Constrained fitting of three-point functions

We determine matrix elements for $B \to D$ semileptonic decay. The use of the constrained fitting method and multiple smearings for both two- and three-point correlators allows an improved calculation of the form factors.Comment: Talk given at Lattice2001(heavyquark), 3 pages, 4 figure

Efficient estimation of Banach parameters in semiparametric models

Consider a semiparametric model with a Euclidean parameter and an infinite-dimensional parameter, to be called a Banach parameter. Assume: (a) There exists an efficient estimator of the Euclidean parameter. (b) When the value of the Euclidean parameter is known, there exists an estimator of the Banach parameter, which depends on this value and is efficient within this restricted model. Substituting the efficient estimator of the Euclidean parameter for the value of this parameter in the estimator of the Banach parameter, one obtains an efficient estimator of the Banach parameter for the full semiparametric model with the Euclidean parameter unknown. This hereditary property of efficiency completes estimation in semiparametric models in which the Euclidean parameter has been estimated efficiently. Typically, estimation of both the Euclidean and the Banach parameter is necessary in order to describe the random phenomenon under study to a sufficient extent. Since efficient estimators are asymptotically linear, the above substitution method is a particular case of substituting asymptotically linear estimators of a Euclidean parameter into estimators that are asymptotically linear themselves and that depend on this Euclidean parameter. This more general substitution case is studied for its own sake as well, and a hereditary property for asymptotic linearity is proved.Comment: Published at http://dx.doi.org/10.1214/009053604000000913 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fidelity threshold for long-range entanglement in quantum networks

We present a strategy to generate long-range entanglement in noisy quantum networks. We consider a cubic lattice whose bonds are partially entangled mixed states of two qubits, and where quantum operations can be applied perfectly at the nodes. In contrast to protocols designed for one- or two-dimensional regular lattices, we find that entanglement can be created between arbitrarily distant qubits if the fidelity of the bonds is higher than a critical value, independent of the system size. Therefore, we show that a constant overhead of local resources, together with connections of finite fidelity, is sufficient to achieve long-distance quantum communication in noisy networks.Comment: published versio

Asymptotically conical Calabi-Yau manifolds, I

This is the first part in a two-part series on complete Calabi-Yau manifolds asymptotic to Riemannian cones at infinity. We begin by proving general existence and uniqueness results. The uniqueness part relaxes the decay condition $O(r^{-n-\epsilon})$ needed in earlier work to $O(r^{-\epsilon})$, relying on some new ideas about harmonic functions. We then look at a few examples: (1) Crepant resolutions of cones. This includes a new class of Ricci-flat small resolutions associated with flag manifolds. (2) Affine deformations of cones. One focus here is the question of the precise rate of decay of the metric to its tangent cone. We prove that the optimal rate for the Stenzel metric on $T^*S^n$ is $-2\frac{n}{n-1}$.Comment: 27 pages, various corrections, final versio

Structure and Phase Transitions of Alkyl Chains on Mica

We use molecular dynamics as a tool to understand the structure and phase transitions [Osman et. al. J. Phys. Chem. B 2000, 104, 4433; 2002, 106, 653] in alkylammonium micas. The consistent force field 91 is extended for accurate simulation of mica and related minerals. We investigate mica sheets with 12 octadecyltrimethylammonium (C18) ions or 12 dioctadecyldimethylammonium (2C18) ions, respectively, as single and layered structures at different temperatures with periodicity in the xy plane by NVT dynamics. The alkylammonium ions reside preferably above the cavities in the mica surface with an aluminum-rich boundary. The nitrogen atoms are 380 to 390 pm distant to the superficial silicon-aluminum plane. With increasing temperature, rearrangements of C18 ions on the mica surface are found, while 2C18 ions remain tethered due to geometric restraints. We present basal-plane spacings in the duplicate structures, tilt angles of the alkyl chains, and gauche-trans ratios to analyze the chain conformation. Also, the individual phase transitions of the two systems on heating are explained. Where experimental data are available, the agreement is very good. We propose a geometric parameter lamba for the saturation of the surface with alkyl chains, which determines the preferred self-assembly pattern, i.e., islands, intermediate, or continuous. Lambda also determines the tilt angles in continuous layers on mica or other surfaces. The thermal decomposition appears to be a Hofmann elimination with mica as a base-template.Comment: 45 pages with 6 tables and 5 figure