The parity vectors of two Latin squares of the same side n provide a necessary condition for the two squares to be biembeddable in an orientable surface. We investigate constraints on the parity vector of a Latin square resulting from structural properties of the square, and show how the parity vector of a direct product may be obtained from the parity vectors of the constituent factors. Parity...

One main goal of this study was to project the costs of providing parity for mental health and substance abuse (MH/SA) insurance benefits. We did this by using an actuarial model to predict the premium increases for three benefit options. One option gives full parity, and the other two give partial parity, for MS/SA benefits. Information about the relative costs of parity options can be used by...

We propose a benchmark suite for parity games that includes the benchmarks that have been used in the literature, and make it available online. We give an overview of the parity games, including a description of how they have been generated. We also describe structural properties of parity games, and using these properties we show that our benchmarks are representative. With this work we provid...

We consider games played on graphs with the winning conditions for the players specified as weak-parity conditions. In weak-parity conditions the winner of a play is decided by looking into the set of states appearing in the play, rather than the set of states appearing infinitely often in the play. A naive analysis of the classical algorithm for weak-parity games yields a quadratic time algori...

We study the process theoretic notion of stuttering equivalence in the setting of parity games. We demonstrate that stuttering equivalent vertices have the same winner in the parity game. This means that solving a parity game can be accelerated by minimising the game graph with respect to stuttering equivalence. While, at the outset, it might not be clear that this strategy should pay off, our ...

We review supersymmetry models with and without R-parity. After briefly describing the Minimal Supersymetric Standard Model and its particle content we move to models where R–parity is broken, either spontaneously or explicitly. In this last case we consider the situation where R–parity is broken via bilinear terms in the superpotential. The radiative breaking of these models is described in th...