利用计算机演示利萨如图形──兼谈教材中一个容易被忽略的问题

本文分析了用示波器观察利萨如图形的缺陷，给出了用计算机演示利萨如图形的ＢＡＳＩＣ程序，并对决定利萨如图形花样的因素进行了讨论。     

光学设计程序中计算机图形技术的应用

介绍在IBM-PC计算机上研制的光学绘图程序,给出应用计算机图形技术的方法、程序结构特点及程序框图等。     

黏性指进的实验与模拟

利用简易装置观察了黏性指进现象,使用照相机拍摄多种黏性指进分形图形,测量了分形维数,并采用数值模拟中的随机模拟演示了黏性指进图形.     

用计算机绘制点电荷对的电场线

根据点电荷对的电场线公式设计程序,用计算机求出几种点电荷对的电场线上所有点,进行逐点描绘得到精确图形。     

计算机辅助测定微波反射式速调管特性

提出了计算机辅助测量微波反射式速调管特性的方案,对用声卡采集实验数据的方法,以及用ＭＡＴＬＡＢ绘制三维图形作了具体的介绍。     

隐函数等值线的计算机绘制及其在大学物理课程内容模拟上的应用

通过介绍有关隐函数等值线的计算机绘制方法,与传统的物理图形强度定标法作了比较。用此方法举例模拟了大学物理课程内容中电荷等势线和波的干涉图象。     

用计算机演示多缝衍射图样的缺级现象

利用计算机的图形功能，采用振幅矢量法演示多缝衍射光强分布曲线的动态变化过程及对应的振幅矢量合成图形，同时动态地演示影响缺级的各种因素的作用。     

基于Matlab的空间滤波实验的计算机仿真

利用阿贝-波特实验装置和空间滤波系统,从改变频谱入手改造一幅光学图形进行光学信息处理。在此基础上,通过Matlab环境编写程序完成阿贝-波特实验的物理模型的构建并进行计算机模拟实验。     

人工神经网络进展(Ⅱ)

六、人工神经网络的应用 人工神经网络靠其状态对外界输入的动态响应来处理信息,在某种意义上讲它是一种非线性变换技术。如前所述,任一神经网络模型均可实现信息的变换,即从一个n维信息空间变到另一m维信息空间,这种变换的例子很多,像从过去贷款申请得出贷款获利的数据;从检测的声呐信号到识别敌友;在装配线上,从图形输入信号到允许通过与否的控制信号;从EEH、EKG和X像片到诊断结果;从病人的症状到医治的药方等。由于在产生这些变换时,不需要     

光谱底片图像的计算机再现与处理

用Ｆｏｒｔｒａｎ语言编程，实现了光谱底片在计算机屏幕上的伪彩色及仿真光谱底片的多级灰度再现，实现了屏幕光标定位、数据的随时读取、图像旋转等功能。并可进一步作出光谱的等密度轮廓曲线和三维立体图形，大大提高了光谱底片数据处理的效率和精度。     

Modeling complex networks with self-similar outerplanar unclustered graphs

This paper introduces a family of modular, self-similar, small-world graphs with clustering zero. Relevant properties of this family are comparable to those of some networks associated with technological systems with a low clustering, like the power grid or some electronic circuits. Moreover, the graphs are outerplanar and it is know that many algorithms that are NP-complete for general graphs perform polynomial in outerplanar graphs. Therefore the graphs constitute a good mathematical model for these systems.     

Investigation of continuous-time quantum walk via spectral distribution associated with adjacency matrix

Using the spectral distribution associated with the adjacency matrix of graphs, we introduce a new method of calculation of amplitudes of continuous-time quantum walk on some rather important graphs, such as line, cycle graph C_n, complete graph K_n, graph G_n, finite path and some other finite and infinite graphs, where all are connected with orthogonal polynomials such as Hermite, Laguerre, Tchebichef, and other orthogonal polynomials. It is shown that using the spectral distribution, one can obtain the infinite time asymptotic behavior of amplitudes simply by using the method of stationary phase approximation (WKB approximation), where as an example, the method is applied to star, two-dimensional comb lattices, infinite Hermite and Laguerre graphs. Also by using the Gauss quadrature formula one can approximate the infinite graphs with finite ones and vice versa, in order to derive large time asymptotic behavior by WKB method. Likewise, using this method, some new graphs are introduced, where their amplitudes are proportional to the product of amplitudes of some elementary graphs, even though the graphs themselves are not the same as the Cartesian product of their elementary graphs. Finally, by calculating the mean end to end distance of some infinite graphs at large enough times, it is shown that continuous-time quantum walk at different infinite graphs belong to different universality classes which are also different from those of the corresponding classical ones.     

Complex networks renormalization: flows and fixed points

Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under renormalization, such as the maximum number of connections of a node, obeys simple scaling laws, characterized by critical exponents. This is true for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalization flows for graphs are similar as in the renormalization of spin systems. An analysis of classic renormalization for percolation and the Ising model on the lattice confirms this analogy. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graphs that are inaccessible to a standard analysis.     

n-Particle Quantum Statistics on Graphs

We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of particles is proven. For non-planar 3-connected graphs we identify bosons and fermions as the only possible statistics, whereas for planar 3-connected graphs we show that one anyon phase exists. Our approach also yields an alternative proof of the structure theorem for the first homology group of n-particle graph configuration spaces. Finally, we determine the topological gauge potentials for 2-connected graphs.     

Automatic generation of min-weighted persistent formations

This paper researched into some methods for generating min-weighted rigid graphs and min-weighted persistent graphs. Rigidity and persistence are currently used in various studies on coordination and control of autonomous multi-agent formations. To minimize the communication complexity of formations and reduce energy consumption, this paper introduces the rigidity matrix and presents three algorithms for generating min-weighted rigid and min-weighted persistent graphs. First, the existence of a min-weighted rigid graph is proved by using the rigidity matrix, and algorithm 1 is presented to generate the min-weighted rigid graphs. Second, the algorithm 2 based on the rigidity matrix is presented to direct the edges of min-weighted rigid graphs to generate min-weighted persistent graphs. Third, the formations with range constraints are considered, and algorithm 3 is presented to find whether a framework can form a min-weighted persistent formation. Finally, some simulations are given to show the efficiency of our research.     

From 2D hyperbolic forests to 3D Euclidean entangled thickets

A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces, including the P, D, gyroid and H surfaces. Some of these graphs are natural generalisations of bicontinuous topologies to bi-, tri-, quadra- and octa-continuous forms. Interwoven layer graphs and periodic sets of finite clusters also emerge from the algorithm. Many of the graphs are chiral. The generated graphs are compared with some organo-metallic molecular crystals with multiple frameworks and molecular mesophases found in copolymer melts. Received 10 December 1999     

Percolation on Infinite Graphs and Isoperimetric Inequalities

We consider the Bernoulli bond percolation process (with parameter p) on infinite graphs and we give a general criterion for bounded degree graphs to exhibit a non-trivial percolation threshold based either on a single isoperimetric inequality if the graph has a bi-infinite geodesic, or two isoperimetric inequalities if the graph has not a bi-infinite geodesic. This new criterion extends previous criteria and brings together a large class of amenable graphs (such as regular lattices) and non-amenable graphs (such trees). We also study the finite connectivity in graphs satisfying the new general criterion and show that graphs in this class with a bi-infinite geodesic always have finite connectivity functions with exponential decay when p is sufficiently close to one. On the other hand, we show that there are graphs in the same class with no bi-infinite geodesic for which the finite connectivity decays sub-exponentially (down to polynomially) in the highly supercritical phase even for p arbitrarily close to one.     

Infinite Graphs with a Nontrivial Bond Percolation Threshold: Some Sufficient Conditions

We consider Bernoulli bond percolation on infinite graphs and we identify a class of graphs for which the critical percolation probability is strictly less than 1. The graphs in this class have to fulfill conditions stated in terms of a minimal cut set property and a logarithmic isoperimetric inequality. For the particular case of planar graphs the condition on minimal cut sets can be be replaced by the assumption that the dual of the graph is bounded degree.     

Temporal graphs

We introduce the idea of temporal graphs, a representation that encodes temporal data into graphs while fully retaining the temporal information of the original data. This representation lets us explore the dynamic temporal properties of data by using existing graph algorithms (such as shortest-path), with no need for data-driven simulations. We also present a number of metrics that can be used to study and explore temporal graphs. Finally, we use temporal graphs to analyse real-world data and present the results of our analysis.     

Multipartite Separability of Density Matrices of Graphs

A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite systems by presenting a class of fully separable states arising from partially symmetric graphs.