Algorithmische Bioinformatik III Graphs, Networks, and Systems SS2008 Ralf Zimmer. Petri Nets
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1 Algorithmische Bioinformatik III Graphs, Networks, and Systems SS2008 Ralf Zimmer Petri Nets Introduction Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 1
2 Algorithmic Bioinformatics III: Graphs, Networks, and Systems Part I: Methods background on Graphs and Systems 1. Biological Networks Regulatory networks Metabolic networks 2. Graph Theory and Graph Algorithms 3. Optimization on Graphs and Networks 4. Complex Networks and Random graphs Structure Evolution 5. Petri Nets Invariants Semantics/Dynamics Part II: Applications of networks in bioinformatics Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 2
3 Petri nets C.A. Petri, Kommunikation mit Automaten, PhD Thesis, Universität Bonn, 1961 Pless, H. Plünnecke. A bibliography of Net Theory, GMD report, 1978, 1980, 1990 ~ references on Petri Net Theory, Algorithms and Applications Theory Algorithms Text Books Tools Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 3
4 Petri nets C.A. Petri, Kommunikation mit Automaten, PhD Thesis, Universität Bonn, 1961 Pless, H. Plünnecke. A bibliography of Net Theory, GMD report, 1978, 1980, 1990 ~ references on Petri Net Theory, Algorithms and Applications Text Books Peter Starke, Petrinetze, VdW, Berlin, 1980 Peterson, Petri Net Theory and the Modelling of Systems, Prentice Hall, 1981 Wilfried Brauer, Net Theory and Application, LNCS 84, 1980 Wolfgang Reisig, Petrinetze, Springer 1982 Wolfgang Reisig, Systementwurf mit Netzen, Springer, 1985 Eike Best, Cesar Fernandez, Nonsequential Processes A Petri net view, Springer, 1988 Kurt Jensen, Coloured Petri Nets, Vol 1-3, Springer 1997 Tools CPN/ML, CPN Tools (University, Aarhus, Denmark, K. Jensen) VisObjNet, U.Ilmenau (Hybrid Petri Nets) INA, PNK (Humboldt U., P. Starke) WFS (G.Csaba, LMU) PNFL (L. Windhager, LMU) + PNMA (F. Erhard, LMU) Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 4
5 Module and Workflow Specification via Petri Nets Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 5
6 Petri Net based Workflow and Make System (WFS) Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 6
7 Petri Net based Workflow System (WFS) Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 7
8 Organization, Modules and Interface Specification CIP Pool Amalienstr. Cluster ~ 30 dual processor/ dual core (4-32GB) Amalienstr. CIP-BioGrid ~ 300 processors/ Dual/quad core (1-8GB) Amalienstr./Oettingen BIM Cluster ~ 30 dual processor/ dual core (4-32GB) Weihenstephan BioGrid Parallelization with BioGrid / Workload Distribution Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 8
9 PNMA Spatio-temporal PNFL System Modeling Ralf Zimmer, LMU Lehrstuhl für Praktische Informatik und Bioinformatik, Kloster Seeon Spring School Systems Biology
10 PNMA Spatio-temporal PNFL System Modeling Ralf Zimmer, LMU Lehrstuhl für Praktische Informatik und Bioinformatik, Kloster Seeon Spring School Systems Biology
11 PNMA Spatio-temporal PNFL System Simulation Ralf Zimmer, LMU Lehrstuhl für Praktische Informatik und Bioinformatik, Kloster Seeon Spring School Systems Biology
12 PNMA Spatio-temporal PNFL System From Interaction Graphs to Systems Ralf Zimmer, LMU Lehrstuhl für Praktische Informatik und Bioinformatik, Kloster Seeon Spring School Systems Biology
13 PNMA Spatio-temporal PNFL System From Interaction Graphs to Systems Ralf Zimmer, LMU Lehrstuhl für Praktische Informatik und Bioinformatik, Kloster Seeon Spring School Systems Biology
14 PNMA Spatio-temporal PNFL System From Interaction Graphs to Systems Ralf Zimmer, LMU Lehrstuhl für Praktische Informatik und Bioinformatik, Kloster Seeon Spring School Systems Biology
15 Systems Biology: Models and Methods Scale (#nodes) Area Method Model Data Software PN = Petri Nets (with extensions) Systems biology, network dynamics, processes Pathways, Processes, Networks Concepts Network Evolution Causal Models (PN, CPN, PNFL) Networks, Pathways (PN, PNFL) Concepts (PN, graphs, gene lists) Mech. Networks (Brenda) Temp-spatio high accuracy measurements of specific systems Kinetic constants Organism and general networks (Kegg, Biocarta, Brenda) Expression data Literature data, DIP, MINT, BIND, HPRD, MIPS, Exon chips, genome tiling chip data CPN/ML, ODE, Matlab, FERN, WFS, PNFL, ToPNet ToPNet, PW scoring, PW Query, significant area ConceptMaker Text mining (ProMiner) PN as unifying language/interface Ralf Zimmer, LMU Lehrstuhl für Praktische Informatik und Bioinformatik, Kloster Seeon Spring School Systems Biology
16 Petri Nets: Features Petri Net Theory = Theory of System Organisation System model for events (processes), organizations, and devices where regulated (controlled) flow (especially information flow) plays a role Language of Petri Nets: Notions and Theory which describe möglichst viele Erscheinungen bei der Informationsübertragung und Informationswandlung in einheitlicher und exakter Weise [Carl Adam Petri, Kommunikation mit Automaten,1961] Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 16
17 Petri nets Petri Net Theory = Theory of System Organisation Applications In almost all areas of computer science Complexity theory, formal languages, circuit theory, computer architecture and organisation, operating systems, cooperating machines, processes, databases, software engineering, In many sciences Business organisation Administration Law Any organized process Foundation Theory of science Classical and non-classical logic Theoretical physics Communication theory Features Simple representation, simple semantics Comprehensive model of non-sequential systems (Concurrency) Finite ressources Consistent representation for different levels of abstraction/modelling Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 17
18 Petri Nets: Features Causal dependencies and independency relations within a set of events Explicit representation No explicit time Instead: concurrency, non-sequentiality Simple notions to describe set-up, workings and properties of a wide range of systems (e.g. real-time systems) Representation on different levels of abstraction in the same language and theory Formal theory and proofs of properties, properties are again described in the same language [logical facts = static components of dynamical systems] Synchronicity is problematic (to achieve and to measure) => technical problems, theoretical physics. Events at the same time could be coincident or by chance in a particular order Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 18
19 Petri Nets: Types There is a large variety of types of Petri Nets CE (condition-event) systems Basic notions of non-sequential processes System properties Synchronic distance PT (place-transition) systems Modelling Invariants High-level Nets (Predicate/relation nets, individual markings, Coloured Petri Nets (CPN) ) System description Abstraction Embedding and Refinement Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 19
20 Petri Nets: Basic Definitions A Petri Net (PN) is a graph with two types of nodes (S-elements (states) and T-elements (transitions/actions) and a flow relation between S-elements and T-elements (edges never connect nodes of the same type) [Bipartite graph] Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 20
21 Example: A Petri Net (CE system) summer start spring summer spring start autumn start winter autumn winter start Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 21
22 Petri net semantics: The firing rule s1 1 t1 2 1 t2 2 s2 Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 22
23 Petri Nets: Firing Example Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 23
24 Occurrence rule k=4 m t m m [t> m k=4 Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 24
25 Petri Nets : Definition Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 28
26 Petri Nets What is a Petri net? A graphical notion (model = picture?) A mathematical notion (model = graph?) A programming notion (model = program?) An executable model (one semantics?) An analyzable model (verification/proof) A model of distributed systems with discrete events Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 29
27 S - and T - Invariants of S/T (P/T) Nets s1 1 t1 S-invariant s: 2 1 N t * s = 0 => s = (1,1) t2 2 s2 s : weighting of tokens such that weighted sum of tokens is constant Incidence matrix N = t1 t2 s1-1 2 s2 1-2 T-invariant t: N * t = 0 => t = (2,1) s : number of firing the transitions such that marking is reproduced Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik, SS 2008, Algorithmic Bioinformatics III: Graphs and Networks 30
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