On Minimum Violations Ranking in Paired Comparisons

Ranking a set of objects from the most dominant one to the least, based on the results of paired comparisons, proves to be useful in many contexts. Using the rankings of teams or individuals players in sports to seed tournaments is an example. The quality of a ranking is often evaluated by the number of violations, cases in which an object is ranked lower than another that it has dominated in a comparison, that it contains. A minimum violations ranking (MVR) method, as its name suggests, searches specifically for rankings that have the minimum possible number of violations which may or may not be zero. In this paper, we present a method based on statistical physics that overcomes conceptual and practical difficulties faced by earlier studies of the problem.Comment: 10 pages, 10 figures; typos corrected (v2

A network-based ranking system for American college football

American college football faces a conflict created by the desire to stage national championship games between the best teams of a season when there is no conventional playoff system to decide which those teams are. Instead, ranking of teams is based on their record of wins and losses during the season, but each team plays only a small fraction of eligible opponents, making the system underdetermined or contradictory or both. It is an interesting challenge to create a ranking system that at once is mathematically well-founded, gives results in general accord with received wisdom concerning the relative strengths of the teams, and is based upon intuitive principles, allowing it to be accepted readily by fans and experts alike. Here we introduce a one-parameter ranking method that satisfies all of these requirements and is based on a network representation of college football schedules.Comment: 15 pages, 3 figure

Dopplerfluxometria no estudo da circulação fetal: revisão do aspecto segurança Doppler velocimetry in the study of the fetal circulation: review on safety

Os autores apresentam os métodos Doppler e sua evolução no estudo da circulação fetal, dando ênfase à segurança e aos bioefeitos. Os aparelhos de ultra-sonografia utilizados correntemente funcionam com índice térmico máximo e índice mecânico automaticamente mantidos em níveis inferiores a 1,0. Até os dias atuais, não foi descrita lesão biológica em fetos humanos submetidos ao Doppler diagnóstico. Portanto, o Doppler pulsado, o colorido e o "power" Doppler são seguros na exposição ultra-sonográfica do pré-natal.<br>The authors review the Doppler imaging methods and their evolution for the study of the fetal circulation emphasizing safety and bioeffects. Ultrasound machines work with thermal and mechanical indexes that are automatically kept under 1.0. Up to date, there have been no reports on biological lesions in human fetuses caused by diagnostic Doppler. Consequently, color, pulsed and power Doppler sonography are considered safe in prenatal exposure