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Dynamical networks of person to person
interactions from RFID sensor networks

     Lorenzo Isella1 , Alain Barrat1,2 , Juliette Stehlé2 ,
   Jean-François Pinton3 , Wouter Van den Broeck1 and
                       Ciro Cattuto1
1 Complex  Networks and Systems Group, Institute for Scientific Interchange (ISI)
                           Foundation, Turin, Italy.
     2 Centre de Physique Théorique, CNRS UMR 6207, Marseille, France.
  3 Laboratoire de Physique de l’ENS Lyon, CNRS UMR 5672, Lyon, France.




                ICCS, Amsterdam, Holland, 2010
Goals and Case Studies

       Deployment of wearable RFID devices to collect data
       about human interaction in different social environments.
       Focus on two main case studies
           Science Gallery (SG) at the Trinity College, Dublin, Ireland
           (∼ 3 months, ∼ 10000 visitors).
           HT09 conference, Turin, Italy (3 days, ∼ 100 participants).
       Technology and data from Sociopatterns Project
       (http://www.sociopatterns.org/).
       Applications in computer science (ubiquitous computing,
       P2P) and computational epidemiology (causality,
       non-homogeneous mixing).
Goals and Case Studies

       Deployment of wearable RFID devices to collect data
       about human interaction in different social environments.
       Focus on two main case studies
           Science Gallery (SG) at the Trinity College, Dublin, Ireland
           (∼ 3 months, ∼ 10000 visitors).
           HT09 conference, Turin, Italy (3 days, ∼ 100 participants).
       Technology and data from Sociopatterns Project
       (http://www.sociopatterns.org/).
       Applications in computer science (ubiquitous computing,
       P2P) and computational epidemiology (causality,
       non-homogeneous mixing).
Goals and Case Studies

       Deployment of wearable RFID devices to collect data
       about human interaction in different social environments.
       Focus on two main case studies
           Science Gallery (SG) at the Trinity College, Dublin, Ireland
           (∼ 3 months, ∼ 10000 visitors).
           HT09 conference, Turin, Italy (3 days, ∼ 100 participants).
       Technology and data from Sociopatterns Project
       (http://www.sociopatterns.org/).
       Applications in computer science (ubiquitous computing,
       P2P) and computational epidemiology (causality,
       non-homogeneous mixing).
Goals and Case Studies

       Deployment of wearable RFID devices to collect data
       about human interaction in different social environments.
       Focus on two main case studies
           Science Gallery (SG) at the Trinity College, Dublin, Ireland
           (∼ 3 months, ∼ 10000 visitors).
           HT09 conference, Turin, Italy (3 days, ∼ 100 participants).
       Technology and data from Sociopatterns Project
       (http://www.sociopatterns.org/).
       Applications in computer science (ubiquitous computing,
       P2P) and computational epidemiology (causality,
       non-homogeneous mixing).
Goals and Case Studies

       Deployment of wearable RFID devices to collect data
       about human interaction in different social environments.
       Focus on two main case studies
           Science Gallery (SG) at the Trinity College, Dublin, Ireland
           (∼ 3 months, ∼ 10000 visitors).
           HT09 conference, Turin, Italy (3 days, ∼ 100 participants).
       Technology and data from Sociopatterns Project
       (http://www.sociopatterns.org/).
       Applications in computer science (ubiquitous computing,
       P2P) and computational epidemiology (causality,
       non-homogeneous mixing).
Goals and Case Studies

       Deployment of wearable RFID devices to collect data
       about human interaction in different social environments.
       Focus on two main case studies
           Science Gallery (SG) at the Trinity College, Dublin, Ireland
           (∼ 3 months, ∼ 10000 visitors).
           HT09 conference, Turin, Italy (3 days, ∼ 100 participants).
       Technology and data from Sociopatterns Project
       (http://www.sociopatterns.org/).
       Applications in computer science (ubiquitous computing,
       P2P) and computational epidemiology (causality,
       non-homogeneous mixing).
Goals and Case Studies

       Deployment of wearable RFID devices to collect data
       about human interaction in different social environments.
       Focus on two main case studies
           Science Gallery (SG) at the Trinity College, Dublin, Ireland
           (∼ 3 months, ∼ 10000 visitors).
           HT09 conference, Turin, Italy (3 days, ∼ 100 participants).
       Technology and data from Sociopatterns Project
       (http://www.sociopatterns.org/).
       Applications in computer science (ubiquitous computing,
       P2P) and computational epidemiology (causality,
       non-homogeneous mixing).
Overview of the Infrastructure
       Tags exchange packets at various powers and report their
       contacts to antennas broadcasting the data to a server.
       Low-power packets expose face-to-face interactions at
       small distances (∼ 1m).
From Physical Proximity to Networks
       Natural representation of physical proximity as a network in
       addition to
           scalability
           unobtrusiveness
           low cost
           high spatial resolution ∼ 1 meter
           high temporal resolution ∼ 5 − 20 seconds.
From Physical Proximity to Networks
       Natural representation of physical proximity as a network in
       addition to
           scalability
           unobtrusiveness
           low cost
           high spatial resolution ∼ 1 meter
           high temporal resolution ∼ 5 − 20 seconds.
From Physical Proximity to Networks
       Natural representation of physical proximity as a network in
       addition to
           scalability
           unobtrusiveness
           low cost
           high spatial resolution ∼ 1 meter
           high temporal resolution ∼ 5 − 20 seconds.
From Physical Proximity to Networks
       Natural representation of physical proximity as a network in
       addition to
           scalability
           unobtrusiveness
           low cost
           high spatial resolution ∼ 1 meter
           high temporal resolution ∼ 5 − 20 seconds.
From Physical Proximity to Networks
       Natural representation of physical proximity as a network in
       addition to
           scalability
           unobtrusiveness
           low cost
           high spatial resolution ∼ 1 meter
           high temporal resolution ∼ 5 − 20 seconds.
From Physical Proximity to Networks
       Natural representation of physical proximity as a network in
       addition to
           scalability
           unobtrusiveness
           low cost
           high spatial resolution ∼ 1 meter
           high temporal resolution ∼ 5 − 20 seconds.
From Physical Proximity to Networks
       Natural representation of physical proximity as a network in
       addition to
           scalability
           unobtrusiveness
           low cost
           high spatial resolution ∼ 1 meter
           high temporal resolution ∼ 5 − 20 seconds.
Aggregated Networks
       Aggregate all the contacts along 24 hours.
                          HT09: June, 30th                  SG: July, 14th

                                                                                          q       q
                                                                              q
                                                        q

                                                              q




                                                q                 q
                                            q



                                                                              q
                                                                      q                                   q
                                                                                              q

                                q       q                                                                         q
                                                                                                                          q




                           SG: May, 19th                    SG: May, 20th



              q                                                                                                       q


                                                                                                                      q
                  q
                                                                                                                  q
              q


                                                                                                              q
                      q                                                                                   q
                                                    q

                            q                                                                 q
                                                q
                                    q
                                            q                                         q
                                                q                             q
                                                                          q
                                                                              q                       q
                                                                                  q       q       q
Human Dynamics and Network Topology 1/2
       Entanglement of human behavior and network topology.
                                         0.008




                    P (visit duration)
                                         0.006


                                         0.004


                                         0.002


                                         0.000
                                                      101                102
                                                 Visit duration (min)




                                                        12:00 to 13:00
                                                        13:00 to 14:00
                                                        14:00 to 15:00
                                                        15:00 to 16:00
                                                        16:00 to 17:00
                                                        17:00 to 18:00
                                                        18:00 to 19:00
                                                        19:00 to 20:00
Human Dynamics and Network Topology 2/2
       Short-tailed P(k ) and broad P(wij ) and P(∆tij ).
                                          SG                                              HT09
                     10-1                                               10-1

                     10-2
                                                                        10-2
             P (k)




                                                                P (k)
                           -3
                     10
                                                                        10-3
                     10-4

                     10-5                                               10-4
                                 0 10 20 30 40 50 60 70                            0     20         40         60     80
                                              k                                                 k
                          100                                               100
                            -1
                          10                       SG
                                                                            10-1                          SG
                                                   HT09                                                   HT09
                          10-2                                                -2
                                                                            10
              P (∆tij )




                                                                 P (wij )


                          10-3
                                                                            10-3
                          10-4
                          10-5                                              10-4
                            -6
                          10                                                10-5
                                 101    102       103     104                      101    102            103        104
                                       ∆tij (sec)                                        wij (sec)
Random Networks and Smallworldness
      Network topology↔ information spreading.
                         HT09: June, 30th (rewired)                                     SG: July, 14th (rewired)
                         q
                                                                                                                  q




                                                                                                          q

                                              q
                                      q
                                                  q
                                                                                                  q




                                                                                                      q


                                                          q
                                                                                                              q
                                                                                                                      q




                             HT09: June, 30th                                                SG: July, 14th
                   1.0                                                        1.0

                                                                              0.8
                   0.8
       M(l)/M(∞)




                                                                  M(l)/M(∞)
                                                                              0.6
                   0.6
                                                                              0.4

                   0.4
                                  Aggregated network                          0.2                     Aggregated network
                                  Rewired networks                                                    Rewired networks

                   0.2                                                        0.0
                         1        2                   3       4                     1    2    3   4           5       6   7   8   9   10
                                          l                                                                   l
Deterministic SI model 1/3

       SI model S + I → 2I, infection probability .
       Set = 1: snowball deterministic model (avoid
       stochasticity).
       Beyond epidemiology: paradigm for information diffusion
       and causality on the network.

                      I       S         I     I
                          +
Deterministic SI model 1/3

       SI model S + I → 2I, infection probability .
       Set = 1: snowball deterministic model (avoid
       stochasticity).
       Beyond epidemiology: paradigm for information diffusion
       and causality on the network.

                      I       S         I     I
                          +



       Collect distributions of infected visitors/conference
       participants at the end of each day by varying the seed
       (inter day variability).
Deterministic SI model 1/3

       SI model S + I → 2I, infection probability .
       Set = 1: snowball deterministic model (avoid
       stochasticity).
       Beyond epidemiology: paradigm for information diffusion
       and causality on the network.

                      I       S         I     I
                          +



       Collect distributions of infected visitors/conference
       participants at the end of each day by varying the seed
       (inter day variability).
       Dependence of the epidemic spreading during a single day
       on the choice of the seed (intra day variability).
Deterministic SI model 2/3
       Nsus for a given seed ≡ number of individuals in the seed’s
       CC.
                                                          Ninf
       In a static network framework, P(Ninf /Nsus ) = δ( Nsus − 1).
       Information propagates differently at HT09 and SG.

                                              HT09                                                            SG
                           1.0                                                           1.0

                           0.8                                                           0.8
         P (Ninf /Nsus )




                                                                       P (Ninf /Nsus )
                           0.6                                                           0.6

                           0.4                                                           0.4

                           0.2                                                           0.2

                           0.0                                                           0.0
                                 0.0   0.2     0.4   0.6   0.8   1.0                           0.0   0.2     0.4   0.6   0.8   1.0
                                             Ninf /Nsus                                                    Ninf /Nsus
Deterministic SI model 3/3
       Impact of social events (e.g. coffee breaks).
       Highlight role played by each seed (hard to achieve in a
       static network framework).

                                  HT09: June, 30th                                                           SG: July, 14th
                                                                                           300
                      100       8:00 to 9:00                                                            12:00   to   13:00
                                9:00 to 10:00                                                           13:00   to   14:00
                                10:00 to 11:00                                             250          14:00   to   15:00
                           80   11:00 to 12:00                                                          15:00   to   16:00
         Incidence curve




                                                                              Incidence curve
                                12:00 to 13:00                                                          16:00   to   17:00
                                13:00 to 14:00                                             200          17:00   to   18:00
                                14:00 to 15:00                                                          18:00   to   19:00
                           60   15:00 to 16:00                                                          19:00   to   20:00
                                16:00 to 17:00                                             150
                           40
                                                                                           100

                           20                                                                   50

                            0                                                                    0
                                  08:00 10:00 12:00 14:00 16:00 18:00 20:00                          12:00       14:00       16:00   18:00   20:00
                                                 Time                                                                    Time
Conclusions

       A posteriori validation of the infrastructure by
       post-processing the collected data.
       Network aggregation over different time periods
       (seasonality, trends, etc..).
       Network static properties (P(k ), diameter, assortativity,
       etc..).
       Network dynamic properties: spread of epidemics and
       diffusion processes on a longitudinal network hence
       dynamics of the network and dynamics on the network.
Conclusions

       A posteriori validation of the infrastructure by
       post-processing the collected data.
       Network aggregation over different time periods
       (seasonality, trends, etc..).
       Network static properties (P(k ), diameter, assortativity,
       etc..).
       Network dynamic properties: spread of epidemics and
       diffusion processes on a longitudinal network hence
       dynamics of the network and dynamics on the network.
Conclusions

       A posteriori validation of the infrastructure by
       post-processing the collected data.
       Network aggregation over different time periods
       (seasonality, trends, etc..).
       Network static properties (P(k ), diameter, assortativity,
       etc..).
       Network dynamic properties: spread of epidemics and
       diffusion processes on a longitudinal network hence
       dynamics of the network and dynamics on the network.
Conclusions

       A posteriori validation of the infrastructure by
       post-processing the collected data.
       Network aggregation over different time periods
       (seasonality, trends, etc..).
       Network static properties (P(k ), diameter, assortativity,
       etc..).
       Network dynamic properties: spread of epidemics and
       diffusion processes on a longitudinal network hence
       dynamics of the network and dynamics on the network.
Conclusions

       A posteriori validation of the infrastructure by
       post-processing the collected data.
       Network aggregation over different time periods
       (seasonality, trends, etc..).
       Network static properties (P(k ), diameter, assortativity,
       etc..).
       Network dynamic properties: spread of epidemics and
       diffusion processes on a longitudinal network hence
       dynamics of the network and dynamics on the network.
Conclusions

       A posteriori validation of the infrastructure by
       post-processing the collected data.
       Network aggregation over different time periods
       (seasonality, trends, etc..).
       Network static properties (P(k ), diameter, assortativity,
       etc..).
       Network dynamic properties: spread of epidemics and
       diffusion processes on a longitudinal network hence
       dynamics of the network and dynamics on the network.
Conclusions

       A posteriori validation of the infrastructure by
       post-processing the collected data.
       Network aggregation over different time periods
       (seasonality, trends, etc..).
       Network static properties (P(k ), diameter, assortativity,
       etc..).
       Network dynamic properties: spread of epidemics and
       diffusion processes on a longitudinal network hence
       dynamics of the network and dynamics on the network.
Acknowlegements

      Michael John Gorman, director of the Science Gallery at
      Trinity College, Dublin
      http://sciencegallery.com/content/
      science-gallery-2009-infectious
      Organizers of Hypertext 2009 conference
      http://www.ht2009.org/
      SocioPatterns project and partners
      http://www.sociopatterns.org
      DynaNets project
      http://www.dynanets.org/

                  Thank you for your attention!
Acknowlegements

      Michael John Gorman, director of the Science Gallery at
      Trinity College, Dublin
      http://sciencegallery.com/content/
      science-gallery-2009-infectious
      Organizers of Hypertext 2009 conference
      http://www.ht2009.org/
      SocioPatterns project and partners
      http://www.sociopatterns.org
      DynaNets project
      http://www.dynanets.org/

                  Thank you for your attention!
Acknowlegements

      Michael John Gorman, director of the Science Gallery at
      Trinity College, Dublin
      http://sciencegallery.com/content/
      science-gallery-2009-infectious
      Organizers of Hypertext 2009 conference
      http://www.ht2009.org/
      SocioPatterns project and partners
      http://www.sociopatterns.org
      DynaNets project
      http://www.dynanets.org/

                  Thank you for your attention!
Acknowlegements

      Michael John Gorman, director of the Science Gallery at
      Trinity College, Dublin
      http://sciencegallery.com/content/
      science-gallery-2009-infectious
      Organizers of Hypertext 2009 conference
      http://www.ht2009.org/
      SocioPatterns project and partners
      http://www.sociopatterns.org
      DynaNets project
      http://www.dynanets.org/

                  Thank you for your attention!
Acknowlegements

      Michael John Gorman, director of the Science Gallery at
      Trinity College, Dublin
      http://sciencegallery.com/content/
      science-gallery-2009-infectious
      Organizers of Hypertext 2009 conference
      http://www.ht2009.org/
      SocioPatterns project and partners
      http://www.sociopatterns.org
      DynaNets project
      http://www.dynanets.org/

                  Thank you for your attention!
Acknowlegements

      Michael John Gorman, director of the Science Gallery at
      Trinity College, Dublin
      http://sciencegallery.com/content/
      science-gallery-2009-infectious
      Organizers of Hypertext 2009 conference
      http://www.ht2009.org/
      SocioPatterns project and partners
      http://www.sociopatterns.org
      DynaNets project
      http://www.dynanets.org/

                  Thank you for your attention!
Information diffusion on the network

       Aggregated network (since introduction of the seed) and
       transmission network.
       Branching nature of information diffusion.
       Network diameter going back and forth in time.
       Fastest path = shortest path.

                                                 q                                                                   qqq


                                                                                                             q qq    q q

                         q       q       q       q       q
                                                                                                             qqq      qq


                                                                                                             q qqqq       q    q qq

                 q       q               q               q
                                                                                 q                q          q   q qqqqqqqqqqqqq


                                                                                 qqq              q          q   q    q       q qqq       qq
                 q                       q   q       q       q   q   q
                                                                                 q qq             qq        qq            q           q       qqqqq


                                                                                 qqqqqqqqqqqqqqqq                                         qq     qqqq
         q   q       q       q       q       q       q           q   q

                                                                             qqqqq       qq   q q       q    q                            q       q   qqq


                                                                             qqqq        qq   q         q                 q                       qqqqq
                 q                       q                   q   q   q   q

                                                                             q       q              q                                 qqq             qq


                                                         q                                                                q

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ICCS2010

  • 1. Dynamical networks of person to person interactions from RFID sensor networks Lorenzo Isella1 , Alain Barrat1,2 , Juliette Stehlé2 , Jean-François Pinton3 , Wouter Van den Broeck1 and Ciro Cattuto1 1 Complex Networks and Systems Group, Institute for Scientific Interchange (ISI) Foundation, Turin, Italy. 2 Centre de Physique Théorique, CNRS UMR 6207, Marseille, France. 3 Laboratoire de Physique de l’ENS Lyon, CNRS UMR 5672, Lyon, France. ICCS, Amsterdam, Holland, 2010
  • 2. Goals and Case Studies Deployment of wearable RFID devices to collect data about human interaction in different social environments. Focus on two main case studies Science Gallery (SG) at the Trinity College, Dublin, Ireland (∼ 3 months, ∼ 10000 visitors). HT09 conference, Turin, Italy (3 days, ∼ 100 participants). Technology and data from Sociopatterns Project (http://www.sociopatterns.org/). Applications in computer science (ubiquitous computing, P2P) and computational epidemiology (causality, non-homogeneous mixing).
  • 3. Goals and Case Studies Deployment of wearable RFID devices to collect data about human interaction in different social environments. Focus on two main case studies Science Gallery (SG) at the Trinity College, Dublin, Ireland (∼ 3 months, ∼ 10000 visitors). HT09 conference, Turin, Italy (3 days, ∼ 100 participants). Technology and data from Sociopatterns Project (http://www.sociopatterns.org/). Applications in computer science (ubiquitous computing, P2P) and computational epidemiology (causality, non-homogeneous mixing).
  • 4. Goals and Case Studies Deployment of wearable RFID devices to collect data about human interaction in different social environments. Focus on two main case studies Science Gallery (SG) at the Trinity College, Dublin, Ireland (∼ 3 months, ∼ 10000 visitors). HT09 conference, Turin, Italy (3 days, ∼ 100 participants). Technology and data from Sociopatterns Project (http://www.sociopatterns.org/). Applications in computer science (ubiquitous computing, P2P) and computational epidemiology (causality, non-homogeneous mixing).
  • 5. Goals and Case Studies Deployment of wearable RFID devices to collect data about human interaction in different social environments. Focus on two main case studies Science Gallery (SG) at the Trinity College, Dublin, Ireland (∼ 3 months, ∼ 10000 visitors). HT09 conference, Turin, Italy (3 days, ∼ 100 participants). Technology and data from Sociopatterns Project (http://www.sociopatterns.org/). Applications in computer science (ubiquitous computing, P2P) and computational epidemiology (causality, non-homogeneous mixing).
  • 6. Goals and Case Studies Deployment of wearable RFID devices to collect data about human interaction in different social environments. Focus on two main case studies Science Gallery (SG) at the Trinity College, Dublin, Ireland (∼ 3 months, ∼ 10000 visitors). HT09 conference, Turin, Italy (3 days, ∼ 100 participants). Technology and data from Sociopatterns Project (http://www.sociopatterns.org/). Applications in computer science (ubiquitous computing, P2P) and computational epidemiology (causality, non-homogeneous mixing).
  • 7. Goals and Case Studies Deployment of wearable RFID devices to collect data about human interaction in different social environments. Focus on two main case studies Science Gallery (SG) at the Trinity College, Dublin, Ireland (∼ 3 months, ∼ 10000 visitors). HT09 conference, Turin, Italy (3 days, ∼ 100 participants). Technology and data from Sociopatterns Project (http://www.sociopatterns.org/). Applications in computer science (ubiquitous computing, P2P) and computational epidemiology (causality, non-homogeneous mixing).
  • 8. Goals and Case Studies Deployment of wearable RFID devices to collect data about human interaction in different social environments. Focus on two main case studies Science Gallery (SG) at the Trinity College, Dublin, Ireland (∼ 3 months, ∼ 10000 visitors). HT09 conference, Turin, Italy (3 days, ∼ 100 participants). Technology and data from Sociopatterns Project (http://www.sociopatterns.org/). Applications in computer science (ubiquitous computing, P2P) and computational epidemiology (causality, non-homogeneous mixing).
  • 9. Overview of the Infrastructure Tags exchange packets at various powers and report their contacts to antennas broadcasting the data to a server. Low-power packets expose face-to-face interactions at small distances (∼ 1m).
  • 10. From Physical Proximity to Networks Natural representation of physical proximity as a network in addition to scalability unobtrusiveness low cost high spatial resolution ∼ 1 meter high temporal resolution ∼ 5 − 20 seconds.
  • 11. From Physical Proximity to Networks Natural representation of physical proximity as a network in addition to scalability unobtrusiveness low cost high spatial resolution ∼ 1 meter high temporal resolution ∼ 5 − 20 seconds.
  • 12. From Physical Proximity to Networks Natural representation of physical proximity as a network in addition to scalability unobtrusiveness low cost high spatial resolution ∼ 1 meter high temporal resolution ∼ 5 − 20 seconds.
  • 13. From Physical Proximity to Networks Natural representation of physical proximity as a network in addition to scalability unobtrusiveness low cost high spatial resolution ∼ 1 meter high temporal resolution ∼ 5 − 20 seconds.
  • 14. From Physical Proximity to Networks Natural representation of physical proximity as a network in addition to scalability unobtrusiveness low cost high spatial resolution ∼ 1 meter high temporal resolution ∼ 5 − 20 seconds.
  • 15. From Physical Proximity to Networks Natural representation of physical proximity as a network in addition to scalability unobtrusiveness low cost high spatial resolution ∼ 1 meter high temporal resolution ∼ 5 − 20 seconds.
  • 16. From Physical Proximity to Networks Natural representation of physical proximity as a network in addition to scalability unobtrusiveness low cost high spatial resolution ∼ 1 meter high temporal resolution ∼ 5 − 20 seconds.
  • 17. Aggregated Networks Aggregate all the contacts along 24 hours. HT09: June, 30th SG: July, 14th q q q q q q q q q q q q q q q q SG: May, 19th SG: May, 20th q q q q q q q q q q q q q q q q q q q q q q q q
  • 18. Human Dynamics and Network Topology 1/2 Entanglement of human behavior and network topology. 0.008 P (visit duration) 0.006 0.004 0.002 0.000 101 102 Visit duration (min) 12:00 to 13:00 13:00 to 14:00 14:00 to 15:00 15:00 to 16:00 16:00 to 17:00 17:00 to 18:00 18:00 to 19:00 19:00 to 20:00
  • 19. Human Dynamics and Network Topology 2/2 Short-tailed P(k ) and broad P(wij ) and P(∆tij ). SG HT09 10-1 10-1 10-2 10-2 P (k) P (k) -3 10 10-3 10-4 10-5 10-4 0 10 20 30 40 50 60 70 0 20 40 60 80 k k 100 100 -1 10 SG 10-1 SG HT09 HT09 10-2 -2 10 P (∆tij ) P (wij ) 10-3 10-3 10-4 10-5 10-4 -6 10 10-5 101 102 103 104 101 102 103 104 ∆tij (sec) wij (sec)
  • 20. Random Networks and Smallworldness Network topology↔ information spreading. HT09: June, 30th (rewired) SG: July, 14th (rewired) q q q q q q q q q q q HT09: June, 30th SG: July, 14th 1.0 1.0 0.8 0.8 M(l)/M(∞) M(l)/M(∞) 0.6 0.6 0.4 0.4 Aggregated network 0.2 Aggregated network Rewired networks Rewired networks 0.2 0.0 1 2 3 4 1 2 3 4 5 6 7 8 9 10 l l
  • 21. Deterministic SI model 1/3 SI model S + I → 2I, infection probability . Set = 1: snowball deterministic model (avoid stochasticity). Beyond epidemiology: paradigm for information diffusion and causality on the network. I S I I +
  • 22. Deterministic SI model 1/3 SI model S + I → 2I, infection probability . Set = 1: snowball deterministic model (avoid stochasticity). Beyond epidemiology: paradigm for information diffusion and causality on the network. I S I I + Collect distributions of infected visitors/conference participants at the end of each day by varying the seed (inter day variability).
  • 23. Deterministic SI model 1/3 SI model S + I → 2I, infection probability . Set = 1: snowball deterministic model (avoid stochasticity). Beyond epidemiology: paradigm for information diffusion and causality on the network. I S I I + Collect distributions of infected visitors/conference participants at the end of each day by varying the seed (inter day variability). Dependence of the epidemic spreading during a single day on the choice of the seed (intra day variability).
  • 24. Deterministic SI model 2/3 Nsus for a given seed ≡ number of individuals in the seed’s CC. Ninf In a static network framework, P(Ninf /Nsus ) = δ( Nsus − 1). Information propagates differently at HT09 and SG. HT09 SG 1.0 1.0 0.8 0.8 P (Ninf /Nsus ) P (Ninf /Nsus ) 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Ninf /Nsus Ninf /Nsus
  • 25. Deterministic SI model 3/3 Impact of social events (e.g. coffee breaks). Highlight role played by each seed (hard to achieve in a static network framework). HT09: June, 30th SG: July, 14th 300 100 8:00 to 9:00 12:00 to 13:00 9:00 to 10:00 13:00 to 14:00 10:00 to 11:00 250 14:00 to 15:00 80 11:00 to 12:00 15:00 to 16:00 Incidence curve Incidence curve 12:00 to 13:00 16:00 to 17:00 13:00 to 14:00 200 17:00 to 18:00 14:00 to 15:00 18:00 to 19:00 60 15:00 to 16:00 19:00 to 20:00 16:00 to 17:00 150 40 100 20 50 0 0 08:00 10:00 12:00 14:00 16:00 18:00 20:00 12:00 14:00 16:00 18:00 20:00 Time Time
  • 26. Conclusions A posteriori validation of the infrastructure by post-processing the collected data. Network aggregation over different time periods (seasonality, trends, etc..). Network static properties (P(k ), diameter, assortativity, etc..). Network dynamic properties: spread of epidemics and diffusion processes on a longitudinal network hence dynamics of the network and dynamics on the network.
  • 27. Conclusions A posteriori validation of the infrastructure by post-processing the collected data. Network aggregation over different time periods (seasonality, trends, etc..). Network static properties (P(k ), diameter, assortativity, etc..). Network dynamic properties: spread of epidemics and diffusion processes on a longitudinal network hence dynamics of the network and dynamics on the network.
  • 28. Conclusions A posteriori validation of the infrastructure by post-processing the collected data. Network aggregation over different time periods (seasonality, trends, etc..). Network static properties (P(k ), diameter, assortativity, etc..). Network dynamic properties: spread of epidemics and diffusion processes on a longitudinal network hence dynamics of the network and dynamics on the network.
  • 29. Conclusions A posteriori validation of the infrastructure by post-processing the collected data. Network aggregation over different time periods (seasonality, trends, etc..). Network static properties (P(k ), diameter, assortativity, etc..). Network dynamic properties: spread of epidemics and diffusion processes on a longitudinal network hence dynamics of the network and dynamics on the network.
  • 30. Conclusions A posteriori validation of the infrastructure by post-processing the collected data. Network aggregation over different time periods (seasonality, trends, etc..). Network static properties (P(k ), diameter, assortativity, etc..). Network dynamic properties: spread of epidemics and diffusion processes on a longitudinal network hence dynamics of the network and dynamics on the network.
  • 31. Conclusions A posteriori validation of the infrastructure by post-processing the collected data. Network aggregation over different time periods (seasonality, trends, etc..). Network static properties (P(k ), diameter, assortativity, etc..). Network dynamic properties: spread of epidemics and diffusion processes on a longitudinal network hence dynamics of the network and dynamics on the network.
  • 32. Conclusions A posteriori validation of the infrastructure by post-processing the collected data. Network aggregation over different time periods (seasonality, trends, etc..). Network static properties (P(k ), diameter, assortativity, etc..). Network dynamic properties: spread of epidemics and diffusion processes on a longitudinal network hence dynamics of the network and dynamics on the network.
  • 33. Acknowlegements Michael John Gorman, director of the Science Gallery at Trinity College, Dublin http://sciencegallery.com/content/ science-gallery-2009-infectious Organizers of Hypertext 2009 conference http://www.ht2009.org/ SocioPatterns project and partners http://www.sociopatterns.org DynaNets project http://www.dynanets.org/ Thank you for your attention!
  • 34. Acknowlegements Michael John Gorman, director of the Science Gallery at Trinity College, Dublin http://sciencegallery.com/content/ science-gallery-2009-infectious Organizers of Hypertext 2009 conference http://www.ht2009.org/ SocioPatterns project and partners http://www.sociopatterns.org DynaNets project http://www.dynanets.org/ Thank you for your attention!
  • 35. Acknowlegements Michael John Gorman, director of the Science Gallery at Trinity College, Dublin http://sciencegallery.com/content/ science-gallery-2009-infectious Organizers of Hypertext 2009 conference http://www.ht2009.org/ SocioPatterns project and partners http://www.sociopatterns.org DynaNets project http://www.dynanets.org/ Thank you for your attention!
  • 36. Acknowlegements Michael John Gorman, director of the Science Gallery at Trinity College, Dublin http://sciencegallery.com/content/ science-gallery-2009-infectious Organizers of Hypertext 2009 conference http://www.ht2009.org/ SocioPatterns project and partners http://www.sociopatterns.org DynaNets project http://www.dynanets.org/ Thank you for your attention!
  • 37. Acknowlegements Michael John Gorman, director of the Science Gallery at Trinity College, Dublin http://sciencegallery.com/content/ science-gallery-2009-infectious Organizers of Hypertext 2009 conference http://www.ht2009.org/ SocioPatterns project and partners http://www.sociopatterns.org DynaNets project http://www.dynanets.org/ Thank you for your attention!
  • 38. Acknowlegements Michael John Gorman, director of the Science Gallery at Trinity College, Dublin http://sciencegallery.com/content/ science-gallery-2009-infectious Organizers of Hypertext 2009 conference http://www.ht2009.org/ SocioPatterns project and partners http://www.sociopatterns.org DynaNets project http://www.dynanets.org/ Thank you for your attention!
  • 39. Information diffusion on the network Aggregated network (since introduction of the seed) and transmission network. Branching nature of information diffusion. Network diameter going back and forth in time. Fastest path = shortest path. q qqq q qq q q q q q q q qqq qq q qqqq q q qq q q q q q q q q qqqqqqqqqqqqq qqq q q q q q qqq qq q q q q q q q q qq qq qq q q qqqqq qqqqqqqqqqqqqqqq qq qqqq q q q q q q q q q qqqqq qq q q q q q q qqq qqqq qq q q q qqqqq q q q q q q q q q qqq qq q q