A. Tozzi and D. Papo
Progress in Biophysics and Molecular Biology, 151:1-13 (2020)
Causal relationships lie at the very core of scientific description of biophysical phenomena. Nevertheless, observable facts involving changes in system shape, dimension and symmetry may elude simple cause and effect inductive explanations. Here we argue that numerous physical and biological phenomena such as chaotic dynamics, symmetry breaking, long-range collisionless neural interactions, zero-value energy singularities, particle/wave duality can be accounted for in terms of purely topological mechanisms devoid of causality. We illustrate how simple topological claims, seemingly far away from scientific inquiry (e.g., “given at least some wind on Earth, there must at all times be a cyclone or anticyclone somewhere”; “if one stirs to dissolve a lump of sugar in a cup of coffee, it appears there is always a point without motion”; “at any moment, there is always a pair of antipodal points on the Earth’s surface with equal temperatures and barometric pressures” ) reflect the action of non-causal topological rules. To do so, we introduce some fundamental topological tools and illustrate how phenomena such as double slit experiments, cellular mechanisms and some aspects of brain function can be explained in terms of geometric projections and mappings, rather than local physical effects. We conclude that unavoidable, passive, spontaneous topological modifications may lead to novel functional biophysical features, independent of exerted physical forces, thermodynamic constraints, temporal correlations and probabilistic a priori knowledge of previous cases.
[Read more in Progress in Biophysics and Molecular Biology]
Keywords: topology; topological explanation; causality; Poincaré-Hopf theorem; hairy ball theorem; Borsuk-Ulam theorem; Kneser graph; non-Hermitian systems
M. Zanin, B. Güntekin, T. Aktürk, L. Hanoğlu, and D. Papo
Frontiers in Physiology, 10:1619 (2020)
Characterizing brain activity at rest is of paramount importance to our understanding both of general principles of brain functioning and of the way brain dynamics is affected in the presence of neurological of psychiatric pathologies. We measured the time-reversal symmetry of spontaneous electroencephalographic brain activity recorded from three groups of patients and their respective control group under two experimental conditions (eyes open and closed). We evaluated differences in time irreversibility in terms of possible underlying physical generating mechanisms. The results showed that resting brain activity is generically time-irreversible at sufﬁciently long time scales, and that brain pathology is generally associated with a reduction in time asymmetry, albeit with pathology-speciﬁc patterns. The signiﬁcance of these results and their possible dynamical aetiology are discussed. Some implications of the differential modulation of time asymmetry by pathology and experimental condition are examined.
[Read more in Frontiers in Physiology] [Read more in arXiv]
Keywords: resting state; functional; entropy production; time reversal symmetry; Parkinson’s disease; Schizophrenia; EEG
Frontiers in Physiology, 10:509 (2019)
Standard neuroimaging techniques provide non-invasive access not only to human brain anatomy but also to its physiology. The activity recorded with these techniques is generally called functional imaging, but what is observed per se is an instance of dynamics, from which functional brain activity should be extracted. Distinguishing between bare dynamics and genuine function is a highly non-trivial task, but a crucially important one when comparing experimental observations and interpreting their significance. Here we illustrate how the ability of neuroimaging to extract genuine functional brain activity is bounded by the structure of functional representations. To do so, we first provide a simple definition of functional brain activity from a system-level brain imaging perspective. We then review how the properties of the space on which brain activity is represented allow defining relations ranging from distinguishability to accessibility of observed imaging data. We show how these properties result from the structure defined on dynamical data and dynamics-to-function projections, and consider some implications that the way and extent to which these are defined have for the interpretation of experimental data from standard system-level brain recording techniques.
[Read more in ArXiv]
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
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]
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]
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]