“Assessing time series reversibility through permutation patterns“
M. Zanin, A.R. Rodriguéz-González, E. Menasalvas Ruiz and D. Papo
Time irreversibility, i.e. the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation.
“What is ‘functional brain activity’?”
The development of neuroimaging techniques such as PET and MRI made it possible to not only look non-invasively at the anatomy of the human brain but also to have access to its physiology. Recording of brain activity is generally called functional imaging. This terminology implicitly entails that any activity recorded by these devices should be thought of as functional. Here, it is submitted that a stricter definition of what should be regarded as ‘functional‘ in brain activity would suppose some important advantages for neuroscientists. It is argued that 1) the functional space need not be isomorphic to the anatomical one; 2) brain function should not be equated with brain dynamics; 3) for brain functional descriptions to be specific it is necessary to define the structure of the functional space.
“Mapping highways of the functional space“
At large spatial and temporal scales, brain activity can be thought of as a complex high-dimensional object, and both cognitive functions and the relationships between them as possibly non-local functionals on this object. But how can we define relationships within this space? What does describing the functional space actually mean?
Physics of Life Reviews
“Can multilayer brain networks be a real step forward?“
J.M. Buldú and D. Papo
Physics of Life Reviews
“Beyond the anatomy-based representation of brain function“
Often, viz. in tumour removal procedures, neurosurgeons operate on a sedated but awake patient to precisely locate functional brain areas that must be avoided. To do so, brain regions are electrically stimulated while the patient performs tasks such as talking, counting or looking at pictures. The patient’s responses are then used to create a map of the functional areas of the brain and remove as much of the tumour as possible. In so doing, neurosurgeons parse the Euclidean space of brain anatomy to navigate into the space of cognitive function. However the map between these two spaces is not smooth, and the topology induced by local electrical stimulation non-trivial. So, how should stimulation be carried out, i.e. on what space should it act to render the application smooth and the resulting topology “tractable”?
“On the relation of dynamics and structure in brain networks”
D. Papo, J. Goñi and J.M. Buldú
Expected date of publication: April 2017
Despite more than a century-long effort, the functioning of the few-pound lump of white and grey matter that forms the brain remains at least partially a mystery. Physicists have made some significant contributions to the understanding of brain physiology, none perhaps more notable than Hodgkin and Huxley’s, who discovered the ionic basis of nerve cell conduction. But could they also help shedding light on how large numbers of neurons interact to give rise to sophisticated behaviour?
“Detecting switching and intermittent causalities in time series”
M. Zanin and D. Papo
In biological systems such as the brain, interactions can be fast and short-lived. However, robust causal relationships are usually quantified over time-windows much larger than functionally meaningful time scales. We propose a method to overcome this drawback and quantify causal dynamical connectivity in which every possible time window is considered and non-overlapping ones in which the causality is strongest eventually selected. Our results show that transient but not classical time-averaged causality estimations can discriminate between the electroencephalographic activity of a small sample of alcoholic subjects and a matched healthy control group. Differences between groups appear to be a local rather than a global network property. The implications of these results for the modelling of brain functioning and pathology are briefly discussed.
Frontiers in Human Neuroscience
“Commentary: The entropic brain: a theory of conscious states informed by neuroimaging research with psychedelic drugs”
The “entropic brain hypothesis” holds that the quality of conscious states depends on the system’s entropy . Brain activity is said to become “more random and so harder to predict in primary states – of which the psychedelic state is an exemplar”. Psychedelic-induced brain activity would be associated with elevated entropy in some of its aspects with respect to normal wakeful consciousness. This would indicate that psychedelic-induced brain activity would exhibit criticality, while normal wakeful consciousness would be subcritical.
But can entropy be a unique indicator of the “quality of consciousness”? Are there reasons to believe that psychedelic-induced activity is not critical?
 Carhart-Harris, R.L., Leech, R., Hellyer, P.J., Shanahan, M., Feilding, A., Tagliazucchi, E., Chialvo, D.R., and Nutt, D. (2014). The entropic brain: a theory of conscious states informed by neuroimaging research with psychedelic drugs. Front. Hum. Neurosci. 8, 20.
Frontiers in Human Neuroscience
“Beware of the Small-world, neuroscientist!”
D. Papo, M. Zanin, J.H. Martínez, and J.M. Buldú
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.
Frontiers in Human Neuroscience
“How can we study reasoning in the brain?”
The brain did not develop a dedicated device for reasoning. This seemingly trivial fact bears dramatic consequences. While for perceptuo-motor functions neural activity is shaped by the input’s statistical properties, and processing is carried out at high speed in hardwired spatially segregated modules, in reasoning, neural activity is driven by internal dynamics, and processing times, stages, and functional brain geometry are largely unconstrained a priori. In this study, it is argued that to characterize the neural correlates of reasoning implies defining these quantities in terms of non-trivial generic properties of ongoing brain activity, and resorting to concepts, analytical tools, and ways of designing experiments that are as yet non-standard in the cognitive neuroscience of reasoning.
Philosophical Transactions of the Royal Society, B
“Complex network theory and the brain“
D. Papo, J.M. Buldú, S. Boccaletti, and E.T. Bullmore
Published online: 1 September 2014
Many physical and biological systems can be studied using complex network theory, a new statistical physics understanding of graph theory. Its recent application to the study of anatomical and functional brain networks has generated great enthusiasm as it allowed neuroscientists to address an entirely new set of experimental questions. In this Theme Issue we propose a critical review of the main advances in the field of complex network theory applications to neuroscience, highlight some of the current shortcomings and propose a series of promising lines for future developments. Ways in which neuroscience could not only use but also promote advances complex network theory are also proposed.
Frontiers in Computational Neuroscience
“Computation beyond the Boolean world”
M. Zanin, D. Papo and J.M. Buldú
Understanding how computational tasks are performed in the brain is a challenging task. This is clearly due to the intrinsic complexity of the brain, but also to the presence of three elements that are usually not part of an engineering view of computation.
Deadline for abstract submission: 01 Jul 2014
Deadline for full article submission: 01 Nov 2014
Frontiers in Systems Neuroscience
“Functional significance of complex fluctuations in brain activity: from rest to cognitive neuroscience”
Behavioural studies have shown that human cognition is characterized by properties such as temporal scale invariance, heavy-tailed non-Gaussian distributions, and long-range correlations at long time scales, suggesting models of how (non observable) components of cognition interact. On the other hand, results from functional neuroimaging studies show that complex scaling and intermittency may be generic spatio-temporal properties of the brain at rest. Somehow surprisingly, though, hardly ever have the neural correlates of cognition been studied at time scales comparable to those at which cognition shows scaling properties. Here, we analyze the meanings of scaling properties and the significance of their task-related modulations for cognitive neuroscience. It is proposed that cognitive processes can be framed in terms of complex generic properties of brain activity at rest and, ultimately, of functional equations, limiting distributions, symmetries, and possibly universality classes characterizing them.
Philosophical Transactions of the Royal Society, B
“Functional brain networks: great expectations, hard times, and the big leap forward”
D. Papo, M. Zanin, J.A. Pineda-Pardo, S. Boccaletti, and J.M. Buldú
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.
Physical Review Letters
“Synchronization of interconnected networks: The role of connector nodes”
J. Aguirre, R. Sevilla-Escoboza, R. Gutiérrez, D. Papo, and J.M. Buldú
In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically and experimentally how the degree of the nodes through which two networks are connected inﬂuences the ability of the whole system to synchronize. We show that connecting the high-degree (low-degree) nodes of each network turns out to be the most (least) effective strategy to achieve synchronization. We ﬁnd the functional relation between synchronizability and size for a given network-of-networks, and report the existence of the optimal connector link weights for the different interconnection strategies. Finally, we perform an electronic experiment with two coupled star networks and conclude that the analytical results are indeed valid in the presence of noise and parameter mismatches.
“Parenclitic networks: uncovering new functions in biological data”
M. Zanin, J. Medina Alcazar, J. Vicente Carbajosa, M. Gomez Paez, D. Papo, P. Sousa, E. Menasalvas, and S. Boccaletti
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 stressof Arabidopsis thaliana. In the proposed network representation, the most important genesfor 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 geneswere 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.