Foreword to the Special Focus on Mathematics,Data and Knowledge

There is a growing interest in applying mathematical theories and methods from topology, computational geometry, differential equations, fluid dynamics, quantum statistics, etc. to describe and to analyze scientific regularities of diverse, massive, complex, nonlinear, and fast changing data accumulated continuously around the world and in discovering and revealing valid, insightful, and valuable knowledge that data imply. With increasingly solid mathematical foundations, various methods and techniques have been studied and developed for data mining, modeling, and processing, and knowledge representation, organization, and verification; different systems and mechanisms have been designed to perform data-intensive tasks in many application fields for classification, predication, recommendation, ranking, filtering, etc. This special focus of Mathematics in Computer Science is organized to stimulate original research on the interaction of mathematics with data and knowledge, in particular the exploration of new mathematical theories and methodologies for data modeling and analysis and knowledge discovery and management, the study of mathematical models of big data and complex knowledge, and the development of novel solutions and strategies to enhance the performance of existing systems and mechanisms for data and knowledge processing. The present foreword provides a short review of some key ideas and techniques on how mathematics interacts with data and knowledge, together with a few selected research directions and problems and a brief introduction to the four papers published in the focus.     

动态投入产出模型及其在高等教育成本分析中的应用

高等院校教育成本核算一直是人们关心的重要问题.把高等院校大学生培养过程,看作人才的生产与加工过程,投入高中毕业生(原材料)以及教学、办公楼等固定资本与教职员工等劳动工时,生产或毕业高校大学毕业生,从而建立高等教育的动态投入产出模型,并由此推导高等院校大学生教育成本的计算公式,指出在计算教育成本时,固定资本租金率与高校规模扩张速度之间的关系,指出进一步深入研究的方向.     

复杂装备研制协调超网络均衡与实现路径

复杂装备研制主体间呈现社会关系、合作关系、协调关系等网络关系,并且相互影响相互作用,其影响复杂装备研制的重要参数。为有效描述在资源环境约束下制造商和供应商的关系,探讨复杂装备研制协调机理与实现路径,本文利用超网络方法,设计了相互影响、相互作用的社会关系网络、协调网络和合作网络的复杂装备研制协调超网络,并将社会关系水平、协调度和合作水平作为超网络的3个决策变量,建立基于关系价值最大、协调成本最低、协调风险最小、合作收益最大、合作风险最小和成本最小等不同偏好下的多目标最优决策模型,构建了复杂装备研制超网络均衡模型,并利用其探讨超网络均衡和实现路径。     

OUTPUT VERSUS INPUT CONTROLS UNDER UNCERTAINTY: THE CASE OF A FISHERY

Abstract The paper compares the management outcomes with a total allowable catch (TAC) and a total allowable effort (TAE) in a fishery under uncertainty. Using a dynamic programming model with multiple uncertainties and estimated growth, harvest, and effort functions from one of the world's largest fisheries, the relative economic and biological benefits of a TAC and TAE are compared and contrasted in a stochastic environment. This approach provides a decision and modeling framework to compare instruments and achieve desired management goals. A key finding is that neither instrument is always preferred in a world of uncertainty and that regulator's risk aversion and weighting in terms of expected net profits and biomass, and the trade‐offs in terms of expected values and variance determine instrument choice.     

Market-based pricing in grids: On strategic manipulation and computational cost

Grid technologies and the related concepts of utility computing and cloud computing enable the dynamic sourcing of computer resources and services, thus allowing enterprises to cut down on hardware and software expenses and to focus on key competencies and processes. Resources are shared across administrative boundaries, e.g. between enterprises and/or business units. In this dynamic and inter-organizational setting, scheduling and pricing become key challenges. Market mechanisms show promise for enhancing resource allocation and pricing in grids. Current mechanisms, however, are not adequately able to handle large-scale settings with strategic users and providers who try to benefit from manipulating the mechanism. In this paper, a market-based heuristic for clearing large-scale grid settings is developed. The proposed heuristic and pricing schemes find an interesting match between scalability and strategic behavior.     

双渠道供应链中的价格决策与服务决策研究

在集中式和分散式决策条件下,应用两阶段优化技术和Stackelberg博弈的理论与方法,对一个制造商与一个零售商组成的双渠道供应链,重点考虑了制造商在网络渠道的服务决策,建立了利润最大化模型,得到了最优的价格策略和服务策略,研究表明,网络渠道的服务水平对制造商和零售商的价格决策有着重要影响,而且消费者对网络直销渠道的偏好对制造商和零售商价格决策和服务决策会产生很大影响．     

Reexamination of processing time uncertainty

This paper presents the insights gained from the use of data mining and multivariate statistical techniques to identify important factors associated with a country's competitiveness and the development of knowledge discovery in databases (KDD) models to predict it. In addition to stepwise regression and weighted non-linear programming techniques, intelligent learning techniques (artificial neural networks), and inferential techniques (classification and regression trees), were applied to a dataset of 43 countries from the World Competitiveness Yearbook (WCY). The dataset included 55 variables on economic, internationalization, governmental, financial, infrastructure, management, science and technology, as well as demographic and cultural characteristics. Exploratory data analysis and parameter calibration of the intelligent method architectures preceded the development and evaluation of reasonably accurate models (mean absolute error <5.5%), and subsequent out-of-sample validations. The strengths and weaknesses of each of the KDD techniques were assessed, along with their relative performance and the primary input variables influencing a country's competitiveness. Our analysis reveals that the primary drivers of competitiveness are lower country risk rating and higher computer usage, in entrepreneurial urbanized societies with less male dominance and basic infrastructure, with higher gross domestic investment, savings and private consumption, more imports of goods and services than exports, increased purchase power parity GDP, larger and more productive but not less expensive labor force, and higher R&;D expenditures. Without diminishing the role and importance of WCY reports, our approach can be useful to estimate the competitiveness of many countries not included in WCY, while our findings may benefit policy makers and international agencies to expand their own abilities, insights and establish priorities for improving country competitiveness.     

环境治理政策的减排、增效与结构优化效果动态评价

为测度环境治理政策波动对产出、减排、要素配置、消费与产业结构的影响及其传导机制,将异质性消费偏好、产出差异性、环境效用和环境损失函数引入E-DSGE模型。政策强度分析发现,技术进步、排污税和消费税政策效果较强,环境控制和治污支出冲击效果较弱。政策效应分析发现,技术进步政策效应最优,能实现增产和减排双重目标,促进要素配置和居民消费、产出与消费结构改进;排污税和政府治污支出政策次优,能实现增产和减排的双赢目标,促进要素供给和产出结构清洁化,不利于消费提升和消费结构优化;环境控制与消费税政策效果最差,以牺牲产出实现减排,不利于要素配置,产出与消费结构改进效果较弱,消费税会抑制居民消费,但消费税政策效果随环境友好型家庭比例提升而加强。     

农业科技资源错配对农业科技创新全要素生产率影响的空间溢出效应

为研究农业科技资源错配与农业科技创新全要素生产率之间的空间溢出效应,利用2005-2017年所选取的25个省份的面板数据,通过动态空间杜宾模型进行实证研究.研究显示:①农业科技人力、财力资源错配与农业科技创新全要素生产率存在较强的空间相关性且分别呈现负向的区域内和区域间空间溢出效应.②农业科技财力资源错配程度每提升1%,农业科技创新全要素生产率就会下降0.264%,其中直接效应贡献0.255%,空间溢出效应贡献0.009%;农业科技人力资源错配对于农业科技创新全要素生产率的影响中间接效应起主要作用.③农业科技资源错配对于农业科技创新全要素生产率的空间效应存在显著的地区差异.     

定积分概念中蕴涵的对立统一思想

讨论了定积分定义中所蕴涵的对立统一思想,并从直与曲、整体与局部、近似与精确、有限与无限、特殊与一般、常量与变量等十个方面进行了论述.     

ESTIMATING A STOCHASTIC MODEL OF POPULATION DYNAMICS WITH AN APPLICATION TO KANGAROOS

In this study, we derive stochastic models of population dynamics and devise a new method of estimating the models. The models allow growth and harvest to be nonlinear functions of stochastic processes and the error terms to be nonlinear and heteroskedastic. Ordinary least-squares estimates would be biased and inefficient and generalized least-squares estimates cannot be calculated. Therefore, we implement nonlinear maximum likelihood methods to find unbiased and efficient estimates of parameters. The method is applied to the population dynamics of kangaroos in South Australia. Aerial survey data of kangaroo numbers are combined with harvest, effort and rainfall data to estimate the growth and harvest functions and the variances of the stochastic processes which drive the system. Results suggest that growth and harvest should be modeled as functions of stochastic processes and that observations on kangaroo numbers are critical for estimating population dynamics. The results also indicate that the estimation method works well and is a viable alternative to ARIMA and GARCH models, particularly for small data sets.     

Collaborative Curriculum Investigation as a Vehicle for Teacher Enhancement and Mathematics Curriculum Reform

The Missouri Middle Mathematics (M³) Project is an NSF-funded 3-year professional development project involving teacher/administrator teams from districts statewide. Project activities focus on collaborative investigation of emerging reform-based middle school mathematics curricula to support individual and systemic reform. Collaborative review and field-testing of material facilitates awareness and exploration of alternative instructional and assessment strategies and informed decision making. Early indicators of the model's success are reflected in participants’ enthusiasm and professional growth. Project activities stimulate discussions of critical topics including questioning appropriateness of various teaching practices, research about teaching and learning, tracking policies, appropriate assessment models for gauging student learning and the importance of calculators and manipulatives as teaching and learning tools. These discussions transcend curriculum materials being reviewed and serve as a powerful vehicle for professional growth and development for individual teachers and districts.     

Maintenance models in warranty: A literature review

Along with increasing the warranty period for complex systems, reducing the warranty servicing costs has become an issue of great importance to the manufacturers. One possible way to reduce the expected warranty servicing cost is by making sound decision on the product warranty and maintenance strategies. Therefore, warranties (basic warranty and extended warranty) and maintenance (corrective and preventive) are strongly interlinked and of great interest to both manufacturers and customers. This paper is the first identifiable academic literature review to deal with warranty and maintenance. It provides a classification scheme for the articles that link warranty and maintenance published between 2001 and 2011 covering 44 journals and proposes a taxonomy scheme to classify these articles. Nine hundred articles were identified for their relevance to warranty and were carefully reviewed. One-hundred and twenty-two articles were subsequently selected for their relevance to maintenance and included in the classification.     

格蕴涵代数的关联理想与模糊关联理想(英文)

本文提出了格蕴涵代数的关联理想和模糊关联理想的概念 ,讨论了它们的性质 ,指出了关联理想与理想、关联理想与关联滤子、关联理想与模糊关联理想、模糊关联理想与模糊关联滤子、模糊关联理想与模糊理想之间的关系     

矿井煤与瓦斯突出预测的物元模型方法

为了正确预测媒与瓦斯突出的趋势和危险性,根据影响煤与瓦斯突出危险性分类的一些主要因素,应用物元理论建立了煤与瓦斯突出危险性分类与判别模型.给出了煤与瓦斯突出危险性评价的物元关联函数及物元关联度的计算方法;建立了适合可拓学理论的煤与瓦斯突出危险性等级分类标准;采用指标的综合权重,充分利用主观赋权法和客观赋权法各自带来的信息.应用证明此方法适合于煤与瓦斯突出危险性等级的评判和预测.     

未确知集

分析了模糊集与R ough集两种不确定性集合的异同,指出模糊集中存在的不足和缺陷,在此基础上定义一种新的不确定性集合称作未确知集.在未确知集中模糊集的不足与缺陷得到弥补与修正,并且未确知集具有普通集合的含义.通过分析未确知集与模糊集的相同点及本质区别来论证未确知集存在与值得研究的价值.最后例举了常用的未确知隶属函数的构造方法.     

Email Surveillance Using Non-negative Matrix Factorization

In this study, we apply a non-negative matrix factorization approach for the extraction and detection of concepts or topics from electronic mail messages. For the publicly released Enron electronic mail collection, we encode sparse term-by-message matrices and use a low rank non-negative matrix factorization algorithm to preserve natural data non-negativity and avoid subtractive basis vector and encoding interactions present in techniques such as principal component analysis. Results in topic detection and message clustering are discussed in the context of published Enron business practices and activities, and benchmarks addressing the computational complexity of our approach are provided. The resulting basis vectors and matrix projections of this approach can be used to identify and monitor underlying semantic features (topics) and message clusters in a general or high-level way without the need to read individual electronic mail messages. Michael W. Berry is a Professor and Interim Department Head in the Department of Computer Science at the University of Tennessee and a faculty member in the Graduate School in Genome Science and Technology Program at the University of Tennessee and Oak Ridge National Laboratory. His research interests include information retrieval, data mining, scientific computing, computational science, and numerical linear algebra. He is a member of the Society for Industrial and Applied Mathematics (SIAM), Association for Computing Machinery (ACM), and the Computer Society of the Institute of Electrical and Electronics (IEEE). Professor Berry is on the editorial boards of “Computing in Science and Engineering” (IEEE Computer Society and the American Institute of Physics) and the SIAM Journal of Scientific Computing. Murray Browne is a Research Associate in the Department of Computer Science at the University of Tennessee. He is a member of the American Society for Information Science and Technology and has published numerous essays, book reviews, newspaper articles, and feature stories.     

Lagrange necessary conditions for Pareto minimizers in Asplund spaces and applications

In this paper, new necessary conditions for Pareto minimal points to sets and Pareto minimizers for constrained multiobjective optimization problems are established without the sequentially normal compactness property and the asymptotical compactness condition imposed on closed and convex ordering cones in Bao and Mordukhovich [10] and Durea and Dutta [5], respectively. Our approach is based on a version of the separation theorem for nonconvex sets and the subdifferentials of vector-valued and set-valued mappings. Furthermore, applications in mathematical finance and approximation theory are discussed.     

微生物组学的大数据研究

微生物组学大数据在生态环境、人类健康和疾病研究方面都起到了重要作用。通过数学、统计等数据挖掘方法,从高维复杂数据中提取有用信息,是微生物组学大数据建模和分析的关键问题。本文分析了微生物组学大数据的特点,对当前数据分析和计算研究中存在的热点和难点进行了探讨分析,并综述了当前微生物组学大数据模式挖掘、网络重建与分析的研究概况。