5,081 research outputs found
Likelihood Analysis for Mega-Pixel Maps
The derivation of cosmological parameters from astrophysical data sets
routinely involves operations counts which scale as O(N^3) where N is the
number of data points. Currently planned missions, including MAP and Planck,
will generate sky maps with N_d = 10^6 or more pixels. Simple ``brute force''
analysis, applied to such mega-pixel data, would require years of computing
even on the fastest computers. We describe an algorithm which allows estimation
of the likelihood function in the direct pixel basis. The algorithm uses a
conjugate gradient approach to evaluate chi-squared and a geometric
approximation to evaluate the determinant. Monte Carlo simulations provide a
correction to the determinant, yielding an unbiased estimate of the likelihood
surface in an arbitrary region surrounding the likelihood peak. The algorithm
requires O(N_d^{3/2}) operations and O(N_d) storage for each likelihood
evaluation, and allows for significant parallel computation.Comment: 9 pages LaTeX including 2 PostScript figures. Additional discussion
of conjugate gradient chi-squared algorithm. Matches accepted versio
Lattice QCD at finite isospin density at zero and finite temperature
We simulate lattice QCD with dynamical and quarks at finite chemical
potential, , for the third component of isospin (), at both zero
and at finite temperature. At zero temperature there is some ,
say, above which and parity are spontaneously broken by a charged pion
condensate. This is in qualitative agreement with the prediction of effective
(chiral) Lagrangians which also predict . This transition appears
to be second order, with scaling properties consistent with the mean-field
predictions of such effective Lagrangian models. We have also studied the
restoration of symmetry at high temperature for . For
sufficiently large, this finite temperature phase transition appears to
be first order. As is decreased it becomes second order connecting
continuously with the zero temperature transition.Comment: 23 pages, Revtex, 9 figures. Major revision of sections 3 and 4 to
include new analyses of critical scaling which we now find to be in the
universality class of mean-field theor
Parameter in 2 Color QCD at Finite Baryon and Isospin Density
We use 2-color QCD as a model to study the effects of simultaneous presence
of the so-called parameter, chemical potentials for baryon number,
and for isospin charge, . We pay special attention to ,
, dependence of different vacuum condensates, including chiral
and diquark condensates, as well as the gluon condensate, , and the
topological susceptibility. We find that two phase transitions of the second
order will occur when relaxes from to , if
is of order of the pion mass. We demonstrate that the transition to the
superfluid phase at occurs at a much lower chemical potential
than at . We also show that the strong dependence present
near in vacuum (Dashen's phenomenon), becomes smoothed out in
the superfluid phase. Finally, we comment on the relevance of this study for
the real world with N_c=3
THE VOLUME OPERATOR IN DISCRETIZED QUANTUM GRAVITY
We investigate the spectral properties of the volume operator in quantum
gravity in the framework of a previously introduced lattice discretization. The
presence of a well-defined scalar product in this approach permits us to make
definite statements about the hermiticity of quantum operators. We find that
the spectrum of the volume operator is discrete, but that the nature of its
eigenstates differs from that found in an earlier continuum treatment.Comment: 15 pages, TeX, 3 figures (postscript, compressed and uu-encoded), May
9
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