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Abstract Background Alveolar macrophages activation to the pro-inflammatory phenotype M1 is pivotal in the pathophysiology of Ventilator-Induced Lung Injury (VILI). Increased lung strain is a known determinant of VILI, but a direct correspondence between regional lung strain and macrophagic activation remains unestablished. [68Ga]Ga-DOTA-TATE is a Positron Emission Tomography (PET) radiopharmaceutical with a high affinity for somatostatin receptor subtype 2 (SSTR2), which is overexpressed by pro-inflammatory-activated macrophages. Aim of the study was to determine, in a porcine model of VILI, whether mechanical strain correlates topographically with distribution of activated macrophages detected by [68Ga]Ga-DOTA-TATE uptake. Methods Seven anesthetized pigs underwent VILI, while three served as control. Lung CT scans were acquired at incremental tidal volumes, simultaneously recording lung mechanics. [68Ga]Ga-DOTA-TATE was administered, followed by dynamic PET scans. Custom MatLab scripts generated voxel-by-voxel gas volume and strain maps from CT slices at para-diaphragmatic (Para-D) and mid-thoracic (Mid-T) levels. Analysis of regional Voxel-associated Normal Strain (VoStrain) and [68Ga]Ga-DOTA-TATE uptake was performed and a measure of the statistical correlation between these two variables was quantified using the linear mutual information (LMI) method. Results Compared to controls, the VILI group exhibited statistically significant higher VoStrain and Standardized Uptake Value Ratios (SUVR) both at Para-D and Mid-T levels. Both VoStrain and SUVR increased along the gravitational axis with an increment described by statistically different regression lines between VILI and healthy controls and reaching the peak in the dependent regions of the lung (for strain in VILI vs. control was at Para-D: 760 ± 210 vs. 449 ± 106; at Mid-T level 497 ± 373 vs. 193 ± 160; for SUVR, in VILI vs. control was at Para-D: 2.2 ± 1.3 vs. 1.3 ± 0.1; at Mid-T level 1.3 ± 1.0 vs. 0.6 ± 0.03). LMI in both Para-D and Mid-T was statistically significantly higher in VILI than in controls. Conclusions In this porcine model of VILI, we found a topographical correlation between lung strain and [68Ga]Ga-DOTA-TATE uptake at voxel level, suggesting that mechanical alteration and specific activation of inflammatory cells are strongly linked in VILI. This study represents the first voxel-by-voxel examination of this relationship in a multi-modal imaging analysis.

Transfer entropy (TE), the primary method for determining directed information flow within a network system, can exhibit bias—either in deficiency or excess—during both pairwise and conditioned calculations, owing to high-order dependencies among the dynamic processes under consideration and the remaining processes in the system used for conditioning. Here, we propose a novel approach. Instead of conditioning TE on all network processes except the driver and the target, as in its fully conditioned version, or not conditioning at all, as in the pairwise approach, our method searches for both the multiplets of variables that maximize information flow and those that minimize it. This provides a decomposition of TE into unique, redundant, and synergistic atoms. Our approach enables the quantification of the relative importance of high-order effects compared to pure two-body effects in information transfer between two processes, while also highlighting the processes that contribute to building these high-order effects alongside the driver. We demonstrate the application of our approach in climatology by analyzing data from El Niño and the Southern Oscillation.

Abstract The human brain is an extremely complex network of structural and functional connections that operate at multiple spatial and temporal scales. Investigating the relationship between these multi-scale connections is critical to advancing our comprehension of brain function and disorders. However, accurately predicting structural connectivity from its functional counterpart remains a challenging pursuit. One of the major impediments is the lack of public repositories that integrate structural and functional networks at diverse resolutions, in conjunction with modular transcriptomic profiles, which are essential for comprehensive biological interpretation. To mitigate this limitation, our contribution encompasses the provision of an open-access dataset consisting of derivative matrices of functional and structural connectivity across multiple scales, accompanied by code that facilitates the investigation of their interrelations. We also provide additional resources focused on neuro-genetic associations of module-level network metrics, which present promising opportunities to further advance research in the field of network neuroscience, particularly concerning brain disorders.

Goal: The network representation is becoming increasingly popular for the description of cardiovascular interactions based on the analysis of multiple simultaneously collected variables. However, the traditional methods to assess network links based on pairwise interaction measures cannot reveal high-order effects involving more than two nodes, and are not appropriate to infer the underlying network topology. To address these limitations, here we introduce a framework which combines the assessment of high-order interactions with statistical inference for the characterization of the functional links sustaining physiological networks. Methods: The framework develops information-theoretic measures quantifying how two nodes interact in a redundant or synergistic way with the rest of the network, and employs these measures for reconstructing the functional structure of the network. The measures are implemented for both static and dynamic networks mapped respectively by random variables and random processes using plug-in and model-based entropy estimators. Results: The validation on theoretical and numerical simulated networks documents the ability of the framework to represent high-order interactions as networks and to detect statistical structures associated to cascade, common drive and common target effects. The application to cardiovascular networks mapped by the beat-to-beat variability of heart rate, respiration, arterial pressure, cardiac output and vascular resistance allowed noninvasive characterization of several mechanisms of cardiovascular control operating in resting state and during orthostatic stress. Conclusion: Our approach brings to new comprehensive assessment of physiological interactions and complements existing strategies for the classification of pathophysiological states.

In stock markets, nonlinear interdependencies between various companies result in nontrivial time-varying patterns in stock prices. A network representation of these interdependencies has been successful in identifying and understanding hidden signals before major events like stock market crashes. However, these studies have revolved around the assumption that correlations are mediated in a pairwise manner, whereas, in a system as intricate as this, the interactions need not be limited to pairwise only. Here, we introduce a general methodology using information-theoretic tools to construct a higher-order representation of the stock market data, which we call functional hypergraphs. This framework enables us to examine stock market events by analyzing the following functional hypergraph quantities: Forman–Ricci curvature, von Neumann entropy, and eigenvector centrality. We compare the corresponding quantities of networks and hypergraphs to analyze the evolution of both structures and observe features like robustness towards events like crashes during the course of a time period.

The study of high order dependencies in complex systems has recently led to the introduction of statistical synergy, a novel quantity corresponding to a form of emergence in which patterns at large scales are not traceable from lower scales. As a consequence, several works in the last years dealt with the synergy and its counterpart, the redundancy. In particular, the O-information is a signed metric that measures the balance between redundant and synergistic statistical dependencies. In spite of its growing use, this metric does not provide insight about the role played by low-order scales in the formation of high order effects. To fill this gap, the framework for the computation of the O-information has been recently expanded introducing the so-called gradients of this metric, which measure the irreducible contribution of a variable (or a group of variables) to the high order informational circuits of a system. Here, we review the theory behind the O-information and its gradients and present the potential of these concepts in the field of network physiology, showing two new applications relevant to brain functional connectivity probed via functional resonance imaging and physiological interactions among the variability of heart rate, arterial pressure, respiration and cerebral blood flow.

IntroductionSubtle cognitive dysfunction and mental fatigue are frequent after severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, characterizing the so-called long COVID-19 syndrome. This study aimed to correlate cognitive, neurophysiological, and olfactory function in a group of subjects who experienced acute SARS-CoV-2 infection with persistent hyposmia at least 12 weeks before the observation.MethodsFor each participant (32 post-COVID-19 patients and 16 controls), electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS) data were acquired using an integrated EEG–fNIRS system during the execution of a P300 odd-ball task and a Stroop test. The Sniffin' Sticks test was conducted to assess subjects' olfactory performance. The Montreal Cognitive Assessment (MoCA) and the Frontal Assessment Battery (FAB) were also administered.ResultsThe post-COVID-19 group consisted of 32 individuals (20 women and 12 men) with an average education level of 12.9 ± 3.12 years, while the control group consisted of 16 individuals (10 women and 6 men) with an average education level of 14.9 ± 3.2 years. There were no significant differences in gender (X2 = 0, p = 1) or age between the two groups (age 44.81 ± 13.9 vs. 36.62 ± 11.4, p = 0.058). We identified a lower concentration of oxyhemoglobin (p < 0.05) at the prefrontal cortical level in post-COVID-19 subjects during the execution of the Stroop task, as well as a reduction in the amplitude of the P3a response. Moreover, we found that post-COVID-19 subjects performed worst at the MoCA screening test (p = 0.001), Sniffin's Sticks test (p < 0.001), and Stroop task response latency test (p < 0.001).ConclusionsThis study showed that post-COVID-19 patients with persistent hyposmia present mild deficits in prefrontal function, even 4 months after the end of the infection. These deficits, although subtle, could have long-term implications for quality of life and cognitive wellbeing. It is essential to continue monitoring and evaluating these patients to better understand the extent and duration of cognitive impairments associated with long COVID-19.

Abstract In this paper we analyse the effects of information flows in cryptocurrency markets. We first define a cryptocurrency trading network, i.e. the network made using cryptocurrencies as nodes and the Granger causality among their weekly log returns as links, later we analyse its evolution over time. In particular, with reference to years 2020 and 2021, we study the logarithmic US dollar price returns of the cryptocurrency trading network using both pairwise and high-order statistical dependencies, quantified by Granger causality and O-information, respectively. With reference to the former, we find that it shows peaks in correspondence of important events, like e.g., Covid-19 pandemic turbulence or occasional sudden prices rise. The corresponding network structure is rather stable, across weekly time windows in the period considered and the coins are the most influential nodes in the network. In the pairwise description of the network, stable coins seem to play a marginal role whereas, turning high-order dependencies, they appear in the highest number of synergistic information circuits, thus proving that they play a major role for high order effects. With reference to redundancy and synergy with the time evolution of the total transactions in US dollars, we find that their large volume in the first semester of 2021 seems to have triggered a transition in the cryptocurrency network toward a more complex dynamical landscape. Our results show that pairwise and high-order descriptions of complex financial systems provide complementary information for cryptocurrency analysis.

Mediation analysis aims to clarify the nature of the relationship between two variables, by elucidating the role of a third variable, which can allow or suppress the relationship, or being simply not involved in the process. The authors introduce this framework in the analysis of three-layered multiplex networks, assessing whether a link between two nodes in one layer affects the probability of having a link between the two same nodes in the other two layers, and present some applications to social and biological networks.

Many complex systems in physics, biology and engineering are modeled as dynamical networks and described using multivariate time series analysis. Recent developments have shown that the emergent dynamics of a network system are significantly affected by interactions involving multiple network nodes which cannot be described using pairwise links. While these higher-order interactions can be probed using information-theoretic measures, a rigorous framework to describe them in the frequency domain is still lacking. This work presents an approach for the spectral decomposition of multivariate information measures, capable of identifying higher-order synergistic and redundant interactions between oscillatory processes. We show theoretically that synergy and redundancy can coexist at different frequencies among the output signals of a network system and can be detected only using the proposed spectral method. To demonstrate the broad applicability of the framework, we provide parametric and non-parametric data-efficient estimators for the spectral information measures, and employ them to describe multivariate interactions in three complex systems producing rich oscillatory dynamics, namely the human brain, a ring of electronic oscillators, and the global climate system. In these systems, we show that the use of our framework for the spectral decomposition of information measures reveals multivariate and higher-order interactions not detectable in the time domain. Our results are exemplary of how the frequency-specific analysis of multivariate dynamics can aid the implementation of assessment and control strategies in real-world network systems.

AbstractWe implement the dynamical Ising model on the large-scale architecture of white matter connections of healthy subjects in the age range 4–85 years, and analyze the dynamics in terms of the synergy, a quantity measuring the extent to which the joint state of pairs of variables is projected onto the dynamics of a target one. We find that the amount of synergy in explaining the dynamics of the hubs of the structural connectivity (in terms of degree strength) peaks before the critical temperature, and can thus be considered as a precursor of a critical transition. Conversely, the greatest amount of synergy goes into explaining the dynamics of more central nodes. We also find that the aging of structural connectivity is associated with significant changes in the simulated dynamics: There are brain regions whose synergy decreases with age, in particular the frontal pole, the subcallosal area, and the supplementary motor area; these areas could then be more likely to show a decline in terms of the capability to perform higher order computation (if structural connectivity was the sole variable). On the other hand, several regions in the temporal cortex show a positive correlation with age in the first 30 years of life, that is, during brain maturation.

A fundamental challenge in preprocessing pipelines for neuroimaging datasets is to increase the signal-to-noise ratio for subsequent analyses. In the same line, we suggest here that the application of the consensus clustering approach to brain connectivity matrices can be a valid additional step for connectome processing to find subgroups of subjects with reduced intragroup variability and therefore increasing the separability of the distinct subgroups when connectomes are used as a biomarker. Moreover, by partitioning the data with consensus clustering before any group comparison (for instance, between a healthy population vs. a pathological one), we demonstrate that unique regions within each cluster arise and bring new information that could be relevant from a clinical point of view.

We address the problem of efficiently and informatively quantifying how multiplets of variables carry information about the future of the dynamical system they belong to. In particular we want to identify groups of variables carrying redundant or synergistic information, and track how the size and the composition of these multiplets changes as the collective behavior of the system evolves. In order to afford a parsimonious expansion of shared information, and at the same time control for lagged interactions and common effect, we develop a dynamical, conditioned version of the O-information, a framework recently proposed to quantify high-order interdependencies via multivariate extension of the mutual information. The dynamic O-information, here introduced, allows to separate multiplets of variables which influence synergistically the future of the system from redundant multiplets. We apply this framework to a dataset of spiking neurons from a monkey performing a perceptual discrimination task. The method identifies synergistic multiplets that include neurons previously categorized as containing little relevant information individually.

This work investigates the temporal statistical structure of time series of electric field (EF) intensity recorded with the aim of exploring the dynamical patterns associated with periods with different human activity in urban areas. The analyzed time series were obtained from a sensor of the EMF RATEL monitoring system installed in the campus area of the University of Novi Sad, Serbia. The sensor performs wideband cumulative EF intensity monitoring of all active commercial EF sources, thus including those linked to human utilization of wireless communication systems. Monitoring was performed continuously during the years 2019 and 2020, allowing us to investigate the effects on the patterns of EF intensity of varying conditions of human mobility, including regular teaching and exam activity within the campus, as well as limitations to mobility related to the COVID-19 pandemic. Time series analysis was performed using both simple statistics (mean and variance) and combining the information-theoretic measure of information storage (IS) with the method of surrogate data to quantify the regularity of EF dynamic patterns and detect the presence of nonlinear dynamics. Moreover, to assess the possible coexistence of dynamic behaviors across multiple temporal scales, IS analysis was performed over consecutive observation windows lasting one day, week, month, and year, respectively coarse grained at time scales of 6 min, 30 min, 2 h, and 1 day. Our results document that the EF intensity patterns of variability are modulated by the movement of people at daily, weekly, and monthly scales, and are blunted during periods of restricted mobility related to the COVID-19 pandemic. Mobility restrictions also affected significantly the regularity of the EF intensity time series, resulting in lower values of IS observed simultaneously with a loss of nonlinear dynamics. Thus, our analysis can be useful to investigate changes in the global patterns of human mobility both during pandemics or other types of events, and from this perspective may serve to implement strategies for safety assessment and for optimizing the design of networks of EF sensors.

High-order, beyond-pairwise interdependencies are at the core of biological, economic, and social complex systems, and their adequate analysis is paramount to understand, engineer, and control such systems. This paper presents a framework to measure high-order interdependence that disentangles their effect on each individual pattern exhibited by a multivariate system. The approach is centered on the local O-information, a new measure that assesses the balance between synergistic and redundant interdependencies at each pattern. To illustrate the potential of this framework, we present a detailed analysis of music scores from J. S. Bach, which reveals how high-order interdependence is deeply connected with highly nontrivial aspects of the musical discourse. Our results place the local O-information as a promising tool of wide applicability, which opens other perspectives for analyzing high-order relationships in the patterns exhibited by complex systems.

Multiorgan failure (MOF) is a life-threating condition that affects two or more systems of organs not involved in the disorder that motivates admission to an Intensive Care Unit (ICU). Patients who survive MOF frequently present long-term functional, neurological, cognitive, and psychiatric sequelae. However, the changes to the brain that explain such symptoms remain unclear. Objective: To determine brain connectivity and cognitive functioning differences between a group of MOF patients six months after ICU discharge and healthy controls (HC). Methods: 22 MOF patients and 22 HC matched by age, sex, and years of education were recruited. Both groups were administered a 3T magnetic resonance imaging (MRI), including structural T1 and functional BOLD, as well as a comprehensive neuropsychological evaluation that included tests of learning and memory, speed of information processing and attention, executive function, visual constructional abilities, and language. Voxel-based morphometry was used to analyses T1 images. For the functional data at rest, functional connectivity (FC) analyses were performed. Results: There were no significant differences in structural imaging and neuropsychological performance between groups, even though patients with MOF performed worse in all the cognitive tests. Functional neuroimaging in the default mode network (DMN) showed hyper-connectivity towards sensory-motor, cerebellum, and visual networks. DMN connectivity had a significant association with the severity of MOF during ICU stay and with the neuropsychological scores in tests of attention and visual constructional abilities. Conclusions: In MOF patients without structural brain injury, DMN connectivity six months after ICU discharge is associated with MOF severity and neuropsychological impairment, which supports the use of resting-state functional MRI as a potential tool to predict the onset of long-term cognitive deficits in these patients. Similar to what occurs at the onset of other pathologies, the observed hyper-connectivity might suggest network re-adaptation following MOF. Keywords: Multiorgan failure, Multiple organ dysfunction syndrome, Functional connectivity, Resting state, Hyper-connectivity, Default Mode Network, Neuropsychological Evaluation

Visibility algorithms are a family of methods that map time series into graphs, such that the tools of graph theory and network science can be used for the characterization of time series. This approach has proved a convenient tool, and visibility graphs have found applications across several disciplines. Recently, an approach has been proposed to extend this framework to multivariate time series, allowing a novel way to describe collective dynamics. Here we test their application to fMRI time series, following two main motivations, namely that (a) this approach allows vs to simultaneously capture and process relevant aspects of both local and global dynamics in an easy and intuitive way, and (b) this provides a suggestive bridge between time series and network theory that nicely fits the consolidating field of network neuroscience. Our application to a large open dataset reveals differences in the similarities of temporal networks (and thus in correlated dynamics) across resting-state networks, and gives indications that some differences in brain activity connected to psychiatric disorders could be picked up by this approach. Here we present the first application of multivariate visibility graphs to fMRI data. Visibility graphs are a way to represent a time series as a temporal network, evidencing specific aspects of its dynamics, such as extreme events. Multivariate time series, as those encountered in neuroscience, and in fMRI in particular, can be seen as a multiplex network, in which each layer represents a time series (a region of interest in the brain in our case). Here we report the method, we describe some relevant aspects of its application to BOLD time series, and we discuss the analogies and differences with existing methods. Finally, we present an application to a high-quality, publicly available dataset, containing healthy subjects and psychotic patients, and we discuss our findings. All the code to reproduce the analyses and the figures is publicly available.

A novel approach rooted on the notion of consensus clustering, a strategy developed for community detection in complex networks, is proposed to cope with the heterogeneity that characterizes connectivity matrices in health and disease. The method can be summarized as follows: (a) define, for each node, a distance matrix for the set of subjects by comparing the connectivity pattern of that node in all pairs of subjects; (b) cluster the distance matrix for each node; (c) build the consensus network from the corresponding partitions; and (d) extract groups of subjects by finding the communities of the consensus network thus obtained. Different from the previous implementations of consensus clustering, we thus propose to use the consensus strategy to combine the information arising from the connectivity patterns of each node. The proposed approach may be seen either as an exploratory technique or as an unsupervised pretraining step to help the subsequent construction of a supervised classifier. Applications on a toy model and two real datasets show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix.

Abstract Background To apply effective connectivity by means of nonlinear Granger Causality (GC) and brain networking analysis to basal EEG and under visual stimulation by checkerboard gratings with 0.5 and 2.0 cpd as spatial frequency in migraine with aura (MA) and without aura (MO), and to compare these findings with Blood Oxygen Level Dependent (BOLD) signal changes. Methods Nineteen asymptomatic MA and MO patients and 11 age and sex matched controls (C) were recorded by 65 EEG channels. The same visual stimulation was employed to evaluate BOLD signal changes in a subgroup of MA and MO. The GC and brain networking were applied to EEG signals. Results A different pattern of reduced vs increased GC respectively in MO and MA patients, emerged in resting state. During visual stimulation, both MA and MO showed increased information transfer toward the fronto-central regions, while MA patients showed a segregated cluster of connections in the posterior regions, and an increased bold signal in the visual cortex, more evident at 2 cpd spatial frequency. Conclusions The wealth of information exchange in the parietal-occipital regions indicates a peculiar excitability of the visual cortex, a pivotal condition for the manifestation of typical aura symptoms.

Traumatic brain injury (TBI) affects structural connectivity, triggering the reorganization of structural–functional circuits in a manner that remains poorly understood. We focus here on brain network reorganization in relation to postural control deficits after TBI. We enrolled young participants who had suffered moderate to severe TBI, comparing them to young, typically developing control participants. TBI patients (but not controls) recruited prefrontal regions to interact with two separated networks: (1) a subcortical network, including parts of the motor network, basal ganglia, cerebellum, hippocampus, amygdala, posterior cingulate gyrus, and precuneus; and (2) a task-positive network, involving regions of the dorsal attention system, together with dorsolateral and ventrolateral prefrontal regions. We also found that the increased prefrontal connectivity in TBI patients was correlated with some postural control indices, such as the amount of body sway, whereby patients with worse balance increased their connectivity in frontal regions more strongly. The increased prefrontal connectivity found in TBI patients may provide the structural scaffolding for stronger cognitive control of certain behavioral functions, consistent with the observations that various motor tasks are performed less automatically following TBI and that more cognitive control is associated with such actions. Using a new hierarchical atlas whose modules are relevant for both structure and function, we found increased structural and functional connectivity in prefrontal regions in TBI patients as compared to controls, in addition to a general pattern of overall decreased connectivity across the TBI brain. Although this increased prefrontal connectivity reflected interactions between brain areas when participants were at rest, the enhanced connectivity was found to be negatively correlated with active behavior such as postural control performance. Thus our findings, obtained when the brain was at rest, potentially reflect how TBI patients orchestrate task-related activations to support behavior in everyday life. In particular, our findings of enhanced connectivity in TBI might help these patients overcome deficits in cerebellar and subcortical connections, in addition to compensating for deficits when interacting with the task-positive network. Hence, it appears that greater cognitive control is exerted over certain actions in order to overcome deficits in their automatic processing.

Abstract Introduction Considerable connections between migraine with aura and cortical spreading depression (CSD), a depolarization wave originating in the visual cortex and traveling toward the frontal lobe, lead to the hypothesis that CSD is underlying migraine aura. The highly individual and complex characteristics of the brain cortex suggest that the geometry might impact the propagation of cortical spreading depression. Methods In a single‐case study, we simulated the CSD propagation for five migraine with aura patients, matching their symptoms during a migraine attack to the CSD wavefront propagation. This CSD wavefront was simulated on a patient‐specific triangulated cortical mesh obtained from individual MRI imaging and personalized diffusivity tensors derived locally from diffusion tensor imaging data. Results The CSD wave propagation was simulated on both hemispheres, despite in all but one patient the symptoms were attributable to one hemisphere. The CSD wave diffused with a large wavefront toward somatosensory and prefrontal regions, devoted to pain processing. Discussion This case‐control study suggests that the cortical geometry may contribute to the modality of CSD evolution and partly to clinical expression of aura symptoms. The simulated CSD is a large and diffuse phenomenon, possibly capable to activate trigeminal nociceptors and to involve cortical areas devoted to pain processing.

Uncovering dynamic information flow between stock market indices has been the topic of several studies which exploited the notion of transfer entropy or Granger causality, its linear version. The output of the transfer entropy approach is a directed weighted graph measuring the information about the future state of each target provided by the knowledge of the state of each driving stock market index. In order to go beyond the pairwise description of the information flow, thus looking at higher order informational circuits, here we apply the partial information decomposition to triplets consisting of a pair of driving markets (belonging to America or Europe) and a target market in Asia. Our analysis, on daily data recorded during the years 2000 to 2019, allows the identification of the synergistic information that a pair of drivers carry about the target. By studying the influence of the closing returns of drivers on the subsequent overnight changes of target indexes, we find that (i) Korea, Tokyo, Hong Kong, and Singapore are, in order, the most influenced Asian markets; (ii) US indices SP500 and Russell are the strongest drivers with respect to the bivariate Granger causality; and (iii) concerning higher order effects, pairs of European and American stock market indices play a major role as the most synergetic three-variables circuits. Our results show that the Synergy, a proxy of higher order predictive information flow rooted in information theory, provides details that are complementary to those obtained from bivariate and global Granger causality, and can thus be used to get a better characterization of the global financial system.

Intrinsic Connectivity Networks, patterns of correlated activity emerging from "resting-state" BOLD time series, are increasingly being associated with cognitive, clinical, and behavioral aspects, and compared with patterns of activity elicited by specific tasks. We study the reconfiguration of brain networks between task and resting-state conditions by a machine learning approach, to highlight the Intrinsic Connectivity Networks (ICNs) which are more affected by the change of network configurations in task vs. rest. To this end, we use a large cohort of publicly available data in both resting and task-based fMRI paradigms. By applying a battery of different supervised classifiers relying only on task-based measurements, we show that the highest accuracy to predict ICNs is reached with a simple neural network of one hidden layer. In addition, when testing the fitted model on resting state measurements, such architecture yields a performance close to 90% for areas connected to the task performed, which mainly involve the visual and sensorimotor cortex, whilst a relevant decrease of the performance is observed in the other ICNs. On one hand, our results confirm the correspondence of ICNs in both paradigms (task and resting) thus opening a window for future clinical applications to subjects whose participation in a required task cannot be guaranteed. On the other hand it is shown that brain areas not involved in the task display different connectivity patterns in the two paradigms.

This Correspondence article is a comment which directly relates to the paper “A study of problems encountered in Granger causality analysis from a neuroscience perspective” (Stokes and Purdon, 2017). We agree that interpretation issues of Granger causality (GC) in neuroscience exist, partially due to the historically unfortunate use of the name “causality”, as described in previous literature. On the other hand, we think that Stokes and Purdon use a formulation of GC which is outdated (albeit still used) and do not fully account for the potential of the different frequency-domain versions of GC; in doing so, their paper dismisses GC measures based on a suboptimal use of them. Furthermore, since data from simulated systems are used, the pitfalls that are found with the used formulation are intended to be general, and not limited to neuroscience. It would be a pity if this paper, even if written in good faith, became a wildcard against all possible applications of GC, regardless of the large body of work recently published which aims to address faults in methodology and interpretation. In order to provide a balanced view, we replicate the simulations of Stokes and Purdon, using an updated GC implementation and exploiting the combination of spectral and causal information, showing that in this way the pitfalls are mitigated or directly solved.

Alzheimer’s disease (AD) is a chronically progressive neurodegenerative disease highly correlated to aging. Whether AD originates by targeting a localized brain area and propagates to the rest of the brain across disease-severity progression is a question with an unknown answer. Here, we aim to provide an answer to this question at the group-level by looking at differences in diffusion-tensor brain networks. In particular, making use of data from Alzheimer’s Disease Neuroimaging Initiative (ADNI), four different groups were defined (all of them matched by age, sex and education level): G1 (N1 = 36, healthy control subjects, Control), G2 (N2 = 36, early mild cognitive impairment, EMCI), G3 (N3 = 36, late mild cognitive impairment, LMCI) and G4 (N4 = 36, AD). Diffusion-tensor brain networks were compared across three disease stages: stage I (Control vs. EMCI), stage II (Control vs. LMCI) and stage III (Control vs. AD). The group comparison was performed using the multivariate distance matrix regression analysis, a technique that was born in genomics and was recently proposed to handle brain functional networks, but here applied to diffusion-tensor data. The results were threefold: First, no significant differences were found in stage I. Second, significant differences were found in stage II in the connectivity pattern of a subnetwork strongly associated to memory function (including part of the hippocampus, amygdala, entorhinal cortex, fusiform gyrus, inferior and middle temporal gyrus, parahippocampal gyrus and temporal pole). Third, a widespread disconnection across the entire AD brain was found in stage III, affecting more strongly the same memory subnetwork appearing in stage II, plus the other new subnetworks, including the default mode network, medial visual network, frontoparietal regions and striatum. Our results are consistent with a scenario where progressive alterations of connectivity arise as the disease severity increases and provide the brain areas possibly involved in such a degenerative process. Further studies applying the same strategy to longitudinal data are needed to fully confirm this scenario.

Alzheimer's disease (AD) is the most common form of dementia among older people and increasing longevity ensures its prevalence will rise even further. Whether AD originates by disconnecting a localized brain area and propagates to the rest of the brain across disease-severity progression is a question with an unknown answer. An important related challenge is to predict whether a given subject, with a mild cognitive impairment (MCI), will convert or not to AD. Here, our aim is to characterize the structural connectivity pattern of MCI and AD subjects using the multivariate distance matrix regression (MDMR) analysis, and to compare it to those of healthy subjects. MDMR is a technique developed in genomics that has been recently applied to functional brain network data, and here applied to identify brain nodes with different connectivity patterns, in controls and patients, because of brain atrophy. We address this issue at the macroscale by looking to differences in individual structural MRI brain networks, obtained from MR images according to a recently proposed definition of connectivity which measures the image similarity between patches at different locations in the brain. In particular, using data from ADNI, we selected four groups of subjects (all of them matched by age and sex): HC (healthy control participants), ncMCI (mild cognitive impairment not converting to AD), cMCI (mild cognitive impairment converting to AD) and AD. Next, we built structural MRI brain networks and performed group comparison for all the pairs of groups. Our results were three-fold: (i) considering the comparison of HC with the three other groups, the number of significant brain regions was 4 for ncMCI, 290 for cMCI and 74 for AD, out of a total of 549 regions; hence, in terms of the structural MRI connectivity here adopted, cMCI subjects have the maximal altered pattern w.r.t. healthy conditions. (ii) Eight and seven nodes were significant for the comparisons AD-ncMCI and AD-cMCI, respectively; six nodes, among them, were significant in both comparisons and these nodes form a connected brain region (corresponding to hippocampus, amygdala, Parahippocampal Gyrus, Planum Polare, Frontal Orbital Cortex, Temporal Pole and subcallosal cortex) showing reduced strength of connectivity in the MCI stages; (iii) The connectivity maps of cMCI and ncMCI subjects significantly differ from the connectome of healthy subjects in three regions all corresponding to Frontal Orbital Cortex.

Barth syndrome is a rare X-linked disease affecting less than 200 individuals worldwide. Several comorbidities have been associated with the pathology and, among those, cardiac myopathy and neutropenia are the most life threatening. The appropriate nutritive support is important to sustain the everyday life of Barth syndrome patients given the chronic fatigue they experience. Since they often prefer salty and fried food, and avoid vegetables and fruits, their eating habit and food preferences do not always provide the proper amount of vitamins and amino acids. It has been indeed reported that Barth syndrome patients have altered taste sensitivity. As olfaction also contributes to food consumption and flavor perception, we decided to investigate their olfactory abilities using the "Sniffin' sticks' extended test". We found no significant difference in any of the tested olfactory abilities between the group of Barth syndrome patients and the healthy controls. In summary, altered food preference of Barth boys could not be easily explained with an altered olfactory perception.

Heart rate variability (HRV; variability of the RR interval of the electrocardiogram) results from the activity of several coexisting control mechanisms, which involve the influence of respiration (RESP) and systolic blood pressure (SBP) oscillations operating across multiple temporal scales and changing in different physiological states. In this study, multiscale information decomposition is used to dissect the physiological mechanisms related to the genesis of HRV in 78 young volunteers monitored at rest and during postural and mental stress evoked by head-up tilt (HUT) and mental arithmetics (MA). After representing RR, RESP and SBP at different time scales through a recently proposed method based on multivariate state space models, the joint information transfer T RESP , SBP → RR is decomposed into unique, redundant and synergistic components, describing the strength of baroreflex modulation independent of respiration ( U SBP → RR ), nonbaroreflex ( U RESP → RR ) and baroreflex-mediated ( R RESP , SBP → RR ) respiratory influences, and simultaneous presence of baroreflex and nonbaroreflex respiratory influences ( S RESP , SBP → RR ), respectively. We find that fast (short time scale) HRV oscillations—respiratory sinus arrhythmia—originate from the coexistence of baroreflex and nonbaroreflex (central) mechanisms at rest, with a stronger baroreflex involvement during HUT. Focusing on slower HRV oscillations, the baroreflex origin is dominant and MA leads to its higher involvement. Respiration influences independent on baroreflex are present at long time scales, and are enhanced during HUT.

Interaction Information (II) generalizes the univariate Shannon entropy to triplets of variables, allowing the detection of redundant (R) or synergetic (S) interactions in dynamical networks. Here, we calculated II from functional magnetic resonance imaging data and asked whether R or S vary across brain regions and along lifespan. Preserved along lifespan, we found high overlapping between the pattern of high R and the default mode network, whereas high values of S were overlapping with different cognitive domains, such as spatial and temporal memory, emotion processing and motor skills. Moreover, we have found a robust balance between R and S among different age intervals, indicating informational compensatory mechanisms in brain networks.

Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by prevalently redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone.

We implement the Ising model on a structural connectivity matrix describing the brain at two different resolutions. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the the sum of the weights to that node and to the average time between consecutive time flips of spins. The results for the connectome of 66 nodes and for that of 998 nodes are similar, thus suggesting that these properties are scale-independent. Finally, we also find that the brain dynamics at criticality is organized maximally to a rich-club w.r.t. the network of information flows.

A network approach to brain and dynamics opens new perspectives towards understanding of its function. The functional connectivity from functional MRI recordings in humans is widely explored at large scale, and recently also at the voxel level. The networks of dynamical directed connections are far less investigated, in particular at the voxel level. To reconstruct full brain effective connectivity network and study its topological organization, we present a novel approach to multivariate Granger causality which integrates information theory and the architecture of the dynamical network to efficiently select a limited number of variables. The proposed method aggregates conditional information sets according to community organization, allowing to perform Granger causality analysis avoiding redundancy and overfitting even for high-dimensional and short datasets, such as time series from individual voxels in fMRI. We for the first time depicted the voxel-wise hubs of incoming and outgoing information, called Granger causality density (GCD), as a complement to previous repertoire of functional and anatomical connectomes. Analogies with these networks have been presented in most part of default mode network; while differences suggested differences in the specific measure of centrality. Our findings could open the way to a new description of global organization and information influence of brain function. With this approach is thus feasible to study the architecture of directed networks at the voxel level and individuating hubs by investigation of degree, betweenness and clustering coefficient.

We analyze simple dynamical network models which describe the limited capacity of nodes to process the input information. For a proper range of their parameters, the information flow pattern in these models is characterized by exponential distribution of the incoming information and a fat-tailed distribution of the outgoing information, as a signature of the law of diminishing marginal returns. We apply this analysis to effective connectivity networks from human EEG signals, obtained by Granger Causality, which has recently been given an interpretation in the framework of information theory. From the distributions of the incoming versus the outgoing values of the information flow it is evident that the incoming information is exponentially distributed whilst the outgoing information shows a fat tail. This suggests that overall brain effective connectivity networks may also be considered in the light of the law of diminishing marginal returns. Interestingly, this pattern is reproduced locally but with a clear modulation: a topographic analysis has also been made considering the distribution of incoming and outgoing values at each electrode, suggesting a functional role for this phenomenon.

We analyze, by means of Granger causality (GC), the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. While we show that fully conditioned GC (CGC) is not affected by synergy, the pairwise analysis fails to prove synergetic effects. In cases when the number of samples is low, thus making the fully conditioned approach unfeasible, we show that partially conditioned GC (PCGC) is an effective approach if the set of conditioning variables is properly chosen. Here we consider two different strategies (based either on informational content for the candidate driver or on selecting the variables with highest pairwise influences) for PCGC and show that, depending on the data structure, either one or the other might be equally valid. On the other hand, we observe that fully conditioned approaches do not work well in the presence of redundancy, thus suggesting the strategy of separating the pairwise links in two subsets: those corresponding to indirect connections of the CGC (which should thus be excluded) and links that can be ascribed to redundancy effects and, together with the results from the fully connected approach, provide a better description of the causality pattern in the presence of redundancy. Finally we apply these methods to two different real datasets. First, analyzing electrophysiological data from an epileptic brain, we show that synergetic effects are dominant just before seizure occurrences. Second, our analysis applied to gene expression time series from HeLa culture shows that the underlying regulatory networks are characterized by both redundancy and synergy.