Modular Organization in a Cell: Concepts and Applications

Network biology is conceptualized as an interdisciplinary field, lying at the intersection among graph theory, statistical mechanics and biology. Great efforts have been made to promote the concept of network biology and its various applications in life s

algorithms for computing weak bisimulation equivalence

IEEE Comp Soc, IFIP, Tianjin Normal Univ

Study on QSPR of alcohols with a novel edge connectivity index F-m

A novel edge degree f(i) for heteroatom and multiple bonds in molecular graph is derived on the basis of the edge degree delta(e(r)). A novel edge connectivity index F-m is introduced. The multiple linear regression by using the edge connectivity index F-m and alcohol-type parameter delta, alcohol-distance parameter L can provide high-quality QSPR models for the normal boiling points (BPs), molar volumes (MVs), molar refraction (MRs), water solubility(log(1/S)) and octanol/water partition (logP) of alcohols with up to 17 non-hydrogen atoms. The results imply that these physical properties may be expressed as a liner combination of the edge connectivity index and alcohol-type parameter, 6, alcohol-distance parameter, L. For the models of the five properties, the correlation coefficient r and the standard errors are 0.9969,3.022; 0.9993, 1.504; 0.9992, 0.446; 0.9924,0.129 and 0.9973,0.123 for BPs, MVs, MRs, log(1/S) and logP, respectively. The cross-validation by using the leave-one-out method demonstrates the models to be highly reliable from the point of view of statistics.

A new topological index for the Changchun institute of applied chemistry C-13 NMR information system

A method to assign a single number representation for each atom (node) in a molecular graph, Atomic IDentification (AID) number, is proposed based on the counts of weighted paths terminated on that atom. Then, a new topological index, Molecular IDentification (MID) number is developed from AID. The MID is tested systematically, over half a million of structures are examined, and MID shows high discrimination for various structural isomers. Thus it can be used for documentation in the Changchun Institute of Chemistry C-13 NMR information system.

GENERAL ALPHA-N INDEX AND ITS APPLICATION .2. THE CORRELATION BETWEEN THE GENERAL ALPHA-N INDEX AND PHYSICAL-PROPERTIES OF NEUTRAL PHOSPHORUS-COMPOUNDS

The relationship between the alpha-N index and physical properties of neutral phosphorus extractants is studied. Using the general alpha-N index which could describe extractants with minute difference in structure, the good correlation between it and various physical properties of the neutral phosphorus extractants (e.g., densities, refractive index, shift ratio of paper chromatography and IR frequencies of bond P = O) is obtained. The result indicates that general alpha-N index is a good topological index of organic compounds.

网络控制系统稳定性的图理论

针对具有有界时延和数据包丢失的网络控制系统,提出了一种新的稳定性判据.基于Lyapunov方法和图论理论,给出非线性离散和连续网络控制系统渐近稳定的充分条件,获得保持这两类系统稳定的最大允许时延界,得到控制器设计方法.并且,利用区间矩阵的谱特征,给出网络控制系统区间稳定的充分条件.设计算法,获得比例积分反馈控制器增益.算例表明所提方法的有效性。

基于图论的无线传感器网络拓扑控制方法研究

传感器技术、通信技术和计算机技术的飞速发展，孕育了具有现代意义的无线传感器网络，带来了一项新的信息革命。无线传感器网络的出现改变了人与自然的交互方式，其应用领域已经深入到了社会生活的各个方面。 无线传感器网络是一种测控网络，网络设计一般侧重网络的节能性、生命周期的延长、网络的扩展性等方面。对于网络拓扑控制来说，由于网络中节点数量众多、能力有限，网络的拓扑结构相当复杂，同时节点易失效也导致了网络拓扑结构的频繁变化，所以拓扑控制是无线传感器网络中重要的研究问题。本文基于图论中的理论知识，对无线传感器网络中的拓扑控制进行了研究，主要内容和研究成果包括以下几个方面。  论述了无线传感器网络拓扑控制问题研究的基本内容、分类、评价指标，并且指出了前人研究的成果的不足之处。  为了对无线传感器网络中节点进行功率控制，以单位圆盘图为模型构造了一个几何支撑图结构。此支撑图满足连通性、平面性、t-支撑图以及稀疏性，并且构造此支撑图的通信开销相对于其它支撑图构造算法大大降低。  针对无线传感器网络中没有基础结构的特点，利用连通支配集理论构造了无线传感器网络的虚拟骨干结构，从而把无线传感器网络映射成一个层次型的骨干结构。  基于修剪策略提出了一种极小连通支配集构造算法。算法又分为集中式和分布式两个版本。集中式算法中不仅考虑了节点的度、节点id，还综合考虑了节点的剩余能量，从而平衡了网络中节点的能量消耗，延长了算法的稳定运行时间，减少了拓扑结构重构的频率，有利于延长网络的生存时间。分布式算法中，节点根据两条邻居信息，采用了一种本地化的启发式搜索策略，从而降低了整个算法的信息复杂度。此外，这种基于修剪策略的构造算法实现方法非常简单，且够在算法运行的任何时刻得到一个可行的解。  基于极大独立集技术提出了一种启发式的极小连通支配集构造算法。在求解极大独立集过程中只需要根据节点和一跳邻居节点之间的信息确定极大独立集，在求解连通集时，根据独立节点的性质采用了本地化的启发式算法，从而提高了算法的性能，构造算法的信息复杂度也相对较低。仿真结果表明，构造算法在整个过程中所需要的通信开销大大降低，从而节省了节点的能量，有利于延长网络的生存时间。  根据无线传感器网络中节点易失效的特点，提出了一个容错的虚拟骨干构造算法。算法基于极大独立集构造方法，首先构造一个连通支配集，然后基于本地化信息得到一个支配度为k的冗余连通支配集，最后再使用协商和贪心策略使得连通支配集的连通度为m，从而得到一个m-连通k-支配集。仿真结果表明算法信息复杂度低，构造算法所需要的数据通信量降低。 本文基于图论知识，针对无线传感器网络的特点，对无线传感器网络的拓扑结构控制方法进行了研究，各项研究成果可以为无线传感器网络设计者提供一些有益的指导。

积分偏移的计算几何与并行实现

The Second Round of Oil & Gas Exploration needs more precision imaging method, velocity vs. depth model and geometry description on Complicated Geological Mass. Prestack time migration on inhomogeneous media was the technical basic of velocity analysis, prestack time migration on Rugged surface, angle gather and multi-domain noise suppression. In order to realize this technique, several critical technical problems need to be solved, such as parallel computation, velocity algorithm on ununiform grid and visualization. The key problem is organic combination theories of migration and computational geometry. Based on technical problems of 3-D prestack time migration existing in inhomogeneous media and requirements from nonuniform grid, parallel process and visualization, the thesis was studied systematically on three aspects: Infrastructure of velocity varies laterally Green function traveltime computation on ununiform grid, parallel computational of kirchhoff integral migration and 3D visualization, by combining integral migration theory and Computational Geometry. The results will provide powerful technical support to the implement of prestack time migration and convenient compute infrastructure of wave number domain simulation in inhomogeneous media. The main results were obtained as follows: 1. Symbol of one way wave Lie algebra integral, phase and green function traveltime expressions were analyzed, and simple 2-D expression of Lie algebra integral symbol phase and green function traveltime in time domain were given in inhomogeneous media by using pseudo-differential operators’ exponential map and Lie group algorithm preserving geometry structure. Infrastructure calculation of five parts, including derivative, commutating operator, Lie algebra root tree, exponential map root tree and traveltime coefficients , was brought forward when calculating asymmetry traveltime equation containing lateral differential in 3-D by this method. 2. By studying the infrastructure calculation of asymmetry traveltime in 3-D based on lateral velocity differential and combining computational geometry, a method to build velocity library and interpolate on velocity library using triangulate was obtained, which fit traveltime calculate requirements of parallel time migration and velocity estimate. 3. Combining velocity library triangulate and computational geometry, a structure which was convenient to calculate differential in horizontal, commutating operator and integral in vertical was built. Furthermore, recursive algorithm, for calculating architecture on lie algebra integral and exponential map root tree (Magnus in Math), was build and asymmetry traveltime based on lateral differential algorithm was also realized. 4. Based on graph theory and computational geometry, a minimum cycle method to decompose area into polygon blocks, which can be used as topological representation of migration result was proposed, which provided a practical method to block representation and research to migration interpretation results. 5. Based on MPI library, a process of bringing parallel migration algorithm at arbitrary sequence traces into practical was realized by using asymmetry traveltime based on lateral differential calculation and Kirchhoff integral method. 6. Visualization of geological data and seismic data were studied by the tools of OpenGL and Open Inventor, based on computational geometry theory, and a 3D visualize system on seismic imaging data was designed.