Alternative methods for calculating sensitivity of optimized designs to problem parameters

Optimum sensitivity is defined as the derivative of the optimum design with respect to some problem parameter, P. The problem parameter is usually fixed during optimization, but may be changed later. Thus, optimum sensitivity is used to estimate the effect of changes in loads, materials or constraint bounds on the design without expensive re-optimization. Here, the general topic of optimum sensitivity is discussed, available methods identified, examples given, and the difficulties encountered in calculating this information in nonlinear constrained optimization are identified

Gravitational collapse of magnetized clouds II. The role of Ohmic dissipation

We formulate the problem of magnetic field dissipation during the accretion phase of low-mass star formation, and we carry out the first step of an iterative solution procedure by assuming that the gas is in free-fall along radial field lines. This so-called ``kinematic approximation'' ignores the back reaction of the Lorentz force on the accretion flow. In quasi steady-state, and assuming the resistivity coefficient to be spatially uniform, the problem is analytically soluble in terms of Legendre's polynomials and confluent hypergeometric functions. The dissipation of the magnetic field occurs inside a region of radius inversely proportional to the mass of the central star (the ``Ohm radius''), where the magnetic field becomes asymptotically straight and uniform. In our solution, the magnetic flux problem of star formation is avoided because the magnetic flux dragged in the accreting protostar is always zero. Our results imply that the effective resistivity of the infalling gas must be higher by several orders of magnitude than the microscopic electric resistivity, to avoid conflict with measurements of paleomagnetism in meteorites and with the observed luminosity of regions of low-mass star formation.Comment: 20 pages, 4 figures, The Astrophysical Journal, in pres

Robust nonparametric estimation via wavelet median regression

In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are heavy-tailed, and may not even possess variances or means. Our approach is to first use local medians to turn the problem of nonparametric regression with unknown noise distribution into a standard Gaussian regression problem and then apply a wavelet block thresholding procedure to construct an estimator of the regression function. It is shown that the estimator simultaneously attains the optimal rate of convergence over a wide range of the Besov classes, without prior knowledge of the smoothness of the underlying functions or prior knowledge of the error distribution. The estimator also automatically adapts to the local smoothness of the underlying function, and attains the local adaptive minimax rate for estimating functions at a point. A key technical result in our development is a quantile coupling theorem which gives a tight bound for the quantile coupling between the sample medians and a normal variable. This median coupling inequality may be of independent interest.Comment: Published in at http://dx.doi.org/10.1214/07-AOS513 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonparametric regression in exponential families

Most results in nonparametric regression theory are developed only for the case of additive noise. In such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive. In this paper we consider nonparametric regression in exponential families with the main focus on the natural exponential families with a quadratic variance function, which include, for example, Poisson regression, binomial regression and gamma regression. We propose a unified approach of using a mean-matching variance stabilizing transformation to turn the relatively complicated problem of nonparametric regression in exponential families into a standard homoscedastic Gaussian regression problem. Then in principle any good nonparametric Gaussian regression procedure can be applied to the transformed data. To illustrate our general methodology, in this paper we use wavelet block thresholding to construct the final estimators of the regression function. The procedures are easily implementable. Both theoretical and numerical properties of the estimators are investigated. The estimators are shown to enjoy a high degree of adaptivity and spatial adaptivity with near-optimal asymptotic performance over a wide range of Besov spaces. The estimators also perform well numerically.Comment: Published in at http://dx.doi.org/10.1214/09-AOS762 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Photon-number-solving Decoy State Quantum Key Distribution

In this paper, a photon-number-resolving decoy state quantum key distribution scheme is presented based on recent experimental advancements. A new upper bound on the fraction of counts caused by multiphoton pulses is given. This upper bound is independent of intensity of the decoy source, so that both the signal pulses and the decoy pulses can be used to generate the raw key after verified the security of the communication. This upper bound is also the lower bound on the fraction of counts caused by multiphoton pulses as long as faint coherent sources and high lossy channels are used. We show that Eve's coherent multiphoton pulse (CMP) attack is more efficient than symmetric individual (SI) attack when quantum bit error rate is small, so that CMP attack should be considered to ensure the security of the final key. finally, optimal intensity of laser source is presented which provides 23.9 km increase in the transmission distance. 03.67.DdComment: This is a detailed and extended version of quant-ph/0504221. In this paper, a detailed discussion of photon-number-resolving QKD scheme is presented. Moreover, the detailed discussion of coherent multiphoton pulse attack (CMP) is presented. 2 figures and some discussions are added. A detailed cauculation of the "new" upper bound 'is presente

Breathing oscillations of a trapped impurity in a Bose gas

Motivated by a recent experiment [J. Catani et al., arXiv:1106.0828v1 preprint, 2011], we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. In the Gross-Pitaevskii regime we obtain breathing oscillations whose amplitudes are suppressed by self trapping, due to interactions with the Bose gas. Introducing phonons in the Bose gas leads to the damping of breathing oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results reproduce the main features of the impurity dynamics observed by Catani et al. despite experimental thermal effects, and are supported by simulations of the system in the Gross-Pitaevskii regime. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas.Comment: 7 pages, 3 figure

Annihilation Type Radiative Decays of BB Meson in Perturbative QCD Approach

With the perturbative QCD approach based on $k_T$ factorization, we study the pure annihilation type radiative decays $B^0 \to \phi\gamma$ and $B^0\to J/\psi \gamma$. We find that the branching ratio of $B^0 \to \phi\gamma$ is $(2.7^{+0.3+1.2}_{-0.6-0.6})\times10^{-11}$, which is too small to be measured in the current $B$ factories of BaBar and Belle. The branching ratio of $B^0\to J/\psi \gamma$ is $({4.5^{+0.6+0.7}_{-0.5-0.6}})\times10^{-7}$, which is just at the corner of being observable in the $B$ factories. A larger branching ratio $BR(B_s^0 \to J/\psi \gamma) \simeq 5 \times 10^{-6}$ is also predicted. These decay modes will help us testing the standard model and searching for new physics signals.Comment: 4 pages, revtex, with 1 eps figur

Phase-reference VLBI Observations of the Compact Steep-Spectrum Source 3C 138

We investigate a phase-reference VLBI observation that was conducted at 15.4 GHz by fast switching VLBA antennas between the compact steep-spectrum radio source 3C 138 and the quasar PKS 0528+134 which are about 4$^\circ$ away on the sky. By comparing the phase-reference mapping with the conventional hybrid mapping, we demonstrate the feasibility of high precision astrometric measurements for sources separated by 4$^\circ$. VLBI phase-reference mapping preserves the relative phase information, and thus provides an accurate relative position between 3C 138 and PKS 0528+134 of $\Delta\alpha=-9^m46^s.531000\pm0^s.000003$ and $\Delta\delta=3^\circ6^\prime26^{\prime\prime}.90311\pm0^{\prime\prime}.00007$ (J2000.0) in right ascension and declination, respectively. This gives an improved position of the nucleus (component A) of 3C 138 in J2000.0 to be RA=$05^h 21^m 9^s.885748$ and Dec=$16^\circ 38' 22''.05261$ under the assumption that the position of calibrator PKS 0528+134 is correct. We further made a hybrid map by performing several iterations of CLEAN and self-calibration on the phase-referenced data with the phase-reference map as an input model for the first phase self-calibration. Compared with the hybrid map from the limited visibility data directly obtained from fringe fitting 3C 138 data, this map has a similar dynamic range, but a higher angular resolution. Therefore, phase-reference technique is not only a means of phase connection, but also a means of increasing phase coherence time allowing self-calibration technique to be applied to much weaker sources.Comment: 9 pages plus 2 figures, accepted by PASJ (Vol.58 No.6