A new method for obtaining the star formation law in galaxies

We present a new observational method to evaluate the star formation law as formulated by Schmidt: the power-law expression assumed to relate the rate of star formation in a volume of space to the local total gas volume density. Volume densities in the clouds surrounding an OB association are determined with a simple model which considers atomic hydrogen as a photodissociation product on cloud surfaces. The photodissociating flux incident on the cloud is computed from the far-UV luminosity of the OB association and the geometry. We have applied this "PDR Method" to a sample of star-forming regions in M33 using VLA 21-cm data for the HI and GALEX imagery in the far-UV. It provides an estimate of the total volume density of hydrogen (atomic + molecular) in the gas clouds surrounding the young star cluster. A logarithmic graph of the cluster UV luminosity versus the surrounding gas density is a direct measure of the star formation law. However, this plot is severely affected by observational selection, rendering large areas of the diagram inaccessible to the data. An ordinary least-squares regression fit therefore gives a strongly biased result. Its slope primarily reflects the boundary defined when the 21-cm line becomes optically thick, no longer reliably measuring the HI column density. We use a maximum-likelihood statistical approach which can deal with truncated and skewed data, taking into account the large uncertainties in the derived total gas densities. The exponent we obtain for the Schmidt law in M33 is 1.4 \pm 0.2.Comment: Accepted for publication in Ap

A bound on the effective gravitational coupling from semiclassical black holes

We show that the existence of semiclassical black holes of size as small as a minimal length scale $l_{UV}$ implies a bound on a gravitational analogue of 't-Hooft's coupling $\lambda_G(l)\equiv N(l) G_N/l^2$ at all scales $l \ge l_{UV}$. The proof is valid for any metric theory of gravity that consistently extends Einstein's gravity and is based on two assumptions about semiclassical black holes: i) that they emit as black bodies, and ii) that they are perfect quantum emitters. The examples of higher dimensional gravity and of weakly coupled string theory are used to explicitly check our assumptions and to verify that the proposed bound holds. Finally, we discuss some consequences of the bound for theories of quantum gravity in general and for string theory in particular.Comment: 16 page

Testing chromatic adaption models using object colors

The objective of this research was to determine which published chromatic adaptation model performed best under a single set of conditions. Previous research has been conducted to study chromatic adaptation, develop models and to indirectly test those models. This research directly tested the performance of these models using printed, simple-field, object colors through a successive-ganzfe/cf haploscopic, paired comparison, matching experiment. The chromatic adaptation models tested were CIELAB, CIELUV, Fairchild \u2791, Hunt \u2791, LABHNU2, Nayatani et al. \u2790 and von Kries. The test illuminant was incandescent at 231 lux. Model predictions were calculated for the reference simulated daylight at 2,396 lux. The Hunt model was found to predict the best matches for each color sample, and across all ten color centers. The other models\u27 performances were significantly different, but not nearly as good. However, two versions of the Hunt model were tested, and neither performed consistently, although they both performed better than the other models. For a wide chromatic range of object colors, an alternative form of the Hunt model is suggested for implementing the prediction of corresponding colors

N-Relaxion: Large Field Excursions from a Few Site Relaxion Model

Relaxion models are an interesting new avenue to explain the radiative stability of the Standard Model scalar sector. They require very large field excursions, which are difficult to generate in a consistent UV completion and to reconcile with the compact field space of the relaxion. We propose an N-site model which naturally generates the large decay constant needed to address these issues. Our model offers distinct advantages with respect to previous proposals: the construction involves non-abelian fields, allowing for controlled high energy behaviour and more model building possibilities, both in particle physics and inflationary models, and also admits a continuum limit when the number of sites is large, which may be interpreted as a warped extra dimension.Comment: 7 pages, 2 figures; v2: version to appear in PR

The Federal Circuit\u27s Summary Affirmance Habit

The Federal Circuit is certainly unique among the circuit courts of appeals. Its exclusive jurisdiction over patents places it in a powerful position. But with that power comes a responsibility to oversee the development of the law. And in the last decade, the court has fallen short of fulfilling this obligation—particularly with regard to clarifying provisions of the America Invents Act. The court has repeatedly disregarded important questions of law by use of Rule 36 summary affirmance. Though other courts of appeals regularly use summary disposition as a means of dealing with burgeoning dockets, the Federal Circuit uses summary affirmance at a much higher rate and to dismiss unresolved legal questions. This Comment explores some of the possible reasons why the court uses summary affirmance so frequently. After discussing summary disposition more generally, it specifically presents the theory of certproofing—or avoiding Supreme Court review—as one possible explanation. It concludes by offering some solutions to curb the court’s summary affirmance habit

Defensive Patent Litigation Strategy for Chinese Companies: A Review of the Extraterritorial Reach of the United States Patent Laws

China has experienced an extraordinary transformation from a poor, developing nation into a global economic power. With China becoming one of the U.S.’s largest trading partners, however, Chinese companies have become increasingly enmeshed in U.S. patent litigations. Although the U.S. patent laws are intended only to govern conduct within the nation’s borders, the line between domestic and foreign economic activities has become increasingly blurred. Modern sales transactions often span multiple countries, and in such situations, it may not be clear whether the U.S. patent laws apply. For Chinese companies facing exposure to U.S. patent litigations, it is critical to understand what qualifies as an infringing “sale” and “offer to sell” within the U.S. for purposes of determining patent infringement liability and damages. It is also important to understand the circumstances under which a foreign company may be liable for patent infringement in the U.S. if products that are manufactured and sold overseas independently make their way into the U.S. This Article addresses the foregoing issues against the backdrop of the extraterritorial reach and limitations of the U.S. patent laws