On well-covered triangulations: Part II

A graph G is said to be well-covered if every maximal independent set of vertices has the same cardinality. A planar (simple) graph in which each face is a triangle is called a triangulation. It was proved in an earlier paper [A. Finbow, B. Hartnell, R. Nowakowski, M. Plummer, On well-covered triangulations: Part I, Discrete Appl. Math., 132, 2004, 97-108] that there are no 5-connected planar well-covered triangulations. It is the aim of the present paper to completely determine the 4-connected well-covered triangulations containing two adjacent vertices of degree 4. In a subsequent paper [A. Finbow, B. Hartnell, R. Nowakowski, M. Plummer, On well-covered triangulations: Part III (submitted for publication)], we show that every 4-connected well-covered triangulation contains two adjacent vertices of degree 4 and hence complete the task of characterizing all 4-connected well-covered planar triangulations. There turn out to be only four such graphs. This stands in stark contrast to the fact that there are infinitely many 3-connected well-covered planar triangulations.     

On the sizes of Delaunay meshes

Let be a polyhedral domain occupying a convex volume. We prove that the size of a graded mesh of with bounded vertex degree is within a factor of the size of any Delaunay mesh of with bounded radius-edge ratio. The term depends on the geometry of and it is likely a small constant when the boundaries of are fine triangular meshes. There are several consequences. First, among all Delaunay meshes with bounded radius-edge ratio, those returned by Delaunay refinement algorithms have asymptotically optimal sizes. This is another advantage of meshing with Delaunay refinement algorithms. Second, if no input angle is acute, the minimum Delaunay mesh with bounded radius-edge ratio is not much smaller than any minimum mesh with aspect ratio bounded by a particular constant.     

Dominating sets in triangulations on surfaces

Let G be a graph and let S?V(G). We say that S is dominating in G if each vertex of G is in S or adjacent to a vertex in S. We show that every triangulation on the torus and the Klein bottle with n vertices has a dominating set of cardinality at most $\frac{n}{3}Let G be a graph and let S?V(G). We say that S is dominating in G if each vertex of G is in S or adjacent to a vertex in S. We show that every triangulation on the torus and the Klein bottle with n vertices has a dominating set of cardinality at most $\frac{n}{3}$. Moreover, we show that the same conclusion holds for a triangulation on any non‐spherical surface with sufficiently large representativity. These results generalize that for plane triangulations proved by Matheson and Tarjan (European J Combin 17 (1996), 565–568), and solve a conjecture by Plummer (Private Communication). © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 17–30, 2010     

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The IPSP algorithm is an efficient algorithm for computing maximum likelihood estimation of Gaussian graphical models. It first divides clique marginals of graphical models into several groups, and then it adjusts clique marginals in each group locally. This paper uses the IIPS algorithm on junction tree to replace local adjustment on each group in the IPSP algorithm and propose a resulting algorithm called IPSP-JT to reduce the complexity of the IPSP algorithm. Moreover, we give a graph with minimum edges used by IIPS to adjust locally, and we prove its existence and uniqueness and construct a local junction tree. Numerical experiments show that the IPSP-JT algorithm runs faster than the IPSP algorithm for large Gaussian graphical models.     

R-Local Delaunay Inhibition Model

Unlike in the classical framework of Gibbs point processes (usually acting on the complete graph), in the context of nearest-neighbour Gibbs point processes the nonnegativeness of the interaction functions do not ensure the local stability property. This paper introduces domain-wise (but not pointwise) inhibition stationary Gibbs models based on some tailor-made Delaunay subgraphs. All of them are subgraphs of the R-local Delaunay graph, defined as the Delaunay subgraph specifically not containing the edges of Delaunay triangles with circumscribed circles of radii greater than some large positive real value R. The usual relative compactness criterion for point processes needed for the existence result is directly derived from the Ruelle-bound of the correlation functions. Furthermore, assuming only the nonnegativeness of the energy function, we have managed to prove the existence of the existence of R-local Delaunay stationary Gibbs states based on nonnegative interaction functions thanks to the use of the compactness of sublevel sets of the relative entropy. In memory of Etienne Bertin.     

Recursive constructions for triangulations

Three recursive constructions are presented; two deal with embeddings of complete graphs and one with embeddings of complete tripartite graphs. All three facilitate the construction of 2) non‐isomorphic face 2‐colourable triangulations of K_n and K_n,n,n in orientable and non‐orientable surfaces for values of n lying in certain residue classes and for appropriate constants a. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 87–107, 2002     

急性心肌梗塞患者血清硒,锌,铜,钙,镁,铁,锶含量的测定

分别对２９例急性心肌梗塞（ＡＭＩ）病人和４０例健康人进行血清中七种微量、常量元素含量测定，结果表明，ＡＭＩ患者血清Ｓｅ、Ｚｎ、Ｃａ较正常对照组明显降低；血清Ｃｕ显著增高，血清Ｆｅ、Ｍｇ较对照组低，差异不显著；血清Ｓｒ两组无差异。对ＡＭＩ患者与血清硒及各元素间相互关系进行了探讨，指出调整人体微量、常量元素的不平衡状况，对冠心病和ＡＭＩ的发生、发展和康复有一定的临床意义。     

尼古丁的“口供”

This is a piece of confession made by Nicotine where its molecular structure and some physiological functions are introduced. The toxicity of Nicotine on human body has been revealed, based on an authentic suicide case. Combined with medical knowledge, the process of Nicotine intoxication, the mechanism of smoking addition and Nicotine's negative effect on human body, have been presented. Ultimately non-smoking advice is suggested for the sake of human health.     

人胚胎干细胞与急性早幼粒细胞白血病细胞的拉曼光谱特征研究

急性早幼粒细胞白血病(APL)属于急性髓系白血病(AML),是FAB分型中的M3亚型。部分APL患者形成早幼粒细胞白血病/维甲酸受体融合基因,即PML-RARα融合基因。在内外界多种因素的共同作用下,早幼粒细胞白血病发病。胚胎干细胞(ESCs)具有多向分化的能力,在一定诱导条件下, ESCs可以向造血系统分化。早幼粒细胞位于ESCs分化下游,为粒系分化阶段的一种细胞。探索一种非标记的技术方法鉴别不同分化阶段造血细胞具有重要的科研和实践意义。拉曼光谱技术可用于多种类型疾病的鉴别诊断研究,近年来应用前景愈加广阔。实验研究人胚胎干细胞系(ES)、急性早幼粒细胞白血病细胞系(NB4)和急性早幼粒细胞白血病患者(M3)白血病细胞的拉曼光谱特征,建立拉曼光谱非标记鉴别不同分化阶段白血病的方法,为临床实验研究提供基础。分别收集胚胎干细胞系(ES)、急性早幼粒细胞白血病细胞系(NB4)和4例M3患者白血病细胞,使用Horiba Xplora拉曼光谱仪获取拉曼光谱,每组或每例患者采集25~30个白血病细胞光谱。结合应用主成分分析法(PCA)、判别函数分析(DFA)、系统聚类分析和偏最小二乘判别分析(PLS-DA),对三类细胞的光谱进行分析并建立模型,进而对三类细胞进行鉴别,应用交互验证法对模型进行验证。同时结合细胞超微结构分析三种细胞的拉曼光谱特征。M3, NB4和ES细胞的拉曼光谱差别显著,主要表现为M3和NB4细胞光谱中对应核酸、蛋白质及脂类物质的谱峰明显高于ES细胞,其生物学机制包含了APL与PI3K/Akt/mTOR通路的密切关系。PI3K/Akt/mTOR通路在急性早幼粒细胞白血病细胞中存在异常激活,影响白血病细胞的生物大分子代谢;鉴别建模的总体分类准确率达100%(181/181),交互验证的分类准确率达98.9%(179/181),表明鉴别模型预测能力良好。拉曼光谱分析显示M3细胞和NB4细胞增殖代谢明显高于ES细胞,根据PCA-DFA、聚类分析及PLS-DA建立的拉曼光谱鉴别模型能够准确区分3种不同分化阶段白血病相关细胞,其结果与电镜结果相符。     

Strobovideolaryngoscopy in the management of acute laryngeal trauma

Surgical intervention in the management of acute laryngeal trauma can sometimes pose a difficult decision. The objective of this study is to evaluate the effectiveness of strobovideolaryngoscopy (SVL) in determining the course of management for patients sustaining acute laryngeal trauma. A 20-year retrospective study of patients presenting with acute laryngeal trauma was performed in order to determine if the addition of SVL during the study period changed the management of certain acute laryngeal injuries. Patients sustaining blunt laryngeal trauma evaluated at our institution from 1981 to the present were reviewed. There were 40 patients identified that were grouped by severity according to the Schaefer classification. Analysis included mechanism of injury, clinical presentation, assessment, treatment, and outcome. Group 1 injuries were the most common, with motor vehicle accident (MVA) the most frequent mechanism of injury. Initial assessment included fiberoptic laryngoscopy and computed tomography (CT) imaging in all patients not requiring immediate exploration. SVL was used in 20 patients, with 7 undergoing stroboscopy within 24 hours of presentation. All 7 patients were managed conservatively without surgical intervention or the need to establish an alternative airway. SVL improves the clinical assessment of patients with acute laryngeal injury. This study supports its use and found it to be an important factor in determining the need for surgical intervention. SVL may also shorten the hospital stay in these patients.