Face recognition based on PCA and multi-degree of freedom neurons

An algorithm of PCA face recognition based on Multi-degree of Freedom Neurons theory is proposed, which based on the sample sets' topological character in the feature space which is different from "classification". Compare with the traditional PCA+NN algorithm, experiments prove its efficiency.

Research on multi-degree-of-freedom neurons with weighted graphs

In this paper, we redefine the sample points set in the feature space from the point of view of weighted graph and propose a new covering model - Multi-Degree-of-Freedorn Neurons (MDFN). Base on this model, we describe a geometric learning algorithm with 3-degree-of-freedom neurons. It identifies the sample points secs topological character in the feature space, which is different from the traditional "separation" method. Experiment results demonstrates the general superiority of this algorithm over the traditional PCA+NN algorithm in terms of efficiency and accuracy.

Complex networks constructed from irrational number sequences

In this paper, we construct (d, r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length M into groups of d digits which represent the nodes while two consecutive groups overlap by r digits (r = 0,1,...,d-1), and the undirected edges indicate the adjacency between two consecutive groups. (3, r) and (4, r) networks are respectively constructed from 14 different irrational numbers and their topological properties are examined. By observation, we find that network topologies change with different values of d, r and even sequence length M instead of the types of irrational numbers, although they share some similar features with traditional random graphs. We make a further investigation to explain these interesting phenomena and propose the identical-degree random graph model. The results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers.

有机化合物结构自动解析专家系统研究

本文建立了一个能用于含N、P、O、S、Si及卤素等多种杂原子的有机化合物结构自动解析专家系统ESESOC(Expert System for the Elucidation of the Structure of Orsanic Compounds)。它可从未知化合物的分子式、光谱数据(包括IR, MS，~1HNMK ~(13)CNMR, 2D-NMR等)及其它化学信息自动地推衍出与己知信息相一致的候选化合物结构。ESESOC系统由三个部分组成：(1)光谱知识库及其光谱解释模块；(2)结构产生器；(3)结构验证模块。其结构解析基本过程为：从分子式、光谱数据或其它化学信息出发，由未知化合物的光谱数据去检索光谱知识库，即进行数据分析并推断出该未知化合物中可能含有的结构碎片，然后由结构产生器从这些结构碎片进行候选化合物结构的穷举生成，最后对候选结构进行验证并输出结果。从而实现由化合物光谱数据鉴别未知化合物结构的自动化。结构产生器是系统的核心模块。对一个结构产生器的基本要求是：穷举性，非冗余性，有效性。要完成一个能实际使用的结构产生器，效率则是至关重要的。ESESOC系统生成结果的穷举和非冗余性己通过与图论计算结果及著名的DENDRAL系统的生成结果相比较得以证明。如由本系统生成的烷烃系列C_nH_(2n+2)，及醇、醚系列C_nH_(2n+2)0的异构体数目与图论理论计算的数目相同；对C_5H_n n = 12，10，8，6，4，2，O；C_6H_n n = 14，12，lO，8，6，4，2，O系列，及含多种杂原子(O、N、S等)的复杂体系，其异构体生成结果则与DENDRAL系统的生成结果完全一致(DENDRAL系统的结构生成算法是经数学证明了是正确的，其结果已被很多系统引为穷举和非冗余性的例证)。关于ESESOC系统的有效性，在同一计算机上测试结果表明ESESOC系统的结构生成效率比著名的日本的CHEMICS系统高很多倍。结构解析专家系统另一重要组成部分为谱图知识库，它是逻辑推理的基础。专家系统的效能取决于其子结构一子光谱相关的知识库的有效性，所以要建造一个有效的~(13)CNMR知识库，关键在于建立一个好的子结构模型．在~(13)CNMR知识库中，子结构的概念与常规的子结构概念有所不同，它包括两个组成部分，(1)中心原子，它对应于一个化学位移；(2)环境部分，结构环境决定了中心原子的化学位移峰的位置。子结构模型的选择要适当兼顾信息全面和防止“组合爆炸”两个因素。ESESOC系统从~(13)CNMR本身的特征出发，提出了不确定层数的子结构模型。即以共振碳原子为中心，以与之相连的完整的官能团为外围环境，对这样的子结构，其外围环境根据官能团的不同可以是一层、或二层乃至多层，即环境层数是可变的。此即为ESESOC系统的广义-层子结构模型，它具有包含结构信息全，所有可能存在的子结构数量适中等优点。在此子结构模型的基础上，从CIAC-~(13)CNMR谱图数据库统计出。~(13)CNMR知识库，即子结构-~(13)CNMR化学位移相关表。ESESOC系统中结构验证方法有： ~(13)CNMR谱峰数预测，~(13)CNMR波谱模拟，应力能计算等。在结构解析专家系统研究中还涉及到如下三个问题：(1)结构编码；(2)结构之间相互比较；(3)结构中原子的对称性分析。在本研究中，对这些问题都提出了新的方案，并均获得较好结果。(1)在建造化合物结构信息系统时，首先要解决化合物结构的计算描述，即结构编码问题，以进行化合物结构的计算机存储和管理。为此我们提出了两种新的拓扑指数编码方案，即ID指数和EAID指数。由ESESOC结构产生器穷生成了含1-22个碳原子的380多万个链烷烃异构体，含1-12四价碳原子的20多万仑复杂多环异构体及40多万个含杂原子的化合物，通过对这3个系列共440多万个化合物结构的验证，结果表明，ID和EAID指数对这440多万个化合物结构均能唯一地区分，即没有出现简并(简并是指两个或多个不同的结构具有相同的拓扑指数值)。这是迄今未见报道的。(2)在计算机结构信息处理中，最常遇到的一个问题就是确认一个结构是新结构还是为已知结构，这就要把该结构与库中的结构进行逐个比较。为了结构的比较，我们以二维连接表描述化合物的结构，因连接表随化合中原子的编序的变化而变化，因而就需要有一套序号赋值规则，无论结构图在画法或形状以及原子的序号上如何变化，都可使得结构图中的各原子按该规则得到唯一的排序方案。ESESOC系统的唯一性序号方案集中了Morgan算法及其改进方案之所长，并加入新的图的不变量，如最小环指数等以正确地划分分子中的原子，从而得到一个新的唯一性排序方案，该方案效率较高，可适用于各类复杂化合物。在ESESOC系统中，我们还以一维的整数数组来存贮和管理二维连接表，即得到压缩连接表，这在结构比较时大大地节省了系统开销，提高了比较速度。在同一结构中，若各原子由两种不同编序方案得到同一连接矩阵，则与某一序号所对应的两个原子所在结构图中的拓扑环境是等价的，也就是说两个节点是拓扑等价的，或具有拓扑对称性(Topological Symmetry)。化合物结构中原子的唯一性排序算法，有机化物结构异构体穷举生成过程中冗余对接的消除，NMR谱模拟等都与拓扑对称性密切相关。在ESESOC系统建造过程中，我们提出了三个新的拓扑等价性分析算法，它们是基于节点矩阵的拓扑等价性算法，基于全通道算法的拓扑等价性算法，以及基于扩展连接矩阵算法的拓扑等价性算法。这些算法结果准确，效率高，适用于各类化合物。

Structures of energy spectrum and persistent currents in mesoscopic rings with radial potential barrier in magnetic field

The energy spectrum and the persistent currents are calculated for finite-width mesoscopic annular structures with radial potential barrier in the presence of a magnetic field. The introduction of the tunneling barrier leads to the creation of extra edge states around the barrier and the occurrence of oscillatory structures superimposed on the bulk Landau level plateaus in the energy spectrum. We found that the Fermi energy E-F increases with the number of electrons N emerging many kinks. The single eigenstate persistent current exhibits complicated structures with vortex-like texture, ''bifurcation'', and multiple ''furcation'' patterns as N is increased. The total currents versus N display wild fluctuations.

Evolution of Localized Damage Zone in Heterogeneous Media

Evolution of localized damage zone is a key to catastrophic rupture in heterogeneous materials. In the present article, the evolutions of strain fields of rock specimens are investigated experimentally. The observed evolution of fluctuations and autocorrelations of strain fields under uniaxial compression demonstrates that the localization of deformation always appears ahead of catastrophic rupture. In particular, the localization evolves pronouncedly with increasing deformation in the rock experiments. By means of the definition of the zone with high strain rate and likely damage localization, it is found that the size of the localized zone decreases from the sample size at peak load to an eventual value. Actually, the deformation field beyond peak load is bound to suffer bifurcation, namely an elastic unloading part and a continuing but localized damage part will co-exist in series in a specimen. To describe this continuous bifurcation and localization process observed in experiments, a model on continuum mechanics is developed. The model can explain why the decreasing width of localized zone can lead stable deformation to unstable, but it still has not provided the complete equations governing the evolution of the localized zone.

香港地区湍蛙遗传多样性研究

依据线粒体上ND2和CO1两个变异较大的基因序列分析了香港地区香港湍蛙7种群、华南湍蛙1种群，以及大陆其他地区华南湍蛙7种群，戴云湍蛙1种群，武夷湍蛙1种群的系统发育关系，进而探讨香港湍蛙的遗传多样性、香港湍蛙特有性、如何确定香港湍蛙最佳保护单元以及这四种湍蛙的物种分类地位。 1． 香港湍蛙保护遗传学研究 香港湍蛙核苷酸传多样性较低，从其遗传多样性信息、单倍型网络分析、中性检验值以及岐点分布结果一致显示香港湍蛙很可能经历了瓶颈后的扩张，种群正在由一个较小的有效种群大小迅速增长, 有足够的时间通过变异用于积累单倍型的多态性, 而对于提高核苷酸多样化而言, 时间尚短（Nei M et al，1975，Avise J C，2000；李明等，2003）。 分子变异分析结果显示香港湍蛙种群间存在较多的基因交流，且系统发育树上各种群间交叉在一起，没有形成与地理单元相关的分支，而从其单倍型网络看，他们源于共同的祖先，是一个单系群，与地理单元间没有形成显著的遗传分化。因此应作为一个进化显著单元（ESU）。结合其与其他湍蛙发育关系及遗传距离以及野外采集信息认为香港湍蛙只在香港地区有分布，属于香港特有种。该物种内遗传多样性较低，又属于世界自然保护联盟红皮书中的近危种，同时也是《野生动物保护条例》中的受保护野生动物，且由于香港城市建设等使得其栖息环境受到威胁，因此在香港特别行政区应该受到重点保护。 从单倍型分布和核苷酸多样性可以看出大榄涌种群和城门种群具有较高的单倍型多样性和核苷酸多样性，应该作为保护的重点区域。 2. 华南湍蛙东、南沿海种群间系统关系 华南湍蛙分布广，各种群存在着丰富的遗传多样性信息且中部种群广西龙胜和湖南张家界种群核苷酸多样性明显高于其他边缘种群华南湍蛙。种群间几乎没有基因交流，且各种群间无共享单倍型，可见已形成了显著的遗传分化。各种群间遗传距离都较远，其中广东南昆山种群以及福建三港种群与其他种群距离最远，因此可以推测其他种群（广东深圳、香港大屿山、广西龙胜和防城以及湖南张家界种群）可能为独立进化的种群。但是否是一新种或一隐存种，还需要结合形态学进行更深入的研究。 本研究中无论从系统关系看还是从遗传距离看，大屿山种群与深圳种群最近，支持陈坚峰等将其定为华南湍蛙，即华南湍蛙新增一个分布点：香港大屿山。 系统树上广西防城种群（支B）与龙胜和湖南种群（支A）形成姐妹群。香港大屿山种群与深圳种群先形成姐妹群（支C），但却没有与其距离很近的广东南岭及南昆山种群（支D）形成姐妹群，可能粤北和粤中的环境及气候较复杂因此与粤南其他种群形成了明显的隔离。同时可以看出华南湍蛙种群遗传分化与地理距离没有显著的相关性。 3. 四种湍蛙间的系统关系 根据线粒体CO1基因建立四种湍蛙间的系统关系及其遗传距离，很清楚地看到，香港湍蛙与戴云湍蛙关系很近，而华南湍蛙则与武夷湍蛙较近。然而，戴云湍蛙同一个种群内部共有两个单倍型DY1和DY2，且两个单倍型间遗传距离大于DY1与香港湍蛙间遗传距离，更远远大于香港湍蛙种群内部的距离，即戴云湍蛙内部两个单倍型间遗传距离达到了种级水平，同样在系统发育树上这两个单倍型与香港湍蛙形成并系。但是，戴云湍蛙种内在形态上差异不显著。因此，其是否属于萌芽物种分化形成（budding speciation）或已经完全分化为两个不同的种值得进一步研究？ 与戴云湍蛙香港湍蛙关系类似，从系统树上看华南湍蛙不形成单系，而是分成两个大支，与武夷湍蛙形成并系，且福建和南昆山的华南湍蛙与武夷湍蛙遗传距离远大于武夷湍蛙种内福建种群与浙江种群的遗传距离，达到了种级分化水平。由此，可以推断武夷湍蛙是有效种。系统树上广东深圳、香港大屿山、广西防城和龙胜以及湖南张家界种群与华南湍蛙福建及南昆山各种群间遗传距离已超出了种内各种群间的遗传距离，但是至于这一支是否应为另外一个种，有必要扩大采样，并结合核基因及形态信息进行进一步研究。 MtDNA of ND2 and CO1 gene were used to investigate genetic diversity of Amolops in Hongkong .We collected seven populations of A. hongkongensis,，one population of A.ricketti from Hong Kong and other seven populations of A.ricketti from East and South of Chinese mainland. As well as one population of A. daiyunensis and one population of A.wuyiensis Phylogenetic relationship were analyzed of four species. Discussed whether A.hongkongensis is an endemic species and how can we make the conservation and management decisions. 1. Conservation Genetics of A. hongkongensis A. hongkongensis has a low nucleotide diversity, the results of genetic diversity, haplotype network, neutrality test and the mismatch distributions indicate that A. hongkongensis experienced a recent expansion after a bottle neck. They had enough time to accumulated haplotype diversity, but it’s too short to have a high nucleotide diversity（Nei M et al，1975，Avise J C，2000；Li et al，2003）. The result of AMOVA reveals that it has much gene exchange among the populations of A. hongkongensis. The clades of the phylogenetic tree were mixed together, no significant genetic differentiation among 8 populations and they share the same ancestor from the network analysis, these indicate that they are monophyly and should be protected as one ESU. Combined with the information of relationships of interspecies, genetic distance and distribution investigate, We conclude that A. hongkongensis is an endemic species of Hong Kong. Considering on the status of low genetic diversity in A.hongkongensis, and this species was listed in the IUCN red list as near threatened, as well as listed in the . Furthermore, it’s habitat loss and degradation more rapidly as the human activity got higher and higher. So it’s urgent to protect them in Hong Kong. Our results suggest that Tai Lam Wu and TAI MO Shan -Shing Mun populations have the higher priority to be protected because their higher genetic diversity. 2．Phylogenetic relationships among populations of Amolops ricketti from the Southern and eastern China A. ricketti has the considerable genetic diversity of mitochondrial haplotypes within and among populations, and Mitochondrial DNA diversity was higher in populations at the central area of the present distribution range of the frog，i. e. the Longsheng population and Zhangjiajie population, than at the edges of their distribution range. They have no share haplotype among populations, and have a significant genetic differentiation. Genetic distance is high among the populations, especially the distance of Nankun and Sangang group with others, which suggested that they evolved independently. May be there is a cryptic species or a new species, a further study is needed. The results of gene tree and the genetic distance clearly demonstrate that the population from LanTau island is A. ricketti, so we agree with Chen et al(2005) . That means A.ricketti have a new distribution site: LanTau island, HongKong. Phylogenetic relationships were analyzed through NJ and Mrbayes methods and got a consistent topological structure, the structure indicated that the ingroup were comprised four groups. Populations Longsheng and Zhangjiajie were first clustered as clade A; Populations Fangcheng was clustered together (clade B) as a sister group to clade A；Populations Shenzhen and Lantau island were sister groups and clustered as clade C；Then the clade D included populations Nankunshan and Nanling in Guangdong province and Sangang in Fujian province. 3. Phylogenetic Relationships among these four specises Phylogenetic relationships based on 1503bp CO1 gene and the genetic distance show that A. hongkongensis close to A. daiyunensis whereas A.ricketti near to A.wuyiensis. Nevertheless, there are two haplotypes in A.daiyunensis and the genetic distance between them higher than the distance between DY1 with A. hongkongensis. A. hongkongensis is nested in the paraphyletic ancestral species A. daiyunensis. Without significant difference in the morphological characters, So, we considered both A.daiyunensis and A.hongkongensis are valid species, may be this represents a case of ‘budding speciation’ like Batrachuperus pinchonii(Fu and Zeng,2008) in the population of A. daiyunensis. Just like two species above A. wuyiensis and A. ricketti are not monophyly, instead, A.wuyiensis is nested in the paraphyletic ancestral species A.ricketti. We need do more research to make sure whether they are new species.

Vortices in (Abelian) Chern-Simons gauge theory

The vortex solutions of various classical planar field theories with (Abelian) Chern-Simons term are reviewed. Relativistic vortices, put forward by Paul and Khare, arise when the Abelian Higgs model is augmented with the Chern-Simons term. Adding a suitable sixth-order potential and turning off the Maxwell term provides us with pure Chern-Simons theory, with both topological and non-topological self-dual vortices, as found by Hong-Kim-Pac, and by Jackiw-Lee-Weinberg. The non-relativistic limit of the latter leads to non-topological Jackiw-Pi vortices with a pure fourth-order potential. Explicit solutions are found by solving the Liouville equation. The scalar matter field can be replaced by spinors, leading to fermionic vortices. Alternatively, topological vortices in external field are constructed in the phenomenological model proposed by Zhang-Hansson-Kivelson. Non-relativistic Maxwell-Chern-Simons vortices are also studied. The Schrodinger symmetry of Jackiw-Pi vortices, as well as the construction of some time-dependent vortices, can be explained by the conformal properties of non-relativistic space-time, derived in a Kaluza-Klein-type framework. (c) 2009 Elsevier B.V. All rights reserved.

Development and transition of spiral wave in the coupled Hindmarsh-Rose neurons in two-dimensional space

The dynamics and the transition of spiral waves in the coupled Hindmarsh-Rose (H-R) neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D', is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons (or sites) and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.

Inner structure of Spin(c)(4) gauge potential on 4-dimensional manifolds

The decomposition of Spin(c)(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation Delta A(mu) = -lambda A(mu) has been discovered. Here, lambda is the vacuum expectation value of the spinor field, lambda = parallel to Phi parallel to(2), and A(mu) the twisting U(1) potential. It is found that when), takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.

Decomposition of Noncommutative U(1) Gauge Potential

We investigate the decomposition of noncommutative gauge potential (A) over cap (i), and find that it has inner structure, namely, (A) over cap (i) can he decomposed in two parts, (b) over cap (i) and (a) over cap (i), where (b) over cap (i) satisfies gauge transformations while (a) over cap (i) satisfies adjoint transformations, so close the Seiberg-Witten mapping of noncommutative, U(1) gauge potential. By, means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor

New vortex solutions of Jackiw-Pi model

Based on current phi-mapping topological theory, a kind of self-dual equations in Jackiw-Pi model are studied. We first obtain explicit, self-dual solutions that satisfy Liouville equation which contains delta-function. Then we get perfect vortex solutions which reflect the system's internal topological structure, and consequently the quantization of flux.