Opportunities for the Mathematical Sciences

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Table of Contents
Preface
Summary Article
  Introduction
  Models and Simulations
  Computing with Large Data Sets
  Geometrization of Topology and Physics
  Noise and Randomness
  Nonlinearity
  Beyond Fermat
  Mathematics for Biology and Medicine
  Information Technology
Individual Contributions
List of Contributors with Affiliations


Summary Article

Mathematics -- The Science of Patterns and Algorithms

Mathematics for Biology and Medicine

Biology and medicine are poised to climb the twin peaks of understanding the life process and greatly improving human health. Success of these efforts depends on the increasing involvement of the mathematical sciences. Combinatorics and statistics have already made essential contributions to the rapid and successful sequencing of the human genome. Obtaining the DNA sequence is just the first step in computing the secrets of life; decoding the meaning of the sequence poses serious long-term scientific and mathematical challenges. We must design new methods of exploration and analysis that combine the power and precision of both biology and mathematics. At the cellular level, we must find both the genes which encode for currently unknown proteins and the non-coding DNA regions which regulate the expression of these new genes. This step will involve pattern recognition, signal processing, database mining, statistical methods both exploratory and confirmatory, and new biomathematical cryptology techniques many of which have yet to be invented. After discovering a new protein, we must determine its function, regulation, and role in a cascade network of interaction with other proteins. This will involve comparison of characteristics of the unknown protein to those of known proteins, both human and non-human. This involves measurement of similarity of DNA sequences (coding and regulatory), similarity of spatial geometry of native folded states, similarity of regulation patterns using microarray chips, and the establishment of cause and effect relationships between the many actors in these processes. New mathematical and statistical ideas are required for this step: we need new biologically relevant similarity measures of 1D sequences, 3D geometry, clustering algorithms and other statistical analysis methods for expression vectors of very high dimension. At the macroscopic level, a fundamental problem in medicine is to define and understand ranges of parameters which correspond to "normal" anatomy and function for an organ, a necessary first step before understanding and treating the "abnormal." Due to high variability, comparison of anatomical and functional information across individuals and groups requires new mathematical and statistical models as well as highly sophisticated computational algorithms. A goal in medicine is to have normal organs and organ systems "in silico," allowing non-invasive computational comparison between subject and template, enhancing detection of disease states and design of treatment. The mathematical sciences have played and will continue to play an essential role in the team effort to understand the complexities of biology and harness this understanding to improve human health.

 

Last Modified:
Jan 24, 2013
 

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