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A bstract We establish an orientifold Calabi-Yau threefold database for h 1 , 1 ( X ) ≤ 6 by considering non-trivial ℤ 2 divisor exchange involutions, using a toric Calabi-Yau database ( www.rossealtman.com/tcy ). We first determine the topology for each individual divisor (Hodge diamond), then identify and classify the proper involutions which are globally consistent across all disjoint phases of the Kähler cone for each unique geometry. Each of the proper involutions will result in an orientifold Calabi-Yau manifold. Then we clarify all possible fixed loci under the proper involution, thereby determining the locations of different types of O -planes. It is shown that under the proper involutions, one typically ends up with a system of O 3 /O 7-planes, and most of these will further admit naive Type IIB string vacua. The geometries with freely acting involutions are also determined. We further determine the splitting of the Hodge numbers into odd/even parity in the orbifold limit. The final result is a class of orientifold Calabi-Yau threefolds with non-trivial odd class cohomology ( $$ {h}_{-}^{1,1} $$ h − 1 , 1 ( X/σ * ) ≠ 0). 

We introduce a free probabilistic quantity called free Stein irregularity, which is defined in terms of free Stein discrepancies. It turns out that this quantity is related via a simple formula to the Murray–von Neumann dimension of the closure of the domain of the adjoint of the non-commutative Jacobian associated to Voiculescu’s free difference quotients. We call this dimension the free Stein dimension, and show that it is a ∗-algebra invariant. We relate these quantities to the free Fisher information, the non-microstates free entropy, and the non-microstates free entropy dimension. In the one-variable case, we show that the free Stein dimension agrees with the free entropy dimension, and in the multivariable case compute it in a number of examples. 

A bstract Dark Yang-Mills sectors, which are ubiquitous in the string landscape, may be reheated above their critical temperature and subsequently go through a confining first-order phase transition that produces stochastic gravitational waves in the early universe. Taking into account constraints from lattice and from Yang-Mills (center and Weyl) symmetries, we use a phenomenological model to construct an effective potential of the semi quark-gluon plasma phase, from which we compute the gravitational wave signal produced during confinement for numerous gauge groups. The signal is maximized when the dark sector dominates the energy density of the universe at the time of the phase transition. In that case, we find that it is within reach of the next-to-next generation of experiments (BBO, DECIGO) for a range of dark confinement scales near the weak scale. 

Abstract This paper gives a free entropy theoretic perspective on amenable absorption results for free products of tracial von Neumann algebras. In particular, we give the 1st free entropy proof of Popa’s famous result that the generator MASA in a free group factor is maximal amenable, and we partially recover Houdayer’s results on amenable absorption and Gamma stability. Moreover, we give a unified approach to all these results using $$1$$-bounded entropy. We show that if $${\mathcal{M}} = {\mathcal{P}} * {\mathcal{Q}}$$, then $${\mathcal{P}}$$ absorbs any subalgebra of $${\mathcal{M}}$$ that intersects it diffusely and that has $$1$$-bounded entropy zero (which includes amenable and property Gamma algebras as well as many others). In fact, for a subalgebra $${\mathcal{P}} \leq{\mathcal{M}}$$ to have this absorption property, it suffices for $${\mathcal{M}}$$ to admit random matrix models that have exponential concentration of measure and that “simulate” the conditional expectation onto $${\mathcal{P}}$$. 

The FPGA community is at an exciting juncture in the development of 3rd party CAD tools for FPGA design. Much has been learned in the past decade in the development and use of 3rd party tools such RapidSmith, Torc, and IceStorm. New independent open-source CAD tool projects are emerging which promise to provide alternatives to existing vendor tools. The recent release of the RapidWright tool suggests that Xilinx itself is interested in enabling the user community to develop new use cases and specialized tools for FPGA design. This paper provides a survey of the current landscape, discusses parts of what has been learned over the past decade in the author’s work with 3rd party CAD tool development, and provides some thoughts on the future.