The strength of weak proximity

This paper studies weak proximity drawings of graphs and demonstrates their advantages over strong proximity drawings in certain cases. Weak proximity drawings are straight line drawings such that if the proximity region of two points p and q representing vertices is devoid of other points representing vertices, then segment (p,q) is allowed, but not forced, to appear in the drawing. This differs from the usual, strong, notion of proximity drawing in which such segments must appear in the drawing.Most previously studied proximity regions are associated with a parameter β, 0β∞. For fixed β, weak β-drawability is at least as expressive as strong β-drawability, as a strong β-drawing is also a weak one. We give examples of graph families and β values where the two notions coincide, and a situation in which it is NP-hard to determine weak β-drawability. On the other hand, we give situations where weak proximity significantly increases the expressive power of β-drawability: we show that every graph has, for all sufficiently small β, a weak β-proximity drawing that is computable in linear time, and we show that every tree has, for every β less than 2, a weak β-drawing that is computable in linear time.     

Investigating young students’ multiplicative thinking: The 12 little ducks problem

Children’s multiplicative thinking as the visualization of equal group structures and the enumeration the composite units was the subject of this study. The results were obtained from a small sample of Australian children (n = 18) in their first year of school (mean age 5 years 6 months) who participated in a lesson taught by their classroom teacher. The 12 Little Ducks problem stimulated children to visualize and to draw different ways of making equal groups. Fifteen children (83 %) could identify and create equal groups; eight of these children (44 %) could also quantify the number of groups they formed. These findings show that some young children understand early multiplicative ideas and can visualize equal group situations and communicate about these through their drawings and talk. The study emphasises the value of encouraging mathematical visualization from an early age; using open thought-provoking problems to reveal children’s thinking; and promoting drawing as a form of mathematical communication.     

Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree

The contour tree is an abstraction of a scalar field that encodes the nesting relationships of isosurfaces. We show how to use the contour tree to represent individual contours of a scalar field, how to simplify both the contour tree and the topology of the scalar field, how to compute and store geometric properties for all possible contours in the contour tree, and how to use the simplified contour tree as an interface for exploratory visualization.     

Graphical Explanation in Belief Networks

Abstract

Belief networks provide an important bridge between statistical modeling and expert systems. This article presents methods for visualizing probabilistic “evidence flows” in belief networks, thereby enabling belief networks to explain their behavior. Building on earlier research on explanation in expert systems, we present a hierarchy of explanations, ranging from simple colorings to detailed displays. Our approach complements parallel work on textual explanations in belief networks. Graphical-Belief, Mathsoft Inc.'s belief network software, implements the methods.     

Variable Resolution Bivariate Plots

Abstract

Scatterplots are the method of choice for displaying the distribution of points in two dimensions. They are used to discover patterns such as holes, outliers, modes, and association between the two variables. A common problem is overstriking—the overlap on the plotting surface of glyphs representing individual observations. Overstriking can create a misleading impression of the data distribution. The variable resolution bivariate plots (Varebi plots) proposed in this article deal with the problem of overstriking by mixing display of a density estimate and display of individual observations. The idea is to determine the display format by analyzing the actual amount of overstriking on the screen. Thus, the display format will depend on the sample size, the distribution of the observations, the size and shape of individual icons, and the size of the window. It may change automatically when the window is resized. Varebi plots reveal detail wherever possible, and show the overall trend when displaying detail is not feasible.     

Visualization of Multivariate Density Estimates With Shape Trees

This article introduces graphical tools for visualizing multivariate functions, specializing to the case of visualizing multivariate density estimates. We visualize a density estimate by visualizing a series of its level sets. From each connected part of a level set a shape tree is formed. A shape tree is a tree whose nodes are associated with regions of the level set. With the help of a shape tree we define a transformation of a multivariate set to a univariate function. The shape trees are visualized with the shape plots and the location plot. By studying these plots one may identify the regions of the Euclidean space where the probability mass is concentrated. An application of shape trees to visualize the distribution of stock index returns is presented.     

Expansion phenomena of aerosols generated by laser ablation under helium and argon atmosphere

Specific expansion phenomena of aerosols generated by near infrared femtosecond laser ablation (NIR-fs-LA) of brass under helium and argon atmosphere were studied. For this purpose, particles were visualized by light scattering using a pulsed laser source. Aerosols were found to be captured in symmetric vortices when striking a solid boundary during their kinetic stage of expansion. Furthermore, high-repetitive LA resulted in the formation of a complex, macroscopic flow pattern driven by a pressure gradient locally built up. Our data indicate that aerosols released under those conditions experience only minor losses of around 1% if they get in contact with the inner walls of ablation cells operated at atmospheric pressures.     

Flexible sheet with radiophotoluminescence glass beads for remotely monitoring high beta-surface-contamination

A flexible sheet was made with radiophotoluminescence (RPL) glass beads on an experimental basis for visualization of high beta-surface-contamination. A simple RPL observation system for remote contamination monitoring was constructed with a homemade UV floodlight and a commercially available digital camera with supplementary optical lenses and filters. In preliminary experiments, RPL images were well observed with the digital camera of the present system. Their precise RPL intensity was determined after the correction of nonlinear response of the camera. It was expected from experiments that RPL images of beta-surface-contamination could be quantitatively evaluated through calibration, i.e., the conversion of camera images to dose data on the sheet-type glass dosimeter.     

基于PC机的一种多功能声显微镜及可视化技术的研究

近来研制成功了一种基于ＰＣ机、我们称为“ＴＨＳＡＭＭ”型的多功能声显微镜。在ＰＣ机内插入采样率１ＧＳＰＳ的超高速Ａ／Ｄ卡和信号产生和接收卡,利用软件完成信号检测、处理、显示功能。仪器工作频率为１－１００ＭＨｚ;在检测样品时,同时多层显示Ａ、Ｂ、Ｃ扫描结果。根据声学理论、Ｍａｒｃｈｉｎｇ Ｃｕｂｅ等值面抽取方法和ＯｐｅｎＧＬ技术完成了三维数据的可视化处理,显示样品的内部三维结构。该系统已成功应用于多     

高光谱成像的马铃薯叶片含水率分布可视化

为了快速检测马铃薯叶片的水分含量,并探究受到干旱胁迫时叶片含水率变化情况,利用高光谱成像对马铃薯叶片含水率进行检测和可视化研究。采集71个叶片,用烘干法对叶片水分梯度进行控制,共得到355个样本。使用高光谱分选仪器采集叶片862.9~1 704.2 nm(256个波长)的光谱成像数据,采用称重法测量含水率。利用Sample set partitioning based on joint X-Y distance(SPXY)算法将总样本按照2∶1的比例划分为建模集(240个样本)和验证集(115个样本)。对采集的数据进行光谱特征分析,本文分别用CA和RF两种算法,各筛选得到15个特征波长。基于CA筛选出相关系数高于0.96的15个波长分别为1 406.82,1 410.12,1 403.62,1 413.32,1 416.62,1 419.82,1 400.32,1 423.12,1 426.32,1 429.62,1 432.82,1 436.12,1 439.32,1 442.52和1 445.8 nm。基于RF算法筛选被选概率高于0.3的15个特征波长,按照被选择概率值从大到小排列,分别为1 071.62,1 041.12,1 222.52,1 465.22,1 397.02,1 449.02,1 034.32,1 523.22,976.42,1 172.52,979.82,1 165.82,1 037.72,1 426.32和869.8 nm。用CA和RF算法筛选到的特征波长建立PLSR模型,分别记为CA-PLSR模型和RF-PLSR模型。利用高精度模型检测结果,对马铃薯叶片含水率进行可视化分析,首先计算马铃薯叶片图像每个像素点的含水率,得到灰度图像,然后对灰度图像进行伪彩色变换,绘制出叶片含水率可视化彩色图像。为了体现马铃薯叶片烘干处理中含水率变化进程,用HSV彩色模型对样本叶片的伪彩色图像进行分割,获得分割图像结果,显示出在某含水率区间的叶片面积比例。结果显示,CA算法选取的15个波长均在1 400.3~1 450.0 nm范围内,CA-PLSR模型的建模精度(R2_c)为0.975 5、建模集均方根误差(RMSEC)为2.81%,验证集精度(R2_v)为0.933 2、验证集均方根误差(RMSEV)为2.31%。RF算法选取的特征波长分布范围较CA法选取范围广,具有局部“峰谷”特性,且RF-PLSR模型的建模集精度(R2_c)为0.983 2、RMSEC为2.32%,验证集精度(R2_v)为0.947 1、RMSEV为2.15%。选取RF-PLS模型计算马铃薯每个像素点的含水率,得到伪彩色变换图像,观察可知随着烘干时间的增加含水率逐渐下降;并能够从叶片结构角度看到,随着水分胁迫的加强,叶片从边缘开始失水,逐渐向叶片中间蔓延,其中叶茎和叶脉的含水率较其他部位高。计算得到叶片伪彩色图像中含水率大于90%,80%和70%的像素点占整个叶片图像的比例。利用高光谱成像技术可以实现马铃薯叶片的含水率检测与分布可视化表达,为监测马铃薯生长状况以及叶片含水率分析提供新的理论根据。