Reducing the Effects of Unequal Number of Games on Rankings

Ranking is an important mathematical process in a variety of contexts such as information retrieval, sports and business. Sports ranking methods can be applied both in and beyond the context of athletics. In both settings, once the concept of a game has been defined, teams (or individuals) accumulate wins, losses, and ties, which are then factored into the ranking computation. Many settings involve an unequal number of games between competitors. This paper demonstrates how to adapt two sports rankings methods, the Colley and Massey ranking methods, to settings where an unequal number of games are played between the teams. In such settings, the standard derivations of the methods can produce nonsensical rankings. This paper introduces the idea of including a super-user into the rankings and considers the effect of this fictitious player on the ratings. We apply such techniques to rank batters and pitchers in Major League baseball, professional tennis players, and participants in a free online social game. The ideas introduced in this paper can further the scope that such methods are applied and the depth of insight they offer

Corynebacterium lipophiloflavum sp. nov. isolated from a patient with bacterial vaginosis

A unique coryneform bacterium was isolated from a patient with bacterial vaginosis. Chemotaxonomical investigations demonstrated that the unknown bacterium belonged to the genus Corynebacterium. The yellow-pigmented, slightly lipophilic, oxidative, urea-hydrolyzing bacterium could be phenotypically readily differentiated from the other members of the genus Corynebacterium. Comparative 16S rRNA gene analysis revealed that the bacterium represented a new subline within the genus Corynebacterium for which the name Corynebacterium lipophiloflavum sp. nov. is proposed. The type strain is CCUG 37336 (DSM 44291

Interaction of surface acoustic waves with a two-dimensional electron gas in the presence of spin splitting of the Landau bands

The absorption and variation of the velocity of a surface acoustic wave of frequency $f$= 30 MHz interacting with two-dimensional electrons are investigated in GaAs/AlGaAs heterostructures with an electron density $n=(1.3 - 2.8) \times 10^{11} cm^{-2}$ at $T$=1.5 - 4.2 K in magnetic fields up to 7 T. Characteristic features associated with spin splitting of the Landau level are observed. The effective g factor and the width of the spin-split Landau bands are determined: $g^* \simeq 5$ and $A$=0.6 meV. The greater width of the orbital-split Landau bands (2 meV) relative to the spin-split bands is attributed to different shielding of the random fluctuation potential of charged impurities by 2D electrons. The mechanisms of the nonlinearities manifested in the dependence of the absorption and the velocity increment of the SAW on the SAW power in the presence of spin splitting of the Landau levels are investigated.Comment: Revtex 5 pages + 5 EPS Figures, v.2 - minor corrections in text and pic

BMP signaling modulates hedgehog-induced secondary heart field proliferation

AbstractSonic hedgehog signaling in the secondary heart field has a clear role in cardiac arterial pole development. In the absence of hedgehog signaling, proliferation is reduced in secondary heart field progenitors, and embryos predominantly develop pulmonary atresia. While it is expected that proliferation in the secondary heart field would be increased with elevated hedgehog signaling, this idea has never been tested. We hypothesized that up-regulating hedgehog signaling would increase secondary heart field proliferation, which would lead to arterial pole defects. In culture, secondary heart field explants proliferated up to 6-fold more in response to the hedgehog signaling agonist SAG, while myocardial differentiation and migration were unaffected. Treatment of chick embryos with SAG at HH14, just before the peak in secondary heart field proliferation, resulted unexpectedly in stenosis of both the aortic and pulmonary outlets. We examined proliferation in the secondary heart field and found that SAG-treated embryos exhibited a much milder increase in proliferation than was indicated by the in vitro experiments. To determine the source of other signaling factors that could modulate increased hedgehog signaling, we co-cultured secondary heart field explants with isolated pharyngeal endoderm or outflow tract and found that outflow tract co-cultures prevented SAG-induced proliferation. BMP2 is made and secreted by the outflow tract myocardium. To determine whether BMP signaling could prevent SAG-induced proliferation, we treated explants with SAG and BMP2 and found that BMP2 inhibited SAG-induced proliferation. In vivo, SAG-treated embryos showed up-regulated BMP2 expression and signaling. Together, these results indicate that BMP signaling from the outflow tract modulates hedgehog-induced proliferation in the secondary heart field

Cold collisions of OH and Rb. I: the free collision

We have calculated elastic and state-resolved inelastic cross sections for cold and ultracold collisions in the Rb($^1 S$) + OH($^2 \Pi_{3/2}$) system, including fine-structure and hyperfine effects. We have developed a new set of five potential energy surfaces for Rb-OH($^2 \Pi$) from high-level {\em ab initio} electronic structure calculations, which exhibit conical intersections between covalent and ion-pair states. The surfaces are transformed to a quasidiabatic representation. The collision problem is expanded in a set of channels suitable for handling the system in the presence of electric and/or magnetic fields, although we consider the zero-field limit in this work. Because of the large number of scattering channels involved, we propose and make use of suitable approximations. To account for the hyperfine structure of both collision partners in the short-range region we develop a frame-transformation procedure which includes most of the hyperfine Hamiltonian. Scattering cross sections on the order of $10^{-13}$ cm$^2$ are predicted for temperatures typical of Stark decelerators. We also conclude that spin orientation of the partners is completely disrupted during the collision. Implications for both sympathetic cooling of OH molecules in an environment of ultracold Rb atoms and experimental observability of the collisions are discussed.Comment: 20 pages, 16 figure

Long beating wavelength in the Schwarz-Hora effect

Thirty years ago, H.Schwarz has attempted to modulate an electron beam with optical frequency. When a 50-keV electron beam crossed a thin crystalline dielectric film illuminated with laser light, electrons produced the electron-diffraction pattern not only at a fluorescent target but also at a nonfluorescent target. In the latter case the pattern was of the same color as the laser light (the Schwarz-Hora effect). This effect was discussed extensively in the early 1970s. However, since 1972 no reports on the results of further attempts to repeat those experiments in other groups have appeared, while the failures of the initial such attempts have been explained by Schwarz. The analysis of the literature shows there are several unresolved up to now contradictions between the theory and the Schwarz experiments. In this work we consider the interpretation of the long-wavelength spatial beating of the Schwarz-Hora radiation. A more accurate expression for the spatial period has been obtained, taking into account the mode structure of the laser field within the dielectric film. It is shown that the discrepancy of more than 10% between the experimental and theoretical results for the spatial period cannot be reduced by using the existing quantum models that consider a collimated electron beam.Comment: 3 pages, RevTe

Physical Electronics

Contains reports on three research projects