On the distribution of career longevity and the evolution of home run prowess in professional baseball

Statistical analysis is a major aspect of baseball, from player averages to historical benchmarks and records. Much of baseball fanfare is based around players exceeding the norm, some in a single game and others over a long career. Career statistics serve as a metric for classifying players and establishing their historical legacy. However, the concept of records and benchmarks assumes that the level of competition in baseball is stationary in time. Here we show that power-law probability density functions, a hallmark of many complex systems that are driven by competition, govern career longevity in baseball. We also find similar power laws in the density functions of all major performance metrics for pitchers and batters. The use of performance-enhancing drugs has a dark history, emerging as a problem for both amateur and professional sports. We find statistical evidence consistent with performance-enhancing drugs in the analysis of home runs hit by players in the last 25 years. This is corroborated by the findings of the Mitchell Report [1], a two-year investigation into the use of illegal steroids in major league baseball, which recently revealed that over 5 percent of major league baseball players tested positive for performance-enhancing drugs in an anonymous 2003 survey.Comment: 5 pages, 5 figures, 2-column revtex4 format. Revision has change of title, a figure added, and minor changes in response to referee comment

A Scaling Behavior of Spectral Weight Changes in Perovskite Manganites La_{0.7-y}Pr_{y}Ca_{0.3}MnO_3

Optical conductivity spectra of La_{0.7-y}Pr_{y}Ca_{0.3}MnO_3 were systematically investigated. For metallic samples, the spectral weight below 0.5 eV, whose magnitude can be represented by the effective carrier number N_{eff}(0.5 eV), increases as temperature becomes lower. Regardless of the Pr doping, all the measured values of N_{eff}(0.5 eV)/T_C fall into one scaling curve. This scaling behavior could be explained by the theoretical model by Roeder et al. [Phys. Rev. Lett. 76, 1356 (1996)], which includes spin double exchange and Jahn-Teller lattice coupling to holes. With the Pr doping, far-infrared conductivities were found to be suppressed, probably due to the Anderson localization.Comment: Latex 2e, 8 pages including 4 postscript figures, submitted at Apr 2

Optical Studies of a Layered Manganite La_{1.2}Sr_{1.8}Mn_2O_7 : Polaron Correlation Effect

Optical conductivity spectra of a cleaved ab-plane of a La_{1.2}Sr_{1.8}Mn_2O_7 single crystal exhibit a small polaron absorption band in the mid-infrared region at overall temperatures. With decreasing temperature (T) to Curie temperature (T_C), the center frequency of the small polaron band moves to a higher frequency, resulting in a gap-like feature, and that it collapses to a lower frequency below T_C. Interestingly, with decreasing T, the stretching phonon mode hardens above T_C and softens below T_C. These concurring changes of lattice and electronic structure indicate that short range polaron correlation exist above T_C but disappear with a magnetic ordering.Comment: 4 pages including 5 figures. submitted to Phys. Rev.

Beam profile measurements at 40 MHz in the PS to SPS transfer channel

Bunch to bunch beam profile measurements provide a valuable tool to control the injection lines to the SPS. A fast profile monitor based on a 2.5 µm Mylar coated with Aluminium Optical Transition Radiation (OTR) radiator, has been developed, installed and tested in the transfer line between the PS and SPS. The OTR beam image is focused onto a fast Linear Multianode Photo Multiplier Tube and the associated electronics sample and store profiles every 25 ns. The paper describes the detector design, the electronic processing, and presents the results of different measurements made with bunches of 109-1011 protons at 26 GeV, and bunches of 106 Pb82 ions at 5.11 GeV/u

Spin/Orbital Pattern-Dependent Polaron Absorption in Nd(1-x)Sr(x)MnO3

We investigated optical properties of Nd(1-x)Sr(x)MnO3 (x= 0.40, 0.50, 0.55, and 0.65) single crystals. In the spin/orbital disordered state, their conductivity spectra look quite similar, and the strength of the mid-infrared absorption peak is proportional to x(1-x) consistent with the polaron picture. As temperature lowers, the Nd(1-x)Sr(x)MnO3 samples enter into various spin/orbital ordered states, whose optical responses are quite different. These optical responses can be explained by the spin/orbital ordering pattern-dependent polaron hopping.Comment: 3 figures (gzipped

Polaron Absorption in a Perovskite Manganite La0.7Ca0.3MnO3

Temperature dependent optical conductivity spectra of a La0.7Ca0.3MnO3 (LCMO) sample were measured. In the metallic regime at very low temperatures, they clearly showed two types of absorption features, i.e., a sharp Drude peak and a broad mid-infrared absorption band, which could be explained as coherent and incoherent bands of a large lattice polaron. This elementary excitation in LCMO was found to be in a strong coupling regime and to have interactions with the spin degree of freedom.Comment: 4 pages and separate 4 figure