美国数学建模竞赛MCM简介

MCM全称：The Mathematical Contest in Modeling（数学建模竞赛，国内称为美国国际数模竞赛）

ICM全称：The Interdisciplinary Contest in Modeling（交叉学科建模竞赛，国内称为美国大学生数学建模与交叉学科竞赛）

MCM始于1985年，由美国自然基金协会和美国数学应用协会共同主办，美国运筹学学会、工业与应用数学学会、数学学会等多家机构协办。其宗旨是鼓励大学生对范围并不固定的各种实际问题予以阐明、分析并提出解法，每队在4天内对问题展开设计，要以清楚定义的格式写出解法论文。该项比赛吸引了中国（含香港）、美国、英国、加拿大、芬兰、爱尔兰、澳大利亚、南非、新加坡等多个国家的著名大学代表队参加。1999年COMAP推出了交叉学科建模竞赛。其特等奖论文将刊登于同年 UMAP杂志。

近年来，MCM/ICM比赛越来越具有影响力，也得到越来越多的学校和单位认可。其获奖学生在出国留学、保送研究生、找工作时，在激烈的竞争中胜出的机会要多很多。

MCM将题目公开在网络上这种开放式的竞赛方式，竞赛环境相对而言比较自由，然而参赛选手来世界各地，竞争之激烈可想而知。MCM/ICM其要求与国内竞赛大致相同，除了要求用英语阅读、写作水平外。这对于中国的学生来说是一个非常大的挑战，如果成功参赛，将极大程度上提高英语水平。

总而言之，在建模期间，知识将会进一步积累，知识面也会得到提高，而英语写作能力、资料的检索能力、创新能力等都将得到训练，这些能力综合起来其实就是科研能力，将为今后的科研打下坚实的基础。

首先进入中国数学建模网站，点击友情链接页面，找到美国大学生数学建模竞赛，点击即可直接进入网站。具体过程如下：

2011年美国大学生数学建模竞赛（MCM/ICM）竞赛于（美国东部时间）2011年2月10日晚8:01~14日晚8:00举行。

2011年参赛前必须在美国大学生数学建模竞赛网站上的注册系统上注册，注册截至时间为美国东部时间）：2011年2月10号（星期四）下午2：00, 注册费为100$每个队，通过银行卡网上支付。

具体见附件材料-2011年MCM国际数学建模赛参赛规则中英文对照说明

Address:	MCM Coordinator
	COMAP, Inc.
	175 Middlesex Turnpike, Suite 3B
	Bedford, MA 01730 USA
Email:	mcm@comap.com

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?

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。为什么这个点不在棒球棒的最末端？基于力矩的解释或许可以解释确定棒球棒的最末端就是最佳的击球点，但是实际当中并不是这样的。构建一个模型帮助解释实际当中的这个发现。

有一些棒球手相信在最佳击球点添充上软木塞可以提高打击效果（在球棒头部挖一个圆柱状槽，填充上软木塞或者橡皮）。进一步扩展模型确认或者否定该结论。这个解释是否可以解释为什么棒球联盟否定这种做法。

每个击球者都知道，在棒球棒的大头部分有一个点，当用这一点击球时转移的能量会达到最大。这一点为什么不在棒球棒的顶端呢？一个基于扭矩的简单解释似乎可以确定“最佳点”应该出现在球棒的顶端，但是这与实际的经验不符。建立一个模型，解释这一经验结论。

一些球员认为，给球棒“软木化”（在球棒头部掏出一个圆柱空腔，在里面塞入软木或橡胶，然后盖上木帽）能够增加“最佳点”的效果。补充你的模型，以证实或否认这种效果。这是否能解释为什么美国职棒大联盟禁止“软木化”？

球棒的构造问题是否会涉及材料的选择？也就是说，是否这个模型能预测木质（通常是岑木）或金属（通常是铝）球棒的不同特性？为什么美国职棒大联盟要禁止使用金属球棒？

In 1981 Peter Sutcliffe was convicted of thirteen murders and subjecting a number of other people to vicious attacks. One of the methods used to narrow the search for Mr. Sutcliffe was to find a “center of mass” of the locations of the attacks. In the end, the suspect happened to live in the same town predicted by this technique. Since that time, a number of more sophisticated techniques have been developed to determine the “geographical profile” of a suspected serial criminal based on the locations of the crimes.

Your team has been asked by a local police agency to develop a method to aid in their investigations of serial criminals. The approach that you develop should make use of at least two different schemes to generate a geographical profile. You should develop a technique to combine the results of the different schemes and generate a useful prediction for law enforcement officers. The prediction should provide some kind of estimate or guidance about possible locations of the next crime based on the time and locations of the past crime scenes. If you make use of any other evidence in your estimate, you must provide specific details about how you incorporate the extra information. Your method should also provide some kind of estimate about how reliable the estimate will be in a given situation, including appropriate warnings.

In addition to the required one-page summary, your report should include an additional two-page executive summary. The executive summary should provide a broad overview of the potential issues. It should provide an overview of your approach and describe situations when it is an appropriate tool and situations in which it is not an appropriate tool. The executive summary will be read by a chief of police and should include technical details appropriate to the intended audience.

　　在1981年，彼得萨克利夫被判犯有十三起谋杀罪和一系列的恶意伤害罪。在该案中，一种用来缩小搜索萨克利夫先生所在范围的方法是找到这些犯罪地点发生的“重心”。最后, 这个嫌疑犯恰好生活在用这种技术所预测的那个城镇里。从那时起,许多更复杂的技术被发展起来，用来确定系列犯罪的嫌疑人位置的“地理轮廓”。
　　一个当地的**机构要求你的团队开发一种方法来帮助他们调查连环犯罪。你开发的这种方法, 应至少使用两种不同的方案来产生一个地理轮廓。你需要发展一种技术，能综合不同方案的结果为执法人员产生一种有用的预测。这种预测应基于过去的系列犯罪现场的时间和地点，提供下次犯罪发生的可能位置。如果在你们的模型中，使用了除时间和地点之外的证据,你必须提供具体的细节,说明你是如何纳入额外信息的。你的方法还应提供，在某一特定情况下方法可靠度的某种形式的估计,包括适当的警告。
　除了要求的一页摘要以外，你的报告应该包括一个额外的2页纸的实施概要。这个概要应该对潜在问题进行综述。它要概述你的方法,描述你的方法适合以及不适合的情况。概要将会被呈给**局长阅读，所以概要中应包括适当的技术细节以适合其读者。

在1981年，彼得萨克利夫被判犯有十三起谋杀罪和一系列的恶意伤害罪。在该案中，一种用来缩小搜索萨克利夫先生所在范围的方法是找到这些犯罪地点发生的“重心”。最后,这个嫌疑犯恰好生活在用这种技术所预测的那个城镇里。从那时起,许多更复杂的技术被发展起来，用来确定系列犯罪的嫌疑人位置的“地理轮廓”。

一个当地的**机构要求你的团队开发一种方法来帮助他们调查连环犯罪。你开发的这种方法,应至少使用两种不同的方案来产生一个地理轮廓。你需要发展一种技术，能综合不同方案的结果为执法人员产生一种有用的预测。这种预测应基于过去的系列犯罪现场的时间和地点，提供下次犯罪发生的可能位置。如果在你们的模型中，使用了除时间和地点之外的证据,你必须提供具体的细节,说明你是如何纳入额外信息的。你的方法还应提供，在某一特定情况下方法可靠度的某种形式的估计,包括适当的警告。

除了要求的一页摘要以外，你的报告应该包括一个额外的2页纸的实施概要。这个概要应该对潜在问题进行综述。它要概述你的方法,描述你的方法适合以及不适合的情况。概要将会被呈给**局长阅读，所以概要中应包括适当的技术细节以适合其读者。

Recently, there has been considerable news coverage of the “Great Pacific Ocean Garbage Patch.”

Based on recent scientific expeditions into the Pacific Ocean Gyre (a convergence zone where debris is accumulating), a wide variety of technical and scientific problems associated with this debris mass are coming to light. While dumping waste into the ocean is not a new activity, the scientific community’s realization that much of the debris (plastics, in particular) are accumulating in high densities over a large area of the Pacific Ocean is new. The scientific community also is learning that this debris creates many potential threats to marine ecology, and, therefore, to human well-being. Those who study this accumulation often describe it as plastic soup or confetti.

See: http://news.nationalgeographic.com/news/2009/09/photogalleries/pacific-garbage-patch-pictures/

This year’s ICM problem uses interdisciplinary modeling to addresses the complex issues stemming from the presence and accumulation of ocean debris, in order to help researchers and ultimately government policy makers to understand the severity, range, and potential global impact of the situation.

As modeling advisors to the expedition, your job is to focus on one element of this debris problem, model and analyze its behavior, and determine its potential effect on marine ecology and the government policies and practices that should be implemented to ameliorate its negative effects. Be sure to consider needs for future scientific research and the economic aspects of the problem, and then write a report to your expedition leader summarizing your findings and proposals for solutions and needed policies and practices. Some of the possible issues/questions you could investigate with your model include:

1. What are the potential short- and long-term effects of the plastic on the ocean environment? What

kind of monitoring is required to track the impact on the marine ecosystem? Be sure to account for temporal and spatial variability. What are the associated resourcing requirements?

2. How can the extent, density and distribution of the plastic in the gyre be best understood and described? What kind of monitoring plan is required to track the growth/decay/movement of the plastics, and what kind of resourcing is required to implement that plan?

3. What is the nature or mechanism of the photodegradation of the plastic and its composition as it

enters the ocean and accumulates in the gyre? (For example, we are amazed to find that the particles of degraded plastic tend to reach a similar size.)

4. Where does the plastic come from and what steps can be taken to control or reduce the risks associated with this situation? What are the economic costs and the economic benefits of controlling or ending the situation, and how do they compare? How much plastic is manufactured, discarded, and recycled? How much of that is likely to go into the ocean? How much of that is likely to float? 5. Could similar situations develop in other places in the oceans? What should we monitor and how?

What is happening in the North Atlantic Gyre and the Alaskan Gyre? Use your model to estimate the plastic density in the future in the southern gyres (South Atlantic, South Pacific)?

6. What is the immediate impact of banning polystyrene takeout containers? (See:

7. Any other scientific/technological issue associated with this situation is also acceptable, as long as modeling is an important component of your investigation and analysis.

To clarify your task, focus on one critical aspect of this problem and model the behavior of the important matters or phenomena. Specify the quantities that are of greatest present or future interest to the one aspect you choose to model and analyze. Your ICM report should be in the form of a ten-page team report to an expedition leader who has asked you to help her identify the relevant behaviors of the matters and phenomena under consideration, provide the analysis for impact of the behavior of those matters or phenomena, and advise her on the government’s potential to act on the problem to improve this situation before it worsens.

Here are some suggested papers you can use to inform your model formulation and obtain more data:

Note: As a reminder, it is best to stick to the scientific literature, not the media coverage, for your facts.

The mainstream media coverage of this issue has been misleading in many cases. For further explanation, see: http://seaplexscience.com/2009/11/13/millions-billions-trillions-of-scientific-errors-in-the-nyt/

Committee on the Effectiveness of International and National Measures to Prevent and Reduce Marine Debris and Its Impacts (National Research Council). (2009). Tackling Marine Debris in the 21st Century, National Academies Press, Washington D.C.

Dameron, O.J., Parke, M., Albins M.A., and Brainard R. (2007). Marine debris accumulation in the Northwestern Hawaiian Islands: An examination of rates and processes. Marine Pollution Bulletin, 54:423–433.

Derraik, J.G.B. (2002). The pollution of the marine environment by plastic debris: a review. Marine

Matsumura, S., and Nasu, K. (1997). Distribution of floating debris in the north Pacific Ocean: sighting

surveys 1986–1991. In: Coe, J. and Rogers, D. (eds.). Marine Debris: Sources, Impacts and Solutions. Springer, New York, pp. 15–24.

Moore, C.J., Moore, S.L., Leecaster, M.K., and Weisberg, S.B. (2001). A comparison of plastic and plankton in the North Pacific central gyre. Marine Pollution Bulletin, 42:1297–1300.

Pichel, W.G., Churnside, J.H., Veenstra, T.S., Foley, D.G., Friedman, K.S., Brainard, R.E., Nicoll, J.B., Zheng, Q., and Clemente-Colon, P. (2007). Marine debris collects within the North Pacific Subtropical Convergence Zone. Marine Pollution Bulletin, 54:1207–1211.

Robards, M.D., Gould, P., Platt, J. (1997). The highest global concentrations and increased abundance of oceanic plastic debris in the North Pacific: evidence from seabirds. In: Coe J. and Rogers, D. (eds.) Marine Debris: Sources, Impact and Solutions. Springer, New York, pp. 15–24.

Venrick, E.L., Backman, T.W., Bartram, W.C., Platt, C.J., Thornhill, M.S., and Yates, R.E. (1973). Man-made objects on the surface of the central north pacific ocean. Nature, 241:271–271.

Yamashita, R., Tanimura, A. (2007). Floating plastic in the Kuroshio Current area, western North Pacific Ocean. Marine Pollution Bulletin, 54:485–488.

最近的一项深入太平洋涡旋（垃圾碎片不断累积的汇流地带）进行的科学探险，揭露出大量与处理这些垃圾碎片相关的科技问题。倾倒废弃物流入海洋不是新鲜事，但是科学界却首次发现这些垃圾碎片（尤其是塑料制品）在太平洋**领域中密集出现。科学界同时也发现这些垃圾碎片对海洋生态，对人类的福祉都带来了许多潜在威胁。研究者把这些塑料垃圾描述成塑料汤或是塑料彩屑。
http://news.nationalgeographic.com/news/2009/09/photogalleries/pacific-garbage-patch-pictures/

今年ICM的问题是利用跨学科建模，来解决由于海洋中垃圾存在与累积所带来的各种复杂问题，借此帮助研究者，最终帮助政府政策制定者来了解该问题的程度、范围和对全球潜在的影响。

作为科学探险的建模顾问，你的任务是要关注垃圾问题中的某一个因素，建立模型并分析它的性质，确定其对影响海洋生态、政府政策的潜在影响，以及改善它的负面影响的具体措施。一定要考虑未来科研的需求和这一问题的经济因素，然后给科学探险的领队写一份报告，总结你的研究发现，提出解决建议、需要制定的政策和采取的措施。以下是你可以建模研究的一些问题：

1. 海洋中的塑料垃圾有哪些潜在的短期或长期影响？需要何种监测来追踪它对海洋生态系统的影响？务必要说明时空变异性。有哪些相关的资源需求？

2. 如何才能让涡旋中塑料垃圾的广度、密度、分布情况得到最佳理解和描述？需要何种监测计划来追踪塑料垃圾的增加减/运动，要实施该监测计划需要哪些资源？

3. 当这些塑料垃圾进入海洋并在涡旋中累积之后，它组成成分的的光降解机理是什么？（比如说我们惊讶地发现了降解塑料的粒子最终会达到相似的大小。）

4. 这些塑料从何处来？可以采取什么步骤来控制或减少与这一情况相关的各种风险？经济成本如何？控制或结束这种状态会带来什么经济效益？如何比较成本与效益？有多少塑料被生产，丢弃与回收？有多少有可能被排入海洋？进入海洋的又有多少可能会到处漂浮？

5. 同样的情况会在海洋的其他地方发生吗？我们应当监控那些因素，应该如何监控？北大西洋洋流和阿拉斯加洋流目前的情况如何？使用你的模型来预测一下南部洋流（南大西洋，南太平洋）未来的塑料垃圾密度。

6. 禁用聚丙烯外卖食品包装的即时效果如何？参考 http://bit.ly/5koJHB。十到五十年后的远期效果又如何？

7. 只要你主要依靠建模的方式来进行分析，也可以探讨其他一些同该情况相关的科学和技术问题。

为了明确你的任务，重点应该集中在问题的某个重要方面，对重要的问题和现象的表现进行建模分析，对你选择进行建模和分析的那个方面当中对当前和未来影响最显著的因素进行定量分析。你的ICM 报告应以如下形式提交：它将是篇幅为10页的小组报告，提交给一位调查负责人，目的在于帮助她找出所探讨问题或现象的相关表现，主要分析这些问题或者现象的后果，并针对在问题进一步恶化之前政府能够采取哪些措施来遏制该问题向她提出可行性建议。

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