Hierarchical coordinate systems for understanding complexity and its evolution, with applications to genetic regulatory networks

Artificial Life

Volumn 14, Issue 3, 2008, Pages 299-312

  Egri Nagy, Attila ^a   Nehaniv, Chrystopher L ^a  

^a UNIVERSITY OF HERTFORDSHIRE   (United Kingdom)

Author keywords

Algebraic biology; Computational biology; Coordinate systems; Finite state automata; Krohn Rhodes theory

Indexed keywords

AUTOMATA THEORY; ESCHERICHIA COLI; FINITE AUTOMATA; HIERARCHICAL SYSTEMS; ROBOTS;

CO-ORDINATE SYSTEM; COMPUTATIONAL BIOLOGY; EVOLUTIONARY PROCESS; GENETIC REGULATORY NETWORKS; HIERARCHICAL DECOMPOSITIONS; HOLONOMY DECOMPOSITION; KROHN-RHODES THEORY; STRUCTURAL COMPLEXITY;

COMPLEX NETWORKS;

ESCHERICHIA COLI PROTEIN;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; BIOLOGICAL MODEL; BIOLOGY; CHEMISTRY; COMPUTER SIMULATION; ESCHERICHIA COLI; EVOLUTION; GENE; GENE REGULATORY NETWORK; LACTOSE OPERON; METABOLISM; MOLECULAR EVOLUTION; SYSTEMS BIOLOGY; THEORETICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; ESCHERICHIA COLI; ESCHERICHIA COLI PROTEINS; EVOLUTION; EVOLUTION, MOLECULAR; GENE REGULATORY NETWORKS; GENES; LAC OPERON; MODELS, BIOLOGICAL; MODELS, GENETIC; MODELS, THEORETICAL; SYSTEMS BIOLOGY;

EID: 50649115542     PISSN: 10645462     EISSN: 15309185     Source Type: Journal    
DOI: 10.1162/artl.2008.14.3.14305     Document Type: Article

References (30)

1. Chung, F. R. K. (1997). Spectral graph theory. American Mathematical Society.
2. Crutchfield, J. P. (1994). The calculi of emergence: Computation, dynamics, and induction. Physica D, 75, 11-54.
3. Davidson, E. H. (2006). The regulatory genome: Gene regulatory networks in development and evolution. San Diego, CA: Academic Press.
4. Devadas, S., & Newton, A. R. (1989). Decomposition and factorization of sequential finite state machinces. IEEE Transactions on Computer-Aided Design, 8, 1206-1217.
5. Dömösi, P., & Nehaniv, C. L. (2005). Krohn-Rhodes theory and complete classes. Algebraic theory of automata networks: An introduction (Chap. 3, pp. 73-109). SIAM.
6. Dömösi, P., & Nehaniv, C. L. (2005). Algebraic theory of automata networks: An introduction. SIAM.
7. Egri-Nagy, A. (2005). Algebraic hierarchical decomposition of finite state automata - A computational approach. Ph.D. thesis, School of Computer Science, University of Hertfordshire, UK.
8. Egri-Nagy, A., & Nehaniv, C. L. (2003). Formal models of understanding. http://graspermachine.sf.net.
9. Egri-Nagy, A., & Nehaniv, C. L. (2004). Algebraic hierarchical decomposition of finite state automata: Comparison of implementations for Krohn-Rhodes theory. In Implementations and Applications of Automata CIAA 2004 (pp. 315-316). Berlin: Springer.
10. Egri-Nagy, A., & Nehaniv, C. L. (2005). Cycle structure in automata and the holonomy decomposition. Acta Cybernetica, 17, 199-211.
11. Eilenberg, S. (1976). Automata, languages and machines, Vol. B. San Diego, CA: Academic Press.
12. Ginzburg, A. (1968). Algebraic theory of automata. San Diego, CA: Academic Press.
13. Kauffman, S. A. (1969). Metabolic stability and epigenesis in randomly connected genetic nets. Journal of Theoretical Biology, 22, 437-467.
14. Knabe, J. F., Nehaniv, C. L., Schilstra, M. J., & Quick, T. (2006). Evolving biological clocks using genetic regulatory networks. In L. M. Rocha, L. S. Yaeger, M. A. Bedau, D. Floreano, R. L. Goldstone, & A. Vespignani (Eds.), Proceedings of the Artificial Life X Conference (pp. 15-21). Cambridge, MA: MIT Press.
15. Krohn, K., & Rhodes, J. (1965). Results on finite semigroups derived from the algebraic theory of machines. Proceedings of the National Academy of Sciences of the USA, 53, 499-501.
16. Krohn, K., & Rhodes, J. (1965). Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines. Transactions of the American Mathematical Society, 116, 450-464.
17. Krohn, K., Rhodes, J. L., & Tilson, B. R. (1968). The prime decomposition theorem of the algebraic theory of machines. In M. A. Arbib (Ed.), Algebraic theory of machines, languages, and semigroups (Chap. 5, pp. 81-125). San Diego, CA: Academic Press.
18. Lenaerts, T., Chu, D., & Watson, R. (2005). Dynamical hierarchies. Artificial Life, 11, 403-405.
19. Nehaniv, C. L. (2000). Measuring evolvability as the rate of complexity increase. In C. C. Maley & E. Boudreau (Eds.), Artificial Life 7 Workshop proceedings, pp. 55-57.
20. Nehaniv, C. L., & Rhodes, J. L. (1999). On the mamer in which biological complexity may grow. In Mathematical and Computational Biology (pp. 93-102). American Mathematical Society.
21. Nehaniv, C. L., & Rhodes, J. L. (2000). The evolution and understanding of hierarchical complexity in biology from an algebraic perspective. Artificial Life, 6, 45-67.
22. Peleg, M., Rubin, D., & Altman, R. B. (2005). Using Petri net tools to study properties and dynamics of biological systems. Journal of the American Medical Informatics Association, 12, 181-199.
23. Ptashne, M. (1992). A genetic switch: λ and higher organisms, 2nd ed. London: Blackwell Publishers..
24. Ptashne, M., & Gann, A. (2001). Genes and signals. Cold Spring Harbor Laboratory Press.
25. Rhodes, J. L. (in press). Applications of automata theory and algebra via the mathematical theory of complexity to finite-state physics, biology, philosophy, and games. Singapore: World Scientific Press. (Original version: University of California at Berkeley, Mathematics Library, 1971.)
26. Robinson, D. J. S. (1995). A course in the theory of groups, 2nd ed. Berlin: Springer.
27. Schrödinger, E. (1967). Statistical thermodynamics. Cambridge, UK: Cambridge University Press.
28. Tilson, B. (1976). Complexity of semigroups and morphisms. In S. Eilenberg (Ed.), Automata, languages and machines (Vol. B, Chap. XII). San Diego, CA: Academic Press.
29. Zeiger, H. P. (1967). Cascade synthesis of finite state machines. Information and Control, 10, 419-433. Erratum, 11(4), 471.
30. Zeiger, H. P. (1968). Cascade decomposition using covers. In M. A. Arbib (Ed.), Algebraic theory of machines, languages, and semigroups (Chap. 4, pp. 55-80). San Diego, CA: Academic Press.