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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.

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.