关键词： few-views computed tomography   strongly absorbing media   metal shell models   algebraic reconstruction technique   total variation regularization   adaptive segmentation  

摘要： The paper presents an original hybrid image reconstruction algorithm ART-TVS for few-views computed tomography of strongly absorbing media. It is based on the well-known algebraic reconstruction technique (ART), regularization of interim results through minimization of the total variation norm (TV-regularization), and a method of adaptive segmentation, which is a modernization of the known region growing algorithm. It is shown that the ART-TVS algorithm does not give stripe artifacts even if the number of views is very small (eight or less). ART-TVS reconstruction results for two numerical models of metal shells are compared with those obtained with the ART-TV algorithm (ART with TV-regularization and without adaptive segmentation), the iterative Potts minimization algorithm (IPMA), and our MART-AP algorithm (multiplicative ART with a priori information) we developed earlier for few-views discrete tomography. It is shown that ART-TVS outperforms ART-TV and IPMA and is comparable with MART-AP in reconstruction accuracy. Also, ART-TVS converges markedly faster than IRMA in cases where strongly underdetermined systems are treated. The algorithm we propose also demonstrates quite satisfactory resistance to projection data noise that is inherent in tomography of strongly absorbing media. (C) 2018 SPIE and IS&T

关键词： Conditional dependence   GMRF   Lattice spatial model   Sparse inverse subset   Takahashi equations  

摘要： Gaussian Markov random fields are used in a large number of disciplines in machine vision and spatial statistics. The models take advantage of sparsity in matrices introduced through the Markov assumptions, and all operations in inference and prediction use sparse linear algebra operations that scale well with dimensionality. Yet, for very high-dimensional models, exact computation of predictive variances of linear combinations of variables is generally computationally prohibitive, and approximate methods (generally interpolation or conditional simulation) are typically used instead. A set of conditions is established under which the variances of linear combinations of random variables can be computed exactly using the Takahashi recursions. The ensuing computational simplification has wide applicability and may be used to enhance several software packages where model fitting is seated in a maximum-likelihood framework. The resulting algorithm is ideal for use in a variety of spatial statistical applications, including LatticeKrig modelling, statistical downscaling, and fixed rank kriging. It can compute hundreds of thousands exact predictive variances of linear combinations on a standard desktop with ease, even when large spatial GMRF models are used. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Permutation   Shuffle   Permutation avoidance   Coproduct  

摘要： A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the problem of recognizing square permutations from both the point of view of algebra and algorithms. On the one hand, we present some algebraic and combinatorial properties of the shuffle product of permutations. We follow an unusual line consisting in defining the shuffle of permutations by means of an unshuffling operator, known as a coproduct. This strategy allows to obtain easy proofs for algebraic and combinatorial properties of our shuffle product. We besides exhibit a bijection between square (213, 231)-avoiding permutations and square binary words. On the other hand, by using a pattern avoidance criterion on directed perfect matchings, we prove that recognizing square permutations is NP-complete. (C) 2018 Published by Elsevier B.V.

关键词： 智能算法   数学建模比赛   应用  

摘要： 随着计算机技术和人工智能的快速发展,智能算法在数学建模比赛得到了广泛的应用,智能算法的运用极大的推动了数学建模比赛的发展,本文就针对智能算法在数学建模比赛中的实际应用进行详细的阐述。

关键词： 数学算法   计算机编程   探究   对比  

摘要： 随着我国科技水平逐步提升,人们的日常生活都会用到计算机。计算机软件是依靠编程来实现的,软件运行效率的高低是由编程语言来决定的。在研发一项软件的时候一定要优化好它的整体程序,这样才能使它的运行工作效率更高。当今盛行的计算机信息网络,数学算法就是计算机数学,在计算机中充分地运用了数学的算法原理,利用好数学算法里面的算法原理可以适当地建立数学模型,再利用计算机转换成计算机编程,以此可以提升计算机编程的工作效率。

关键词： 人工智能算法   数学建模  

摘要： 数学作为学生学习生活中比较重要的一个科目日益受到人们的重视,其中数学建模竞赛更是体现学生的课外实践动手能力的一个指标。数学建模主要是将日常生活中的各种问题经过简化来加以解决,它的主要目的就是帮助人们解决平常生活中解决不了的问题,解决的途径是将源于生活中各种复杂的事物通过建模型来解决。就目前而言,我国科学技术日新月异的发展,应用于数学建模中的技术手段也越来越多样化,尤其是人工智能算法的运用极大的促进了数学建模的发展。本文主要是在我国建模技术发展的基础上,进一步就人工神经网络方法和遗传算法展开研究探讨,进而不断推进我国数学建模水平的发展。

关键词： 计算机算法   数学方法   研究  

摘要： 数学方法是计算机算法的重要组成部分,不管是在编程方面,还是在解题方面都需要将数学方法作为基础,因此,本文围绕计算机算法当中的数学方法进行探讨,对数学方法的相关特点加以了解,并探讨数学方法在计算机算法中的具体应用。

关键词： 小学数学   数学教学   运算法则   人教版   混合   基础知识   数学教育   社会需求  

摘要： 数学核心素养的培养对学生的个性发展及适应社会需求具有重要意义。良好的数学教育能够使学生在理解并且熟练应用数学概念及定律等基础知识的基础上,得到数学技能方面的提升,积累数学活动经验,形成数学独特的思维方式和价值观念,最终影响学生的综合发展,为学生适应社会生活奠定基础。基于这样的教育背景,教师在数学教学中,必须改变应试教育中重知识传授,轻知识形成过程中所蕴含的素养培植的固化思维.

关键词： string counting   recognizable series   algebraic series   context-free grammar  

摘要： Formal series are a natural extension of formal languages by associating each word with a value called a coefficient or a weight. Among them, recognizable series and algebraic series can be regarded as extensions of regular languages and context-free languages, respectively. The coefficient of a word w can represent quantities such as the cost taken by an operation on w, the probability that w is emitted. One of the possible applications of formal series is the string counting in quantitative analysis of software. In this paper, we define the counting problems for formal series and propose algorithms for the problems. The membership problem for an automaton or a grammar corresponds to the problem of computing the coefficient of a given word in a given series. Accordingly, we define the counting problem for formal series in the following two ways. For a formal series S and a natural number d, we define CC (S ,d) to be the sum of the coefficients of all the words of length d in S and S C(S, d) to be the number of words of length d that have non-zero coefficients in S. We show that for a given recognizable series S and a natural number d, CC(S, d) can be computed in O(eta log d) time where eta is an upper-bound of time needed for a single state-transition matrix operation, and if the state-transition matrices of S are commutative for multiplication, S C(S, d) can be computed in polynomial time of d. We extend the notions to tree series and discuss how to compute them efficiently. Also, we propose an algorithm that computes CC(S, d) in square time of d for an algebraic series S. We show the CPU time of the proposed algorithm for computing CC(S, d) for some context-free grammars as S, one of which represents the syntax of C language. To examine the applicability of the proposed algorithms to string counting for the vulnerability analysis, we also present results on string counting for Kaluza Benchmark.

关键词： modular functions   Dedekind eta function   symbolic computation  

摘要： In this paper, we present an algorithm which can prove algebraic relations involving -quotients, where is the Dedekind eta function.