Géza Ódor, Michael Gastner, Jeffrey Kelling, Gustavo Deco
In this review, we discuss critical dynamics of simple nonequilibrium models on large connectomes, obtained by diffusion MRI, representing the white matter of the human brain. In the first chapter, we overview graph theoretical and topological analysis of these networks, pointing out that universality allows selecting a representative network, the KKI-18, which has been used for dynamical simulation. The critical and sub-critical behaviour of simple, two- or three-state threshold models is discussed with special emphasis on rare-region effects leading to robust Griffiths Phases (GP). Numerical results of synchronization phenomena, studied by the Kuramoto model, are also shown, leading to a continuous analog of the GP, termed frustrated synchronization. The models presented here exhibit dynamical scaling behaviour with exponents in agreement with brain experimental data if local homeostasis is provided.
José A. Carrillo, Stéphane Cordier, Gustavo Deco, Simona Mancini
We are concerned with the complexity reduction of a stochastic system of differential equations governing the dynamics of a neuronal circuit describing a decision-making task. This reduction is based on the slow-fast behavior of the problem and holds on the whole phase space and not only locally around the spontaneous state. Macroscopic quantities, such as performance and reaction times, computed applying this reduction are in agreement with previous works in which the complexity reduction is locally performed at the spontaneous point by means of a Taylor expansion.
Robert Ton, Gustavo Deco, Morten L Kringelbach, Mark Woolrich, Andreas Daffertshofer
Converging research suggests that the resting brain operates at the cusp of dynamic instability signified by scale-free temporal correlations. We asked if the scaling properties of these correlations differ between amplitude and phase fluctuations, which may reflect different aspects of cortical functioning. Using source-reconstructed magneto-encephalographic signals, we found power-law scaling for the collective amplitude and for phase synchronization, both capturing whole-brain activity. The temporal changes of the amplitude comprise slow, persistent memory processes, whereas phase synchronization exhibits less temporally structured and more complex correlations, indicating a fast and flexible coding. This distinct temporal scaling supports the idea of different roles of amplitude and phase in cortical functioning.
Ignacio Martín, Gorka Zamora, Jan Fousek, Michael Schirner, Petra Ritter, Viktor Jirsa, Gustavo Deco, Gustavo Patow
May 29, 2024·q-bio.NC·PDF This paper introduces TVB C++, a streamlined and fast C++ Back-End for The Virtual Brain (TVB), a renowned platform and a benchmark tool for full-brain simulation. TVB C++ is engineered with speed as a primary focus while retaining the flexibility and ease of use characteristic of the original TVB platform. Positioned as a complementary tool, TVB serves as a prototyping platform, whereas TVB C++ becomes indispensable when performance is paramount, particularly for large-scale simulations and leveraging advanced computation facilities like supercomputers. Developed as a TVB-compatible Back-End, TVB C++ seamlessly integrates with the original TVB implementation, facilitating effortless usage. Users can easily configure TVB C++ to execute the same code as in TVB but with enhanced performance and parallelism capabilities.
Michelle Cirunay, Géza Ódor, István Papp, Gustavo Deco
To determine the precise link between anatomical structure and function, brain studies primarily concentrate on the anatomical wiring of the brain and its topological properties. In this work, we investigate the weighted degree and connection length distributions of the KKI-113 and KKI-18 human connectomes, the fruit fly, and of the mouse retina. We found that the node strength (weighted degree) distribution behavior differs depending on the considered scale. On the global scale, the distributions are found to follow a power-law behavior, with a roughly universal exponent close to 3. However, this behavior breaks at the local scale as the node strength distributions of the KKI-18 follow a stretched exponential, and the fly and mouse retina follow the lognormal distribution, respectively which are indicative of underlying random multiplicative processes and underpins non-locality of learning in a brain close to the critical state. However, for the case of the KKI-113 and the H01 human (1mm$^3$) datasets, the local weighted degree distributions follow an exponentially truncated power-law, which may hint at the fact that the critical learning mechanism may have manifested at the node level too.
Géza Ódor, Jeffrey Kelling, Gustavo Deco
We have extended the study of the Kuramoto model with additive Gaussian noise running on the KKI-18 large human connectome graph. We determined the dynamical behavior of this model by solving it numerically in an assumed homeostatic state, below the synchronization crossover point we determined previously. The de-synchronization duration distributions exhibit power-law tails, characterized by the exponent in the range $1.1 < τ_t < 2$, overlapping the in vivo human brain activity experiments by Palva et al. We show that these scaling results remain valid, by a transformation of the ultra-slow eigen-frequencies to Gaussian with unit variance. We also compare the connectome results with those, obtained on a regular cube with $N=10^6$ nodes, related to the embedding space, and show that the quenched internal frequencies themselves can cause frustrated synchronization scaling in an extended coupling space.
Ignacio Perez Ipiña, Patricio Donnelly Kehoe, Morten Kringelbach, Helmut Laufs, Agustín Ibañez, Gustavo Deco, Yonatan Sanz Perl, Enzo Tagliazucchi
Global brain activity self-organizes into discrete patterns characterized by distinct behavioral observables and modes of information processing. The human thalamocortical system is a densely connected network where local neural activation reciprocally influences coordinated collective dynamics. We introduce a semi-empirical model to investigate the relationship between regional activation and long-range functional connectivity in the different brain states visited during the natural wake-sleep cycle. Our model combines functional magnetic resonance imaging (fMRI) data, in vivo estimates of structural connectivity, and anatomically-informed priors that constrain the independent variation of regional activation. As expected, priors based on functionally coherent networks resulted in the best fit between empirical and simulated brain activity. We show that sleep progressively divided the cortex into regions presenting opposite dynamical behavior: frontoparietal regions approached a bifurcation towards local oscillatory dynamics, while sensorimotor regions presented stable dynamics governed by noise. In agreement with human electrophysiological experiments, sleep onset induced subcortical deactivation and uncoupling, which was subsequently reversed for deeper stages. Finally, we introduced external forcing of variable intensity to simulate external perturbations, and identifiedthe key regionsespecially relevant for the recovery of wakefulness from deep sleep. Our model represents sleep as a state where long-range decoupling and regional deactivation coexist with the latent capacity for a rapid transition towards wakefulness. The mechanistic insights provided by our simulations allow the in silico parametric exploration of such transitions in terms of external perturbations, with potential applications for the control of physiological and pathological brain states.
Géza Ódor, István Papp, Gustavo Deco
We investigate the distance from equilibrium using the Kuramoto model via the degree of fluctuation-dissipation violation as the consequence of different levels of edge weight anisotropies. This is achieved by solving the synchronization equations on the raw, homeostatic weighted and a random inhibitory edge variant of a real full fly (FF) connectome, containing $\simeq 10^5$ neuron cell nodes. We investigate these systems close to their synchronization transition critical points. While the topological(graph) dimension is high: $d \simeq 6$ the spectral dimensions of the variants, relevant in describing the synchronization behavior, are lower than the upper critical dimension: $d_s \simeq 2 < d_c=4$, suggesting relevant fluctuation effects and non mean-field scaling behavior. By measuring the auto-correlations and the auto-response functions for small perturbations we calculate the fluctuation-dissipation ratios (FDR) for the different variants of different anisotropy levels of the FF connectome. Numerical evidence is presented that the FDRs follow the level of anisotropy of these non-equilibrium systems in agreement with the expectations. We also compare these results with those on a symmetric random graph of similar size. We provide a detailed network analysis of the FF connectome and calculate the level of hierarchy, also related to the anisotropy. Finally, we provide some partial results for the periodic forced Kuramoto, the Shinomoto-Kuramoto model.
Yonatan Sanz Perl, Hernán Boccacio, Ignacio Pérez-Ipiña, Federico Zamberlán, Helmut Laufs, Morten Kringelbach, Gustavo Deco, Enzo Tagliazucchi
We consider the problem of encoding pairwise correlations between coupled dynamical systems in a low-dimensional latent space based on few distinct observations. We used variational autoencoders (VAE) to embed temporal correlations between coupled nonlinear oscillators that model brain states in the wake-sleep cycle into a two-dimensional manifold. Training a VAE with samples generated using two different parameter combinations resulted in an embedding that represented the whole repertoire of collective dynamics, as well as the topology of the underlying connectivity network. We first followed this approach to infer the trajectory of brain states measured from wakefulness to deep sleep from the two endpoints of this trajectory; next, we showed that the same architecture was capable of representing the pairwise correlations of generic Landau-Stuart oscillators coupled by complex network topology
Emilia Gómez, Carlos Castillo, Vicky Charisi, Verónica Dahl, Gustavo Deco, Blagoj Delipetrev, Nicole Dewandre, Miguel Ángel González-Ballester, Fabien Gouyon, José Hernández-Orallo, Perfecto Herrera, Anders Jonsson, Ansgar Koene, Martha Larson, Ramón López de Mántaras, Bertin Martens, Marius Miron, Rubén Moreno-Bote, Nuria Oliver, Antonio Puertas Gallardo, Heike Schweitzer, Nuria Sebastian, Xavier Serra, Joan Serrà, Songül Tolan, Karina Vold
This document contains the outcome of the first Human behaviour and machine intelligence (HUMAINT) workshop that took place 5-6 March 2018 in Barcelona, Spain. The workshop was organized in the context of a new research programme at the Centre for Advanced Studies, Joint Research Centre of the European Commission, which focuses on studying the potential impact of artificial intelligence on human behaviour. The workshop gathered an interdisciplinary group of experts to establish the state of the art research in the field and a list of future research challenges to be addressed on the topic of human and machine intelligence, algorithm's potential impact on human cognitive capabilities and decision making, and evaluation and regulation needs. The document is made of short position statements and identification of challenges provided by each expert, and incorporates the result of the discussions carried out during the workshop. In the conclusion section, we provide a list of emerging research topics and strategies to be addressed in the near future.
Michael Schirner, Lia Domide, Dionysios Perdikis, Paul Triebkorn, Leon Stefanovski, Roopa Pai, Paula Popa, Bogdan Valean, Jessica Palmer, Chloê Langford, André Blickensdörfer, Michiel van der Vlag, Sandra Diaz-Pier, Alexander Peyser, Wouter Klijn, Dirk Pleiter, Anne Nahm, Oliver Schmid, Marmaduke Woodman, Lyuba Zehl, Jan Fousek, Spase Petkoski, Lionel Kusch, Meysam Hashemi, Daniele Marinazzo, Jean-François Mangin, Agnes Flöel, Simisola Akintoye, Bernd Carsten Stahl, Michael Cepic, Emily Johnson, Gustavo Deco, Anthony R. McIntosh, Claus C. Hilgetag, Marc Morgan, Bernd Schuller, Alex Upton, Colin McMurtrie, Timo Dickscheid, Jan G. Bjaalie, Katrin Amunts, Jochen Mersmann, Viktor Jirsa, Petra Ritter
The Virtual Brain (TVB) is now available as open-source cloud ecosystem on EBRAINS, a shared digital research platform for brain science. It offers services for constructing, simulating and analysing brain network models (BNMs) including the TVB network simulator; magnetic resonance imaging (MRI) processing pipelines to extract structural and functional connectomes; multiscale co-simulation of spiking and large-scale networks; a domain specific language for automatic high-performance code generation from user-specified models; simulation-ready BNMs of patients and healthy volunteers; Bayesian inference of epilepsy spread; data and code for mouse brain simulation; and extensive educational material. TVB cloud services facilitate reproducible online collaboration and discovery of data assets, models, and software embedded in scalable and secure workflows, a precondition for research on large cohort data sets, better generalizability and clinical translation.
Ruggero G. Bettinardi, Gustavo Deco, Vasilis M. Karlaftis, Timothy J. Van Hartevelt, Henrique M. Fernandes, Zoe Kourtzi, Morten L. Kringelbach, Gorka Zamora-López
Intrinsic brain activity is characterized by highly structured co-activations between different regions, whose origin is still under debate. In this paper, we address the question whether it is possible to unveil how the underlying anatomical connectivity shape the brain's spontaneous correlation structure. We start from the assumption that in order for two nodes to exhibit large covariation, they must be exposed to similar input patterns from the entire network. We then acknowledge that information rarely spreads only along an unique route, but rather travels along all possible paths. In real networks the strength of local perturbations tends to decay as they propagate away from the sources, leading to a progressive attenuation of the original information content and, thus, of their influence. We use these notions to derive a novel analytical measure, $\mathcal{T}$ , which quantifies the similarity of the whole-network input patterns arriving at any two nodes only due to the underlying topology, in what is a generalization of the matching index. We show that this measure of topological similarity can indeed be used to predict the contribution of network topology to the expected correlation structure, thus unveiling the mechanism behind the tight but elusive relationship between structure and function in complex networks. Finally, we use this measure to investigate brain connectivity, showing that information about the topology defined by the complex fabric of brain axonal pathways specifies to a large extent the time-average functional connectivity observed at rest.
Yang Qi, Jiexiang Wang, Weiyang Ding, Gustavo Deco, Viktor Jirsa, Wenlian Lu, Jianfeng Feng
Dec 22, 2024·q-bio.NC·PDF Cortical neurons exhibit a hierarchy of timescales across brain regions in response to input stimuli, which is thought to be crucial for information processing of different temporal scales. Modeling studies suggest that both intra-regional circuit dynamics as well as cross-regional connectome may contribute to this timescale diversity. Equally important to diverse timescales is the ability to transmit sensory signals reliably across the whole brain. Therefore, the brain must be able to generate diverse timescales while simultaneously minimizing signal attenuation. To understand the dynamical mechanism behind these phenomena, we develop a second-order mean field model of the human brain by applying moment closure and coarse-graining to a digital twin brain model endowed with whole brain structural connectome. Cross-regional coupling strength is found to induced a phase transition from asynchronous activity to synchronous oscillation. By analyzing the input-response properties of the model, we reveal criticality as a unifying mechanism for enabling simultaneously optimal signal transmission and timescales diversity. We show how structural connectome and criticality jointly shape intrinsic timescale hierarchy across the brain.
Jiangnan Zhang, Chengyuan Qian, Wenlian Lu, Gustavo Deco, Weiyang Ding, Jianfeng Feng
Sep 29, 2025·q-bio.NC·PDF Recordings of brain activity, such as functional MRI (fMRI), provide low-dimensional, indirect observations of neural dynamics evolving in high-dimensional, unobservable spaces. Embedding observed brain dynamics into a higher-dimensional representation may help reveal functional organization, but precisely how remains unclear. Hamiltonian mechanics suggests that, by introducing an additional dimension of conjugate momenta, the dynamical behaviour of a conservative system can be formulated in a more compact and mathematically elegant manner. Here we develop a physics-informed, data-driven framework that lifts whole-brain activity to the complex-valued field. Specifically, we augment observed signals (generalized coordinates) with latent ``dark signals'' that play the role of conjugate momenta in a whole-brain Hamiltonian system. We show that the Hilbert transform provides an augmentation approach with optimal fitting accuracy within this framework, yielding a Schrödinger-like equation governing complex-valued, augmented brain dynamics. Empirically, this complex-valued model consistently outperforms its real-valued counterpart, improving short-horizon prediction in the linear regime (correlation 0.12$\to$0.82) and achieving superior fits under nonlinear, nonequilibrium dynamics (0.47$\to$0.88). The framework strengthens structure-function coupling, recovers hierarchical intrinsic timescales, and yields biologically plausible directed effective connectivity that varies systematically with age and reconfigures from rest to task via global rescaling plus targeted rewiring. Together, these results establish a principled, testable paradigm for network neuroscience and offer transformative insight into the spatiotemporal organization and functional roles of large-scale brain dynamics.
Facundo Roffet, Gustavo Deco, Claudio Delrieux, Gustavo Patow
Dec 26, 2024·q-bio.NC·PDF Background: Brain network models offer insights into brain dynamics, but the utility of model-derived bifurcation parameters as biomarkers remains underexplored. Objective: This study evaluates bifurcation parameters from a whole-brain network model as biomarkers for distinguishing brain states associated with resting-state and task-based cognitive conditions. Methods: Synthetic BOLD signals were generated using a supercritical Hopf brain network model to train deep learning models for bifurcation parameter prediction. Inference was performed on Human Connectome Project data, including both resting-state and task-based conditions. Statistical analyses assessed the separability of brain states based on bifurcation parameter distributions. Results: Bifurcation parameter distributions differed significantly across task and resting-state conditions ($p < 0.0001$ for all but one comparison). Task-based brain states exhibited higher bifurcation values compared to rest. Conclusion: Bifurcation parameters effectively differentiate cognitive and resting states, warranting further investigation as biomarkers for brain state characterization and neurological disorder assessment.
Géza Ódor, Gustavo Deco, Jeffrey Kelling
Jan 26, 2022·q-bio.NC·PDF Previous simulation studies on human connectomes suggested, that critical dynamics emerge subcrititcally in the so called Griffiths Phases. %This is the consequence of the strong heterogeneity of the graphs. Now we investigate this on the largest available brain network, the $21.662$ node fruit-fly connectome, using the Kuramoto synchronization model. As this graph is less heterogeneous, lacking modular structure and exhibit high topological dimension, we expect a difference from the previous results. Indeed, the synchronization transition is mean-field like, and the width of the transition region is larger than in random graphs, but much smaller than as for the KKI-18 human connectome. This demonstrates the effect of modular structure and dimension on the dynamics, providing a basis for better understanding the complex critical dynamics of humans.
Andrea I Luppi, Fernando E. Rosas, Gustavo Deco, Morten L. Kringelbach, Pedro A. M. Mediano
Aug 10, 2023·q-bio.NC·PDF Temporal irreversibility, often referred to as the arrow of time, is a fundamental concept in statistical mechanics. Markers of irreversibility also provide a powerful characterisation of information processing in biological systems. However, current approaches tend to describe temporal irreversibility in terms of a single scalar quantity, without disentangling the underlying dynamics that contribute to irreversibility. Here we propose a broadly applicable information-theoretic framework to characterise the arrow of time in multivariate time series, which yields qualitatively different types of irreversible information dynamics. This multidimensional characterisation reveals previously unreported high-order modes of irreversibility, and establishes a formal connection between recent heuristic markers of temporal irreversibility and metrics of information processing. We demonstrate the prevalence of high-order irreversibility in the hyperactive regime of a biophysical model of brain dynamics, showing that our framework is both theoretically principled and empirically useful. This work challenges the view of the arrow of time as a monolithic entity, enhancing both our theoretical understanding of irreversibility and our ability to detect it in practical applications.
Matthieu Gilson, Nikos E Kouvaris, Gustavo Deco, Gorka Zamora-López
Graph theory constitutes a widely used and established field providing powerful tools for the characterization of complex networks. The intricate topology of networks can also be investigated by means of the collective dynamics observed in the interactions of self-sustained oscillations (synchronization patterns) or propagation-like processes such as random walks. However, networks are often inferred from real data forming dynamic systems, which are different from those employed to reveal their topological characteristics. This stresses the necessity for a theoretical framework dedicated to the mutual relationship between the structure and dynamics in complex networks, as the two sides of the same coin. Here we propose a rigorous framework based on the network response over time (i.e., Green function) to study interactions between nodes across time. For this purpose we define the \emph{flow} that describes the interplay between the network connectivity and external inputs. This multivariate measure relates to the concepts of graph communicability and the map equation. We illustrate our theory using the multivariate Ornstein-Uhlenbeck process, which describes stable and non-conservative dynamics, but the formalism can be adapted to other local dynamics for which the Green function is known. We provide applications to classical network examples, such as small-world ring and hierarchical networks. Our theory defines a comprehensive framework that is canonically related to directed and weighted networks, thus paving a new way to revise the standards for network analysis, from the pairwise interactions between nodes to the global properties of networks including community detection.
Adrià Tauste Campo, Antonio Zainos, Yuriria Vázquez, Raul Adell Segarra, Manuel Álvarez, Gustavo Deco, Héctor Díaz, Sergio Parra, Ranulfo Romo, Román Rossi-Pool
Mar 15, 2024·q-bio.NC·PDF The brain is hierarchically organized to process sensory signals. But, to what extent do functional connections within and across areas shape this hierarchical order? We addressed this problem in the thalamocortical network, while monkeys judged the presence or absence of a vibrotactile stimulus. We quantified the variability by means of intrinsic timescales and Fano factor, and functional connectivity by means of a directionality measure in simultaneously recorded neurons sharing the same cutaneous receptive field from the somatosensory thalamus (VPL) and areas 3b and 1 from the somatosensory cortex. During the pre-stimulus periods, VPL and area 3b exhibited similarly fast dynamics while area 1 showed much slower timescales. Furthermore, during the stimulus presence, the Fano factor increased along the network VPL-3b-1. In parallel, VPL established two separate main feedforward pathways with areas 3b and 1 to process stimulus information. While feedforward interactions from VPL and area 3b were favored by neurons within specific Fano factor ranges, neural variability in area 1 was invariant to the incoming pathways. In contrast to VPL and area 3b, during the stimulus arrival, area 1 showed significant intra-area interactions, which mainly pointed to neurons with slow intrinsic timescales. Overall, our results suggest that the lower variability of VPL and area 3b regulates feedforward thalamocortical communication, while the higher variability of area 1 supports intra-cortical interactions during sensory processing. These results provide evidence of a hierarchical order along the thalamocortical network.
Guido Gigante, Gustavo Deco, Shimon Marom, Paolo Del Giudice
Feb 18, 2015·q-bio.NC·PDF Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them have been variously recognized in previous works as expressions of the excitability of the cortical tissue and the associated nonlinear dynamics, a unified picture of their determinant factors (dynamical and architectural) is desirable and not yet available. Progress has also been partially hindered by the use of a variety of statistical measures to define the network events of interest. We propose here a common probabilistic definition of network events that, applied to the firing activity of cultured neural networks, highlights the co-occurrence of network spikes, power-law distributed avalanches, and exponentially distributed `quasi-orbits', which offer a third type of collective behavior. A rate model, including synaptic excitation and inhibition with no imposed topology, synaptic short-term depression, and finite-size noise, accounts for all these different, coexisting phenomena. We find that their emergence is largely regulated by the proximity to an oscillatory instability of the dynamics, where the non-linear excitable behavior leads to a self-amplification of activity fluctuations over a wide range of scales in space and time. In this sense, the cultured network dynamics is compatible with an excitation-inhibition balance corresponding to a slightly sub-critical regime. Finally, we propose and test a method to infer the characteristic time of the fatigue process, from the observed time course of the network's firing rate. Unlike the model, possessing a single fatigue mechanism, the cultured network appears to show multiple time scales, signalling the possible coexistence of different fatigue mechanisms.