search that addresses intrinsic characteristics of biological systems that reappear at many levels of biological organization: high dimensionality, heterogeneity, robustness, and the existence of multiple spatial and temporal scales.

The committee attempted to identify subdisciplines of mathematics in which broadly based advances would be particularly likely to enhance biological research. However, it concluded that since critical advances had come from nearly every subdiscipline within the mathematical sciences, any such prognostication would be mere guesswork. The committee believes that excellent biology research can be achieved only by answering key questions within that discipline. Specifying a priori the tools to be developed inverts that goal. However, it is clear that if DOE’s applied mathematics program is to contribute to computational biology, it should focus on research that is linked to the intrinsic characteristics of biological systems that reappear at many levels of biological organization: high dimensionality, heterogeneity, robustness, and the existence of multiple spatial and temporal scales. All areas of biology will benefit from improved mathematical representations of biological systems.

STRUCTURE OF THIS REPORT

Future biologists will use an enormous variety of mathematical tools. What will be distinctive about their research are the problems they aspire to solve rather than the tools they use to solve them. For this reason, this report is organized primarily around biological, rather than mathematical, themes. Its survey of mathematical challenges in biology, which ranges from molecular to ecological levels of organization, is necessarily cursory. However, the report provides an introduction to the diverse challenges that characterize contemporary applications of mathematics to biology. The daunting task facing policy makers will be to develop mechanisms that encourage the deep integration of mathematics and biology needed for sustained progress across this vast, exciting, and rapidly evolving scientific frontier.

REFERENCES

Alizadeh, F., R.M. Karp, D.K. Weisser, and G. Zweig. 1995. Physical mapping of chromosomes using unique probes. J. Comput. Biol. 2: 159-184.


Benzer, S. 1959. On the topology of the genetic fine structure. Proc. Natl. Acad. Sci. U.S.A. 45: 1607-1620.


Lipan, O., and W.H. Wong. 2005. The use of oscillatory signals in the study of genetic networks. Proc. Natl. Acad. Sciences U.S.A. 10.1073.


Mayr, E. 1982. The Growth of Biological Thought. Cambridge, Mass.: Belknap Press.



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