EEG functional connectivity as a Riemannian mediator: An application to malnutrition and cognition.

Mediation analysis assesses whether an exposure directly produces changes in cognitive behavior or is influenced by intermediate "mediators". Electroencephalographic (EEG) spectral measurements have been previously used as effective mediators representing diverse aspects of brain function. However, it has been necessary to collapse EEG measures onto a single scalar using standard mediation methods. In this article, we overcome this limitation and examine EEG frequency-resolved functional connectivity measures as a mediator using the full EEG cross-spectral tensor (CST). Since CST samples do not exist in Euclidean space but in the Riemannian manifold of positive-definite tensors, we transform the problem, allowing for the use of classic multivariate statistics. Toward this end, we map the data from the original manifold space to the Euclidean tangent space, eliminating redundant information to conform to a "compressed CST." The resulting object is a matrix with rows corresponding to frequencies and columns to cross spectra between channels. We have developed a novel matrix mediation approach that leverages a nuclear norm regularization to determine the matrix-valued regression parameters. Furthermore, we introduced a global test for the overall CST mediation and a test to determine specific channels and frequencies driving the mediation. We validated the method through simulations and applied it to our well-studied 50+-year Barbados Nutrition Study dataset by comparing EEGs collected in school-age children (5-11 years) who were malnourished in the first year of life with those of healthy classmate controls. We hypothesized that the CST mediates the effect of malnutrition on cognitive performance. We can now explicitly pinpoint the frequencies (delta, theta, alpha, and beta bands) and regions (frontal, central, and occipital) in which functional connectivity was altered in previously malnourished children, an improvement to prior studies. Understanding the specific networks impacted by a history of postnatal malnutrition could pave the way for developing more targeted and personalized therapeutic interventions. Our methods offer a versatile framework applicable to mediation studies encompassing matrix and Hermitian 3D tensor mediators alongside scalar exposures and outcomes, facilitating comprehensive analyses across diverse research domains.

CiftiStorm pipeline: facilitating reproducible EEG/MEG source connectomics.

We present CiftiStorm, an electrophysiological source imaging (ESI) pipeline incorporating recently developed methods to improve forward and inverse solutions. The CiftiStorm pipeline produces Human Connectome Project (HCP) and megconnectome-compliant outputs from dataset inputs with varying degrees of spatial resolution. The input data can range from low-sensor-density electroencephalogram (EEG) or magnetoencephalogram (MEG) recordings without structural magnetic resonance imaging (sMRI) to high-density EEG/MEG recordings with an HCP multimodal sMRI compliant protocol. CiftiStorm introduces a numerical quality control of the lead field and geometrical corrections to the head and source models for forward modeling. For the inverse modeling, we present a Bayesian estimation of the cross-spectrum of sources based on multiple priors. We facilitate ESI in the T1w/FSAverage32k high-resolution space obtained from individual sMRI. We validate this feature by comparing CiftiStorm outputs for EEG and MRI data from the Cuban Human Brain Mapping Project (CHBMP) acquired with technologies a decade before the HCP MEG and MRI standardized dataset.

Differential processing of intrinsic vs. extrinsic coordinates in wrist movement: connectivity and chronometry perspectives.

This study explores brain-network differences between the intrinsic and extrinsic motor coordinate frames. A connectivity model showing the coordinate frames difference was obtained using brain fMRI data of right wrist isometric flexions and extensions movements, performed in two forearm postures. The connectivity model was calculated by machine-learning-based neural representation and effective functional connectivity using psychophysiological interaction and dynamic causal modeling analyses. The model indicated the network difference wherein the inferior parietal lobule receives extrinsic information from the rostral lingual gyrus through the superior parietal lobule and transmits intrinsic information to the Handknob, whereas extrinsic information is transmitted to the Handknob directly from the rostral lingual gyrus. A behavioral experiment provided further evidence on the difference between motor coordinate frames showing onset timing delay of muscle activity of intrinsic coordinate-directed wrist movement compared to extrinsic one. These results suggest that, if the movement is externally directed, intrinsic coordinate system information is bypassed to reach the primary motor area.

Accurate and Efficient Simulation of Very High-Dimensional Neural Mass Models with Distributed-Delay Connectome Tensors.

This paper introduces methods and a novel toolbox that efficiently integrates high-dimensional Neural Mass Models (NMMs) specified by two essential components. The first is the set of nonlinear Random Differential Equations (RDEs) of the dynamics of each neural mass. The second is the highly sparse three-dimensional Connectome Tensor (CT) that encodes the strength of the connections and the delays of information transfer along the axons of each connection. To date, simplistic assumptions prevail about delays in the CT, often assumed to be Dirac-delta functions. In reality, delays are distributed due to heterogeneous conduction velocities of the axons connecting neural masses. These distributed-delay CTs are challenging to model. Our approach implements these models by leveraging several innovations. Semi-analytical integration of RDEs is done with the Local Linearization (LL) scheme for each neural mass, ensuring dynamical fidelity to the original continuous-time nonlinear dynamic. This semi-analytic LL integration is highly computationally-efficient. In addition, a tensor representation of the CT facilitates parallel computation. It also seamlessly allows modeling distributed delays CT with any level of complexity or realism. This ease of implementation includes models with distributed-delay CTs. Consequently, our algorithm scales linearly with the number of neural masses and the number of equations they are represented with, contrasting with more traditional methods that scale quadratically at best. To illustrate the toolbox's usefulness, we simulate a single Zetterberg-Jansen and Rit (ZJR) cortical column, a single thalmo-cortical unit, and a toy example comprising 1000 interconnected ZJR columns. These simulations demonstrate the consequences of modifying the CT, especially by introducing distributed delays. The examples illustrate the complexity of explaining EEG oscillations, e.g., split alpha peaks, since they only appear for distinct neural masses. We provide an open-source Script for the toolbox.

Optimal placement of sensor and actuator for controlling low-dimensional chaotic systems based on global modeling.

Controlling chaos is fundamental in many applications, and for this reason, many techniques have been proposed to address this problem. Here, we propose a strategy based on an optimal placement of the sensor and actuator providing global observability of the state space and global controllability to any desired state. The first of these two conditions enables the derivation of a model of the system by using a global modeling technique. In turn, this permits the use of feedback linearization for designing the control law based on the equations of the obtained model and providing a zero-flat system. The procedure is applied to three case studies, including two piecewise linear circuits, namely, the Carroll circuit and the Chua circuit whose governing equations are approximated by a continuous global model. The sensitivity of the procedure to the time constant of the dynamics is also discussed.

A new Framework for the Spectral Information Decomposition of Multivariate Gaussian Processes.

Different information-theoretic measures are available in the literature for the study of pairwise and higher-order interactions in multivariate dynamical systems. While these measures operate in the time domain, several physiological and non-physiological systems exhibit a rich oscillatory content that is typically analyzed in the frequency domain through spectral and cross-spectral approaches. For Gaussian systems, the relation between information and spectral measures has been established considering coupling and causality measures, but not for higher-order interactions. To fill this gap, in this work we introduce an information-theoretic framework in the frequency domain to quantify the information shared between a target process and two sources, even multivariate, and to highlight the presence of redundancy and synergy in the analyzed dynamical system. Firstly, we simulate different linear interacting processes by showing the capability of the proposed framework to retrieve amounts of information shared by the processes in specific frequency bands which are not detectable by the related time-domain measures. Then, the framework is applied on EEG time series representative of the brain activity during a motor execution task in a group of healthy subjects.

Node differentiation dynamics along the route to synchronization in complex networks.

Synchronization has been the subject of intense research during decades mainly focused on determining the structural and dynamical conditions driving a set of interacting units to a coherent state globally stable. However, little attention has been paid to the description of the dynamical development of each individual networked unit in the process towards the synchronization of the whole ensemble. In this paper we show how in a network of identical dynamical systems, nodes belonging to the same degree class, differentiate in the same manner, visiting a sequence of states of diverse complexity along the route to synchronization independently on the global network structure. In particular, we observe, just after interaction starts pulling orbits from the initially uncoupled attractor, a general reduction of the complexity of the dynamics of all units being more pronounced in those with higher connectivity. In the weak-coupling regime, when synchronization starts to build up, there is an increase in the dynamical complexity, whose maximum is achieved, in general, first in the hubs due to their earlier synchronization with the mean field. For very strong coupling, just before complete synchronization, we found a hierarchical dynamical differentiation with lower degree nodes being the ones exhibiting the largest complexity departure. We unveil how this differentiation route holds for several models of nonlinear dynamics, including toroidal chaos and how it depends on the coupling function. This study provides insights to understand better strategies for network identification or to devise effective methods for network inference.

Estimation of Granger causality through Artificial Neural Networks: applications to physiological systems and chaotic electronic oscillators.

One of the most challenging problems in the study of complex dynamical systems is to find the statistical interdependencies among the system components. Granger causality (GC) represents one of the most employed approaches, based on modeling the system dynamics with a linear vector autoregressive (VAR) model and on evaluating the information flow between two processes in terms of prediction error variances. In its most advanced setting, GC analysis is performed through a state-space (SS) representation of the VAR model that allows to compute both conditional and unconditional forms of GC by solving only one regression problem. While this problem is typically solved through Ordinary Least Square (OLS) estimation, a viable alternative is to use Artificial Neural Networks (ANNs) implemented in a simple structure with one input and one output layer and trained in a way such that the weights matrix corresponds to the matrix of VAR parameters. In this work, we introduce an ANN combined with SS models for the computation of GC. The ANN is trained through the Stochastic Gradient Descent L1 (SGD-L1) algorithm, and a cumulative penalty inspired from penalized regression is applied to the network weights to encourage sparsity. Simulating networks of coupled Gaussian systems, we show how the combination of ANNs and SGD-L1 allows to mitigate the strong reduction in accuracy of OLS identification in settings of low ratio between number of time series points and of VAR parameters. We also report how the performances in GC estimation are influenced by the number of iterations of gradient descent and by the learning rate used for training the ANN. We recommend using some specific combinations for these parameters to optimize the performance of GC estimation. Then, the performances of ANN and OLS are compared in terms of GC magnitude and statistical significance to highlight the potential of the new approach to reconstruct causal coupling strength and network topology even in challenging conditions of data paucity. The results highlight the importance of of a proper selection of regularization parameter which determines the degree of sparsity in the estimated network. Furthermore, we apply the two approaches to real data scenarios, to study the physiological network of brain and peripheral interactions in humans under different conditions of rest and mental stress, and the effects of the newly emerged concept of remote synchronization on the information exchanged in a ring of electronic oscillators. The results highlight how ANNs provide a mesoscopic description of the information exchanged in networks of multiple interacting physiological systems, preserving the most active causal interactions between cardiovascular, respiratory and brain systems. Moreover, ANNs can reconstruct the flow of directed information in a ring of oscillators whose statistical properties can be related to those of physiological networks.

An Information-Theoretic Framework to Measure the Dynamic Interaction Between Neural Spike Trains.

OBJECTIVE: While understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience, existing methods either do not consider the inherent point-process nature of spike trains or are based on parametric assumptions. This work presents an information-theoretic framework for the model-free, continuous-time estimation of both undirected (symmetric) and directed (Granger-causal) interactions between spike trains. METHODS: The framework computes the mutual information rate (MIR) and the transfer entropy rate (TER) for two point processes X and Y, showing that the MIR between X and Y can be decomposed as the sum of the TER along the directions X → Y and Y → X. We present theoretical expressions and introduce strategies to estimate efficiently the two measures through nearest neighbor statistics. RESULTS: Using simulations of independent and coupled point processes, we show the accuracy of MIR and TER to assess interactions even for weakly coupled and short realizations, and demonstrate the superiority of continuous-time estimation over the standard discrete-time approach. We also apply the MIR and TER to real-world data, specifically, recordings from in-vitro preparations of spontaneously-growing cultures of cortical neurons. Using this dataset, we demonstrate the ability of MIR and TER to describe how the functional networks between recording units emerge over the course of the maturation of the neuronal cultures. CONCLUSION AND SIGNIFICANCE: the proposed framework provides principled measures to assess undirected and directed spike train interactions with more efficiency and flexibility than previous discrete-time or parametric approaches, opening new perspectives for the analysis of point-process data in neuroscience and many other fields.

Visual fixation in disorders of consciousness: Development of predictive models to support differential diagnosis.

The visual fixation represents a doubtful behavioral sign to discriminate Vegetative from Minimally Conscious State (MCS). To disentangle its meaning, we fitted univariate and multivariable logistic regression models matching different neurophysiological and neuroimaging data of 54 patients with Disorders of Consciousness to select the best model predicting which visual performance (visual blink or pursuit) was shown by patients and the best predictors set. The best models found highlighted the importance of the structural MRI and the visual evoked potentials data in predicting visual pursuit. Then, a qualitative pilot test was made on four patients showing visual fixation revealing that the obtained models correctly predict whether the patients' visual performance could support/correlate to a cognitively mediated behavior. The present pilot models could help clinicians to evaluate if the visual fixation response can support the MCS diagnosis.

Generation of diverse insect-like gait patterns using networks of coupled Rössler systems.

The generation of walking patterns is central to bio-inspired robotics and has been attained using methods encompassing diverse numerical as well as analog implementations. Here, we demonstrate the possibility of synthesizing viable gaits using a paradigmatic low-dimensional non-linear entity, namely, the Rössler system, as a dynamical unit. Through a minimalistic network wherein each instance is univocally associated with one leg, it is possible to readily reproduce the canonical gaits as well as generate new ones via changing the coupling scheme and the associated delays. Varying levels of irregularity can be introduced by rendering individual systems or the entire network chaotic. Moreover, through tailored mapping of the state variables to physical angles, adequate leg trajectories can be accessed directly from the coupled systems. The functionality of the resulting generator was confirmed in laboratory experiments by means of an instrumented six-legged ant-like robot. Owing to their simple form, the 18 coupled equations could be rapidly integrated on a bare-metal microcontroller, leading to the demonstration of real-time robot control navigating an arena using a brain-machine interface.

Age-Related Decline of Sensorimotor Integration Influences Resting-State Functional Brain Connectivity.

Age-related decline in sensorimotor integration involves both peripheral and central components related to proprioception and kinesthesia. To explore the role of cortical motor networks, we investigated the association between resting-state functional connectivity and a gap-detection angle measured during an arm-reaching task. Four region pairs, namely the left primary sensory area with the left primary motor area (S1left-M1left), the left supplementary motor area with M1left (SMAleft-M1left), the left pre-supplementary motor area with SMAleft (preSMAleft-SMAleft), and the right pre-supplementary motor area with the right premotor area (preSMAright-PMdright), showed significant age-by-gap detection ability interactions in connectivity in the form of opposite-sign correlations with gap detection ability between younger and older participants. Morphometry and tractography analyses did not reveal corresponding structural effects. These results suggest that the impact of aging on sensorimotor integration at the cortical level may be tracked by resting-state brain activity and is primarily functional, rather than structural. From the observation of opposite-sign correlations, we hypothesize that in aging, a "low-level" motor system may hyper-engage unsuccessfully, its dysfunction possibly being compensated by a "high-level" motor system, wherein stronger connectivity predicts higher gap-detection performance. This hypothesis should be tested in future neuroimaging and clinical studies.

Generic Rotating-Frame-Based Approach to Chaos Generation in Nonlinear Micro- and Nanoelectromechanical System Resonators.

This Letter provides a low-power method for chaos generation that is generally applicable to nonlinear micro- and nanoelectromechanical systems (MNEMS) resonators. The approach taken is independent of the material, scale, design, and actuation of the device in question; it simply assumes a good quality factor and a Duffing type nonlinearity, features that are commonplace to MNEMS resonators. The approach models the rotating-frame dynamics to analytically constrain the parameter space required for chaos generation. By leveraging these common properties of MNEMS devices, a period-doubling route to chaos is generated using smaller forcing than typically reported in the literature.

Behavioral and physiological correlates of kinetically tracking a chaotic target.

Humans can innately track a moving target by anticipating its future position from a brief history of observations. While ballistic trajectories can be readily extrapolated, many natural and artificial systems are governed by more general nonlinear dynamics and, therefore, can produce highly irregular motion. Yet, relatively little is known regarding the behavioral and physiological underpinnings of prediction and tracking in the presence of chaos. Here, we investigated in lab settings whether participants could manually follow the orbit of a paradigmatic chaotic system, the Rössler equations, on the (x,y) plane under different settings of a control parameter, which determined the prominence of transients in the target position. Tracking accuracy was negatively related to the level of unpredictability and folding. Nevertheless, while participants initially reacted to the transients, they gradually learned to anticipate it. This was accompanied by a decrease in muscular co-contraction, alongside enhanced activity in the theta and beta EEG bands for the highest levels of chaoticity. Furthermore, greater phase synchronization of breathing was observed. Taken together, these findings point to the possible ability of the nervous system to implicitly learn topological regularities even in the context of highly irregular motion, reflecting in multiple observables at the physiological level.

SpiSeMe: A multi-language package for spike train surrogate generation.

Many studies in nonlinear science heavily rely on surrogate-based hypothesis testing to provide significance estimations of analysis results. Among the complex data produced by nonlinear systems, spike trains are a class of sequences requiring algorithms for surrogate generation that are typically more sophisticated and computationally demanding than methods developed for continuous signals. Although algorithms to specifically generate surrogate spike trains exist, the availability of open-source, portable implementations is still incomplete. In this paper, we introduce the SpiSeMe (Spike Sequence Mime) software package that implements four algorithms for the generation of surrogate data out of spike trains and more generally out of any sequence of discrete events. The purpose of the package is to provide a unified and portable toolbox to carry out surrogate generation on point-process data. Code is provided in three languages, namely, C++, Matlab, and Python, thus allowing straightforward integration of package functions into most analysis pipelines.

Visual behaviors in disorders of consciousness: Disentangling conscious visual processing by a multimodal approach.

One of the major challenges for clinicians who treat patients with Disorders of Consciousness (DoCs) concerns the detection of signs of consciousness that distinguish patients in Vegetative State from those in Minimally Conscious State. Recent studies showed how visual responses to tailored stimuli are one of the first evidence revealing that one patient is changing from one state to another. This study aimed to explore the integrity of the neural structures being part of the visual system in patients with DoCs manifesting a reflexive behavior (visual blink) and in those manifesting a cognitively and cortically mediated behavior (visual pursuit). We collected instrumental data using specialized equipment (EEG following the rules of the International 10-20 system, 3T Magnetic Resonance, and Positron Emission Tomography) in 54 DoC patients. Our results indicated that visual pursuit group showed a better fVEPs response than the visual blink group, because of a greater area under the N2/P2 component of fVEPs (AUC could be seen as an indicator of the residual activity of visual areas). Considering neuroimaging data, the main structural differences between groups were found in the retrochiasmatic areas, specifically in the right optic radiation and visual cortex (V1), areas statistically less impaired in patients able to perform a visual pursuit. FDG-PET analysis confirmed difference between groups at the level of the right calcarine cortex and neighboring right lingual gyrus. In conclusion, although there are methodological and theoretical limitations that should be considered, our study suggests a new perspective to consider for a future diagnostic protocol.

Competition of noise and collectivity in global cryptocurrency trading: Route to a self-contained market.

Cross correlations in fluctuations of the daily exchange rates within the basket of the 100 highest-capitalization cryptocurrencies over the period October 1, 2015-March 31, 2019 are studied. The corresponding dynamics predominantly involve one leading eigenvalue of the correlation matrix, while the others largely coincide with those of Wishart random matrices. However, the magnitude of the principal eigenvalue, and thus the degree of collectivity, strongly depends on which cryptocurrency is used as a base. It is largest when the base is the most peripheral cryptocurrency; when more significant ones are taken into consideration, its magnitude systematically decreases, nevertheless preserving a sizable gap with respect to the random bulk, which in turn indicates that the organization of correlations becomes more heterogeneous. This finding provides a criterion for recognizing which currencies or cryptocurrencies play a dominant role in the global cryptomarket. The present study shows that over the period under consideration, the Bitcoin (BTC) predominates, hallmarking exchange rate dynamics at least as influential as the U.S. dollar (USD). Even more, the BTC started dominating around the year 2017, while other cryptocurrencies, such as the Ethereum and even Ripple, assumed similar trends. At the same time, the USD, an original value determinant for the cryptocurrency market, became increasingly disconnected, and its related characteristics eventually started approaching those of a fictitious currency. These results are strong indicators of incipient independence of the global cryptocurrency market, delineating a self-contained trade resembling the Forex.

Scale-resolved analysis of brain functional connectivity networks with spectral entropy.

Functional connectivity is derived from inter-regional correlations in spontaneous fluctuations of brain activity, and can be represented in terms of complete graphs with continuous (real-valued) edges. The structure of functional connectivity networks is strongly affected by signal processing procedures to remove the effects of motion, physiological noise and other sources of experimental error. However, in the absence of an established ground truth, it is difficult to determine the optimal procedure, and no consensus has been reached on the most effective approach to remove nuisance signals without unduly affecting the network intrinsic structural features. Here, we use a novel information-theoretic approach, based on von Neumann entropy, which provides a measure of information encoded in the networks at different scales. We also define a measure of distance between networks, based on information divergence, and optimal null models appropriate for the description of functional connectivity networks, to test for the presence of nontrivial structural patterns that are not the result of simple local constraints. This formalism enables a scale-resolved analysis of the distance between a functional connectivity network and its maximally random counterpart, thus providing a means to assess the effects of noise and image processing on network structure. We apply this novel approach to address a few open questions in the analysis of brain functional connectivity networks. Specifically, we demonstrate a strongly beneficial effect of network sparsification by removal of the weakest links, and the existence of an optimal threshold that maximizes the ability to extract information on large-scale network structures. Additionally, we investigate the effects of different degrees of motion at different scales, and compare the most popular processing pipelines designed to mitigate its deleterious effect on functional connectivity networks. We show that network sparsification, in combination with motion correction algorithms, dramatically improves detection of large scale network structure.

Hyperexcitability in Cultured Cortical Neuron Networks from the G93A-SOD1 Amyotrophic Lateral Sclerosis Model Mouse and its Molecular Correlates.

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease affecting the corticospinal tract and leading to motor neuron death. According to a recent study, magnetic resonance imaging-visible changes suggestive of neurodegeneration seem absent in the motor cortex of G93A-SOD1 ALS mice. However, it has not yet been ascertained whether the cortical neural activity is intact, or alterations are present, perhaps even from an early stage. Here, cortical neurons from this model were isolated at post-natal day 1 and cultured on multielectrode arrays. Their activity was studied with a comprehensive pool of neurophysiological analyses probing excitability, criticality and network architecture, alongside immunocytochemistry and molecular investigations. Significant hyperexcitability was visible through increased network firing rate and bursting, whereas topological changes in the synchronization patterns were apparently absent. The number of dendritic spines was increased, accompanied by elevated transcriptional levels of the DLG4 gene, NMDA receptor 1 and the early pro-apoptotic APAF1 gene. The extracellular Na+, Ca2+, K+ and Cl- concentrations were elevated, pointing to perturbations in the culture micro-environment. Our findings highlight remarkable early changes in ALS cortical neuron activity and physiology. These changes suggest that the causative factors of hyperexcitability and associated toxicity could become established much earlier than the appearance of disease symptoms, with implications for the discovery of new hypothetical therapeutic targets.

Fading of remote synchronization in tree networks of Stuart-Landau oscillators.

Remote synchronization (RS) is characterized by the appearance of phase coherence between oscillators that do not directly interact through a structural link in a network but exclusively through other units that are not synchronized or more weakly synchronized with them. This form of phase synchronization was observed initially in starlike motifs and later in random networks. In this paper, we report on an experimental setup for the analysis of RS in networks of Stuart-Landau oscillators and in particular investigate the behavior of tree structures focusing on the path to synchronization, that is, on the analysis of how synchronization emerges as the coupling strength increases from zero. We find that RS occurs in a region wherein further increases of the coupling strength lead to a direct transition to global synchronization but may also be observed in a second region, corresponding to lower coupling values, wherein it first emerges and then disappears, hallmarking a scenario that we denote as fading of remote synchronization. We show that this result is related to the behavior of pairs of remotely synchronized nodes observed in networks with more general topologies. Experiments are corroborated by numerical simulations confirming the major findings and providing further characterization of the phenomenon. We demonstrate that the distribution of natural oscillation frequencies and the parameter uncertainty in the links both play a fundamental role in shaping the behaviors observed.