Energy-momentum/Cotton tensor duality for AdS4 black holes

We consider the theory of gravitational quasi-normal modes for general linear perturbations of AdS4 black holes. Special emphasis is placed on the effective Schrodinger problems for axial and polar perturbations that realize supersymmetric partner potential barriers on the half-line. Using the holographic renormalization method, we compute the energy-momentum tensor for perturbations satisfying arbitrary boundary conditions at spatial infinity and discuss some aspects of the problem in the hydrodynamic representation. It is also observed in this general framework that the energy-momentum tensor of black hole perturbations and the energy momentum tensor of the gravitational Chern-Simons action (known as Cotton tensor) exhibit an axial-polar duality with respect to appropriately chosen supersymmetric partner boundary conditions on the effective Schrodinger wave-functions. This correspondence applies to perturbations of very large AdS4 black holes with shear viscosity to entropy density ratio equal to 1/4\pi, thus providing a dual graviton description of their hydrodynamic modes. We also entertain the idea that the purely dissipative modes of black hole hydrodynamics may admit Ricci flow description in the non-linear regime.Comment: 38 pages; minor typos corrected, a few extra references and a note adde

The TDNNS method for Reissner-Mindlin plates

A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The elements are based on the "tangential-displacement normal-normal-stress" formulation of elasticity. In this formulation, the bending moments are treated as separate unknowns. The degrees of freedom for the plate element are the nodal values of the deflection, tangential components of the rotations and normal-normal components of the bending strain. Contrary to other plate bending elements, no special treatment for the shear term such as reduced integration is necessary. The elements attain an optimal order of convergence

Distributionally Robust Games with Risk-averse Players

We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that our "Distributionally Robust Game" constitutes a true generalization of three popular finite games. These are the Complete Information Games, Bayesian Games and Robust Games. Subsequently, we prove that the set of equilibria of an arbitrary distributionally robust game with specified ambiguity set can be computed as the component-wise projection of the solution set of a multi-linear system of equations and inequalities. For special cases of such games we show equivalence to complete information finite games (Nash Games) with the same number of players and same action spaces. Thus, when our game falls within these special cases one can simply solve the corresponding Nash Game. Finally, we demonstrate the applicability of our new model of games and highlight its importance.Comment: 11 pages, 3 figures, Proceedings of 5th the International Conference on Operations Research and Enterprise Systems ({ICORES} 2016), Rome, Italy, February 23-25, 201

A duality principle for selection games

A dinner table seats k guests and holds n discrete morsels of food. Guests select morsels in turn until all are consumed. Each guest has a ranking of the morsels according to how much he would enjoy eating them; these rankings are commonly known. A gallant knight always prefers one food division over another if it provides strictly more enjoyable collections of food to one or more other players (without giving a less enjoyable collection to any other player) even if it makes his own collection less enjoyable. A boorish lout always selects the morsel that gives him the most enjoyment on the current turn, regardless of future consumption by himself and others. We show the way the food is divided when all guests are gallant knights is the same as when all guests are boorish louts but turn order is reversed. This implies and generalizes a classical result of Kohler and Chandrasekaran (1971) about two players strategically maximizing their own enjoyments. We also treat the case that the table contains a mixture of boorish louts and gallant knights. Our main result can also be formulated in terms of games in which selections are made by groups. In this formulation, the surprising fact is that a group can always find a selection that is simultaneously optimal for each member of the group.Comment: 8 pages, 2 figure