Comparison of some Reduced Representation Approximations

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE's. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category

SEARCH FOR Fe4+ IN YIG : Ca GARNET FILMS

Spectral and temperature dependences of the Faraday rotation and X-ray photoemission spectroscopy of YIG: Ca garnet films have shown features characteristic for the presence of tetravalent iron ions in tetrahedral positions. The charge compensation of Ca2+ by Fe4+ ions becomes saturated at 0.16 Ca per formula unit suggesting the existence of O- ions at higher calcium contents

Parrot: A practical runtime for deterministic, stable, and reliable threads

Multithreaded programs are hard to get right. A key reason is that the contract between developers and runtimes grants exponentially many schedules to the runtimes. We present Parrot, a simple, practical runtime with a new contract to developers. By default, it orders thread synchronizations in the well-defined round-robin order, vastly reducing schedules to provide determinism (more precisely, deterministic synchronizations) and stability (i.e., robustness against input or code perturbations, a more useful property than determinism). When default schedules are slow, it allows developers to write intuitive performance hints in their code to switch or add schedules for speed. We believe this "meet in the middle" contract eases writing correct, efficient programs. We further present an ecosystem formed by integrating Parrot with a model checker called dbug. This ecosystem is more effective than either system alone: dbug checks the schedules that matter to Parrot, and Parrot greatly increases the coverage of dbug. Results on a diverse set of 108 programs, roughly 10x more than any prior evaluation, show that Parrot is easy to use (averaging 1.2 lines of hints per program); achieves low overhead (6.9% for 55 real-world programs and 12.7% for all 108 programs), 10x better than two prior systems; scales well to the maximum allowed cores on a 24-core server and to different scales/types of workloads; and increases Dbug's coverage by 10 6 - 1019734 for 56 programs. Parrot's source code, entire benchmark suite, and raw results are available at github.com/columbia/smt-mc. © 2013 ACM.link_to_subscribed_fulltex