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The dynamics of correlated novelties Vittorio Loreto Sapienza University of Rome ISI Foundation, Turin with V. Servedio S. Strogatz F. Tria.

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Presentation on theme: "The dynamics of correlated novelties Vittorio Loreto Sapienza University of Rome ISI Foundation, Turin with V. Servedio S. Strogatz F. Tria."— Presentation transcript:

1 The dynamics of correlated novelties Vittorio Loreto Sapienza University of Rome ISI Foundation, Turin with V. Servedio S. Strogatz F. Tria

2 Bio-techno-social systems community level user level cognitive, behavioural, biologic social, interactive infrastructure level ICT, networks, physical-digital

3 A new platform for web-gaming and social computation

4 Biology Social systems Technology Arts, Science, Architecture, Urbanism,....

5 Diffusion Ahead of time Serendipity Tinkering Exaptation Success Trial and Error Multiples Mutation / Fixation

6 Our lives are spiced with little novelties... a new song a new book a new person a new word a new web page and often one thing leads to another one innovation sets the stage for another

7 GravityGravitation... a matter of scale...

8 Adjacent possible Consists of all those things (depending on the context, these could be ideas, molecules, genomes, technological products, etc.) that are one step away from what actually exists, and hence can arise from incremental modifications and recombinations of existing material. S. A. Kauffman, Investigations (Oxford University Press, New York/Oxford, 2000). The strange and beautiful truth about the adjacent possible is that its boundaries grow as you explore those boundaries.

9 A mathematical framework for the adjacent possible

10 Aims provide a mathematical framework to support the idea of the adjacent possible: Assess the relevance of the adjacent possible in datasets mirroring human activities exploration of a physical, biological or conceptual space that enlarges whenever a novelty occurs Wikipedia, Last.fm, del.icio.us, text corpora

11 Can we model it ? Is the adjacent possible for real ? Can we find its signature in reality ?

12 natural texts

13 Let us imagine a language...The language is meant to serve for communication between a builder A and an assistant B. A is building with building-stones; there are blocks, pillars, slabs and beams. B has to pass the stones, and that in the order in which A needs them. For this purpose they use a language consisting of the words 'block', 'pillar', 'slab', 'beam'. A calls them out; --B brings the stone which he has learnt to bring at such-and-such a call. -- Conceive of this as a complete primitive language. (L. Wittgenstein) Let us imagine a language...The language is meant to serve for communication between a builder A and an assistant B. A is building with building-stones; there are blocks, pillars, slabs and beams. B has to pass the stones, and that in the order in which A needs them. For this purpose they use a language consisting of the words 'block', 'pillar', 'slab', 'beam'. A calls them out; --B brings the stone which he has learnt to bring at such-and-such a call. -- Conceive of this as a complete primitive language. (L. Wittgenstein) frequency of words rank

14 Zipfs law (frequency rank plot) Zipf's law in city populations Zipf's law in Web Access Statistics and Internet Traffic Zipf's law in bibliometrics, informetrics, scientometrics, and library scienceZipf's law in finance and business Zipf's law in ecological systems Zipf's law in earthquake?

15 Zipfs law Zipfs law in texts Gutenberg Project ebook collection documents words distinct words

16 innovation in natural texts Let us imagine a language...The language is meant to serve for communication between a builder A and an assistant B. A is building with building-stones; there are blocks, pillars, slabs and beams. B has to pass the stones, and that in the order in which A needs them. For this purpose they use a language consisting of the words 'block', 'pillar', 'slab', 'beam'. A calls them out; --B brings the stone which he has learnt to bring at such-and-such a call. -- Conceive of this as a complete primitive language. (L. Wittgenstein) Let us imagine a language...The language is meant to serve for communication between a builder A and an assistant B. A is building with building-stones; there are blocks, pillars, slabs and beams. B has to pass the stones, and that in the order in which A needs them. For this purpose they use a language consisting of the words 'block', 'pillar', 'slab', 'beam'. A calls them out; --B brings the stone which he has learnt to bring at such-and-such a call. -- Conceive of this as a complete primitive language. (L. Wittgenstein) number of distinct words number of words

17 Heaps law in texts Gutenberg Project ebook collection documents words distinct words

18 Heaps vs. Zipfs laws Hyp.: random-sampling from a pure Zipfs law Heaps law with BUT: random-sampling is strong and sometimes unrealistic !! Heaps and Zips laws should emerge self-consistently !! INSTEAD:

19 # of new words frequency of words

20 L. Lu, Z.-K. Zhang, T. Zhou, PLoS ONE 5, e14139 (2010). finite-size effects

21 Single books

22 social annotation

23 resource user { tags } post

24 del.icio.us

25 Zipfs law high rank Heaps law

26 we start with n 0 words at time t : with probability p, a new word is appended with probability 1-p, a word is copied at random from the past the Yule-Simon process

27 stream correlations

28 number of views offset Δt into photostream inject N photos into a Flickr photostream, at once after time t, measure number of views per photo access patterns: an experiment (Courtesy of C. Cattuto)

29 a Yule-Simon model with memory start with n 0 words at time t : with probability p, a new word is appended with probability 1-p, a word is copied from position t-x x is distributed according to a fat-tailed memory kernel Q(x) ln x

30 frequency-rank plot: exp. vs model p = 0.06 p = 0.03 τ = 20 τ = 100 blog ajax C. Cattuto, VL, L. Pietronero PNAS 104, 1461 (2007)

31 tag frequencies: data vs model C. Cattuto, VL, L. Pietronero, PNAS 104, 1461 (2007) copying + skewed memory kernel + invention

32 English Wikipedia 20 TB (downloaded on March the 7th 2012)

33 Data structure For each edit of B we collect: the wikipedia page exclusive identification number (ID) the user (wikipedia contributor) ID (UID) the edit ID (EID) its time stamp (TS), the PID of its mother page Wikipedia dump 20 TBbytes (3/2012) Mother page A Red Link Page B

34 Red Link Mother page Wikipedia dump 20 TBbytes (3/2012)

35 # of new edits frequency of edits

36 Wikipedia: individual editors

37 Last.fm 1000 users;listened tracks user, time stamp, artist, track-id and track name

38

39 Last.fm: individual users

40 Modeling the adjacent possible Everything Should Be Made as Simple as Possible, But Not Simpler. A. Einstein

41 t t+1 Reinforcement (rich-get-richer) G. Polya, Annales de lI.H.P. 1, 117 (1930). Polyas Urn model Actual Possible

42 tt+1 Adjacent possible tt+1 Reinforcement Polya Urn model with triggering Actual history

43 Derivation of the Heaps law the total number of elements in the Urn at time t number of elements in the Urn never appeared in S at time t sub-linear growth linear growth

44 Derivation of the Zipfs law number of occurrences of the element i in

45 like Yule-Simon model Zipfs law Generalized Zipfs law + Heaps Urn model with triggering (results)

46 no-reinforcement on new wordsuniform distributions power-law distributionsexponential distributions Robustness for the Heaps law

47 Robustness for the Zipfs law no-reinforcement on new wordsuniform distributions power-law distributionsexponential distributions

48 Adjacent possible Reinforcement + Zipfs AND Heaps laws First conclusion:

49 Grounding the notion of one thing leads to another

50 Semantics Artists Mother page Words

51 A old A A BB BC new Urn model with semantic triggering at time step t we assign a weight semantic groups sharing the same label all the elements semantically related to all the other elements Reinforcement with labels Adjacent possible with labels

52 A old A A BB BC new Urn model with semantic triggering at time step t we assign a weight semantic groups sharing the same label * each element in the Urn with the same label as ** the element that triggered the enter in the Urn of the element with that label *** the elements triggered by all the other elements Reinforcement with labels Adjacent possible with labels

53 Quantifying triggering effects number of occurrences of the label A in the interval i Distribution of time intervals between two successive appearances of events belonging to the same semantic group

54 Results Wikipedia Last.fmModel

55 Individual vs. collective phenomena individual texts Wikipedia

56 Random Walk innovation dynamics

57 Random Walker Clique Random Walker A A A BB BC new old C C C A A B B C Random Walk based innovation dynamics model Reinforcement with labels Adjacent possible with labels

58 cliques nodes prob. of an inter-clique link Actual vs. possible

59 Results

60 Entropy Distribution of time-intervals

61 Conclusions Reinforcement and adjacent possible help explaining how one innovation sets the stage for another. Human activities feature strong correlations in their innovation processes

62 Challenges early adoption vs. large-scale spreading multiples and competition of several innovations innovations too far ahead of their time Relevant fields biology (pangenome, influenza, etc.) social sciences (opinions, languages, norms, cultural traits, policy making, marketing, etc.) technology best environments and strategies individual vs. collective behaviors

63 C. Cattuto, VL and L. Pietronero, Semiotic Dynamics and Collaborative Tagging, Proc. Natl. Acad. Sci. USA (PNAS), 104, (2007). C. Cattuto, A. Barrat, A. Baldassarri, G. Schehr and VL, Collective dynamics of social annotation, Proc. Natl. Acad. Sci. USA (PNAS), 106, (2009). C. Castellano, S. Fortunato and VL, Statistical physics of social dynamics Rev. Mod. Phys., 81, (2009). F. Tria, V.D.P. Servedio, S. Strogatz and VL The dynamics of correlated novelties submitted (2013). Recent publications Vito D.P. Servedio Steven Strogatz Francesca Tria Thank you


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