Abstract
The page rank of a webpage is a numerical estimate of its authority. In Google’s PageRank algorithm the ranking is derived as the invariant probability distribution of a Markov chain random surfer model. The crucial point in this algorithm is the addition of a small probability transition for each pair of states to render the transition matrix irreducible and aperiodic. The same idea can be applied to P systems, and the resulting invariant probability distribution characterizes their dynamical behavior, analogous to recurrent states in deterministic dynamical systems. The modification made to the original P system gives rise to a new class of P systems with the property that their computations need to be robust against random mutations. Another application is the pathway identification problem, where a metabolite graph is constructed from information about biochemical reactions available in public databases. The invariant distribution of this graph, properly interpreted as a Markov chain, should allow to search pathways more efficiently than current algorithms. Such automatic pathway calculations can be used to derive appropriate P system models of metabolic processes.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Alongi, J.M., Nelson, G.S.: Recurrence and Topology. American Mathematical Society (2007)
Altman, A., Tennenholtz, M.: Ranking systems: the PageRank axioms. In: Proc. 6th ACM conference on Electronic Commerce, pp. 1–8 (2005)
Arnold, L.: Random Dynamical Systems. Springer, Heidelberg (1998)
Badii, R., Politi, A.: Complexity. Hierarchical Structures and Scaling in Physics. Cambridge University Press, Cambridge (1997)
Bapat, R.B., Raghavan, T.E.S.: Nonnegative Matrices and Applications. Cambridge University Press, Cambridge (1997)
Bianco, L., Fontana, F., Manca, V.: P systems with reaction maps. Int. J. Found. Comp. Sci. 17, 3–26 (2006)
Brémaud, P.: Markov Chains. Gibbs Fields, Monte Carlo Simulation, and Queues. Springer, Heidelberg (1999)
Brin, S., Page, L.: The anatomy of a large-scale hypertextual Web search engine. Computer Networks and ISDN Systems 30, 107–117 (1998)
Chakrabarti, D., Faloutsos, C.: Graph mining: Laws, generators, and algorithms. ACM Computing Surveys 38, 1–69 (2006)
Ciobanu, G., Păun, G., Pérez-Jiménez, M.J. (eds.): Applications of Membrane Computing. Springer, Heidelberg (2006)
Cordón-Franco, A., Sancho-Caparrini, F.: A note on complexity measures for probabilistic P systems. J. Universal Computer Sci. 10, 559–568 (2004)
Croes, D., Couche, F., Wodak, S.J., van Helden, J.: Inferring meaningful pathways in weighted metabolic networks. J. Mol. Bio. 356, 222–236 (2006)
Epstein, E.: Finding the k shortest paths. SIAM J. Comput. 28, 652–673 (1998)
Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, Heidelberg (1983)
Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins University Press (1996)
Google: Google Technology, http://www.google.com/technology/
Goto, S., Nishioka, T., Kanehisa, M.: LIGAND: chemical database for enzyme reactions. Bioinformatics 14, 591–599 (1998)
Heinrich, R., Schuster, S.: The Regulation of Cellular Systems. Springer, Heidelberg (1996)
Huss, M., Holme, P.: Currency and commodity metabolites: their identification and relation to the modularity of metabolic networks. IET Syst. Biol. 1, 280–285 (2007)
Kamvar, S., Haveliwala, T., Golub, G.: Adaptive methods for the computation of PageRank. Linear Algebra Appl. 386, 51–65 (2004)
Kanehisa, M., Araki, M., Goto, S., Hattori, M., et al.: KEGG for linking genomes to life and the environment. Nucleic Acids Research 484, D380–D484.(2008)
Karp, P.D., Riley, M., Saier, M., Paulsen, I.T., et al.: The EcoCyc and MetaCyc databases. Nucleic Acids Research 28, 56–59 (2000)
Kauffman, K.J., Prakash, P., Edwards, J.S.: Advances in flux balance analysis. Current Opinion in Biotechnology 14, 491–496 (2003)
Klipp, E., Herwig, R., Kowald, A., Wierling, C., et al.: Systems Biology in Practice. Wiley-VCH, Chichester (2005)
Kuffner, R., Zimmer, R., Lengauer, T.: Pathway analysis in metabolic databases via differential metabolic display (DMD). Bioinformatics 16, 825–836 (2000)
Langville, A.N., Meyer, C.D.: Deeper inside PageRank. Internet Math. 1, 335–380 (2004)
Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (1995)
Ma, N., Guan, J., Zhao, Y.: Bringing PageRank to the citation analysis. Information Processing & Management 44, 800–810 (2008)
Manca, V., Bianco, L.: Biological networks in metabolic P systems. BioSystems 91, 489–498 (2008)
Muskulus, M.: Identification of P system models assisted by biochemical databases. In: Ibarra, O.H., Sosík, P. (eds.) Prague International Workshop on Membrane Computing, Preliminary Proc., pp. 46–49 (2008)
Muskulus, M., Besozzi, D., Brijder, R., Cazzaniga, P., et al.: Cycles and communicating classes in membrane systems and molecular dynamics. Theoretial Computer Sci. 372, 242–266 (2007)
Noirel, J., Ow, S.Y., Sanguinetti, G., Jaramillo, A., et al.: Automated extraction of meaningful pathways from quantitative proteomics data. Briefings in Functional Genomics and Proteomics (in press)
Page, L., Brin, S., Motwani, R., Winograd, T.: The PageRank citation ranking. Bringing order to the web. Technical Report, Stanford University (1998), http://dbpubs.stanford.edu:8090/pub/1999-66
Păun, G.: Computing with membranes. J. Computer System Sci. 61, 108–143 (2000)
Păun, G.: Membrane Computing. An Introduction. Springer, Heidelberg (2002)
Pescini, D., Besozzi, D., Mauri, G., Zandron, C.: Dynamical probabilistic P systems. Intern. J. Found. Comp. Sci. 17, 183–204 (2006)
Romero-Campero, F.J., Pérez-Jiménez, M.J.: Modelling gene expression control using P systems. The Lac operon, a case study. Biosystems 91, 438–457 (2008)
Vise, D., Malseed, M.: The Google Story. Random House (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Muskulus, M. (2009). Applications of Page Ranking in P Systems. In: Corne, D.W., Frisco, P., Păun, G., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2008. Lecture Notes in Computer Science, vol 5391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95885-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-95885-7_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-95884-0
Online ISBN: 978-3-540-95885-7
eBook Packages: Computer ScienceComputer Science (R0)