1. Biomathematics: Using Graph Models for High School DIMACS Conference on Linking Mathematics & Biology In High Schools 29 April 2005 L. Charles (Chuck) Biehl The Charter School of Wilmington Wilmington, DE cbiehl@charterschool.org Biomathematics: Using Graph Models

2. What Are These?

3. The phylogeny and classification of life as proposed by Haeckel in 1866 Haeckel’s tree

4. A Possible Evolutionary Phylogenetic Tree http://www.talkorigins.org/faqs/comdesc

5. Accugenix Tree Report

6. A Sample of a Computed Tree Leaves are species – internal vertices minimize differences

7. Constructing Phylogenetic Trees David E. Joyce, Dept. of Mathematics & Computer Science, Clark University Actual Tree (yellow) Distance matrix (pink) Reconstructed tree from mutations (blue)

8. Epidemic Model: Basic Majority Process Model

9. Digraph as a State Model for Smallpox (Kaplan-Craft-Wein 2002)

10. Dynamic Programming for Path Problems A 3 2 1 4 7272 3333 6 2 5 6565 3333 5252 4646 3 4 6 8282 3232 7575 1414 3 3 4 1111 2525 6767 3131 4 3 5 6 3 21 3 B

11. Dynamic Programming for String Alignment Image Source: Christopher Lewis, bioinformatics analyst, Saskatoon Research Centre of Agriculture & Agri-food Canada

12. Voronoi Diagram model for Cell Growth, Mitosis, and Interaction http://biology.beloit.edu/students/zdravko/vor_gallery_bio.html

13. The Internet (at night)

14. Protein-Protein Interactions Pathmap ™ Protein-Protein Interaction Data Set for Yeast http://www.protana.com

15. Proteome* Interaction Network (*Prote[in] + [Gen]ome)