Almost Commuting Orthogonal Matrices

We show that almost commuting real orthogonal matrices are uniformly close to exactly commuting real orthogonal matrices. We prove the same for symplectic unitary matrices. This is in contrast to the general complex case, where not all pairs of almost commuting unitaries are close to commuting pairs. Our techniques also yield results about almost normal matrices over the reals and the quaternions.Comment: 13 pages, 3 figure

A Decentralized Parallelization-in-Time Approach with Parareal

With steadily increasing parallelism for high-performance architectures, simulations requiring a good strong scalability are prone to be limited in scalability with standard spatial-decomposition strategies at a certain amount of parallel processors. This can be a show-stopper if the simulation results have to be computed with wallclock time restrictions (e.g.\,for weather forecasts) or as fast as possible (e.g. for urgent computing). Here, the time-dimension is the only one left for parallelization and we focus on Parareal as one particular parallelization-in-time method. We discuss a software approach for making Parareal parallelization transparent for application developers, hence allowing fast prototyping for Parareal. Further, we introduce a decentralized Parareal which results in autonomous simulation instances which only require communicating with the previous and next simulation instances, hence with strong locality for communication. This concept is evaluated by a prototypical solver for the rotational shallow-water equations which we use as a representative black-box solver

PAST WHAT YOU CAN SEE: INNOCENCE, EXPERIENCE, AND REALIZATION IN STEPHEN SONDHEIM’S INTO THE WOODS

A deeper appreciation of Stephen Sondheim’s Into the Woods may be achieved by examining the work under a new magnifying glass. After a synopsis of background information of the musical itself, the assertion is made that Into the Woods shows three basic stages of life that occur in a cycle: innocence, experience, and realization. This is supported by the proposition that the idea of innocence is represented by a recurring five-note motive (commonly referred to as the “bean theme”), and that the ideas of experience and realization are revealed through particular musical numbers. The overarching entity that binds the work together is innocence. By examining the music under this philosophical lens, the reader is guided to a better understanding not only of this specific work, but also of the creative process of Sondheim as a composer

Terrace grading of SiGe for high-quality virtual substrates

Silicon germanium (SiGe) virtual substrates of final germanium composition x = 0.50 have been fabricated using solid-source molecular beam epitaxy with a thickness of 2 µm. A layer structure that helps limit the size of dislocation pileups associated with the modified Frank–Read dislocation multiplication mechanism has been studied. It is shown that this structure can produce lower threading dislocation densities than conventional linearly graded virtual substrates. Cross-sectional transmission electron microscopy shows the superior quality of the dislocation network in the graded regions with a lower rms roughness shown by atomic force microscopy. X-ray diffractometry shows these layers to be highly relaxed. This method of Ge grading suggests that high-quality virtual substrates can be grown considerably thinner than with conventional grading methods

Draft Genome Sequence for Desulfovibrio africanus Strain PCS.

Desulfovibrio africanus strain PCS is an anaerobic sulfate-reducing bacterium (SRB) isolated from sediment from Paleta Creek, San Diego, CA. Strain PCS is capable of reducing metals such as Fe(III) and Cr(VI), has a cell cycle, and is predicted to produce methylmercury. We present the D. africanus PCS genome sequence

A 3D antiferromagnetic ground state in a quasi-1D π-stacked charge-transfer system

With the rising interest in organic based materials for spintronic and multiferroic applications it is important to fully understand their electrical and magnetic properties and to identify correlations between their structural and physical attributes. One material that still holds some ambiguity is triethylammonium bis-7,7,8,8-tetracyanoquinodimethane (TEA(TCNQ)2). This charge transfer compound has one electron delocalised across two TCNQ molecules along quasi-1D stacks. Previous work has shown that there is magneto-electrical coupling associated with the magnetic transition at ∼120 K, however the magnetism and magnetic ground-state are not well understood. Within this manuscript we provide evidence for a long range magnetic order that is 3D in nature

Maximizing The Value Of Your Small Business

This paper offers business owners a step-by-step valuation process for establishing the fair market value of their firms and stresses the importance of preparing for the due diligence process

F22RS SGB No. 17 (MEGSA Website)

To allocate $1,500 from the Student Government Contingency Account to fund the renovation and optimization of the Mechanical Engineering Graduate repositor

Intermittent electron density and temperature fluctuations and associated fluxes in the Alcator C-Mod scrape-off layer

The Alcator C-Mod mirror Langmuir probe system has been used to sample data time series of fluctuating plasma parameters in the outboard mid-plane far scrape-off layer. We present a statistical analysis of one second long time series of electron density, temperature, radial electric drift velocity and the corresponding particle and electron heat fluxes. These are sampled during stationary plasma conditions in an ohmically heated, lower single null diverted discharge. The electron density and temperature are strongly correlated and feature fluctuation statistics similar to the ion saturation current. Both electron density and temperature time series are dominated by intermittent, large-amplitude burst with an exponential distribution of both burst amplitudes and waiting times between them. The characteristic time scale of the large-amplitude bursts is approximately 15{\mu}s. Large-amplitude velocity fluctuations feature a slightly faster characteristic time scale and appear at a faster rate than electron density and temperature fluctuations. Describing these time series as a superposition of uncorrelated exponential pulses, we find that probability distribution functions, power spectral densities as well as auto-correlation functions of the data time series agree well with predictions from the stochastic model. The electron particle and heat fluxes present large-amplitude fluctuations. For this low-density plasma, the radial electron heat flux is dominated by convection, that is, correlations of fluctuations in the electron density and radial velocity. Hot and dense blobs contribute approximately 6% of the total fluctuation driven heat flux