美国大学生数学建模竞赛（MCM/ICM）由美国数学及其应用联合会主办，是唯一的国际性数学建模竞赛，也是世界范围内最具影响力的数学建模竞赛。由Ben Fursaro主办，要求学生将数学理论转为实践，以更好地帮助我们理解和管理世界。
ACHIEVE
美国大学生数学建模竞赛（MCM/ICM）内容涉及经济、管理、环境、资源、生态、医学、安全、等众多领域。竞赛要求三人（本科生）为一组，在四天时间内，就指定的问题完成从建立模型、求解、验证到论文撰 写的全部工作，体现了参赛选手研究问题、解决方案的能力及团队合作精神。
MCM竞赛自 1985 年以来，一直由the Consortium for Mathematics and Its Applications美国数学及应用联合会组织管理（简称：COMAP），每年有超过18个国家的学生参与到该竞赛中。
美国大学生数学建模竞赛目前分为两种类型：
MCM
Mathematical Contest In Modeling
ICM
Interdisciplinary Contest In Modeling
其中，MCM竞赛旨在考验学生对开放性问题的阐明、分析和解决问题的综合能力；而ICM竞赛则是MCM的衍生，更侧重于培养和提高学生跨学科解决问题的能力及书面沟通及表达能力。两种类型竞赛采用统一标准进行，竞赛题目出来之后，参数队伍通过美赛官网进行选题，一共分为六种题型。
这六种不同类型的题型可由学生自由选择，让参赛者能在相对熟悉和喜爱的领域，充分展示自己的才 华。美赛相较于国赛更加看重一个人的学术潜力。美赛一支队伍最多三人，最少一人。将在四天左右的时间里完成小组选择的那一道题的数据采集、建模、论文写作等一系列工作。
竞赛优势
着重学术潜力、综合提升学习实践及思维能力：参赛队伍需在四天左右的参赛时间里，完成数据采集、 建模、论文写作等一系列工作，这对每个参与者都是一次锻炼，让参与者感受到学术的氛围，显著提升 其学术能力及对团队协调的经验；
助力通往高等学府：MCM/ICM作为世界范围内最具影响力的数学建模竞赛，同时还包含了International COMAP Scholarship Award在内的十余个奖项，可助力表现优异的参赛者们获得高校的青睐；
锻炼解决问题的能力：竞赛鼓励参赛选手通过自己的努力来解决一个个或是实际或是虚构的问题，体验探索、尝试和从新想法中获取价值的过程。
竞赛基本信息
参赛资格：在校高中生及本科生
竞赛语言：英语（所有提交材料需为英文）
竞赛形式：团队比赛，每个团队由1-3名参赛者组成，要求来自同一学校
注意事项：参赛论文需要以电子文档的形式发送邮件给 solutions@comap.com，提交后记得通过导师查看COMAP 是否确认收到论文电子版。
1) 文件小于17MB；
2) 邮件题目以COMAP#控制号命名，如：COMAP1234；
3) 附件以Team#控制号命名，如：Team1234。
参赛时间以及方式
报名时间：
美东时间 2022年2月17日15:00
参赛时间：
美东时间 2022年2月17日17:00至2月21日21:00
结果公布：
2022年5月20日或之前
报名链接：
https://www.comap.com/undergraduate/contests/mcm/register.php
参赛地点：
线上竞赛
评判规则
经评审后，所有论文将被分成以下7个级别：
Disqualified 无资格：违反了竞赛规则，被取消评奖资格。
Unsuccessful 不成功参赛：没有按照竞赛题目的要求完成问题的作答。
Successful Participant 合格论文：回答了竞赛题目所要求的问题并给出了相应的答案，除去不合格论文大约占50%左右。
Honorable Mention 乙级论文：在符合所有竞赛要求的前提下，包含建模和问题解决的全部要素，论文实际超过了平均水平，大约占30%左右。
Meritorious 甲级论文：在符合所有竞赛要求的前提下，在建模和问题解决的诸多方面都表现突出，且给出了一定水平的答案。同时，在所有参赛论文中属于相对较好的文章，大约占10%-15%。
Finalist 特技提名论文：在符合所有竞赛要求的前提下，在所有参赛论文中属于比较优秀的论文，可以进入到最后一轮评审，占所有参赛论文的 2%。
Outstanding Winner 优胜论文：在符合所有竞赛要求的前提下，属于全部参赛论文中最夺目的论文，高水准的完成了竞赛题目并给予了有特色的答案；这些论文很可能最终会被作为优秀学生作品出版，大约仅占 1%左右。
奖项设置
MCM/ICM 共有奖项
International COMAP Scholarship Award：颁发给在 MCM/ICM竞赛中获得最高分数的4个团队（无论国籍），团队成员可平分$9,000奖金，团队所在学校将获得$1000奖金。
Institute for Operations Research and the Management Sciences (简称：INFORMS)：由the Institute for Operations Research and the Management Sciences 美国运筹及管理学协会设立，颁发给 6个问题下每个问题得分最高的团队。
MCM 奖项
Mathematical Association of America (简称：MAA)：由美国数学会设立，颁发给MCM竞赛中表现最突出的两个团队。
Society for Industrial and Applied Mathematics (简称：SIAM)：由美国工业与应用数学学会设立, 颁发给在MCM Problem A和B下表现最突出的各一个团队。
American Statistical Association (简称：ASA)：由美国统计协会设立，颁发给在MCM Problem C题目下得分最高的一个团队。
Ben Fusaro Award：从最终的finalists中进行挑选。
Frank R. Giordano Award：颁发给在建模运行过程中有卓越效果及成果的论文。
ICM 奖项
Leonhard Euler Award：由 ICM Problem D 的总评审员挑选一个团队获得，要求论文必须在 Meritorious/Finalist/Outstanding 水平，包含具有创意性的模型，并且对 interdisciplinary science 跨学科科学有着非常深刻的理解。
Rachel Carson Award：由 ICM Problem E 的总评审员挑选一个在此问题中 scientific theory and data 科学理论和数据使用最好的团队。
ICM Pareto Award：由 ICM Problem F 的总评审员挑选一个在论文中使简化或细化模型非常困难的 因素用更动态且更具有挑战性的模型表达出来的团队。
竞赛例题
2021 MCMProblem A: Fungi
The carbon cycle describes the process of the exchange of carbon throughout the geochemical cycle of the Earth, and is a vital component for life on the planet. Part of the carbon cycle includes the decomposition of compounds, allowing carbon to be renewed and used in other forms. One key component of this part of the process is the decomposition of plant material and woody fibers.
Some of the key agents in decomposing woody fibers are fungi. The authors of a recent research article on wood decomposition by fungi identified fungi traits that determine decomposition rates and also noted links between certain traits [1] . In particular, the slow growing strains of fungi tend to be better able to survive and grow in the presence of environmental changes with respect to moisture and temperature, while the faster growing strains tend to be less robust to the same changes. A synopsis of this article can be found below on page 3.
These researchers examined a large number of traits associated with different fungi and their role in the decomposition of ground litter (dead plant material) and woody fibers. For this MCM Problem you should focus on just two traits of a fungus: the growth rate of the fungus and the fungus’ tolerance to moisture. Your primary goal is to model the decomposition of woody fibers in a given patch of land, and do so in the presence of multiple types of fungi breaking down woody fibers in the same area.
As you explore the relationship of the two traits of interest, growth rate and moisture tolerance, with the rate of decomposition, several questions may arise to include: Using these two traits, how do the different fungi interact and decompose ground litter in a fixed patch of land in different environments? Within these different environments, how will the decomposition be impacted over time as conditions vary? How do environmental changes and the variation in environmental change impact the long-term dynamics with respect to decomposition, as well as competition between fungi in a given environment? The estimation for the decomposition rates, given the growth rate, is shown in Figure 1. The estimation of the decomposition rates, given the relative moisture tolerance, is shown in Figure 2.
Figure 1: The relationship between the hyphal extension rate (mm/day) of various fungi and the resulting wood decomposition rate (% mass loss over 122 days) at various temperatures. (Figure 1C in [1]).
Figure 2: The relationship between the moisture tolerance (difference of each isolate’s competitive ranking and their moisture niche width, both scaled to [0,1]) of various fungi and the resulting wood decomposition rate (% mass loss over 122 days, log transformed). (Figure 4A in [1]).
Requirement:Your paper should explore and address the following aspects.
Build a mathematical model that describes the breakdown of ground litter and woody fibers through fungal activity in the presence of multiple species of fungi.
In your model, incorporate the interactions between different species of fungi, which have different growth rates and different moisture tolerances as shown in Figures 1 and 2.
Provide an analysis of the model and describe the interactions between the different types of fungi. The dynamics of the interactions should be characterized and described including both short- and long-term trends. Your analysis should examine the sensitivity to rapid fluctuations in the environment, and you should determine the overall impact of changing atmospheric trends to assess the impact of variation of local weather patterns.
Include predictions about the relative advantages and disadvantages for each species and combinations of species likely to persist, and do so for different environments including arid, semi-arid, temperate, arboreal, and tropical rain forests.
Describe how the diversity of fungal communities of a system impacts the overall efficiency of a system with respect to the breakdown of ground litter. Predict the importance and role of biodiversity in the presence of different degrees of variability in the local environment. Include a two-page article of your results. Your article should be appropriate for inclusion in an introductory college level biology textbook to discuss recent developments in our understanding of the roles fungi play in ecological systems.
Your PDF solution of no more than 25 total pages should include:
One-page Summary Sheet.
Table of Contents.
Your complete solution.
Two-page Article.
References list.
Note:The MCM Contest now has a 25 page limit. All aspects of your submission count toward the 25 page limit (Summary Sheet, Table of Contents, Reference List and any Appendices).
参考资料
[1]
Nicky Lustenhouwer, Daniel S. Maynard, Mark A. Bradford, Daniel L. Lindner, Brad Oberle, Amy E. Zanne, and Thomas W. Crowther. A trait-based understanding of wood decomposition by fungi. Proceedings of the National Academy of Sciences of the United States, May 13, 2020:
https://www.pnas.org/content/pnas/117/21/11551.full.pdf
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