Iterated smoothed bootstrap confidence intervals for population quantiles

This paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap-t confidence intervals for population quantiles, and establishes the optimal kernel bandwidths at various stages of the smoothing procedures. The conventional smoothed bootstrap and bootstrap-t methods have been known to yield one-sided coverage errors of orders O(n^{-1/2}) and o(n^{-2/3}), respectively, for intervals based on the sample quantile of a random sample of size n. We sharpen the latter result to O(n^{-5/6}) with proper choices of bandwidths at the bootstrapping and Studentization steps. We show further that calibration of the nominal coverage level by means of the iterated bootstrap succeeds in reducing the coverage error of the smoothed bootstrap percentile interval to the order O(n^{-2/3}) and that of the smoothed bootstrap-t interval to O(n^{-58/57}), provided that bandwidths are selected of appropriate orders. Simulation results confirm our asymptotic findings, suggesting that the iterated smoothed bootstrap-t method yields the most accurate coverage. On the other hand, the iterated smoothed bootstrap percentile method interval has the advantage of being shorter and more stable than the bootstrap-t intervals.Comment: Published at http://dx.doi.org/10.1214/009053604000000878 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Noncommutative D-Brane in Non-Constant NS-NS B Field Background

We show that when the field strength H of the NS-NS B field does not vanish, the coordinates X and momenta P of an open string endpoints satisfy a set of mixed commutation relations among themselves. Identifying X and P with the coordinates and derivatives of the D-brane world volume, we find a new type of noncommutative spaces which is very different from those associated with a constant B field background.Comment: 11 pages, Latex, minor modification

Spinor Bose Condensates in Optical Traps

In an optical trap, the ground state of spin-1 Bosons such as $^{23}$Na, $^{39}$K, and $^{87}$Rb can be either a ferromagnetic or a "polar" state, depending on the scattering lengths in different angular momentum channel. The collective modes of these states have very different spin character and spatial distributions. While ordinary vortices are stable in the polar state, only those with unit circulation are stable in the ferromagnetic state. The ferromagnetic state also has coreless (or Skyrmion) vortices like those of superfluid $^{3}$He-A. Current estimates of scattering lengths suggest that the ground states of $^{23}$Na and $^{87}$Rb condensate are a polar state and a ferromagnetic state respectively.Comment: 11 pages, no figures. email : [email protected]

Aspects of U-duality in BLG models with Lorentzian metric 3-algebras

In our previous paper, it was shown that BLG model based on a Lorentzian metric 3-algebra gives Dp-brane action whose worldvolume is compactified on torus T^d (d=p-2). Here the 3-algebra was a generalized one with d+1 pairs of Lorentzian metric generators and expressed in terms of a loop algebra with central extensions. In this paper, we derive the precise relation between the coupling constant of the super Yang-Mills, the moduli of T^d and some R-R flux with VEV's of ghost fields associated with Lorentzian metric generators. In particular, for d=1, we derive the Yang-Mills action with theta term and show that SL(2,Z) Montonen-Olive duality is realized as the rotation of two VEV's. Furthermore, some moduli parameters such as NS-NS 2-form flux are identified as the deformation parameters of the 3-algebras. By combining them, we recover most of the moduli parameters which are required by U-duality symmetry.Comment: 27 pages, v2: minor correction

Chiral Electronics

We consider the properties of electric circuits involving Weyl semimetals. The existence of the anomaly-induced chiral magnetic current in a Weyl semimetal subjected to magnetic field causes an interesting and unusual behavior of such circuits. We consider two explicit examples: i) a circuit involving the "chiral battery" and ii) a circuit that can be used as a "quantum amplifier" of magnetic field. The unique properties of these circuits stem from the chiral anomaly and may be utilized for creating "chiral electronic" devices.Comment: 5 pages, 2 figures; final version to appear in Physical Review

Quantum Key Distribution with Blind Polarization Bases

We propose a new quantum key distribution scheme that uses the blind polarization basis. In our scheme the sender and the receiver share key information by exchanging qubits with arbitrary polarization angles without basis reconciliation. As only random polarizations are transmitted, our protocol is secure even when a key is embedded in a not-so-weak coherent-state pulse. We show its security against the photon number splitting attack and the impersonation attack.Comment: Security has been improved upon referee's comment. 4 pages and 2 figure