Kuramoto dynamics, glassy synchronization and rare regions in the human connectome - Pablo Villegas
7
Kuramoto dynamics, glassy synchronization and rare regions in the human connectome Pablo Villegas Quantitative Laws II (University of Granada)
-
Upload
lake-como-school-of-advanced-studies -
Category
Science
-
view
145 -
download
0
Transcript of Kuramoto dynamics, glassy synchronization and rare regions in the human connectome - Pablo Villegas
Kuramoto dynamics, glassy synchronization and rare
regions in the human connectome
Pablo Villegas
Quantitative Laws II
(University of Granada)
The Kuramoto model
Intrinsic frecuency
·
θi = ωi + k
N∑
j=1
Wijsin (θj − θi) + ηi (t) i = 1, ...,N
Coupling term
Noise
z = re iψ = 1N
N∑j=1
e iθj
Pablo Villegas | Kuramoto dynamics, glassy synchronization and rare regions in the human connectome 2/7
The Human Connectome
Figure : Adjacency matrix and modular structure
Pablo Villegas | Kuramoto dynamics, glassy synchronization and rare regions in the human connectome 3/7
The Human Connectome
A hierarchical synchronization process appears, with local phase transitions
and a new intermediate phase between order and disorder.
Pablo Villegas | Kuramoto dynamics, glassy synchronization and rare regions in the human connectome 4/7
A model: Hierarchical Modular Network
We can see the same phenomena in synthetic Hierarchic Modular Networks
(HMNs), with local phase transitions and a bottom to up synchronization
process.
Pablo Villegas | Kuramoto dynamics, glassy synchronization and rare regions in the human connectome 5/7
Metastability in HMNs
Switching behavior in the HC and HMNs. This behavior closely resembles
’up and down’ states.
200 400 600 8000.3
0.5
0.7
0.3
0.5
0.7
0.3
0.5
0.7HC(a)
ord
erp
ara
met
er
(b)
0.2
0.3
0.4
0.2
0.3
0.4
20000 40000 60000 80000
time
0.2
0.3
0.4
HMN
time
0 200 400 600 800 1000
time
0.20
0.22
0.24
0.26
0.28
0.30
ord
erp
aram
eter
ord
erp
aram
eter
(s
tead
y)
(a) (b)
10−1 100 101 102
noise coeff.
0.200
0.205
0.210
0.215
0.220
0.225
0.230
Resonant peaks for some levels of intermediate noise in HMN networks.
Perturbations lead the system to more coherent attractors in the
intermediate phase.
Pablo Villegas | Kuramoto dynamics, glassy synchronization and rare regions in the human connectome 6/7
Thanks for your attention
Collaborators
We acknowledge financial support from MINECO (National Plan of I+D+i), grant FIS2013-43201-P.
Pablo Villegas | Kuramoto dynamics, glassy synchronization and rare regions in the human connectome 7/7
