2014年数学建模美赛ABC_题翻译
2014年美赛C题翻译
This will take some skilled data extraction and modeling efforts to obtain the correct set of nodes (the Erdös coauthors) and their links (connections with one another as coauthors). 这需要熟练数据提取 并 在建模上下功夫， 以便得到正确的节点和边
Once built, analyze the properties of this network. 建完后分析网络性能(Again, do not include Erdös --- he is the most infnodes 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.)
One of the techniques to determine influence of academic research is to build and measure properties of citation or co-author networks.
学术研究的技术来确定影响之一是构建和引文或合著网络的度量属性。
Google Scholar is also a good data tool to use for network influence or impact data collection and analysis.
谷歌学术搜索也是一个好的数据工具用于网络数据收集和分析影响或影响。
2014 数学建模美赛B题
PROBLEM B: College Coaching LegendsSports 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 choosethe 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.问题B：大学教练的故事体育画报，为运动爱好者杂志，正在寻找上个世纪堪称“史上最优秀大学教练”的男性或女性。
2014美赛b题 分析
上一篇文章中我们用题意分解的办法详细解读了2014MCM A题的要点,并总结了6个题意的关键点，大家可以对照自己的文章,看看有没有把这些关键问题解释和说明清楚，如果这些问题全部回答到位，M奖就到手啦，在这些部分中有1～2个有所创新，能够令评委眼前一亮的话，那么就有机会得到更高的奖项哦，大家是不是心里更加有底了呢?接下来，我们继续用上篇文章提到的方法来解析B题的关键点，上题：PROBLEM B: CollegeCoaching Legends （bk1: the topic）Sports Illustrated, amagazine for sports enthusiasts, is looking for the “best all time college coach” male or femalefor the previous century. （bk2：briefintroduction of background）Build a mathematical model （spm1) tochoose the best college coach or coaches (past or present）(rsc1) from among either male or female （rsc2)coaches in such sports as college hockey or fieldhockey, football, baseball or softball，basketball, or soccer (rsc3）。
(These 3 restrictiveconditions ask us the range of our evaluation model should contain thedifference above。
)Does it make a difference which time line horizon thatyou use in your analysis, i.e。
2014美赛ICM翻译
2014 ICM ProblemUsing 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 500co-authors and published over 1400 technical research papers. It is ironic, or perhapsnot, that Erdös is also one of the influencers in building the foundation for the emerging interdisciplinary science of networks, particularly, through his publication with AlfredRényi of the paper “On Random Graphs” in 1959. Erdös’s role as a collaborator was sosignificant in the field of mathematics that mathematicians often measure their closeness to Erdös through analysis of Erdös’s amazingly large and robust co-authornetwork (see the website /enp/ ). The unusual and fascinatingstory of Paul Erdös as a gifted mathematician, talented problem solver, and mastercollaborator is provided in many books and on-line websites(e.g.,/Biographies/Erd os.html). Perhaps his itinerantlifestyle, frequently staying with or residing with his collaborators, and giving much of hismoney to students as prizes for solving problems, enabled his co-authorships to flourishand helped build his astounding network of influence in several areas of mathematics.In order to measure such influence as Erdös produced, there are network-basedevaluation tools that use co-author and citation data to determine impact factor ofresearchers, publications, and journals. Some of these are Science Citation Index, Hfactor,Impact factor, Eigenfactor, etc. Google Scholar is also a good data tool to use fornetwork influence or impact data collection and analysis. Your team’s goal for ICM2014 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 network of the Erdos1 authors (you can use the file from thewebsitehttps:///users/grossman/enp/Erdos1. html or the one weinclude at Erdos1.htm ). You should build a co-author network of theapproximately 510 researchers from the file Erdos1, who coauthored a paperwith Erdös, but do not include Erdös. This will take some skilled data extractionand modeling efforts to obtain the correct set of nodes (the Erdös coauthors) andtheir links (connections with one another as coauthors). There are over 18,000lines of raw data in Erdos1 file, but many of them will not be used since they arelinks to people outside the Erdos1 network. If necessary, you can limit the size ofyour network to analyze in order to calibrate your influence measurementalgorithm. Once built, analyze the properties of this network. (Again, do notinclude Erdös --- he is the most influential and would be connected to all nodes inthe network. In this case, it’s co-authorship with him that builds the network, buthe is not part of the network or the analysis.)2) Develop influence measure(s) to determine who in this Erdos1 network hassignificant influence within the network. Consider who has published importantworks or connects important researchers within Erdos1. Again, assume Erdös isnot there to play these roles.3) Another type of influence measure might be to compare the significance of aresearch paper by analyzing the important works that follow from its publication.Choose some set of foundational papers in the emerging field of network scienceeither from the attached list (NetSciFoundation.pdf) or papers you discover.Use these papers to analyze and develop a model to determine their relativeinfluence. Build the influence (coauthor or citation) networks and calculateappropriate measures for your analysis. Which of the papers in your set do youconsider is the most influential in network science and why? Is there a similarway to determine the role or influence measure of an individual networkresearcher? Consider how you would measure the role, influence, or impact of aspecific university, department, or a journal in network science? Discussmethodology to develop such measures and the data that would need to becollected.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. Youmay wish to restrict the network to a specific genre or geographic location orpredetermined size.5) Finally, discuss the science, understanding and utility of modeling influence andimpact within networks. Could individuals, organizations, nations, and society useinfluence methodology to improve relationships, conduct business, and makewise decisions? For instance, at the individual level, describe how you could useyour measures and algorithms to choose who to try to co-author with in order toboost your mathematical influence as rapidly as possible. Or how can you useyour models and results to help decide on a graduate school or thesis advisor toselect for your future academic work?6) Write a report explaining your modeling methodology, your network-basedinfluence and impact measures, and your progress and results for the previousfive tasks. The report must not exceed 20 pages (not including your summarysheet) and should present solid analysis of your network data; strengths,weaknesses, and sensitivity of your methodology; and the power of modelingthese phenomena using network science.*Your submission should consist of a 1 page Summary Sheet and your solution cannotexceed 20 pages for a maximum of 21 pages.This is a listing of possible papers that could be included in a foundational set ofinfluential publications in network science. Network science is a new, emerging, diverse, interdisciplinary field so there is no large, concentrated set of journals that are easy touse to find network papers even though several new journals were recently establishedand new academic programs in network science are beginning to be offered inuniversities throughout the world. You can use some of these papers or others of yourown choice for your team’s set to analyze and compare for influence or impact innetwork science for task #3.Erdös, P. and Rényi, A., On Random Graphs, Publicationes Mathematicae, 6: 290-297,1959.Albert, R. and Barabási, A-L. Statistical mechanics of complex networks. Reviews ofModern Physics, 74:47-97, 2002.Bonacich, P.F., Power and Centrality: A family of measures, Am J. Sociology. 92: 1170-1182, 1987.Barabási, A-L, and Albert, R. Emergence of scaling in random networks. Science, 286:509-512, 1999.Borgatti, S. Identifying sets of key players in a network. Computational andMathematical Organization Theory, 12: 21-34, 2006. Borgatti, S. and Everett, M. Models of core/periphery structures. Social Networks, 21:375-395, October 2000Graham, R. On properties of a well-known graph, or, What is your Ramseynumber? Annals of the New York Academy of Sciences, 328:166-172, June 1979.Kleinberg, J. Navigation in a small world. Nature, 406: 845, 2000.Newman, M. Scientific collaboration networks: II. Shortest paths, weightednetworks, and centrality. Physical Review E, 64:016132, 2001.Newman, M. The structure of scientific collaboration networks. Proc. Natl.Acad. Sci. USA, 98: 404-409, January 2001. Newman, M. The structure and function of complex networks. SIAM Review,45:167-256, 2003.Watts, D. and Dodds, P. Networks, influence, and public opinion formation. Journal ofConsumer Research, 34: 441-458, 2007.Watts, D., Dodds, P., and Newman, M. Identity and search in social networks. Science,296:1302-1305, May 2002.Watts, D. and Strogatz, S. Collective dynamics of `small-world' networks. Nature, 393:440-442, 1998.Snijders, T. Statistical models for social networks. Annual Review of Sociology, 37:131–153, 2011.Valente, T. Social network thresholds in the diffusion of innovations, Social Networks,18: 69-89, 1996.Erdos1, V ersion 2010, October 20, 2010This is a list of the 511 coauthors of Paul Erdos, together with their coauthors listed beneath them. The date of first joint paper with Erdos is given, followed by the number of joint publications (ifit is more than one). An asterisk following the name indicates that this Erdos coauthor is known to be deceased; additional information about the status of Erdos coauthors would be most welcomed. (This convention is not used for those with Erdos number 2, as to do so would involve too much work.) Numbers preceded by carets follow the convention used by Mathematical Reviews in MathSciNet to distinguish people with the same names.Please send corrections and comments to grossman@The Erdos Number Project Web site can be found at the following URL:/enpABBOTT, HARVEY LESLIE 1974Aull, Charles E.Brown, Ezra A.Dierker, Paul F.Exoo, GeoffreyGardner, BenHANSON, DENISHare, Donovan R. Katchalski, MeirLiu, Andy C. F.MEIR, AMRAMMOON, JOHN W.MOSER, LEO*Pareek, Chandra MohanRiddell, JamesSAUER, NORBERT W.SIMMONS, GUSTA VUS J.Smuga-Otto, M. J.SUBBARAO, MA TUKUMALLI VENKATA* Suryanarayana, D.Toft, BjarneWang, Edward Tzu HsiaWilliams, Emlyn R.Zhou, BingACZEL, JANOS D. 1965Abbas, Ali E.Aczel, S.Alsina Catala, ClaudiBaker, John A.Beckenbach, Edwin F.Beda, GyulaBelousov, Valentin DanilovichBenz, WalterBerg, LotharBoros, ZoltanChudziak, JacekDaroczy, ZoltanDhombres, Jean G.Djokovic, Dragomir Z.Egervary, Jeno2014 ICM问题使用网络来测量的影响和冲击其中一项技术来确定学术研究的影响力是建立和测量引文或合著者网络的性能。
2014美国数学建模竞赛赛题翻译
问题A：右行左超规则在美国、中国和大多数除了英国、澳大利亚和一些前英国殖民地的国家，多车道高速公路常常有这样一种规则。
司机必须尽量在最右的车道行使，只有超车时，司机才可以向左移动一个车道来达成目的。
当司机超车完毕后必须回到原车道继续行使。
建立并分析一个数学模型，使得这个模型能够分析这个规则在交通高负荷和低负荷情况下的表现。
你可以从许多角度来思考这个问题，比如车流量和车辆安全之间的权衡，或者一个过快或过慢的车辆限速带来的影响等等。
这个规则可以使我们获得更好的交通流？如果不可以，请提出并分析一个替代方案使得交通流得到优化、安全得到保障、或者其他你认为重要的因素得到实现。
在靠左行使才是规则的国家，论证你的解决方案是否可以通过简单的变换或者通过增加一些新的要求来解决相同的问题。
最后，以上的规则的实行是建立在人们遵守它的基础上的，然而不是所有人都愿意去遵守。
那么现在我们使同一条道（可以只是一段，也可以是全段公路）上的交通车辆都在一个智能系统的严格控制下，这个变化对你之前的分析结果有多大的影响？问题B：体育画刊是一个为体育爱好者们设计的杂志。
这个杂志正在寻找上世纪女性或者男性的“历来最优秀的大学教练”。
建立一个数学模型，从男性或者女性体育教练中选择最好的大学教练（退役或者在役的都可以）。
这些体育教练可以是大学曲棍球、陆上曲棍球、足球、橄榄球、棒球、排球、篮球的教练。
你选择划分的时间会对你的分析有影响吗？也就是说，1913年的教练方式和2013年的会有什么不同吗？清楚的阐述你的评估方式。
讨论你的模型如何通用于两性教练和所有可能的运动项目上。
用你的模型为三项体育项目分别找到五个最佳教练。
再为体育画刊提供一篇1－2页的不涉及技术性问题解释的通俗易懂的文章来解释你们的结果，你们必须保证体育爱好者们能够理解。
2014年数学建模美赛ABC 题翻译
问题A：除非超车否则靠右行驶的交通规则在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。
建立数学模型来分析这条规则在低负荷和高负荷状态下的交通路况的表现。
你不妨考察一下流量和安全的权衡问题,车速过高过低的限制，或者这个问题陈述中可能出现的其他因素。
这条规则在提升车流量的方面是否有效？如果不是，提出能够提升车流量、安全系数或其他因素的替代品（包括完全没有这种规律）并加以分析。
在一些国家，汽车靠左形式是常态，探讨你的解决方案是否稍作修改即可适用，或者需要一些额外的需要。
最后，以上规则依赖于人的判断，如果相同规则的交通运输完全在智能系统的控制下，无论是部分网络还是嵌入使用的车辆的设计，在何种程度上会修改你前面的结果？问题B：大学传奇教练体育画报是一个为运动爱好者服务的杂志，正在寻找在整个上个世纪的“史上最好的大学教练”。
建立数学模型选择大学中在一下体育项目中最好的教练：曲棍球或场地曲棍球，足球，棒球或垒球，篮球，足球。
时间轴在你的分析中是否会有影响？比如1913年的教练和2013年的教练是否会有所不同？清晰的对你的指标进行评估，讨论一下你的模型应用在跨越性别和所有可能对的体育项目中的效果。
展示你的模型中的在三种不同体育项目中的前五名教练。
除了传统的MCM格式，准备一个1到2页的文章给体育画报，解释你的结果和包括一个体育迷都明白的数学模型的非技术性解释。
使用网络测量的影响和冲击学术研究的技术来确定影响之一是构建和引文或合著网络的度量属性。
与人合写一手稿通常意味着一个强大的影响力的研究人员之间的联系。
最著名的学术合作者是20世纪的数学家保罗鄂尔多斯曾超过500的合作者和超过1400个技术研究论文发表。
讽刺的是,或者不是,鄂尔多斯也是影响者在构建网络的新兴交叉学科的基础科学,尤其是，尽管他与Alfred Rényi的出版物“随即图标”在1959年。
2014美赛题目(翻译版)
2014 MCM ProblemsPROBLEM A: The Keep-Right-Except-To-Pass RuleIn 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.在一些以行车靠右为规则的国家中（比如美国、中国以及除了大不列颠、澳大利亚和一些前英属殖民国家以外的其他国家），多行道的高速公路经常采用要求驾驶人在除超车以外时都靠右行驶的交通规则。
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.1、请你建立和分析一个数学模型来分析这个规则在交通畅通和交通堵塞条件下的表现。
建模美赛C题带翻译
Problem C: “Cooperate and navigate”Traffic capacity is limited in many regions of the United States due to the number of lanes of roads. For example, in the Greater Seattle area drivers experience long delays during peak traffic hours because the volume of traffic exceeds the designed capacity of the road networks. This is particularly pronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interest for this problem.Self-driving, cooperating cars have been proposed as a solution to increase capacity of highways without increasing number of lanes or roads. The behavior of these cars interacting with the existing traffic flow and each other is not well understood at this point.The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving, cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties. (See the provided map and Excel spreadsheet). In particular, how do the effects change as the percentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there a tipping point where performance changes markedly? Under what conditions, if any, should lanes be dedicated to these cars? Does your analysis of your model suggest any other policy changes?Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/or average traffic volume, and percentage of vehicles using self-driving, cooperating systems. Your model should address cooperation between self-driving cars as well as the interaction between self- driving and non-self-driving vehicles. Your model should then be applied to the data for the roads of interest, provided in the attached Excel spreadsheet.Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to the Governor’s office, and your solution (not to exceed 20 pages) for a maximum of 23 pages. Note: The appendix and references do not count toward the 23 page limit. Some useful background information:On average, 8% of the daily traffic volume occurs during peak travel hours.•The nominal speed limit for all these roads is 60 miles per hour.•Mileposts are numbered from south to north, and west to east.•Lane widths are the standard 12 feet.•Highway 90 is classified as a state route until it intersects Interstate 5.•In case of any conflict between the data provided in this problem and any other source, use the data provided in this problem.Definitions:milepost: A marker on the road that measures distance in miles from either the start of the route or astate boundary.average daily traffic: The average number of cars per day driving on the road.interstate: A limited access highway, part of a national system.state route: A state highway that may or may not be limited access.route ID: The number of the highway.increasing direction: Northbound for N-S roads, Eastbound for E-W roads.decreasing direction: Southbound for N-S roads, Westbound for E-W roads.问题C：“合作和导航”由于道路的数量，美国许多地区的交通容量有限。
数学建模美赛论文标准格式参考--中英文对照
Your Paper's Title Starts Here: Please Centeruse Helvetica (Arial) 14论文的题目从这里开始：用Helvetica (Arial)14号FULL First Author1, a, FULL Second Author2,b and Last Author3,c第一第二第三作者的全名1Full address of first author, including country第一作者的地址全名，包括国家2Full address of second author, including country第二作者的地址全名，包括国家3List all distinct addresses in the same way第三作者同上a email,b email,c email第一第二第三作者的邮箱地址Keywords:List the keywords covered in your paper. These keywords will also be used by the publisher to produce a keyword index.关键字：列出你论文中的关键词。
这些关键词将会被出版者用作制作一个关键词索引。
For the rest of the paper, please use Times Roman (Times New Roman) 12论文的其他部分请用Times Roman (Times New Roman) 12号字Abstract. This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.Please make the page settings of your word processor to A4 format (21 x 29,7 cm or 8 x 11 inches); with the margins: bottom 1.5 cm (0.59 in) and top 2.5 cm (0.98 in), right/left margins must be 2 cm (0.78 in).摘要：这个模板解释和示范供稿技术刊物有限公司时，如何准备你的供相机使用文件。
【VIP专享】2010 -2014MCM Problems建模竞赛美赛题目中英文双语翻译版
2010 MCM ProblemsPROBLEM A: The Sweet SpotExplain the “sweet spot” on a baseball bat.Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power is transferred to the ball when hit. Why isn’t this spot at the end of the bat? A simple explanation based on torque might seem to identify the end of the bat as the sweet spot, but this is known to be empirically incorrect. Develop a model that helps explain this empirical finding.Some players believe that “corking” a bat (hollowing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhances the “sweet spot” effect. Augment your model to confirm or deny this effect. Does this explain why Major League Baseball prohibits “corking”?Does the material out of which the bat is constructed matter? That is, does this model predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major League Baseball prohibits metal bats?MCM 2010 A题：解释棒球棒上的“最佳击球点”每一个棒球手都知道在棒球棒比较粗的部分有一个击球点，这里可以把打击球的力量最大程度地转移到球上。
2014美赛题目翻译
问题A：保持向右行驶除非要超车的交通规则在一些国家，汽车行驶在右边是规则，比如，美国，中国和其他大多数国家，除了英国，澳大利亚和一些前英国殖民地。
多车道高速公路经常使用一个规则，就是要求司机在最右边的车道驾驶，除非它们要超车。
超车就是他们开到左边的一个车道，超越，并恢复到原来的行驶车道。
（1）建立和分析一个数学模型来分析这一规则在车流量少和车流量大的不同时刻的表现。
不妨检查权衡交通流量和其安全性。
这些保持原车道或者被超车的速度限制（即限制最大速度和最小速度），或者其他的因素，可以不用考虑到问题中。
（2）这个规则，能有效地促进了更多的车流量吗？如果不能，提出并分析备选方案（之中最好不要用到题目中这类规则），能够促进更多的交通流量，安全性，或者你认为重要的其他因素。
（3）在一些国家，汽车行驶在左边是常态，讨论你的解决方案是否能够转用，仅仅是要一个简单的方向改变，或者需要额外的要求。
（4）最后，如上所述的规则依赖于人的判断为标准。
如果运输车辆在相同的道路上完全被处于一个智能系统（无论是部分路网或是嵌入设计到所有车辆里）的控制下，在何种程度上这会改变你刚才分析的结果？问题B：大学传奇教练《体育画报》，一个给运动爱好者的杂志，正在寻找上个世纪（以前世纪）男女教练中“一直表现最佳的大学教练”。
（1）建立一个数学模型，选择最佳的大学教练（一个或多个，过去的或者现在的）。
根据男性或女性教练在高校曲棍球或曲棍球，足球，棒球或垒球，篮球，足等体育项目中的表现。
（2）清楚地说明你进行评估的指标。
讨论你在分析中使用的时间轴，是否对结果有所影响，也就是说，教练的执教能力在1913年是否不同于在2013年？（3）讨论你的模型是如何能在不同性别和所有可能的运动领域中普遍应用。
运用你的模型分别从3个不同的运动领域上展示你的前5名教练。
（4）除了MCM的格式和要求，为体育画报准备一份1-2页文章，解释你的结果，并包括你的数学模型的非技术性解释，以便体育迷们能够理解。
2014美赛ICM赛题翻译
2014 ICM Problem使用网络来测量的影响和冲击Using Networks to Measure Influence and Impact确定学术研究的影响力的一种方法是构建和测量引文或合著者网络的属性.共同创作的文章通常意味着研究者之间的影响力有了重要的连接。
其中最有名的学术合著者是20世纪的数学家保罗·埃尔德什（Paul Erdös）他拥有超过500共同作者，并发表了超过1400的技术研究论文。
说埃尔德什（Erdös）是具有学科交叉特点的网络科学（science of networks）这一新兴研究的奠基人之一或许具有讽刺意味，或者也不。
特别是1959年，他和阿尔弗雷德的共同撰写的论文“关于随机图”（“On Random Graphs”）的发表，使得埃尔德什的作为合作者的角色在数学领域变得十分重要以至于数学家们经常会通过分析埃尔德什数量惊人的合作者来衡量自己与埃尔德什联系的紧密程度（their closeness to Erdös）。
(see the website http://www.oakla /enp/ )保罗.埃尔德什作为一个天才的数学家，天才的问题解决者，和著名合作者的不寻常和令人着迷的故事公布也在了许多书籍和在线网站上。
(例如,/Biographies/Erdos.html ).也许，他的生活方式就是经常和他的合作者待在一起或者住在一起。
或者把钱给他的学生作为解决问题的奖励，从而使他的合作蓬勃发展，并帮助他在数学的几个领域里建立了具有惊人影响力的网络。
为了衡量诸如埃尔德什等人产生的影响力，已经有了一些基于网络评价的工具（network-based evaluation tools）。
即是利用共同作者和引文数据来确定学者，出版物和学术期刊的影响因子，比如：科学文献索引（Science Citation Index，SCI的），H- factor（一种评价学术成就的新方法）Impact factor （期刊影响因子，SCI），Eigenfactor等等。
2014年数学建模美赛题目原文及翻译
2014年数学建模美赛题目原文及翻译作者：Ternence Zhang转载注明出处：MCM原题PDF：PROBLEM A: The Keep-Right-Except-To-Pass RuleIn 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 ruleeffective 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?问题A：车辆右行在一些规定汽车靠右行驶的国家（即美国，中国和其他大多数国家，除了英国，澳大利亚和一些前英国殖民地），多车道的高速公路经常使用这样一条规则：要求司机开车时在最右侧车道行驶，除了在超车的情况下，他们应移动到左侧相邻的车道，超车，然后恢复到原来的行驶车道（即最右车道）。
美赛历年赛题及其翻译-推荐下载
2015年：A题一个国际性组织声称他们研发出了一种能够阻止埃博拉，并治愈隐性病毒携带者的新药。
建立一个实际、敏捷、有效的模型，不仅考虑到疾病的传播、药物的需求量、可能的给药措施、给药地点、疫苗或药物的生产速度，而且考虑你们队伍认为重要的、作为模型一部分的其他因素，用于优化埃博拉的根除，或至少缓解目前（治疗）的紧张压力。
除了竞赛需要的建模方案以外，为世界医学协会撰写一封1-2页的非技术性的发言稿，以便其公告使用。
B题回顾马航MH370失事事件。
建立一个通用的数学模型，用以帮助失联飞机的搜救者们规划一个有效的搜索方案。
失联飞机从A地飞往B地，可能坠毁在了大片水域（如大西洋、太平洋、印度洋、南印度洋、北冰洋）中。
假设被淹没的飞机无法发出信号。
你们的模型需要考虑到，有很多种不同型号的可选的飞机，并且有很多种搜救飞机，这些搜救飞机通常使用不同的电子设备和传感器。
此外，为航空公司撰写一份1-2页的文件，以便在其公布未来搜救进展的新闻发布会上发表。
2014美赛A题翻译问题一:通勤列车的负载问题在中央车站,经常有许多的联系从大城市到郊区的通勤列车“通勤”线到达。
大多数火车很长(也许10个或更多的汽车长)。
乘客走到出口的距离也很长，有整个火车区域。
每个火车车厢只有两个出口,一个靠近终端, 因此可以携带尽可能多的人。
每个火车车厢有一个中心过道和过道两边的座椅，一边每排有两个座椅，另一边每排有三个座椅。
走出这样一个典型车站,乘客必须先出火车车厢,然后走入楼梯再到下一个级别的出站口。
通常情况下这些列车都非常拥挤,有大量的火车上的乘客试图挤向楼梯，而楼梯可以容纳两列人退出。
大多数通勤列车站台有两个相邻的轨道平台。
在最坏的情况下,如果两个满载的列车同时到达,所有的乘客可能需要很长时间才能到达主站台。
建立一个数学模型来估计旅客退出这种复杂的状况到达出站口路上的时间。
假设一列火车有n个汽车那么长,每个汽车的长度为d。
站台的长度是p,每个楼梯间的楼梯数量是q。
2014数模美赛A
Solutions for Homework for Traffic Flow Analysis1. On a specific westbound section of highway, studies show that the speed-density relationship is: ])(1[5.3jf k k u u -=. The highway’s capacity is 3800 vehicles/hour and the jam density is 140 vehicles/km. What is the space mean speed of the traffic at capacity and what is the free flow speed.Solution: as we know q = ku, thus, we can write the following: q = ku = k*])(1[5.3jf k k u -. When traffic flow is at the maximum, dq/dk = 0. Thus, we can write the following: 0]15.41[5.35.3=⨯-=k k u dk dq jf . As the free-flow speed u f can not be equal to zero, thus, we can write: 0]15.41[5.35.3=⨯-k k j . Therefore, k m = 91.1 vehicles/km.Since we know q m = 3800 vehicles/hour. And again, q m = k m u m , then we can calculate u m= 41.7 km/hour. Then, we can calculate u f from the given equation: ])(1[5.3jf k k u u -=. In the end, we may obtain: u f = 53.5 km/hr.2. A section of highway has the following flow-density relationship: q = 80k – 0.4k 2. What is the capacity of the highway section, the speed at capacity, and the density when the highway is one-quarter of its capacity?Solution: since we know the q-k relationship, we apply the same logic: dq/dk = 0 in order to obtain k m . (dq/dk) = 80-0.8k = 0, thus, k m = 100 vehicles/km. We can also obtain q m = 4000 vehicles/hour. We also know that q = km. Then, u m = q m /k m = 40 km/hour. When the highway is one quarter of its capacity, it means that q = 0.25q m = 1000 vehicles/hour, we can use the given equation: q = 80k – 0.4k 2, to calculate the density when q = (1/4)q m . Thus, k = 186 km/hour or 13.8 km/hour.3. An observer has determined that the time headways between successive vehicles on a section of highway are exponentially distributed, and that 60% of the headways between vehicles are 13 seconds or greater. If the observer decides to count traffic in 30 second intervals, estimate the probability of the observer counting exactly four vehicles in an interval.Solution: let us denote h as the random variable, representing the time headways between successive vehicles. We know that Pr(h ≥ 13) = 0.6. In other words, if we set t = 13, we know that Pr(h ≥ 13) = e -λ*13, then we can calculate λ based on these two equations. λ = 0.039 vehicles/second. Now, let X be the random variable representing the number ofvehicle arrivals during time t, then X is poisson distributed. Pr(X=4) ==⨯=⨯--!4)30039.0(!)(30039.4e x e t t x λλ0.024.4. A vehicle pulls out onto a single-lane highway that has a flow rate of 280 vehicles/hour (poisson distributed). The driver of the vehicle does not look for oncoming traffic. Road conditions and vehicle speeds on the highway are such that it takes 1.5 seconds for an oncoming vehicle to stop once the brakes are applied. Assuming that a standard driver reaction time is 2.5 seconds, what is the probability that the vehicle pulling out will be in an accident with oncoming traffic?Solution: in this case, if the vehicle headways between successive vehicles are greater than 4 seconds, then the driver pulling out will not be in an accident. Or say, if the headways are less than 4 seconds, the driver pulling out will be in an accident.Since q = 280 vehicles/hour, then λ = 0.078 vehicles/second.Pr(h < 4) = 1-e -λt = 1-e -0.078*4 = 0.268.5. Reconsider the problem 4 above, how quick would the driver reaction times of oncoming vehicles have to be to have the probability of an accident equal to 0.15?Solution: let t denote the new driver reaction time. So,Pr[h < (1.5+t)] = 1 – e -0.078*(1.5+t) = 0.15, then, we can obtain t = 0.58.In other words, to reduce the probability of an accident to 0.15, the driver reaction must be less than 0.58 seconds.6. A toll booth on a turnpike is open from 8:00 am to 12 midnight. Vehicles start arriving at 7:45 am at a uniform deterministic rate of 6 per minute until 8:15 am and from then on at 2 per minute. If vehicles are processed at a uniform deterministic rate of 6 per minute, determine when the queue will dissipate, total delay, longest queue length (in vehicles), longest vehicle delay under first-in and first-out rule.Solutions: arrival rate λ1 = 6 vehicles/minute from 7:45 am to 8:15 am. λ2 = 2vehicles/minute from 8:15 am to the rest of the day. Departure rate μ = 2 vehicles/minute.Solution: the time when the queue will dissipate is then the arrival curve intersects with the departure curve. Q1 = 6t; Q2 = 120+2t; Q3 = -90 + 6t, where Q1 is the arrival curve between 7:45 am to 8 am and Q2 is the arrival curve starting from 8:15 am to the rest of the day and Q3 is the departure curve. By setting Q2 = Q3, we can obtain the value for t, the time when the queue dissipates, we obtain that t = 52.5 minutes. In other words, at 8:375 am, the queue completely dissipates.Because Q2 and Q3 are parallel to each other, the long delay happens anywhere on the Q1 curve and it is equal to 15 minutes. This means that every car arriving between 7:45 am to 8:15 am has to wait for 15 minutes in the queue. Also because Q2 and Q3 areparallel, the queue length is uniform between 7:45 am to 8:15 am too. The queue length is equal to 90 vehicles (Q1=6t = 6*15 = 90 vehicles).To calculate the total delay, we simply do the following:8 am 7:45 am 8:15 amTotal delay = ⎰+--⎰++⎰5.52155.5230300)690()2120(6dt t dt t tdt= 5.521525.523023002|)390(|)120(|3t t t t t +--++ = )155.52(*3)155.52(*90)305.52()305.52(*120)030(322222---+-+-+-= 2700 + 2700 + 1856.25 + 3375 – 7953.5 = 3037.5 vehicle-minutes.7. Vehicles begin to arrive at a toll booth at 8:50 am, with an arrival rate of λ(t) = 4.1 + 0.01t (with t in minutes and λ(t) in vehicles per minute). The toll booth opens at 9:00 am and process vehicles at a rate of 12 per minute throughout the day. Assume D/D/1 queuing, when will the queue dissipate and what will be the total vehicle delay? Solution: we follow the same procedure as applied in problem number 6. The arrival curve is equal to λt = 4.1t + 0.01t2 and departure curve is equal to –120 + 12t. Setting the departure curve to be equal to the arrival curve, we obtain that t = 15 minutes or 774 minutes. We take the first value, which is equal to 15 minutes.About the total delay, we integrate the arrival curve and the departure curve and substract the latter from the former, and we obtain:Total delay = 2.05t2|(0,15) + (1/300)t3 (0,15) + 120t|(10,15) – 6t2|(10,15)= 322.5 vehicle-m.。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
问题A：除非超车否则靠右行驶的交通规则在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。
建立数学模型来分析这条规则在低负荷和高负荷状态下的交通路况的表现。
你不妨考察一下流量和安全的权衡问题,车速过高过低的限制，或者这个问题陈述中可能出现的其他因素。
这条规则在提升车流量的方面是否有效？如果不是，提出能够提升车流量、安全系数或其他因素的替代品（包括完全没有这种规律）并加以分析。
在一些国家，汽车靠左形式是常态，探讨你的解决方案是否稍作修改即可适用，或者需要一些额外的需要。
最后，以上规则依赖于人的判断，如果相同规则的交通运输完全在智能系统的控制下，无论是部分网络还是嵌入使用的车辆的设计，在何种程度上会修改你前面的结果？问题B：大学传奇教练体育画报是一个为运动爱好者服务的杂志，正在寻找在整个上个世纪的“史上最好的大学教练”。
建立数学模型选择大学中在一下体育项目中最好的教练：曲棍球或场地曲棍球，足球，棒球或垒球，篮球，足球。
时间轴在你的分析中是否会有影响？比如1913年的教练和2013年的教练是否会有所不同？清晰的对你的指标进行评估，讨论一下你的模型应用在跨越性别和所有可能对的体育项目中的效果。
展示你的模型中的在三种不同体育项目中的前五名教练。
除了传统的MCM格式，准备一个1到2页的文章给体育画报，解释你的结果和包括一个体育迷都明白的数学模型的非技术性解释。
使用网络测量的影响和冲击学术研究的技术来确定影响之一是构建和引文或合著网络的度量属性。
与人合写一手稿通常意味着一个强大的影响力的研究人员之间的联系。
最著名的学术合作者是20世纪的数学家保罗鄂尔多斯曾超过500的合作者和超过1400个技术研究论文发表。
讽刺的是,或者不是,鄂尔多斯也是影响者在构建网络的新兴交叉学科的基础科学,尤其是，尽管他与Alfred Rényi的出版物“随即图标”在1959年。
鄂尔多斯作为合作者的角色非常重要领域的数学,数学家通常衡量他们亲近鄂尔多斯通过分析鄂尔多斯的令人惊讶的是大型和健壮的合著网络网站(见http:// /enp/)。
保罗的与众不同、引人入胜的故事鄂尔多斯作为一个天才的数学家,才华横溢的problemsolver,掌握合作者提供了许多书籍和在线网站(如。
,/Biographies/Erdos.html)。
也许他流动的生活方式,经常住在带着合作者或居住,并给他的钱来解决问题学生奖,使他co-authorships蓬勃发展并帮助构建了惊人的网络在几个数学领域的影响力。
为了衡量这种影响asErdos生产,有基于网络的评价工具,使用作者和引文数据来确定影响因素的研究,出版物和期刊。
一些科学引文索引,Hfactor、影响因素,特征因子等。
谷歌学术搜索也是一个好的数据工具用于网络数据收集和分析影响或影响。
ICM 2014你的团队的目标是分析研究网络和其他地区的影响力和影响社会。
你这样做的任务包括:1)构建networkof Erdos1作者合著者(你可以使用我们网站https://files.oak /users/grossman/enp/Erdos1.htmlor的文件包括Erdos1.htm)。
你应该建立一个合作者网络Erdos1大约有510名研究人员的文件,与鄂尔多斯的一篇论文的合著者,他但不包括鄂尔多斯。
这将需要一些技术数据提取和建模工作获得的节点correctset(鄂尔多斯合作者)和他们的链接(彼此连接ascoauthors)。
有超过18000行Erdos1的原始数据文件,但是很多人不会用因为它们链接Erdos 1网络之外的人。
如果有必要,你可以限制你的网络的规模分析,以校准你的影响力度量算法。
一旦建立,分析该网络的属性。
(不包括鄂尔多斯——他是最有影响力的,将连接到网络中的所有节点。
在这种情况下,它的co-authorship营造网络与他,但他不属于网络或分析。
)2)开发影响措施(s)决定谁在这个Erdos1网络在网络中有显著的影响。
考虑谁发表了重要的作品在Erdos1或连接重要人员。
同样,假设没有鄂尔多斯扮演这些角色。
3)另一种类型的影响测量)比较研究论文通过分析的意义重要的作品,从其出版。
选择一些新兴领域的基础性文件网络科学从附表(NetSciFoundation.pdf)或论文你发现。
使用这些文件来分析和开发一个模型来确定它们的相对影响力。
构建的影响(合著者或引用)网络和计算分析适当措施。
论文在你设定你认为是最具影响力的网络科学,为什么? 有类似的方式来确定个体的作用或影响测量网络研究员? 考虑如何测量作用、影响或影响特定大学的部门,或在网络科学杂志吗? 讨论开发这些措施和方法需要收集的数据。
4)一组完全不同的网络上实现算法影响的数据——例如,影响力的作曲家,音乐乐队,表演者,电影演员、导演、电影、电视节目、专栏作家、记者、报纸、杂志、小说,小说,博客,推特,或者任何你愿意分析的数据集。
您可能希望限制网络特定类型或地理位置或预定的大小。
5)最后,讨论科学、理解和建模的影响和影响在网络的效用。
可以个人、组织、国家和社会使用影响方法改善人际关系,做生意,和做出明智的决定吗? 例如,在个体层面,描述如何使用你的措施和算法选择谁试图与合著者为了尽快提高你的数学的影响。
或你如何使用你的模型和结果来帮助决定毕业学校或导师的选择为你的未来学术工作吗?6)写报告解释您的建模方法,基于网络的影响和影响的措施,和之前的五项任务的进程和结果。
报告不能exceed20页(不包括你的汇总表),应该提供确凿的网络数据的分析,优势,劣势,和灵敏度的方法,建模这些现象使用网络科学的力量。
你的提交应该由一个1页汇总表和您的解决方案不能超过20页最长21页。
这是一个可能的论文清单,可以包含在一组基本的有影响力的网络科学出版物。
网络科学是一个新的、新兴、多样化、跨学科领域所以没有大型、集中组易于使用找到的期刊网络报纸,尽管一些新的期刊最近网络科学的建立和新的学术项目正开始在世界各地被提供在大学。
您可以使用其中的一些文件或其他你的选择你的团队的设置来分析和比较影响或影响在网络科学任务# 3。
Erdös, P. and Rényi, A., On Random Graphs, Publicationes Mathematicae, 6: 290-297, 1959.Albert, R. and Barabási, A-L. Statistical mechanics of complex networks. Reviews of Modern Physics, 74:47-97, 2002.Bonacich, P.F., Power and Centrality: A family of measures, Am J. Sociology. 92: 1170-1182, 1987.Barabási, A-L, and Albert, R. Emergence of scaling in random networks. Science, 286:509-512, 1999.Borgatti, S. Identifying sets of key players in a network. Computationaland Mathematical Organization Theory, 12: 21-34, 2006.Borgatti, S. and Everett, M. Models of core/periphery structures. Social Networks, 21:375-395, October 2000Graham, R. On properties of a well-known graph, or, What is your Ramseynumber? Annals of the New York Academy of Sciences, 328:166-172, June 1979.Kleinberg, J. Navigation in a small world. Nature, 406: 845, 2000. Newman, M. Scientific collaboration networks: II. Shortest paths, weightednetworks, and centrality. Physical Review E, 64:016132, 2001. Newman, M. The structure of scientific collaboration networks. Proc. Natl.Acad. Sci. USA, 98: 404-409, January 2001.Newman, M. The structure and function of complex networks. SIAM Review,45:167-256, 2003.Watts, D. and Dodds, P. Networks, influence, and public opinion formation. Journal of Consumer Research, 34: 441-458, 2007.Watts, D., Dodds, P., and Newman, M. Identity and search in social networks. Science, 296:1302-1305, May 2002.Watts, D. and Strogatz, S. Collective dynamics of `small-world' networks. Nature, 393:440-442, 1998.Snijders, T. Statistical models for social networks. Annual Review of Sociology, 37:131–153, 2011.Valente, T. Social network thresholds in the diffusion of innovations, Social Networks, 18: 69-89, 1996.。