60,454 research outputs found
Uniform convergence of Vapnik--Chervonenkis classes under ergodic sampling
We show that if is a complete separable metric space and
is a countable family of Borel subsets of with
finite VC dimension, then, for every stationary ergodic process with values in
, the relative frequencies of sets converge
uniformly to their limiting probabilities. Beyond ergodicity, no assumptions
are imposed on the sampling process, and no regularity conditions are imposed
on the elements of . The result extends existing work of Vapnik
and Chervonenkis, among others, who have studied uniform convergence for i.i.d.
and strongly mixing processes. Our method of proof is new and direct: it does
not rely on symmetrization techniques, probability inequalities or mixing
conditions. The uniform convergence of relative frequencies for VC-major and
VC-graph classes of functions under ergodic sampling is established as a
corollary of the basic result for sets.Comment: Published in at http://dx.doi.org/10.1214/09-AOP511 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Beam-Energy and System-Size Dependence of Dynamical Net Charge Fluctuations
We present measurements of net charge fluctuations in collisions at
19.6, 62.4, 130, and 200 GeV, collisions at
62.4, 200 GeV, and collisions at 200
GeV using the net charge dynamical fluctuations measure . The
dynamical fluctuations are non-zero at all energies and exhibit a rather modest
dependence on beam energy. We find that at a given energy and collision system,
net charge dynamical fluctuations violate scaling, but display
approximate scaling. We observe strong dependence of dynamical
fluctuations on the azimuthal angular range and pseudorapidity widths.Comment: 4 pages, 4 figures, presented at the 19th International Conference on
Ultra-Relativistic Nucleus-Nucleus Collisions, "Quark Matter 2008", Jaipur,
India, February 4-10, 200
Interpretation of AIS Images of Cuprite, Nevada Using Constraints of Spectral Mixtures
A technique is outlined that tests the hypothesis Airborne Imaging Spectrometer (AIS) image spectra are produced by mixtures of surface materials. This technique allows separation of AIS images into concentration images of spectral endmembers (e.g., surface materials causing spectral variation). Using a spectral reference library it was possible to uniquely identify these spectral endmembers with respect to the reference library and to calibrate the AIS images
Systematic study of the jet fragmentation function for inclusive jet-production in p+p collisions at sqrt{s}=200 GeV in STAR
Jet fragmentation functions measured in e^+e^- and p+\bar{p} experiments are
well-described on an inclusive hadron level by QCD-based calculations.
Fragmentation is expected to be modified by the presence of a strongly
interacting medium, but full theoretical description of this modification must
still be developed. It has recently been suggested that particle-identified
fragmentation functions may provide additional insight into the processes
underlying jet quenching. To assess the applicability of QCD-based
fragmentation calculations to RHIC data, and to provide a baseline with which
to compare fragmentation function measurements in heavy ion collisions, we
present the first measurements of charged hadron and particle-identified
fragmentation functions of jets reconstructed via a midpoint-cone algorithm
from p+p collisions at 200 GeV in STAR. We study the dependence on jet
cone-size and jet-energy, and compare the results to PYTHIA simulations based
on the Modified Leading Log Approximation (MLLA).Comment: 6 pages, 5 figures, proceedings of Hard Probes 2008 conferenc
Hyperspherical Harmonics, Separation of Variables and the Bethe Ansatz
The relation between solutions to Helmholtz's equation on the sphere
and the [{\gr sl}(2)]^n Gaudin spin chain is clarified. The joint
eigenfuctions of the Laplacian and a complete set of commuting second order
operators suggested by the --matrix approach to integrable systems, based on
the loop algebra \wt{sl}(2)_R, are found in terms of homogeneous polynomials
in the ambient space. The relation of this method of determining a basis of
harmonic functions on to the Bethe ansatz approach to integrable
systems is explained.Comment: 14 pgs, Plain Tex, preprint CRM--2174 (May, 1994
Pseudorapidity dependence of parton energy loss in relativistic heavy ion collisions
We analyze the recent data from the BRAHMS Collaboration on the
pseudorapidity dependence of nuclear modification factors in Au+Au collisions
at = 200 GeV by using the full three dimensional hydrodynamic
simulations for the density effects on parton energy loss. We first compute the
transverse spectra at and 2.2, and next take a ratio
, where is a nuclear
modification factor. It is shown that hydrodynamic components account for
at low and that quenched pQCD components lead
at high which are consistent with the data.
Strong suppression at is compatible with the parton energy loss in
the final state.Comment: 5 pages, 4 figures; one figure adde
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