On Minimum Violations Ranking in Paired Comparisons

Ranking a set of objects from the most dominant one to the least, based on the results of paired comparisons, proves to be useful in many contexts. Using the rankings of teams or individuals players in sports to seed tournaments is an example. The quality of a ranking is often evaluated by the number of violations, cases in which an object is ranked lower than another that it has dominated in a comparison, that it contains. A minimum violations ranking (MVR) method, as its name suggests, searches specifically for rankings that have the minimum possible number of violations which may or may not be zero. In this paper, we present a method based on statistical physics that overcomes conceptual and practical difficulties faced by earlier studies of the problem.Comment: 10 pages, 10 figures; typos corrected (v2

A network-based ranking system for American college football

American college football faces a conflict created by the desire to stage national championship games between the best teams of a season when there is no conventional playoff system to decide which those teams are. Instead, ranking of teams is based on their record of wins and losses during the season, but each team plays only a small fraction of eligible opponents, making the system underdetermined or contradictory or both. It is an interesting challenge to create a ranking system that at once is mathematically well-founded, gives results in general accord with received wisdom concerning the relative strengths of the teams, and is based upon intuitive principles, allowing it to be accepted readily by fans and experts alike. Here we introduce a one-parameter ranking method that satisfies all of these requirements and is based on a network representation of college football schedules.Comment: 15 pages, 3 figure

Upper bounds on the first eigenvalue for a diffusion operator via Bakry-\'{E}mery Ricci curvature II

Let $L=\Delta-\nabla\varphi\cdot\nabla$ be a symmetric diffusion operator with an invariant measure $d\mu=e^{-\varphi}dx$ on a complete Riemannian manifold. In this paper we prove Li-Yau gradient estimates for weighted elliptic equations on the complete manifold with $|\nabla \varphi|\leq\theta$ and $\infty$-dimensional Bakry-\'{E}mery Ricci curvature bounded below by some negative constant. Based on this, we give an upper bound on the first eigenvalue of the diffusion operator $L$ on this kind manifold, and thereby generalize a Cheng's result on the Laplacian case (Math. Z., 143 (1975) 289-297).Comment: Final version. The original proof of Theorem 2.1 using Li-Yau gradient estimate method has been moved to the appendix. The new proof is simple and direc

Element-Specific Depth Profile of Magnetism and Stoichiometry at the La0.67Sr0.33MnO3/BiFeO3 Interface

Depth-sensitive magnetic, structural and chemical characterization is important in the understanding and optimization of novel physical phenomena emerging at interfaces of transition metal oxide heterostructures. In a simultaneous approach we have used polarized neutron and resonant X-ray reflectometry to determine the magnetic profile across atomically sharp interfaces of ferromagnetic La0.67Sr0.33MnO3 / multiferroic BiFeO3 bi-layers with sub-nanometer resolution. In particular, the X-ray resonant magnetic reflectivity measurements at the Fe and Mn resonance edges allowed us to determine the element specific depth profile of the ferromagnetic moments in both the La0.67Sr0.33MnO3 and BiFeO3 layers. Our measurements indicate a magnetically diluted interface layer within the La0.67Sr0.33MnO3 layer, in contrast to previous observations on inversely deposited layers. Additional resonant X-ray reflection measurements indicate a region of an altered Mn- and O-content at the interface, with a thickness matching that of the magnetic diluted layer, as origin of the reduction of the magnetic moment.Comment: 13 pages, 4 figures, supplemental material include

Observation of an atomic exchange bias effect in DyCo4 film

The fundamental important and technologically widely employed exchange bias effect occurs in general in bilayers of magnetic thin films consisting of antiferromagnetic and ferromagnetic layers where the hard magnetization behavior of an antiferromagnetic thin film causes a shift in the magnetization curve of a soft ferromagnetic film. The minimization of the single magnetic grain size to increase the storage density and the subsequent demand for magnetic materials with very high magnetic anisotropy requires a system with high HEB. Here we report an extremely high HEB of 4 Tesla observed in a single amorphous DyCo4 film close to room temperature. The origin of the exchange bias can be associated with the variation of the magnetic behavior from the surface towards the bulk part of the film revealed by X ray absorption spectroscopy and X ray magnetic circular dichroism techniques utilizing the bulk sensitive transmission and the surface sensitive total electron yield modes. The competition between the atomic exchange coupling in the single film and the Zeeman interaction lead to an intrinsic exchanged coupled system and the so far highest exchange bias effect HEB amp; 8201; amp; 8201;4 Tesla reported in a single film, which is accommodated by a partial domain wall formatio

Mrk 421, Mrk 501, and 1ES 1426+428 at 100 GeV with the CELESTE Cherenkov Telescope

We have measured the gamma-ray fluxes of the blazars Mrk 421 and Mrk 501 in the energy range between 50 and 350 GeV (1.2 to 8.3 x 10^25 Hz). The detector, called CELESTE, used first 40, then 53 heliostats of the former solar facility "Themis" in the French Pyrenees to collect Cherenkov light generated in atmospheric particle cascades. The signal from Mrk 421 is often strong. We compare its flux with previously published multi-wavelength studies and infer that we are straddling the high energy peak of the spectral energy distribution. The signal from Mrk 501 in 2000 was weak (3.4 sigma). We obtain an upper limit on the flux from 1ES 1426+428 of less than half that of the Crab flux near 100 GeV. The data analysis and understanding of systematic biases have improved compared to previous work, increasing the detector's sensitivity.Comment: 15 pages, 14 figures, accepted to A&A (July 2006) August 19 -- corrected error in author lis

Un système d'acquisition de données pour l'analyse en ligne des photographies de grandes chambres à bulles

Ce travail présente le système d'analyse des clichés de grandes chambres à bulles telles que Gargamelle et BEBC, réalisé au Groupe de Chambre à Bulles à Liquide Lourd à l'aide d'appareils de projection mis en ligne sur ordinateur CDC 1700. Ce travail présente les caractéristiques générales de ces appareils ainsi que celles de l'ordinateur et développe la conception et les fonctions des programmes d'analyse des photographies : prémesures, mesures et gestion des données. L'ensemble du système d'acquisition de données fonctionne dans un contexte de multiprogrammation en temps réel

Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds

Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property.Comment: 49 page