PROBLEM A: The Keep-Right-Except-To-Pass Rule
In 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 employa 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 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.
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?
問題A：除非超車否則靠右行駛的交通規則
在一些汽車靠右行駛的國家（比如美國，中國等等），多車道的高速公路常常遵循以下原則：司機必須在最右側駕駛，除非他們正在超車，超車時必須先移到左側車道在超車後再返回。
在一些國家，汽車靠左形式是常態，探討你的解決方案是否稍作修改即可適用，或者需要一些額外的需要。
最後，以上規則依賴於人的判斷，如果相同規則的交通運輸完全在智能系統的控制下，無論是部分網絡還是嵌入使用的車輛的設計，在何種程度上會修改你前面的結果？
PROBLEM B: College Coaching Legends
Sports 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 choose thebest 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 thatsports fanswill understand.
問題B：大學傳奇教練
體育畫報是一個爲運動愛好者服務的雜誌，正在尋找在整個上個世紀的“史上最好的大學教練”。建立數學模型選擇大學中在一下體育項目中最好的教練：曲棍球或場地曲棍球，足球，棒球或壘球，籃球，足球。
時間軸在你的分析中是否會有影響？比如1913年的教練和2013年的教練是否會有所不同？清晰的對你的指標進行評估，討論一下你的模型應用在跨越性別和所有可能對的體育項目中的效果。展示你的模型中的在三種不同體育項目中的前五名教練。
除了傳統的MCM格式，準備一個1到2頁的文章給體育畫報，解釋你的結果和包括一個體育迷都明白的數學模型的非技術性解釋。
2014 ICM Problem
Using 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 500
co-authors and published over 1400 technical research papers. It is ironic, or perhaps
not, that Erdös is also one of the influencers in building the foundation for the emerging
interdisciplinary science of networks, particularly, through his publication with Alfred
Rényi of the paper “On Random Graphs” in 1959. Erdös’s role as a collaborator was so
significant in the field of mathematics that mathematicians often measure their
closeness to Erdös through analysis of Erdös’s amazingly large and robust co-author
network (see the website http://www.oakland.edu/enp/ ). The unusual and fascinating
story of Paul Erdös as a gifted mathematician, talented problem solver, and master
collaborator is provided in many books and on-line websites
(e.g., http://www-history.mcs.st-and.ac.uk/Biographies/Erdos.html). Perhaps his itinerant
lifestyle, frequently staying with or residing with his collaborators, and giving much of his
money to students as prizes for solving problems, enabled his co-authorships to flourish
and helped build his astounding network of influence in several areas of mathematics.
In order to measure such influence as Erdös produced, there are network-based
evaluation tools that use co-author and citation data to determine impact factor of
researchers, 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 for
network influence or impact data collection and analysis. Your team’s goal for ICM
2014 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 the
website https://files.oakland.edu/users/grossman/enp/Erdos1.html or the one we
include at Erdos1.htm ). You should build a co-author network of the
approximately 510 researchers from the file Erdos1, who coauthored a paper
with Erdös, but do not include Erdös. 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). There are over 18,000
lines of raw data in Erdos1 file, but many of them will not be used since they are
links to people outside the Erdos1 network. If necessary, you can limit the size of
your network to analyze in order to calibrate your influence measurement
algorithm. Once built, analyze the properties of this network. (Again, do not
include Erdös --- he is the most influential and would be connected to all nodes 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.)
2) Develop influence measure(s) to determine who in this Erdos1 network has
significant influence within the network. Consider who has published important
works or connects important researchers within Erdos1. Again, assume Erdös is
not there to play these roles.
3) Another type of influence measure might be to compare the significance of a
research paper by analyzing the important works that follow from its publication.
Choose some set of foundational papers in the emerging field of network science
either from the attached list (NetSciFoundation.pdf) or papers you discover.
Use these papers to analyze and develop a model to determine their relative
influence. Build the influence (coauthor or citation) networks and calculate
appropriate measures for your analysis. Which of the papers in your set do you
consider is the most influential in network science and why? Is there a similar
way to determine the role or influence measure of an individual network
researcher? Consider how you would measure the role, influence, or impact of a
specific university, department, or a journal in network science? Discuss
methodology to develop such measures and the data that would need to be
collected.
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. You
may wish to restrict the network to a specific genre or geographic location or
predetermined size.
5) Finally, discuss the science, understanding and utility of modeling influence and
impact within networks. Could individuals, organizations, nations, and society use
influence methodology to improve relationships, conduct business, and make
wise decisions? For instance, at the individual level, describe how you could use
your measures and algorithms to choose who to try to co-author with in order to
boost your mathematical influence as rapidly as possible. Or how can you use
your models and results to help decide on a graduate school or thesis advisor to
select for your future academic work?
6) Write a report explaining your modeling methodology, your network-based
influence and impact measures, and your progress and results for the previous
five tasks. The report must not exceed 20 pages (not including your summary
sheet) and should present solid analysis of your network data; strengths,
weaknesses, and sensitivity of your methodology; and the power of modeling
these phenomena using network science.
*Your submission should consist of a 1 page Summary Sheet and your solution cannot
exceed 20 pages for a maximum of 21 pages.
C題：
其中一項技術來確定學術研究的影響力是建立和
測量引文或合著者網絡的性能。共同創作的手稿通常
張三研究者之間有很強的影響力的連接。其中最有名的
學術合著者是20世紀的數學家保羅·埃爾德什誰擁有超過500
共同作者，並發表了1400的技術研究論文。這是具有諷刺意味的，或者
不，那埃爾德什也是建設爲新興的基礎上有影響力之一
網絡的跨學科的科學，特別是通過他的出版物，阿爾弗雷德
論文“關於隨機圖”在1959年萊利。埃爾德什的作爲合作者的角色是如此
在數學，數學家經常測量領域顯著的
通過鄂爾多斯的驚人的大，健壯的合著者分析親近到鄂爾多斯
網絡（見網站http://www.oakland.edu/enp/ ） 。不尋常和令人着迷
保羅鄂爾多斯故事作爲一個天才的數學家，天才的問題解決者，和主
合作者在許多書籍和在線網站提供
（例如， http://www-history.mcs.st-and.ac.uk/Biographies/Erdos.html ） 。也許他的江湖
生活方式，經常住在或居住與他的合作者，並給了他的
錢給學生作爲獎品解決問題，使他的合作authorships蓬勃發展
並幫助建立他的驚人影響力的網絡數學的幾個領域。
爲了衡量這種影響力鄂爾多斯生產的，也有基於網絡的
使用共同作者和引文數據，以確定影響因子評估工具
研究人員，出版物和期刊。其中有些是科學引文索引， Hfactor ，
影響因子，特徵因子等谷歌學術搜索也是一個不錯的數據的工具來使用的
網絡影響或影響數據的收集和分析。你的團隊的爲ICM的目標
2014來分析研究網絡和其他領域的影響和衝擊
社會。你的任務做到這一點，包括：
1 ）構建Erdos1作者的合著者網絡（您可以使用該文件從
網站https://files.oakland.edu/users/grossman/enp/Erdos1.html或一個我們
包括Erdos1.htm ） 。你應該建立的一個合著者網絡
從文件Erdos1 ，誰合着的論文約510研究人員
與鄂爾多斯，但不包括埃爾德什。這將需要一些熟練的數據提取
和建模的努力，以獲得正確的節點集（鄂爾多斯合著者）和
他們的鏈接（彼此作爲合著者連接） 。有超過18,000
在Erdos1文件中的原始數據線，但很多人不會使用，因爲它們是
鏈接到Erdos1網絡之外的人。如果有必要，你可以限制的大小
您的網絡進行分析，以校準你的影響力測量
算法。一旦建成，分析這個網絡的性能。 （同樣，不
包括埃爾德什---他是最有影響力的，並會被連接到的所有節點
網絡。在這種情況下，它的合著者與他建立的網絡，但
他不是網絡或分析的一部分。 ）
2 ）發展影響的措施，以確定誰在這個Erdos1網絡有
網絡內的顯著影響。考慮誰曾發表重要
工程或內Erdos1連接重要的研究人員。同樣，假設埃爾德什是
不存在玩這些角色。
3 ）另一種類型的影響措施可能是比較的意義
研究論文通過分析它的出版遵循的重要作品。
在選擇網絡科學的新興領域設置了一些基礎性的論文
無論是從所附清單（ NetSciFoundation.pdf ）或試卷你發現。
使用這些文件來分析和建立一個模型來確定它們的相對
影響。打造影響力（或合着引文）網絡和計算
適當的措施，供您分析。其中的文件在你設定你
認爲是最有影響力的網絡科學，爲什麼？是否有一個類似
的方法來確定個體網絡的作用或影響的措施
研究員？考慮一下如何去衡量的作用，影響力，還是一個影響
具體的大學，部門，或在網絡科學期刊？討論
的方法來開發這樣的措施，以及數據將需要
收集。
4 ）執行你的算法對一組完全不同的網絡影響力數據
---例如，有影響力的作曲家，音樂樂隊，表演，電影演員，
導演，電影，電視節目，專欄作者，記者，報紙，雜誌，
小說家，小說，博客，高音喇叭，或任何數據集，你在乎分析。您
不妨到網絡限制到一個特定的風格或地理位置或
預定的大小。
5 ）最後，討論科學，理解和建模的影響和效用
網絡中的影響。可以個人，組織，國家和社會使用
影響力的方法來改善關係，開展業務，並進行
明智的決定？例如，在個人層面上，描述了可以如何使用
你的措施和算法來選擇誰嘗試共同創作與以
提高你的數學的影響儘可能快。不然你怎麼能使用
你的模型和結果，以幫助決定一個研究生院或論文顧問
選擇你的未來學術工作？
6）寫一份報告，說明你的建模方法，你的基於網絡的
影響和衝擊的措施，和你的進度和結果爲前
五項任務。該報告不得超過20頁（不包括您彙總
表），並應出示您的網絡數據分析固體;優勢，
弱點，你的方法的靈敏度;和建模的能力
這些現象用網絡科學。
*您提交的內容應包括1頁摘要表及解決方案不能
超過20頁，最多21頁。
這是可能的論文，可以包括在一個基礎集的清單
有影響力的出版物在網絡科學。網絡科學是一個新的，新興的，多樣的，
跨學科的領域所以沒有大的，濃集期刊，很容易的
用它來尋找網絡方面的論文，即使一些新的雜誌最近才建立起來
而在網絡科學的新的學術課程都開始將予提呈發售
大學在世界各地。你可以使用一些你的這些論文或其他
自己的選擇爲您的團隊的一套分析和比較在影響或影響
網絡科學的任務3 。