硅和锗纳米线的原子排布和电荷分布的密度泛函紧束缚方法研究

低维硅锗材料是制备纳米电子器件的重要候选材料，是研发高效率、低能耗和超高速新一代纳米电子器件的基础材料之一，有着潜在的应用价值。采用密度泛函紧束缚方法分别对厚度相同、宽度在0.272 nm~0.554 nm之间的硅纳米线和宽度在0.283 nm~0.567 nm之间的锗纳米线的原子排布和电荷分布进行了计算研究。硅、锗纳米线宽度的改变使原子排布，纳米线的原子间键长和键角发生明显改变。纳米线表层结构的改变对各层内的电荷分布产生重要影响。纳米线中各原子的电荷转移量与该原子在表层内的位置相关。纳米线的尺寸和表层内原子排列结构对体系的稳定性产生重要影响。     

正交匹配追踪算法的迭代残差重建方法

正交匹配追踪(Orthogonal Matching Pursuit, OMP)算法是一种重要的压缩感知重构算法. OMP算法在每次迭代中选择与当前残差最相关的原子. 针对每次迭代需要重新计算残差的问题, 本文考虑偶数次迭代下残差未知的情况. 首先, 研究了奇数次迭代的残差与下一次迭代的残差之间的关系, 得到了一种偶数次迭代时选择原子的标准. 然后, 引入一种回溯机制来处理前面所得的迭代结果, 这种机制通过剔除其中多余的原子来实现精确重建. 据此, 提出了可减少计算残差的改进型正交匹配追踪算法.     

Shotgun reconstruction in the hypercube

Mossel and Ross raised the question of when a random coloring of a graph can be reconstructed from local information, namely, the colorings (with multiplicity) of balls of given radius. In this article, we are concerned with random 2-colorings of the vertices of the -dimensional hypercube, or equivalently random Boolean functions. In the worst case, balls of diameter are required to reconstruct. However, the situation for random colorings is dramatically different: we show that almost every 2-coloring can be reconstructed from the multiset of colorings of balls of radius 2. Furthermore, we show that for , almost every -coloring can be reconstructed from the multiset of colorings of 1-balls.     

The connected partition lattice of a graph and the reconstruction conjecture

Previously we showed that many invariants of a graph can be computed from its abstract induced subgraph poset, which is the isomorphism class of the induced subgraph poset, suitably weighted by subgraph counting numbers. In this paper, we study the abstract bond lattice of a graph, which is the isomorphism class of the lattice of distinct unlabelled connected partitions of a graph, suitably weighted by subgraph counting numbers. We show that these two abstract posets can be constructed from each other except in a few trivial cases. The constructions rely on certain generalisations of a lemma of Kocay in graph reconstruction theory to abstract induced subgraph posets. As a corollary, trees are reconstructible from their abstract bond lattice. We show that the chromatic symmetric function and the symmetric Tutte polynomial of a graph can be computed from its abstract induced subgraph poset. Stanley has asked if every tree is determined up to isomorphism by its chromatic symmetric function. We prove a counting lemma, and indicate future directions for a study of Stanley's question.     

A framework to perform high-order deconvolution for finite-volume method on simplicial meshes

In this article, a new framework to design high-order approximations in the context of node-centered finite volumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple and compact differential operators, which is a critical point to achieve good performances in the High-performance computing context. This method is based on deconvolution between nodal and volume-average values, which can be conducted to any order. The interest of the new method is illustrated through three different applications: mesh-to-mesh interpolation, levelset curvature computation, and numerical scheme for convection. Higher order can also be achieved within the present framework by introducing high-rank tensors. Although these tensors feature much symmetries, their manipulation can quickly become an overwhelming task. For this reason and without loss of generality, the present articles are limited to third-order expansion. This method, although tightly connected to the k-exact schemes theory, does not rely on successive corrections: the high-order property is obtained in a single operation, which makes them more attractive in terms of performances.     

A discontinuous Galerkin method for Stokes equation by divergence-free patch reconstruction

A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal component penalty terms to cancel out the pressure term. Consequently, the Stokes equation can be solved as an elliptic system instead of a saddle-point problem due to such weak form. The number of degree of freedoms of our method is the same as the number of elements in the mesh for different order of accuracy. The error estimations of the proposed method are given in a classical style, which are then verified by some numerical examples.     

A mathematical model for the 3d location estimation of 2D echocardiography data

The recovery of 3D left ventricle(LV) shape using 2D echocardiography is very attractable topic in the field of ultrasound imaging. In this paper, we propose a mathematical model to determine the 3D position of LV contours extracted from multiple 2D echocardiography images. We formulate the proposed model as a non-convex constrained minimization problem. To solve it, we propose a proximal alternating minimization algorithm with a solver OPTI for quadratically constrained quadratic program. For validating the proposed model, numerical experiments are performed with real ultrasound data. The experimental results show that the proposed model is promising and available for real echocardiography data.     

IDose^4迭代重建技术应用于低剂量CT肾动脉血管造影的临床分析

为探讨IDose 4迭代重建技术在低剂量CT肾动脉血管造影中的应用价值,选取205例拟行肾动脉CT血管造影患者,随机将其分为4组,A组(51例)采用管电压100 kV、管电流100 mA,碘海醇370 mg I/mL及IDose 4迭代重建技术,B组(51例)采用管电压100 kV、管电流150 mA,碘海醇270 mg I/mL及IDose 4迭代重建技术,C组(51例)采用管电压80 kV、管电流180 mA,碘海醇270 mg I/mL及IDose 4迭代重建技术,D组(52例)管电压120 kV、管电流120 mA,碘海醇370 mg I/mL及滤波反投影(FBP)重建技术。分析各组图像肾主动脉干CT值、噪声(SD)、信噪比(SNR)和噪声比(CNR),受检者接受CT有效剂量(ED)、容积CT剂量指数(CTDI vol)、剂量长度乘积(DLP)、碘摄入量以及重建图像评分差异和诊断效能。结果显示,A、B、C组重建图像评分优于D组,肾动脉主干CT值、SD、SNR、CNR均高于D组,B、C组肾动脉主干CT值、SD略低于A组。A、B、C组CTDI vol、DLP、ED均低于D组,B组CTDI vol、DLP、ED高于A组。A、B、C、D组诊断肾主动脉狭窄准确率分别为92.68%、86.49%、84.62%、82.86%。证实IDose 4迭代重建技术能降低受试者受辐射和造影剂剂量,提高成像质量,在低剂量CT肾动脉血管造影中具有较高可行性和实用性。     

Polymer Scaffolds for Biomedical Applications in Peripheral Nerve Reconstruction

The nervous system is a significant part of the human body, and peripheral nerve injury caused by trauma can cause various functional disorders. When the broken end defect is large and cannot be repaired by direct suture, small gap sutures of nerve conduits can effectively replace nerve transplantation and avoid the side effect of donor area disorders. There are many choices for nerve conduits, and natural materials and synthetic polymers have their advantages. Among them, the nerve scaffold should meet the requirements of good degradability, biocompatibility, promoting axon growth, supporting axon expansion and regeneration, and higher cell adhesion. Polymer biological scaffolds can change some shortcomings of raw materials by using electrospinning filling technology and surface modification technology to make them more suitable for nerve regeneration. Therefore, polymer scaffolds have a substantial prospect in the field of biomedicine in future. This paper reviews the application of nerve conduits in the field of repairing peripheral nerve injury, and we discuss the latest progress of materials and fabrication techniques of these polymer scaffolds.     

d-Orbital Reconstructions Forced by Double Bow-Shaped Deformations and Second Coordination Sphere Effects of Cu(II) Heme Analogs in HER**

Both geometric architecture and electronic configurations of heme proteins contribute to its activity. In this work we designed and synthesized a series of four copper(II) porphyrin complexes ( 4 -, 3 -, 2 - and 1 -Cu) where the molecular conformations are modulated by a pair of stepwise shortened straps on the same porphyrin side (cis-ortho) to give double bow-shaped skeletons. Single crystal structures demonstrate that the straps gradually increase the saddle deformation and the deviation of the metal centers, which is in accordance with two, unusual d-orbital reconstructions of two different ground states, as revealed by 4 K EPR and DFT calculations. In the study of the electrocatalytic hydrogen evolution reaction (HER), 1 -Cu, with the shortest straps, showed the most apparent improvement of activity. Second coordination sphere (SCS) effects created by the double bow-shaped architecture and the strong saddle porphyrin core in 1 -Cu are found to play key roles in proton trapping during the catalytic process. The work contributes a novel strategy to improve the catalytic performance of heme analogs through ligand geometric modulation.