美國大學生數學建模競賽（MCM/ICM）由美國數學及其應用聯合會主辦，是唯一的國際性數學建模競賽，也是世界范圍內最具影響力的數學建模競賽。由Ben Fursaro主辦，要求學生將數學理論轉為實踐，以更好地幫助我們理解和管理世界。
ACHIEVE
美國大學生數學建模競賽（MCM/ICM）內容涉及經濟、管理、環境、資源、生態、醫學、安全、等眾多領域。競賽要求三人（本科生）為一組，在四天時間內，就指定的問題完成從建立模型、求解、驗證到論文撰 寫的全部工作，體現了參賽選手研究問題、解決方案的能力及團隊合作精神。
MCM競賽自 1985 年以來，一直由the Consortium for Mathematics and Its Applications美國數學及應用聯合會組織管理（簡稱：COMAP），每年有超過18個國家的學生參與到該競賽中。
美國大學生數學建模競賽目前分為兩種類型：
MCM
Mathematical Contest In Modeling
ICM
Interdisciplinary Contest In Modeling
其中，MCM競賽旨在考驗學生對開放性問題的闡明、分析和解決問題的綜合能力；而ICM競賽則是MCM的衍生，更側重于培養和提高學生跨學科解決問題的能力及書面溝通及表達能力。兩種類型競賽采用統一標準進行，競賽題目出來之后，參數隊伍通過美賽官網進行選題，一共分為六種題型。
這六種不同類型的題型可由學生自由選擇，讓參賽者能在相對熟悉和喜愛的領域，充分展示自己的才 華。美賽相較于國賽更加看重一個人的學術潛力。美賽一支隊伍最多三人，最少一人。將在四天左右的時間里完成小組選擇的那一道題的數據采集、建模、論文寫作等一系列工作。
競賽優勢
著重學術潛力、綜合提升學習實踐及思維能力：參賽隊伍需在四天左右的參賽時間里，完成數據采集、 建模、論文寫作等一系列工作，這對每個參與者都是一次鍛煉，讓參與者感受到學術的氛圍，顯著提升 其學術能力及對團隊協調的經驗；
助力通往高等學府：MCM/ICM作為世界范圍內最具影響力的數學建模競賽，同時還包含了International COMAP Scholarship Award在內的十余個獎項，可助力表現優異的參賽者們獲得高校的青睞；
鍛煉解決問題的能力：競賽鼓勵參賽選手通過自己的努力來解決一個個或是實際或是虛構的問題，體驗探索、嘗試和從新想法中獲取價值的過程。
競賽基本信息
參賽資格：在校高中生及本科生
競賽語言：英語（所有提交材料需為英文）
競賽形式：團隊比賽，每個團隊由1-3名參賽者組成，要求來自同一學校
注意事項：參賽論文需要以電子文檔的形式發送郵件給 solutions@comap.com，提交后記得通過導師查看COMAP 是否確認收到論文電子版。
1) 文件小于17MB；
2) 郵件題目以COMAP#控制號命名，如：COMAP1234；
3) 附件以Team#控制號命名，如：Team1234。
參賽時間以及方式
報名時間：
美東時間 2022年2月17日15:00
參賽時間：
美東時間 2022年2月17日17:00至2月21日21:00
結果公布：
2022年5月20日或之前
報名鏈接：
https://www.comap.com/undergraduate/contests/mcm/register.php
參賽地點：
線上競賽
評判規則
經評審后，所有論文將被分成以下7個級別：
Disqualified 無資格：違反了競賽規則，被取消評獎資格。
Unsuccessful 不成功參賽：沒有按照競賽題目的要求完成問題的作答。
Successful Participant 合格論文：回答了競賽題目所要求的問題并給出了相應的答案，除去不合格論文大約占50%左右。
Honorable Mention 乙級論文：在符合所有競賽要求的前提下，包含建模和問題解決的全部要素，論文實際超過了平均水平，大約占30%左右。
Meritorious 甲級論文：在符合所有競賽要求的前提下，在建模和問題解決的諸多方面都表現突出，且給出了一定水平的答案。同時，在所有參賽論文中屬于相對較好的文章，大約占10%-15%。
Finalist 特技提名論文：在符合所有競賽要求的前提下，在所有參賽論文中屬于比較優秀的論文，可以進入到最后一輪評審，占所有參賽論文的 2%。
Outstanding Winner 優勝論文：在符合所有競賽要求的前提下，屬于全部參賽論文中最奪目的論文，高水準的完成了競賽題目并給予了有特色的答案；這些論文很可能最終會被作為優秀學生作品出版，大約僅占 1%左右。
獎項設置
MCM/ICM 共有獎項
International COMAP Scholarship Award：頒發給在 MCM/ICM競賽中獲得最高分數的4個團隊（無論國籍），團隊成員可平分$9,000獎金，團隊所在學校將獲得$1000獎金。
Institute for Operations Research and the Management Sciences (簡稱：INFORMS)：由the Institute for Operations Research and the Management Sciences 美國運籌及管理學協會設立，頒發給 6個問題下每個問題得分最高的團隊。
MCM 獎項
Mathematical Association of America (簡稱：MAA)：由美國數學會設立，頒發給MCM競賽中表現最突出的兩個團隊。
Society for Industrial and Applied Mathematics (簡稱：SIAM)：由美國工業與應用數學學會設立, 頒發給在MCM Problem A和B下表現最突出的各一個團隊。
American Statistical Association (簡稱：ASA)：由美國統計協會設立，頒發給在MCM Problem C題目下得分最高的一個團隊。
Ben Fusaro Award：從最終的finalists中進行挑選。
Frank R. Giordano Award：頒發給在建模運行過程中有卓越效果及成果的論文。
ICM 獎項
Leonhard Euler Award：由 ICM Problem D 的總評審員挑選一個團隊獲得，要求論文必須在 Meritorious/Finalist/Outstanding 水平，包含具有創意性的模型，并且對 interdisciplinary science 跨學科科學有著非常深刻的理解。
Rachel Carson Award：由 ICM Problem E 的總評審員挑選一個在此問題中 scientific theory and data 科學理論和數據使用最好的團隊。
ICM Pareto Award：由 ICM Problem F 的總評審員挑選一個在論文中使簡化或細化模型非常困難的 因素用更動態且更具有挑戰性的模型表達出來的團隊。
競賽例題
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).
參考資料
[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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