Assessing time series reversibility through permutation patterns

Zanin, M., Rodríguez-González, A., Menasalvas Ruiz, E., & Papo, D. 

Entropy, 20:665 (2018)

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.

[Read more in Entropy]

Keywords: time-reversal symmetry; permutation entropy; entropy production; visibility graphs; out-of-equilibrium system; time series analysis; predictability; Efficient Market Hypothesis

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Brain synchronizability, a false friend

D. Papo and J.M. Buldú

Neuroimage, 196:195-199 (2019)

Synchronization plays a fundamental role in healthy cognitive and motor function. However, how synchronization depends on the interplay between local dynamics, coupling and topology and how prone to synchronization a network with given topological organization is are still poorly understood issues. To investigate the synchronizability of both anatomical and functional brain networks various studies resorted to the Master Stability Function (MSF) formalism, an elegant tool which allows analysing the stability of synchronous states in a dynamical system consisting of many coupled oscillators. Here, we argue that brain dynamics does not fulfil the formal criteria under which synchronizability is usually quantified and, perhaps more importantly, what this measure itself quantifies refers to a global dynamical condition that never holds in the brain (not even in the most pathological conditions), and therefore no neurophysiological conclusions should be drawn based on it. We discuss the meaning of synchronizability and its applicability to neuroscience and propose alternative ways to quantify brain networks synchronization.

[Read more in NeuroImage] [Read more in arXiv]

Neurofeedback: principles, appraisal and outstanding issues

D. Papo  

European Journal of Neuroscience, 00:1–16, (2019); arXiv:1805.05303

Neurofeedback is a form of brain training in which subjects are fed back information about some measure of their brain activity which they are instructed to modify in a way thought to be functionally advantageous. Over the last twenty years, NF has been used to treat various neurological and psychiatric conditions, and to improve cognitive function in various contexts. However, in spite of a growing popularity, NF protocols typically make (often covert) assumptions on what aspects of brain activity to target, where in the brain to act and how, which have far-reaching implications for the assessment of its potential and efficacy. Here we critically examine some conceptual and methodological issues associated with the way NF’s general objectives and neural targets are defined. The neural mechanisms through which NF may act at various spatial and temporal scales, and the way its efficacy is appraised are reviewed, and the extent to which NF may be used to control functional brain activity discussed. Finally, it is proposed that gauging NF’s potential, as well as assessing and improving its efficacy will require better understanding of various fundamental aspects of brain dynamics and a more precise definition of functional brain activity and brain-behaviour relationships.

[Read more in EJN] [Read more in arXiv]

Beyond the anatomy-based representation of brain function

D. Papo

Physics of Life Reviews, 21:42-45 (2017).

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”?

[Read more in Physics of Life Reviews]

Detecting switching and intermittent causalities in time series

M. Zanin and D. Papo

Chaos, 27:047403 (2017).

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.

[Read more in Chaos]

The ACE brain

M. Zanin and D. Papo   

Frontiers in Computational Neuroscience, 10:122 (2016).

Neuroscientists’ models of brain functional organization, and in particular of how a given task recruits brain resources, bear important analogies with the way computer elements are arranged and activated to perform complex operations. In modern CPUs, data are distributed across different sub-units by a central controller, a structure inspired by the research performed in the 40s by von Neumann (1993). However, this is not the only possible configuration, and we compare it with the alternative proposed by Alan Turing in the same decade (Carpenter and Doran, 1986). How does the underlying model of computer functioning influence the way neuroscientists describe the brain? For instance, at a system-level of description, neuroscientists typically want to extract the minimum sub-system of the whole brain necessary to execute a given task. Suppose in particular that brain activity is endowed with a network representation (Bullmore and Sporns, 2009). What would the minimal subsystem look like? We propose that Turing’s approach is more representative of the human brain, and discuss when functional networks may yield misleading results when applied to such a system.

[Read more in Frontiers in Computational Neuroscience]

Commentary: The entropic brain: a theory of conscious states informed by neuroimaging research with psychedelic drugs

D. Papo

Frontiers in Human Neuroscience, 10:423 (2016).

The “entropic brain hypothesis” holds that the quality of conscious states depends on the system’s entropy [1]. 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?

[1] 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.

[Read more in Frontiers in Human Neuroscience]

Beware of the Small-world, neuroscientist!

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]

How can we study reasoning in the brain?

D. Papo

Frontiers in Human Neuroscience, 10:423 (2016).

The brain did not develop a dedicated device for reasoning. This 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. Here, it is shown that the complex properties of spontaneous activity, which can be ignored in a short-lived event-related world, become prominent at the long time scales of certain forms of reasoning. It is argued that the neural correlates of reasoning should in fact be defined in terms of non-trivial generic properties of spontaneous brain activity, and that this implies resorting to concepts, analytical tools, and ways of designing experiments that are as yet non-standard in cognitive neuroscience. The implications in terms of models of brain activity, shape of the neural correlates, methods of data analysis, observability of the phenomenon and experimental designs are discussed.

Characterizing Motif Dynamics of Electric Brain Activity Using Symbolic Analysis

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]