《备战美国数学建模竞赛与论文剖析》由会员分享，可在线阅读，更多相关《备战美国数学建模竞赛与论文剖析（36页珍藏版）》请在金锄头文库上搜索。
1、数学建模竞赛讲座,1. 美国数学建模竞赛概况 2. 竞赛论文剖析 3. 一些建议,主讲: 龚劬,美国数学建模竞赛概况,1 美国大学生数学建模竞赛（MCM）, 始于1985年 学生三人一组在四天之内合作完成一个实际问题 参赛者来自美国、中国、加拿大、德国、英国以及印尼等国家或地区 我国于1989年起组织大学生参加MCM 我校从1994年开始组织学生参加MCM 2006年我校共有8个队参赛，3个队获一等奖、2个队获二等奖和3个队获三等奖。,2 部分MCM/ICM题目, 指纹唯一吗？（2004A) 飓风来临时的疏散问题（2001B） 信息技术安全问题（2004C) 核磁共振切片成像(1998A) 伽
2、玛刀治疗计划(2003B) 机场安全检查(2003C) 特技表演(2003A) 公园快速通道系统（2004B) 风与喷泉(2002A) 过路收费站(2005B) 灌木蜥蜴问题(2002C),3 评阅,Judging will be completed by March 31, 2008. The solutions will be recognized as Successful Participant,Honorable Mention, Meritorious, or Outstanding Winner. You have about 43% chance of being ranked
3、 higher than Successful Participant The first(triage) round Each paper is skimmed by two or three judges,who spend between 5 and 10 minuts each reading the paper. If you survive the triage round, you have about an 80% chance of being ranked higher than Successful Participant.,4 Outstanding Winner,IN
4、FORMS winner The Institute for Operations Research and the Management Sciences (INFORMS) will designate an Outstanding team from each of the three problems as an INFORMS winner SIAM winner The Society for Industrial and Applied Mathematics (SIAM) will designate one Outstanding team from each problem
5、 as a SIAM winner. MAA winner The Mathematical Association of America (MAA) will designate one Outstanding team from each problem for the MCM as a MAA winner.,竞赛论文剖析,1 Summary (The most important part of the paper ),provide a brief overview of the problem describe clearly the approach taken to model
6、ing the problem state the most important results and conclusions. mention any recommendations directly relevant to the problem. If you did anything creative, it must be here.,竞赛论文剖析,1 Summary,特色和创新之处必须在这里强调（稍夸张地）。 长度：理想长度很难说，必须包括上述要点，但简洁也非常重要。一般掌握在半页至2/3页左右。 是文章最重要的部分。要保证准确、简明、条理清晰，突出特色和创新点。 注：评阅时将首
7、先根据摘要和论文整体结构及概貌对论文优劣进行初步筛选。,A good example of a clear,concise and thorough summary (2004A) Fingerprint identification depends on the assumption that a persons fingerprints are unique. We assess the truth of this assumption by calculating the total number of distinct fingerprints. We assume accurate
8、fingerprints (ignoring procedural error) are defined by 12 points of detail or minutiae.The number of distinct fingerprints depends also on the number of potential positions of these minutiae. Two historical methods and a geometric analysis estimate there to be 1,400 positions, a figure confirmed by
9、 our algorithm for counting ridges in a fingerprint. We create two models to estimate the number of unique fingerprints: One model computes fingerprints as arrangements in minutiae; the other extrapolates the number of fingerprints from the Shannon entropy of the information that defines a fingerpri
10、nt.,A good example of a clear,concise and thorough summary (2004A) These two models agree to within an order of magnitude that there are 51033 unique fingerprints, a compelling validation of our general approach. To handle the large number of fingerprints, we implement an approximation for the calcu
11、lation of probabilities. Given a cumulative world population of 120 billion, the probability of two people ever having the same fingerprint is 1.4 10-6. The probability of two humans living today sharing a fingerprint is 3.5 10-15 , which suggests that fingerprints are a theoretically more reliable
12、method of identification than DNA analysis, which has a false positive probability of 10-9. None of these calculations take into account procedural errors.,竞赛论文剖析,2 Introduction,重述问题，用自己的语言陈述你将要做的工作 根据自己的理解，用自己的语言清楚简明地阐述问题的背景、条件和要求。 Example 1： The possibility of duplicate fingerprints,or fingerprint
13、s likely to be mistaken for each other, has led to recent criticism of fingerprints as a means of identification. The key problem is: How many distinct fingerprints are there? We approach this problem with two general methods: “building” a fingerprint from the ground up, using different models; and
14、using the information content of a fingerprint,到2004A.doc,Example 2： Introduction We develop some models, a pattern model, a shape model and a practical model, to analyze the uniqueness of fingerprints and odds of misidentification by fingerprint evidence. Through comparison, we also develop a seque
15、nce model to analyze odds of misidentification by DNA evidence. Noticing that there are several patterns of fingerprints, and the ridges and furrows in fingerprints are different from one to another, we use these characteristics to develop our model. Considering the incompleteness of the fingerprint
16、s, we analyze the probability of misidentification of fingerprints. Based on our limited knowledge about DNA and genetics, we create a sequence model to calculate the odds. Ignoring those complicated biochemical restrictions and biomolecular requirements, we establish a pure mathematical model relat
17、ed to our problem.,竞赛论文剖析,Example 2： Considering some fundamental assumptions and requirements of both fingerprint and DNA identifications for their accuracy, we propose our opinions on this identification problem. Background Fingerprints of humankind are formed in the period of a fetus. We know tha
18、t they are decided genetically by genes which are inherited from their parents. The ridges and furrows formed the patterns or features of fingerprints, and it is commonplace belief that everyone s fingerprints are unique. Even twinborn babies, their fingerprints are different. Till now, there isnt any case that two persons, either Chinese or American people, have the same fingerprints exactly all over the world. Actually, nobody has found any related record appeared in any governments in the processes of fingerprint management, identification, check and recognition.,
