This paper elucidates the conceptual role that independent randomization plays in non-cooperative game theory. In the context of large (atomless) games in normal form, we present precise formalizations of the notions of a mixed strategy equilibrium (MSE) and of a randomized strategy equilibrium in distributional form (RSED). We offer a resolution of two longstanding open problems and show that ...

Stock price forecasting models with lower Mean Squared Error (MSE) are more “welcome" than those who have higher MSE. However, this “welcome" may disappear when lower MSE leads to an unexpected loss whereas higher MSE leads to a positive profit in a practical investment. The reason is that MSE aims to evaluate models in the view of “accuracy", which has nothing to do with profit. We therefore p...

The use of selenomethionine (MSe)-p-cyanophenylalanine (FCN) pairs to probe protein structure is demonstrated. MSe quenches FCN fluorescence via electron transfer. Both residues can be incorporated recombinantly or by peptide synthesis. Time-resolved and steady-state fluorescence measurements demonstrate that MSe-FCN pairs provide specific local probes of helical structure.

Daily averaged TOGA COARE data are analyzed to test our hypothesis that convection is amplified (attenuated) via sub-critical (super-critical) gross moist stability which corresponds to a bottom-heavy (top-heavy) vertical velocity profile. Gross moist stability (GMS) is a quantity which represents efficiency of moist static energy (MSE) export by convection and associated large-scale circulatio...