D. Papo, M. Zanin, J.H. Martínez, and J.M. Buldú
Frontiers in Human Neuroscience, 10:96 (2016).
Whether or not the brain is indeed a SW network is still very much an open question. The question that we address is of a pragmatical rather than an ontological nature: independently of whether the brain is a SW network or not, to what extent can neuroscientists using standard system-level neuroimaging techniques interpret the SW construct in the context of functional brain networks? In a typical experimental setting, neuroscientists record brain images, define nodes and links, construct a network, extract its topological properties, to finally assess their statistical significance and their possible functional meaning. We review evidence showing that behind each of these stages lurk fundamental technical, methodological or theoretical stumbling blocks that render the experimental quantification of the SW structure and its interpretation in terms of information processing problematic, questioning its usefulness as a descriptor of global brain organization. The emphasis is on functional brain activity reconstructed using standard system-level brain recording techniques, where the SW construct appears to be the most problematic.
[Read more in Frontiers in Human Neuroscience] [arXiv]
M. Zanin and D. Papo
Entropy, 16:5655-5667 (2014).
Motifs are small recurring circuits of interactions which constitute the backbone of networked systems. Characterizing motif dynamics is therefore key to understanding the functioning of such systems. Here we propose a method to deﬁne and quantify the temporal variability and time scales of electroencephalogram (EEG) motifs of resting brain activity. Given a triplet of EEG sensors, links between them are calculated by means of linear correlation; each pattern of links (i.e., each motif) is then associated to a symbol, and its appearance frequency is analyzed by means of Shannon entropy. Our results show that each motif becomes observable with different coupling thresholds and evolves at its own time scale, with fronto-temporal sensors emerging at high thresholds and changing at fast time scales, and parietal ones at low thresholds and changing at slower rates. Finally, while motif dynamics differed across individuals, for each subject, it showed robustness across experimental conditions, indicating that it could represent an individual dynamical signature.
[Read more in Entropy]
D. Papo, J.M. Buldú, S. Boccaletti and E.T. Bullmore
Philosophical Transactions of the Royal Society B, 369:20130520 (2014).
Complex network theory is a statistical physics understanding of graph theory, itself a much older branch of pure mathematics. The statistical physics approach aims at explaining observable macroscopic behaviour of a given system as emerging in a non-trivial way from the interactions of a vast number of microscopic units or agents. Complex network theory can be thought of as a subfield of statistical physics for structurally disordered, dynamically heterogeneous systems with non-trivial topology; and as an extension of graph theory to systems with high structural heterogeneity and inherently dynamical properties, two key properties of the vast majority of real-life systems, including brains.
Can this approach be useful when studying brain anatomy and function?
Read more in Philosophical Transactions] [Read interview in Phil. Trans Blog] [Listen to podcast in Nature]
D. Papo, M. Zanin, J.A. Pineda-Pardo, S. Boccaletti, and J.M. Buldú
Philosophical Transactions of the Royal Society B 369:20130525 (2014).
Many physical and biological systems can be studied using complex network theory, a new statistical physics understanding of graph theory. The recent application of complex network theory to the study of functional brain networks generated great enthusiasm as it allows addressing hitherto non-standard issues in the field, such as efficiency of brain functioning or vulnerability to damage. However, in spite of its high degree of generality, the theory was originally designed to describe systems profoundly different from the brain. We discuss some important caveats in the wholesale application of existing tools and concepts to a field they were not originally designed to describe. At the same time, we argue that complex network theory has not yet been taken full advantage of, as many of its important aspects are yet to make their appearance in the neuroscience literature. Finally, we propose that, rather than simply borrowing from an existing theory, functional neural networks can inspire a fundamental reformulation of complex network theory, to account for its exquisitely complex functioning mode.
[Read more in Philosophical Transactions] [Read more in ArXiv] [Read interview in Phil. Trans Blog] [Listen to podcast in Nature]
M. Zanin, J. Medina Alcazar, J. Vicente Carbajosa, M. Gomez Paez, D. Papo, P. Sousa, E. Menasalvas, and S. Boccaletti
Scientific Reports, 4:5112 (2014).
We introduce a novel method to represent time independent, scalar data sets as complex networks. We apply our method to investigate gene expression in the response to osmotic stress of Arabidopsis thaliana. In the proposed network representation, the most important genes for the plant response turn out to be the nodes with highest centrality in appropriately reconstructed networks. We also performed a target experiment, in which the predicted genes were artiﬁcially induced one by one, and the growth of the corresponding phenotypes compared to that of the wild-type. The joint application of the network reconstruction method and of the in vivo experiments allowed identifying 15 previously unknown key genes, and provided models of their mutual relationships. This novel representation extends the use of graph theory to data sets hitherto considered outside of the realm of its application, vastly simplifying the characterization of their underlying structure.
[Read more in Scientific Reports] [Read more in ArXiv]
D. Papo, M. Zanin and J.M. Buldú
Frontiers in Human Neuroscience, 8:107 (2014).
Both at rest and during the executions of cognitive tasks, the brain continuously creates and reshapes complex patterns of correlated dynamics. Thus, brain functional activity is naturally described in terms of networks, i.e. sets of nodes, representing distinct subsystems, and links connecting node pairs, representing relationships between them. Recently, brain function has started being investigated using a statistical physics understanding of graph theory, an old branch of pure mathematics (Newman, 2010). Within this framework, networks properties are independent of the identity of their nodes, as they emerge in a non-trivial way from their interactions. Observed topologies are instances of a network ensemble, falling into one of few universality classes and are therefore inherently statistical in nature. Functional network reconstruction comprises various steps: first, nodes are identified; then, links are established according to a certain metric. This gives rise to a clique with an all-to-all connectivity. Deciding which links are significant is done by choosing which values of these metrics should be taken into account. Finally, network properties are computed and used to characterize the network. Each of these steps contains an element of arbitrariness, as graph theory allows characterizing systems once a network is reconstructed, but is neutral as to what should be treated as a system and to how to isolate its constituent parts. Here we discuss some aspects related to the way nodes, links and networks in general are defined in system-level studies using noninvasive techniques, which may be critical when interpreting the results of functional brain network analyses.
[Read more in Frontiers in Human Neuroscience]