数学建模美国优秀2004a.pptx

2004 MCM-A; It is a commonplace belief that the thumbprint of every human who has ever lived is different. Develop and analyze a model that will allow you to assess the probability that this is true. Compare the odds (that you found in this problem) of misidentification by fingerprint evidence against the odds of misidentification by DNA evidence.;Can’t Quite Put Our Finger On It; We subdivide a print into a grid of square cells, consider the distribution of ridge features, and calculate probabilities from combinatorial analysis. We make predictions by refining parameters of the model, such as the number of minutiae required for a positive match between two generic prints, and the size of a cell in the main grid. We compare our results to previous studies and discuss the relation to DNA profiling. The simplicity of our model is its key strength. We conclude that it is extremely unlikely that any two randomly selected people have, or have ever had, the same set of fingerprints. Despite the apparently simplistic nature of fingerprinting, it is vastly more reliable in identification than a DNA comparison test.;机动 目录 上页 下页 返回 结束 ;Assumptions;? The probability of a minutia occurring in a grid box is .234 [Osterburg 1977]. ? The orientation of the minutiae was not taken into account by Osterburg; we assign a minutiae one of eight angles, from 0? to 157.5?, in steps of 22.5?. ? When comparing two prints, we know one print arbitrarily well. ? The number of people who have ever lived is [Haub 1995].;The Model Global Analysis Ridge Patterns And Orientation Fields Global analysis concerns ridge patterns, which distinguish prints into six main pattern groups: Arch, Tented Arch, Left Loop, Right Loop, Twin Loop and Whorl. Each pattern is determined by an orientation field, which may have specific stationary points, known as the the delta and the core. If a print contains 0 or 1 delta points and 0 or 1 core points, then it is classi