2014美赛数模题目

Teams (Student or Advisor) are now required to submit an electronic copy (summary sheet and solution) of their solution paper by email toosolutions@comap.com as a Word or PDF attachment. Your email MUST be received at COMAP by the submission deadline of 8:00 PM EST, February 10, 2014.Note you will not receive an auto reponse. Subject line COMAP your control number  Example: COMAP 11111 Click here to download a PDF of the complete contest instructions. Click here to download a copy of the Summary Sheet in Microsoft Word format. *Be sure to change the control number and problem select before printing out the page. Teams are free to choose between MCM Problem A, MCM Problem B or ICM Problem C. COMAP Mirror Site: For more in: http://www.comap.com/undergraduate/contests/mcm/ MCM: The Mathematical Contest in Modeling ICM: The Interdisciplinary Contest in Modeling 2014 Contest Problems MCM PROBLEMS PROBLEM A: The Keep-Right-Except-To-Pass Rule In countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.  Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important. In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirements be needed. Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system – either part of the road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results of your earlier analysis? PROBLEM B: College Coaching Legends Sports Illustrated, a magazine for sports enthusiasts, is looking for the “best all time college coach” male or female for the previous century. Build a mathematical model to choose the best college coach or coaches (past or present) from among either male or female coaches in such sports as college hockey or field hockey, football, baseball or softball, basketball, or soccer. Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differ from coaching in 2013? Clearly articulate your metrics for assessment. Discuss how your model can be applied in general across both genders and all possible sports. Present your model’s top 5 coaches in each of 3 different sports. In addition to the MCM format and requirements, prepare a 1-2 page article for Sports Illustrated that explains your results and includes a non-technical explanation of your mathematical model that sports fans will understand. ICM PROBLEM PROBLEM C: Using Networks to Measure Influence and Impact Click the title below to download a PDF of the 2014 ICM Problem. Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages. Using Networks to Measure Influence and Impact    2014 ICM Problem Using Networks to Measure Influence and Impact One of the techniques to determine influence of academic research is to build and measure properties of citation or co-author networks. Co-authoring a manuscript usually connotes a strong influential connection between researchers. One of the most famous academic co-authors was the 20th century mathematician Paul Erdös who had over 500 co-authors and published over 1400 technical research papers. It is ironic, or perhaps not, that Erdös is also one of the influencers in building the foundation for the emerging interdisciplinary science of networks, particularly, through his publication with Alfred Rényi of the paper “On Random Graphs” in 1959. Erdös’s role as a collaborator was so significant in the field of mathematics that mathematicians often measure their closeness to Erdös through analysis of Erdös’s amazingly large and robust co-author network (see the website http://www.oakland.edu/enp/ ). The unusual and fascinating story of Paul Erdös as a gifted mathematician, talented problemsolver, and master collaborator is provided in many books and on-line websites (e.g. http://www-history.mcs.st-and.ac.uk/Biographies/Erdos.html ). Perhaps his itinerant lifestyle, frequently staying with or residing with his collaborators, and giving much of his money to students as prizes for solving problems, enabled his co-authorships to flourish and helped build his astounding network of influence in several areas of mathematics. In order to measure such influence as Erdös produced, there are network-based evaluation tools that use co-author and citation data to determine impact factor of researchers, publications, and journals. Some of these are Science Citation Index, H factor, Impact factor, Eigen factor, etc. Google Scholar is also a good data tool to use for network influence or impact data collection and analysis. Your team’s goal for ICM 2014 is to analyze influence and impact in research networks and other areas of society. Your tasks to do this include: 1) Build the co-author networkof the Erdos1 authors (you can use the file from the website https://files.oakland.edu/users/grossman/enp/Erdos1.htmlor the one we include at Erdos1.htm). You should build a co-author network of the approximately 510 researchers from the file Erdos1, who coauthored a paper with Erdös, but do not include Erdös. This will take some skilled data extraction and modeling efforts to obtain the correctset of nodes (the Erdös coauthors) and their links (connections with one another ascoauthors). There are over 18,000 lines of raw data in Erdos1 file, but manyof them will not be used since they are links to people outside the Erdos1 network. If necessary, you can limit the size of your network to analyze in order to calibrate your influence measurement algorithm. Once built, analyze the properties of this network. (Again, do not include Erdös --- he is the most influential and would be connected to all nodes in the network. In this case, it’s co-authorship with him that builds the network, but he is not part of the network or the analysis.) 1）建立erdos1作者里面的合著者网络（你可以用https://files.oakland.edu/users/grossman/enp/erdos1.htmlor这个网站上的文件或者我们包括在Erdos1. htm中的文件）。你应该从文件erdos1（与Erdös合著一篇论文的人）里建立一个大约510的研究人员的合著网络（但不包括Erdös），这将需要提取一些技术数据和建模的努力来获得节点（Erdös的合著者）的正确设置以及他们之间的链接（与另一个合著者的连接）。在erdos1文件有超过18000的原始数据线，但他们中的许多人不会被使用，因为他们联系了erdos1网络以外的人。如果有必要，你可以限制您的网络大小去分析，来校准你的影响的测量算法。建成网络之后，分析这个网络的性能。（再次，不包括Erdös---他是最有影响力的也将被连接到所有节点网络。在这种情况下，它是共同作者和他建立的网络，但他不是网络或分析的一部分。） 2) Develop influence measure(s) to determine who in this Erdos1 network has significant influence within the network. Consider who has published important works or connects important researchers within Erdos1. Again, assume Erdös is not there to play these roles. 2）改进影响的方法来判定谁在erdos1网络中有最重要的影响。考虑谁发表了重要的工作或和在erdos1网络中重要的研究者联系。再次，假定Erdös没有发挥这些作用。 3) Another type of influence measure mightbe to compare the significance of a research paper by analyzing the important works that follow from its publication. Choose some set of foundational papers in the emerging field of network science either from the attached list (NetSciFoundation.pdf) or papers you discover. Use these papers to analyze and develop a model to determine their relative influence. Build the influence (coauthor or citation) networks and calculate appropriate measures for your analysis. Which of the papers in your set do you consider is the most influential in network science and why? Is there a similar way to determine the role or influence measure of an individual network researcher? Consider how you would measure the role, influence, or impact of a specific university, department, or a journal in network science? Discuss methodology to develop such measures and the data that would need to be collected. 3）另一种类型的影响的方法可能是通过分析随着它的出版而产生的重要作品来比较一篇研究论文的重要性，。从所附清单（NetSciFoundation.pdf）中选择一套在网络科学的新领域的基础性文件或你自己找的文件。用这些文件来分析和建立一个模型来确定它们的相对影响。建立影响（合著者或引用）的网络和为你的分析 计划 项目进度计划表范例计划下载计划下载计划下载课程教学计划下载 合适的方法。在你的论文中，你认为哪一个在网络科学最有影响力，为什么？是否存在一个类似的方法来确定地作用或影响一个人的网络测量研究？考虑你如何开发这样的度量法和需要收集的数据。 4) Implement your algorithm on a completely different set of network influence data --- for instance, influential songwriters, music bands, performers, movie actors, directors, movies, TV shows, columnists, journalists, newspapers, magazines, novelists, novels, bloggers, tweeters, or any data set you care to analyze. You may wish to restrict the network to a specific genre or geographic location or predetermined size. 4）在一个完全不同的网络影响数据中实现你的算法---例如，有影响力的作曲家，音乐的乐队，表演，电影演员，导演，电影，电视，报纸，杂志的专栏作家，记者，小说家，小说，博客，高音喇叭，或任何你想分析的数据集。你可以限制网络到一个特定的风格或地理位置或预定尺寸。 5) Finally, discuss the science, understanding and utility of modeling influence and impact within networks. Could individuals, organizations, nations, and society use influence methodology to improve relationships, conduct business, and make wise decisions? For instance, at the individual level, describe how you could use your measures and algorithms to choose who to try to co-author with in order to boost your mathematical influence as rapidly as possible. Or how can you use your models and results to help decide on a graduate school or thesis advisor to select for your future academic work? 5）最后，理解建立“网络中的影响”模型的作用，讨论模型的科学性。个人，组织，国家和社会，可以用“影响的方法”来改善关系，开展业务，并使明智的决定吗？例如，在个人层面上，为了尽可能迅速地提高你的数学的影响，应该怎样用你的措施和算法来选择和谁一起合著论文。或者您可以如何利用你的模型和结果可以为你未来的学术工作选择一个研究生学校或研究生导师？ 6) Write a report explaining your modeling methodology, your network-based influence and impact measures, and your progress and results for the previous five tasks. The report must not exceed20 pages (not including your summary sheet) and should present solid analysis of your network data; strengths, weaknesses, and sensitivity of your methodology; and the power of modeling these phenomena using network science. 6）写一份报告，说明你的建模方法，你的网络的影响的措施，和你之前五项任务的进展和结果。本报告不得超过20页（不包括你的总结表），并且应该使用网络科学对你做的网络的数据、优势、弱点、方法的灵敏度、建模的能力这些方面进行具体分析。     © 2014 COMAP, The Consortium for Mathematics and Its Applications May be reproduced for academic/research purposes For More information on COMAP and this project visit http://www.comap.com