关键词： Conformal geometric algebra   HOL-light   Formalization   Grasping algorithm   Robot  

摘要： Conformal geometric algebra (CGA) is an advanced geometric language used in solving three-dimensional Euclidean geometric problems due to its simple, compact and coordinate-free formulations. It promises to stimulate new methods and algorithms in all areas of science dealing with geometric properties, especially for engineering applications. This paper presents a higher-order logic formalization of CGA theories in the HOL-Light theorem prover. First, we formally define the classical algebraic operations and representations of geometric entities in the new framework. Second, we use these results to reason about the correctness of operation properties and geometric features such as the distance between the geometric entities and their rigid transformations in higher-order logic. Finally, in order to demonstrate the practical effectiveness and utilization of this formalization, we use it to formally model the grasping algorithm of a robot based on the conformal geometric control technique and verify the property that whether the robot can grasp firmly or not.

关键词： 小学数学   算法   多样化  

摘要： “算法多样化”是数学新课程标准的重要理念之一,引导学生根据自己的知识掌握情况、生活经验来探索自己最易理解和运用的算法。在教学中是要求每一名学生都掌握许多种方法,还是让学生掌握一种最适合自己的方法?有时教师让学生把每一种算法一一罗列出来,但是其中有些方法并不高效,甚至有的方法并不合理,这时我们该如何取舍?因此,新课标在提倡和鼓励算法多样化时,我们数学教师应对小学数学中的算法多样化有一个正确的认识。

关键词： Bin packing   Cutting stock   Exact algorithms   Computational evaluation  

摘要： We review the most important mathematical models and algorithms developed for the exact solution of the one-dimensional bin packing and cutting stock problems, and experimentally evaluate, on state-of-the art computers, the performance of the main available software tools. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Tensor modeling   Evolutionary algorithms   Symbolic regression   Gene expression programming   RANS   Explicit algebraic stress modeling  

摘要： This paper presents a novel and promising approach to turbulence model formulation, rather than putting forward a particular new model. Evolutionary computation has brought symbolic regression of scalar fields into the domain of algorithms and this paper describes a novel expansion of Gene Expression Programming for the purpose of tensor modeling. By utilizing high-fidelity data and uncertainty measures, mathematical models for tensors are created. The philosophy behind the framework is to give freedom to the algorithm to produce a constraint-free model;its own functional form that was not previously imposed. Turbulence modeling is the target application, specifically the improvement of separated flow prediction. Models are created by considering the anisotropy of the turbulent stress tensor and formulating non-linear constitutive stress-strain relationships. A previously unseen flow field is computed and compared to the baseline linear model and an established non-linear model of comparable complexity. The results are highly encouraging. (C) 2016 Elsevier Inc. All rights reserved.

关键词： 比较思想   算法教学   应用  

摘要： 在小学数学算法教学中应用比较思想无疑是开展有效教学活动,引发学生对数学的思考,是学生快速掌握算法的有效途径。

关键词： Artifact removal   EEG signal processing   real-time algorithm   wearable  

摘要： Electroencephalography (EEG) is a non-invasive technique to record brain activities in natural settings. Ocular Artifacts (OA) usually contaminates EEG signals, removal of which is critical for accurate feature extraction and classification. With the increasing adoption of wearable technologies, single-channel real-time EEG systems that often require real-time signal processing for immediate real-time feedback are becoming more prevalent. However, traditional OA removal algorithms usually requiremultiple channels of EEG data, are computationally expensive, and do not perform well in real-time. In this article, a new hybrid algorithm is proposed that autonomously detects OA and subsequently removes OA from a single-channel steaming EEG data in real-time. The proposed single EEG channel algorithm also does not require additional reference electrooculography (EOG) channel. The algorithm has also been implemented on an embedded hardware platform of single channel wearable EEG system (NeuroMonitor). The algorithm first detects the OA zones using an Algebraic approach and then removes these artifacts from the detected OA zones using the Discrete Wavelet Transform (DWT) decomposition method. The de-noising technique is applied only to the OA zone, which minimizes loss of neural information outside the OA zone. A qualitative and quantitative performance evaluation was carried out with a 0.5s epoch in overlapping sliding window technique using time-frequency analysis, mean square coherence, and correlation coefficient statistics. The hybrid OA removal algorithm demonstrated real-time operation with 3s latency on the PSoC-3-microcontroller-based EEG system. Successful implementation of OA removal from single-channel real-time EEG data using the proposed algorithm shows promise for real-time feedback applications of wearable EEG devices.

关键词： Malcev algebra   abelian subalgebra   abelian ideal   invariant   invariant   algorithm  

摘要： In this paper, we introduce an algorithmic procedure that computes abelian subalgebras and ideals of a given finite-dimensional Malcev algebra. All the computations are performed by using the non-zero brackets in the law of the algebra as input. Additionally, the algorithm also computes the and invariants of these algebras, and as a supporting output, a list of abelian ideals and subalgebras of maximal dimension is returned too. To implement this algorithm, we have used the symbolic computation package MAPLE 12, performing a brief computational and statistical study for it and its implementation. Copyright (c) 2016 John Wiley & Sons, Ltd.

关键词： Dimension reduction   Principal component analysis   Tensor principal component analysis   Singular value decomposition   Discrete cosine transform  

摘要： We clarify the mathematical equivalence between low-dimensional singular value decomposition and low-order tensor principal component analysis for two- and three-dimensional images. Furthermore, we show that the two-and three-dimensional discrete cosine transforms are, respectively, acceptable approximations to two-and three-dimensional singular value decomposition and classical principal component analysis. Moreover, for the practical computation in two-dimensional singular value decomposition, we introduce the marginal eigenvector method, which was proposed for image compression. For three-dimensional singular value decomposition, we also show an iterative algorithm. To evaluate the performances of the marginal eigenvector method and two-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for six datasets of two-dimensional image patterns. To evaluate the performances of the iterative algorithm and three-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for datasets of gait patterns and human organs. For two-and three-dimensional images, the two-and three-dimensional discrete cosine trans-forms give almost the same recognition rates as the marginal eigenvector method and iterative algorithm, respectively.

关键词： 渐变色字符   字符定位   数学形态学   sobel算子   孔洞填充  

摘要： 为处理渐变色字符的字符定位,文章提出了一种基于数学形态学的字符定位算法。该算法很好地利用字符的特有属性,采用形态学中的边缘提取与膨胀操作,取得整体的字符骨架,再通过填充与腐蚀操作使得渐变色字符周围变得平滑,最后利用反色操作与top-hat滤波进行整体提亮,从而提取出字符。实验表明,该算法对渐变色字符有较强的定位能力,并能有效地去掉绝大部分噪声,字符提取率高达90%,与目前基于边缘分割,神经网络等算法相比有较大改进。