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PhD Thesis Proposal

PhD Thesis Proposal. Tutor: Prof. Lucia Pomello Supervisors: Prof. Giancarlo Mauri Dr. Luciano Milanesi. Membrane systems: a framework for stochastic processes analysis and modelling. Dr. Ettore Mosca Bioinformatics Istituto Tecnologie Biomediche – CNR. Natural computing.

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PhD Thesis Proposal

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  1. PhD Thesis Proposal Tutor: Prof. Lucia Pomello Supervisors: Prof. Giancarlo Mauri Dr. Luciano Milanesi Membrane systems: a framework for stochastic processes analysis and modelling Dr. EttoreMosca Bioinformatics Istituto Tecnologie Biomediche – CNR

  2. Natural computing A field of research which tries to imitate nature in the way it computes • Evolution • Neurons, synapses • DNA, enzymes • Cell(s) Evolutionary computing Neural computing DNA computing Membrane computing

  3. P systems: definition • V is an alphabet, elements are called objects • µ is a membrane structure of degree n • wi, are strings from V* representing multisets over V • Ri, are finite sets of evolution rules over V; ρi is a partial order relation over Ri; • Evolutio n rule is a pair (u,v), u v, u is a string over V and v=v’ or v=v’δ • v’ is a string over (V x {here,out}) U (V x { inj|1 ≤ j ≤ n }) • i0 specifies the output membrane Evolution: at each step apply all the possible rules in parallel and non-deterministically (G. Păun, 2000)

  4. P systems: facts Initial studies related to area of formal languages, grammars and computational models. “a fast Emerging Research Front in Computer Science” (2003, Thompson Institute for Scientific Information) • Several variants exist: • cell like: symport and antiport, active membranes, rewriting, splicing • cells are nodes of an arbitrary graph: tissue, population, neuronal • Applications (Ciobanu, Pérez-Jiménez, Paŭn, 2006): • Computer science: computer graphics, sorting, criptography, evolutionary computing, computationally hard problems • Linguistic: parsing • Bio-applications: molecular pathways, cell populations 39 open problems and research topics (G. Păun, 2007)

  5. Research proposal topics • Introduce the spatialingredient (physical dimensions or spatial coordinates) in membrane systems • Up to now: space included only topologically • Q35: “define and examine P systems with ‘approximate’ components, in terms of probabilistic, fuzzy, or rough set theory. [...] this direction of research [...] is expected to have an important development and significant applications”. • Q31: “compare P systems with other distributed computing systems” • gain alredy developed theory for the analysis of certain system properties (G. Păun, 2007)

  6. Applications: systems biology SYSTEMS BIOLOGY “However, not planned at beginning, membrane computing turned out to be a useful framework for represent biological processes” Computer Science Physics Mathematics Engeenering Molecular biology Biochemistry Physiology (Life Sciences) (G. Păun and Pérez-Jiménez, 2006) USEFUL PROPERTIES Inherent compartimentalization Discreteness Stochasticity Easy extensibility (modularity) Non-linear behaviuor Direct understandability Easy programmability A DYNAMICAL APPROACH IS REQUIRED How to simulate the evolution? How to analyse the dynamics of a stochastic, discrete system? (G. Păun and J. Romero-Campero, 2006)

  7. Stochastic Discrete Systems • Simulation • Quantitative simulation based on modifications of the Stochastic Simulation Algorithm (SSA) (D.T. Gillespie, 1977) • Analysis of the dynamics • Repeated simulation with different initial conditions • Reformulate the problem in different modelling framework (s) for which there is the theory already developed

  8. Project Plan p-systems formalization (space, fuzzy) implementation of the simulation algorithm (space, fuzzy) Selection of a biological process (application) Parameter estimation EA P systems implementation Is the model fitted to data? no yes Compare P systems with other formal methods Model checking Sensitivity Analysis Analysis of dynamics

  9. References • G. Păun, 2000, Computing with membranes, Journal of Computer and System Sciences, 61, 108-143 • G. Ciobanu, M. Pérez-Jiménez, G. Paŭn, 2006, Applications of Membrane Computing, Natural Computing Series, ISBN 978-3-540-25017-3 • G. Păun, 2007, Tracing Some Open Problems in Membrane Computing, Romanian Journal of Information Science and Technology, 10,4 • G. Păun and M. Pérez-Jiménez, 2006, Membrane computing: Brief introduction, recent results and applications, Biosystems, 85, 11-22 • D.T. Gillespie, 1977, Exact stochastic simulation of coupled chemical reactions, Journ. Phys. Chem., 81, 2340-2361

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