Judge's Commentary 339 here were a number of mathematically rigorous papers that started with a partial differential equation, derived one of the macroscopic formulas, de termined appropriate values for the constants, calculated the density giving the optimal flow, and incorporated this flow value into an algorithm for de- termining evacuation time. In spite of the impressive mathematics, if no plan was given to regulate traffic density, the team missed an important concept of the mCm: the realistic application of a mathematical solution to a real-world problem One key to successful model building is to adapt existing theory or models properly to the problem at hand, so judges see little difference between deriv ing these equations from first principles and researching them from a book. Whether derived or researched, it is imperative to demonstrate an understand ing of the model you are using The judging No paper completely analyzed all 6 questions, so the judges were intrigued by what aspects of the problem that a team found most important and /or interesting. We were similarly interested in determining what aspects of the problem a team found least relevant and how they divided their effort among the remaining questions. To be considered Outstanding, a paper had to meet several minimum requirements. the paper must address all 6 questions, all required elements(e. g, the newspaper article)must be included, and some sort of validation of the model must be included We were also particularly interested in how teams modeled the i-26/I-95 inter- change and the congestion problem in Columbia. Many teams chose to treat Columbia as the terminal point of their model and assumed that all cars arriving there would be absorbed without creating backups To survive the cut between Honorable Mention and Meritorious, a paper had to have a unique aspect on some portion of the problem. Two examples that come to mind are a unique modeling approach or some aspect of the problem analyzed particularly well. Thus, papers that failed to address all questions or had a fatal weakness that prevented their model from being extended could still be considered Meritorious. The Meritorious papers typically had very good insight into the problem, but deficiencies as minor as missing parame ter descriptions or model implementation details prevented them from being considered OutstandingJudgeís Commentary 339 There were a number of mathematically rigorous papers that started with a partial differential equation, derived one of the macroscopic formulas, de￾termined appropriate values for the constants, calculated the density giving the optimal flow, and incorporated this flow value into an algorithm for de￾termining evacuation time. In spite of the impressive mathematics, if no plan was given to regulate traffic density, the team missed an important concept of the MCM: the realistic application of a mathematical solution to a real-world problem. One key to successful model building is to adapt existing theory or models properly to the problem at hand, so judges see little difference between deriv￾ing these equations from first principles and researching them from a book. Whether derived or researched, it is imperative to demonstrate an understand￾ing of the model you are using. The Judging No paper completely analyzed all 6 questions, so the judges were intrigued by what aspects of the problem that a team found most important and/or interesting. We were similarly interested in determining what aspects of the problem a team found least relevant and how they divided their effort among the remaining questions. To be considered Outstanding, a paper had to meet several minimum requirements: • the paper must address all 6 questions, • all required elements (e.g., the newspaper article) must be included, and • some sort of validation of the model must be included. We were also particularly interested in how teams modeled the I-26/I-95 inter￾change and the congestion problem in Columbia. Many teams chose to treat Columbia as the terminal point of their model and assumed that all cars arriving there would be absorbed without creating backups. To survive the cut between Honorable Mention and Meritorious, a paper had to have a unique aspect on some portion of the problem. Two examples that come to mind are a unique modeling approach or some aspect of the problem analyzed particularly well. Thus, papers that failed to address all questions or had a fatal weakness that prevented their model from being extended could still be considered Meritorious. The Meritorious papers typically had very good insight into the problem, but deficiencies as minor as missing parame￾ter descriptions or model implementation details prevented them from being considered Outstanding