18,501 research outputs found
Hierarchical Bayesian Modeling of Hitting Performance in Baseball
We have developed a sophisticated statistical model for predicting the
hitting performance of Major League baseball players. The Bayesian paradigm
provides a principled method for balancing past performance with crucial
covariates, such as player age and position. We share information across time
and across players by using mixture distributions to control shrinkage for
improved accuracy. We compare the performance of our model to current
sabermetric methods on a held-out season (2006), and discuss both successes and
limitations
Was the Universe Reionized by Massive Population-III Stars?
The WMAP satellite has measured a large optical depth to electron scattering
after cosmological recombination of 0.17+-0.04, implying significant
reionization of the primordial gas only ~200 million years after the big bang.
However, the most recent overlap of intergalactic HII regions must have occured
at z<9 based on the Lyman-alpha forest constraint on the thermal history of the
intergalactic medium. Here we argue that a first generation of metal-free stars
with a heavy (rather than Salpeter) mass function is therefore required to
account for much of the inferred optical depth. This conclusion holds if
feedback regulates star formation in early dwarf galaxies as observed in
present-day dwarfs.Comment: 4 pages, 1 figure, replaced to match version accepted by ApJ Letter
Correlations of a bound interface over a random substrate
The correlation function of a one-dimensional interface over a random
substrate, bound to the substrate by a pressure term, is studied by Monte-Carlo
simulation. It is found that the height correlation , averaged
over the substrate disorder, fits a form exp(-(j/b)^c) to a surprising
precision in the full range of j where the correlation is non-negligible. The
exponent c increases from 1.0 to 1.5 when the interface tension is taken larger
and larger.Comment: 7 pages, 5 figure
Apparent first-order wetting and anomalous scaling in the two-dimensional Ising model
The global phase diagram of wetting in the two-dimensional (2d) Ising model
is obtained through exact calculation of the surface excess free energy.
Besides a surface field for inducing wetting, a surface-coupling enhancement is
included. The wetting transition is critical (second order) for any finite
ratio of surface coupling J_s to bulk coupling J, and turns first order in the
limit J_s/J to infinity. However, for J_s/J much larger than 1 the critical
region is exponentially small and practically invisible to numerical studies. A
distinct pre-asymptotic regime exists in which the transition displays
first-order character. Surprisingly, in this regime the surface susceptibility
and surface specific heat develop a divergence and show anomalous scaling with
an exponent equal to 3/2.Comment: This new version presents the exact solution and its properties
whereas the older version was based on an approximate numerical study of the
mode
Non-equilibrium Dynamics of Finite Interfaces
We present an exact solution to an interface model representing the dynamics
of a domain wall in a two-phase Ising system. The model is microscopically
motivated, yet we find that in the scaling regime our results are consistent
with those obtained previously from a phenomenological, coarse-grained Langevin
approach.Comment: 12 pages LATEX (figures available on request), Oxford preprint
OUTP-94-07
The Eastern and Western “Scriptures” for Postmodernity: toward a Unified Ethos in Religion, Science, and Philosophy
Postmodernism underscores the impossibility of discovering any truth. One can at best only construct a truth capable of ensuring optimal wellbeing for everyone. The traditional undifferentiated efforts of science, religion, and philosophy, which became compartmentalized in the Enlightenment, are again streamlined in postmodernity. A new ethics is the point of convergence for these three disciplines to fashion a sustainable universe. Yet Nagarjuna, who has long been overlooked, advocates a passage beyond language. It is an initiative that finds resonance in some postmodern masters as well
Solving for Micro- and Macro- Scale Electrostatic Configurations Using the Robin Hood Algorithm
We present a novel technique by which highly-segmented electrostatic
configurations can be solved. The Robin Hood method is a matrix-inversion
algorithm optimized for solving high density boundary element method (BEM)
problems. We illustrate the capabilities of this solver by studying two
distinct geometry scales: (a) the electrostatic potential of a large volume
beta-detector and (b) the field enhancement present at surface of electrode
nano-structures. Geometries with elements numbering in the O(10^5) are easily
modeled and solved without loss of accuracy. The technique has recently been
expanded so as to include dielectrics and magnetic materials.Comment: 40 pages, 20 figure
Lorentz Violation for Photons and Ultra-High Energy Cosmic Rays
Lorentz symmetry breaking at very high energies may lead to photon dispersion
relations of the form omega^2=k^2+xi_n k^2(k/M_Pl)^n with new terms suppressed
by a power n of the Planck mass M_Pl. We show that first and second order terms
of size xi_1 > 10^(-14) and xi_2 < -10^(-6), respectively, would lead to a
photon component in cosmic rays above 10^(19) eV that should already have been
detected, if corresponding terms for electrons and positrons are significantly
smaller. This suggests that Lorentz invariance breakings suppressed up to
second order in the Planck scale are unlikely to be phenomenologically viable
for photons.Comment: 4 revtex pages, 3 postscript figures included, version published in
PR
Cosmological Origin of the Stellar Velocity Dispersions in Massive Early-Type Galaxies
We show that the observed upper bound on the line-of-sight velocity
dispersion of the stars in an early-type galaxy, sigma<400km/s, may have a
simple dynamical origin within the LCDM cosmological model, under two main
hypotheses. The first is that most of the stars now in the luminous parts of a
giant elliptical formed at redshift z>6. Subsequently, the stars behaved
dynamically just as an additional component of the dark matter. The second
hypothesis is that the mass distribution characteristic of a newly formed dark
matter halo forgets such details of the initial conditions as the stellar
"collisionless matter" that was added to the dense parts of earlier generations
of halos. We also assume that the stellar velocity dispersion does not evolve
much at z<6, because a massive host halo grows mainly by the addition of
material at large radii well away from the stellar core of the galaxy. These
assumptions lead to a predicted number density of ellipticals as a function of
stellar velocity dispersion that is in promising agreement with the Sloan
Digital Sky Survey data.Comment: ApJ, in press (2003); matches published versio
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