Optimal two-treatment, $p$ period crossover designs for binary responses are determined. The optimal designs are obtained by minimizing the variance of the treatment contrast estimator over all possible allocations of $n$ subjects to $2^p$ possible t
reatment sequences. An appropriate logistic regression model is postulated and the within subject covariances are modeled through a working correlation matrix. The marginal mean of the binary responses are fitted using generalized estimating equations. The efficiencies of some crossover designs for $p=2,3,4$ periods are calculated. The effect of misspecified working correlation matrix on design efficiency is also studied.
Nuclear magnetic resonance (NMR) and transport measurements have been performed at high magnetic fields and low temperatures in a series of $n$-type Bi$_{2}$Se$_{3}$ crystals. In low density samples, a complete spin polarization of the electronic sys
tem is achieved, as observed from the saturation of the isotropic component of the $^{209}$Bi NMR shift above a certain magnetic field. The corresponding spin splitting, defined in the phenomenological approach of a 3D electron gas with a large (spin-orbit-induced) effective $g$-factor, scales as expected with the Fermi energy independently determined by simultaneous transport measurements. Both the effective electronic $g$-factor and the contact hyperfine coupling constant are precisely determined. The magnitude of this latter reveals a non negligible $s$-character of the electronic wave function at the bottom of the conduction band. Our results show that the bulk electronic spin polarization can be directly probed via NMR and pave the way for future NMR investigations of the electronic states in Bi-based topological insulators.
By means of nuclear spin-lattice relaxation rate 1/T1, we follow the spin dynamics as a function of the applied magnetic field in two gapped one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl2-4SC(NH2)2 and the spin-ladd
er system (C5H12N)2CuBr4. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapples Tomonaga-Luttinger-liquid state. In between, 1/T1 exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for 1/T1, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum critical behavior.
This paper outlines a unified framework for high dimensional variable selection for classification problems. Traditional approaches to finding interesting variables mostly utilize only partial information through moments (like mean difference). On th
e contrary, in this paper we address the question of variable selection in full generality from a distributional point of view. If a variable is not important for classification, then it will have similar distributional aspect under different classes. This simple and straightforward observation motivates us to quantify `How and Why the distribution of a variable changes over classes through CR-statistic. The second contribution of our paper is to develop and investigate the FDR based thresholding technology from a completely new point of view for adaptive thresholding, which leads to a elegant algorithm called CDfdr. This paper attempts to show how all of these problems of detection, extraction and interpretation for interesting variables can be treated in a unified way under one broad general theme - comparison analysis. It is proposed that a key to accomplishing this unification is to think in terms of the quantile function and the comparison density. We illustrate and demonstrate the power of our methodology using three real data sets.
The superconducting state of an optimally doped single crystal of Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$ was investigated by $^{75}$As NMR in high magnetic fields from 6.4 T to 28 T. It was found that the Knight shift is least affected by vortex superc
urrents in high magnetic fields, $H>11$ T, revealing slow, possibly higher order than linear, increase with temperature at $T lesssim 0.5 , T_c$, with $T_c approx 23 , K$. This is consistent with the extended s-wave state with $A_{1g}$ symmetry but the precise details of the gap structure are harder to resolve. Measurements of the NMR spin-spin relaxation time, $T_2$, indicate a strong indirect exchange interaction at all temperatures. Below the superconducting transition temperature vortex dynamics lead to an anomalous dip in $T_2$ at the vortex freezing transition from which we obtain the vortex phase diagram up to $H = 28$ T.
Competition with magnetism is at the heart of high temperature superconductivity, most intensely felt near a vortex core. To investigate vortex magnetism we have developed a spatially resolved probe using nuclear magnetic resonance. Our spin-lattice-
relaxation spectroscopy is spatially resolved both within a conduction plane as well as from one plane to another. With this approach we have found a spin-density wave associated with the vortex core in Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$, which is expected from scanning tunneling microscope observations of checkerboard patterns in the local density of electronic states.[1] We determine both the spin-modulation amplitude and decay length from the vortex core in fields up to H=30 T.
It has been predicted that superconducting vortices should be electrically charged and that this effect is particularly enhanced for, high temperature superconductors.cite{kho95,bla96} Hall effectcite{hag91} and nuclear magnetic resonance (NMR) exper
imentscite{kum01} suggest the existence of vortex charging, but the effects are small and the interpretation controversial. Here we show that the Abrikosov vortex lattice, characteristic of the mixed state of superconductors, will become unstable at sufficiently high magnetic field if there is charge trapped on the vortex core. Our NMR measurements of the magnetic fields generated by vortices in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+y}$ single crystalscite{che07} provide evidence for an electrostatically driven vortex lattice reconstruction with the magnitude of charge on each vortex pancake of $mathbf{sim 2}$x$mathbf{10^{-3} e}$, depending on doping, in line with theoretical estimates.cite{kho95,kna05}
We report the first observation of high-spin states in nuclei in the vicinity of the island of inversion, populated via the 18O+18O fusion reaction at an incident beam energy of 34 MeV. The fusion reaction mechanism circumvents the limitations of non
-equilibrated reactions used to populate these nuclei. Detailed spin-parity measurements in these difficult to populate nuclei have been possible from the observed coincidence anisotropy and the linear polarization measurements. The spectroscopy of 33,34P and 33S is presented in detail along with the results of calculations within the shell model framework.
High energy gamma-rays in coincidence with low energy yrast gamma-rays have been measured from 113Sb, at excitation energies of 109 and 122 MeV, formed by bombarding 20Ne on 93Nb at projectile energies of 145 and 160 MeV respectively to study the rol
e of angular momentum (J) and temperature (T) over Giant Dipole Resonance (GDR) width. The maximum populated angular momenta for fusion were 67hbar and 73hbar respectively for the above-mentioned beam energies. The high energy photons were detected using a Large Area Modular BaF2 Detector Array (LAMBDA) along with a 24-element multiplicity filter. After pre-equilibrium corrections, the excitation energy E* was averaged over the decay steps of the compound nucleus (CN). The average values of temperature, angular momentum, CN mass etc. have been calculated by the statistical model code CASCADE. Using those average values, results show the systematic increase of GDR width with T which is consistent with Kusnezov parametrization and the Thermal Shape Fluctuation Model. The rise of GDR width with temperature also supports the assumptions of adiabatic coupling in the Thermal Shape Fluctuation Model. But the GDR widths and corresponding reduced plots with J are not consistent with the theoretical model at high spins.
Excited states of the neutron deficient $^{103}$Cd nucleus have been investigated via the $^{72}$Ge($^{35}$Cl, p3n) reaction at beam energy of 135 MeV by use of in-beam spectroscopic methods. Gamma rays depopulating the excited states were detected u
sing the Gammasphere spectrometer with high-fold $gamma$-ray coincidences. A quadrupole $gamma$-ray coincidence analysis ($gamma^{4}$) has been used to extend the known level scheme. The positive parity levels have been established up to $J = 35/2hbar$ and $E_{x} = 7.071$ MeV. In addition to the observation of highly-fragmented level scheme belonging to the positive-parity sequences at E$_{x}sim$ 5 MeV, the termination of a negative-parity sequence connected by $E2$ transitions has been established at $J = 47/2 hbar$ and $E_{x} = 11.877$ MeV. The experimental results corresponding to both the positive- and negative-parity sequences have been theoretically interpreted in the framework of the core particle coupling model. Evidence is presented for a shape change from collective prolate to non-collective oblate above the $J^{pi} = 39/2^{-}$ (8011 keV) level and for a smooth termination of the negative-parity band.
