On the power of conditional independence testing under model-X

For testing conditional independence (CI) of a response Y and a predictor X given covariates Z, the recently introduced model-X (MX) framework has been the subject of active methodological research, especially in the context of MX knockoffs and their successful application to genome-wide association studies. In this paper, we study the power of MX CI tests, yielding quantitative explanations for empirically observed phenomena and novel insights to guide the design of MX methodology. We show that any valid MX CI test must also be valid conditionally on Y and Z; this conditioning allows us to reformulate the problem as testing a point null hypothesis involving the conditional distribution of X. The Neyman-Pearson lemma then implies that the conditional randomization test (CRT) based on a likelihood statistic is the most powerful MX CI test against a point alternative. We also obtain a related optimality result for MX knockoffs. Switching to an asymptotic framework with arbitrarily growing covariate dimension, we derive an expression for the limiting power of the CRT against local semiparametric alternatives in terms of the prediction error of the machine learning algorithm on which its test statistic is based. Finally, we exhibit a resampling-free test with uniform asymptotic Type-I error control under the assumption that only the first two moments of X given Z are known, a significant relaxation of the MX assumption

Electronic, optical and transport properties of van der Waals Transition-metal Dichalcogenides Heterostructures: A First-principle Study

Two-dimensional (2D) transition-metal dichalcogenide (TMD) MX$_2$ (M = Mo, W; X= S, Se, Te) possess unique properties and novel applications. In this work, we perform first-principles calculations on the van der Waals (vdW) stacked MX$_2$ heterostructures to investigate their electronic, optical and transport properties systematically. We perform the so-called Anderson's rule to classify the heterostructures by providing the scheme of the construction of energy band diagrams for the heterostructure consisting of two semiconductor materials. For most of the MX$_2$ heterostructures, the conduction band maximum (CBM) and valence band minimum (VBM) reside in two separate semiconductors, forming type II band structure, thus the electron-holes pairs are spatially separated. We also find strong interlayer coupling at $\Gamma$ point after forming MX$_2$ heterostructures, even leading to the indirect band gap. While the band structure near $K$ point remain as the independent monolayer. The carrier mobilities of MX$_2$ heterostructures depend on three decisive factors, elastic modulus, effective mass and deformation potential constant, which are discussed and contrasted with those of monolayer MX$_2$, respectively.Comment: 7 figure

Graphene-like Dirac states and Quantum Spin Hall Insulators in the square-octagonal MX2 (M=Mo, W; X=S, Se, Te) Isomers

We studied the square-octagonal lattice of the transition metal dichalcogenide MX$_2$ (with $M$=Mo, W; $X$=S, Se and Te), as an isomer of the normal hexagonal compound of MX$_2$. By band structure calculations, we observe the graphene-like Dirac band structure in a rectangular lattice of MX$_2$ with nonsymmorphic space group symmetry. Two bands with van Hove singularity points cross each at the Fermi energy, leading to two Dirac cones that locates at opposite momenta. Spin-orbit coupling can open a nontrivial gap at these Dirac points and induce the quantum spin Hall (QSH) phase, the 2D topological insulator. Here, square-octagonal MX$_2$ structures realize the interesting graphene physics, such as Dirac bands and QSH effect, in the transition metal dichalcogenides.Comment: 4 pages, 3 figures, 1 Tabl

The Calibration of the WISE W1 and W2 Tully-Fisher Relation

In order to explore local large-scale structures and velocity fields, accurate galaxy distance measures are needed. We now extend the well-tested recipe for calibrating the correlation between galaxy rotation rates and luminosities -- capable of providing such distance measures -- to the all-sky, space-based imaging data from the Wide-field Infrared Survey Explorer (WISE) W1 ($3.4\mu$m) and W2 ($4.6\mu$m) filters. We find a linewidth to absolute magnitude correlation (known as the Tully-Fisher Relation, TFR) of $\mathcal{M}^{b,i,k,a}_{W1} = -20.35 - 9.56 (\log W^i_{mx} - 2.5)$ (0.54 magnitudes rms) and $\mathcal{M}^{b,i,k,a}_{W2} = -19.76 - 9.74 (\log W^i_{mx} - 2.5)$ (0.56 magnitudes rms) from 310 galaxies in 13 clusters. We update the I-band TFR using a sample 9% larger than in Tully & Courtois (2012). We derive $\mathcal{M}^{b,i,k}_I = -21.34 - 8.95 (\log W^i_{mx} - 2.5)$ (0.46 magnitudes rms). The WISE TFRs show evidence of curvature. Quadratic fits give $\mathcal{M}^{b,i,k,a}_{W1} = -20.48 - 8.36 (\log W^i_{mx} - 2.5) + 3.60 (\log W^i_{mx} - 2.5)^2$ (0.52 magnitudes rms) and $\mathcal{M}^{b,i,k,a}_{W2} = -19.91 - 8.40 (\log W^i_{mx} - 2.5) + 4.32 (\log W^i_{mx} - 2.5)^2$ (0.55 magnitudes rms). We apply an I-band -- WISE color correction to lower the scatter and derive $\mathcal{M}_{C_{W1}} = -20.22 - 9.12 (\log W^i_{mx} - 2.5)$ and $\mathcal{M}_{C_{W2}} = -19.63 - 9.11 (\log W^i_{mx} - 2.5)$ (both 0.46 magnitudes rms). Using our three independent TFRs (W1 curved, W2 curved and I-band), we calibrate the UNION2 supernova Type Ia sample distance scale and derive $H_0 = 74.4 \pm 1.4$(stat) $\pm\ 2.4$(sys) kms$^{-1}$ Mpc$^{-1}$ with 4% total error.Comment: 22 page, 21 figures, accepted to ApJ, Table 1 data at http://spartan.srl.caltech.edu/~neill/tfwisecal/table1.tx

The MX-Helix of Muscle nAChR Subunits Regulates Receptor Assembly and Surface Trafficking.

Nicotinic acetylcholine receptors (AChRs) are pentameric channels that mediate fast transmission at the neuromuscular junction (NMJ) and defects in receptor expression underlie neuromuscular disorders such as myasthenia gravis and congenital myasthenic syndrome (CMS). Nicotinic receptor expression at the NMJ is tightly regulated and we previously identified novel Golgi-retention signals in the β and δ subunit cytoplasmic loops that regulate trafficking of the receptor to the cell surface. Here, we show that the Golgi retention motifs are localized in the MX-helix, a juxta-membrane alpha-helix present in the proximal cytoplasmic loop of receptor subunits, which was defined in recent crystal structures of cys-loop receptor family members. First, mutational analysis of CD4-MX-helix chimeric proteins showed that the Golgi retention signal was dependent on both the amphipathic nature of the MX-helix and on specific lysine residues (βK353 and δK351). Moreover, retention was associated with ubiquitination of the lysines, and βK353R and δK351R mutations reduced ubiquitination and increased surface expression of CD4-β and δ MX-helix chimeric proteins. Second, mutation of these lysines in intact β and δ subunits perturbed Golgi-based glycosylation and surface trafficking of the AChR. Notably, combined βK353R and δK351R mutations increased the amount of surface AChR with immature forms of glycosylation, consistent with decreased Golgi retention and processing. Third, we found that previously identified CMS mutations in the ε subunit MX-helix decreased receptor assembly and surface levels, as did an analogous mutation introduced into the β subunit MX-helix. Together, these findings indicate that the subunit MX-helix contributes to receptor assembly and is required for normal expression of the AChR and function of the NMJ. In addition, specific determinants in the β and δ subunit MX-helix contribute to quality control of AChR expression by intracellular retention and ubiquitination of unassembled subunits, and by facilitating the appropriate glycosylation of assembled surface AChR

Phase transformation B1 to B2 in TiC, TiN, ZrC and ZrN under pressure

Phase stability of various phases of MX (M = Ti, Zr; X = C, N) at equilibrium and under pressure is examined based on first-principles calculations of the electronic and phonon structures. The results reveal that all B1 (NaCl-type) MX structures undergo a phase transition to the B2-structures under high pressure in agreement with the previous total-energy calculations. The B1-MX structures are dynamically stable under very high pressure (210-570 GPa). The pressure-induced B2 (CsCl-type) MC phases are dynamically unstable even at high pressures, and TiN and ZrN are found to crystallize with the B2-structure only at pressures above 55 GPa. The first-order B1-to-B2 phase transition in these nitrides is not related to the softening of phonon modes, and the dynamical instability of B2-MX is associated with a high density of states at the Fermi level.Comment: 9 pages, 4 figure

Implementation and performance of SIBYLS: a dual endstation small-angle X-ray scattering and macromolecular crystallography beamline at the Advanced Light Source.

The SIBYLS beamline (12.3.1) of the Advanced Light Source at Lawrence Berkeley National Laboratory, supported by the US Department of Energy and the National Institutes of Health, is optimized for both small-angle X-ray scattering (SAXS) and macromolecular crystallography (MX), making it unique among the world's mostly SAXS or MX dedicated beamlines. Since SIBYLS was commissioned, assessments of the limitations and advantages of a combined SAXS and MX beamline have suggested new strategies for integration and optimal data collection methods and have led to additional hardware and software enhancements. Features described include a dual mode monochromator [containing both Si(111) crystals and Mo/B(4)C multilayer elements], rapid beamline optics conversion between SAXS and MX modes, active beam stabilization, sample-loading robotics, and mail-in and remote data collection. These features allow users to gain valuable insights from both dynamic solution scattering and high-resolution atomic diffraction experiments performed at a single synchrotron beamline. Key practical issues considered for data collection and analysis include radiation damage, structural ensembles, alternative conformers and flexibility. SIBYLS develops and applies efficient combined MX and SAXS methods that deliver high-impact results by providing robust cost-effective routes to connect structures to biology and by performing experiments that aid beamline designs for next generation light sources