Approximating Nearest Neighbor Distances

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the Euclidean cluster diameter is large. Therefore, it is preferred to assign smaller costs to the paths that stay close to the input points. In this paper, we consider the most natural metric with this property, which we call the nearest neighbor metric. Given a point set P and a path $\gamma$, our metric charges each point of $\gamma$ with its distance to P. The total charge along $\gamma$ determines its nearest neighbor length, which is formally defined as the integral of the distance to the input points along the curve. We describe a $(3+\varepsilon)$-approximation algorithm and a $(1+\varepsilon)$-approximation algorithm to compute the nearest neighbor metric. Both approximation algorithms work in near-linear time. The former uses shortest paths on a sparse graph using only the input points. The latter uses a sparse sample of the ambient space, to find good approximate geodesic paths.Comment: corrected author nam

Vacuum-Induction, Vacuum-Arc, and Air-Induction Melting of a Complex Heat-Resistant Alloy

The relative hot-workability and creep-rupture properties at 1600 F of a complex 55Ni-20Cr-15Co-4Mo-3Ti-3Al alloy were evaluated for vacuum-induction, vacuum-arc, and air-induction melting. A limited study of the role of oxygen and nitrogen and the structural effects in the alloy associated with the melting process was carried out. The results showed that the level of boron and/or zirconium was far more influential on properties than the melting method. Vacuum melting did reduce corner cracking and improve surface during hot-rolling. It also resulted in more uniform properties within heats. The creep-rupture properties were slightly superior in vacuum heats at low boron plus zirconium or in heats with zirconium. There was little advantage at high boron levels and air heats were superior at high levels of boron plus zirconium. Vacuum heats also had fewer oxide and carbonitride inclusions although this was a function of the opportunity for separation of the inclusions from high oxygen plus nitrogen heats. The removal of phosphorous by vacuum melting was not found to be related to properties. Oxygen plus nitrogen appeared to increase ductility in creep-rupture tests suggesting that vacuum melting removes unidentified elements detrimental to ductility. Oxides and carbonitrides in themselves did not initiate microcracks. Carbonitrides in the grain boundaries of air heats did initiate microcracks. The role of microcracking from this source and as a function of oxygen and nitrogen content was not clear. Oxygen and nitrogen did intensify corner cracking during hot-rolling but were not responsible for poor surface which resulted from rolling heats melted in air

Influence of Crucible Materials on High-temperature Properties of Vacuum-melted Nickel-chromium-cobalt Alloy

A study of the effect of induction-vacuum-melting procedure on the high-temperature properties of a titanium-and-aluminum-hardened nickel-base alloy revealed that a major variable was the type of ceramic used as a crucible. Reactions between the melt and magnesia or zirconia crucibles apparently increased high-temperature properties by introducing small amounts of boron or zirconium into the melts. Heats melted in alumina crucibles had relatively low rupture life and ductility at 1,600 F and cracked during hot-working as a result of deriving no boron or zirconium from the crucible

Boron and Zirconium from Crucible Refractories in a Complex Heat-Resistant Alloy

In a laboratory study of the factors involved in the influence of induction vacuum melting on 55ni-20cr-15co-4mo-3ti-3al heat resistant alloy, it was found that the major factor was the type of ceramic used as the crucible. The study concluded that trace amounts of boron or zirconium derived from reaction of the melt with the crucible refactories improved creep-rupture properties at 1,600 degrees F. Boron was most effective and, in addition, markedly improved hot-workability

Kepler Observations of the Three Pre-Launch Exoplanet Candidates: Discover of Two Eclipsing Binaries and a New Exoplanet

Three transiting exoplanet candidate stars were discovered in a ground-based photometric survey prior to the launch of NASA's Kepler mission. Kepler observations of them were obtained during Quarter 1 of the Kepler mission. All three stars are faint by radial velocity follow-up standards, so we have examined these candidates with regard to eliminating false positives and providing high confidence exoplanet selection. We present a first attempt to exclude false positives for this set of faint stars without high-resolution radial velocity analysis. This method of exoplanet confirmation will form a large part of the Kepler mission follow-up for Jupiter-sized exoplanet candidates orbiting faint stars. Using the Kepler light curves and pixel data, as well as medium-resolution reconnaissance spectroscopy and speckle imaging, we find that two of our candidates are binary stars. One consists of a late-F star with an early M companion, while the other is a K0 star plus a late M-dwarf/brown dwarf in a 19 day elliptical orbit. The third candidate (BOKS-1) is an r = 15 G8V star hosting a newly discovered exoplanet with a radius of 1.12 R_(Jupiter) in a 3.9 day orbit

The design and realization of uniplanar CPW fed PICA slot antennas

In modern wireless communication system design, antennas with wide impedance bandwidth are desirable for numerous reasons. An antenna with a wide impedance bandwidth may be used for transmission and reception of multiple narrowband services in a multi-purpose platform. Alternatively a single wideband service may be of interest for various radar and imaging applications, or for impulse based radio communications in the FCC ultra-wideband (UWB) regime from 3.1 GHz to 10.6 GHz

Mental Processes and Strategic Equilibration: An fMRI Study of Selling Strategies in Second Price Auctions

This study is the first to attempt to isolate a relationship between cognitive activity and equilibration to a Nash Equilibrium. Subjects, while undergoing fMRI scans of brain activity, participated in second price auctions against a single competitor following predetermined strategy that was unknown to the subject. For this auction there is a unique strategy that will maximize the subjects' earnings, which is also a Nash equilibrium of the associated game theoretic model of the auction. As is the case with all games, the bidding strategies of subjects participating in second price auctions most often do not reflect the equilibrium bidding strategy at first but with experience, typically exhibit a process of equilibration, or convergence toward the equilibrium. This research is focused on the process of convergence