关键词： 计算机辅助诊断   肺结节检测   数学形态学   图像分割  

摘要： 肺癌是最常见的内脏恶性肿瘤之一，近半个世纪以来，肺癌的发病率和死亡率都急速上升，已成为绝大多数国家癌症死亡的主要原因，被认为是当前危害人类生命健康的头号杀手。如果能在早期发现并及时治疗肺癌，患者的五年存活率可从14%提高到49%。肺癌的早期表现是肺结节，因此肺结节的早期检测和诊断对提高肺癌患者的生存率显得尤为重要。 计算机辅助检测(Computer Aided Detection,CAD)是近年来随着计算机技术的飞速发展而应用于影像诊断领域的一项新技术。它利用专业的计算机算法分析医学影像，对图像进行自动分析后向医生提示可疑的肺结节，从而帮助医生更加安全有效地分析数据，克服了因主观因素而产生的漏判及误判。计算机辅助检测和诊断的关键在于如何从图像中正确地检测出肺结节。 本文针对肺结节检测算法进行了相关研究，提出了基于CT图像的肺结节自动检测算法。该检测算法分为五大步骤，对于每个步骤，分别提出了各自有效的算法。首先结合肺部CT图像的特点，对图像进行阀值分割及反操作，实现了对肺实质区域的完整提取；在此基础上，提出了针对肺部CT图像的形态学滤波方法，取得了较好的滤波效果；然后使用了直方图规定化和TopHat的方法对滤波后的图像进行增强，为后续的分割奠定了基础；接着提出了一种将EM算法和区域生长相结合的图像分割算法，以EM分割后的图像为种子点进行区域生长，比原先仅使用EM方法的抗噪性更强，且不容易陷入局部最优，取得了很好的分割效果；最后以面积为特征量，结合数学形态学，将分割后图像中的肺结节点检测出来。 论文最后对上述方法进行了实验验证，实验的结果表明，本文提出的算法取得了良好的检测效果，相信通过不断的努力和改进，这一检测算法将具有广阔的应用前景。

关键词： quasi-metric   complexity space   fixed point   improver   worsener   complexity class   Quicksort   Hanoi   Largetwo  

摘要： Schellekens [The Smyth completion: A common foundation for denotational semantics and complexity analysis, Electron. Notes Theor. Comput. Sci. 1 (1995), pp. 211-232.] introduced the theory of complexity (quasi-metric) spaces as a part of the development of a topological foundation for the asymptotic complexity analysis of programs and algorithms in 1995. The applicability of this theory to the asymptotic complexity analysis of divide and conquer algorithms was also illustrated by Schellekens in the same paper. In particular, he gave a new formal proof, based on the use of the Banach fixed-point theorem, of the well-known fact that the asymptotic upper bound of the average running time of computing of Mergesort belongs to the asymptotic complexity class of n log(2) n. Recently, Schellekens' method has been shown to be useful in yielding asymptotic upper bounds for a class of algorithms whose running time of computing leads to recurrence equations different from the divide and conquer ones reported in Cerda-Uguet et al. [The Baire partial quasi-metric space: A mathematical tool for the asymptotic complexity analysis in Computer Science, Theory Comput. Syst. 50 (2012), pp. 387-399.]. However, the variety of algorithms whose complexity can be analysed with this approach is not much larger than that of algorithms that can be analysed with the original Schellekens method. In this paper, on the one hand, we extend Schellekens' method in order to yield asymptotic upper bounds for a certain class of recursive algorithms whose running time of computing cannot be discussed following the techniques given by Cerda-Uguet et al. and, on the other hand, we improve the original Schellekens method by introducing a new fixed-point technique for providing, contrary to the case of the method introduced by Cerda-Uguet et al., lower asymptotic bounds of the running time of computing of the aforementioned algorithms and those studied by Cerda-Uguet et al. We illustrate and validate the dev

关键词： probit-based stochastic user equilibrium   elastic demand   asymmetric link travel time functions   variational inequality   computational algorithm  

摘要： This article addresses model development and computational algorithm design for the probit-based asymmetric stochastic user equilibrium (SUE) problem with elastic demand. Two variational inequality (VI) models are first proposed for the SUE problem and then existence and uniqueness of their solutions are examined. These two VI models are, in reality, built by means of a probit-based stochastic network loading (SNL) map. Since there is no computational procedure available for calculating the SNL map, we thus propose a two-stage Monte Carlo simulation-based method to estimate the SNL map. To compromise computational time with accuracy in the estimation, a lower bound of sample size required by the Monte Carlo simulation is also investigated. Based on these two VI models and Monte Carlo simulation-based method, we design two hybrid predictioncorrection (PC) cost averaging (CA) algorithms for solving the SUE problem. Finally, two numerical examples are carried out to assess performance of the proposed algorithms.

关键词： Buckyball   Graph algorithms   Dynamic programming   Greedy algorithm   Nanocomputational calculations  

摘要： Purpose - One of the significant underlying principles of nanorobotic systems deals with the understanding and conceptualization of their respective complex nanocomponents. This paper introduces a new methodology to compute a set of optimal electronic and mathematical properties of Buckyball nanoparticle using graph algorithms based on dynamic programming and greedy algorithm. Design/methodology/approach - Buckyball, C-60, is composed of sixty equivalent carbon atoms arranged as a highly symmetric hollow spherical cage in the form of a soccer ball. At first, Wiener, hyper-Wiener, Harary and reciprocal Wiener indices were computed using dynamic programming and presented them as: W(Buckyball) = 11870.4, WW(Buckyball) = 52570.9, Ha(Buckyball) = 1022 and RW(Buckyball) = 346.9. The polynomials of Buckyball, Hosoya and hyper-Hosoya, which are in relationship with Buckyball's indices, have also been computed. The relationships between Buckyball's indices and polynomials were then computed and demonstrated a good agreement with their mathematical equations. Also, a graph algorithm based on greedy algorithms was used to find some optimal electronic aspects of Buckyball's structure by computing the Minimum Weight Spanning Tree (MWST) of Buckyball. Findings - The computed MWST was indicated that for connecting sixty carbon atoms of Buckyball together: the minimum numbers of double bonds were 30;the minimum numbers of single bonds were 29;and the minimum numbers of electrons were 178. These results also had good agreement with the principles of the authors' used greedy algorithm. Originality/value - This paper has used the graph algorithms for computing the optimal electronic and mathematical properties of BB. It has focused on mathematical properties of BB including Wiener, hyper-Wiener, Harary and reciprocal Wiener indices as well as Hosoya and Hyper-Hosoya polynomials and computerized them with dynamic programming graph algorithms.

关键词： matrix bound   unified coupled algebraic Riccati equation   eigenvalue  

摘要： In this paper, combining the equivalent form of the unified coupled algebraic Riccati equation (UCARE) with the eigenvalue inequalities of a matrix's sum and product, using the properties of an M-matrix and its inverse matrix, we offer new lower and upper matrix bounds for the solution of the UCARE. Furthermore, applying the derived lower and upper matrix bounds and a fixed-point theorem, an existence uniqueness condition of the solution of the UCARE is proposed. Then, we propose a new fixed-point iterative algorithm for the solution of the UCARE. Finally, we present a corresponding numerical example to demonstrate the effectiveness of our results.

关键词： 算法初步   高中数学   算法教学  

摘要： 第八次课程改革实施已接近十年，课程设置发生了很多变化。其中数学由阶段性学习变为模块式学习，即分为必修和选修两部分。《普通高中课程标准（实验）》（以下简称《标准》）把“算法初步”作为一个新的内容列入了必修课程五个模块中的数学3。然而，通过查阅相关文献，调卷问卷分析发现目前高中在职数学教师对算法及算法教学的相关内容准备和掌握不是十分充分理想，学生接受程度并未达到标准要求，具体有体现如下： 1、吉林省实施新课改近5年,目前中学教师的算法教学素养总体不高，需要进一步加强和学习； 2、对于进行的算法教学，多数一线教师并未接触过，系统学过，准备尚不充分，需要时间对《标准》进行钻研，学习中国传统数学中的算法教学案例； 3、学生只是为了应付考试而单纯的学习算法内容，程序设计，编写框图只有少数人掌握； 4、教师在此方面的教学内容缺少与学生的系统交流分析，没有形成规范教学模式。 因此，可以看出算法教学作为新课程改革中新出现的内容，在现行的教学中并没有成熟的教学经验可以用来借鉴。为此，本文通过对一线教师及学生的调查和数据分析来探讨算法教学内容及教师的算法知识，希望对教师，学生都能够提供相应的帮助。 本文将从以下方面研究中学数学算法的教学及教师的算法知识： 1、以高中课程标准为依据研究人教A版数学必修3中的算法内容，与不同国家不同地区的算法内容作比较；通过阅读相关文献，并进行分析，借鉴其中算法教学先进的理念，探讨高中数学算法教学的方法、思想、内容及价值。 2、通过调查问卷的形式了解在职教师与学生对算法知识的理解程度，通过分析问卷和访谈内容，提出研究建议。 最后，提出本文的不足之处和对研究的展望。

关键词： abelian Lie subalgebra   abelian ideal   alpha invariant   beta invariant   algorithm  

摘要： In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals of finite-dimensional Lie algebras, starting from the non-zero brackets in its law. In order to implement this method, we use the symbolic computation package MAPLE 12. Moreover, we also give a brief computational study considering both the computing time and the memory used in the two main routines of the implementation. Finally, we determine the maximal dimension of abelian subalgebras and ideals for non-decomposable solvable non-nilpotent Lie algebras of dimension 6 over both the fields R and C, showing the differences between these fields.

关键词： 算法初步   高中数学新课程   算法思想   教学实践  

摘要： 算法是计算科学的重要基础,算法思想已经成为现代人应该具备的一种数学素养[1].众所周知,计算机在现代科技和社会生活中发挥着越来越大的作用,而算法恰恰是计算机得以运行的前提,所以算法的科学价值自然不言而喻.为了体现高中数学内容的与时俱进,"算法初步"被编进高中数学新课程,并被编写

关键词： 子公式权重   公式相关度   计算机代数系统(CAS)   排序算法  

摘要： 目前,Web中的数学信息量逐渐增加,数学搜索成为人们关注的焦点。近几年,浏览器对数学公式的显示和存储问题己得到逐步解决,为面向数学公式的搜索引擎的研究和开发提供了良好的基础。 尽管数学公式可以存储在web文档中,在网络中搜索数学公式仍具有局限性。数学公式具有复杂的二维结构以及蕴涵有复杂的数学表达意义,不同描述的数学公式可能具有相同的意义,同一数学公式的表示形式可能有多种,另外用户查询公式可能为某一公式的子公式,因此用传统的文本检索系统搜索数学公式显得力所不足。国际上现有的或者正在研究的数学公式检索系统,在建立索引方面已取得逐步发展,在返回结果集的排序算法方面大部分仍应用文本搜索引擎的排序算法,未深入研究面向数学公式搜索结果排序的算法。因此,本文将在深入研究现有的基于文本搜索引擎排序算法的原理和基础上,结合数学公式的特点以及数学公式间的关系(等价、代数相关、子公式等)尝试提出面向数学公式搜索排序的算法。本文将计算机代数系统(CAS)和数学公式搜索引擎相结合去挖掘公式与公式之间的关系,不但为查询公式和网页之间相关度的计算方面提供更加合理可靠的相关度量方法,还将促进系统对数学公式语义检索的能力。