A topological approach to neural complexity

Considerable efforts in modern statistical physics is devoted to the study of networked systems. One of the most important example of them is the brain, which creates and continuously develops complex networks of correlated dynamics. An important quantity which captures fundamental aspects of brain network organization is the neural complexity C(X)introduced by Tononi et al. This work addresses the dependence of this measure on the topological features of a network in the case of gaussian stationary process. Both anlytical and numerical results show that the degree of complexity has a clear and simple meaning from a topological point of view. Moreover the analytical result offers a straightforward algorithm to compute the complexity than the standard one.Comment: 6 pages, 4 figure

Performance of networks of artificial neurons: The role of clustering

The performance of the Hopfield neural network model is numerically studied on various complex networks, such as the Watts-Strogatz network, the Barab{\'a}si-Albert network, and the neuronal network of the C. elegans. Through the use of a systematic way of controlling the clustering coefficient, with the degree of each neuron kept unchanged, we find that the networks with the lower clustering exhibit much better performance. The results are discussed in the practical viewpoint of application, and the biological implications are also suggested.Comment: 4 pages, to appear in PRE as Rapid Com

Structural subnetwork evolution across the life-span: rich-club, feeder, seeder

The impact of developmental and aging processes on brain connectivity and the connectome has been widely studied. Network theoretical measures and certain topological principles are computed from the entire brain, however there is a need to separate and understand the underlying subnetworks which contribute towards these observed holistic connectomic alterations. One organizational principle is the rich-club - a core subnetwork of brain regions that are strongly connected, forming a high-cost, high-capacity backbone that is critical for effective communication in the network. Investigations primarily focus on its alterations with disease and age. Here, we present a systematic analysis of not only the rich-club, but also other subnetworks derived from this backbone - namely feeder and seeder subnetworks. Our analysis is applied to structural connectomes in a normal cohort from a large, publicly available lifespan study. We demonstrate changes in rich-club membership with age alongside a shift in importance from 'peripheral' seeder to feeder subnetworks. Our results show a refinement within the rich-club structure (increase in transitivity and betweenness centrality), as well as increased efficiency in the feeder subnetwork and decreased measures of network integration and segregation in the seeder subnetwork. These results demonstrate the different developmental patterns when analyzing the connectome stratified according to its rich-club and the potential of utilizing this subnetwork analysis to reveal the evolution of brain architectural alterations across the life-span

Structure-function clustering in multiplex brain networks

A key question in neuroscience is to understand how a rich functional repertoire of brain activity arises within relatively static networks of structurally-connected neural populations: elucidating the subtle interactions between evoked ‘functional connectivity’ and the underlying ‘structural connectivity’ has the potential to address this. These structural-functional networks (and neural networks more generally) are more naturally described using a multilayer or multiplex network approach, in favour of standard single-layer network analyses that are more typically applied to such systems. In this letter, we address such issues by exploring important structure-function relations in the Macaque cortical network by modelling it as a duplex network that comprises an anatomical layer, describing the known (macro-scale) network topology of the Macaque monkey, and a functional layer derived from simulated neural activity. We investigate and characterize correlations between structural and functional layers, as system parameters controlling simulated neural activity are varied, by employing recently described multiplex network measures. Moreover, we propose a novel measure of multiplex structure-function clustering which allows us to investigate the emergence of functional connections that are distinct from the underlying cortical structure, and to highlight the dependence of multiplex structure on the neural dynamical regime

Influence of wiring cost on the large-scale architecture of human cortical connectivity

In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain's function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain's connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained (‘random’), connection length preserving (‘spatial’), and connection length optimised (‘reduced’) surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain

An Adaptive Complex Network Model for Brain Functional Networks

Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence) of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution

Topology and Computational Performance of Attractor Neural Networks

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most efficient for storage and retrieval of patterns by the entire network. However, in the scale-free case retrieval errors are not distributed uniformly: the portion of a pattern encoded by the subset of highly connected nodes is more robust and efficiently recognized than the rest of the pattern. The scale-free network thus achieves a very strong partial recognition. Implications for brain function and social dynamics are suggestive.Comment: 2 figures included. Submitted to Phys. Rev. Letter

Structural and functional, empirical and modeled connectivity in the cerebral cortex of the rat

[EN] Connectomics data from animal models provide an invaluable opportunity to reveal the complex interplay between structure and function in the mammalian brain. In this work, we investigate the relationship between structural and functional connectivity in the rat brain cortex using a directed anatomical network generated from a carefully curated meta-analysis of published tracing data, along with resting-state functional MRI data obtained from a group of 14 anesthetized Wistar rats. We found a high correspondence between the strength of functional connections, measured as blood oxygen level dependent (BOLD) signal correlations between cortical regions, and the weight of the corresponding anatomical links in the connectome graph (maximum Spearman rank-order correlation rho = 0.48). At the network-level, regions belonging to the same functionally defined community tend to form more mutual weighted connections between each other compared to regions located in different communities. We further found that functional communities in resting-state networks are enriched in densely connected anatomical motifs. Importantly, these higher-order structural subgraphs cannot be explained by lower-order topological properties, suggesting that dense structural patterns support functional associations in the resting brain. Simulations of brain-wide resting-state activity based on neural mass models implemented on the empirical rat anatomical connectome demonstrated high correlation between the simulated and the measured functional connectivity (maximum Pearson correlation rho = 0: 53), further suggesting that the topology of structural connections plays an important role in shaping functional cortical networks.This work was supported in part by the Spanish Ministerio de Economia y Competitividad (MINECO) and FEDER funds under grants BFU2015-64380-C2-1-R (S.C) and BFU2015-64380-C2-2-R (D.M.) and EU Horizon 2020 Program 668863-SyBil-AA grant (S.C.). S.C. acknowledges financial support from the Spanish State Research Agency, through the "Severo Ochoa" Programme for Centres of Excellence in R&D (ref. SEV-2013-0317). A. D.-P., was supported by grant FPU13/01475 from the Spanish Ministerio de Educacion, Cultura y Deporte (MECD). O.S. acknowledges support by the J.S. McDonnell Foundation (#220020387) and the National Institutes of Health (NIH R01 AT009036-01). We are also grateful to Andrea Avena-Koenigsberger and Begona Fernandez for their technical support.Díaz-Parra, A.; Osborn, Z.; Canals Gamoneda, S.; Moratal, D.; Sporns, O. (2017). Structural and functional, empirical and modeled connectivity in the cerebral cortex of the rat. NeuroImage. 159:170-184. https://doi.org/10.1016/j.neuroimage.2017.07.046S17018415