Reflection positivity and invertible topological phases

We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable homotopy theory. We apply these field theory considerations to lattice systems, assuming the existence and validity of low energy effective field theory approximations, and thereby produce a general formula for the group of Symmetry Protected Topological (SPT) phases in terms of Thom's bordism spectra; the only input is the dimension and symmetry group. We provide computations for fermionic systems in physically relevant dimensions. Other topics include symmetry in quantum field theories, a relativistic 10-fold way, the homotopy theory of relativistic free fermions, and a topological spin-statistics theorem.Comment: 136 pages, 16 figures; minor changes/corrections in version 2; v3 major revision; v4 minor revision: corrected proof of Lemma 9.55, many small changes throughout; v5 version for publication in Geometry & Topolog

Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under a wide class of learning processes. We study two versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. The unique Nash equilibrium places a weight of 1/2 on Dumb in both games, but in one game the NE is stable, while in the other game the NE is unstable and the TASP places zero weight on Dumb. Consistent with TASP, we find that the frequency of Dumb is lower and play is further from Nash in the high payoff unstable treatment than in the other treatments. However, the frequency of Dumb is substantially greater than zero in all treatments.games, experiments, TASP, learning, unstable, mixed equilibrium, fictitious play

Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.games, experiments, TASP, learning, unstable, mixed equilibrium, fictitious play.

The Constraining Power of International Treaties: Theory and Methods

We acknowledge the contribution of von Stein (2005) in calling attention to the very real problem of selection bias in estimating treaty effects. Nonetheless, we dispute both von Stein's theoretical and empirical conclusions. Theoretically, we contend that treaties can both screen and constrain simultaneously, meaning that findings of screening do nothing to undermine the claim that treaties constrain state behavior as well. Empirically, we question von Stein's estimator on sevral grounds, including its strong distributional assumptions and its statistical inconsistency. we then illustrate that selection bias does not account for much of the difference between Simmon's (2000) and von Stein's (2005) estimated treaty effects, and instead reframe the problem as one of model dependency. Using a preprocessing matching step to reduce that dependency, we then illustrate treaty effects that are both substantively and statistically significant- and that are quite close in magnitude to those reported by Simmons.Governmen

Many Low Income Women In Texas Do Not Get the Effective Contraception They Want After Giving Birth

Population Research Cente

The Uncertainty of Fluxes

In the ordinary quantum Maxwell theory of a free electromagnetic field, formulated on a curved 3-manifold, we observe that magnetic and electric fluxes cannot be simultaneously measured. This uncertainty principle reflects torsion: fluxes modulo torsion can be simultaneously measured. We also develop the Hamilton theory of self-dual fields, noting that they are quantized by Pontrjagin self-dual cohomology theories and that the quantum Hilbert space is Z/2-graded, so typically contains both bosonic and fermionic states. Significantly, these ideas apply to the Ramond-Ramond field in string theory, showing that its K-theory class cannot be measured.Comment: 33 pages; minor modifications for publication in Commun. Math. Phy