Precision Matrix Estimation by Inverse Principal Orthogonal Decomposition

We investigate the structure of a large precision matrix in Gaussian graphical models by decomposing it into a low rank component and a remainder part with sparse precision matrix.Based on the decomposition,we propose to estimate the large precision matrix by inverting a principal orthogonal decomposition(IPOD).The IPOD approach has appealing practical interpretations in conditional graphical models given the low rank component,and it connects to Gaussian graphical models with latent variables.Specifically,we show that the low rank component in the decomposition of the large precision matrix can be viewed as the contribution from the latent variables in a Gaussian graphical model.Compared with existing approaches for latent variable graphical models,the IPOD is conveniently feasible in practice where only inverting a low-dimensional matrix is required.To identify the number of latent variables,which is an objective of its own interest,we investigate and justify an approach by examining the ratios of adjacent eigenvalues of the sample covariance matrix?Theoretical properties,numerical examples,and a real data application demonstrate the merits of the IPOD approach in its convenience,performance,and interpretability.     

A symmetric integrated radial basis function method for solving differential equations

In this article, integrated radial basis functions (IRBFs) are used for Hermite interpolation in the solution of differential equations, resulting in a new meshless symmetric RBF method. Both global and local approximation‐based schemes are derived. For the latter, the focus is on the construction of compact approximation stencils, where a sparse system matrix and a high‐order accuracy can be achieved together. Cartesian‐grid‐based stencils are possible for problems defined on nonrectangular domains. Furthermore, the effects of the RBF width on the solution accuracy for a given grid size are fully explored with a reasonable computational cost. The proposed schemes are numerically verified in some elliptic boundary‐value problems governed by the Poisson and convection‐diffusion equations. High levels of the solution accuracy are obtained using relatively coarse discretisations.     

A three-stage, VSVO, Hermite-Birkhoff-Taylor, ODE solver

The new variable-step, variable-order, ODE solver, HBT(p) of order p, presented in this paper, combines a three-stage Runge-Kutta method of order 3 with a Taylor series method of order p-2 to solve initial value problems , where y:R→R^d and f:R×R^d→R^d. The order conditions satisfied by HBT(p) are formulated and they lead to Vandermonde-type linear algebraic systems whose solutions are the coefficients in the formulae for HBT(p). A detailed formulation of variable-step HBT(p) in both fixed-order and variable-order modes is presented. The new method and the Taylor series method have similar regions of absolute stability. To obtain high-accuracy results at high order, this method has been implemented in multiple precision.     

基于月球探测数据的月面地形重构方法研究

在比较不同探月任务取得的月表三维影像数据的基础上,选择中国嫦娥一号全月分幅数字高程模型（DEM）数据作为构建月表地形模型的数据源,并利用ArcGIS、Cass和AutoCAD等软件的功能及其之间的连接关系,研究了基于月球探测数据构建月表三维模型的技术和方法。以月表撞击坑Lichtenberg为例,建立了撞击坑的三维地形模型,并对其精度和影响精度的因素进行了分析。分析结果表明,对于500m分辨率的原始数据,模型误差较小,产生误差的原因主要包括生成等高线的密度、采点间距等因素。     

基于正弦函数变换的灰色预测模型研究及其应用

本文研究了灰色预测模型的应用问题.利用正弦函数变换提高了原始数据光滑度,获得了比对数及幂函数变换所建GM(1,1)模型的精度更高的基于正弦函数变换的灰色预测模型,推广了灰色预测模型的使用范围.     

Melting behaviours of nickel nanorods

We report the synthesis and measurement of an ultra-precise and extremely stable optical frequency in the telecommunications window around 1543 nm. Using a fibre-based femtosecond frequency comb we have phase-stabilised a fibre laser at 194 THz to an optical frequency standard at 344 THz, thus transferring the properties of the optical frequency standard to another spectral region. Relative to the optical frequency standard, the synthesised frequency at 194 THz is determined to within 1 mHz and its fractional frequency instability is measured to be less than 2×10^-15 at 1 s, reaching 5× 10^-18 after 8000 s. We also measured the synthesised frequency against a caesium fountain clock: here the frequency comparison itself contributes less than 4 mHz (2×10^-17) to the uncertainty. Our results confirm the suitability of fibre based frequency comb technology for precision measurements and frequency synthesis, and enable long-distance comparison of optical clocks by using optical fibres to transmit the frequency information.     

On-Surface Synthesis of One-Dimensional Carbon-Based Nanostructures via C−X and C−H Activation Reactions

The past decades have witnessed the emergence of low-dimensional carbon-based nanostructures owing to their unique properties and various subsequent applications. It is of fundamental importance to explore ways to achieve atomically precise fabrication of these interesting structures. The newly developed on-surface synthesis approach provides an efficient strategy for this challenging issue, demonstrating the potential of atomically precise preparation of low-dimensional nanostructures. Up to now, the formation of various surface nanostructures, especially carbon-based ones, such as graphene nanoribbons (GNRs), kinds of organic (organometallic) chains and films, have been achieved via on-surface synthesis strategy, in which in-depth understanding of the reaction mechanism has also been explored. This review article will provide a general overview on the formation of one-dimensional carbon-based nanostructures via on-surface synthesis method. In this review, only a part of the on-surface chemical reactions (specifically, C−X (X=Cl, Br, I) and C−H activation reactions) under ultra-high vacuum conditions will be covered.     

Sequence‐Defined Introduction of Hydrophobic Motifs and Effects in Lectin Binding of Precision Glycomacromolecules

This study investigates the influence of an increasingly hydrophobic backbone of multivalent glycomimetics based on sequence‐defined oligo(amidoamines) on their resulting affinity toward bacterial lectins. Glycomacromolecules are obtained by stepwise assembly of tailor‐made building blocks on solid support, using both hydrophobic aliphatic and aromatic building blocks to enable a gradual change in hydrophobicity of the backbone. Their binding behavior toward model lectin Concanavalin A (ConA) is evaluated using isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR) showing higher affinities for glycomacromolecules with higher content of hydrophobic and aromatic moieties in the backbone. Finally, glycomacromolecules are tested in a bacterial adhesion inhibition study against Escherichia coli where more hydrophobic backbones yield higher inhibitory potentials most likely due to additional secondary interactions with hydrophobic regions of the protein receptor as well as a change in conformation exposing carbohydrate ligands for increased binding. Overall, the results highlight the influence and thereby importance of the polymer backbone itself on the resulting properties of polymeric biomimetics.     

瞄准精度对中子半影成像的影响

在Monte Carlo方法模拟中子半影成像的基础上,对视场内点的空间线性不变性进行了研究.在视场范围内,离轴点产生了与离轴距离成正比的展宽现象,但点的积分强度保持了很好一致性,证明系统满足线性不变性假设.利用这一结果,分析了瞄准精度对成像系统的影响.结果表明：靶心在物面上的径向偏差应控制在50μm之内;物距误差控制应在300μm以内;编码孔旋转弧度须小于0.1mrad. 关键词： 空间线性不变性 瞄准精度 展宽效应 图像畸变     

固体沿光轴方向的极缓慢速度和微小位移的激光多普勒测量

为了实现目标极缓慢速度和微小位移的实时、准确监测,消除各种干扰对微弱多普勒信号的影响,设计了一套激光多普勒测速(LDV)系统。该系统采用迈克尔逊干涉光路和调幅解调、相敏检测技术,具有较强的抗干扰能力。实验结果表明,该系统可实现固体目标沿光轴方向μm/s级速度和μm级位移的实时、准确测量。该系统光路结构简单,对目标的表面状况无特殊要求,可用于滑坡、地陷等地质灾害的监测,及桥梁、大坝等工程结构变形状况的检测,该方案对相关科学实验和工件精密测量也有重要意义。