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Abstract Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable complex functions. Yet, understanding, and ultimately harnessing, the structure-function relationship in oscillator networks remains an outstanding challenge of modern science. Here, we address this challenge by presenting a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators’ parameters. To quantify the behavioral synchrony between coupled oscillators, we introduce the notion offunctional pattern, which encodes the pairwise relationships between the oscillators’ phases. Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. These conditions provide an interpretable mapping between the structural constraints and their functional implications in oscillator networks. As a proof of concept, we apply the proposed method to replicate empirically recorded functional relationships from cortical oscillations in a human brain, and to redistribute the active power flow in different models of electrical grids. 

Abstract Context.Large multi-site neuroimaging datasets have significantly advanced our quest to understand brain-behavior relationships and to develop biomarkers of psychiatric and neurodegenerative disorders. Yet, such data collections come at a cost, as the inevitable differences across samples may lead to biased or erroneous conclusions.Objective.We aim to validate the estimation of individual brain network dynamics fingerprints and appraise sources of variability in large resting-state functional magnetic resonance imaging (rs-fMRI) datasets by providing a novel point of view based on data-driven dynamical models.Approach.Previous work has investigated this critical issue in terms of effects on static measures, such as functional connectivity and brain parcellations. Here, we utilize dynamical models (hidden Markov models—HMM) to examine how diverse scanning factors in multi-site fMRI recordings affect our ability to infer the brain’s spatiotemporal wandering between large-scale networks of activity. Specifically, we leverage a stable HMM trained on the Human Connectome Project (homogeneous) dataset, which we then apply to an heterogeneous dataset of traveling subjects scanned under a multitude of conditions.Main Results.Building upon this premise, we first replicate previous work on the emergence of non-random sequences of brain states. We next highlight how these time-varying brain activity patterns are robust subject-specific fingerprints. Finally, we suggest these fingerprints may be used to assess which scanning factors induce high variability in the data.Significance.These results demonstrate that we can (i) use large scale dataset to train models that can be then used to interrogate subject-specific data, (ii) recover the unique trajectories of brain activity changes in each individual, but also (iii) urge caution as our ability to infer such patterns is affected by how, where and when we do so. 

Network control theory (NCT) is a simple and powerful tool for studying how network topology informs and constrains the dynamics of a system. Compared to other structure–function coupling approaches, the strength of NCT lies in its capacity to predict the patterns of external control signals that may alter the dynamics of a system in a desired way. An interesting development for NCT in the neuroscience field is its application to study behavior and mental health symptoms. To date, NCT has been validated to study different aspects of the human structural connectome. NCT outputs can be monitored throughout developmental stages to study the effects of connectome topology on neural dynamics and, separately, to test the coherence of empirical datasets with brain function and stimulation. Here, we provide a comprehensive pipeline for applying NCT to structural connectomes by following two procedures. The main procedure focuses on computing the control energy associated with the transitions between specific neural activity states. The second procedure focuses on computing average controllability, which indexes nodes’ general capacity to control the dynamics of the system. We provide recommendations for comparing NCT outputs against null network models, and we further support this approach with a Python-based software package called ‘network control theory for python’. The procedures in this protocol are appropriate for users with a background in network neuroscience and experience in dynamical systems theory. 

Astrocytes are a ubiquitous and enigmatic type of non-neuronal cell and are found in the brain of all vertebrates. While traditionally viewed as being supportive of neurons, it is increasingly recognized that astrocytes play a more direct and active role in brain function and neural computation. On account of their sensitivity to a host of physiological covariates and ability to modulate neuronal activity and connectivity on slower time scales, astrocytes may be particularly well poised to modulate the dynamics of neural circuits in functionally salient ways. In the current paper, we seek to capture these features via actionable abstractions within computational models of neuron-astrocyte interaction. Specifically, we engage how nested feedback loops of neuron-astrocyte interaction, acting over separated time-scales, may endow astrocytes with the capability to enable learning in context-dependent settings, where fluctuations in task parameters may occur much more slowly than within-task requirements. We pose a general model of neuron-synapse-astrocyte interaction and use formal analysis to characterize how astrocytic modulation may constitute a form of meta-plasticity, altering the ways in which synapses and neurons adapt as a function of time. We then embed this model in a bandit-based reinforcement learning task environment, and show how the presence of time-scale separated astrocytic modulation enables learning over multiple fluctuating contexts. Indeed, these networks learn far more reliably compared to dynamically homogeneous networks and conventional non-network-based bandit algorithms. Our results fuel the notion that neuron-astrocyte interactions in the brain benefit learning over different time-scales and the conveyance of task-relevant contextual information onto circuit dynamics. 

The structural and metabolic basis of control energy in the brain is uncovered by leveraging epilepsy as a human lesion model.