Tutor: Prof. Lucia PomelloSupervisors: Prof. Giancarlo Mauri
Dr. Luciano Milanesi
PhD Thesis Proposal
Membrane systems: a framework for stochastic processes analysis and modelling
Dr. Ettore MoscaBioinformatics
Istituto Tecnologie Biomediche – CNR
Natural computing
A field of research which tries to imitate nature in the way it computes
Evolutionary computing
Neural computing
DNA computing
Membrane computing
• Evolution
• Neurons, synapses
• DNA, enzymes
• Cell(s)
P systems: definition)),,(),...,,(,...,,,( 0111 iRRwwV nnn
1. V is an alphabet, elements are called objects2. µ is a membrane structure of degree n3. wi, are strings from V* representing multisets over V4. 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 })
5. i0 specifies the output membrane
(G. Păun, 2000)
Evolution: at each step apply all the possible rules in parallel and non-deterministically
P systems: facts
Several variants exist:• cell like: symport and antiport, active membranes, rewriting, splicing• cells are nodes of an arbitrary graph: tissue, population, neuronalApplications (Ciobanu, Pérez-Jiménez, Paŭn, 2006):• Computer science: computer graphics, sorting, criptography, evolutionary
computing, computationally hard problems• Linguistic: parsing • Bio-applications: molecular pathways, cell populations
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)
39 open problems and research topics (G. Păun, 2007)
Research proposal topics
1. Introduce the spatial ingredient (physical dimensions or spatial coordinates) in membrane systems
• Up to now: space included only topologically
2. 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”.
3. Q31: “compare P systems with other distributed computing systems”
• gain alredy developed theory for the analysis of certain system properties
(G. Păun, 2007)
Applications: systems biology
“However, not planned at beginning, membrane computing turned out to be a useful framework for represent biological processes”
Molecular biology
Biochemistry
Physiology
(Life Sciences)
Computer Science
Physics
Mathematics
Engeenering
Inherent compartimentalization
Discreteness
Stochasticity
Easy extensibility (modularity)
Non-linear behaviuor
Direct understandability
Easy programmability
(G. Păun and Pérez-Jiménez, 2006)
A DYNAMICAL APPROACH IS REQUIRED
How to simulate the evolution?How to analyse the dynamics of a
stochastic, discrete system?
USEFUL PROPERTIES
(G. Păun and J. Romero-Campero, 2006)
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
Project Planp-systems formalization (space, fuzzy)
Compare P systems with other formal
methods
Parameterestimation
EA
Model checkingSensitivity Analysis
Analysis of dynamics
implementation of the simulation algorithm (space, fuzzy)
Selection of a biological process(application)
P systems implementation
Is the model fitted to data? noyes
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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