Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization

In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns), which is equivalent to the hyperspectral unmixing problem under the linear mixing model and the pure-pixel assumption. We present a family of fast recursive algorithms, and prove they are robust under any small perturbations of the input data matrix. This family generalizes several existing hyperspectral unmixing algorithms and hence provides for the first time a theoretical justification of their better practical performance.Comment: 30 pages, 2 figures, 7 tables. Main change: Improvement of the bound of the main theorem (Th. 3), replacing r with sqrt(r

Binary Pulsar Constraints on the Parameterized post-Einsteinian Framework

We constrain the parameterized post-Einsteinian framework with binary pulsar observations of orbital period decay due to gravitational wave emission. This framework proposes to enhance the amplitude and phase of gravitational waveform templates through post-Einsteinian parameters to search for generic deviations from General Relativity in gravitational wave data. Such enhancements interpolate between General Relativity and alternative theory predictions, but their magnitude must be such as to satisfy all current experiments and observations. The data that currently constrains the parameterized post-Einsteinian framework the most is the orbital period decay of binary pulsars. We use such observations to place upper limits on the magnitude of post-Einsteinian parameters, which will be critical when gravitational waves are detected and this framework is implemented.Comment: 4 pages, 2 figures, submitted to Phys. Rev.

The Feeding Zones of Terrestrial Planets and Insights into Moon Formation

[Abridged] We present an extensive suite of terrestrial planet formation simulations that allows quantitative analysis of the stochastic late stages of planet formation. We quantify the feeding zone width, Delta a, as the mass-weighted standard deviation of the initial semi-major axes of the planetary embryos and planetesimals that make up the final planet. The size of a planet's feeding zone in our simulations does not correlate with its final mass or semi-major axis, suggesting there is no systematic trend between a planet's mass and its volatile inventory. Instead, we find that the feeding zone of any planet more massive than 0.1M_Earth is roughly proportional to the radial extent of the initial disk from which it formed: Delta a~0.25(a_max-a_min), where a_min and a_max are the inner and outer edge of the initial planetesimal disk. These wide stochastic feeding zones have significant consequences for the origin of the Moon, since the canonical scenario predicts the Moon should be primarily composed of material from Earth's last major impactor (Theia), yet its isotopic composition is indistinguishable from Earth. In particular, we find that the feeding zones of Theia analogs are significantly more stochastic than the planetary analogs. Depending on our assumed initial distribution of oxygen isotopes within the planetesimal disk, we find a ~5% or less probability that the Earth and Theia will form with an isotopic difference equal to or smaller than the Earth and Moon's. In fact we predict that every planetary mass body should be expected to have a unique isotopic signature. In addition, we find paucities of massive Theia analogs and high velocity moon-forming collisions, two recently proposed explanations for the Moon's isotopic composition. Our work suggests that there is still no scenario for the Moon's origin that explains its isotopic composition with a high probability event.Comment: 16 pages, 22 figures, accepted for publication in Icarus; fixed typo

Temporal-mode continuous-variable cluster states using linear optics

I present an extensible experimental design for optical continuous-variable cluster states of arbitrary size using four offline (vacuum) squeezers and six beamsplitters. This method has all the advantages of a temporal-mode encoding [Phys. Rev. Lett. 104, 250503], including finite requirements for coherence and stability even as the computation length increases indefinitely, with none of the difficulty of inline squeezing. The extensibility stems from a construction based on Gaussian projected entangled pair states (GPEPS). The potential for use of this design within a fully fault tolerant model is discussed.Comment: 9 pages, 19 color figure

The history of video quality model validation

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Impact of Diet and Quality Grade on Shelf Life of Beef Steaks

Steers were fed a diet containing dry rolled corn, steam flaked corn, dry rolled corn with 30% dried distillers grains, or steam flaked corn with 30% dried distillers grains. Strip loins from upper 2/3 Choice and Select- grade carcasses were obtained to evaluate the effects of diet and quality grade on shelf life characteristics. Strip loins were aged for 2, 9, 16, or 23 days. Results suggest that steaks from cattle fed steam flaked corn (with or without dried distillers grains) and from cattle fed dried distillers grains (regardless of corn type) had higher levels of many unsaturated fatty acids, more discoloration, and greater lipid oxidation compared to the dry rolled corn treatments or the no dried distillers grains treatments, respectively. Feeding of dry rolled corn or diets without dried distillers grains maintained red color better during retail display. Choice- grade steaks had significantly higher levels of unsaturated fatty acids like 18:2 and total polyunsaturated fatty acids than Select- grade steaks but did not diff er in color stability or oxidation. These data indicate the longest shelf life will occur when cattle are fed diets containing dry rolled corn (versus steam flaked corn) or without dried distillers grains (versus with dried distillers grains) and that both steam flaked corn and distillers grains have a negative impact on shelf life. Quality grade did not affect color stability

A search for ^(70)Zn anomalies in meteorites

No ^(70)Zn isotopic anomalies have been detected in primitive meteorites to a level of precision of less than 40 parts per million (2σ). Any pre-existing nucleosynthetic anomaly on ^(70)Zn was averaged out by mixing in the solar nebula before planetary accretion in the solar system. Because neutron-rich nuclides ^(70)Zn and ^(60)Fe are produced by similar nucleosynthetic processes in core-collapse supernovae, the homogeneity of ^(70)Zn in meteorites limits the possible heterogeneity of extinct 60Fe radioactivity in the early solar system. Assuming that Fe and Zn have not been decoupled during incorporation into the solar system, the homogeneity of the ^(70)Zn/^(64)Zn ratio measured here implies that the ^(60)Fe/^(56)Fe ratio was homogenized to less than 15% dispersion before the formation of planetary bodies. The lack (Zn, Ni, Fe) or presence (Ti, Cr) of neutron-rich isotopic anomalies in the iron mass region may be controlled by the volatility of presolar carriers in the nebula

A Unified Framework for Producing CAI Melting, Wark-Lovering Rims and Bowl-Shaped CAIs

Calcium Aluminium Inclusions (CAIs) formed in the Solar System, some 4,567 million years ago. CAIs are almost always surrounded by Wark-Lovering Rims (WLRs), which are a sequence of thin, mono/bi-mineralic layers of refractory minerals, with a total thickness in the range of 1 to 100 microns. Recently, some CAIs have been found that have tektite-like bowl-shapes. To form such shapes, the CAI must have travelled through a rarefied gas at hypersonic speeds. We show how CAIs may have been ejected from the inner solar accretion disc via the centrifugal interaction between the solar magnetosphere and the inner disc rim. They subsequently punched through the hot, inner disc rim wall at hypersonic speeds. This re-entry heating partially or completely evaporated the CAIs. Such evaporation could have significantly increased the metal abundances of the inner disc rim. High speed movement through the inner disc produced WLRs. To match the observed thickness of WLRs required metal abundances at the inner disc wall that are of order ten times that of standard solar abundances. The CAIs cooled as they moved away from the protosun, the deduced CAI cooling rates are consistent with the CAI cooling rates obtained from experiment and observation. The speeds and gas densities required to form bowl-shaped CAIs are also consistent with the expected speeds and gas densities for larger, ~ 1 cm, CAIs punching through an inner accretion disc wall.Comment: 70 pages, 41 figure