Using dynamic programming to determine an optimal strategy in a contract bridge tournament

One form of contract bridge tournament comprises several rounds of matches in which players compete as pairs for ‘masterpoints’ awarded for each match won or drawn and for being highly placed at the end of the tournament. In the second and subsequent rounds, pairs are matched against other pairs that have been approximately equally successful so far. There has been vague discussion among bridge players of the possible advantages of ‘throwing’, that is, deliberately losing a match in round r so as to obtain a lower ranking and face an easier opponent in round r+1. This paper uses dynamic programming and data from one tournament to identify an optimal strategy (either ‘throw’ or ‘play to win’). The optimal strategy is a function of a pair's ability, its placing after each round, the relative rewards for winning a match and finishing high, the opponent's skill, and the round. For example, we find that a very weak pair should ‘throw’ and ‘play to win’ in alternate rounds.     

Flow patterns of bubble nucleation sites (called fliers) freely floating in champagne glasses

Laser tomography techniques were used to capture the dynamics of bubbles released from particles (arbitrarily called fliers) freely floating in traditional flutes poured with champagne. By use of long exposure time photography, the trajectories of bubbles released by fliers were found to leave very elegant and characteristic "prints" as they crossed a section of champagne illuminated with a 1 mm thick laser sheet. This characteristic print was made with a succession of lighting filaments. Fine analysis of these prints left by fliers enabled us to deduce the bubbling frequency of each flier (which ranged from about 4 bubbles/s up to about 22 bubbles/s a few seconds after pouring), as well as its velocity through the liquid medium (which ranged from about 0.8 mm/s to about 7.6 mm/s). Finally, this flow visualization technique, very recently applied to the science of champagne and sparkling wines, also proved to be a useful technique to underscore fliers' bubbling instabilities along their rather erratic way through the liquid medium.     

SINGLET OXYGEN PRODUCTION BY SOME FUROCOUMARIN DERIVATIVES IN THE PRESENCE OF DNA: TIME RESOLVED LUMINESCENCE MEASUREMENTS

Abstract— The yield of singlet oxygen (¹Δ_g) from some furocoumarins in the presence of DNA has been measured using time resolved techniques. For both psoralen and 4'-aminomethyl-4,5',8-trimethylpsoralen, increasing DNA concentration leads to a decrease in the yield of singlet oxygen. In addition, there is a linear dependence between the yield of singlet oxygen and the observed triplet yield determined by laser flash photolysis. In view of this observation it seems unlikely that singlet oxygen production occurs from these two furocoumarins when they are complexed with DNA. Preliminary, albeit inconclusive, results for 8-methoxypsoralen are also presented.