利用空间点过程提取丛集点算法的适用性研究

以二维泊松过程理论为基础,结合空间点过程理论,引入k阶最近邻距离的概念,介绍了基于k阶最近距离的丛集点的提取算法,对该算法的适用范围进行了讨论和分析,发现丛集区域和背景区域疏密程度差异以及所研究的数据点数目对该方法有影响,疏密程度差异较小时,该算法的有效性不强,疏密程度差异较大时,该算法较为适用,同时,数据点的总数不同时,算法的适用范围有所差异,但差异不大.此外,引入权重的思想,对算法中理想数据点的设置进行了一定程度的拓展,将所研究区域内的数据点赋予不同的权重,进行丛集数据点的提取,从而扩展了该算法的使用范围.关键词：丛集点最近邻距离EM算法分布参数比值     

局部k最近邻加权线性回归的光谱反射率重建

现实中很多场景都需要精确的颜色表示,如纺织、印刷、艺术品扫描存档、在线商品展示等。光谱反射率是决定物体颜色的本质属性,如果知道了光谱反射率,就可以重现物体在任何光照和观测条件下的颜色。采用专业仪器测量光谱反射率有成本高、分辨率低、测量时间慢等问题。随着数码成像设备的普及,基于相机RGB响应值的光谱反射率重建算法具有重要现实意义。光谱反射率重建的目的是建立低维RGB响应值到高维光谱反射率向量的映射关系,回归方法在这一领域已取得广泛应用。由于光谱反射率向量所处的空间是嵌在高维欧氏空间中的一个低维子流形,在训练样本有限的条件下,传统的全局回归方法不能有效地学习该流形结构,往往导致过拟合,使得学习出来的模型泛化能力较差。局部线性回归方法虽然可以改善全局回归过拟合的问题,但是局部学习方法易受例外点的影响,导致拟合不足。针对这一问题,提出一种基于局部加权线性回归的光谱反射率重建方法,这种方法在一个k最近邻范围约束内,给每个局部训练样本赋予不同的权重,从而有所侧重地利用局部训练样本来估计光谱反射率。实验结果表明,基于局部k最近邻加权线性回归的方法能更有效地利用局部信息,缓解过拟合和拟合不足,更准确地重建光谱反射率。     

Infinite clusters in percolation models

The qualitative nature of infinite clusters in percolation models is investigated. The results, which apply to both independent and correlated percolation in any dimension, concern the number and density of infinite clusters, the size of their external surface, the value of their (total) surface-to-volume ratio, and the fluctuations in their density. In particular it is shown thatN ₀, the number of distinct infinite clusters, is either 0, 1, or and the caseN ₀= (which might occur in sufficiently high dimension) is analyzed.Alfred P. Sloan Research Fellow, Research supported in part by National Science Foundation grant No. MCS 77-20683 and by the U.S.-Israel Binational Science Foundation.Research supported in part by the U.S.Israel Binational Science Foundation.     

Stability of gold cages (Au<Subscript>16</Subscript> and Au<Subscript>17</Subscript>) at finite temperature

We have employed ab initio molecular dynamics to investigate the stability of the smallest gold cages, namely Au₁₆ and Au₁₇, at finite temperatures. First, we obtain the ground state structure along with at least 50 distinct isomers for both the clusters. This is followed by the finite temperature simulations of these clusters. Each cluster is maintained at 12 different temperatures for a time period of at least 150 ps. Thus, the total simulation time is of the order of 2.4 ns for each cluster. We observe that the cages are stable at least up to 850 K. Although both clusters melt around the same temperature, i.e. around 900 K, Au₁₇ shows a peak in the heat capacity curve in contrast to the broad peak seen for Au₁₆.      

Self-segregation in chemical reactions,diffusion in a catalytic environment and an ideal polymer near a defect

We study a family of equivalent continuum models in one dimension. All these models map onto a single equation and include simple chemical reactions, diffusion in presence of a trap or a source and an ideal polymer chain near an attractive or repulsive site. We have obtained analytical results for the survival probability, total growth rate, statistical properties of nearest-neighbour distribution between a trap and unreacted particle and mean-squared displacement of the polymer chain. Our results are compared with the known asymptotic results in the theory of discrete random walks on a lattice in presence of a defect.     

计入次近邻作用的─维点阵的定＂长＂比热

计算了计入次近邻相互作用后一维点阵在低温下的定＂长＂比热,结果表明次近邻的影响使比热减小．比热;次近邻作用     

递归方法和团簇磁性的计算

介绍了如何应用递归方法将哈密顿矩阵三对角化,从而求得局域态密度 ,并以计算铑团簇的磁矩为例,说明了递归方法在研究团簇的电子结构方面的应用。     

TinMg (n=1—10)掺杂团簇的密度泛函研究

采用密度泛函(DFT)中的B3LYP方法,选择sto-3g基组,优化并得到了Ti_nMg(n=1—10)小团簇的基态平衡结构,计算出了掺杂团簇的基态结构的平均键长、对称性、原子化能、能级分布、能级间隙、束缚能、总能的二阶差分. 结果表明,随着团簇原子数的增加,镁原子更容易趋于团簇表面位置,镁-钛平均键长大于钛-钛平均键长,以对称性结构为最稳定的基态结构,且呈多个五角双锥结构. 其中Ti₅Mg和Ti₈Mg的结构更为稳定.关键词：密度泛函钛-镁团簇基态结构     

MgnLa(n=2-6)掺杂团簇的密度泛函研究

采用密度泛函(DFT)中的B3LYP方法,选择CEP-31g基组,优化并得到了MgnLa(n=2- 6)小团簇的基态平衡结构,计算出了掺杂团簇的基态结构的平均键长、对称性、费米能级、能级间隙、束缚能、总能的二阶差分．结果表明,随着团簇原子数的增加,La原子更容易趋于团簇表面位置. 与未掺杂Mg团簇相比,La原子多采用取代其稳定基态结构的一个Mg原子形成掺杂团簇的稳定结构. 从有限的结果看,其中 Mg3La和 Mg6La的结构更为稳定．     

Benchmark CCSD(T) and DFT study of binding energies in Be7 − 12: in search of reliable DFT functional for beryllium clusters

We present a computational study of the stability of small homonuclear beryllium clusters Be_{7 ? 12} in singlet electronic states. Our predictions are based on highly correlated CCSD(T) coupled cluster calculations. Basis set convergence towards the complete basis set limit as well as the role of the 1s core electron correlation are carefully examined. Our CCSD(T) data for binding energies of Be_{7 ? 12} clusters serve as a benchmark for performance assessment of several density functional theory (DFT) methods frequently used in beryllium cluster chemistry. We observe that, from Be₁₀ clusters on, the deviation from CCSD(T) benchmarks is stable with respect to size, and fluctuating within 0.02 eV error bar for most examined functionals. This opens up the possibility of scaling the DFT binding energies for large Be clusters using CCSD(T) benchmark values for smaller clusters. We also tried to find analogies between the performance of DFT functionals for Be clusters and for the valence-isoelectronic Mg clusters investigated recently in Truhlar's group. We conclude that it is difficult to find DFT functionals that perform reasonably well for both beryllium and magnesium clusters. Out of 12 functionals examined, only the M06-2X functional gives reasonably accurate and balanced binding energies for both Be and Mg clusters.     

First-principle study of geometries, electronic structures and vibrational spectra of neutral and anionic onion-like [As@Ni12@As20］

We present results of first-principle study for both neutral and anionic onion-like [As@Ni₁₂@As₂₀］. The ground-states of singly-charged and doubly-charged anions deviate from ideal I_h symmetrical geometry because of Jahn--Teller effect, whereas the triply-charged singlet and neutral quartet have similar stable geometries of I_h symmetry. The infrared and Raman spectra may provide a way to determine various charge states of this molecule with the same symmetry. Based on our systematical calculations, we suggest additional experimental measurements in order to determine the appropriate functional with great confidence, which should be important in the research for future quantum dot devices.