p systems: a modelling language marian gheorghe department of computer science university of...

P systems: A Modelling P systems: A Modelling LanguageLanguage

Marian GheorgheMarian Gheorghe

Department of Computer ScienceDepartment of Computer Science

University of SheffieldUniversity of Sheffield

Unconventional Programming Paradigms; 15-17 Sept’04 – Mont Saint Michel

SummarySummary

Modelling bio-communitiesModelling bio-communities

State machines & P systemsState machines & P systems

ExperimentsExperiments

P systems – modelling paradigmP systems – modelling paradigm

Future workFuture work


What is a model?What is a model?

A A simplified descriptionsimplified description of a complex entity or of a complex entity or process process www.cogsci.princeton.edu/cgi-bin/webwnwww.cogsci.princeton.edu/cgi-bin/webwn

A A representationrepresentation of a set of components of a of a set of components of a process, system, or subject area, generally developed process, system, or subject area, generally developed for understanding, analysis, improvement, and/or for understanding, analysis, improvement, and/or replacement of the process replacement of the process www.ichnet.org/glossary.htmwww.ichnet.org/glossary.htm

A representation of reality used to simulate a A representation of reality used to simulate a process, understand a situation, predict an outcome, or process, understand a situation, predict an outcome, or analyze a problem analyze a problem www.epa.gov/maia/html/glossary.htmlwww.epa.gov/maia/html/glossary.html


What to model?What to model?

Bio-communities: Bio-communities: social insects (ants, social insects (ants, bees, wasps), bacterium communities, bees, wasps), bacterium communities, cellscells

Component description/behaviour:Component description/behaviour: structure, rules, structure, rules,

Interactions: Interactions: type, dynamicity type, dynamicity



Integrative Bio-research Integrative Bio-research

Abstract Modelling

Empirical Research

Parameters

Hypotheses

Testing – Specifications

Assumptions – RequirementsRobust

biosystem rules

Bioinspired computing

General biologic

al theory

Holistic view

Verification

Modelling Bio-CommunitiesModelling Bio-Communities

Multi-agent systemsMulti-agent systems: social insect : social insect communities provide an accessible model communities provide an accessible model of requisites in their design of requisites in their design e.g.e.g. minimal minimal rule set and population size. rule set and population size.

Biological system simulationBiological system simulation: : methods of modelling insect societies methods of modelling insect societies should be of utility when simulating other should be of utility when simulating other organisms organisms e.g.e.g. bacteria, human cells, bacteria, human cells, tissues etc.tissues etc.


Modelling Social insectsModelling Social insects

Top downTop down Probabilistic models of whole Probabilistic models of whole population dynamics e.g. fluid flow population dynamics e.g. fluid flow modelling of army ant traffic.modelling of army ant traffic.

Bottom upBottom up

Agent-based models utilising individual Agent-based models utilising individual rule sets. rule sets. Population dynamic emerges when Population dynamic emerges when sufficient agents interact.sufficient agents interact.


Model Organism – The Pharaoh’s Ant


The Pharaoh’s Ant - ForagingThe Pharaoh’s Ant - Foraging

ExplorationExploration Food Discovery and ReturnFood Discovery and Return RecruitmentRecruitment Trail Dynamics / Traffic Trail Dynamics / Traffic Decision SelectionDecision Selection


Trail FormationTrail Formation A strong trunk trail and a network of minor A strong trunk trail and a network of minor trails emerges.trails emerges.

A preliminary set of rules underlying this A preliminary set of rules underlying this process has been estimatedprocess has been estimated


Nest activitiesNest activities

Feeding (larvae, ants)Feeding (larvae, ants)

Looking for foodLooking for food

Moving aroundMoving around

Foraging Foraging

Doing … nothing (inactive)Doing … nothing (inactive)


X-machine modelX-machine model


Input e.g. pheromones, food, social

and environmental stimuli etc.

Ant + M1

q0 initial stateAnt + M2

q1 next state

Functions

Output ΓBehaviour elicited

e.g. trail following, recruitment

Why X-machines ? Why X-machines ?

State machine model widespread in State machine model widespread in man-made systems’ constructionman-made systems’ construction

Well-developed verification and testing Well-developed verification and testing methodsmethods

Easy to modelEasy to model

Modularity Modularity

Graphical representationGraphical representation

ToolsTools


Simulation results (Nest)Simulation results (Nest)

3cm x 3cm nest size3cm x 3cm nest size

100 workers + 100 larvae100 workers + 100 larvae

worker model: 7 states; 22 transitionsworker model: 7 states; 22 transitions

foraging happens in cycles (alterations foraging happens in cycles (alterations may occur)may occur)

no specialisationno specialisation

problem: tuning different parametersproblem: tuning different parameters


LimitationsLimitations

Communication model rather ad-hocCommunication model rather ad-hoc

No real formalism of functions No real formalism of functions associated with transitionsassociated with transitions

No tool for interacting componentsNo tool for interacting components

… …


A new modelling paradigmA new modelling paradigm

Biologically motivatedBiologically motivated

Fully formal modelFully formal model

Genuinely distributedGenuinely distributed

Dynamic structure Dynamic structure

… …


P systemsP systems

Cellular biology Cellular biology A hierarchical arrangementA hierarchical arrangement Each membrane delimits a regionEach membrane delimits a region Each region contains a multiset of elements Each region contains a multiset of elements (simple molecules, DNA sequences, other (simple molecules, DNA sequences, other regions…)regions…) The chemicals/bio-elements evolve in time The chemicals/bio-elements evolve in time according to some (rewriting/combination) rules according to some (rewriting/combination) rules specific to each region or may be moved across specific to each region or may be moved across the membranesthe membranes The rules may also dissolve/create/move The rules may also dissolve/create/move regionsregions http://http://psystems.disco.unimib.itpsystems.disco.unimib.it


P systems a model of bio-P systems a model of bio-communitiescommunities

Initially an abstract model of cell structure and Initially an abstract model of cell structure and functioning functioning

Tissue P systemsTissue P systems

Population P systemsPopulation P systems

http://psystems.disco.unimib.ithttp://psystems.disco.unimib.it


Population P systemsPopulation P systems

A population of bio-unitsA population of bio-units The units evolveThe units evolve Dynamic structureDynamic structure


Population P systems (2)Population P systems (2)

Usual bio-units components (P systems) Usual bio-units components (P systems) Tissues P systems communication rules Tissues P systems communication rules

Dynamic structureDynamic structure– Components Components – Links (bonds)Links (bonds)


Population P Systems: a Population P Systems: a Modelling paradigm Modelling paradigm

Rule types: transformation, communication Rule types: transformation, communication (exchange of elements) – and a combination of (exchange of elements) – and a combination of both, bond making rules both, bond making rules

Each rule has a guard and refers to local Each rule has a guard and refers to local elementselements

Bio-units created/removed dynamicallyBio-units created/removed dynamically

Bio-units: change their type, divide, die Bio-units: change their type, divide, die

Each bio-unit has a type Each bio-unit has a type

Environment Environment


Code exampleCode example

foodL>=0: foodL--> foodL-FoodDecayRatefoodL>=0: foodL--> foodL-FoodDecayRate

next(this.pos, pos): next(this.pos, pos): <target=Env; out=pos; in=pos><target=Env; out=pos; in=pos>

foodL>HungryL: foodL>HungryL: <target=Worker; out=Food from foodL; in=><target=Worker; out=Food from foodL; in=>

forager:forager:forager --> inactive; pos; pher; foodL forager --> inactive; pos; pher; foodL


AdvantagesAdvantages

Fully formalFully formal Easy/Natural to modelEasy/Natural to model

Easy to extend/reuse (bacteria, tissue)Easy to extend/reuse (bacteria, tissue) Adequate for a bottom-up approachAdequate for a bottom-up approach An underlying graphical representationAn underlying graphical representation


Further developmentsFurther developments

Further investigationsFurther investigations New featuresNew features

More complex case studiesMore complex case studies

ToolsTools

Environment builderEnvironment builder

Handling of data generatedHandling of data generated


ConclusionsConclusions

Two modelling approachesTwo modelling approaches

Bottom-up/local modelling strategyBottom-up/local modelling strategy

Local – global (individual – social)Local – global (individual – social)

Modelling – (small) case studiesModelling – (small) case studies

… … programming; hmmm programming; hmmm


ThanksThanksJean-Pierre BanJean-Pierre BanâtreâtreJean-Louis GiavittoJean-Louis Giavitto

Pascal FradetPascal FradetOlivier MichelOlivier Michel

Mike HolcombeMike Holcombe

Duncan JacksonDuncan JacksonFrancesco BernardiniFrancesco Bernardini

Fei LuoFei LuoJames ClarkeJames ClarkePeter LangtonPeter LangtonTaihong WuTaihong WuYang YangYang Yang


p systems: a modelling language marian gheorghe department of computer science university of...

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