Adaptive confidence intervals for regression functions under shape constraints

Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in terms of an analytic quantity, the local modulus of continuity. This bound depends not only on the function but also the assumed function class. These benchmarks show that the constructed confidence intervals have near minimum expected length for each individual function, while maintaining a given coverage probability for functions within the class. Such adaptivity is much stronger than adaptive minimaxity over a collection of large parameter spaces.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1068 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime

We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation in the nonrelativistic limit regime, involving a small dimensionless parameter $0<\varepsilon\ll 1$ which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e. there are propagating waves with wavelength $O(\varepsilon^2)$ and $O(1)$ in time and space, respectively. We begin with the conservative Crank-Nicolson finite difference (CNFD) method and establish rigorously its error estimate which depends explicitly on the mesh size $h$ and time step $\tau$ as well as the small parameter $0<\varepsilon\le 1$. Based on the error bound, in order to obtain `correct' numerical solutions in the nonrelativistic limit regime, i.e. $0<\varepsilon\ll 1$, the CNFD method requests the $\varepsilon$-scalability: $\tau=O(\varepsilon^3)$ and $h=O(\sqrt{\varepsilon})$. Then we propose and analyze two numerical methods for the discretization of the nonlinear Dirac equation by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and time-splitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their $\varepsilon$-scalability is improved to $\tau=O(\varepsilon^2)$ and $h=O(1)$ when $0<\varepsilon\ll 1$ compared with the CNFD method. Extensive numerical results are reported to confirm our error estimates.Comment: 35 pages. 1 figure. arXiv admin note: substantial text overlap with arXiv:1504.0288

Controlling plant architecture by manipulation of gibberellic acid signalling in petunia.

Since stem elongation is a gibberellic acid (GA) response, GA inhibitors are commonly used to control plant height in the production of potted ornamentals and bedding plants. In this study, we investigated interfering with GA signaling by using molecular techniques as an alternative approach. We isolated three putative GID1 genes (PhGID1A, PhGID1B and PhGID1C) encoding GA receptors from petunia. Virus-induced gene silencing (VIGS) of these genes results in stunted growth, dark-green leaves and late-flowering. We also isolated the gai mutant gene (gai-1) from Arabidopsis. We have generated transgenic petunia plants in which the gai mutant protein is over-expressed under the control of a dexamethasone-inducible promoter. This system permits induction of the dominant Arabidopsis gai mutant gene at a desired stage of plant development in petunia plants by the application of dexamethasone (Dex). The induction of gai in Dex-treated T1 petunia seedlings caused dramatic growth retardation with short internodes

Hollow Gaussian Schell-model beam and its propagation

In this paper, we present a new model, hollow Gaussian-Schell model beams (HGSMBs), to describe the practical dark hollow beams. An analytical propagation formula for HGSMBs passing through a paraxial first-order optical system is derived based on the theory of coherence. Based on the derived formula, an application example showing the influence of spatial coherence on the propagation of beams is illustrated. It is found that the beam propagating properties of HGSMBs will be greatly affected by their spatial coherence. Our model provides a very convenient way for analyzing the propagation properties of partially coherent dark hollow beams.Comment: 13pages, 2 figure

Sudden stoppage of rotor in a thermally driven rotary motor made from double-walled carbon nanotubes

In a thermally driven rotary motor made from double-walled carbon nanotubes, the rotor (inner tube) can be actuated to rotate within the stator (outer tube) when the environmental temperature is high enough. A sudden stoppage of the rotor can occur when the inner tube has been actuated to rotate at a stable high speed. To find the mechanisms of such sudden stoppages, eight motor models with the same rotor but different stators are built and simulated in the canonical NVT ensembles. Numerical results demonstrate that the sudden stoppage of the rotor occurs when the difference between radii is near 0.34 nm at a high environmental temperature. A smaller difference between radii does not imply easier activation of the sudden rotor stoppage. During rotation, the positions and electron density distribution of atoms at the ends of the motor show that a sp(1) bonded atom on the rotor is attracted by the sp(1) atom with the biggest deviation of radial position on the stator, after which they become two sp(2) atoms. The strong bond interaction between the two atoms leads to the loss of rotational speed of the rotor within 1 ps. Hence, the sudden stoppage is attributed to two factors: the deviation of radial position of atoms at the stator's ends and the drastic thermal vibration of atoms on the rotor in rotation. For a stable motor, sudden stoppage could be avoided by reducing deviation of the radial position of atoms at the stator's ends. A nanobrake can be, thus, achieved by adjusting a sp(1) atom at the ends of stator to stop the rotation of rotor quickly.The authors are grateful for financial support from the National Natural-Science-Foundation of China (Grant Nos. 50908190, 11372100)

Interface control of ferroelectricity in LaNiO3-BaTiO3 superlattices

LaNiO$_{3}$-BaTiO$_{3}$ superlattices with different types of interfaces are studied from first-principles density-functional theory. It is revealed that the ferroelectricity in the superlattice with (NiO$_2$)$^-$/(BaO)$^0$ interfaces is enhanced from that of the superlattice with (LaO)$^+$/(TiO$_2$)$^0$ interfaces. The origin lies at the polar discontinuity at the interface, which makes the holes localized within the (NiO$_2$)$^-$/(BaO)$^0$ interface, but drives a penetration of electrons into BaTiO$_3$ component near (LaO)$^+$/(TiO$_2$)$^0$ interface. Our calculations demonstrate an effective avenue to the robust ferroelectricity in BaTiO$_3$ ultrathin films.Comment: 14 pages, 6 figure