8

Summary

Throughout the workshop there was much lively discussion among the participants. It was apparent from many of the talks and mentioned explicitly during the discussions that there has been a big cultural change in mathematics and statistics in recent years. In the past, theory and models would often be developed before data were collected; that is a viable approach when dealing with fields of study that are grounded in fundamental mathematical laws (e.g., Maxwell’s equations or the Navier-Stokes equation). Now, in many areas that are attracting the attention of mathematical scientists, data drive the development of theory. This is certainly true for mathematical sciences research related to the biomedical sciences, and the resulting intellectual stimulation will likely have far-reaching effects on mathematical sciences research.

The workshop’s discussions identified three general ways in which the mathematical sciences have benefited biomedical research:

  • By suggesting insights that could not be observed directly (such as “viewing” the interior of the beating heart via a simulation);

  • By classifying and describing generic features and processes of biomedical systems; and

  • By suggesting how some biomedical systems work and what their limitations are (through tools such as dynamical analysis of mathematical models that emulate cell signaling networks).

The workshop also made clear that there is a great opportunity for many more mathematical scientists to become involved in cross-disciplinary research with biomedical scientists. A major challenge to be overcome before that interface reaches its potential is for more mathematical scientists to be exposed in depth to research in the biomedical sciences and given the opportunity to contribute. As research funding becomes increasingly available, the limiting factor becomes the availability of information about the mathematical formulations of important biomedical research. It is hoped that this workshop summary helps address that need.



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Making Sense of Complexity: Summary of the Workshop on Dynamical Modeling of Complex Biomedical Systems 8 Summary Throughout the workshop there was much lively discussion among the participants. It was apparent from many of the talks and mentioned explicitly during the discussions that there has been a big cultural change in mathematics and statistics in recent years. In the past, theory and models would often be developed before data were collected; that is a viable approach when dealing with fields of study that are grounded in fundamental mathematical laws (e.g., Maxwell’s equations or the Navier-Stokes equation). Now, in many areas that are attracting the attention of mathematical scientists, data drive the development of theory. This is certainly true for mathematical sciences research related to the biomedical sciences, and the resulting intellectual stimulation will likely have far-reaching effects on mathematical sciences research. The workshop’s discussions identified three general ways in which the mathematical sciences have benefited biomedical research: By suggesting insights that could not be observed directly (such as “viewing” the interior of the beating heart via a simulation); By classifying and describing generic features and processes of biomedical systems; and By suggesting how some biomedical systems work and what their limitations are (through tools such as dynamical analysis of mathematical models that emulate cell signaling networks). The workshop also made clear that there is a great opportunity for many more mathematical scientists to become involved in cross-disciplinary research with biomedical scientists. A major challenge to be overcome before that interface reaches its potential is for more mathematical scientists to be exposed in depth to research in the biomedical sciences and given the opportunity to contribute. As research funding becomes increasingly available, the limiting factor becomes the availability of information about the mathematical formulations of important biomedical research. It is hoped that this workshop summary helps address that need.