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Kuramoto dynamics, glassy synchronization and rare
regions in the human connectome
Pablo Villegas
Quantitative Laws II
(Un...
The Kuramoto model
Intrinsic frecuency
·
θi = ωi + k
N
j=1
Wijsin (θj − θi) + ηi (t) i = 1, ..., N
Coupling term
Noise
z =...
The Human Connectome
Figure : Adjacency matrix and modular structure
Pablo Villegas | Kuramoto dynamics, glassy synchroniz...
The Human Connectome
A hierarchical synchronization process appears, with local phase transitions
and a new intermediate p...
A model: Hierarchical Modular Network
We can see the same phenomena in synthetic Hierarchic Modular Networks
(HMNs), with ...
Metastability in HMNs
Switching behavior in the HC and HMNs. This behavior closely resembles
’up and down’ states.
200 400...
Thanks for your attention
Collaborators
We acknowledge financial support from MINECO (National Plan of I+D+i), grant FIS201...
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Kuramoto dynamics, glassy synchronization and rare regions in the human connectome - Pablo Villegas

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QUANTITATIVE LAWS June 13 -June 24

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Kuramoto dynamics, glassy synchronization and rare regions in the human connectome - Pablo Villegas

  1. 1. Kuramoto dynamics, glassy synchronization and rare regions in the human connectome Pablo Villegas Quantitative Laws II (University of Granada)
  2. 2. The Kuramoto model Intrinsic frecuency · θi = ωi + k N j=1 Wijsin (θj − θi) + ηi (t) i = 1, ..., N Coupling term Noise z = reiψ = 1 N N j=1 eiθj Pablo Villegas | Kuramoto dynamics, glassy synchronization and rare regions in the human connectome 2/7
  3. 3. The Human Connectome Figure : Adjacency matrix and modular structure Pablo Villegas | Kuramoto dynamics, glassy synchronization and rare regions in the human connectome 3/7
  4. 4. 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
  5. 5. 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
  6. 6. Metastability in HMNs Switching behavior in the HC and HMNs. This behavior closely resembles ’up and down’ states. 200 400 600 800 0.3 0.5 0.7 0.3 0.5 0.7 0.3 0.5 0.7 HC(a) orderparameter (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 orderparameter orderparameter(steady) (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
  7. 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

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