C-B-样条曲线的升阶算子与几何生成法

因为升阶算子与几何收敛性不易求得,故样条曲线很难像B′ezier曲线那样通过对控制多边形的几何割角生成.为了得到C-B-样条的几何生成算法,首先利用双阶样条解决了升阶算子.接着,证明了对样条曲线进行基于升阶算子的升阶,其控制多边形序列会逐渐收敛到初始的样条曲线.这种几何生成算法具有明显的几何直观性,计算简单稳定,利于硬件执行.由于椭圆、螺旋线等工程上应用广泛的曲线可以由C-B-样条精确表示,因此算法对CAD造型系统有重要的意义.     

用Loop细分曲面插值三角网格

利用Loop细分方法的极限点公式,给出了一种用Loop细分曲面插值三角网格的简单高效方法.其优点有:(1)局部性:改变一个待插值点的位置时,只影响其附近插值曲面的形状.(2)计算简单:新点直接由显式公式给出,不用解复杂的线性方程组.(3)易于实现:只改变第1步细分规则中的几何规则,其他步骤与Loop细分方法相同.(4)自由度多:有足够的自由度调节插值曲面的形状,得到使设计者满意的插值曲面.(5)易推广:几乎适用于任何逼近型细分方法,对逼近型细分方法的唯一要求是:初始顶点处对应的极限点公式由显式公式给出.     

均匀三角多项式B样条曲线

在空间Ω =span(sint, cost, t^k-3,t^k-4,...t, 1) k≥3)上定义了一类均匀样条曲线——k阶三角多项式B样条曲线, 它具有许多与均匀B样条相类似的性质. 给出了三角多项式B样条曲线的离散公式. 由于这类曲线无需有理形式, 既可表示多项式曲线又可表示三角函数曲线, 因此可应用于CAD/CAM领域作为几何造型的一种新的有效模型. 关键词 C-曲线 均匀B样条 C-B样条 三角多项式B样条     

正交平衡对称的区间多小波研究

研究基于任意紧支长度??的L2(R)上2重对称/反对称正交多小波的区间多小波系统构造理论与性质.主要贡献是: (1) 系统研究了保持消失矩不降低的一般正交区间多小波的构造,得到了区间多小波的参数化表示;(2) 给出了区间多小波的分解重构公式;(3) 定义了区间多小波的平衡性概念,研究了正交平衡多小波的构造,这是以往工作所忽视的;(4) 研究了区间多小波关于给定对称性的充要条件.     

ωB样条

提出一种带可变频率的新的样条,称之为ωB样条．它不仅统一了B样条、三角多项式B样条以及双曲多项式B样条,而且能表示更多新的样条模型．ωB样条基定义在由{cosax,sinax,1,t,...,t^,...）所张成的空间上,其中ω为频率序列,n为任意非负整数．ωB样条保有B样条的所有优良性质,并且还具有其他有利于自由曲线曲面造型的独特性质．     

正交平衡对称的区问多小波研究

研究基于任意紧支长度γ的L2(R)上2重对称／反对称正交多小波的区间多小波系统构造理论与性质．主要贡献是：(1)系统研究了保持消失矩不降低的一般正交区间多小波的构造，得到了区间多小波的参数化表示；(2)给出了区间多小波的分解重构公式；(3)定义了区间多小波的平衡性概念，研究了正交平衡多小波的构造，这是以往工作所忽视的；(4)研究了区间多小波关于给定对称性的充要条件．     

非规则颗粒形态表征与离散元模拟方法研究

颗粒物质在自然界和人类生产与生活中广泛存在,对于非规则颗粒,其宏观物理力学特性与几何形态密切相关.本文以本课题组和合作者的相关研究为基础,介绍了非规则颗粒几何形态的获取、重构、评价、随机生成以及离散元模拟方法等方面的研究进展.总结了非规则颗粒形态不同获取方法的优缺点;将颗粒二维形态和三维形态分别划分为星形和非星形两种类型,介绍了各类型几何形态的计算几何重构方法;系统总结了非规则颗粒不同层次形态评价指标的定义,及基于计算几何的指标计算方法;介绍了基于逆蒙特卡罗法的二维星形与三维星形随机颗粒生成方法,以及可考虑一阶系数固有关系和其他阶系数经验相关性的二维非星形与三维非星形虚拟颗粒生成方法;对于非规则颗粒的离散元模拟方法,重点总结了颗粒几何形态表示、颗粒接触判断与颗粒接触力计算方法等核心问题的研究进展.     

基于奇异值分解的多小波图像去噪方法

给出了一种将多小波变换和奇异值分解相结合的图像去噪方法.该方法通过对含噪图像进行多小波变换,克服了单小波变换中无法同时满足正交性和对称性的缺点.对变换得到的高频系数矩阵进行奇异值分解去噪,提取高频系数中淹没在噪声中的信号成分,然后进行多小波重构,得到去噪图像.仿真结果表明,该方法能有效去除噪声,并获得良好的主观视觉效果.     

α进制最小能量区间小波框架的构造

基于小波多尺度特征和信号多通道理论需要,本文对a进制最小能量区间小波框架进行了系统研究,其中a为任意大于等于2的正整数.首先,给出了a进制最小能量区间小波框架的定义,建立了a进制最小能量区间小波框架的充要条件;其次,我们设计了支撑长度为任意整数γ的a进制最小能量区间小波框架的构造算法,并构造性地给出了构造算法所涉及矩阵的表达式;最后,给出了最小能量区间小波框架的分解与重构算法,并构造了数值算例.     

基于优势点检测的晶粒轮廓非均匀B样条逼近

进行复合材料三维重构的一个重要步骤是获取晶粒轮廓简洁的、光顺的数学表达. 在利用小波变换技术和Level set技术得到陶瓷复合材料晶粒闭合边缘的基础上, 根据晶粒轮廓的特点, 研究了其特征型值点的合理提取方法: 提取晶粒轮廓上高曲率的点作为候选点, 利用自适应弯曲度来确定曲线上每个点的支撑区间, 计算评价曲率, 依据评价曲率和最大采样间隔确定合理的优势点. 采用周期非均匀3次B样条曲线逼近的方法, 得到控制误差条件下最简洁的晶粒轮廓曲线. 根据所传递的候选节点矢量, 采用柔性间距选择, 获取序列轮廓的共同的节点矢量, 采用蒙皮技术获得陶瓷复合材料晶粒的3次B样条曲面模型.     

Mathematical formalisms in scientific practice: From denotation to model-based representation

The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible with successful representation, scientists often rely on the existence of a ‘mature mathematical formalism’, where the latter refers to a—mathematically formulated and physically interpreted—notational system of locally applicable rules that derive from (but need not be reducible to) fundamental theory. As mathematical formalisms undergo a process of elaboration, enrichment, and entrenchment, they come to embody theoretical, ontological, and methodological commitments and assumptions. Since these are enshrined in the formalism itself, they are no longer readily obvious to either the novice or the proficient user. At the same time as formalisms constrain what may be represented, they also function as inferential and interpretative resources.     

The making of an intrinsic property: “Symmetry heuristics” in early particle physics

Mathematical invariances, usually referred to as “symmetries”, are today often regarded as providing a privileged heuristic guideline for understanding natural phenomena, especially those of micro-physics. The rise of symmetries in particle physics has often been portrayed by physicists and philosophers as the “application” of mathematical invariances to the ordering of particle phenomena, but no historical studies exist on whether and how mathematical invariances actually played a heuristic role in shaping microphysics. Moreover, speaking of an “application” of invariances conflates the formation of concepts of new intrinsic degrees of freedom of elementary particles with the formulation of models containing invariances with respect to those degrees of freedom. I shall present here a case study from early particle physics (ca. 1930–1954) focussed on the formation of one of the earliest concepts of a new degree of freedom, baryon number, and on the emergence of the invariance today associated to it. The results of the analysis show how concept formation and “application” of mathematical invariances were distinct components of a complex historical constellation in which, beside symmetries, two further elements were essential: the idea of physically conserved quantities and that of selection rules. I shall refer to the collection of different heuristic strategies involving selection rules, invariances and conserved quantities as the “SIC-triangle” and show how different authors made use of them to interpret the wealth of new experimental data. It was only a posteriori that the successes of this hybrid “symmetry heuristics” came to be attributed exclusively to mathematical invariances and group theory, forgetting the role of selection rules and of the notion of physically conserved quantity in the emergence of new degrees of freedom and new invariances. The results of the present investigation clearly indicate that opinions on the role of symmetries in fundamental physics need to be critically reviewed in the spirit of integrated history and philosophy of science.     

Estimating the Out‐of‐Sample Predictive Ability of Trading Rules: A Robust Bootstrap Approach

In this paper, we provide a novel way to estimate the out‐of‐sample predictive ability of a trading rule. Usually, this ability is estimated using a sample‐splitting scheme, true out‐of‐sample data being rarely available. We argue that this method makes poor use of the available data and creates data‐mining possibilities. Instead, we introduce an alternative.632 bootstrap approach. This method enables building in‐sample and out‐of‐sample bootstrap datasets that do not overlap but exhibit the same time dependencies. We show in a simulation study that this technique drastically reduces the mean squared error of the estimated predictive ability. We illustrate our methodology on IBM, MSFT and DJIA stock prices, where we compare 11 trading rules specifications. For the considered datasets, two different filter rule specifications have the highest out‐of‐sample mean excess returns. However, all tested rules cannot beat a simple buy‐and‐hold strategy when trading at a daily frequency. Copyright © 2015 John Wiley & Sons, Ltd.     

一种以特征线为中心的曲面特征表示方法

由于自由曲面特征形状复杂多样，难以有效地进行参数化表示．本文提出了一种以特征线为中心的曲面特征层次参数化的表示方法．该方法将特征线作为曲面构建的基本单元，将特征线划分为几何层、约束层、语法层和语义层，利用特征线信息对曲面特征进行参数分层，实现曲面特征的整体形状和局部形状的层次控制；在参数化表示上，按不同自由度分为半自由和完全自由曲面特征，并对曲面特征进行了统一的定义表示．实验结果表明，本文方法能够表达多种形状的自由曲面，在高层语义参数层面上方便地编辑曲面特征，是一种有效的曲面特征表示方法．     

Aristotle's biological works as scientific literature

This contribution deals with the question of where and why in his biological writings Aristotle uses dialogical elements, examining which dialogical structures can be found and what the meaning of the dialogical structures is in respect of the argumentative strategies used in literature. This discursive style has to be seen in relation to the importance of the dialectical method which was practiced in the Platonic Academy and on which Aristotle reflected in his Topics. For Aristotle the dialectical method also becomes the method of the investigator researching for himself. But more than that one can see the reason for the dialogical structures in Aristotle's writings in his attempt to combine the way of acquiring knowledge with the way of presenting knowledge. It can thus be said that at the moment in which the dialectical procedure is translated into the medium of writing, a fact-oriented presentation is also an addressee-oriented representation. Nowadays we are more accustomed to a technical literature which, after completing the first step of the deduction of knowledge, presents the results in a systematic and hierarchical way in its literary representation; in such technical literature, normally an individual's thought process is not set out in writing. Admittedly, with the application of the dialectical method and with the attempt to set down one's own thought process in the medium of writing, other elements also come in.     

基于特征的矢量场自适应纹理绘制

针对3D流场纹理可视化方法面临的遮挡问题,提出了一种基于流场特征模糊提取的自适应稀疏纹理绘制方法.该方法建立在一种可扩展的模糊流场特征区域描述与提取算法基础上,首先通过采用模糊理论对流场特征区域进行描述,建立了流场特征的测度规则并得到相应特征向量,然后基于特征向量偏差给出了最小平方和误差准则下的模糊测度隶属度的确定方法.根据得到的流场特征模糊隶属度场,生成可突出流场特征信息的自适应高斯噪声以进行纹理LIC卷积.同时针对纹理方法难以明确表示3D流场具体方向的缺陷,提出了两种冷暖光照方法,通过在LIC卷积过程中采用冷暖光照方法突出流场具体方向显示,有效解决了该问题.实验表明,本文方法相对于传统特征提取方法更具有可扩展性.同时自适应技术的采用,有效缓解了3D流场可视化存在的遮挡和混淆现象.而冷暖光照处理的加入,则解决了纹理方法对流场具体方向表现上的缺陷.     

Optimal forecast combination based on ensemble empirical mode decomposition for agricultural commodity futures prices

Improving the prediction accuracy of agricultural product futures prices is important for investors, agricultural producers, and policymakers. This is to evade risks and enable government departments to formulate appropriate agricultural regulations and policies. This study employs the ensemble empirical mode decomposition (EEMD) technique to decompose six different categories of agricultural futures prices. Subsequently, three models—support vector machine (SVM), neural network (NN), and autoregressive integrated moving average (ARIMA)—are used to predict the decomposition components. The final hybrid model is then constructed by comparing the prediction performance of the decomposition components. The predicting performance of the combination model is then compared with the benchmark individual models: SVM, NN, and ARIMA. Our main interest in this study is on short-term forecasting, and thus we only consider 1-day and 3-day forecast horizons. The results indicate that the prediction performance of the EEMD combined model is better than that of individual models, especially for the 3-day forecasting horizon. The study also concluded that the machine learning methods outperform the statistical methods in forecasting high-frequency volatile components. However, there is no obvious difference between individual models in predicting low-frequency components.     

长沙市大河西先导区创新发展状况分析

本文选取长沙大河西先导区、上海浦东新区以厦天津滨海新区三个创新建设实验区为研究对象,通过研究得出结论如下:(1)三个城区竞争力差异显著;(2)三个城区处于创新竞争力演变的不同阶段;(3)三个城区创新发展指教呈现出明显的梯级差异;(4)三个城区处于创新发展的不同阶段.本文通过综合考虑我国整体的创新发展状况,所得出的实证结论是长沙市先导区还处于创新建设的起步阶段.最后,论文通过分析提出了如下建议:长沙大河西先导区应加大创新资源的投入力度,激励企业技术创新,强化产学研互动创新网络功能,优化创新环境,努力提升先导区环境竞争力.     

快速Hermite径向基函数曲面重构

在这篇论文中,我们提出了一个使用局部支撑径向基函数对三维散乱点进行Hermite插值或逼近的快速曲面重构方法.通过构造给定数据点集的一个层次结构,采用逐层精化的方式实现了全局曲面重构的效果,解决了因使用局部支撑径向基函数导致的问题.另外,设计一个基于逼近误差导向的径向基函数中心点选择策略,减少每层进行插值的数据点,从而使Hermite径向基函数曲面重构方法能处理百万以上规模的点云数据.实验结果显示,我们的方法还适用于极度非均匀分布或带噪声的点云数据的曲面重构.     

Ensemble Forecasting for Complex Time Series Using Sparse Representation and Neural Networks

Based on the concept of ‘decomposition and ensemble’, a novel ensemble forecasting approach is proposed for complex time series by coupling sparse representation (SR) and feedforward neural network (FNN), i.e. the SR‐based FNN approach. Three main steps are involved: data decomposition via SR, individual forecasting via FNN and ensemble forecasting via a simple addition method. In particular, to capture various coexisting hidden factors, the effective decomposition tool of SR with its unique virtues of flexibility and generalization is introduced to formulate an overcomplete dictionary covering diverse bases, e.g. exponential basis for main trend, Fourier basis for cyclical (and seasonal) features and wavelet basis for transient actions, different from other techniques with a single basis. Using crude oil price (a typical complex time series) as sample data, the empirical study statistically confirms the superiority of the SR‐based FNN method over some other popular forecasting models and similar ensemble models (with other decomposition tools). Copyright © 2016 John Wiley & Sons, Ltd.