• Corpus ID: 248524685

Synchronization and clustering in complex quadratic networks

  title={Synchronization and clustering in complex quadratic networks},
  author={Anca R. Rădulescu and D. Reid Evans and Amani-Daisa Augustin and Anthony Cooper and Johan Nakuci and Sarah Feldt Muldoon},
In continuation of prior work, we investigate ties between a network’s connectivity and ensemble dynamics. This relationship is notoriously difficult to approach mathematically in natural, complex networks. In our work, we aim to understand it in a canonical framework, using complex quadratic node dynamics, coupled in networks which we call complex quadratic networks (CQNs). After previously defining extensions of the Mandelbrot and Julia sets for networks, we currently focus on the behavior of… 

Computing brain networks with complex dynamics

This study illustrates how topological measures of these asymptotic sets can be used e-ciently as comprehensive descriptors and classifiers of dynamics in tractography-derived connectomes for human subjects.



Real and complex behavior for networks of coupled logistic maps

The object of the study is to relate connectivity to the temporal behavior of a network in which the nodes are (real or complex) logistic maps, coupled according to a connectivity scheme that obeys certain constrains, but also incorporates random aspects.

Asymptotic sets in networks of coupled quadratic nodes

Extensions of traditional results from single map iterations, such as the existence of an escape radius, are discussed; whether crucial information about the network is encoded in the behaviour of the critical orbit is investigated; and a form of averaging uni-Julia and equi-M sets is proposed to describe statistically the likelihood of a specific asymptotic behaviour.

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

The synchronization behavior of this model is determined by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state, and the control-parameter dependent exponent suggests extended dynamical criticality below the transition point.

Clustering in globally coupled inhibitory neurons

Activity Patterns in a Model for the Subthalamopallidal Network of the Basal Ganglia

The results suggest that the subthalamopallidal circuit is capable both of correlated rhythmic activity and of irregular autonomous patterns of activity that block rhythmicity, and may be sufficient to explain the emergence of correlated oscillatory activity after destruction of dopaminergic neurons in Parkinson's disease and in animal models of parkinsonism.

Automated Anatomical Labeling of Activations in SPM Using a Macroscopic Anatomical Parcellation of the MNI MRI Single-Subject Brain

An anatomical parcellation of the spatially normalized single-subject high-resolution T1 volume provided by the Montreal Neurological Institute was performed and it is believed that this tool is an improvement for the macroscopical labeling of activated area compared to labeling assessed using the Talairach atlas brain.

Generalized q-Sampling Imaging

The proposed GQI method can be applied to grid or shell sampling schemes and can provide directional and quantitative information about the crossing fibers.

Deterministic Diffusion Fiber Tracking Improved by Quantitative Anisotropy

The performance of quantitative anisotropy (QA) in facilitating deterministic fiber tracking may assist fiber tracking studies and facilitate the advancement of human connectomics.