces the \textit{truncator} map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify its periodic orbits using properties of endomorphisms of the resulting algebraic structure. A stochastic model is constructed on these endomorphisms, which leads to the classification of the distribution of periodic orbits for random truncator maps. This framework is applied to investigate the periodic transitions of Bornholdt's spin market model.Comment: 8 pages, presented at APFA

Use of the Neurological Pupil Index to Predict Postoperative Visual Function After Resection of a Tuberculum Sellae Meningioma: A Case Report.

The Neurological Pupil index (NPi) is a standardized method for evaluating pupil reactivity that removes inter-examiner variability. Changes in the NPi can predict clinical deterioration in patients with traumatic brain injury (TBI); however, its use to predict visual impairment after the resection of parasellar meningiomas has not been described. A 71-year-old female underwent a modified expanded bifrontal craniotomy for resection of a 3.1 cm tuberculum sella meningioma that caused compression of the optic chiasm and resulted in left temporal and right superior temporal visual field deficits. Postoperatively, she lost vision in the right eye. Pupillometer measurements demonstrated an asymmetrically low NPi at that time, which improved to normal prior to partial vision recovery. The average NPi in the right pupil was 1.67 during the time of vision loss compared to 3.47 in the left pupil (p=1.7x10-10). Statistical analysis was performed with the Student's t-test and the significance level was set at p-value < 0.01. Resection of parasellar meningiomas is challenging because of the proximity of the optic apparatus. We report a case of unilateral vision loss after resection of a tuberculum sella meningioma in which the impaired eye's NPi value correlated closely with visual function. NPi values that decrease below 3 predict spikes in intracranial pressure in TBI patients; similarly, increases in the NPi value above 2.5-3 predict improvement in vision in the case reported here. By monitoring the proximal portion of the oculomotor reflex, the NPi can be a marker of visual impairment after surgery