备战美国数学模建竞赛和论文剖析.ppt

数学建模竞赛讲座;美国数学建模竞赛概况 ;2 部分MCM/ICM题目;3 评阅;4 Outstanding Winner;竞赛论文剖析;竞赛论文剖析;A good example of a clear,concise and thorough summary (2004A) Fingerprint identification depends on the assumption that a person’s fingerprints are unique. We assess the truth of this assumption by calculating the total number of distinct fingerprints. We assume accurate 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 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 fingerprint. ;A good example of a clear,concise and thorough summary (2004A) These two models agree to within an order of magnitude that there are 5?1033 unique fingerprints, a compelling validation of our general approach. To handle the large number of fingerprints, we implement an approximation for the calculation 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 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;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 misident