N-player quantum games in an EPR setting

The $N$-player quantum game is analyzed in the context of an Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players' strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for $N$-qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the mixed Nash equilibrium and the payoffs are determined. Players' payoffs are then defined with linear functions so that common two-player games can be easily extended to the $N$-player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners' Dilemma game for general $N \ge 2$. We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs.Comment: 26 pages, 2 figure

Open Problems and Conjectures Related to the Theory of Mathematical Quasicrystals

This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our meeting was to bring together researchers from a variety of disciplines, with a common goal of understanding different viewpoints and approaches surrounding the theory of mathematical quasicrystals. The problems below reflect this goal and this diversity and we hope that they will motivate further cross-disciplinary research and lead to new advances in our overall vision of this rapidly developing field

Pharmacodynamic evaluation of commonly prescribed oral antibiotics against respiratory bacterial pathogens

<p>Abstract</p> <p>Background</p> <p>Upper and lower respiratory tract infections (RTIs) account for a substantial portion of outpatient antibiotic utilization. However, the pharmacodynamic activity of commonly used oral antibiotic regimens has not been studied against clinically relevant pathogens. The objective of this study was to assess the probability of achieving the requisite pharmacodynamic exposure for oral antibacterial regimens commonly prescribed for RTIs in adults against bacterial isolates frequently involved in these processes (<it>S. pneumoniae</it>, <it>H. influenzae</it>, and <it>M. catharralis</it>).</p> <p>Methods</p> <p>Using a 5000-subject Monte Carlo simulation, the cumulative fractions of response (CFR), (i.e., probabilities of achieving requisite pharmacodynamic targets) for the most commonly prescribed oral antibiotic regimens, as determined by a structured survey of medical prescription patterns, were assessed against local respiratory bacterial isolates from adults in São Paulo collected during the same time period. Minimal inhibitory concentration (MIC) of 230 isolates of <it>Streptococcus pneumoniae </it>(103), <it>Haemophilus influenzae </it>(98), and <it>Moraxella catharralis </it>(29) from a previous local surveillance were used.</p> <p>Results</p> <p>The most commonly prescribed antibiotic regimens were azithromycin 500 mg QD, amoxicillin 500 mg TID, and levofloxacin 500 mg QD, accounting for 58% of the prescriptions. Varied doses of these agents, plus gatifloxacin, amoxicillin-clavulanate, moxifloxacin, and cefaclor made up the remaining regimens. Utilizing aggressive pharmacodynamic exposure targets, the only regimens to achieve greater than 90% CFR against all three pathogens were amoxicillin/amoxicillin-clavulanate 500 mg TID (> 91%), gatifloxacin 400 mg QD (100%), and moxifloxacin 400 mg QD (100%). Considering <it>S. pneumoniae </it>isolates alone, azithromycin 1000 mg QD also achieved greater than 90% CFR (91.3%).</p> <p>Conclusions</p> <p>The only regimens to achieve high CFR against all three pathogen populations in both scenarios were gatifloxacin 400 mg QD, moxifloxacin 400 mg QD, and amoxicillin-clavulanate 500 mg TID. These data suggest the need for reconsideration of empiric antibiotic regimen selection among adult patients with RTIs in the São Paulo area. Additionally, this type of study could be used to optimize prescribing patterns in specific regions in light of emerging resistance.</p