Knotty-Centrality: Finding the Connective Core of a Complex Network

A network measure called knotty-centrality is defined that quantifies the extent to which a given subset of a graph’s nodes constitutes a densely intra-connected topologically central connective core. Using this measure, the knotty centre of a network is defined as a sub-graph with maximal knotty-centrality. A heuristic algorithm for finding subsets of a network with high knotty-centrality is presented, and this is applied to previously published brain structural connectivity data for the cat and the human, as well as to a number of other networks. The cognitive implications of possessing a connective core with high knotty-centrality are briefly discussed

Chimera-like states in modular neural networks

Chimera states, namely the coexistence of coherent and incoherent behavior, were previously analyzed in complex networks. However, they have not been extensively studied in modular networks. Here, we consider a neural network inspired by the connectome of the C. elegans soil worm, organized into six interconnected communities, where neurons obey chaotic bursting dynamics. Neurons are assumed to be connected with electrical synapses within their communities and with chemical synapses across them. As our numerical simulations reveal, the coaction of these two types of coupling can shape the dynamics in such a way that chimera-like states can happen. They consist of a fraction of synchronized neurons which belong to the larger communities, and a fraction of desynchronized neurons which are part of smaller communities. In addition to the Kuramoto order parameter ?, we also employ other measures of coherence, such as the chimera-like ? and metastability ? indices, which quantify the degree of synchronization among communities and along time, respectively. We perform the same analysis for networks that share common features with the C. elegans neural network. Similar results suggest that under certain assumptions, chimera-like states are prominent phenomena in modular networks, and might provide insight for the behavior of more complex modular networks

A biophysical model of dynamic balancing of excitation and inhibition in fast oscillatory large-scale networks

Over long timescales, neuronal dynamics can be robust to quite large perturbations, such as changes in white matter connectivity and grey matter structure through processes including learning, aging, development and certain disease processes. One possible explanation is that robust dynamics are facilitated by homeostatic mechanisms that can dynamically rebalance brain networks. In this study, we simulate a cortical brain network using the Wilson-Cowan neural mass model with conduction delays and noise, and use inhibitory synaptic plasticity (ISP) to dynamically achieve a spatially local balance between excitation and inhibition. Using MEG data from 55 subjects we find that ISP enables us to simultaneously achieve high correlation with multiple measures of functional connectivity, including amplitude envelope correlation and phase locking. Further, we find that ISP successfully achieves local E/I balance, and can consistently predict the functional connectivity computed from real MEG data, for a much wider range of model parameters than is possible with a model without ISP

The dynamics of resting fluctuations in the brain: metastability and its dynamical cortical core

In the human brain, spontaneous activity during resting state consists of rapid transitions between functional network states over time but the underlying mechanisms are not understood. We use connectome based computational brain network modeling to reveal fundamental principles of how the human brain generates large-scale activity observable by noninvasive neuroimaging. We used structural and functional neuroimaging data to construct whole- brain models. With this novel approach, we reveal that the human brain during resting state operates at maximum metastability, i.e. in a state of maximum network switching. In addition, we investigate cortical heterogeneity across areas. Optimization of the spectral characteristics of each local brain region revealed the dynamical cortical core of the human brain, which is driving the activity of the rest of the whole brain. Brain network modelling goes beyond correlational neuroimaging analysis and reveals non-trivial network mechanisms underlying non-invasive observations. Our novel findings significantly pertain to the important role of computational connectomics in understanding principles of brain function.GD is supported by the ERC Advanced Grant DYSTRUCTURE (n. 295129), by the Spanish Research Project PSI2016-75688-P. MLK is supported by the ERC Consolidator Grant: CAREGIVING (n. 615539) and Center for Music in the Brain, funded by the Danish National Research Foundation (DNRF117). VJ and GD are supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement n. 720270 (HBP SGA1). VJ and PR are supported by the James S. McDonnell Foundation (Brain Network Recovery Group JSMF22002082). VJ is supported by FHU EPINEXT [A*MIDEX project (ANR-11-IDEX-0001-02) funded by the ‘Investissements d’Avenir’ French Government]. PR is supported the German Ministry of Education and Research (US-German Collaboration in Computational Neuroscience 100258846 and Bernstein Focus State Dependencies of Learning 01GQ0971-5), the Max-Planck Society and funding from the European Union Horizon 2020 (ERC Consolidator grant BrainModes 683049)