Crossing minimization in extended level drawings of graphs

The most popular method of drawing directed graphs is to place vertices on a set of horizontal or concentric levels, known as level drawings. Level drawings are well studied in Graph Drawing due to their strong application for the visualization of hierarchy in graphs. There are two drawing conventions: Horizontal drawings use a set of parallel lines and radial drawings use a set of concentric circles.In level drawings, edges are only allowed between vertices on different levels. However, many real world graphs exhibit hierarchies with edges between vertices on the same level. In this paper, we initiate the new problem of extended level drawings of graphs, which was addressed as one of the open problems in social network visualization, in particular, displaying centrality values of actors. More specifically, we study minimizing the number of edge crossings in extended level drawings of graphs. The main problem can be formulated as the extended one-sided crossing minimization problem between two adjacent levels, as it is folklore with the one-sided crossing minimization problem in horizontal drawings.We first show that the extended one-sided crossing minimization problem is NP-hard for both horizontal and radial drawings, and then present efficient heuristics for minimizing edge crossings in extended level drawings. Our extensive experimental results show that our new methods reduce up to 30% of edge crossings.     

弹性地基上四边自由矩形厚板非线性大挠度弯曲

基于Ｒｅｉｓｓｎｅｒ－Ｍｉｎｄｌｉｎ一阶剪切变形板理论,采用摄动－Ｇａｌｅｒｋｉｎ混合法,给出双参数弹性地基上四边自由矩形中厚板在对称分布局部荷载作用下的大挠度弯曲渐近解,满足全部自由边界条件和控制方程,同时讨论弹性地基刚度系数对自由矩形厚板大挠度弯曲的影响。     

Bending of an Elastic Rectangular Clamped Plate: Exact Versus ‘Engineering’ Solutions

This paper addresses the fascinating long history of the classical problem of bending of a thin rectangular elastic plate with clamped edges by uniform pressure. Among various mathematical and engineering approaches, a method of superposition proposed by Lamé (1852, 1859) and Mathieu (1881, 1890) and developed by the mathematician Koialovich (1902) and engineers Boobnoff (1902, 1914), Hencky (1913) and Inglis (1925) appears to be very useful for the analysis of distribution of stresses and deflection inside a plate. The object of this paper is both to clarify some purely mathematical questions connected with the solution of the infinite systems of linear algebraic equations and to provide a considerable simplification of the numerical algorithm. This revised version was published online in August 2006 with corrections to the Cover Date.     

The edges and terrace effect of Ag particles on optical resonance absorption property

Alternative Ag and SiO₂ multilayers are prepared by using radio frequency magnetron sputtering. The Ag particles are found to diffuse toward and mostly accumulate near the surface of the Ag—SiO₂ composite film via a rapid thermal treatment. Different shapes of the Ag particles are obtained by changing the thickness of each Ag and SiO₂ layer. The response absorption property of the Ag composite film is also investigated. We relate the resonance absorption to the surface level and the Fermi level. To induce the obvious resonance absorption in an Ag composite film, it is necessary to maintain special shapes with sharp edges and wide terraces and to maintain the particle sizes ranging from 0 nm to 100 nm.     

根点自粘合后图的亏格分布

利用删点、加边原理,多种乘法法则,自粘合定理给出了一个双根图在其中一个根点的度为任意大的情形下根点自粘合后图的亏格分布,推广了Gross在文[Genus distribution of graph amalgamations:self-pasting at root-vertices,Aust.J.Comb.,2011,49:19-38]中两个根点度均为2的类似结果.     

Nanoscale Chemical Imaging of Reversible Photoisomerization of an Azobenzene‐Thiol Self‐Assembled Monolayer by Tip‐Enhanced Raman Spectroscopy

An understanding of the photoisomerization mechanism of molecules bound to a metal surface at the molecular scale is required for designing photoswitches at surfaces. It has remained a challenge to correlate the surface structure and isomerization of photoswitches at ambient conditions. Herein, the photoisomerization of a self‐assembled monolayer of azobenzene‐thiol molecules on a Au surface was investigated using scanning tunneling microscopy and tip‐enhanced Raman spectroscopy. The unique signature of the cis isomer at 1525 cm^?1 observed in tip‐enhanced Raman spectra was clearly distinct from the trans isomer. Furthermore, tip‐enhanced Raman images of azobenzene thiols after ultraviolet and blue light irradiation are shown with nanoscale spatial resolution, demonstrating a reversible conformational change. Interestingly, the cis isomers of azobenzene‐thiol molecules were preferentially observed at Au grain edges, which is confirmed by density functional theory.     

Nonlocal spatial clustering in automated brain hematoma and edema segmentation

Hematoma and edema volume are potential predictors of 30‐day mortality rate and functional outcome (degree of disability or dependence in daily activities after a stroke) for patients with intracerebral hemorrhage. The manual segmentation of hematoma and edema from computed tomography scans is common practice but a time‐consuming and labor‐intensive task. Automated segmentation is an appealing alternative, but it is challenging because of the poorly defined boundary between edema and the surrounding healthy brain tissue. There is limited literature on this problem, and we aim to help fill the gap between the theoretical development of segmentation methods and the practical need. Our framework is fully automated and requires no supervision. The method uses nonlocal regularized spatial fuzzy C‐means clustering in the initialization stage and the active contour without edges method in the refinement stage. To evaluate it, we used 30 subjects with different sizes, shapes, and locations of hematoma and edema. Compared with the manual segmentation results from two independent raters, our method performs hematoma segmentation well, with an average dice score coefficient of 0.92. Although there is a lack of ground truth in edema segmentation due to the high inter and intrarater variation, our results are comparable with manual segmentation results.