Phase Transitions in Coevolving Helping Networks - Google Sites

Emergence of bursts and communities in evolving weighted networks PLoS ONE 6, e22687 (2011)

Hang-Hyun Jo, Raj Kumar Pan, and Kimmo Kaski Department of Biomedical Engineering and Computational Science Aalto University, Finland

weight

burst

?

community

Burst

Community

¿ (inter-event time)

P (¿) » ¿

¡ 0:7

Oij =

j¤ i \ ¤ j j (overlap) j¤ i [ ¤ j j

O(w) [Karsai et al., PRE ’11]

[Onnela et al., PNAS ’07]

event

strong link

weak link

inter-event time

time

time

Weight = Events

Community Model [Kumpula et al., PRL ’07]

global attachment

local attachment

(1)

(pLA )

reset node global attachment (pGA )

preferential neighboring interaction

Triangular Chain Interaction (TCI) = temporal extension of local attachment

t (pLA )

t¡ 1

i

t+1

k t¡ 2

(1)

j

Target & Call At time step t

Target!

t¡ 2 t¡ 1 First, TCI is continued.

t t¡ 1

(pGA )

Pi!j / wij

t¡ 2 t (pLA )

Call!

busy! always AND protocol

OR protocol

Original OR model

AND model

Without links with w=1

OR Model hki ¼ 10:1; hci ¼ 0:08

! pLA = 0:013; pGA = 0:1

c(k) » k¡ 1

s(k) » k

P(¿) » ¿¡ ® exp(¡ ¿=¿c)

® ¼ 2:5 for pLA = 0:013 ® ¼ 1:2 for pLA = 0:1

AND Model hki ¼ 9:6; hci ¼ 0:13

! pLA = 0:07; pGA = 0:1

® ¼ 0:8 for pLA = 0:07 ® ¼ 0:6 for pLA = 0:4 c(k) » k¡ 1

s(k) » k

c(k) =

2e » k¡ 2 k(k ¡ 1)

Link Percolation OR model

Mobile phone call network

AND model

Why Bursty?

Pi!j / wij → preferential selection of neighbor

~ priority queuing process [Barabasi, Nature ’05] t=0

0.6

0.8

0.1

0.9

0.3

t=1

0.6

0.8

0.1

0.5

0.3

t=2

0.6

0.2

0.1

0.5

0.3

t=3

0.4

0.2

0.1

0.5

0.3

¿=2

weight

burst

Tri-Chain Interaction

community

(Pi!j / wij )

Thank you!