A relativistic analysis of clock synchronization

The relativistic conversion between coordinate time and atomic time is reformulated to allow simpler time calculations relating analysis in solar-system barycentric coordinates (using coordinate time) with earth-fixed observations (measuring earth-bound proper time or atomic time.) After an interpretation of terms, this simplified formulation, which has a rate accuracy of about 10 to the minus 15th power, is used to explain the conventions required in the synchronization of a world wide clock network and to analyze two synchronization techniques-portable clocks and radio interferometry. Finally, pertinent experiment tests of relativity are briefly discussed in terms of the reformulated time conversion

Source structure errors in radio-interferometric clock synchronization for ten measured distributions

The effects of source structure on radio interferometry measurements were investigated. The brightness distribution measurements for ten extragalactic sources were analyzed. Significant results are reported

Living Originalism

Originalists routinely argue that originalism is the only coherent and legitimate theory of constitutional interpretation. This Article endeavors to undermine those claims by demonstrating that, despite the suggestion of originalist rhetoric, originalism is not a single, coherent, unified theory of constitutional interpretation, but is rather a disparate collection of distinct constitutional theories that share little more than a misleading reliance on a common label. Originalists generally agree only on certain very broad precepts that serve as the fundamental underlying principles of constitutional interpretation: specifically, that the writtenness of the Constitution necessitates a fixed constitutional meaning, and that courts that see themselves as empowered to give the Constitution some avowedly different meaning are behaving contrary to law. Originalists have been able to achieve agreement on these broad underlying principles, but they have often viewed as unduly narrow and mistaken the understanding held by the original originalists-the framers of originalism, if you will-as to how those principles must be put into action. And originalists disagree so profoundly amongst themselves about how to effectuate those underlying principles that over time they have articulated-and continue to articulate-a wide array of strikingly disparate, and mutually exclusive, constitutional theories. In this regard, originalists have followed a living, evolving approach to constitutional interpretation. Our account of originalism\u27s evolution-and of the extensive disagreement among originalists today-undermines originalists\u27 normative claims about the superiority of their approach. Originalists\u27 claims about the unique and exclusive legitimacy of their theory-that originalism self-evidently represents the correct method of constitutional interpretation-founder when one considers that originalists themselves cannot even begin to agree on what their correct approach actually entails. And their claims that originalism has a unique ability to produce determinate and fixed constitutional meaning, and thus that only originalism properly treats the Constitution as law and properly constrains judges from reading their own values into the Constitution, stumble when one considers the rapid evolution and dizzying array of versions of originalism; because each version has the potential to produce a different constitutional meaning, the constitutional meaning that a committed originalist judge would find turns out to be anything but fixed. As originalism evolves, the constitutional meanings that it produces evolve along with it. Today\u27s originalists not only reach results markedly different from those originalists reached thirty years ago, but also produce widely divergent results amongst themselves. Judges committed to the originalist enterprise thus have significant discretion to choose (consciously or subconsciously) the version of originalism that is most likely to dictate results consistent with their own preferences. As such, originalism suffers from the very flaws that its proponents have identified in its alternatives

Efficient two-sample functional estimation and the super-oracle phenomenon

We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide generality, a weighted nearest neighbour estimator is efficient, in the sense of achieving the local asymptotic minimax lower bound. Moreover, we also prove a corresponding central limit theorem, which facilitates the construction of asymptotically valid confidence intervals for the functional, having asymptotically minimal width. One interesting consequence of our results is the discovery that, for certain functionals, the worst-case performance of our estimator may improve on that of the natural `oracle' estimator, which is given access to the values of the unknown densities at the observations.Comment: 82 page

Multiplex electric discharge gas laser system

A multiple pulse electric discharge gas laser system is described in which a plurality of pulsed electric discharge gas lasers are supported in a common housing. Each laser is supplied with excitation pulses from a separate power supply. A controller, which may be a microprocessor, is connected to each power supply for controlling the application of excitation pulses to each laser so that the lasers can be fired simultaneously or in any desired sequence. The output light beams from the individual lasers may be combined or utilized independently, depending on the desired application. The individual lasers may include multiple pairs of discharge electrodes with a separate power supply connected across each electrode pair so that multiple light output beams can be generated from a single laser tube and combined or utilized separately