Depth First:Optimal Path Discovery Between Designated Nodes in Random Ring-Based Graphs

This paper focuses on optimally determining the existence of connected paths between some given nodes in random ring-based graphs.Serving as a fundamental underlying structure in network modeling,ring topology appears as commonplace in many realistic scenarios.Regarding this,we consider graphs composed of rings,with some possible connected paths between them.Without prior knowledge of the exact node permutations on rings,the existence of each edge can be unraveled through edge testing at a unit cost in one step.The problem examined is that of determining whether the given nodes are connected by a path or separated by a cut,with the minimum expected costs involved.Dividing the problem into different cases based on different topologies of the ring-based networks,we propose the corresponding policies that aim to quickly seek the paths between nodes.A common feature shared by all those policies is that we stick to going in the same direction during edge searching,with edge testing in each step only involving the test between the source and the node that has been tested most.The simple searching rule,interestingly,can be interpreted as a delightful property stemming from the neat structure of ring-based networks,which makes the searching process not rely on any sophisticated behaviors.We prove the optimality of the proposed policies by calculating the expected cost incurred and making a comparison with the other class of strategies.The effectiveness of the proposed policies is also verified through extensive simulations,from which we even disclose three extra intriguing findings:i)in a onering network,the cost will grow drastically with the number of designated nodes when the number is small and will grow slightly when that number is large;ii)in ring-based network,Depth First is optimal in detecting the connectivity between designated nodes;iii)the problem of multi-ring networks shares large similarity with that of two-ring networks,and a larger number of ties between rings will not influence the expected cost.

On Some Properties of Graph of Prefix Code

We investigate decomposition of codes and finite languages. A prime decomposition is a decomposition of a code or languages into a concatenation of nontrivial prime codes or languages. A code is prime if it cannot be decomposed into at least two nontrivial codes as the same for the languages. In the paper, a linear time algorithm is designed, which finds the prime decomposition. If codes or finite languages are presented as given by its minimal deterministic automaton, then from the point of view of abstract algebra and graph theory, this automaton has special properties. The study was conducted using system for computational Discrete Algebra GAP. .

Degree Powers of Minimally k-(edge)-connected Graphs

Let G be a graph on n vertices whose degree sequence is d_1≥…≥d_n.For a positive integer p,the degree power of G is defined by e_p(G)=∑_(i=1)~n d_i~p.In this paper,by majorization,we prove that for a minimally k-connected graph G of order n≥4k,it always holds e_2(G)≤kn(n-k)and the extremal graph is K_(k,n-k).Furthermore,we respectively determine the maximum degree powers among all minimally 2(3)-connected graphs and minimally 2-edgeconnected graphs,whose extremal graphs are also characterized.

Generation of minimally persistent circle formation for a multi-agent system

In this paper, two methods of generating minimally persistent circle formation are presented. The proposed methods adopt a leader-follower strategy and all followers are firstly motivated to move into the leader＇s interaction range. Based on the information about relative angle and relative distance, two numbering schemes are proposed to generate minimally persistent circle formation. Distributed control laws are also designed to maintain the desired relative distance between agents. The distinctive features of the proposed methods are as follows. First, only 2n - 3 unilateral communication links for n agents are needed during the circle formation process and thus the communication complexity can be reduced. In addition, the formation topology is kept fixed for the whole motion and achieves a self-stability property. Finally, each follower keeps a regualr interval with its neighbors and the formation converges to a uniform circle formation. Simulation results are also provided to demonstrate the effectiveness of the proposed methods.

3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization

Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model.Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations.Instead,the minimum cut on a special designed graph need to be computed.The method is tested on data with complicated structures.It is rather stable with respect to initial value and the algorithm is nearly parameter free.Experiments show that it can solve large problems much faster than traditional approaches.

FINITENESS OF HIGHER CODIMENSIONAL DISJOINT MINIMAL GRAPHS

We estimate the number of disjoint open subsets in Rn, which can support area-decreasing minimal graphs. This result generalizes the related results of Li-Wang and Tkachev for minimal hypersurfaces to higher codimensional case.

Bernstein type theorem of minimal Lagrangian graphs in quaternion Euclidean space H^n

In this paper, a Bernstein type theorem for minimal Lagrangian submanifolds in quaternion Euclidean space H^n is studied.

Minimal Realization of Linear Graph Models for Multi-physics Systems

An engineering system may consist of several different types of components,belonging to such physical"domains"as mechanical,electrical,fluid,and thermal.It is termed a multi-domain(or multi-physics)system.The present paper concerns the use of linear graphs(LGs)to generate a minimal model for a multi-physics system.A state-space model has to be a minimal realization.Specifically,the number of state variables in the model should be the minimum number that can completely represent the dynamic state of the system.This choice is not straightforward.Initially,state variables are assigned to all the energy-storage elements of the system.However,some of the energy storage elements may not be independent,and then some of the chosen state variables will be redundant.An approach is presented in the paper,with illustrative examples in the mixed fluid-mechanical domains,to illustrate a way to recognize dependent energy storage elements and thereby obtain a minimal state-space model.System analysis in the frequency domain is known to be more convenient than in the time domain,mainly because the relevant operations are algebraic rather than differential.For achieving this objective,the state space model has to be converted into a transfer function.The direct way is to first convert the state-space model into the input-output differential equation,and then substitute the time derivative by the Laplace variable.This approach is shown in the paper.The same result can be obtained through the transfer function linear graph(TF LG)of the system.In a multi-physics system,first the physical domains have to be converted into an equivalent single domain(preferably,the output domain of the system),when using the method of TFLG.This procedure is illustrated as well,in the present paper.

基于最省刻度尺构造极小优美图的图论方法

[目的]利用最省刻度尺的已有研究成果研究极小优美图的构造方法.[方法]对任意正整数n≥2,在长度是n的无刻度直尺上最少刻多少个刻度,就能度量1-n的所有长度,这就是最省刻度的尺子问题.给定正整数n,存在m个整数组成的集合{a_(i)},满足0=a_(1)<a_(2)<…<a_(m)=n,使得任意整数s(0≤s≤n)均可表示成该集合中两个元素的差a_(j)-a_(i),则称{a_(i)}为n上的受限差基.根据极小优美图和受限差基的定义,将极小优美图问题等效为最省刻度尺问题进而得到极小优美图的构造方法.[结果]由n≥5时K n不是优美图和n≥1时图K 4+K n,n是优美图的结论,得到了边数是6至82的极小优美图顶点数的上下界;用构造方法给出了图K_(3)∨K 1,3,n-3 e,K_(3,n)∨K_(3-e)和K_(2,3,n)∨K_(3)-7e的优美标号,从而证明了这三类图都是优美图,并且当0≤n≤9时,K_(3)∨K_(1,3,,n)-3 e和K_(2,3,n)∨K_(3)-7e都是极小优美图,当0≤n≤8时,K_(3,n)∨K_(3-e)都是极小优美图,由此给出了29组最省刻度尺的刻度值.[结论]最省刻度尺可以为构造极小优美图提供新的研究思路.

最省刻度尺设计的组合差集递推算法

在长度为n(n≥2为正整数)的直尺上最少刻多少个刻度就能度量1到n的所有长度,这便是至今未解决的最省刻度尺问题。阐明了最省刻度尺与极小优美图之间的关系,给出了计算最省刻度尺的所有最省刻度值的组合差集递推算法,得到长度为3~40的最省刻度尺的所有最省刻度值,同时,结合图论模型,给出了长度为41~82的最省刻度尺的最省刻度值。

一种基于Graph Cuts的SAR图像分割方法

在最小化由马尔科夫随机场(MRF)图像分割模型建立的能量函数方面,基于Graph Cuts的alpha-expansion是一种比较有效的算法。但是,由此算法构建的s/t图中边的数目非常多,运算速度很慢。为了减少alpha-expansion算法的计算量,本文在标号为alpha的像素向其它像素膨胀的过程中,先隔离非alpha类间的联系,而只考虑alpha类与非alpha类之间的关系,从而避免了alpha-expansion算法需要构造辅助结点的问题,减少了s/t图中边的数目,提高了算法的计算效率。因放松了非alpha类间的关系对alpha膨胀的约束,使得算法可以更容易得跳出能量函数的局部极小点而获得更优的分割结果。实验中将改进的算法与传统的基于Graph Cuts的算法做了对比,显示了新算法在运算时间和最小化能量方面的有效性。

国内外腰椎间盘突出症微创治疗热点及趋势的可视化分析

目的:对国内外有关腰椎间盘突出症微创治疗的相关文献进行计量学分析,并总结其研究现状、热点与发展趋势。以期为相关学者和医务工作者了解该领域的研究热点和趋势提供有用的参考。方法:以腰椎间盘突出症微创治疗以及相关词汇为检索主题,检索中国知网(CNKI)和Web of Science(WOS)核心合集数据库。运用CiteSpace和VOSviewer软件对2013—2023年收录的相关文献进行知识图谱的可视化分析,对关键词、突现词和时间趋势图谱等进行数据分析。结果:共纳入1065篇来自CNKI的文献和602篇来自WOS的文献。通过可视化分析后于CNKI可得腰椎间盘突出症和经皮椎间孔镜手术等10个聚类结果,在WOS中可得危险因素、腰椎间盘突出症和椎管狭窄等9个聚类结果。结论:CNKI中研究热点主要集中在腰椎功能、复发率、经椎板孔入路、临床疗效、疼痛、并发症等关键词,而在WOS中研究热点主要集中在并发症、复发率、治疗结果、经椎间孔入路、疼痛、学习曲线等关键词。近两年在CNKI中研究热点主要集中在疼痛和经皮椎间孔镜椎间盘切除术等关键词,而在WOS中主要集中在并发症和复发率等关键词。目前国内外学者对于该领域的研究热点既有重叠也有不同的关注方向。

Several Classes of Two-weight or Three-weight Linear Codes and Their Applications

Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].

Improving landscape Characteristics in Port Said’s El Sallam Garden via Observational and Space Syntax Analysis

This paper provides a comprehensive examination of El Sallam Garden in Port Said City,concentrating on its landscape characteristics and potential for design enhancement.This study looks at how space syntax can be used to assess the impact of a tree planting design’s spatial configuration on an urban park’s visual fields.Trees play an important role in determining the spatial characteristics of an outdoor space.According to space syntax theory,an urban area is a collection of connected spaces that can be represented by a matrix of quantitative properties known as syntactic measures.Computer simulations can be used to measure the quantitative properties of these matrices.This study uses space syntax techniques to assess how tree configurations and garden area which can affect the social structures of small-scale gardens in Port Said.It also looks at how these techniques can be used to predict the social structures of four garden zones in El Sallam Garden.The study includes an observational and space syntax study through comparative analysis of four garden zones in El Sallam garden.The results of the study show that the area and planting configurations of the garden had a significant effect on the syntactic social and visual measures of the urban garden.The conclusions and recommendations can be a useful tool for landscape architects,urban planners,and legislators who want to enhance public areas and encourage social interaction in urban settings.

Halin图的无包含边染色

探究给定最大度的Halin图的无包含边色数的上界,通过分析极小反例图的结构,在给定部分子图的染色下,对剩余图进行特殊染色。结果表明:最大度为Δ的Halin图的无包含边色数不超过Δ+2。

Extracting multiple layers from data having graph structures

Much data such as geometric image data and drawings have graph structures. Such data are called graph structured data. In order to manage efficiently such graph structured data, we need to analyze and abstract graph structures of such data. The purpose of this paper is to find knowledge representations which indicate plural abstractions of graph structured data. Firstly, we introduce a term graph as a graph pattern having structural variables, and a substitution over term graphs which is graph rewriting system. Next, for a graph G, we define a multiple layer ( g,(θ 1,…,θ k )) of G as a pair of a term graph g and a list of k substitutions θ 1,…,θ k such that G can be obtained from g by applying substitutions θ 1,…,θ k to g. In the same way, for a set S of graphs, we also define a multiple layer for S as a pair ( D,Θ ) of a set D of term graphs and a list Θ of substitutions. Secondly, for a graph G and a set S of graphs, we present effective algorithms for extracting minimal multiple layers of G and S which give us stratifying abstractions of G and S, respectively. Finally, we report experimental results obtained by applying our algorithms to both artificial data and drawings of power plants which are real world data.

5类图的优美性

用构造方法给出图K_(2,n)-1-3-K_(3),K_(2,n)-2-2-K_(3),K_(2,n)-1-2-K_(3),K_(2,n)-2-K_(3)和K_(2,n)-3-P_(3)的优美标号,并证明这五类图都是优美图.当n≤5时,K_(2,n)-1-3-K_(3),K_(2,n)-2-2-K_(3),K_(2,n)-1-2-K_(3)和K_(2,n)-3-P_(3)都是极小优美图,并给出对应长度尺子刻度数最少的15组刻度值.

子任务调度和时延联合优化的MEC卸载方案

移动边缘计算(mobile edge computing,MEC)为5G超低时延业务提供了解决方案。如何设计低时延、高效率的任务卸载方案,是MEC面临的主要难题之一。为此,针对端边协同MEC服务场景,研究了大型计算任务的低时延、低能耗部分卸载方案,通过将用户任务划分为多个有顺序依赖关系的子任务并构建子任务的有向无环关系图,设计了能够最小化卸载时延的子任务调度方案,提出了基于任务复制的最早卸载执行算法,解决了能耗受限下的任务最小时延卸载计算。仿真结果表明,提出的MEC卸载方案能够有效减少任务处理时延,降低系统能耗。

MINIMALLY (n, λ)-CONNECTED GRAPHS OF LOW ORDER AND MAXIMAL SIZE

A. Kaneko and K. Ota proved that for a minimally （n, λ）-connected graph G, if ｜G｜ = p ≥ 3n - 1, then e（G） ≤ nλ（｜G｜ - n）; and if e（G） = nλ（｜G｜ - n）, then G is isomorphic to the graph Kn^λ,p-n which is obtained from the complete bipartite graph Kn,p-n by replacing each edge with A multiple edges; if 3n - 1 ≥ ｜G}≥ n ＋ 1, then e（G） ≤λ（｜G｜ ＋ n）^2/8. In this paper, we determine all the minimally （n, λ）-connected graphs with order p and the maximum size λ（p＋n）^2/8 for 3n- 1 ≥ p ≥ n＋ 1 for 3n-1≥p≥n＋1.

基于图割的图像分割方法及其新进展

鉴于图割的理论意义和实际应用价值,系统综述了基于图割的图像分割方法.首先,深入分析了基于图割的图像分割方法的基本原理,主要从定性和定量角度剖析了图割与能量函数最小化之间的关系,然后,概括了基于图割的图像分割方法的基本步骤,包括能量函数的设计、图的构造和最小割/最大流方法,其次,系统梳理和评述了基于图割的图像分割方法的国内外研究现状,最后,指出了基于图割的图像分割方法的发展方向.