什么是数学建模?MCM/ICM竞赛题目有哪些?考试内容是什么?

MCM/ICM(Mathematical Contest in Modeling / Interdisciplinary Contest in Modeling)是全球范围内最具影响力的数学建模竞赛之一,由美国数学及其应用联合会(COMAP)主办,每年举办一次。该竞赛旨在通过解决实际问题,培养学生的创新能力、数学建模能力、团队合作能力和交流能力。参赛者需要在规定时间内完成一个开放性问题的建模、分析与报告撰写。

一、什么是数学建模?

数学建模是将实际问题转化为数学语言和数学形式的过程。通过数学建模,复杂的现实问题可以被抽象成数学模型,从而利用数学方法进行分析、求解和优化。数学建模的核心过程包括以下几个组成部分:

决策变量(Decision Variables)

表示决策者可以控制的因素,即模型中需要确定的未知变量。通过建模和求解过程,这些变量的具体取值被优化以实现问题目标。

环境变量(Environmental Variables)

表示不可控的外部因素。它们在建模过程中作为已知常量使用,通常通过数据收集阶段确定其数值。

目标函数(Objective Function)

描述问题目标的数学表达式。目标函数可以是最大化某个量(如收益或效率)或最小化某个量(如成本或风险)。

约束条件(Constraints)

描述问题中的限制因素。这些条件通过数学表达式(等式或不等式)限制决策变量的取值范围或满足特定要求。

完成数学建模后,通过优化算法、数值计算等求解方法可以得出最优解,从而为实际问题提供科学的决策依据。

二、MCM/ICM竞赛题目

MCM/ICM竞赛题目分为6个类别,涵盖不同领域,学生需从中选择一个进行建模与解决:

MCM 问题 A(连续模型)

涉及连续变量的数学建模问题,通常需要微分方程或优化方法。

MCM 问题 B(离散模型)

主要涉及离散变量的模型,重点考察离散数学、图论等知识。

MCM 问题 C(数据洞察)

需要通过数据分析和可视化技术,从大规模数据中提取信息并建模。

ICM 问题 D(运筹学/网络科学)

涉及网络优化、路径规划等运筹学领域的问题。

ICM 问题 E(可持续性)

关注环境和可持续发展领域的问题,如能源管理、资源分配等。

ICM 问题 F(政策建模)

涉及社会科学和政策研究,要求学生从数据和模型中提出政策建议。

三、MCM/ICM考试内容

MCM/ICM竞赛跨越多个学科领域,主要考察以下知识点:

数学

微积分、线性代数、离散数学、概率与统计等。

常微分方程、优化理论、图论等高级数学知识。

计算机科学

算法设计与分析、编程能力(如Python、MATLAB、R等)。

数据处理与可视化工具的应用。

英语

阅读、写作和表达能力是竞赛报告撰写的重要部分。

报告需结构清晰、语言流畅且逻辑严谨。

跨学科知识

根据具体问题,可能涉及自然科学、工程学、经济学、社会科学等领域的知识。

四、MCM/ICM参赛步骤

注册顾问账号

顾问是指导团队的重要角色,需提前在COMAP官网注册账号。

注册团队

每个团队最多由三名学生组成,所有成员需为本科或以下学历,并来自同一学校。

支付注册费

每个团队需支付100美元的注册费用。

五、MCM/ICM竞赛规则与流程

团队合作

每个团队最多由三名学生组成,团队成员需分工明确,密切合作。

解决问题

团队需在竞赛开放期间从6个题目中选择一个进行建模和分析。

报告撰写

解决方案需以数学建模报告的形式提交,报告内容包括:

摘要

模型构建与分析

数据处理与结果

结论与建议

参考文献

提交报告

报告总页数不得超过25页,包括摘要、正文、附录、代码、图表等内容。

六、MCM/ICM奖项设置

MCM/ICM竞赛设有多种奖项,以表彰表现优异的团队:

MCM奖项(问题A、B、C)

Ben Fusaro奖:颁发给具有创意的论文。

弗兰克·R·佐丹奴奖:表彰杰出建模过程的实施。

ICM奖项(问题D、E、F)

莱昂哈德·欧拉奖:授予ICM问题D的最佳团队。

雷切尔·卡森奖:表彰在政策建模问题(ICM问题F)中表现杰出的团队。

ICM帕累托奖:针对ICM问题F的优秀团队。

国际拨款与证书

获奖团队将获得COMAP的国际拨款、奖金和荣誉证书。

七、MCM/ICM的教育价值

培养综合能力

竞赛通过实际问题的解决,帮助学生培养数学建模能力、创新思维和团队合作精神。

提升国际竞争力

MCM/ICM以其国际化视野和高含金量的证书,广受全球顶尖大学和研究机构的认可。

跨学科应用

竞赛题目来源于现实问题,涵盖多个学科,促进学生将数学知识与其他领域结合。

职业发展助力

竞赛经验和获奖证书在申请研究生项目、国际交流和职业发展中具有重要价值。

MCM/ICM竞赛是一个集挑战性与实践性于一体的国际平台,为学生提供了展示数学能力和创新思维的机会。通过参与MCM/ICM,学生不仅可以提升学术水平,还能培养团队协作和解决实际问题的能力。对于希望在数学建模和跨学科领域深入发展的学生,MCM/ICM是一个不可多得的学习与成长机会。希望所有参赛者都能在竞赛中取得优异成绩,展现自己的才华!


备赛的同学可扫码免费下载

【MCM/ICM 2006-2024特等奖论文集+2006-2024中英真题集】⇓

美国数学建模MCM/ICM常考题型有哪些?题目难度如何?

COMAP的数学建模竞赛(Mathematical Contest in Modeling,简称MCM®)和跨学科建模竞赛(Interdisciplinary Contest in Modeling,简称ICM®)是国际性竞赛,旨在为大学生提供团队合作、建模、问题解决和写作技能的实践机会。参赛者需要运用数学知识和技巧,通过建模、开发和交流讨论,共同解决现实世界中的复杂问题。

一、MCM/ICM常考题型

在竞赛周末期间,每个团队由三名学生组成,需从以下六个问题中选择一个进行解决:

MCM问题A:连续性问题

MCM问题B:离散性问题

MCM问题C:数据洞察问题

ICM问题D:运筹学/网络科学问题

ICM问题E:可持续性问题

ICM问题F:政策问题

这些问题涵盖广泛的学科领域,从数学建模到跨学科问题,要求参赛者具备深厚的知识储备和灵活的思维能力。

二、MCM/ICM题目难度

MCM/ICM竞赛的难度极高,对参赛者的知识广度和深度提出了极高要求。具体难度体现在以下几个方面:

复杂的问题背景:参赛者需要快速理解问题,并掌握相关的领域知识。这些问题通常涉及多个学科的交叉内容,如数学、计算机、环境科学、工程与政策等。

时间紧迫:参赛者需要在短短4天内完成问题的建模、求解、仿真、编程以及论文撰写。

团队协作:独立思考与团队合作并重,参赛者需要分工明确,并高效协作完成任务。

综合能力要求:竞赛不仅考察数学能力,还需要参赛者具备编程、论文写作和英语表达能力。

三、MCM/ICM备考方法

1. 团队配合与分工

在参赛过程中,团队合作至关重要。团队通常由以下三种角色组成:

建模手

熟悉各类模型(如回归模型、优化模型、微分方程模型等)的用法、优缺点。

负责提出问题的建模方法,并进行模型的实现与调优。

定期学习新的建模方法和技术,保持对模型的扩展和更新。

编程手

掌握至少一种编程语言(如Python、MATLAB、R等),并熟练使用建模和数据处理工具。

负责将建模手提出的问题转化为计算机模型,进行仿真与优化。

善于利用高效的算法和技术,最大程度提高时间利用效率。

论文手

具备良好的英文阅读和写作能力,能够清晰准确地表达论文的逻辑和意义。

学会使用绘图工具(如MATLAB、Tableau、Origin等),制作简洁直观的图表。

关注比赛要求,特别是摘要部分,确保逻辑清晰且吸引评委注意。

2. 赛前准备策略

熟悉规则与题目要求:仔细阅读比赛官网提供的注意事项,了解题目类型及选题范围。

模拟训练:通过往年题目进行模拟练习,找准团队的优势领域,并确定最适合团队解决的问题类型。

知识储备:系统学习数学建模的常用方法(如线性规划、动态规划、随机过程、微分方程等)以及相关领域的基础知识。

工具熟练度:掌握常用建模和数据处理工具(如MATLAB、Python、Excel等),熟悉论文排版工具(如LaTeX)。

时间规划:制定合理的时间分配方案,确保充足时间完成建模、编程、论文撰写及模型验证。

3. 比赛过程中注意事项

选题策略:根据团队的优势领域选择最适合的问题,避免选择团队知识储备薄弱的领域。

时间管理:合理分配时间,确保建模、编程与论文写作同步进行。建议在竞赛最后一天留出足够时间进行模型仿真和论文修改。

摘要优化:摘要是论文的核心部分,需确保逻辑清晰、语言简洁且吸引评委注意。

图表质量:尽量使用高质量的图表展示结果,避免冗长的文字描述,使图表具有直观性和吸引力。

4. 提高团队协作效率

定期沟通:团队需保持高效沟通,及时反馈进展情况。

文件管理:使用统一的命名规则和版本控制工具(如Git)管理文件,确保团队协作顺畅。

分工明确:明确团队成员的职责分工,避免重复工作或遗漏关键环节。

MCM/ICM竞赛通过其高难度的题目和严谨的规则,为大学生提供了一个展示数学建模能力的国际平台。通过参与竞赛,学生不仅能够提升数学建模、编程和论文写作能力,还能培养团队协作、时间管理和创新思维等综合素质。成功完成MCM/ICM竞赛需要团队的高效协作、扎实的知识储备以及灵活的应变能力。参赛者通过充分的赛前准备和比赛中的高效执行,能够在竞赛中取得优异成绩,为未来的学术和职业发展奠定坚实基础。


备赛的同学可扫码免费下载

【2015-2024美赛历年真题集+MCM/ICM获奖论文集】⇓

【真题在线看】2018 ICM问题F:隐私成本

 问题标题:隐私成本
   
年份:2018  
学生等级:本科生  
来源:ICM

问题  
 
电子通信和社交媒体的普及和依赖已经变得非常普遍。结果之一是,有些人似乎愿意分享有关他们个人互动、关系、购买、信仰、健康和行动的私人信息 (PI),而另一些人则认为这些方面的隐私非常重要和有价值。不同领域的隐私选择也存在显著差异。例如,有些人为了快速降价而迅速放弃对其购买信息的保护,但同时不太可能分享有关其疾病状况或健康风险的信息。同样,如果某些人群或亚群认为某些类型的个人信息对个人或社区构成风险,他们可能不太愿意放弃这些信息。这种风险可能涉及安全、金钱、贵重物品、知识产权 (IP) 或个人电子身份的损失。其他风险包括职业尴尬、失去职位或工作、社会损失(友谊)、社会耻辱或边缘化。虽然对政府发表政治异议的政府雇员可能愿意付费保护其社交媒体数据,但年轻的大学生可能没有压力限制他们发布政治观点或社交信息。看来,个人在个人隐私保护以及网络空间的互联网和系统安全方面的选择可能会在自由、隐私、便利、社会地位、经济利益和医疗等方面带来风险和回报。

私人信息 (PI) 是否类似于私人财产 (PP) 和知识产权 (IP)?合法获取的 PI 是否可以出售或赠予拥有该信息权利或所有权的其他人?随着人类活动的详细信息和元数据对社会越来越有价值,特别是在医学研究、疾病传播、灾难救助、商业(如营销、保险和收入)、个人行为记录、信仰陈述和身体活动等领域,这些数据和详细信息可能成为有价值且可量化的商品。交易自己的私人数据会带来一系列风险和好处,这些风险和好处可能因信息领域(如购买、社交媒体、医疗)和子群体(如公民身份、专业资料、年龄)而异。

我们能否量化全社会电子通信和交易的隐私成本?也就是说,保护个人信息的货币价值是多少,或者其他人拥有或使用个人信息的成本是多少?政府是否应该监管这些信息,还是最好留给隐私行业或个人?这些信息和隐私问题是否仅仅是个人决定,个人必须评估以做出自己的选择并提供自己的保护?

在评估隐私成本时,需要考虑几个问题。首先,数据共享是否属于公共利益?例如,疾病控制中心可能会使用数据来追踪疾病的传播,以防止进一步爆发。其他例子包括管理高风险人群,如 16 岁以下儿童、有自杀风险的人和老年人。此外,考虑那些试图隐藏其活动的极端分子团体。出于国家安全考虑,政府是否应该追踪他们的数据?考虑一个人的浏览器、电话系统和互联网信息流及其个性化广告;这种定制价值多少?

总体而言,在评估隐私成本时,我们需要考虑所有这些权衡。保持数据私密性的潜在收益是什么,而这样做又会失去什么?

作为国家决策者的政策分析团队,您的团队的任务是:

任务 1:制定一个价格点,用于在各种应用中保护个人隐私和 PI。为了评估这一点,您可能需要将个人分类为具有相当相似风险水平的子组或数据的相关域。为了准确地模拟风险,需要考虑哪些参数和度量集,以同时考虑 1) 个人的特征和 2) 特定信息域的特征?

任务 2:给定任务 1中的一组参数和度量,至少在三个领域(社交媒体、金融交易和健康/医疗记录)建立隐私成本模型。在您的基础模型中,考虑保护数据的权衡和风险如何影响您的模型。您可以考虑给予某些权衡和风险比其他权衡和风险更高的权重,以及按子组或类别分层权重。考虑数据的不同基本元素(例如姓名、出生日期、性别、社会保障或公民号码)对您的模型的贡献。这些元素中是否有一些比其他元素更有价值?例如,与附有此人照片的姓名价值相比,姓名本身的价值是多少?您的模型应该为 PI 设计一个定价结构。

任务 3:不久前,人们不知道哪些机构购买了他们的 PI,他们的 PI 值多少钱,或者 PI 是如何使用的。新的提案正在提出,将 PI 变成一种商品。利用您在任务 2中生成的定价结构,为个人、团体和整个国家建立定价系统。随着数据成为受市场波动影响的商品,考虑 PI 的供需力量是否合适?假设人们有权出售自己的数据,这会如何改变模型?

任务 4:您的模型的假设和约束是什么?假设和约束应解决诸如政府法规(例如价格法规、特定数据保护,例如某些可能不受经济体系约束的记录)以及文化和政治问题等问题。根据您的模型以及政治和文化问题,考虑在考虑政策建议时是否应将信息隐私作为一项基本人权。考虑在您的模型中引入动态元素,通过引入人类决策随时间的变化,考虑到个人对自己数据(例如姓名、地址、图片等个人数据)、交易数据(例如在线购买、搜索历史)和社交媒体数据(例如帖子、图片)的价值的信念不断变化。

任务 5:不同代人对 PI 和数据隐私的风险收益比的看法是否存在差异?随着年龄的增长,这会如何改变模型?PI 与 PP 和 IP 有何不同或相似之处?

任务 6:如何解释人类数据高度关联且每个人的行为通常与他人高度相关的事实?一个人的数据可以提供有关其在社交、职业、经济或人口统计学上与其有联系的其他人的信息。因此,个人分享自己数据的决定会影响无数其他人。有没有好的方法来捕捉数据共享的网络效应?这会影响个人、子群体以及整个社区和国家的价格体系吗?如果社区有共同的隐私风险,那么保护公民的 PI 是社区的责任吗?

任务 7:考虑大规模数据泄露的影响,数百万人的个人信息被盗并在暗网上出售、作为身份盗窃团伙的一部分出售或用作赎金。这样的个人信息丢失或连锁事件会如何影响您的模型?现在您有一个可以量化每个人或每种丢失类型的数据价值的定价系统,那么对数据泄露负责的机构是否有责任直接向个人支付滥用或个人信息丢失的费用?

任务 8:根据您对这个问题的政策建模,向决策者写一份两页的政策备忘录,说明效用、结果和建议。请务必指定您的建议中包含哪些类型的 PI。

您的提交内容应包括:
    ● 一页摘要表,
    ● 两页备忘录,
    ● 您的解决方案不超过 20 页,最多 23 页,包括您的摘要和备忘录。
    ●注意:参考列表和任何附录不计入 23 页的限制,应出现在您完成的解决方案之后。

题目内容过长,可到文末下载完整版中英文真题


以下是英文版真题

Problem
Pervasiveness of, and reliance on, electronic communication and social media have become widespread. One result is that some people seem willing to share private information (PI) about their personal interactions, relationships, purchases, beliefs, health, and movements, while others hold their privacy in these areas as very important and valuable. There are also significant differences in privacy choices across various domains. For example, some people are quick to give away the protection of their purchasing information for a quick price reduction, but at the same time are unlikely to share information about their disease conditions or health risks. Similarly, some populations or subgroups may be less willing to give up particular types of personal information if they perceive it posing a personal or community risk. The risk may involve loss of safety, money, valuable items, intellectual property (IP), or the person's electronic identity. Other risks include professional embarrassment, loss of a position or job, social loss (friendships), social stigmatization, or marginalization. While a government employee who has voiced political dissent against the government might be willing to pay to keep their social media data private, a young college student may feel no pressure to restrict their posting of political opinion or social information. It seems that individual choices on PI protection and internet and system security in cyber space can create risks and rewards in elements of freedom, privacy, convenience, social standing, financial benefits, and medical treatment.

Is private information (PI) similar to private personal property (PP) and intellectual property (IP)? Once lawfully obtained, can PI be sold or given to others who then have the right or ownership of the information? As detailed information and meta-data of human activity becomes more and more valuable to society, specifically in the areas of medical research, disease spread, disaster relief, businesses (e.g. marketing, insurance, and income), records of personal behaviors, statements of beliefs, and physical movement, these data and detailed information may become a valuable and quantifiable commodity. Trading in one's own private data comes with a set of risks and benefits that may differ by the domain of information (e.g. purchasing, social media, medical) and by subgroup (e.g. citizenship, professional profile, age).

Can we quantify the cost of privacy of electronic communications and transactions across society? That is, what is the monetary value of keeping PI protected, or how much would it cost for others to have or use PI? Should the government regulate this information or is it better left to privacy industry or the individual? Are these information and privacy issues merely personal decisions that individuals must evaluate to make their own choices and provide their own protection?

There are several things to consider when evaluating the cost of privacy. First, is data sharing a public good? For example, Center for Disease Control may use the data to trace the spread of disease in order to prevent further outbreak. Other examples include managing at risk populations, such as children under 16, people at risk of suicide, and the elderly. Moreover, consider groups of extremists who seek to hide their activities. Should their data be trackable by the government for national security concerns? Consider a person's browser, phone system, and internet feed with their personalized advertisements; how much is this customization worth?

Overall, when evaluating cost of privacy we need to consider all of these tradeoffs. What is the potential gain from keeping data private and what is lost by doing so?

As a policy analysis team for a national decision maker, your team's tasks are:

Task 1: Develop a price point for protecting one's privacy and PI in various applications. To evaluate this, you may want to categorize individuals into subgroups with reasonably similar levels of risk or into related domains of the data. What are the set of parameters and measures that would need to be considered to accurately model risk to account for both 1) characteristics of the individuals, and 2) characteristics of the specific domain of information?

Task 2: Given the set of parameters and measures from Task 1, model for cost of privacy across at least three domains (social media, financial transactions, and health/medical records). In your base model consider how the tradeoffs and risks of keeping data protected affect your model. You may consider giving some of the tradeoffs and risks more weight than others as well as stratifying weights by subgroup or category. Consider how different basic elements of the data (e.g. name, date of birth, gender, social security or citizenship number) contribute to your model. Are some of these elements worth more than others? For example, what is the value of a name alone compared with value of a name with the person's picture attached? Your model should design a pricing structure for PI.

Task 3: Not long ago, people had no knowledge about which agencies had purchased their PI, how much their PI was worth, or how PI was being used. New proposals are being put forth which would turn PI into a commodity. With the pricing structure you generated in Task 2, establish a pricing system for individuals, groups, and entire nations. With data becoming a commodity subject to market fluctuations, is it appropriate to consider forces of supply and demand for PI? Assuming people have control to sell to their own data, how does this change the model?

Task 4: What are the assumptions and constraints of your model? Assumptions and constraints should address issues such as government regulations (e.g. price regulations, specific data protections such as certain records that may not be subject to the economic system) and cultural and political issues. Based on your model and the political and cultural issues, consider if information privacy should be made a basic human right when thinking about policy recommendations. Consider introducing a dynamic element to your model by introducing the variations over time in human decision-making given changing personal beliefs about the worth of their own data (e.g. personal data such as name, address, picture), transaction data (e.g. on-line purchases, search history), and social media data (e.g. posts, pictures).

Task 5: Are there generational differences in perceptions of the risk-to-benefit ratio of PI and data privacy? As generations age, how does this change the model? How is PI different or similar to PP and IP?

Task 6: What are the ways to account for the fact that human data is highly linked and often each individual's behaviors are highly correlated with others? Data on one person can provide information about others whom they are socially, professionally, economically, or demographically connected. Therefore, personal decisions to share one's own data can affect countless others. Are there good ways to capture the network effects of data sharing? Does that effect the price system for individuals, subgroups, and entire communities and nations? If communities have shared privacy risks, is it the responsibility of the communities to protect citizens' PI?

Task 7: Consider the effects of a massive data breach where millions of people's PI are stolen and sold on the dark web, sold as part of an identity theft ring, or used as ransom. How does such a PI loss or cascade event impact your model? Now that you have a pricing system that quantifies the value of data per individual or loss type, are agencies that are to blame for the data breach responsible to pay individuals directly for misuse or loss of PI?

Task 8: Write a two-page policy memo to the decision maker on the utility, results, and recommendations based your policy modeling on this issue. Be sure to specify what types of PI are included in your recommendations.

Your submission should consist of:
    ● One-page Summary Sheet,
    ● Two-page memo,
    ● Your solution of no more than 20 pages, for a maximum of 23 pages with your summary and memo.
    ● Note: Reference list and any appendices do not count toward the 23-page limit and should appear after your completed solution.

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【真题在线看】2018 ICM问题E:气候变化如何影响区域不稳定?

问题标题:气候变化如何影响区域不稳定?

年份:2018
学生等级:本科生
来源:ICM

问题

气候变化的影响已经显现,包括干旱增加、冰川缩小、动物和植物分布范围改变以及海平面上升,这些影响因地区而异。政府间气候变化专门委员会表示,气候变化的净损失成本可能非常巨大。其中许多影响将改变人类的生活方式,并可能导致社会和政府结构的弱化和崩溃。因此,不稳定的政府可能导致国家脆弱。

脆弱国家是指政府无法或选择不向其人民提供基本必需品的国家。就本问题而言,“国家”是指主权国家或国家。脆弱国家会增加一个国家的人口对自然灾害、可耕地减少、天气变化无常和气温升高等气候冲击的影响的脆弱性。发展中国家普遍存在的不可持续的环境实践、移民和资源短缺问题,可能会进一步加剧治理薄弱的国家(Schwartz 和 Randall,2003 年;Theisen、Gleditsch 和 Buhaug,2013 年)。可以说,叙利亚和也门的干旱进一步加剧了本已脆弱的国家。环境压力本身并不一定引发暴力冲突,但有证据表明,当环境压力与治理薄弱和社会分裂相结合时,就会引发暴力冲突。这种融合可能会加剧暴力的恶性循环,通常是沿着潜在的种族和政治分歧(Krakowka、Heimel 和 Galgano,2012 年)。

您的任务如下:

任务 1:开发一个模型来确定一个国家的脆弱性,同时衡量气候变化的影响。你的模型应该确定一个国家是脆弱的、易受影响的还是稳定的。它还应该确定气候变化如何通过直接方式或间接方式增加脆弱性,因为它会影响其他因素和指标。

任务 2:根据脆弱国家指数 ( http://fundforpeace.org/fsi/data/ )确定的十大最脆弱国家之一,并确定气候变化如何增加该国的脆弱性。使用您的模型来说明在没有这些影响的情况下,该国在哪些方面可能不那么脆弱。

任务 3:使用你的模型对另一个不在前 10 名之列的国家进行测量,以了解其脆弱性,并了解气候变化可能以何种方式以及何时使其变得更加脆弱。确定任何明确的指标。你如何定义临界点并预测一个国家何时会达到这个临界点?

任务 4:使用您的模型来展示哪些国家主导的干预措施可以减轻气候变化的风险并防止一个国家​​成为脆弱国家。解释人类干预的效果并预测该国干预的总成本。

任务 5:你的模型适用于较小的“州”(例如城市)还是较大的“州”(例如大陆)?如果不适用,你会如何修改你的模型?

您的提交内容应包括:

● 一页摘要表,
● 您的解决方案不超过 20 页,最多 21 页(含摘要)。
●注意:参考列表和任何附录不计入 21 页限制,应出现在您完成的解决方案之后。

题目内容过长,可到文末下载完整版中英文真题


以下是英文版真题

Problem
The effects of Climate Change, to include increased droughts, shrinking glaciers, changing animal and plant ranges, and sea level rise, are already being realized and vary from region to region. The Intergovernmental Panel on Climate Change suggests that the net damage costs of climate change are likely to be significant. Many of these effects will alter the way humans live, and may have the potential to cause the weakening and breakdown of social and governmental structures. Consequently, destabilized governments could result in fragile states.

A fragile state is one where the state government is not able to, or chooses not to, provide the basic essentials to its people. For the purpose of this problem  refers to a sovereign state or country. Being a fragile state increases the vulnerability of a country's population to the impact of such climate shocks as natural disasters, decreasing arable land, unpredictable weather, and increasing temperatures. Non-sustainable environmental practices, migration, and resource shortages, which are common in developing states, may further aggravate states with weak governance (Schwartz and Randall, 2003; Theisen, Gleditsch, and Buhaug, 2013). Arguably, drought in both Syria and Yemen further exacerbated already fragile states. Environmental stress alone does not necessarily trigger violent conflict, but evidence suggests that it enables violent conflict when it combines with weak governance and social fragmentation. This confluence can enhance a spiral of violence, typically along latent ethnic and political divisions (Krakowka, Heimel, and Galgano 2012).

Your tasks are the following:

Task 1: Develop a model that determines a country's fragility and simultaneously measures the impact of climate change. Your model should identify when a state is fragile, vulnerable, or stable. It should also identify how climate change increases fragility through direct means or indirectly as it influences other factors and indicators.

Task 2: Select one of the top 10 most fragile states as determined by the Fragile State Index (http://fundforpeace.org/fsi/data/) and determine how climate change may have increased fragility of that country. Use your model to show in what way(s) the state may be less fragile without these effects.

Task 3: Use your model on another state not in the top 10 list to measure its fragility, and see in what way and when climate change may push it to become more fragile. Identify any definitive indicators. How do you define a tipping point and predict when a country may reach it?

Task 4: Use your model to show which state driven interventions could mitigate the risk of climate change and prevent a country from becoming a fragile state. Explain the effect of human intervention and predict the total cost of intervention for this country.

Task 5: Will your model work on smaller "states" (such as cities) or larger "states" (such as continents)? If not, how would you modify your model?

Your submission should consist of:
    ● One-page Summary Sheet,
    ● Your solution of no more than 20 pages, for a maximum of 21 pages with your summary.
    ● Note: Reference list and any appendices do not count toward the 21-page limit and should appear after your completed solution.

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【真题在线看】2018 ICM问题D:没油了,仍按 E 行驶(电动,不是空的)

 问题标题:没油了,仍按 E 行驶(电动,不是空的)
   
  年份:2018  
  学生等级:本科生  
  来源:ICM

问题
出于环境和经济原因,全球都希望减少化石燃料的使用,包括汽车汽油。无论是出于环保还是经济原因,消费者都开始转向电动汽车。一些国家已经看到了电动汽车普及率快速增长的早期迹象。在美国和其他国家,更实惠的全电动特斯拉 Model 3 的发布带来了创纪录的预订数量和漫长的等待名单 ( https://www.wired.com/story/tesla-model-3-delivery-timeline/)。为了进一步加速向电动汽车的转变,包括中国在内的一些国家已宣布将在未来几年禁止汽油和柴油汽车 ( http://money.cnn.com/2017/09/11/news/china-gas-electric-car-ban/index.html )。

最终,禁令生效后,需要在适当的地点设立足够数量的汽车充电站,以便人们可以使用汽车进行日常工作,以及偶尔进行长途旅行。然而,从汽油和柴油汽车向电动汽车的转变并不简单,不可能一蹴而就。在幻想世界中,我们有一天醒来时会发现每辆汽油车都被电动汽车取代,每个加油站都被充电站取代。在现实中,资源有限,消费者需要时间才能完成转换。事实上,充电站的位置和便利性至关重要,因为早期采用者和最终的主流消费者都会自愿转换(http://www.govtech.com/fs/Building-Out-Electric-Vehicle-Infrastructure-Where-Are-the-Best-Locations-for-Charging-Stations.html)。

当各国规划这一转型时,他们需要考虑最终的充电站网络(充电站数量、充电站位置、充电站充电器数量以及农村、郊区和城市地区需求的差异),以及充电站网络随时间的增长和演变。例如,当电动汽车占所有汽车的 10%、30%、50% 和 90% 时,充电站网络应该是什么样子?

当各国寻求制定促进电动汽车转型的政策时,他们需要设计一个最适合各自国家的计划。在开始之前,他们希望您的团队能够帮助他们确定充电网络的最终架构,以支持全电动汽车的全面采用。此外,他们希望您能确定在他们规划最终禁止或大幅减少汽油和柴油汽车的时间表时至关重要的关键因素。

为了帮助您的团队管理此问题的范围,我们要求您仅关注个人乘用车(即用于乘客的汽车、货车和轻型卡车)。在报告的最后,您可以简要评论您的发现和结论与商用车(包括重型卡车和公共汽车)的相关性。

您的任务如下:

任务 1:探索美国当前和不断增长的特斯拉充电站网络。特斯拉目前提供两种类型的充电站:(1) 目的地充电站,设计用于一次充电数小时甚至整夜充电(https://www.tesla.com/destination-charging);(2 ) 超级充电站,设计用于长途公路旅行,只需 30 分钟的充电即可提供长达 170 英里的续航里程 ( https://www.tesla.com/supercharger )。这些充电站是许多拥有私人车库或带电车道的特斯拉车主使用的家用充电站的补充。特斯拉是否有望让美国完全转向全电动汽车?如果美国每个人都改用全电动个人乘用车,将需要多少个充电站,以及它们应该如何在城市、郊区和农村地区分布?

任务 2:选择以下国家之一(韩国、爱尔兰或乌拉圭)。

2a.如果您的国家可以立即将所有个人乘用车升级为全电动汽车(无需过渡时间),请确定充电站的最佳数量、位置和分布。影响您计划发展的关键因素是什么?

2b.虽然这些国家已经开始安装充电器,但您可以从头开始。提出一项提案,将您所选国家的充电网络从零充电器发展为完整的电动汽车系统。您建议该国如何投资充电器?该国应该先建造所有城市的充电器,还是所有农村的充电器,还是两者兼而有之?您会先建造充电器并希望人们购买汽车,还是会根据汽车购买情况建造充电器?影响您提议的充电站计划的关键因素是什么?

2c.根据您的发展计划,您建议贵国全面发展电动汽车的时间表是什么?首先,您可能希望考虑一下,在您选择的国家/地区的道路上,电动汽车占比需要多长时间才能达到 10%、30%、50% 或 100%。影响您提出的增长计划时间表的关键因素是什么?

任务 3:现在考虑地理、人口密度分布和财富分布差异很大的国家,例如澳大利亚、中国、印度尼西亚、沙特阿拉伯和新加坡。您提出的发展和改进充电器网络的计划是否仍然适用于这些国家?哪些关键因素促使选择不同的网络发展方法?讨论创建分类系统的可行性,该系统将帮助一个国家确定他们应该遵循的一般增长模式,以便他们成功地从汽油和柴油汽车转向全电动汽车。

任务 4:技术世界不断变化,并影响着交通选择,例如汽车共享和拼车服务、自动驾驶汽车、电动汽车快速电池更换站,甚至飞行汽车和超级高铁。评论这些技术如何影响您对电动汽车使用日益增加的分析。

任务 5:准备一份一页的讲义,供参加国际能源峰会的各国领导人参考。讲义应确定领导人回国时应考虑的关键因素,以制定国家计划,将个人交通工具转向全电动汽车,并设定禁止使用燃气汽车的日期。

您的提交内容应包括:
    ● 一页摘要表,
    ● 一页讲义,
    ● 您的解决方案不超过 20 页,最多 22 页(包括摘要和讲义)。
    ●注意:参考列表和任何附录不计入 22 页的限制,应出现在您完成的解决方案之后。

题目内容过长,可到文末下载完整版中英文真题


以下是英文版真题

Problem
For both environmental and economic reasons, there is global interest in reducing the use of fossil fuels, including gasoline for cars. Whether motivated by the environment or by the economics, consumers are starting to migrate to electric vehicles. Several countries are seeing early signs of the potential for rapid growth in the adoption of electric vehicles. In the US and other countries, the release of the more affordable all-electric Tesla Model 3 has resulted in record numbers of pre-orders and long wait lists (https://www.wired.com/story/tesla-model-3-delivery-timeline/). To further accelerate the switch to electric vehicles, some countries, including China, have announced that they will ban gasoline and diesel cars in the coming years (http://money.cnn.com/2017/09/11/news/china-gas-electric-car-ban/index.html).

Eventually, when a ban goes into effect, there needs to be a sufficient number of vehicle charging stations in all the right places so that people can use their vehicles for their daily business, as well as make occasional long-distance trips. The migration from gasoline and diesel cars to electric vehicles, however, is not simple and can鈥檛 happen overnight. In a fantasy world, we would wake up one day with every gas vehicle replaced by an electric one, and every gas station replaced with a charging station. In reality, there are limited resources, and it will take time for consumers to make the switch. In fact, the location and convenience of charging stations is critical as early adopters and eventually mainstream consumers volunteer to switch (http://www.govtech.com/fs/Building-Out-Electric-Vehicle-Infrastructure-Where-Are-the-Best-Locations-for-Charging-Stations.html).

As nations plan this transition, they need to consider the final network of charging stations (the number of stations, where they will be located, the number of chargers at the stations, and the differences in the needs of rural areas, suburban areas, and urban areas), as well as the growth and evolution of the network of charging stations over time. For example, what should the network look like when electric vehicles represent 10% of all cars, 30% of all cars, 50% of all cars, and 90% of all cars?

As nations seek to develop policies that promote the migration towards electric vehicles, they will need to design a plan that works best for their individual country. Before they can begin, they would like your team鈥檚 help in determining the final architecture of the charging network to support the full adoption of all-electric vehicles. Additionally, they would like you to identify the key factors that will be important as they plan their timeline for an eventual ban or dramatic reduction of gasoline and diesel vehicles.

To help your team manage the scope of this problem, we ask that you focus only on personal passenger vehicles (i.e. cars, vans, and light trucks used for passengers). At the end of your report, you may briefly comment on the relevance of your findings and conclusions on commercial vehicles to include heavy trucks and busses.

Your tasks are the following:

Task 1: Explore the current and growing network of Tesla charging stations in the United States. Tesla currently offers two types of charging stations: (1) destination charging designed for charging for several hours at a time or even overnight (https://www.tesla.com/destination-charging); and (2) supercharging designed for longer road trips to provide up to 170 miles of range in as little as 30 minutes of charging (https://www.tesla.com/supercharger). These stations are in addition to at-home charging used by many Tesla owners who have a personal garage or a driveway with power. Is Tesla on track to allow a complete switch to all-electric in the US? If everyone switched to all-electric personal passenger vehicles in the US, how many charging stations would be needed, and how should they be distributed between urban, suburban, and rural areas?

Task 2: Select one of the following nations (South Korea, Ireland, or Uruguay).

2a. Determine the optimal number, placement, and distribution of charging stations if your country could migrate all their personal passenger vehicles to all-electric vehicles instantaneously (no transition time required). What are the key factors that shaped the development of your plan?

2b. While these countries have already started installing chargers, you get to start with a clean slate. Present a proposal for evolving the charging network of your chosen country from zero chargers to a full electric-vehicle system. How do you propose the country invest in chargers? Should the country build all city-based chargers first, or all rural chargers, or a mix of both? Will you build the chargers first and hope people buy the cars, or will you build chargers in response to car purchases? What are the key factors that shaped your proposed charging station plan?

2c. Based on your growth plan, what is the timeline you propose for the full evolution to electric vehicles in your country? To get started, you may wish to consider how long it will take for there to be 10% electric vehicles, 30% electric vehicles, 50% electric vehicles, or 100% electric vehicles on your selected country鈥檚 roads. What are the key factors that shaped your proposed growth plan timeline?

Task 3: Now consider countries with very different geographies, population density distributions, and wealth distributions, such as Australia, China, Indonesia, Saudi Arabia, and Singapore. Would your proposed plan for growing and evolving the network of chargers still apply to each of these countries? What are the key factors that trigger the selection of different approaches to growing the network? Discuss the feasibility of creating a classification system that would help a nation determine the general growth model they should follow in order for them to successfully migrate away from gasoline and diesel vehicles to all electric cars.

Task 4: The technological world continues to change and is impacting transportation options such as car-share and ride-share services, self-driving cars, rapid battery-swap stations for electric cars, and even flying cars and a Hyperloop. Comment on how these technologies might impact your analyses of the increasing use of electric vehicles.

Task 5: Prepare a one-page handout written for the leaders of a wide range of countries who are attending an international energy summit. The handout should identify the key factors the leaders should consider as they return to their home country to develop a national plan to migrate personal transportation towards all-electric cars and set a gas vehicle-ban date.

Your submission should consist of:
    ● One-page Summary Sheet,
    ● One-page handout,
    ● Your solution of no more than 20 pages, for a maximum of 22 pages with your summary and handout.
    ● Note: Reference list and any appendices do not count toward the 22-page limit and should appear after your completed solution.

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【真题在线看】2018 MCM问题C:能源生产

问题标题:能源生产

年份:2018
学生等级:本科生
来源:MCM

问题  
 
背景:能源生产和使用是任何经济体的重要组成部分。在美国,能源政策的许多方面都分散到州一级。此外,不同州的地理和行业差异也会影响能源的使用和生产。1970 年,美国 12 个西部州成立了西部州际能源协议 (WIEC),其使命是促进这些州在开发和管理核能技术方面的合作。州际协议是两个或多个州之间达成的合同安排,这些州就特定政策问题达成一致,并采用一套标准或就特定地区或国家事务相互合作。

问题:在美国与墨西哥的边境,有四个州——加利福尼亚州 (CA)、亚利桑那州 (AZ)、新墨西哥州 (NM) 和德克萨斯州 (TX) — — 这些州希望形成一个切实可行的新能源协议,重点是增加使用更清洁的可再生能源。这四个州的州长要求您的团队进行数据分析和建模,以指导他们制定州际能源协议的一系列目标。

附件数据文件“ ProblemCData.xlsx ”在第一个工作表(“seseds”)中提供了这四个州 50 年的 605 个变量数据,以及一些人口统计和经济信息。此数据集中使用的 605 个变量名称在第二个工作表(“msncodes”)中定义。

第一部分:

A.使用提供的数据,为四个州分别创建能源概况。

B.开发一个模型来描述四个州从 1960 年到 2009 年的能源概况变化情况。分析和解释模型结果,以州长容易理解的方式解决四个州对更清洁、可再生能源的使用问题,并帮助他们了解四个州之间的相似之处和差异。在讨论中包括可能影响相似之处和差异的因素(例如地理、行业、人口和气候)。

C.确定四个州中哪一个在 2009 年似乎拥有使用更清洁、可再生能源的“最佳”概况。解释您的标准和选择。

D.根据这些州能源使用的历史演变,以及您对所建立的州概况之间差异的理解,预测每个州在 2025 年和 2050 年的能源概况(如您所定义),前提是各州长办公室没有任何政策变化。

第二部分:

A.根据您对四个州的比较、您对“最佳”概况的标准以及您的预测,确定 2025 年和 2050 年的可再生能源使用目标,并将其作为新的四州能源协议的目标。

B.确定并讨论四个州为实现其能源紧凑目标可能采取的至少三项行动。

第三部分:

准备一份一页的备忘录给州长小组,总结截至 2009 年的各州概况、在没有政策变化的情况下对能源使用情况的预测,以及您建议的能源契约目标。

您的提交内容应包括:

    ● 一页摘要表,
    ● 一页备忘录,
    ● 您的解决方案不超过 20 页,最多 22 页(包括摘要和备忘录)。
    ●注意:参考列表和任何附录不计入 22 页限制,应出现在您完成的解决方案之后。

题目内容过长,可到文末下载完整版中英文真题


以下是英文版真题

Problem
Background: Energy production and usage are a major portion of any economy. In the United States, many aspects of energy policy are decentralized to the state level. Additionally, the varying geographies and industries of different states affect energy usage and production. In 1970, 12 western states in the U.S. formed the Western Interstate Energy Compact (WIEC), whose mission focused on fostering cooperation between these states for the development and management of nuclear energy technologies. An interstate compact is a contractual arrangement made between two or more states in which these states agree on a specific policy issue and either adopt a set of standards or cooperate with one another on a particular regional or national matter.

Problem: Along the U.S. border with Mexico, there are four states – California (CA), Arizona (AZ), New Mexico (NM), and Texas (TX) 鈥� that wish to form a realistic new energy compact focused on increased usage of cleaner, renewable energy sources. Your team has been asked by the four governors of these states to perform data analysis and modeling to inform their development of a set of goals for their interstate energy compact.
The attached data file "ProblemCData.xlsx" provides in the first worksheet ("seseds") 50 years of data in 605 variables on each of these four states' energy production and consumption, along with some demographic and economic information. The 605 variable names used in this dataset are defined in the second worksheet ("msncodes").

Part I:
A.
 Using the data provided, create an energy profile for each of the four states.

B. Develop a model to characterize how the energy profile of each of the four states has evolved from 1960 – 2009. Analyze and interpret the results of your model to address the four states鈥� usage of cleaner, renewable energy sources in a way that is easily understood by the governors and helps them to understand the similarities and difference between the four states. Include in your discussion possible influential factors of the similarities and differences (e.g. geography, industry, population, and climate).

C. Determine which of the four states appeared to have the "best" profile for use of cleaner, renewable energy in 2009. Explain your criteria and choice.

D. Based on the historical evolution of energy use in these states, and your understanding of the differences between the state profiles you established, predict the energy profile of each state, as you have defined it, for 2025 and 2050 in the absence of any policy changes by each governor's office.

Part II:
A. Based on your comparison between the four states, your criteria for "best" profile, and your predictions, determine renewable energy usage targets for 2025 and 2050 and state them as goals for this new four-state energy compact.

B. Identify and discuss at least three actions the four states might take to meet their energy compact goals.

Part III:
Prepare a one-page memo to the group of Governors summarizing the state profiles as of 2009, your predictions with regard to energy usage absent any policy changes, and your recommended goals for the energy compact to adopt.

Your submission should consist of:
    ● One-page Summary Sheet,
    ● One-page memo,
    ● Your solution of no more than 20 pages, for a maximum of 22 pages with your summary and memo.
    ● Note: Reference list and any appendices do not count toward the 22-page limit and should appear after your completed solution.

Attachments:
ProblemCData.xlsx Includes two worksheets seseds and msncodes.

References:
State Energy Data System (SEDS) Complete Dataset through 2009 (All 50 states) https://catalog.data.gov/dataset/state-energy-data-system-seds-complete-dataset-through-2009#sec-dates

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【真题在线看】2018 MCM问题B:有多少种语言?

 问题标题:有多少种语言?
   
  年份:2018  
  学生等级:本科生  
  来源:MCM

问题

背景:目前地球上大约有 6,900 种语言。大约一半的世界人口声称以下十种语言之一(按使用人数最多的顺序)是母语:普通话(包括标准中文)、西班牙语、英语、印地语、阿拉伯语、孟加拉语、葡萄牙语、俄语、旁遮普语和日语。但是,世界上大部分人口也讲第二语言。当考虑某种语言的使用者总数(母语使用者加上第二或第三语言使用者等)时,语言及其顺序与提供的母语列表不同。某种语言的使用者总数可能会随着时间的推移而增加或减少,因为各种影响包括但不限于一个国家政府使用和/或推广的语言、学校使用的语言、社会压力、文化群体的移民和同化以及与其他语言国家的移民和移居。此外,在我们全球化、相互联系的世界中,还有其他因素使地理上相距遥远的语言能够互动。这些因素包括国际商业关系、全球旅游业的增长、电子通信和社交媒体的使用、以及使用技术协助快速简便的语言翻译。

按使用者总数列出的语言列表。
检索自https://en.wikipedia.org/wiki/List_of_languages_by_total_number_of_speakers,2018年 1 月 17 日。

问题:一家大型跨国服务公司,在美国纽约市和中国上海设有办事处,正在继续扩张,成为真正的国际公司。该公司正在考虑开设更多的国际办事处,并希望每个办事处的员工都能说英语和一种或多种其他语言。该公司的首席运营官聘请了您的团队来调查全球语言趋势和新办事处的地点选择。

第一部分:

A.考虑上述背景段落中描述的影响和因素,以及您的小组可能确定的其他因素。根据预测的趋势以及这些影响和因素中的部分或全部,对各种语言使用者的分布进行建模。B

.使用您的模型预测未来 50 年母语使用者的数量和总语言使用者的数量将发生什么变化。您是否预测当前前十名列表中的任何一种语言(母语使用者或总使用者)将被另一种语言取代?解释一下。C

.鉴于未来 50 年预测的全球人口和人类迁徙模式,这些语言的地理分布是否会在同一时期发生变化?如果会,请描述这种变化。

第二部分:

A.根据第一部分中的模型,假设您的客户公司希望开设六个新的国际办事处,您会将这些办事处设在哪里以及这些办事处将使用哪些语言?您的建议在短期和长期内会有所不同吗?解释您的选择。

B.考虑到全球通信不断变化的性质,为了节省客户公司的资源,您是否会建议该公司开设少于六个国际办事处?请指出您需要哪些其他信息,并描述您将如何分析此选项以向您的客户提供建议。

第三部分:

向服务公司的首席运营官写一份 1-2 页的备忘录,总结您的结果和建议。
注意:在您的分析中,忽略不可预测或影响大、概率低的事件,例如小行星碰撞,这些事件会导致进化趋势随着时间的推移发生灾难性的跳跃,并可能导致所有语言灭绝。

您的提交内容应包括:
● 一页摘要表,
● 两页备忘录,
● 您的解决方案不超过 20 页,最多 23 页(包括摘要和备忘录)。
●注意:参考列表和任何附录不计入 23 页的限制,应出现在您完成的解决方案之后。

题目内容过长,可到文末下载完整版中英文真题


以下是英文版真题

Problem
Background: There are currently about 6,900 languages spoken on Earth. About half the world鈥檚 population claim one of the following ten languages (in order of most speakers) as a native language: Mandarin (incl. Standard Chinese), Spanish, English, Hindi, Arabic, Bengali, Portuguese, Russian, Punjabi, and Japanese. However, much of the world鈥檚 population also speaks a second language. When considering total numbers of speakers of a particular language (native speakers plus second or third, etc. language speakers), the languages and their order change from the native language list provided. The total number of speakers of a language may increase or decrease over time because of a variety of influences to include, but not limited to, the language(s) used and/or promoted by the government in a country, the language(s) used in schools, social pressures, migration and assimilation of cultural groups, and immigration and emigration with countries that speak other languages. Moreover, in our globalized, interconnected world there are additional factors that allow languages that are geographically distant to interact. These factors include international business relations, increased global tourism, the use of electronic communication and social media, and the use of technology to assist in quick and easy language translation.

List of Languages by Total Numbers of Speakers.
Retrieved from https://en.wikipedia.org/wiki/List_of_languages_by_total_number_of_speakers on January 17, 2018.

Problem: A large multinational service company, with offices in New York City in the United States and Shanghai in China, is continuing to expand to become truly international. This company is investigating opening additional international offices and desires to have the employees of each office speak both in English and one or more additional languages. The Chief Operating Officer of the company has hired your team to investigate trends of global languages and location options for new offices.

Part I:

A. Consider the influences and factors described in the background paragraph above, as well as other factors your group may identify. Based on projected trends, and some or all of these influences and factors, model the distribution of various language speakers over time.

B. Use your model to predict what will happen to the numbers of native speakers and total language speakers in the next 50 years. Do you predict that any of the languages in the current top-ten lists (either native speakers or total speakers) will be replaced by another language? Explain.

C. Given the global population and human migration patterns predicted for the next 50 years, do the geographic distributions of these languages change over this same period of time? If so, describe the change.

Part II:

A. Based on your modeling from Part I, and assuming your client company wants to open six new international offices, where might you locate these offices and what languages would be spoken in the offices? Would your recommendations be different in the short term versus the long term? Explain your choices.

B. Considering the changing nature of global communications, and in an effort to save your client company resources, might you suggest that the company open less than six international offices? Indicate what additional information you would need and describe how you would analyze this option in order to advise your client.

Part III:

Write a 1-2 page memo to the Chief Operating Officer of the service company summarizing your results and recommendations.
Note: In your analysis, ignore unpredictable or high-impact, low probability events such as asteroid collisions that would cause a catastrophic jump in evolutionary trends over time, and possibly render all languages extinct.

Your submission should consist of:
    ● One-page Summary Sheet,
    ● Two-page memo,
    ● Your solution of no more than 20 pages, for a maximum of 23 pages with your summary and memo.
    ● Note: Reference list and any appendices do not count toward the 23-page limit and should appearafter your completed solution.

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【真题在线看】2018 MCM问题A:多跳高频无线电传播

问题A标题:多跳高频无线电传播

年份:2018
学生等级:本科生
来源:MCM

问题  
 
背景:在高频(HF,定义为 3 - 30 MHz)下,无线电波可以通过电离层和地球的多次反射传播很长的距离(从地球表面的一个点到地球表面的另一个远点)。对于低于最大可用频率(MUF) 的频率,来自地面源的 HF 无线电波会从电离层反射回地球,然后它们可能会再次反射回电离层,然后它们可能会再次反射回地球,依此类推,每次连续跳跃都会传播得更远。除其他因素外,反射面的特性决定了反射波的强度以及信号在保持有用信号完整性的情况下最终传播的距离。此外,MUF 会随季节、一天中的时间和太阳条件而变化。高于 MUF 的频率不会被反射/折射,而是穿过电离层进入太空。在这个问题中,重点特别放在海洋表面的反射上。经验表明,湍流海洋的反射比平静海洋的反射衰减更大。海洋湍流会影响海水的电磁梯度,改变海洋的局部介电常数和磁导率,并改变反射面的高度和角度。湍流海洋中的波高、形状和频率变化迅速,波的传播方向也可能发生变化。

第一部分:为这种海洋信号反射建立一个数学模型。对于陆地点源 MUF 下方的 100 瓦 HF 恒载波信号,确定湍流海洋第一次反射的强度,并将其与平静海洋第一次反射的强度进行比较。 (请注意,这意味着该信号在电离层发生了一次反射。)如果在平静的海面上发生额外的反射(2 到 n),那么在信号强度降至可用信噪比 (SNR) 阈值 10 dB 以下之前,信号可以进行的最大跳跃次数是多少?

第二部分:您从第一部分得出的结论与山区或崎岖地形与平坦地形的 HF 反射相比如何?

第三部分:穿越海洋的船只将使用 HF 进行通信以及接收天气和交通报告。您的模型如何变化以适应在湍急海洋上移动的船上接收器?使用相同的多跳路径,船只可以保持通信多长时间?

第四部分:准备一份简短(1 到 2 页)的结果摘要,适合作为短文发表在IEEE 通信杂志上。

您的提交应包括:

     ● 一页摘要表,
     ● 两页概要,
     ● 您的解决方案不超过 20 页,最多 23 页,包括摘要和概要。
     ●注意:参考列表和任何附录不计入 23 页的限制,应出现在您完成的解决方案之后。

题目内容过长,可到文末下载完整版中英文真题


以下是英文版真题

Problem
Background: On high frequencies (HF, defined to be 3 - 30 MHz), radio waves can travel long distances (from one point on the earth鈥檚 surface to another distant point on the earth's surface) by multiple reflections off the ionosphere and off the earth. For frequencies below the maximum usable frequency (MUF), HF radio waves from a ground source reflect off the ionosphere back to the earth, where they may reflect again back to the ionosphere, where they may reflect again back to the earth, and so on, travelling further with each successive hop. Among other factors, the characteristics of the reflecting surface determine the strength of the reflected wave and how far the signal will ultimately travel while maintaining useful signal integrity. Also, the MUF varies with the season, time of day, and solar conditions. Frequencies above the MUF are not reflected/refracted, but pass through the ionosphere into space. In this problem, the focus is particularly on reflections off the ocean surface. It has been found empirically that reflections off a turbulent ocean are attenuated more than reflections off a calm ocean. Ocean turbulence will affect the electromagnetic gradient of seawater, altering the local permittivity and permeability of the ocean, and changing the height and angle of the reflection surface. A turbulent ocean is one in which wave heights, shapes, and frequencies change rapidly, and the direction of wave travel may also change.

Problem:

Part I: Develop a mathematical model for this signal reflection off the ocean. For a 100-watt HF constant-carrier signal, below the MUF, from a point source on land, determine the strength of the first reflection off a turbulent ocean and compare it with the strength of a first reflection off a calm ocean. (Note that this means that there has been one reflection of this signal off the ionosphere.) If additional reflections (2 through n) take place off calm oceans, what is the maximum number of hops the signal can take before its strength falls below a usable signal-to-noise ratio (SNR) threshold of 10 dB?

Part II: How do your findings from Part I compare with HF reflections off mountainous or rugged terrain versus smooth terrain?

Part III: A ship travelling across the ocean will use HF for communications and to receive weather and traffic reports. How does your model change to accommodate a shipboard receiver moving on a turbulent ocean? How long can the ship remain in communication using the same multi-hop path?

Part IV: Prepare a short (1 to 2 pages) synopsis of your results suitable for publication as a short note in IEEE Communications Magazine.

Your submission should consist of:
     ● One-page Summary Sheet,
     ● Two-page synopsis,
     ● Your solution of no more than 20 pages, for a maximum of 23 pages with your summaryand synopsis.
     ● Note: Reference list and any appendices do not count toward the 23-page limit andshould appear after your completed solution.

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【真题在线看】2019ICM问题F:通用、去中心化、数字货币—可能吗?

问题标题:通用、去中心化、数字货币—可能吗?

年份:2019
学生等级:本科生
来源:ICM

问题  
 
数字货币可以像传统货币一样用于买卖商品,只是它是数字化的,没有实物表现。数字货币使用户能够即时进行交易,而不受国界的限制。加密货币是数字货币的一个子集,具有隐私、去中心化、安全和加密等独特功能。加密货币在世界各地大受欢迎,从地下狂热爱好发展成为全球公认的现象。比特币和以太坊都是加密货币,其价值都在增长,而投资者预计其他加密货币(如狗狗币或瑞波币)也将快速增长。除了数字货币和加密货币外,还有新的数字金融交易方法,使用户能够仅凭电子邮件地址或指纹即时兑换货币。PayPal、Stripe、Venmo、Zelle、Apple Pay、Square Cash 和 Google Pay 等公司提供的点对点支付系统可在几秒钟内实现全球范围内的虚拟资金流动,而无需通过银行或货币兑换处验证交易。数字交易比现金和支票交易更快,因为它们不受银行政策、国界、公民身份、债务或其他社会经济因素的影响。这些新的货币体系分散了金融交易,让许多人开始思考传统银行业务可能被淘汰的世界。

对加密货币安全性的担忧让公民和经济分析师都感到担忧。这些担忧限制了加密货币在某些社区的发展。另一方面,加密货币之所以如此受欢迎,很大程度上是因为它脱离了传统的过于严格的安全和债务措施,这些措施依赖于大型银行和政府的监督。这些监督机构往往成本高昂、官僚主义严重,有时甚至腐败。一些专家认为,像区块链这样具有内部安全性的通用、分散的数字货币可以通过消除资金流动障碍来提高市场效率。这在大多数公民没有银行账户、无法投资区域或全球金融市场的国家尤为重要。然而,一些政府认为,这些货币缺乏监管和匿名性风险太大,因为它们很容易被用于非法交易,例如避税或购买非法商品。另一些人认为,安全的数字货币提供了一种更方便、更安全的金融交易形式。例如,一种普遍接受的货币将使真正的全球金融市场成为可能,并保护个人资产免受区域通胀波动和区域政府人为操纵货币的影响。如果替代数字系统变得更加成熟,那么关于数字货币将如何影响现有银行系统和国家货币的问题将会出现很多。

您的团队提交的作品应包括:

单页摘要表,
为国家领导人提供一页政策建议,
您的解决方案不超过 20 页,包括摘要和政策建议,最多 22 页。
评委希望获得完整的参考文献列表以及文内引用,但在评审过程中可能不会考虑附录。
注意:参考文献列表和任何附录均不计入 22 页的限制,并且应在完成的解决方案之后出现。

参考:

保罗·克鲁格曼,《哦,加拿大:一个被忽视的国家获得诺贝尔奖》。Slate ,1999 年 10 月 19 日。https : //slate.com/business/1999/10/o-canada.html

Stephanie Lo 和 J. Christina Wang,“比特币是货币吗?”当前的政策观点,

波士顿联邦储备银行,2014 年。https
://www.bostonfed.org/publications/current-policy-perspectives/2014/bitcoin-as-money.aspx或https://www.bostonfed.org/-/media/Documents/Workingpapers/PDF/cpp1404.pdf

词汇表:

匿名性 -未命名或未确定身份的状态;匿名的状态。

区块链——一种可以以可验证和永久的方式记录双方之间交易的记录保存技术;一个包含可在大型公开可访问的分散网络中共享和同时使用的信息的数字数据库。

加密货币——使用加密技术(通过使用代码保护信息)来保证安全的数字或虚拟货币。

数字货币 - [数字货币、电子货币、电子货币] 是一种以数字(电子)形式而非实物(硬币、纸币)形式存在的货币。

非法 –非法或不诚实。

波动 -变化或振荡;上升和下降。

货币——与货币或财务有关,或与货币在经济中供应和流通的机制有关。

国家货币 - [国家货币]由中央银行发行并在特定国家或国家集团内共同使用的货币体系;例如美元 (USD)、人民币 (RMB 或 CNY)、欧元 (EUR)、英镑 (GBP) 和日元 (JPY)。

地下邪教——隐藏或神秘的一群人,对特定的人、信仰或事物有着过度的虔诚。

题目内容过长,可到文末下载完整版中英文真题


以下是英文版真题

Problem
Digital currency can be used like traditional currencies to buy and sell goods, except that it is digital and has no physical representation. Digital currency enables its users to make transactions instantaneously and without any concern for national borders. Cryptocurrency is a subset of digital currency with unique features of privacy, decentralization, security and encryption. Cryptocurrencies have exploded in popularity in various parts of the world; moving from an underground cult interest to a globally accepted phenomenon. Bitcoin and Ethereum, both cryptocurrencies, have grown in value, while investors are projecting rapid growth for other cryptocurrencies such as Dogecoin or Ripple. In addition to digital and cryptocurrencies, there are also new digital methods for financial transactions that enable users to instantaneously exchange money with nothing more than an email address or a thumbprint. Peer-to-peer payment systems offered by companies like PayPal, Stripe, Venmo, Zelle, Apple Pay, Square Cash, and Google Pay offer virtual movement of money across the globe in seconds without ever having to verify the transaction through a bank or currency exchange. Digital transactions outpace cash and check transactions because they are not delayed by banking policies, national borders, citizenship, debts, or other social-economic factors. These new currency systems decentralize financial transactions, leaving many to consider a world where traditional banking may become obsolete.

Concerns about security of cryptocurrencies worry both citizens and economic analysts. These concerns have constrained its growth in some communities. On the other hand, much of the popularity of cryptocurrency is due to its departure from traditional overly-restrictive security and debt measures that rely on oversight by large banks and governments. These oversight institutions are often expensive, deeply bureaucratic, and sometimes corrupt. Some experts believe that a universal, decentralized, digital currency with internal security like blockchain can make markets more efficient by eliminating barriers to the flow of money. This is particularly important in countries where the majority of citizens do not have bank accounts and are unable to invest in regional or global financial markets. Some governments, however, view the lack of regulation around these currencies and their anonymity as too risky because of how easily they can be used in illicit transactions, such as tax sheltering or purchasing illegal merchandise. Others feel that a secure digital currency offers a more convenient and safer form of financial exchange. For instance, a universally accepted currency would enable truly global financial markets and would protect individual assets against regional inflation fluctuations and artificial manipulation of currency by regional governments. If alternative digital systems become more established, there will be many questions about how digital currency will affect current banking systems and nation-based currencies.

Your team’s submission should consist of:

  • One-page Summary Sheet,
  • One-page policy recommendation for national leaders,
  • Your solution of no more than 20 pages, for a maximum of 22 pages with your summary and policy recommendation.
  • Judges expect a complete list of references with in-text citations, but may not consider appendices in the judging process.
  • Note: Reference list and any appendices do not count toward the 22-page limit and should appear after your completed solution.

References:

Paul Krugman, “O Canada: A neglected nation gets its Nobel”. Slate, Oct 19, 1999.
https://slate.com/business/1999/10/o-canada.html

Stephanie Lo and J. Christina Wang, “Bitcoin as Money?” Current Policy Perspectives,

Federal Reserve Bank of Boston, 2014.
https://www.bostonfed.org/publications/current-policy-perspectives/2014/bitcoin-as-money.aspx or https://www.bostonfed.org/-/media/Documents/Workingpapers/PDF/cpp1404.pdf

Glossary:

Anonymity - the state of being unnamed or unidentified; the state of being anonymous.

Blockchain - the record keeping technology that can document transactions between two parties in a verifiable and permanent way; a digital database containing information that can be shared and simultaneously used across a large publicly accessible and decentralized network.

Cryptocurrency - a digital or virtual currency that uses cryptography (protecting information through the use of codes) for security.

Digital Currency - [digital money, electronic money, electronic currency] is a type of currency in digital (electronic) versus physical (coins, paper) form.

Illicit - illegal or dishonest.

Fluctuations - variations or oscillations; rises and falls. .

Monetary -relating to money or finances, or to the mechanisms by which money is supplied to and circulates in the economy.

Nation-based currencies - [national currencies] a system of money issued by a central bank and in common use within a particular nation or group of nations; examples are United States dollar (USD), Chinese renminbi (RMB or CNY), European Euro (EUR), British pound sterling (GBP), and Japanese yen (JPY).

Underground cult - hidden or mysterious group of people sharing an excessive devotion toward a particular person, belief, or thing.

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【真题在线看】2019ICM问题E:环境恶化的代价是什么?

问题标题:环境恶化的代价是什么?

年份:2019
学生等级:本科生
来源:ICM

问题

经济理论经常忽视其决策对生物圈的影响,或假设其资源或容量无限。这种观点是有缺陷的,环境现在正面临其后果。生物圈提供了许多自然过程来维持人类生活的健康和可持续的环境,这些过程被称为生态系统 服务。例子包括将废物转化为食物、水过滤、种植食物、植物授粉以及将二氧化碳转化为氧气。然而,每当人类改变生态系统时,我们都有可能限制或消除生态系统服务。局部小规模的土地利用变化,例如修建几条道路、下水道、桥梁、房屋或工厂,其影响可能看起来可以忽略不计。除了这些小型项目之外,还有大型项目,例如建造或搬迁大型公司总部、修建全国范围的管道或扩建或改造水道以扩大商业用途。现在想想这些项目对一个地区、国家和世界的影响。虽然这些活动单独来看对于生物圈整体的功能潜力来说似乎微不足道,但累积起来却直接影响着生物多样性并造成环境恶化。

传统上,大多数土地利用项目不考虑生态系统服务的影响或变化。减轻土地利用变化的负面结果的经济成本:河流污染、空气质量差、危险废物场、废水处理不当、气候变化等,通常不包括在计划中。是否有可能对土地利用开发项目的环境成本进行估值?这些项目成本中如何考虑环境退化?一旦生态系统服务被计入项目的成本效益比,就可以确定和评估项目的真实和全面估值。 您的 ICM 团队已被聘请创建一个生态服务估值模型,以了解在考虑生态系统服务时土地利用项目的真实经济成本。使用您的模型对不同规模的土地利用开发项目进行成本效益分析,从小型社区项目到大型国家项目。根据您的分析和模型设计评估模型的有效性。您的建模对土地利用项目规划人员和管理者有何影响?您的模型可能需要如何随时间变化?

您的提交应包括:

单页摘要表,
您的解决方案不得超过 20 页,加上摘要最多可达 21 页。
评委希望获得完整的参考文献列表以及文内引用,但在评审过程中可能不会考虑附录。
注意:参考文献列表和任何附录均不计入 21 页的限制,并且应在完成的解决方案后出现。

参考:

Chee, Y.,2004。生态系统服务价值评估的生态学视角。生物保护 120,549-565。

Costanza, R., d'Arge, R., de Groot, R., Farber, S., Grasso, M., Hannon, B., Limburg, K., Naeem, S., O'Neill, RV, Paruelo, J., Raskin, RG, Sutton, P., van den Belt, M., 1997.《世界生态系统服务和自然资本的价值》。《自然》387,253-260。

Gomaz-Baggethuna, E.、de Groot, R.、Lomas, P.、Montesa, C.,2010 年 4 月 1 日。《经济理论与实践中的生态系统服务史:从早期概念到市场和支付方案》。《生态经济学》69(6),1209-1218。

Norgaard, R.,2010 年 4 月 1 日。生态系统服务:从令人大开眼界的隐喻到令人眼花缭乱的复杂性。生态经济学 69(6),1219-1227。

Richmond, A., Kaufmann R., Myneni, R.,2007,《生态系统服务评估:净初级生产力的影子价格》。《生态经济学》64,454-462。

Yang, Q., Liu, G., Casazza, M., Campbell, E., Giannettia, B., Brown, M., 2018 年 12 月。《生态系统服务评估非货币核算新框架的开发》。《生态系统服务》34A,37-54。

数据来源:

美国数据:https://www.data.gov/ecosystems/
卫星数据:https://www.ncdc.noaa.gov/data-access/satellite-data/satellite-data-access-datasets

词汇表:

生物多样性- 指生态系统中生命的多样性;特定区域内的所有生物。

生物圈- 地球上生物所占据的部分,通常包括这些生物与其物理环境之间的相互作用。

生态系统- 生物圈的一个子集,主要关注生物与其物理环境之间的相互作用。

生态系统服务- 人类从自然环境和功能齐全的生态系统中免费获得的众多好处和资产。

环境退化– 指自然过程或人类活动消耗资产而导致的自然环境恶化或破坏。

减轻-使严重性、痛苦性或影响性降低。

估价——指估计或确定某物的当前价值。

题目内容过长,可到文末下载完整版中英文真题


以下是英文版真题

Problem
Economic theory often disregards the impact of its decisions on the biosphere or assumes unlimited resources or capacity for its needs. There is a flaw in this viewpoint, and the environment is now facing the consequences. The biosphere provides many natural processes to maintain a healthy and sustainable environment for human life, which are known as ecosystem services. Examples include turning waste into food, water filtration, growing food, pollinating plants, and converting carbon dioxide into oxygen. However, whenever humans alter the ecosystem, we potentially limit or remove ecosystem services. The impact of local small-scale changes in land use, such as building a few roads, sewers, bridges, houses, or factories may seem negligible. Add to these small projects, large-scale projects such as building or relocating a large corporate headquarters, building a pipeline across the country, or expanding or altering waterways for extended commercial use. Now think about the impact of many of these projects across a region, country, and the world. While individually these activities may seem inconsequential to the total ability of the biosphere’s functioning potential, cumulatively they are directly impacting the biodiversity and causing environmental degradation.

Traditionally, most land use projects do not consider the impact of, or account for changes to, ecosystem services. The economic costs to mitigate negative results of land use changes: polluted rivers, poor air quality, hazardous waste sites, poorly treated waste water, climate changes, etc., are often not included in the plan. Is it possible to put a value on the environmental cost of land use development projects? How would environmental degradation be accounted for in these project costs? Once ecosystem services are accounted for in the cost-benefit ratio of a project, then the true and comprehensive valuation of the project can be determined and assessed.
Your ICM team has been hired to create an ecological services valuation model to understand the true economic costs of land use projects when ecosystem services are considered. Use your model to perform a cost benefit analysis of land use development projects of varying sizes, from small community-based projects to large national projects. Evaluate the effectiveness of your model based on your analyses and model design. What are the implications of your modeling on land use project planners and managers? How might your model need to change over time?
Your submission should consist of:

  • One-page Summary Sheet,
  • Your solution of no more than 20 pages, for a maximum of 21 pages with your summary.
  • Judges expect a complete list of references with in-text citations, but may not consider appendices in the judging process.
  • Note: Reference list and any appendices do not count toward the 21-page limit and should appear after your completed solution.


References:

Chee, Y., 2004. An ecological perspective on the valuation of ecosystem services. Biological Conservation 120, 549-565.

Costanza, R., d’Arge, R., de Groot, R., Farber, S., Grasso, M., Hannon, B., Limburg, K., Naeem, S., O’Neill, R.V., Paruelo, J., Raskin, R.G., Sutton, P., van den Belt, M., 1997. The value of the world’s ecosystem services and natural capital. Nature 387, 253-260.

G贸mez-Baggethuna, E., de Groot, R., Lomas, P., Montesa, C., 1 April 2010. The history of ecosystem services in economic theory and practice: From early notions to markets and payment schemes. Ecological Economics 69 (6), 1209-1218.

Norgaard, R., 1 April 2010. Ecosystem services: From eye-opening metaphor to complexity blinder. Ecological Economics 69 (6), 1219-1227.

Richmond, A., Kaufmann R., Myneni, R., 2007, Valuing ecosystem services: A shadow price for net primary production. Ecological Economics 64, 454-462.

Yang, Q., Liu, G., Casazza, M., Campbell, E., Giannettia, B., Brown, M., December 2018. Development of a new framework for non-monetary accounting on ecosystem services valuation. Ecosystem Services 34A, 37-54.

Data sources:

US based data: https://www.data.gov/ecosystems/
Satellite data: https://www.ncdc.noaa.gov/data-access/satellite-data/satellite-data-access-datasets

Glossary:

Biodiversity - refers to the variety of life in an ecosystem; all of the living organisms within a given area.

Biosphere - the part of the Earth that is occupied by living organisms and generally includes the interaction between these organisms and their physical environment.

Ecosystem - a subset of the biosphere that primarily focuses on the interaction between living things and their physical environment.

Ecosystem Services - the many benefits and assets that humans receive freely from our natural environment and a fully functioning ecosystem.

Environmental Degradation - the deterioration or compromise of the natural environment through consumption of assets either by natural processes or human activities.

Mitigate - to make less severe, painful, or impactful.

Valuation - refers to the estimating or determining the current worth of something.

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