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

Large Effects of Electric Fields on Atom-Molecule Collisions at Millikelvin Temperatures

Controlling interactions between cold molecules using external fields can elucidate the role of quantum mechanics in molecular collisions. We create a new experimental platform in which ultracold rubidium atoms and cold ammonia molecules are separately trapped by magnetic and electric fields and then combined to study collisions. We observe inelastic processes that are faster than expected from earlier field-free calculations. We use quantum scattering calculations to show that electric fields can have a major effect on collision outcomes, even in the absence of dipole-dipole interactions.Comment: 5 pages, 4 figure

Calculating energy levels of isomerizing tetra-atomic molecules. I. The rovibrational bound states of Ar2HF

A general, six-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is developed. The resulting program is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the Ar2HF van der Waals trimer is presented in which the HF intramolecular stretching coordinate is separated out adiabatically and is not treated explicitly. Vibrational term values up to about 100 cm−1 with absolute convergence to better than 0.1 cm−1 are reported. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than hitherto. States that sample Ar–Ar–HF linear configurations and approach Ar–HF–Ar linear configurations are characterized for the first time. Results for total angular momentumJ=0 and 1 provide the first accurate calculations of rotational constants for this system. The rotational constants for the HF bending states of Ar2HF in the ground and first vibrationally excited states of the HF monomer are in good agreement with experiment, confirming the accuracy of the potential used in this work

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

Immobilization of simulated high-level radioactive waste in borosilicate glass: Pilot scale demonstrations

The Integrated DWPF Melter System (IDMS), operated by the Savannah River Laboratory, is a pilot scale facility used in support of the start-up and operation of the Department of Energy's Defense Waste Processing Facility. The IDMS has successfully demonstrated, on an engineering scale (one-fifth), that simulated high level radioactive waste (HLW) sludge can be chemically treated with formic acid to adjust both its chemical and physical properties, and then blended with simulated precipitate hydrolysis aqueous (PHA) product and borosilicate glass frit to produce a melter feed which can be processed into a durable glass product. The simulated sludge, PHA and frit were blended, based on a product composition program, to optimize the loading of the waste glass as well as to minimize those components which can cause melter processing and/or glass durability problems. During all the IDMS demonstrations completed thus far, the melter feed and the resulting glass that has been produced met all the required specifications, which is very encouraging to future DWPF operations. The IDMS operations also demonstrated that the volatile components of the melter feed (e.g., mercury, nitrogen and carbon, and, to a lesser extent, chlorine, fluorine and sulfur) did not adversely affect the melter performance or the glass product

COMPARZ Post Hoc Analysis: Characterizing Pazopanib Responders With Advanced Renal Cell Carcinoma

Background: The phase III COMPARZ study showed noninferior efficacy of pazopanib versus sunitinib in advanced renal cell carcinoma. In this COMPARZ post hoc analysis we characterized pazopanib responders, patient subgroups with better outcomes, and the effect of dose modification on efficacy and safety. Patients and Methods: Patients were randomized to pazopanib 800 mg/d (n = 557) or sunitinib 50 mg/d, 4 weeks on/2 weeks off (n = 553). Secondary end points included time to complete response (CR)/partial response (PR); the proportion of patients with CR/PR ≥10 months and progression-free survival (PFS) ≥10 months; efficacy in patients with baseline metastasis; and logistic regression analyses of patient characteristics associated with CR/PR ≥10 months. Median PFS, objective response rate (ORR), and safety were evaluated in patients with or without dose reductions or interruptions lasting ≥7 days. Results: Median time to response was numerically shorter for patients treated with pazopanib versus sunitinib (11.9 vs. 17.4 weeks). Similar percentages of pazopanib and sunitinib patients had CR/PR ≥10 months (14% and 13%, respectively), and PFS ≥10 months (31% and 34%, respectively). For patients without versus with adverse event (AE)-related dose reductions, median PFS, median overall survival, and ORR were 7.3 versus 12.5 months, 21.7 versus 36.8 months, and 22% versus 42% (all P <.0001) for pazopanib, and 5.5 versus 13.8 months, 18.1 versus 38.0 months, and 16% versus 34% (all P <.0001) for sunitinib; results were similar for dose interruptions. Conclusion: Dose modifications when required because of AEs were associated with improved efficacy, suggesting that AEs might be used as a surrogate marker of adequate dosing for individual patients

Physical Electronics

Contains reports on three research projects

A Fermi-degenerate three-dimensional optical lattice clock

Strontium optical lattice clocks have the potential to simultaneously interrogate millions of atoms with a high spectroscopic quality factor of $4 \times 10^{-17}$. Previously, atomic interactions have forced a compromise between clock stability, which benefits from a large atom number, and accuracy, which suffers from density-dependent frequency shifts. Here, we demonstrate a scalable solution which takes advantage of the high, correlated density of a degenerate Fermi gas in a three-dimensional optical lattice to guard against on-site interaction shifts. We show that contact interactions are resolved so that their contribution to clock shifts is orders of magnitude lower than in previous experiments. A synchronous clock comparison between two regions of the 3D lattice yields a $5 \times 10^{-19}$ measurement precision in 1 hour of averaging time.Comment: 19 pages, 4 figures; Supplementary Material