Dynamic Kernel Sparsifiers

A geometric graph associated with a set of points $P= \{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$ and a fixed kernel function $\mathsf{K}:\mathbb{R}^d\times \mathbb{R}^d\to\mathbb{R}_{\geq 0}$ is a complete graph on $P$ such that the weight of edge $(x_i, x_j)$ is $\mathsf{K}(x_i, x_j)$. We present a fully-dynamic data structure that maintains a spectral sparsifier of a geometric graph under updates that change the locations of points in $P$ one at a time. The update time of our data structure is $n^{o(1)}$ with high probability, and the initialization time is $n^{1+o(1)}$. Under certain assumption, we can provide a fully dynamic spectral sparsifier with the robostness to adaptive adversary. We further show that, for the Laplacian matrices of these geometric graphs, it is possible to maintain random sketches for the results of matrix vector multiplication and inverse-matrix vector multiplication in $n^{o(1)}$ time, under updates that change the locations of points in $P$ or change the query vector by a sparse difference

Data for the gene expression profiling and alternative splicing events during the chondrogenic differentiation of human cartilage endplate-derived stem cells under hypoxia

AbstractThis article contains relevant data of the research article titled Global profiling of the gene expression and alternative splicing events during the hypoxia-regulated chondrogenic differentiation in human cartilage endplate-derived stem cells (Yao et al., 2016) [1]. The data show global profiling of the DEGs (Differentially expressed genes) and AS (Alternative splicing) events during the hypoxia-regulated chondrogenesis of CESCs (human cartilage endplate-derived stem cells) by using Affymetrix Human Transcriptome Array 2.0 (HTA 2.0) system. In addition, the enriched GO (Gene Ontology) functions and signaling pathways are listed. The information presented here includes the information of patients from which the clinical samples are obtained, the list of primers used for validation, the identification, GO and KEGG analysis of DEG and AS events

Power-Law Decay of Standing Waves on the Surface of Topological Insulators

We propose a general theory on the standing waves (quasiparticle interference pattern) caused by the scattering of surface states off step edges in topological insulators, in which the extremal points on the constant energy contour of surface band play the dominant role. Experimentally we image the interference patterns on both Bi$_2$Te$_3$ and Bi$_2$Se$_3$ films by measuring the local density of states using a scanning tunneling microscope. The observed decay indices of the standing waves agree excellently with the theoretical prediction: In Bi$_2$Se$_3$, only a single decay index of -3/2 exists; while in Bi$_2$Te$_3$ with strongly warped surface band, it varies from -3/2 to -1/2 and finally to -1 as the energy increases. The -1/2 decay indicates that the suppression of backscattering due to time-reversal symmetry does not necessarily lead to a spatial decay rate faster than that in the conventional two-dimensional electron system. Our formalism can also explain the characteristic scattering wave vectors of the standing wave caused by non-magnetic impurities on Bi$_2$Te$_3$.Comment: 4 pages, 3 figure

Data Processing Pipeline for Pointing Observations of Lunar-based Ultraviolet Telescope

We describe the data processing pipeline developed to reduce the pointing observation data of Lunar-based Ultraviolet Telescope (LUT), which belongs to the Chang'e-3 mission of the Chinese Lunar Exploration Program. The pointing observation program of LUT is dedicated to monitor variable objects in a near-ultraviolet (245-345 nm) band. LUT works in lunar daytime for sufficient power supply, so some special data processing strategies have been developed for the pipeline. The procedures of the pipeline include stray light removing, astrometry, flat fielding employing superflat technique, source extraction and cosmic rays rejection, aperture and PSF photometry, aperture correction, and catalogues archiving, etc. It has been intensively tested and works smoothly with observation data. The photometric accuracy is typically ~0.02 mag for LUT 10 mag stars (30 s exposure), with errors come from background noises, residuals of stray light removing, and flat fielding related errors. The accuracy degrades to be ~0.2 mag for stars of 13.5 mag which is the 5{\sigma} detection limit of LUT.Comment: 10 pages, 7 figures, 4 tables. Minor changes and some expounding words added. Version accepted for publication in Astrophysics and Space Science (Ap&SS

Interface induced high temperature superconductivity in single unit-cell FeSe films on SrTiO3

Searching for superconducting materials with high transition temperature (TC) is one of the most exciting and challenging fields in physics and materials science. Although superconductivity has been discovered for more than 100 years, the copper oxides are so far the only materials with TC above 77 K, the liquid nitrogen boiling point. Here we report an interface engineering method for dramatically raising the TC of superconducting films. We find that one unit-cell (UC) thick films of FeSe grown on SrTiO3 (STO) substrates by molecular beam epitaxy (MBE) show signatures of superconducting transition above 50 K by transport measurement. A superconducting gap as large as 20 meV of the 1 UC films observed by scanning tunneling microcopy (STM) suggests that the superconductivity could occur above 77 K. The occurrence of superconductivity is further supported by the presence of superconducting vortices under magnetic field. Our work not only demonstrates a powerful way for finding new superconductors and for raising TC, but also provides a well-defined platform for systematic study of the mechanism of unconventional superconductivity by using different superconducting materials and substrates

Universal critical properties of the Eulerian bond-cubic model

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of $n$. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O($n$) branch for $n < 2$ and the results obtained by previous transfer matrix calculations. For $n=2$, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model. These results confirm that the cubic anisotropy is marginal at $n=2$ but irrelevant for $n<2$