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一致超图中路和圈扩张的反Ramsey数（李瞳、闫桂英）
一致超图中路 圈扩张 反Ramsey数
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2023/2/22
For an r-graph F, the anti-Ramsey number ar(n,r,F) is the minimum number c of colors such that for any edge-coloring of the complete r-graph on n vertices with at least c colors, there is a copy of F ...
应用图论分析与最优化理论来数据挖掘大规模水牛普里昂蛋白结构数据
图论 最优化理论 数据挖掘 应用于大数据
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2018/3/12
图论、最优化理论显然在蛋白质结构的研究中大有用场. 首先, 调查/回顾了研究蛋白质结构的所有图论模型. 其后, 建立了一个图论模型: 让蛋白质的侧链来作为图的顶点, 应用图论的诸如团、 $k$-团、 社群、 枢纽、聚类等概念来建立图的边. 然后, 应用数学最优化的现代摩登数据挖掘算法/方法来分析水牛普里昂蛋白结构的大数据. 成功与令人耳目一新的数值结果将展示给朋友们.
三圈图的极小广义和连通指数
广义和连通指数 三圈图 图的变换
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2018/3/12
图的广义和连通指数作为新提出的一类分子拓扑指数, 在QSPR/QSAR 中有很大的应用价值. 树图、单圈图和双圈图的极值问题已取得很多结果, 而三圈图相关问题的研究较为复杂. 限制 - 1 \leqslant \alpha < 0, 对三圈图的广义和连通指数进行了研究. 通过对三圈图的分析, 构造了一种图的变换, 指出在三圈图中广义和连通指
数的极小值必由其中的七种类型图取得. 然后通过悬挂边...
关于图的规范拉普拉斯特征值和的若干结果
规范拉普拉斯 拉普拉斯 和 下界
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2018/2/6
对任意一个连通图$G$, 记 $L(G)$ 和 ${\cal L}(G)$ 分别为$G$ 的拉普拉斯矩阵和规范拉普拉斯 矩阵. 令 $\mu_1\geq\mu_2\geq \cdots \geq \mu_n=0$ 和$\lambda_1\geq \lambda_2\geq \cdots \geq \lambda_n=0$ 分别为$G$的拉普拉斯特征值和规范 拉普拉斯特征值. 本文给出了 $\lam...
图像处理中全变差正则化数据拟合问题算法回顾
阈值算法 分裂罚算法 交替方向乘子法
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2018/2/8
全变差正则化数据拟合问题产生于许多图像处理任务, 如图像去噪、去模糊、图像修复、磁共振成像、压缩图像感知等. 近年来, 求解此类问题的快速高效算法发展很快. 以最小二乘、最小一乘等为例简要回顾求解此类问题的主要算法, 并讨论一个全变差正则化非凸数据拟合模型在脉冲噪声图像去模糊问题中的应用.
六阶图C_6+3K_2与P_n, C_n的联图交叉数
交叉数 联图 路图 圈图
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2018/2/8
用P_n表示n个点的路, C_n表示长为n的圈, C_6+3K_2表示 圈C_6添加三条相邻的边3K_2=C_3得到的图. 在Kleitman给出的完全二部图的交叉数cr(K_{6,n})=Z(6,n)的基础上, 得到了特殊六阶图C_6+3K_2与路P_{n}, 圈C_{n}的联图交叉数分别为 Z(6,n)+3\lfloor \frac{n}{2} \rfloor+2 与 Z(6,n)+3\lfl...
PUTNAM’S RESOLVING MAPS IN DIMENSION ZERO
PUTNAM’S RESOLVING MAPS DIMENSION ZERO
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2015/9/29
A block code from an irreducible shift of finite type can be lifted canonically through resolving maps to a resolving map. There is an application to Markovian maps.
EXPANSIVE INVERTIBLE ONESIDED CELLULAR AUTOMATA
EXPANSIVE INVERTIBLE ONESIDED CELLULAR AUTOMATA
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2015/9/29
We study expansive invertible onesided cellular automata (i.e., expansive automorphisms of onesided full shifts) and find severe dynamical and arithmetic constraints which provide partial answers to q...
The range of a rotor walk
range rotor walk
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2015/8/14
In a rotor walk the exits from each vertex follow a prescribed periodic sequence. On an infinite Eulerian graph embedded periodically in Rd, we show that any simple rotor walk, regardless of rotor mec...
Formation of an interface by competitive erosion
Formation interface competitive erosion
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2015/8/14
In 2006, the fourth author of this paper proposed a graph-theoretic model of interface dynamics called competitive erosion. Each vertex of the graph is occupied by a particle that can be either red or...
COEULERIAN GRAPHS
COEULERIAN GRAPHS
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2015/8/14
We suggest a measure of “Eulerianness” of a finite directed graph and define a class of “coEulerian” graphs. These are the graphs whose Laplacian lattice is as large as possible. As an application, we...
Discussion of “Latent Variable Graphical Model Selection via Convex Optimization”
Latent Variable Graphical Model Selection Convex Optimization
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2015/6/17
We wish to congratulate the authors for their innovative contribution, which is bound to inspire much further research. We find latent variable model selection to be a fantastic application of matrix ...
不含4圈的平面图的无圈边色数的新上界
边染色 无圈边染色 平面图 差值转移法
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2012/11/7
为了研究平面图的无圈边染色,利用差值转移方法并结合平面图的结构性质,证明了不含4圈的平面图的无圈边色数不超过Δ(G)+6.
Unsolved Problems in Visibility Graphs of Points, Segments and Polygons
Unsolved Problems Visibility Graphs of Points Segments Polygons
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2011/3/3
In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
MD-Predicted Phase diagrams for Pattern Formation due to Ion Irradiation
MD-Predicted Phase diagrams Pattern Formation Ion Irradiation
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2011/3/3
Energetic particle irradiation of solids can cause surface ultra-smoothening 1, selforganized
nanoscale pattern formation 2, or degradation of the structural integrity of nuclear reactor components 3...