MCM2012(A,B,C)中英文对照.doc

PROBLEM A: The Leaves of a Tree How much do the leaves on a tree weigh? How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following: Why do leaves have the various shapes that they have? Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volume” of the tree and its branches effect the shape? Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure? How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings. 一棵树的叶子有多重？如何估计一棵树叶子的实际质量（或者树的某部分的质量）？如何给叶子分类？建立一个数学模型来描述和对树叶进行分类。考虑并回答下述问题：为什么树叶有各自不同的形状？树叶的形状是否通过使树叶间阴影重叠的最小化来获得最大的暴露面积，树叶在一棵树“体积”及树枝内的分布是否影响树叶的形状？谈到轮廓，树叶的形状是否和树的轮郭/分叉结构有关？你如何估计一棵树树叶的质量？树叶质量是否和树的大小（高度，质量，体积）相关？PROBLEM B: Camping along the Big Long River Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long Rivers rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one page summary sheet, prepare a one page memo to the managers of the river describing your key findings. 游客到大长河(the Big Long River)(225英里)可以享受旖旎的风光和令人兴奋的白色水急流。这条河不能徒步进入,因此唯一享受它的方法是通过河上旅行,这需要几天的露营。河上旅行都是在First Launch开始，在Final Exit退出,顺流而下225英里。旅行者可乘坐平均4英里/小时的一个划浆橡胶艇,也可以乘坐平均8英里的机动船。旅行从开始到结束需要6到18晚上的时间，露营在河上。负责管理这条河的机构希望每个旅程（every trip）享受一片野外的经历,和河上其他组的船有最少的接触（联系）。目前, 每年在六个月期间内，有X个旅行团沿着大长河 (一年的其余时间对河流旅行来说，天气太冷)。现有Y个营地相当均匀地分布在整个大长河的廊道。由于漂流的受欢迎的程度上升,公园管理者已经被要求允许更多的旅行团到这条河来顺河旅行。他们想制定一个在考虑变化时间（以在河上的晚上计算），动力（机动或桨划）等方面最优的旅行组合，从而最大限度利用地营地。换句话说,有多少乘船旅行团能够参与到一个大长河的漂流季节里?河道管理者雇你给他们在最佳行程安程和确定河的承载能力两方面的建议。记住没有两套露营者同时占用同一地点。除了的你的一页summary sheet（总述）页外,准备一页备忘录,对河道管理者描述你主要的发现。2012 ICM ProblemModeling for Crime BustingYour organization, the Intergalactic Crime Modelers (ICM), is investigating a conspiracy to commit a criminal act. The investigators are highly confident they know several members of the conspiracy, but hope to identify the other members and the leaders before they make arrests. The conspirators and the possible suspected conspirators all work for the same company in a large office complex. The company has been growing fast and making a name for itself in developing and marketing computer software for banks and credit card companies. ICM has recently found a small set of messages from a group of 82 workers in the company that they believe will help them find the most likely candidates for the unidentified coconspirators and unknown leaders. Since the message traffic is for all the office workers in the company, it is very likely that some (maybe many) of the identified communicators in the message traffic are not involved in the conspiracy. In fact, they are certain that they know some people who are not in the conspiracy. The goal of the modeling effort will be to identify people in the office complex who are the most likely conspirators. A priority list would be ideal so ICM could investigate, place under surveillance, and/or interrogate the most likely candidates. A discriminate line separating conspirators from nonconspirators would also be helpful to distinctly categorize the people in each group. It would also be helpful to the DAs office if the model nominated the conspiracy leaders.你的组织，星际犯罪建模中心，正在调查一个涉及犯罪行为的阴谋。研究人员非常有信心，他们知道一些成员的阴谋，但希望在他们逮捕前能找出其他成员和匪首。阴谋者和有阴谋嫌疑者都为同一个公司工作，集中在一个大办公室。该公司成长快速，在开发和销售银行和信用卡公司的计算机软件方面小有名气。ICM最近发现了一组来自公司的包括82个工人的小组的信息集，他们认为将帮助该公司找到具有最大可能的阴谋者及其匪首。由于信息流的交换与通信是面向公司的所有办公室人员，很可能一些（也许很多）根据信息流识别出来的通信员工并没有参与阴谋。事实上，ICM确信他们知道有些人没有参与阴谋。建模的目标是识别有最大阴谋嫌疑的办公室人员。若能预优先提供一份名单将会很有帮助。这样，ICM就可以集中精力调查，监听，和/或询问最有可能的阴谋者。设立区分阴谋者和非阴谋者的分界线也是有益的，这将有助于各组人员的分类。这也将有助于检察官，如果模型指控阴谋的领导者。Before the data of the current case are given to your crime modeling team, your supervisor gives you the following scenario (called Investigation EZ) that she worked on a few years ago in another city. Even though she is very proud of her work on the EZ case, she says it is just a very small, simple example, but it may help you understand your task. Her data follow: 在提供当前案子的数据情况给你的犯罪建模团队之前，你的主管给你她在几年前在另一个城市的参与的案例（称为调查EZ）。即使她可以为她在EZ 案例中的出色工作引以为傲，她说这只是一个很小的，简单的案子。但它有助于你了解你的任务。她的数据如下。The ten people she was considering as conspirators were: Anne#, Bob, Carol, Dave*, Ellen, Fred, George*, Harry, Inez, and Jaye#. (*indicates prior known conspirators, #indicate prior known nonconspirators) Chronology of the 28 messages that she had for her case with a code number for the topic of each message that she assigned based on her analysis of the message:有十人被她认为有阴谋嫌疑：安妮#，短发，卡罗，戴夫，艾伦，弗莱德，乔治*，哈里，伊内兹，和#贾伊。（*表示事先已知的阴谋者，#表明事先已知非阴谋者）Chronology of the 28 messages that she had for her case with a code number for the topic of each message that she assigned based on her analysis of the message:该案例中按时间顺序的28条对话信息罗列如下。她在分析的基础上，对案例中的每条信息分配了一个代码。Anne to Bob: 你今天为什么迟到？（1）Bob to Carol: 这该死的Anne一直看着我。我没有迟到。（1）Carol to Dave: 因为Bob的工作拖拉，Anne正在与他争吵。（1）Dave to Ellen：今天上午我得见你。你什么时候能来？将预算文件带过来。（2）Dave to Fred：我可以在今天任何时间过来见你。请告诉我合适的时间。我需要带预算文件吗？（2）Dave to George：随后见，还有许多需要交流。我希望其他人已经准备好了。获得这个权利很重要。（3）Harry to George：你似乎感到压力重重。情况如何？我们的预算很好。（2）（4）Inez to George：我是真的累了。你近来怎么样？（5）Jaye to Inez：今天没事。一起去吃午餐吗？（5）Inez to Jaye：太安静了，好事情。我筋疲力尽。今天不想吃午餐抱歉！（5）George to Dave：该说话的时候了，就是现在！（3）Jaye to Anne：你可以去吃午餐吗？（5）Dave to George：不，我随便去见一下Fred。（3）George to Dave：见完后，到我这里来一下。（3）Anne to Carol：谁在看管Bob？他整天游手好闲。（1）Carol to Anne：别管他。他与George 和 Dave的合作很好。（1）George to Dave：这是很重要的。该死的Fred。Ellen如何？（3）Ellen to George：你跟Dave谈过了吗？（3）George to Ellen：没有。你呢？（3）Bob to Anne：我没迟到。只是想让你知道，午餐时间我还在工作。（1）Bob to Dave：告诉他们我没迟到。你是知道的。（1）Ellen to Carol：与Anne一起制定好下周的预算会议的时间表，帮我让George安静下来。（2）Harry to Dave：你有没有注意到，George今天心事重重？（4）Dave to George：该死的Harry以为你心事重重。不要让他担心，否则他会四处打听。（4）George to Harry：只工作到很晚，家里出了一点问题。我会好的。（4）Ellen to Harry：如果我错过了今天的会议，没关系吧？Fred会在那里，他了解预算比我清楚。（2）Harry to Fred：我认为明年的预算会让几个人倍感压力。也许今天我们应该花点时间让的人们恢复信心。(2)(4)Fred to Harry：我觉得我们的预算是非常棒。我也看不出有什么不妥。（2）END of MESSAGE TRAFFIC信息流结束Your supervisor points outs that she assigned and coded only 5 different topics of messages: 1) Bobs tardiness, 2) the budget, 3) important unknown issue but assumed to be part of conspiracy, 4) Georges stress, and 5) lunch and other social issues. As seen in the message coding, some messages had two topics assigned because of the content of the messages.你的主管指出她分配和编码只有5个不同主题的信息：1）Bob的迟到，2）预算，3）重要的未知问题，可能是阴谋的部分，4）圣乔治压力，5）午餐和其他社交话题。信息编码过程中，有一些信息由于信息内容可能对应两个主题。The way your supervisor analyzed her situation was with a network that showed the communication links and the types of messages. The following figure is a model of the message network that resulted with the code for the types of messages annotated on the network graph.你的上司按照通信联系和消息类型构造的通信网络分析案件。下面模型是用来描述通过对注解网状图的信息类型进行编码后所得到的信息网络图。Figure 1: Network of messages from EZ CaseYour supervisor points out that in addition to known conspirators George and Dave, Ellen and Carol were indicted for the conspiracy based on your supervisors analysis and later Bob self-admitted his involvement in a plea bargain for a reduced sentence, but the charges against Carol were later dropped. Your supervisor is still pretty sure Inez was involved, but the case against her was never established. Your supervisors advice to your team is identify the guilty parties so that people like Inez dont get off, people like Carol are not falsely accused, and ICM gets the credit so people like Bob do not have the opportunity to get reduced sentences.你的主管指出，基于她的分析知道George 、Dave、Ellen 和Carol是同谋者。而且不久后，Bob招认出他确实参与其中，从而希望得到减刑；而对Carol的控告后来被放弃了。你的上司还是非常肯定Inez 是参与其中的，但指控她的依据还没有建立起来。这样，你的上司建议你的团队找出真凶，使得像Inez 这样的人不被漏掉，当然，像Carol 这样的也不希望被冤枉，从而增加ICM的信用来不给像Bob 这样的人以减刑的机会。The current case:Your supervisor has put together a networklike database for the current case, which has the same structure, but is a bit larger in scope. The investigators have some indications that a conspiracy is taking place to embezzle funds from the company and use internet fraud to steal funds from credit cards of people who do business with the company. The small example she showed you for case EZ had only 10 people (nodes), 27 links (messages), 5 topics, 1 suspicious/conspiracy topic, 2 known conspirators, and 2 known nonconspirators. So far, the new case has 83 nodes, 400 links (some involving more than 1 topic), over 21,000 words of message traffic, 15 topics (3 have been deemed to be suspicious), 7 known conspirators, and 8 known nonconspirators. These data are given in the attached spreadsheet files: Names.xls, Topics.xls, and Messages.xls. Names.xls contains the key of node number to the office workers names. Topics.xls contains the code for the 15 topic numbers to a short description of the topics. Because of security and privacy issues, your team will not have direct transcripts of all the message traffic. Messages.xls provides the links of the nodes that transmitted messages and the topic code numbers that the messages contained. Several messages contained up to three topics. To help visualize the message traffic, a network model of the people and message links is provided in Figure 2. In this case, the topics of the messages are not shown in the figure as they were in Figure 1. These topic numbers are given in the file Messages.xls and described in Topics.xls.当前的情况你的supervisor收集了一个类似网络的数据库，和EZ的情况类似，不过要大些。调查人员发现一些，conspiracy 通过挪用公款和利用互联网来窃取与公司做生意人信用卡上资金的犯罪迹象。给你展示的EZ情况是一个小的例子，只有10个人，27个连接，5个topics，1个怀疑的topic，2个已知conspirators和2个已知不是conspirators。目前，新的情况有83个人，400个连接（一些包括了不止一个topic），超过21000个字的信息流，15个topics（3个已经确认是怀疑的），7个已知的conspirators，8个不是conspirators。数据见附件Names.xls, Topic.xls, 和Messages.xls。Names.xls包含办公室主要工作人员的名字。Topics.xls包括15个topics的简短描述。考虑到私人保密问题，你的团队没有短信的直接内容。MEssates.xls提供了传递短信的人和短线包含的topic code numbrs之间的联系。为了可视化信息流，图2提供了人员和短信连接的网络模型。这种情况下，短信的topic没有像图1那样显示在图中。这些topic numbers和描述见Messages.xls和Topic.xls。Figure 2: Visual of the network model of the 83 people (nodes) and 400 messages between thesepeople (links).Requirements:Requirement 1: So far, it is known that Jean, Alex, Elsie, Paul, Ulf, Yao, and Harvey are conspirators. Also, it is known that Darlene, Tran, Jia, Ellin, Gard, Chris, Paige, and Este are not conspirators. The three known suspicious message topics are 7, 11, and 13. There is more detail about the topics in file Topics.xls. Build a model and algorithm to prioritize the 83 nodes by likelihood of being part of the conspiracy and explain your model and metrics. Jerome, Delores, and Gretchen are the senior managers of the company. It would be very helpful to know if any of them are involved in the conspiracy.要求1：到目前为止，已知Jean, Alex, Elsie, Paul, Ulf, Yao和Harvey是阴谋者，且Darlene,Tran , Jia, Ellin, Gard , Chris, Paige和Este不是阴谋者。3个可疑信息主题是7,11,13. 关于主题的更多细节在文件Topic.xls中。请建立模型和算法对83个点按构成阴谋组成部分的可能性大小进行排序并解释你的模型。已知Jerome, Delores和Gretchen是公司的高管，如果能知道他们三个人中任何一个涉及阴谋，这也将是非常有益的信息。Requirement 2: How would the priority list change if new information comes to light that Topic 1 is also connected to the conspiracy and that Chris is one of the conspirators? 要求2：如果将Topic 1与阴谋联系起来，并且知道Chris是阴谋者之一，是否能够得到新的信息，对你在要求1中的排序会有怎样的改变。Requirement 3: A powerful technique to obtain and understand text information similar to this message traffic is called semantic network analysis; as a methodology in artificial intelligence and computational linguistics, it provides a structure and process for reasoning about knowledge or language. Another computational linguistics capability in natural language processing is text analysis. For our crime busting scenario, explain how semantic and text analyses of the content and context of the message traffic (if you could obtain the original messages) could empower your team to develop even better models and categorizations of the office personnel. Did you use any of these capabilities on the topic descriptions in file Topics.xls to enhance your model?要求3：用来获取和理解与信息流类似的文本信息问题有一个有力的工具称为语言网络分析，作为人工智能和计算机语言领域的一方法，它提供了获取知识或语言的一个框架和过程。在自然语言进化中另一个计算机语言工具是文本分析。在我们的问题中，请解释如何利用semantic and text analysis of the content及信息流（假如你能得到原始信息）改进你们的模型和对办公人员的分类。试问你们是否利用Topics.xls中主题描述中的信息改进了模型？Requirement 4: Your complete report will eventually go to the DA so it must be detailed and clearly state your assumptions and methodology, but cannot exceed 20 pages of write up. You may include your programs as appen