数学中国w, madio,net Judges'Commentary 171 that would more accurately assess a healthcare system's efficiency or fair ness. Others arranged their metrics into groups that would shed light on the analysis. Another way in which teams distinguished themselves in this area was by exploring the tradeoffs between metrics and their limitations. For example, one team noted that although the lifespan of the population was an would take a long time to impact the overall lifespan of the population. Modeling and Assumptions: The most effective papers made their as sumptions explicitly from the scientific foundation that they developed in order to build their models. Models ranged widely in complexity, with factor analysis the most popular approach to synthesizing metrics. It was important that the modeling process was well formulated and robust; but unfortunately, some papers had wonderful models that offered little expla- nation of how the model functioned or provided little use of the results in the analysis. The ability to use the model to make conclusions and recom- mendations about healthcare systems distinguished the Outstanding papers regardless of model choice Analysis/Reflection: Successful papers discussed how their models ad dressed issues and tasks uf improving the healthcare systen in a cuntry. The later requirements of the project were often not addressed, or only su- ter than another. However, they did not delve into why one country scored higher or to address whether the result was meaningful. In some cases, the final task of restructuring a healthcare system was given very little at- tention. The best papers used the results of their model to support their recommendations for changes in a healthcare system. Communication: Theability to communicateeffectively really distinguished the best papers from the others. In some cases, the mathematical model was presented with little or no explanation: so, while the work appeared promis- g judges could not follow the exposition or determine how the model was sed to address the issues. The judges noted several very specific things that made papers stand out, including presenting the work clearly and concisely and effectively connecting the science to the modeling process. Some pa pers described the healthcare system and issues well but then lost thatthread as they began the modeling process. Additionally, some papers were dis- jointed, possibly because different team members wrote the various sections without ensuring continuity throughout the document数学中国 www.madio.net