Adaptive BDDC in Three Dimensions

The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are implemented by a projection and sparsity of the projected operator is preserved by a generalized change of variables. The effectiveness of the method is illustrated on several engineering problems.Comment: 28 pages, 9 figures, 9 table

Tropical Theta Functions and Log Calabi-Yau Surfaces

We generalize the standard combinatorial techniques of toric geometry to the study of log Calabi-Yau surfaces. The character and cocharacter lattices are replaced by certain integral linear manifolds described by Gross, Hacking, and Keel, and monomials on toric varieties are replaced with the canonical theta functions which GHK defined using ideas from mirror symmetry. We describe the tropicalizations of theta functions and use them to generalize the dual pairing between the character and cocharacter lattices. We use this to describe generalizations of dual cones, Newton and polar polytopes, Minkowski sums, and finite Fourier series expansions. We hope that these techniques will generalize to higher-rank cluster varieties.Comment: 40 pages, 2 figures. The final publication is available at Springer via http://dx.doi.org/10.1007/s00029-015-0221-y, Selecta Math. (2016

Parameter estimation on gravitational waves from multiple coalescing binaries

Future ground-based and space-borne interferometric gravitational-wave detectors may capture between tens and thousands of binary coalescence events per year. There is a significant and growing body of work on the estimation of astrophysically relevant parameters, such as masses and spins, from the gravitational-wave signature of a single event. This paper introduces a robust Bayesian framework for combining the parameter estimates for multiple events into a parameter distribution of the underlying event population. The framework can be readily deployed as a rapid post-processing tool

The symphonies of Antonio Brioschi : aspects of sonata form

The article investigates tonal, thematic, and textural aspects of sonata form in the movement structures of twenty-six symphonies from the 1730s and early-1740s by the Italian composer Antonio Brioschi (active ca. 1725–ca. 1750). It discusses expository events as well as aspects of development and recapitulation of the musical material. In addition, the article provides an account of the major eighteenth-century manuscript source of the works—a French collection known as Fonds Blancheton—and considers some general stylistic characteristics of the music