This paper shows that the efficiency bound for communication equilibria identified by Goltsman, Hörner, Pavlov and Squintani [15] in the leading example of the CrawfordSobel model can be obtained with strategy-correlated equilibria, thus preserving privacy vis-à-vis the mediator. More generally, all equilibrium outcomes of the -noise model of Blume, Board and Kawamura [4], including outcomes wi...

We showed several years ago that the density operator of Markovian open systems can be diagonalized continuously in time. The resulting pure state jump processes correspond to quantum trajectories proposed in recent quantum optics calculations or, at fundamental level, to exact consistent histories. The quantum state of an open quantum system — actually a subsystem of a closed one — cannot be d...

Chen's biharmonic conjecture is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we consider an advanced version of the conjecture, replacing $Delta$ by its extension, $L_1$-operator ($L_1$-conjecture). The $L_1$-conjecture states that any $L_1$-biharmonic Euclidean hypersurface is 1-minimal. We prove that the $L_1$-conje...

The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...