66 research outputs found
Qubit-Qutrit Separability-Probability Ratios
Paralleling our recent computationally-intensive (quasi-Monte Carlo) work for
the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to
high numerical accuracy, the formulas of Sommers and Zyczkowski
(quant-ph/0304041) for the (N^2-1)-dimensional volume and (N^2-2)-dimensional
hyperarea of the (separable and nonseparable) N x N density matrices, based on
the Bures (minimal monotone) metric -- and also their analogous formulas
(quant-ph/0302197) for the (non-monotone) Hilbert-Schmidt metric. With the same
seven billion well-distributed (``low-discrepancy'') sample points, we estimate
the unknown volumes and hyperareas based on five additional (monotone) metrics
of interest, including the Kubo-Mori and Wigner-Yanase. Further, we estimate
all of these seven volume and seven hyperarea (unknown) quantities when
restricted to the separable density matrices. The ratios of separable volumes
(hyperareas) to separable plus nonseparable volumes (hyperareas) yield
estimates of the separability probabilities of generically rank-six (rank-five)
density matrices. The (rank-six) separability probabilities obtained based on
the 35-dimensional volumes appear to be -- independently of the metric (each of
the seven inducing Haar measure) employed -- twice as large as those (rank-five
ones) based on the 34-dimensional hyperareas. Accepting such a relationship, we
fit exact formulas to the estimates of the Bures and Hilbert-Schmidt separable
volumes and hyperareas.(An additional estimate -- 33.9982 -- of the ratio of
the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite
clearly close to integral too.) The doubling relationship also appears to hold
for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit
exact formulas for the Hilbert-Schmidt separable volumes and hyperareas.Comment: 36 pages, 15 figures, 11 tables, final PRA version, new last
paragraph presenting qubit-qutrit probability ratios disaggregated by the two
distinct forms of partial transpositio
MONTE CARLO SIMULATION FOR AMERICAN OPTIONS
This paper reviews the basic properties of American options and the difficulties of applying Monte Carlo valuation to American options. Asymptotic results by Keller and co-workers are described for the singularity in the early exercise boundary for time t near the final time T. Recent progress on application of Monte Carlo to American options is described including the following: Branching processes have been constructed to obtain upper and lower bounds on the American option price. A Martingale optimization formulation for the American option price can be used to obtain an upper bound on the price, which is complementary to the trivial lower bound. The Least Squares Monte Carlo (LSM) provides a direct method for pricing American options. Quasirandom sequences have been used to improve performance of LSM; a brief introduction to quasi-random sequences is presented. Conclusions and prospects for future research are discussed. In particular, we expect that the asymptotic results of Keller and co-workers could be useful for improving Monte Carlo methods
Assessment of female sexual arousal : response specificity and construct validity
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21166.PDF (publisher's version ) (Open Access
Correlating point-referenced radon and areal uranium data arising from a common spatial process
Because exposure to radon gas in buildings is a likely risk factor for lung cancer, estimation of residential radon levels is an important public health endeavour. Radon originates from uranium, and therefore data on the geographical distribution of uranium in the Earth's surface may inform about radon levels. We fit a Bayesian geostatistical model that appropriately combines data on uranium with measurements of indoor home radon in the state of Iowa, thereby obtaining more accurate and precise estimation of the geographic distribution of average residential radon levels than would be possible by using radon data alone. Copyright 2007 Royal Statistical Society.
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