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.

On Graphs with Equal Connected Domination and 2-connected Domination Numbers

A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken over all minimal k-connected dominating sets of G.In this paper,we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.

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.

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.

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. .

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.

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。

Minor and Minimum Cycle Bases of a 3-connected Planar Graph

In this paper, we prove that if any set of ｜E（G）｜- ｜V（G）｜ ＋ 1 facial cycles of a 3-connected planar graph G embedded in the plane doesn＇t form a minimum cycle base of G, then any minimum cycle base of G contains a separating cycle, and G has a minor isomorphic to T6, where T6 is the graph obtained from the complete graph K6 by deleting a path with four edges.

k-Factors and Spanning Subgraph in Graphs

In this paper, we discussed k-factors and spanning subgraph, and propose a conjecture which will lead to a series of important conclusion.

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.

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。

Minimal Elements in the Poset of Graphic Sequences

A nonincreasing sequence ( of n nonnegative integers is said to be graphic if it is the degree sequence of a simple graph G of order n. The set of all graphic sequences of n terms with even sum 2m and trace f is a poset G_(n,m,f) under majorization relation. The paper characterizes the minimal elements in the poset G_(n,m,f) and determines the number of minimal elements in various posets of graphic sequences.

The boundary behavior of domains with complete translating, minimal and CMC graphs in N^2×R

In this paper,we discuss graphs over a domain ??N^2 in the product manifold N^2×R.Here N^2is a complete Riemannian surface and?has piecewise smooth boundary.Letγ???be a smooth connected arc andΣbe a complete graph in N^2×R over?.We show that ifΣis a minimal or translating graph,thenγis a geodesic in N^2.Moreover ifΣis a CMC graph,thenγhas constant principal curvature in N^2.This explains the infinity value boundary condition upon domains having Jenkins-Serrin theorems on minimal and constant mean curvature(CMC)graphs in N^2×R.

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].