Current developments on computational modeling using P systems - PowerPoint PPT Presentation

Current developments on computational modeling using P systems Agustín Riscos-Núñez Research Group on Natural Computing Department of Computer Science and Artificial Intelligence University of Seville CiE 2011 - Natural Computing Session June 27- July 2, Sofia, Bulgary A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 1 / 50

Introduction 1 P systems Modeling framework A P system based modeling framework 2 Example: Tritrophic Interactions 3 A software framework for Membrane Computing 4 Simulation algorithms Simulation results 5 Conclusions and future work A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 2 / 50

Introduction 1 P systems Modeling framework A P system based modeling framework 2 Example: Tritrophic Interactions 3 A software framework for Membrane Computing 4 Simulation algorithms Simulation results 5 Conclusions and future work A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 3 / 50

Membrane Computing Multisets of objects Membranes (regions) Rules Objects Membranes Environment Figure: A P system A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 4 / 50

Membrane Computing Machine oriented model. Non-deterministic devices. Two levels of parallelism (objects & membranes). Global clock. Figure: A P system A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 4 / 50

Diversity of definitions Membranes tree-like / tissue-like structure labels, charges, . . . Rules restricting their type (e.g. forbidding dissolution, using only communication, . . . ) controlling applicability (e.g. priorities, alternatives to maximal parallelism, . . . ) A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 5 / 50

Diversity of definitions Membranes tree-like / tissue-like structure labels, charges, . . . Rules restricting their type (e.g. forbidding dissolution, using only communication, . . . ) controlling applicability (e.g. priorities, alternatives to maximal parallelism, . . . ) A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 5 / 50

Diversity of interpretations Generative devices: fixed initial configuration, we collect the outputs of all the non-deterministic computations. Computing devices: given an input (encoded somehow), compute the resulting output multiset. Decision tools: special objects yes and no , s.t. their presence / absence in the output decides whether the given input was accepted by the P system or not. Simulation tools: no halting configuration, the output is the computation. A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 6 / 50

Diversity of interpretations Generative devices: fixed initial configuration, we collect the outputs of all the non-deterministic computations. Computing devices: given an input (encoded somehow), compute the resulting output multiset. Decision tools: special objects yes and no , s.t. their presence / absence in the output decides whether the given input was accepted by the P system or not. Simulation tools: no halting configuration, the output is the computation. A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 6 / 50

Diversity of interpretations Generative devices: fixed initial configuration, we collect the outputs of all the non-deterministic computations. Computing devices: given an input (encoded somehow), compute the resulting output multiset. Decision tools: special objects yes and no , s.t. their presence / absence in the output decides whether the given input was accepted by the P system or not. Simulation tools: no halting configuration, the output is the computation. A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 6 / 50

Diversity of interpretations Generative devices: fixed initial configuration, we collect the outputs of all the non-deterministic computations. Computing devices: given an input (encoded somehow), compute the resulting output multiset. Decision tools: special objects yes and no , s.t. their presence / absence in the output decides whether the given input was accepted by the P system or not. Simulation tools: no halting configuration, the output is the computation. A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 6 / 50

Membrane computing New modeling framework P Systems based modeling framework Ecosystems Other bioprocesses (e.g. at cellular level) Randomness → probabilistic/stochastic strategies Simulation algorithms Reproduce the behaviour of the models Validation Virtual experimentation Software Implements the algorithms GUI for the end-user A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 7 / 50

Modeling ecosystems Validation process REAL-LIFE PROCESS DATA (e.g. an ecosystem) Compare results Carrying out studies/experimets Inspiration Inspiration Run virtual experiments VALIDATED VALIDATION MODEL MODEL Success Fail Simulator A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 8 / 50

Modeling ecosystems Virtual Experiments Check results Suggest Expert virtual experiments Run virtual experiments SELECTED VALIDATED REAL HYPOTHESES FILTER HYPOTHESES EXPERIMENTS MODEL Simulator NEW KNOWLEDGE A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 9 / 50

Modeling ecosystems Desirable properties of a model Relevant Readable Extensible Computationallly tractable P systems fulfill the requirements A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 10 / 50

Modeling ecosystems Desirable properties of a model Relevant Readable Extensible Computationallly tractable P systems fulfill the requirements A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 10 / 50

Modeling real-life ecosystems Some studies within the RGNC Modeling Ecosystems using P systems: The Bearded Vulture, a case study . Cardona et al. LNCS , 5391, 137–156, (2009). P System Based Model of an Ecosystem of the Scavenger Birds . Cardona et al. LNCS , 5957, 182–195, (2010). A Computational Modeling for real Ecosystems based on P systems . Cardona et al. Natural Computing , 10, 39–53 (2011). A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 11 / 50

Introduction 1 P systems Modeling framework A P system based modeling framework 2 Example: Tritrophic Interactions 3 A software framework for Membrane Computing 4 Simulation algorithms Simulation results 5 Conclusions and future work A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 12 / 50

Need to define a new variant of P Systems Cooperation Randomness Communication between environments Membrane polarization A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 13 / 50

A P system based modeling framework A skeleton of an extended P system with active membranes of degree q ≥ 1, (Γ , µ, R ) A probabilistic functional extended P system with active membranes of degree q ≥ 1, taking T time units, Π = (Γ , µ, R , T , { f r : r ∈ R } , M 0 , . . . , M q − 1 ) A multienvironment probabilistic functional extended P system with active membranes of degree ( m , q ) taking T time units, (Σ , G , R E , Γ , µ, R , T , { f rj : r ∈ R Π , 1 ≤ j ≤ m } , M ij : 0 ≤ i ≤ q − 1 , 1 ≤ j ≤ m ) A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 14 / 50

A P system based modeling framework Skeleton rules → u ′ [ v ′ ] β fr u [ v ] α − h h e 1 e 2 Environment rules fr ( a ) e j − → ( b ) e k e 3 e 4 A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 15 / 50

Introduction 1 P systems Modeling framework A P system based modeling framework 2 Example: Tritrophic Interactions 3 A software framework for Membrane Computing 4 Simulation algorithms Simulation results 5 Conclusions and future work A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 16 / 50

Example: Tritrophic Interactions Simplification of a real ecosystem Three trophic levels (3) A Carnivore (2) Herbivores (1) Grass A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 17 / 50

Tritrophic Interactions The model consists of 5 modules Reproduction + Grass production 1 Feeding / Hunting + Natural mortality 2 Lack of food: migration 3 Feeding 4 Restore Initial Config. 5 represents a one-year cycle several computation steps per module 10 geographical areas A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 18 / 50

Tritrophic Interactions Reproduction + Grass production Grass production mj r 1 , j ≡ X 1 [ ] 0 → [ X 1 , G h j ] + − − − 1 , 1 ≤ j ≤ 3 1 Females which reproduce and generate d i offsprings. ki , 1 · 0 . 5 → [ X 1 + d i ] + r 2 , i ≡ [ X i ] 0 − − − 1 , 2 ≤ i ≤ 7 1 i . . . A. Riscos-Núñez (Univ. Seville) Computational modeling using P systems CiE 2011 19 / 50