Four ball best ball 1.

In this paper a four-ball-best-ball (4BBB) model for pairs of golf players is set up. The 4BBB match-play scoring system is seen to satisfy a basic requirement of fairness. It is shown that it is not strictly possible to rate individual players as 4BBB players. However, a (reasonably broad) class of individual players is identified such that it is possible to rate them individually as 4BBB players. The capacity of an individual to play birdies is seen to be a very important determinant in being a successful member of a 4BBB pair, but there are other minor factors as well. Consideration is given to equal and unequal 4BBB pairs. The transitive law is seen to apply for 4BBB pairs. Thus, if pair A is better than pair B, and pair B is better than pair C, then pair A must be better than pair C. Correspondingly, if pair A is equal to pair B, and pair B is equal to pair C, then pair A is equal to pair C. Consideration is given to some strategic issues in 4BBB match-play golf. For example, the conditions under which a player should take a greater risk and have a higher probability of obtaining a bogie in order to achieve a higher probability of scoring a birdie, are determined. Also, the conditions under which a player, noting that his partner is about to have a 'bad' hole and score only a par or a bogie, should 'play safe', are determined. Thirdly, players who can interact in certain ways are seen to have an advantage over those pairs that cannot do this. Finally, one pair's optimal strategy when they see that their opponents are about to score a par or a bogie, but not a birdie, is analyzed. Key pointsA model for four-ball-best-ball match-play golf is established, and used to show that, although there can be other factors, the capacity of an individual to play birdies is a very important determinant in that player being a successful member of a four-ball-best-ball pair.Although it is not possible in general to rate play-ers individually as 4BBB players, a class of indi-vidual players is identified such that rating the players within that class is possible.Equal and unequal 4BBB pairs are considered, and the transitive law is seen to apply for 4BBB pairs. For example, if pair A is better than pair B, and pair B is better than pair C, then pair A must be better than pair C.Several strategic issues for individual players and pairs of players are considered, and optimal strate-gies identified.

The efficiency of tennis doubles scoring systems.

In this paper a family of scoring systems for tennis doubles for testing the hypothesis that pair A is better than pair B versus the alternative hypothesis that pair B is better than A, is established. This family or benchmark of scoring systems can be used as a benchmark against which the efficiency of any doubles scoring system can be assessed. Thus, the formula for the efficiency of any doubles scoring system is derived. As in tennis singles, one scoring system based on the play-the-loser structure is shown to be more efficient than the benchmark systems. An expression for the relative efficiency of two doubles scoring systems is derived. Thus, the relative efficiency of the various scoring systems presently used in doubles can be assessed. The methods of this paper can be extended to a match between two teams of 2, 4, 8, …doubles pairs, so that it is possible to establish a measure for the relative efficiency of the various systems used for tennis contests between teams of players. Key pointsA relatively straightforward expression or formula for the efficiency of a tennis doubles scoring system has been established.The expression for the relative efficiency of two tennis doubles scoring systems is a simple one, and is the same as that for two singles scoring systems.The methodology of this paper can be used and extended so that the efficiency of a scoring system for a match between two teams of doubles pairs can be measured.

Quantitation in gated perfusion SPECT imaging: the Cedars-Sinai approach.

Cedars-Sinai's approach to the automation of gated perfusion single photon emission computed tomography (SPECT) imaging is based on the identification of key procedural steps (processing, quantitation, reporting), each of which is then implemented, in completely automated fashion, by use of mathematic algorithms and logical rules combined into expert systems. Our current suite of software applications has been designed to be platform- and operating system-independent, and every algorithm is based on the same 3-dimensional sampling scheme for the myocardium. The widespread acceptance of quantitative software by the nuclear cardiology community (QGS alone is used at over 20,000 locations) has provided the opportunity for extensive validation of quantitative measurements of myocardial perfusion and function, in our opinion, helping to make nuclear cardiology the most accurate and reproducible modality available for the assessment of the human heart.