关键词： 在线教育   数学课程   匹配算法   协同过滤   模糊聚类   教学效果   原理分析  

摘要： 针对在线教育平台中大量数学课程资源利用率偏低、资源利用不符合教学逻辑等问题,文中基于模糊聚类算法提出匹配数学课程资源的智能化算法。通过深入分析常用智能匹配算法的主要原理,详细讨论多种常用匹配算法的优点和缺点。在此基础上,利用传统模糊聚类算法和模糊C均值聚类算法的思想,改进基于用户的协同过滤匹配算法,从而降低匹配算法中的数据稀疏性。仿真测试结果表明,在数学课程资源的匹配效果方面,与传统的协同过滤匹配算法相比,基于模糊C均值聚类的智能匹配算法具有更高的推荐准确度,可以有效提升教学效果。

关键词： 连通域标记   高速化   纸病检测  

摘要： 造纸行业竞争日益激烈,纸病的监测对保障纸品质量方面有着不可或缺的作用。针对纸病图像相对于背景图像便于区分的特点,采用连通域标记数学算法来开展纸病检测分析,最后用纸病图像验证算法是否可行。

关键词： Flatness   Constrained switched linear systems   Graph theory  

摘要： The problem of flat output characterization for switched linear discrete-time systems is addressed. First, an algebraic condition for an output to be flat is provided. It applies for I-flat outputs with the integer I potentially strictly greater than 1. Next, it is proved that such a characterization is decidable. Finally, an efficient algorithm which allows to decide in polynomial time whether a given output is flat is given. The algorithm is built from the observation that the flat output characterization can be expressed in terms of dead-beat stability of an associated constrained switched system. Thus, the notions of joint spectral radius and graph theory play relevant roles in this context. (C) 2021 Elsevier B.V. All rights reserved.

ISBN: (纸本)9787118122985

关键词： 数学方法   计算机算法   计算机编程  

摘要： 当下,国家对计算机产业尤为重视,把计算机、信创等有关方面的行业发展放在了战略目标的位置。计算机算法如今在社会中的使用率也逐步提高,在社会中也常被广泛应用到计算机编程和程序中,也因此发展得非常迅速。计算机算法和数学算法关系密切,不可分离,它是数学方法另外的一种表现形式,并且在计算机算法中也可以利用数学算法中的大部分数据。文章旨在讲述数学方法的自身特点和性质以及在计算机算法中的应用。

关键词： Berth allocation problem   Bee colony optimisation   Container terminal   Berth planning   Combinatorial optimisation  

摘要： Berth allocation is one of the crucial points for efficient management of ports. This problem is complex due to all possible combinations for assigning ships to available compatible berths. This paper focuses on solving the Berth Allocation Problem (BAP) by optimising port operations using an innovative model. The problem analysed in this work deals with the Discrete and Dynamic Berth Allocation Problem (DDBAP). We propose a novel mathematical formulation expressed as a Mixed Integer Linear Programming (MILP) for solving the DDBAP. Furthermore, we adapted a metaheuristic solution approach based on the Bee Colony Optimisation (BCO) for solving large-sized combinatorial BAPs. In order to assess the solution performance and efficiency of the proposed model, we introduce a new set of instances based on real data of the Livorno port (Italy), and a comparison between the BCO algorithm and CPLEX in solving the DDBAP is performed. Additionally, the application of the proposed model to a real berth scheduling (Livorno port data) and a comparison with the Ant Colony Optimisation (ACO) metaheuristic are carried out. Results highlight the feasibility of the proposed model and the effectiveness of BCO when compared to both CPLEX and ACO, achieving computation times that ensure a real-time application of the method.

关键词： Tool indexing   genetic algorithm   non-machining time   multi-objective optimisation   SPEA2   mathematical model  

摘要： Machining process efficiencies can be improved by minimising the non-machining time, thereby resulting in short operation cycles. In automatic-machining centres, this is realised via optimum cutting tool allocation on turret-magazine indices - the "tool-indexing problem". Extant literature simplifies TIP as a single-objective optimisation problem by considering minimisation of only the tool-indexing time. In contrast, this study aims to address the multi-objective optimisation tool-indexing problem (MOOTIP) by identifying changes that must be made to current industrial settings as an additional objective. Furthermore, tool duplicates and lifespan have been considered. In addition, a novel mathematical model is proposed for solving MOOTIP. Given the complexity of the problem, the authors suggest the use of a modified strength Pareto evolutionary algorithm combined with a customised environment-selection mechanism. The proposed approach attained a uniform distribution of solutions to realise the above objectives. Additionally, a customised solution representation was developed along with corresponding genetic operators to ensure the feasibility of solutions obtained. Results obtained in this study demonstrate the realization of not only a significant (70%) reduction in non-machining time but also a set of tradeoff solutions for decision makers to manage their tools more efficiently compared to current practices.

关键词： 地质大数据   深度学习   人工智能算法   区块链   深时数字地球   矿产资源预测   数学地球科学  

摘要： 近十年是科学研究从问题驱动向数据驱动转变的转折时期,科学研究的第四范式—数据密集型科学发现应势而生。这期间,大数据与人工智能算法的引入使数学地球科学实现跨越式发展,并正在改变地质学。机器学习是使计算机具有智能的根本途径。深度学习,即多层神经网络的方法,是一种实现机器学习的技术,是过去几年大数据与数学地球科学研究的最重要的热点。贝叶斯网络是贝叶斯公式和图论结合的产物,可用来建立矿床地质的成因网络,进而理解矿床成因。地质大图形问题可以转化为大型的复杂网络空间问题和社区结构问题,社区分析技术可用于地震预报、地质网络分析、特殊地质现象识别、矿床预测。关联规则和推荐系统算法在地质研究中已有成功的应用实例。化探数据及其异常经常包含复杂和非线性模式,深度学习在智能识别与提取复杂地质条件下地球化学异常具有优异的能力,卷积神经网络、堆叠自编码机等是较为常用和有效的方法。非线性矿产资源预测、基于GIS和三维地质建模的三维成矿预测及相应的软件系统得到持续改进。三维虚拟仿真建模技术的应用实现了多模态、跨尺度地学虚拟现实与多维交互,地质过程数值模拟等已有创新性进展。区块链技术以及OneGeology、玻璃地球、深时数字地球等大地质科学计划,将在整合全球地质大数据、共享全球地学知识、推动数学地球科学学科发展方面起到重大的推动作用。

关键词： 中国科学技术大学   数学算法   潘建伟   量子计算   超级计算机   原型机   优越性  

摘要： 200秒只是短短一瞬,6亿年早已是沧海桑田。中国科学技术大学的潘建伟等人成功构建76个光子的量子计算原型机"九章",求解数学算法高斯玻色取样只需200秒,而目前世界最快的超级计算机要用6亿年。我国因此成为全球第二个实现"量子优越性"的国家。

关键词： 高中数学   新课程   课程标准   算法   算法教学  

摘要： 本文在了解近些年算法教学研究的基础上,通过编制调查问卷,从不同的维度对教师和学生对算法的教与学方面进行了现状调查,研究当前高中算法教学的基本情况以及在调查的基础和结果上探究在法初步教学中采取怎样的方法来解决在教学中出现的问题,以便更好地促进算法教学的实施。