Reducing the Effects of Unequal Number of Games on Rankings

Ranking is an important mathematical process in a variety of contexts such as information retrieval, sports and business. Sports ranking methods can be applied both in and beyond the context of athletics. In both settings, once the concept of a game has been defined, teams (or individuals) accumulate wins, losses, and ties, which are then factored into the ranking computation. Many settings involve an unequal number of games between competitors. This paper demonstrates how to adapt two sports rankings methods, the Colley and Massey ranking methods, to settings where an unequal number of games are played between the teams. In such settings, the standard derivations of the methods can produce nonsensical rankings. This paper introduces the idea of including a super-user into the rankings and considers the effect of this fictitious player on the ratings. We apply such techniques to rank batters and pitchers in Major League baseball, professional tennis players, and participants in a free online social game. The ideas introduced in this paper can further the scope that such methods are applied and the depth of insight they offer

Excitation of multiple 2-mode parametric resonances by a single driven mode

We demonstrate autoparametric excitation of two distinct sub-harmonic mechanical modes by the same driven mechanical mode corresponding to different drive frequencies within its resonance dispersion band. This experimental observation is used to motivate a more general physical picture wherein multiple mechanical modes could be excited by the same driven primary mode within the same device as long as the frequency spacing between the sub-harmonic modes is less than half the dispersion bandwidth of the driven primary mode. The excitation of both modes is seen to be threshold-dependent and a parametric back-action is observed impacting on the response of the driven primary mode. Motivated by this experimental observation, modified dynamical equations specifying 2-mode auto-parametric excitation for such systems are presented.Comment: 8 pages, 3 figure

A Wavelet-Based Approach To Monitoring Parkinson's Disease Symptoms

Parkinson's disease is a neuro-degenerative disorder affecting tens of millions of people worldwide. Lately, there has been considerable interest in systems for at-home monitoring of patients, using wearable devices which contain inertial measurement units. We present a new wavelet-based approach for analysis of data from single wrist-worn smart-watches, and show high detection performance for tremor, bradykinesia, and dyskinesia, which have been the major targets for monitoring in this context. We also discuss the implication of our controlled-experiment results for uncontrolled home monitoring of freely behaving patients.Comment: ICASSP 201

Spring Commencement (2007)

https://scholarship.law.campbell.edu/commencement/1008/thumbnail.jp