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Complexity & Interaction: Blurring Bordersbetween Physical, Computational, and Social SystemsA Coordination PerspectiveAnd...
Interaction & Complex SystemsComplexity & Interaction. . . by a complex system I mean one made up of a large numberof part...
Interaction & Complex SystemsInteraction in Complex (Computational) Systems IInteraction as a Computational DimensionInter...
Interaction & Complex SystemsInteraction in Complex (Computational) Systems IIInteraction: From Sciences to Computer Scien...
Interaction & Complex SystemsInteraction in Statistical Mechanics IIndependence from interactionSome physical systems are ...
Interaction & Complex SystemsInteraction in Statistical Mechanics IIInteracting systemsIntroducing interaction among parti...
Interaction & Complex SystemsInteraction in Statistical Mechanics IIIInteracting vs. non-interacting systemsOnly interacti...
Interaction & Complex SystemsComplexity in Statistical Mechanics IThe case of magnetic particlesThe simplest standard prot...
Interaction & Complex SystemsComplexity in Statistical Mechanics IIInteraction is not enoughInteraction is a necessary ing...
Interaction & Complex SystemsFrom Statistical Mechanics to Social Systems ILarge numbersThe key point in statistical mecha...
Interaction & Complex SystemsFrom Statistical Mechanics to Social Systems IIBeyond the boundariesMethods for complex syste...
Interaction & Complex SystemsFrom Statistical Mechanics to Social Systems IIISocial systems as statistical mechanical syst...
PerspectivesCoordinated Systems as Interacting Systems IPhysical vs. computational systemsPhysical systems are to be obser...
PerspectivesCoordinated Systems as Interacting Systems IICoordination media for ruling interactionDefining the abstractions...
PerspectivesCoordinated Systems as Interacting Systems IIICoordinated systems as interacting systems: Research perspective...
PerspectivesSocio-Technical Systems: Physical & Computational ISocio-technical systemsNowadays, a particularly-relevant cl...
PerspectivesSocio-Technical Systems: Physical & Computational IIA twofold view of socio-technical systemsThe nature of soc...
PerspectivesSocio-Technical Systems: Physical & Computational IIIComputational systems meet physical systemsIn socio-techn...
Final RemarksConclusion IInteraction in Complex SystemsInteraction is key issue for complex systemsInteracting systems in ...
Final RemarksConclusion IISocio-technical systemsSocio-technical systems such as large social platforms could represent ap...
Final RemarksFurther ReferencesPaperReference [Omicini and Contucci, 2013]APICe http://apice.unibo.it/xwiki/bin/view/Publi...
Final RemarksAcknowledgementsThanks to. . .Christine Julien & Rocco De Nicola for organising this sessionCostin Badica for...
ReferencesReferences IBoltzmann, L. (1964).Lectures on Gas Theory.University of California Press.Bouchaud, J.-P. and Potte...
ReferencesReferences IIContucci, P. and Giardin`a, C. (2012).Perspectives on Spin Glasses.Cambridge University Press, Camb...
ReferencesReferences IIIGelernter, D. and Carriero, N. (1992).Coordination languages and their significance.Communications ...
ReferencesReferences IVMantegna, R. N. and Stanley, H. E. (1999).Introduction to Econophysics: Correlations and Complexity...
ReferencesReferences VNishimori, H. (2001).Statistical Physics of Spin Glasses and Information Processing: AnIntroduction,...
ReferencesReferences VIOmicini, A. (2013).Nature-inspired coordination for complex distributed systems.In Fortino, G., B˘a...
ReferencesReferences VIIOmicini, A., Ricci, A., and Viroli, M. (2006).The multidisciplinary patterns of interaction from s...
ReferencesReferences VIIIStanley, H. E. (2008).Econophysics and the current economic turmoil.American Physical Society New...
ReferencesReferences IXWegner, P. (1997).Why interaction is more powerful than algorithms.Communications of the ACM, 40(5)...
Complexity & Interaction: Blurring Bordersbetween Physical, Computational, and Social SystemsA Coordination PerspectiveAnd...
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Complexity & Interaction: Blurring Borders between Physical, Computational, and Social Systems. A Coordination Perspective

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Complex systems of any kind are characterised by autonomous components interacting with each other in a non-trivial way. In this short talk, we discuss how the views on complexity are evolving in fields like physics, social sciences, and computer science, and – most significantly – how they are converging. In particular, we focus on the role of interaction as the foremost dimension for modelling complexity, and discuss first how coordination via mediated interaction could determine the general dynamics of complex software system, then how this applies to complex socio-technical systems like social networks.

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Transcript of "Complexity & Interaction: Blurring Borders between Physical, Computational, and Social Systems. A Coordination Perspective"

  1. 1. Complexity & Interaction: Blurring Bordersbetween Physical, Computational, and Social SystemsA Coordination PerspectiveAndrea Omiciniandrea.omicini@unibo.itwith Pierluigi Contuccipierluigi.contucci@unibo.itDISI / DM, Universit`a di BolognaSession “New Directions in Coordination Models and Languages”COORDINATION 2013Firenze, Italy, 3 June 2013Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 1 / 32
  2. 2. Interaction & Complex SystemsComplexity & Interaction. . . by a complex system I mean one made up of a large numberof parts that interact in a non simple way [Simon, 1962]Laws of complexitySome “laws of complexity” exists that characterise any complexsystem, independently of its specific nature [Kauffman, 2003]The precise source of what all complex systems share is still unknownin essenceInteractionWe argue that interaction – its nature, structure, dynamics – is the key tounderstand some fundamental properties of complex systems of any kindOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 2 / 32
  3. 3. Interaction & Complex SystemsInteraction in Complex (Computational) Systems IInteraction as a Computational DimensionInteraction as a fundamental dimension for modelling and engineeringcomplex computational systems [Wegner, 1997]Interaction is the most relevant source of complexity forcomputational systems nowadaysOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 3 / 32
  4. 4. Interaction & Complex SystemsInteraction in Complex (Computational) Systems IIInteraction: From Sciences to Computer Science [Omicini et al., 2006]The study of interaction as a first-class subject of research in many diversescientific areas dealing with complex systems basically draws the foremostlines of evolution of contemporary computational systems:Interaction — has become an essential and independent dimension ofcomputational systems, orthogonal to mere computation[Gelernter and Carriero, 1992, Wegner, 1997]Environment — is nowadays conceived as a first-class abstraction in the modellingand engineering of complex computational systems, such as pervasive,adaptive, and multi-agent systems [Weyns et al., 2007]Mediation — environment-based mediation [Ricci and Viroli, 2005] is the key todesigning and shaping the interaction space within complex softwaresystems, in particular socio-technical ones [Omicini, 2012]Middleware — and software infrastructure provide complex socio-technical systemswith the mediating abstractions required to rule and govern social andenvironment interaction [Viroli et al., 2007]Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 4 / 32
  5. 5. Interaction & Complex SystemsInteraction in Statistical Mechanics IIndependence from interactionSome physical systems are described under the assumption of mutualindependence among particles—that is, the behaviour of the particlesis unaffected by their mutual interactione.g., ideal gas [Boltzmann, 1964]There, the probability distribution of the whole system is the productof those of each of its particlesIn computer science terms, the properties of the system can becompositionally derived by the properties of the single components[Wegner, 1997]→ Neither macroscopic sudden shift nor abrupt change for the system asa whole: technically, those systems have no phase transitionsOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 5 / 32
  6. 6. Interaction & Complex SystemsInteraction in Statistical Mechanics IIInteracting systemsIntroducing interaction among particles structurally changes themacroscopic properties, along with the mathematical onesThe probability distribution of the system does not factorise anymoreIn computer science terms, the system is no longer compositionalInteracting systems are systems where particles do not behaveindependently of each otherOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 6 / 32
  7. 7. Interaction & Complex SystemsInteraction in Statistical Mechanics IIIInteracting vs. non-interacting systemsOnly interacting systems can describe real cases beyond the idealisedonese.g., they can explain phase transitions – like liquid-gas transition – andmuch more, such as collective emerging effectsWhile a system made of independent parts can be represented byisolated single nodes, an interacting system is better described bynodes connected by lines or higher-dimensional objectsFrom the point of view of information and communication theories,an ideal non-interacting gas is a system of non-communicating nodes,whereas an interacting system is made of nodes connected by channelsOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 7 / 32
  8. 8. Interaction & Complex SystemsComplexity in Statistical Mechanics IThe case of magnetic particlesThe simplest standard prototype of an interacting system is the one made ofmagnetic particlesThere, individual particles can behave according to a magnetic field whichleaves their probabilistic independence undisturbedAt the same time, two magnetic particles interact with each other, and thestrength of their interaction is a crucial tuning parameter to observe a phasetransitionIf interaction is weak, the effect of a magnetic field is smooth on the systemInstead, if the interaction is strong – in particular, higher than a threshold –even a negligible magnetic field can cause a powerful cooperative effect onthe systemThe system can be in one of two equilibrium states: the up and the downphaseOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 8 / 32
  9. 9. Interaction & Complex SystemsComplexity in Statistical Mechanics IIInteraction is not enoughInteraction is a necessary ingredient for complexity in statistical mechanicsbut definitely not a sufficient oneComplexity arises when the possible equilibrium states of a system grow veryquickly with the number of particles, regardless of the simplicity of the lawsgoverning each particle and their mutual interactionRoughly speaking, complexity is much more related to size in number, ratherthan to complexity of the laws ruling interactionIn the so-called mean field theory of spin glasses [M´ezard et al., 1986],particles do not just interact, but are alternatively either imitative oranti-imitative with the same probability [Contucci and Giardin`a, 2012]Both prototypical cooperation and competition effects can be observed, andthe resulting emerging collective effect is totally newOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 9 / 32
  10. 10. Interaction & Complex SystemsFrom Statistical Mechanics to Social Systems ILarge numbersThe key point in statistical mechanics is to relate the macroscopicobservables quantities – like pressure, temperature, etc. – to suitableaverages of microscopic observables—like particle speed, kineticenergy, etc.Based on the laws of large numbers, the method works for thosesystems made of a large number of particles / basic componentsOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 10 / 32
  11. 11. Interaction & Complex SystemsFrom Statistical Mechanics to Social Systems IIBeyond the boundariesMethods for complex systems from statistical mechanics haveexpanded from physics to fields as diverse as biology[Kauffman, 1993], economics[Bouchaud and Potters, 2003, Mantegna and Stanley, 1999], andcomputer science itself[M´ezard and Montanari, 2009, Nishimori, 2001]Recently, they have been applied to social sciences as well: there isevidence that the complex behaviour of many observedsocio-economic systems can be approached with the quantitativetools from statistical mechanicse.g., crisis events [Stanley, 2008]Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 11 / 32
  12. 12. Interaction & Complex SystemsFrom Statistical Mechanics to Social Systems IIISocial systems as statistical mechanical systemsA group of isolated individuals neither knowing nor communicatingwith each other is the typical example of a compositional socialsystemNo sudden shifts are expected in this case at the collective level,unless it is caused by strong external exogenous causesTo obtain a collective behaviour displaying endogenous phenomena,the individual agents should meaningfully interact with each otherThe foremost issue here is that the nature of the interactiondetermines the nature of the collective behaviour at the aggregatelevele.g., a simple imitative interaction is capable to cause strongpolarisation effects even in presence of extremely small external inputsOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 12 / 32
  13. 13. PerspectivesCoordinated Systems as Interacting Systems IPhysical vs. computational systemsPhysical systems are to be observed, understood, and possiblymodelled→ For physical systems, the laws of interaction, and their role forcomplexity, are to be taken as given, to be possibly formalisedmathematically by physicistsComputational systems are to be designed and built→ For computational systems, the laws of interaction have first to bedefined through amenable abstractions and computational models bycomputer scientists, then exploited by computer engineers in order tobuild systemsOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 13 / 32
  14. 14. PerspectivesCoordinated Systems as Interacting Systems IICoordination media for ruling interactionDefining the abstractions for ruling the interaction space incomputational systems basically means to define their coordinationmodel [Gelernter and Carriero, 1992, Ciancarini, 1996,Ciancarini et al., 1999]Global properties of complex coordinated systems depending oninteraction can be enforced through the coordination model,essentially based on its expressiveness[Zavattaro, 1998, Denti et al., 1998]For instance, tuple-based coordination models have been shown to beexpressive enough to support self-organising coordination patterns fornature-inspired distributed systems [Omicini, 2013]→ Coordinated systems as interacting systems: coordination models todefine new sorts of global, macroscopic properties for computationalsystems inspired by physical onesOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 14 / 32
  15. 15. PerspectivesCoordinated Systems as Interacting Systems IIICoordinated systems as interacting systems: Research perspectivesWe need to understandwhether notions such as phase, phase transition, or any othermacroscopic system property, could be transferred from statisticalmechanics to computer sciencewhat such notions would imply for computational systemswhich sort of coordination model could, if any, support such notionsOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 15 / 32
  16. 16. PerspectivesSocio-Technical Systems: Physical & Computational ISocio-technical systemsNowadays, a particularly-relevant class of social systems is representedby socio-technical systemsIn socio-technical systems, active components are mostly representedby humans, whereas interaction is almost-totally regulated by thesoftware infrastructureFor instance, social platforms like FaceBook [FaceBook, 2013] andLiquidFeedback [LiquidFeedback, 2013]Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 16 / 32
  17. 17. PerspectivesSocio-Technical Systems: Physical & Computational IIA twofold view of socio-technical systemsThe nature of socio-technical systems is twofold: they are both socialsystems and computational systems[Verhagen et al., 2013, Omicini, 2012]As complex social systems, their complex behaviour is in principleamenable of mathematical modelling and prediction through notionsand tools from statistical mechanicsAs complex computational systems, they are designed and builtaround some (either implicit or explicit) notion of coordination, rulingthe interaction within components of any sort—be them eithersoftware or human onesOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 17 / 32
  18. 18. PerspectivesSocio-Technical Systems: Physical & Computational IIIComputational systems meet physical systemsIn socio-technical systems, macroscopic properties could bedescribed by exploiting the conceptual tools from physicsenforced by the coordination abstractionsSocio-technical systems could exploit boththe notion of complexity by statistical mechanics, along with themathematical tools for behaviour modelling and prediction, andcoordination models and languages to suitably shape the interactionspaceWe envision complex socio-technical systemswhose implementation is based on suitable coordination modelswhose macroscopic properties can be modelled and predicted by meansof mathematical tools from statistical physicsOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 18 / 32
  19. 19. Final RemarksConclusion IInteraction in Complex SystemsInteraction is key issue for complex systemsInteracting systems in physicsCoordinated systems in computer scienceSocio-technical systems such as social platforms—e.g., FaceBook,LiquidFeedbackThe Role of Coordination ModelsCoordination models and middleware as the sources of abstractions andtechnology for enforcing global properties in complex computationalsystems, which could then bemodelled as physical systems, andengineered as computational systemsOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 19 / 32
  20. 20. Final RemarksConclusion IISocio-technical systemsSocio-technical systems such as large social platforms could represent aperfect case study for the convergence of the ideas and tools fromstatistical mechanics and computer science, being both social andcomputational systems at the same timeNext stepsWe plan to experiment with social platforms like FaceBook andLiquidFeedback, by exploitingcoordination technologies for setting macroscopic system propertiesstatistical mechanics tools for predicting global system behaviourOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 20 / 32
  21. 21. Final RemarksFurther ReferencesPaperReference [Omicini and Contucci, 2013]APICe http://apice.unibo.it/xwiki/bin/view/Publications/InteractioncomplexityIccci2013PresentationAPICe http://apice.unibo.it/xwiki/bin/view/Talks/NewdirectionsCoordination2013Slideshare http://www.slideshare.net/andreaomicini/complexity-interaction-blurring-borders-between-physical-computational-and-social-systems-a-coordination-perspectiveOmicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 21 / 32
  22. 22. Final RemarksAcknowledgementsThanks to. . .Christine Julien & Rocco De Nicola for organising this sessionCostin Badica for inviting me for the Keynote Speech at ICCCI 2013[Omicini and Contucci, 2013]http://apice.unibo.it/xwiki/bin/view/Events/Iccci13Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 22 / 32
  23. 23. ReferencesReferences IBoltzmann, L. (1964).Lectures on Gas Theory.University of California Press.Bouchaud, J.-P. and Potters, M. (2003).Theory of Financial Risk and Derivative Pricing: From Statistical Physics toRisk Management.Cambridge University Press, Cambridge, UK, 2nd edition.Ciancarini, P. (1996).Coordination models and languages as software integrators.ACM Computing Surveys, 28(2):300–302.Ciancarini, P., Omicini, A., and Zambonelli, F. (1999).Coordination technologies for Internet agents.Nordic Journal of Computing, 6(3):215–240.Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 23 / 32
  24. 24. ReferencesReferences IIContucci, P. and Giardin`a, C. (2012).Perspectives on Spin Glasses.Cambridge University Press, Cambridge, UK.Denti, E., Natali, A., and Omicini, A. (1998).On the expressive power of a language for programming coordination media.In 1998 ACM Symposium on Applied Computing (SAC’98), pages 169–177,Atlanta, GA, USA. ACM.Special Track on Coordination Models, Languages and Applications.FaceBook (2013).Home page.http://www.facebook.com.Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 24 / 32
  25. 25. ReferencesReferences IIIGelernter, D. and Carriero, N. (1992).Coordination languages and their significance.Communications of the ACM, 35(2):97–107.Kauffman, S. A. (1993).The Origins of Order: Self-organization and Selection in Evolution.Oxford University Press.Kauffman, S. A. (2003).Investigations.Oxford University Press.LiquidFeedback (2013).Home page.http://liquidfeedback.org.Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 25 / 32
  26. 26. ReferencesReferences IVMantegna, R. N. and Stanley, H. E. (1999).Introduction to Econophysics: Correlations and Complexity in Finance.Cambridge University Press, Cambridge, UK.M´ezard, M. and Montanari, A. (2009).Information, Physics, and Computation.Oxford University Press, Oxford, UK.M´ezard, M., Parisi, G., and Virasoro, M. A. (1986).Spin Glass Theory and Beyond. An Introduction to the Replica Method andIts Applications, volume 9 of World Scientific Lecture Notes in Physics.World Scientific Singapore.Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 26 / 32
  27. 27. ReferencesReferences VNishimori, H. (2001).Statistical Physics of Spin Glasses and Information Processing: AnIntroduction, volume 111 of International Series of Monographs on Physics.Clarendon Press, Oxford, UK.Omicini, A. (2012).Agents writing on walls: Cognitive stigmergy and beyond.In Paglieri, F., Tummolini, L., Falcone, R., and Miceli, M., editors, The Goalsof Cognition. Essays in Honor of Cristiano Castelfranchi, volume 20 ofTributes, chapter 29, pages 543–556. College Publications, London.Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 27 / 32
  28. 28. ReferencesReferences VIOmicini, A. (2013).Nature-inspired coordination for complex distributed systems.In Fortino, G., B˘adic˘a, C., Malgeri, M., and Unland, R., editors, IntelligentDistributed Computing VI, volume 446 of Studies in ComputationalIntelligence, pages 1–6. Springer.6th International Symposium on Intelligent Distributed Computing (IDC2012), Calabria, Italy, 24-26 September 2012. Proceedings. Invited paper.Omicini, A. and Contucci, P. (2013).Complexity & interaction: Blurring borders between physical, computational,and social systems. Preliminary notes.In 5th International Conference on Computational Collective IntelligenceTechnologies and Applications (ICCCI 2013), Craiova, Romania.Invited Paper.Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 28 / 32
  29. 29. ReferencesReferences VIIOmicini, A., Ricci, A., and Viroli, M. (2006).The multidisciplinary patterns of interaction from sciences to ComputerScience.In Goldin, D. Q., Smolka, S. A., and Wegner, P., editors, InteractiveComputation: The New Paradigm, pages 395–414. Springer.Ricci, A. and Viroli, M. (2005).Coordination artifacts: A unifying abstraction for engineeringenvironment-mediated coordination in MAS.Informatica, 29(4):433–443.Simon, H. A. (1962).The architecture of complexity.Proceedings of the American Philosophical Society, 106(6):467–482.Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 29 / 32
  30. 30. ReferencesReferences VIIIStanley, H. E. (2008).Econophysics and the current economic turmoil.American Physical Society News, 17(11):8.The Back Page.Verhagen, H., Noriega, P., Balke, T., and de Vos, M., editors (2013).Social Coordination: Principles, Artefacts and Theories (SOCIAL.PATH),AISB Convention 2013, University of Exeter, UK. The Society for the Studyof Artificial Intelligence and the Simulation of Behaviour.Viroli, M., Holvoet, T., Ricci, A., Schelfthout, K., and Zambonelli, F.(2007).Infrastructures for the environment of multiagent systems.Autonomous Agents and Multi-Agent Systems, 14(1):49–60.Special Issue: Environment for Multi-Agent Systems.Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 30 / 32
  31. 31. ReferencesReferences IXWegner, P. (1997).Why interaction is more powerful than algorithms.Communications of the ACM, 40(5):80–91.Weyns, D., Omicini, A., and Odell, J. J. (2007).Environment as a first-class abstraction in multi-agent systems.Autonomous Agents and Multi-Agent Systems, 14(1):5–30.Special Issue on Environments for Multi-agent Systems.Zavattaro, G. (1998).On the incomparability of Gamma and Linda.Technical Report SEN-R9827, CWI, Amsterdam, The Netherlands.Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 31 / 32
  32. 32. Complexity & Interaction: Blurring Bordersbetween Physical, Computational, and Social SystemsA Coordination PerspectiveAndrea Omiciniandrea.omicini@unibo.itwith Pierluigi Contuccipierluigi.contucci@unibo.itDISI / DM, Universit`a di BolognaSession “New Directions in Coordination Models and Languages”COORDINATION 2013Firenze, Italy, 3 June 2013Omicini, Contucci (DISI, Alma Mater) Complexity & Interaction Firenze, 3/6/2013 32 / 32
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