Inspired by sample splitting and the reusable holdout introduced in the field of differential privacy, we consider selective inference with a randomized response. We discuss two major advantages of using a randomized response for model selection. Fir
st, the selectively valid tests are more powerful after randomized selection. Second, it allows consistent estimation and weak convergence of selective inference procedures. Under independent sampling, we prove a selective (or privatized) central limit theorem that transfers procedures valid under asymptotic normality without selection to their corresponding selective counterparts. This allows selective inference in nonparametric settings. Finally, we propose a framework of inference after combining multiple randomized selection procedures. We focus on the classical asymptotic setting, leaving the interesting high-dimensional asymptotic questions for future work.
The Next Generation Virgo Cluster Survey has recently determined the luminosity function of galaxies in the core of the Virgo cluster down to unprecedented magnitude and surface brightness limits. Comparing simulations of cluster formation to the der
ived central stellar mass function, we attempt to estimate the stellar-to-halo-mass ratio (SHMR) for dwarf galaxies, as it would have been before they fell into the cluster. This approach ignores several details and complications, e.g., the contribution of ongoing star formation to the present-day stellar mass of cluster members, and the effects of adiabatic contraction and/or violent feedback on the subhalo and cluster potentials. The final results are startlingly simple, however; we find that the trends in the SHMR determined previously for bright galaxies appear to extend down in a scale-invariant way to the faintest objects detected in the survey. These results extend measurements of the formation efficiency of field galaxies by two decades in halo mass, or five decades in stellar mass, down to some of the least massive dwarf galaxies known, with stellar masses of $sim 10^5 M_odot$.
Bismuth chalcogenides Bi$_2$Se$_3$ and Bi$_2$Te$_3$ are semiconductors, which can be both thermoelectric materials (TE) and topological insulators (TI). Lattice defects arising from vacancies, impurities, or dopants in these materials are important i
n that they provide the charge carriers in TE applications and compromise the performance of these materials as TIs. We present the first solid-state nuclear magnetic resonance (NMR) study of the $^{77}$Se and $^{125}$Te NMR resonances in polycrystalline powders of Bi$_2$Se$_3$ and Bi$_2$Te$_3$, respectively. The spin-lattice ($T_1$) relaxation is modeled by at most two exponentials. Within the framework of this model, the NMR measurement is sensitive to the distribution of native defects within these materials. One component corresponds to a stoichiometric fraction, an insulator with a very long $T_1$, whereas the other component is attributed to a sample fraction with high defect content with a short $T_1$ resulting from interaction with the conduction carriers. The absence of a very long $T_1$ in the bismuth telluride suggests defects throughout the sample. For the bismuth selenide, defect regions segregate into domains. We also find a substantial difference in the short $T_1$ component for $^{125}$Te nuclei (76 ms) and $^{77}$Se (0.63 s) in spite of the fact that these materials have nearly identical lattice structures, chemical and physical properties. Investigations of the NMR shift and Korringa law indicate that the coupling to the conduction band electrons at the chalcogenide sites is much stronger in the telluride. The results are consistent with a stronger spin-orbit coupling (SOC) to the $p$-band electrons in the telluride. If most parameters of a given material are kept equal, this type of experiment could provide a useful probe of SOC in engineered TI materials.
In this study we present an alternative approach to separating contributions to the NMR shift originating from the Knight shift and chemical shielding by a combination of experimental solid-state NMR results and ab initio calculations. The chemical a
nd Knight shifts are normally distinguished through detailed studies of the resonance frequency as function of temperature and carrier concentration, followed by extrapolation of the shift to zero carrier concentration. This approach is time-consuming and requires studies of multiple samples. Here, we analyzed $^{207}$Pb and $^{125}$Te NMR spin-lattice relaxation rates and NMR shifts for bulk and nanoscale PbTe. The shifts are compared with calculations of the $^{207}$Pb and $^{125}$Te chemical shift resonances to determine the chemical shift at zero charge carrier concentration. The results are in good agreement with literature values from carrier concentration-dependent studies. The measurements are also compared to literature reports of the $^{207}$Pb and $^{125}$Te Knight shifts of $n$- and $p$-type PbTe semiconductors. The literature data have been converted to the currently accepted shift scale. We also provide possible evidence for the self-cleaning effect property of PbTe nanocrystals whereby defects are removed from the core of the particles, while preserving the crystal structure.
We report elastic and inelastic neutron scattering measurements of the high-TC ferromagnet Mn(1+delta)Sb. Measurements were performed on a large, TC=434 K, single crystal with interstitial Mn content of delta~0.13. The neutron diffraction results rev
eal that the interstitial Mn has a magnetic moment, and that it is aligned antiparallel to the main Mn moment. We perform density functional theory calculations including the interstitial Mn, and find the interstitial to be magnetic in agreement with the diffraction data. The inelastic neutron scattering measurements reveal two features in the magnetic dynamics: i) a spin-wave-like dispersion emanating from ferromagnetic Bragg positions (H K 2n), and ii) a broad, non-dispersive signal centered at forbidden Bragg positions (H$,$K$,$2$n$+1). The inelastic spectrum cannot be modeled by simple linear spin-wave theory calculations, and appears to be significantly altered by the presence of the interstitial Mn ions. The results show that the influence of the interstitial Mn on the magnetic state in this system is more important than previously understood.
The magnetic susceptibility, crystal and magnetic structures, and electronic structure of double perovskite Sr2ScOsO6 are reported. Using both neutron and x-ray powder diffraction we find that the crystal structure is monoclinic P21/n from 3.5 to 300
K. Magnetization measurements indicate an antiferromagnetic transition at TN=92K, one of the highest transition temperatures of any double perovskite hosting only one magnetic ion. Type I antiferromagnetic order is determined by neutron powder diffraction, with an Os moment of only 1.6(1) muB, close to half the spin-only value for a crystal field split 5d electron state with t2g^3 ground state. Density functional calculations show that this reduction is largely the result of strong Os-O hybridization, with spin-orbit coupling responsible for only a ~0.1 muB reduction in the moment.
Electric resistivity, specific heat, magnetic susceptibility, and inelastic neutron scattering experiments were performed on a single crystal of the heavy fermion compound Ce(Ni$_{0.935}$Pd$_{0.065}$)$_2$Ge$_2$ in order to study the spin fluctuations
near an antiferromagnetic (AF) quantum critical point (QCP). The resistivity and the specific heat coefficient for $T leq$ 1 K exhibit the power law behavior expected for a 3D itinerant AF QCP ($rho(T) sim T^{3/2}$ and $gamma(T) sim gamma_0 - b T^{1/2}$). However, for 2 $leq T leq$ 10 K, the susceptibility and specific heat vary as $log T$ and the resistivity varies linearly with temperature. Furthermore, despite the fact that the resistivity and specific heat exhibit the non-Fermi liquid behavior expected at a QCP, the correlation length, correlation time, and staggered susceptibility of the spin fluctuations remain finite at low temperature. We suggest that these deviations from the divergent behavior expected for a QCP may result from alloy disorder.
Magnetic fluctuations in the molecular-intercalated FeSe superconductor Li{x}(ND2){y}(ND3){1-y}Fe2Se2 (Tc = 43K) have been measured by inelastic neutron scattering from a powder sample. The strongest magnetic scattering is observed at a wave vector Q
~ 1.4 A^{-1}, which is not consistent with the (pi,0) nesting wave vector that characterizes magnetic fluctuations in several other iron-based superconductors, but is close to the (pi, pi/2) position found for A{x}Fe{2-y}Se2 systems. At the energies probed (~ 5kB Tc), the magnetic scattering increases in intensity with decreasing temperature below Tc, consistent with the superconductivity-induced magnetic resonance found in other iron-based superconductors.
We report neutron inelastic scattering measurements on polycrystalline LaFePO and Sr2ScO3FeP, two members of the iron phosphide families of superconductors. No evidence is found for any magnetic fluctuations in the spectrum of either material in the
energy and wavevector ranges probed. Special attention is paid to the wavevector at which spin-density-wave-like fluctuations are seen in other iron-based superconductors. We estimate that the magnetic signal, if present, is at least a factor of four (Sr2ScO3FeP) or seven (LaFePO) smaller than in the related iron arsenide and chalcogenide superconductors. These results suggest that magnetic fluctuations are not as influential on the electronic properties of the iron phosphide systems as they are in other iron-based superconductors.
We report neutron inelastic scattering measurements on the normal and superconducting states of single-crystalline Cs0.8Fe1.9Se2. Consistent with previous measurements on Rb(x)Fe(2-y)Se2, we observe two distinct spin excitation signals: (i) spin-wave
excitations characteristic of the block antiferromagnetic order found in insulating A(x)Fe(2-y)Se2 compounds, and (ii) a resonance-like magnetic peak localized in energy at 11 meV and at an in-plane wave vector of (0.25, 0.5). The resonance peak increases below Tc = 27 K, and has a similar absolute intensity to the resonance peaks observed in other Fe-based superconductors. The existence of a magnetic resonance in the spectrum of Rb(x)Fe(2-y)Se2 and now of Cs(x)Fe(2-y)Se2 suggests that this is a common feature of superconductivity in this family. The low energy spin-wave excitations in Cs0.8Fe1.9Se2 show no measurable response to superconductivity, consistent with the notion of spatially separate magnetic and superconducting phases.
