15,799 research outputs found
Stochastic approximation of score functions for Gaussian processes
We discuss the statistical properties of a recently introduced unbiased
stochastic approximation to the score equations for maximum likelihood
calculation for Gaussian processes. Under certain conditions, including bounded
condition number of the covariance matrix, the approach achieves storage
and nearly computational effort per optimization step, where is the
number of data sites. Here, we prove that if the condition number of the
covariance matrix is bounded, then the approximate score equations are nearly
optimal in a well-defined sense. Therefore, not only is the approximation
efficient to compute, but it also has comparable statistical properties to the
exact maximum likelihood estimates. We discuss a modification of the stochastic
approximation in which design elements of the stochastic terms mimic patterns
from a factorial design. We prove these designs are always at least as
good as the unstructured design, and we demonstrate through simulation that
they can produce a substantial improvement over random designs. Our findings
are validated by numerical experiments on simulated data sets of up to 1
million observations. We apply the approach to fit a space-time model to over
80,000 observations of total column ozone contained in the latitude band
-N during April 2012.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS627 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
New Anomalies in Topological String Theory
We show that the topological string partition function with D-branes on a compact Calabi-Yau manifold has new anomalies that spoil the recursive structure of the holomorphic anomaly equation and introduce dependence on wrong moduli (such as complex structure moduli in the A-model), unless the disk one-point functions vanish. This provides a microscopic explanation for the recent result of Walcher in arXiv:0712.2775 on counting of BPS states in M-theory using the topological string partition function. The relevance of vanishing disk one-point functions to large N duality for compact Calabi-Yau manifolds is noted
Quantum states of a binary mixture of spinor Bose-Einstein condensates
We study the structure of quantum states for a binary mixture of spin-1
atomic Bose-Einstein condensates. In contrast to collision between identical
bosons, the s-wave scattering channel between inter-species does not conform to
a fixed symmetry. The spin-dependent Hamiltonian thus contains non-commuting
terms, making the exact eigenstates more challenging to obtain because they now
depend more generally on both the intra- and inter-species interactions. We
discuss two limiting cases, where the spin-dependent Hamiltonian reduces
respectively to sums of commuting operators. All eigenstates can then be
directly constructed, and they are independent of the detailed interaction
parameters.Comment: 5 pages, no figure
Atomic number fluctuations in a mixture of two spinor condensates
We study particle number fluctuations in the quantum ground states of a
mixture of two spin-1 atomic condensates when the interspecies spin-exchange
coupling interaction is adjusted. The two spin-1 condensates
forming the mixture are respectively ferromagnetic and polar in the absence of
an external magnetic (B-) field. We categorize all possible ground states using
the angular momentum algebra and compute their characteristic atom number
fluctuations, focusing especially on the the AA phase (when ),
where the ground state becomes fragmented and atomic number fluctuations
exhibit drastically different features from a single stand alone spin-1 polar
condensate. Our results are further supported by numerical simulations of the
full quantum many-body system.Comment: 5 pages, 2 figures, in press PR
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