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Vlad Tarko - Modele, emergenta si simulari sociale

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Vlad Tarko - Modele, emergenta si simulari sociale

  1. 1. Modele, Emergenta & SimulariSociale<br />VladTarko<br />Pebazacartii<br />John H. Miller & Scott E. Page (2007), Complex Adaptive Systems: An introduction to computational models of social life. Princeton University Press<br />
  2. 2. Ce-i un model<br />O simplificare a realitatiifacuta cu scopul de a prezicecevace ne intereseaza.<br />Cum facemaceastasimplificare?<br />
  3. 3. Cevremsamodelam: realitatea<br />Realitatea are o anumitastructuraobiectiva𝑆sievolueaza in timpdupafunctia𝐹:<br />Starileobiective din realitate: 𝑆={𝑆1, 𝑆2,…}<br />O anumitaevolutie in timp: <br />Determinism: 𝑆(𝑡1) = 𝐹(𝑆(𝑡0))<br />Nedeterminism: 𝑝𝑟𝑜𝑏(𝑆(𝑡1)) = 𝐹(𝑆(𝑡0))<br />𝑆si𝐹 nu suntcunoscute.<br />𝑆si𝐹suntadeseafoarte complicate.<br /> <br />
  4. 4. Cum arata un model<br />Modelul are si el o anumitastructura𝑠 si evolueaza in timpdupafunctia𝑓:<br />Starile din model: 𝑠={𝑠1, 𝑠2,…}<br />O anumitaevolutie in timp: <br />Determinism: 𝑠(𝑡1) =𝑓(𝑠(𝑡0))<br />Nedeterminism: 𝑝𝑟𝑜𝑏(𝑠(𝑡1)) = 𝑓(𝑠(𝑡0))<br />𝑠si𝑓suntinventate de noi.<br />𝑠descriunisteproprietati de interespentrunoi.<br /> <br />
  5. 5. Legaturadintre model sirealitate<br />Fiecare stare din model 𝑠𝑖este o multime de stari din naturagrupatedupa o anumitaregula𝐸: 𝑠𝑖=𝐸𝑆,𝑖={𝑆𝑎,𝑆𝑏,…}<br />Daca nu cunoastem𝑆, regula 𝐸 nu poate fi definitaexplicit.<br />Regula𝐸 e definitaimplicit de aparatelesausistemelenoastre de masura:<br />Chiardaca nu cunoastem explicit regula𝐸este ok pentrucafolosindaparate de masura bine definite ne asiguramca𝑬existasi e stabila – nu variazahaotic de la cercetator la cercetatorsau de la caz la caz.<br />Dacaavemaparatesausisteme de masura bine definite, modelelebazatepeelevoravea o baza in realitate.<br />𝐸descrieprocesulnostru de masurare.<br /> <br />
  6. 6. Miller & Page (2007), p. 38<br />
  7. 7. Homomorfism: Descriemrealitatea, nu o influentam<br />Urmatoarele doualucruritrebuiesaduca la acelasirezultat:<br />Masuramstarea𝑠0, aplicammodelulsiobtinempredictia: 𝑠1𝑝𝑟𝑒𝑧𝑖𝑠=𝑓𝑠0=𝑓𝐸𝑆0<br />Ce se-ntampla in realitate: <br />𝑠0=𝐸𝑆0<br />𝑠1𝑟𝑒𝑎𝑙=𝐸𝑆1=𝐸𝐹𝑆0<br />𝑠1𝑝𝑟𝑒𝑧𝑖𝑠=?𝑠1𝑟𝑒𝑎𝑙<br />Trebuiesaavem:<br />𝑓𝐸𝑆0=𝐸𝐹𝑆0<br /> <br />
  8. 8. Niveluriierarhice de organizare: reductionism<br />Uneoricunoastem (intr-un anumitsens) starilereale𝑆pentrucaelesuntstarile de la un nivelmaiprimar.<br />Exemple:<br />Chimistiicunoscstarile “reale” 𝑆 din fizica: electronisinucleeatomice; pebazalorcreeazamodele ale fenomenelorchimice: moleculesiinteractiiledintreele<br />Biologiicunoscstarile “reale” 𝑆 din chimie: molecule; creeazamodele ale fiintelor viisi ale structuriilor interne (celule, organe etc.)<br />Psihologiicunoscstarile “reale” 𝑆 din biologiesichimie: organe, moleculesicomportamente; creeazamodele ale cauzelorcomportamentelor: starimentale (emotii, dorinte, opinii etc.)<br />Economistiicunoscstarile “reale” 𝑆 din psihologie: dorinte, opinii; creeazamodele ale comportamenteloragregate ale oamenilor: cerere, oferta, inflatie, PIB etc.<br /> <br />
  9. 9. [Desenul anterior]<br />Nivelul inferior<br />de organizare<br />𝑋 e functia care <br />face tranzitia de la <br />un nivel la altul<br /> <br />Nivelul superior<br />de organizare<br />Miller & Page (2007), p. 41<br />
  10. 10. Reductionismul<br />Consta in doualucruri:<br />Reducereastarilor de la nivelul superior la starile de la nivelul inferior<br />Starile macro sunt definite exclusiv in termeniielementelor de la nivelul micro<br />Reducereafunctiei de evolutie de la nivelul superior la functia de evolutie de la nivelul inferior<br />Dacastim cum evolueazasistemul la nivelul micro putemprezice cum evolueaza la nivelul macro<br />
  11. 11. Reductionismulintelescorect (“hierarchical reductionism”)<br />nivelurile de organizaresuperioaresuntconstruite din elementele de la nivelul de organizare inferior:<br /><ul><li>𝑆𝑠𝑢𝑝=𝑋(𝑆𝑖𝑛𝑓)
  12. 12. 𝑋este un model exact in sensuldiscutatanterior (𝑆𝑠𝑢𝑝=𝑠) doar catranzitia nu se mai face in timp, ci de la un nivel de organizare inferior la unul superior.
  13. 13. Dacacunoastempe𝐹si𝑆𝑠𝑢𝑝 cunoastem si𝐺.</li></ul>Exemple de modele:<br />In timp: stareaatmosfereimaine in functie de stareaatmosfereiazi.<br />De la un nivel de organizare la altul: pun sare in apa (nivel micro) siingheatamaigreu (o proprietate macro).<br />Structuralogica e aceeasi in ambeletipuri de modele.<br /> <br />
  14. 14. Emergenta: problemareductionismului<br />Emergenta:<br />Dacacunoastem starile la niveul inferior, 𝑆𝑖𝑛𝑓, sifunctia de evolutie, 𝐹, nu cunoastemneaparat pe 𝑋.<br />I.e. dacaintelegemnivelul inferior de organizare, nu e obligatoriucaintelegem cum safacemtranzitiasprenivelul superior de organizare.<br />Nu oriceorganizareipotetica la nivel superior e la fel de buna:nivelurile de organizareexista in mod obiectivsi nu doarconventional.<br />Negareaemergentei = “greedy reductionism” (cf. Dennett)<br />Daca nu arexistaemergentalumeaaravea un singurnivel de organizare – cel al particulelorelementare.<br /> <br />
  15. 15. Miller & Page (2007), p. 45<br />
  16. 16. De ceexistaemergenta?<br />Multecombinatii de stari la nivelul inferior conduc la aceeasi stare la nivelul superior.<br />Acestlucrueste un faptobiectiv.<br />De aicidecurgefaptulcanivelurile de organizareexista in mod obiectivsi nu doar conventional.<br />“Real patterns” (Dennett)<br />Exemple:<br />Multemodificariposibile ale pixelilorunuidesenlasanemodificatasemnificatiadesenului.<br />Multemicrostari ale unuigaz (moleculele de aer din camera pot fi in multepozitiidiferite) conduc la aceleasiproprietatimacroscopice (temperatura, presiune).<br />Multeseturiposibile de activitatineuronaleconduc la aceleasiproprietatimentale (aceleasiperceptii, emotii, ganduri etc.)<br />Multecombinatiiposibile de firmeconduc la acelasi PIB, rata a somajului etc.<br />
  17. 17. Celmaisimplucaz de emergenta: “disorganized complexity”<br />Legea numerelormari (Central Limit Theorem):<br />Elementeleindividuale ale sistemului, 𝑆𝑖∈𝑆, suntindependentesauinteractiile se anuleazareciproc (e casi cumaractiona independent)<br />Toatevariaza in jurulaceleasimedii, ∀𝑖, 𝑆𝑖=𝜇<br />Variatia de la medie e finita<br />𝑉𝑎𝑟𝑆=𝑖𝑝𝑟𝑜𝑏𝑆𝑖𝑆𝑖−𝜇2≈𝑆 𝑝𝑟𝑜𝑏𝑥𝑥−𝜇2𝑑𝑥=𝑓𝑖𝑛𝑖𝑡𝑎<br /><ul><li>Comportamentagregatdescris de o gaussiana.</li></ul>𝑉𝑎𝑟𝑆=𝜎2<br /><ul><li>Putemsa ne referimdoar la medie.
  18. 18. Media estemarimeaagregataemergenta</li></ul> <br />
  19. 19. 𝑝𝑟𝑜𝑏𝜇,𝜎2(𝑆)<br /> <br />𝑆<br /> <br />http://en.wikipedia.org/wiki/Normal_distribution<br />
  20. 20. Exemple de utilizare a medieicamarimeagregataemergenta<br />Termodinamica<br />Temperatura = energiacineticamedie a moleculelor<br />Presiunea = fortamedie cu care moleculelelovescceva pus in fluid<br />Etc.<br />Economie<br />Rata uneiasiguraridecurge din media cu care se intamplaaccidentele<br />Inflatiaestevariatiapretuluimediu al produselorsiserviciilor<br />Sisteme de recomandare<br />Ti se recomandaprodusul care in medieestecelmaiapreciat de ceilalti<br />
  21. 21. Cazuri complicate de emergenta:“organized complexity”<br />Interactiuniledintreelementeconteazasi nu pot fi ignorate.<br />“In systems characterized by the Central Limit Theorem, interactions cancel one another out and result in a smooth bell curve. In complex systems, interactions reinforce one another and result in behavior that is very different from the norm. The complex phenomena that arise in physical systems (like earthquakes, floods, and fires) and social ones (like stock market crashes, riots, and traffic jams) are decidedly not ‘normal’, nor are the patterns that emerge as we see birds flock, fish school, and pedestrians follow sidewalks demarcated by invisible traffic lanes.”<br /><ul><li>Power laws, sialtedistributii complicate</li></li></ul><li>Exemplu: Wikipedia[Clay Shirky, Here Comes Everybody]<br />Distributia contributoriloreste o power law<br />Distribuitia: numarul de editarifacute de persoana 1, persoana 2, …, persoana𝑛<br />Putinepersoane cu foartemulteeditari, foarte-foartemultepersoane cu doarcatevaeditari: Celemaimulteeditari nu suntfacute de ceimaiactivicontributori<br />Media numarului de editarifacute de o persoana, 1𝑛𝑖=1𝑛𝑁𝑒𝑑𝑖𝑡𝑎𝑟𝑖(𝑆𝑖)≠numarul de editarifacute de ceimai multi oameni (la o gaussianaastea 2 suntegale)<br />Consecinta – proportiaceamai mare a editarilor:<br />In cazuluneigausienevreisa-i ieipeaia din jurulmediei (pecei cu celemaimulteeditari) – ipotezaimplicitautilizata de abordareatraditionalabazatapeexperti (Britannica, Encarta etc.)<br />In cazuluneipower lawvreisa-i ieipetotiaia (un numarurias) care facputineeditari – cazul Wikipedia.<br /> <br />
  22. 22. Frank Gens, The IT Market’s $150B SMB “Long Tail”, IDC eXchange Blog<br />http://blogs.idc.com/ie/?p=53<br />
  23. 23. Simularisimodelarisociale<br />Elementelesuntagentidefinitiprin<br />Ceeace au<br />Locatiape un teren<br />Proprietati (sugar, spice etc.)<br />Regulilelor de<br />Miscare<br />Interatiune<br />Ne intereseazaevolutia a tot felul de marimiagregate<br /><ul><li>Schimburi
  24. 24. Lupta
  25. 25. Reproducere</li></li></ul><li>Reductionismulsiemergentasociala<br />In cazulmodelarii (care simplificalucrurile in locsa le replice in toatedetaliile) marimileagregatetrebuie definite (functia𝑋 nu se reduce la regulileindividuale ale agentilor).<br />Putemdefini in douafeluri:<br />Cevremsaobtinem (echivalentulselectieiartificiale): “abstraction based”<br />Mecanismul care sagenerezecevremsaobtinem (echivalentulselectieinaturale care functioneazape o bazastructurala data): “agent based”<br />Odatadefinite marimileagregatesaumecanismele de emergenta, evolutia la nivelulmacro lor se reduce la regulileindividuale.<br /> <br />
  26. 26. Simularesimodelare<br />In cazulsimularii – functia𝑋trebuiesaaparasingura:<br />Existasuficientedetaliipentrucasaexistemultemicrostari care conduc la aceeasimacrostare<br />i.e. suficientedetaliipentru a creapremizeleemergentei<br />In cazulmodelarii – functia𝑋esteintrodusa de noi:<br />Ne intereseazasamodelam direct ce se intampla la nivelul macro<br />Acelasi program poate fi simulare din unelepuncte de vederesimodelare din altele.<br />Exemplu:<br />Agentii ii modelam (rational choice model), nu le facemproprietatilementalesaemeargadintr-o simulareneuronala<br />Proprietatilesocialeemerg – asociatii, migratie, razboi etc.<br />In plus, poateinglobaatatelemente de selectieartificiala cat sinaturala.<br /> <br />
  27. 27. Miller & Page (2007), p. 68<br />
  28. 28. Abordareacomputationala e o generalizare a celeianalitice<br />Care-i alternativa cu care comparam?<br />Metodaanalitica:<br />Ecuatii care descriu in mod agregatproblema, independent de o anumita stare initiala<br />Rezolvate:<br />Numeric<br />Analitic (solutiiexacte)<br />Stephen Wolfram: elementelemetodeianaliticesunt de faptcazuriparticulare ale celeicomputationale:<br />O ecuatiediferentialaeste de fapt un algoritm<br />Integrareauneiecuatiidiferentialeeste o metoda de a vedeace face un algoritmfarasaai computer<br />
  29. 29. Exemplucomparativsimplu<br />Datele empirice: Toatecorpurile cad cu acceleratieconstanta𝑎(𝑡)=𝑔<br />Algoritmul: Acceleratia e derivatavitezei, viteza e derivatapozitiei in timp: 𝑣𝑡=𝑑𝑥𝑡𝑑𝑡; 𝑑𝑣𝑡𝑑𝑡=𝑔<br />Rezolvarea:<br />Computationala: plecam de la o pozitiesivitezainitiale, 𝑥𝑡0=𝑥0,𝑣𝑡0=𝑣0siobtinemsuccesivpozitiile𝑥𝑡1,𝑥𝑡2,… cu ajutorulalgoritmuluidat:<br />𝑣0=𝑥1−𝑥0𝑡1−𝑡0⇒𝑥1; 𝑔=𝑣1−𝑣0𝑡1−𝑡0⇒𝑣1<br />𝑣1=𝑥2−𝑥1𝑡2−𝑡1⇒𝑥2; 𝑔=𝑣2−𝑣1𝑡2−𝑡1⇒𝑣2<br />Etc.<br />Analitica: Integram de douaori:<br />𝑥𝑡=𝑔𝑑𝑡=𝑔𝑡+𝑣0𝑑𝑡=12𝑔𝑡2+𝑣0𝑡+𝑥0<br /> <br />
  30. 30. Posibileprobleme ale abordariicomputationale (1/4)<br />Computations Build in Their Results<br />Valabil in general pentruoricesistemdeductiv<br />Computations Lack Discipline<br />O problema a cercetatorilor, nu a metodei de cercetare<br />“The flexibility and creativity embodied in computer models often seduce practitioners to continually add features to their work—a practice that must be moderated if good-quality models are to be maintained.”<br />Ce-nseamnaca un model computational se verifica?<br />“Mathematical models surmount this issue by having a rigorous set of solution techniques and verification mechanisms. Given the newness of many computational approaches, there has yet to emerge an agreed-upon set of standards.”<br />
  31. 31. Posibileprobleme ale abordariicomputationale (2/4)<br />Computational Models Are Only Approximations to Specific Circumstances<br />“Computational models often result in answers that may be approximations that cannot be directly verified as being correct.”<br />Cum nu obtinemrezultategeneraleexplicite e maigreusaverificamceobtinemfacandpredictii la altecazuri. De faptputemdoarca-i maigreu.<br />“traditional modeling methods … are more generalizable. At the most basic level, a parametric mathematical solution can be used to solve a variety of cases via simple calculations ... Bottom-up computational models do not have this feature directly and often must be recalculated each time a new solution is desired. Although this process can be automated, nonetheless it is costly.”<br />
  32. 32. Posibileprobleme ale abordariicomputationale (3/4)<br />Computational Models Are Brittle<br />“slight changes in one area can dramatically alter their results”<br />Solutii:<br />“simple and obvious design”<br />“automated searches attempt to uncover brittle areas of the model”<br />Computational Models Are Hard to Test<br />“equilibrium is often not unique, as it may depend on various random elements of the model or nonlinearities. Complex systems models can also remain alive and not settle down to any obvious equilibrium. In these worlds, agents continually respond to the actions of others, and the system is in perpetual motion”<br />Nu-i neaparatproblema – realitateainsasi e complexa<br />
  33. 33. Posibileprobleme ale abordariicomputationale (4/4)<br />Computational Models Are Hard to Understand<br />“difficult to fully understand the structure of the model and the various routines that drive it … most computer programmers have had the experience of looking at someone else’s code (or even their own) and not being able to decipher it without a very intensive analysis.”<br />Mai mult o problema de dezvoltare a unorprotocoale de comunicaremaibune. Intr-un sensproblemaexistasi in cazulmetodeianalitice – semnificatiaunuisistem de ecuatii nu-i neaparatevidenta.<br />Rezolvareauneiproblemeprinmetodaanaliticaadeseorisugereazamarimiimportante (e.g. frecventaproprie de rezonanta)<br />

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