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A Survey on Privacy in Graph Neural Networks: Attacks, Preservation, and Applications

Graph Neural Networks (GNNs) have gained significant attention owing to their ability to handle graph-structured data and the improvement in practical applications. However, many of these models prioritize high utility performance, such as accuracy, with a lack of privacy consideration, which is a major concern in modern society where privacy attacks are rampant. To address this issue, researchers have started to develop privacy-preserving GNNs. Despite this progress, there is a lack of a comprehensive overview of the attacks and the techniques for preserving privacy in the graph domain. In this survey, we aim to address this gap by summarizing the attacks on graph data according to the targeted information, categorizing the privacy preservation techniques in GNNs, and reviewing the datasets and applications that could be used for analyzing/solving privacy issues in GNNs. We also outline potential directions for future research in order to build better privacy-preserving GNNs.

97 MATHEMATICS AND COMPUTING

Estimating soybean yields from high-temporal-resolution multi-source data using deep learning

Accurate and timely crop yield prediction is crucial for ensuring food security and maintaining stable agricultural markets. In recent years, there has been a surge in interest in leveraging high-temporal-resolution, multi-source data for effective crop growth monitoring and yield estimation. A notable challenge arises from the difficulty in capturing the intricate interactions between variables across different time steps within these high-temporal-resolution time series datasets. This complexity hinders the reliable extraction of yield information from voluminous and often noisy datasets, especially during periods of extreme weather events. Here, in this study, we propose an Attention and Graph Isomorphism Network-enhanced Bi-directional Long Short-Term Memory network (AGB-LSTM) for estimating county-level soybean yield in the United States. This model integrates a diverse set of remote sensing data, including Near-Infrared Reflectance of Vegetation (NIRv), Sun-Induced chlorophyll Fluorescence (SIF), and Gross Primary Productivity (GPP), along with environmental covariates. The AGB-LSTM effectively leverages information related to crop yield from high-temporal-resolution time series data (5-days), achieving an accuracy of R²= 0.67 and rRMSE = 14.46%. This approach significantly outperforms traditional machine learning methods such as Random Forest (RF) (R²= 0.52, rRMSE = 17.36%) and Bi-LSTM (R²= 0.58, rRMSE = 16.17%). Sensitivity experiments with different time steps and ranges demonstrated that our model could accurately and stably predict yields 1 to 2 months before harvest. Moreover, data with a finer temporal resolution consistently improved prediction performance, resulting in an approximately 20% increase in and an approximately 20% decrease in rRMSE compared to using monthly composites. We also evaluated the robustness of the model under extreme climate events and observed strong performance (R²= 0.50, rRMSE = 21.32%). Finally, yield mapping for major soybean-producing regions in North America in 2023 revealed spatial patterns that closely matched USDA yield reports. Our findings suggest that the AGB-LSTM model is a promising and effective method for estimating yield and has notable potential for global crop yield forecasting.

Deep learning

When does global attention help: a unified empirical study on atomistic graph learning

Graph neural networks (GNNs) are widely used as surrogates for costly experiments and first-principles simulations to study the behavior of compounds at atomistic scale, and their architectural complexity is constantly increasing to enable the modeling of complex physics. While most recent GNNs combine more traditional message passing neural networks (MPNNs) layers to model short-range interactions with more advanced graph transformers (GTs) with global attention mechanisms to model long-range interactions, it is still unclear when global attention mechanisms provide real benefits over well-tuned MPNN layers due to inconsistent implementations, features, or hyperparameter tuning. We introduce the first unified, reproducible benchmarking framework–built on HydraGNN–that enables seamless switching among four controlled model classes: MPNN, MPNN with chemistry/topology encoders, GPS-style hybrids of MPNN with global attention, and fully fused localglobal models with encoders. Using seven diverse open-source datasets for benchmarking across regression and classification tasks, we systematically isolate the contributions of message passing, global attention, and encoder-based feature augmentation. Our study shows that encoder-augmented MPNNs form a robust baseline, while fused localglobal models yield the clearest benefits for properties governed by long-range interaction effects. We further quantify the accuracycompute trade-offs of attention, reporting its overhead in memory. Together, these results establish the first controlled evaluation of global attention in atomistic graph learning and provide a reproducible testbed for future model development.

Equivariant graph neural networks

Development of Whole System Digital Twins for Advanced Reactors: Leveraging Graph Neural Networks and SAM Simulations

Here, in this work, we introduce a novel method to develop whole system digital twins (DTs) for advanced nuclear reactors. This method treats a complex reactor system as a heterogeneous graph: with the system components as different types of graph nodes and their physical interconnections as edges. Based on the heterogeneous graph, a graph neural network combining graph convolution and temporal node attention is developed as the DT, facilitating a comprehensive understanding of the system's dynamic behavior. By utilizing the System Analysis Module (SAM) code for simulating various operational transients, we develop a graph-based database that trains the DT. This DT is characterized by two primary functions: It can infer the entire system's status using sparse node information, and it can predict the progress of transients based on current and historical system information. Our approach is validated through case studies on the Experimental Breeder Reactor II (EBR-II) system and a generic Fluoride-salt-cooled High-temperature Reactor (gFHR), demonstrating the DT's accuracy in forecasting operational transients. The DT's rapid computation capabilities enhance its potential for supporting advanced reactor operations, offering benefits in intelligent simulation, autonomous control, and anomaly detection, paving the way for improved safety analysis and intelligent component health management for advanced reactor systems and reducing their operations and maintenance cost.

EBR-II

Distributed-Memory Sparse Deep Neural Network Inference Using Global Arrays

Partitioned Global Address Space (PGAS) models exhibit tremendous promise in developing efficient and productive distributed-memory parallel applications. They have been used extensively in scientific computations due to conveniently offering a ``shared-memory''-like model and convenient interfaces that separate communication with synchronization. Traditionally, PGAS communication models have been applied to dense/contiguously distributed data, but most modern applications depict varied levels of sparsity. Existing PGAS models require certain adaptations to support distributed sparse computations, since associated computations often require matrix arithmetic, in addition to data movement. The Global Arrays toolkit from Pacific Northwest National Laboratory (PNNL) is one of the earliest PGAS models to combine one-sided data communication and distributed matrix operations and is still used in the popular NWChem quantum chemistry suite. Recently, we have expanded the Global Arrays toolkit to support common sparse operations, like sparse matrix-dense matrix multiplies (SpMM), sparse matrix-sparse matrix multiplication (SpGEMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM). As it turns out, these operations are the bedrock of sparse Deep Learning (DL); sparse deep neural networks and Graph Neural Networks (GNNs) have gained increasing attention recently in achieving speedups on training and inference with reduced memory footprints. Unlike scientific applications in High Performance Computing (HPC), modern (distributed-memory capable) DL toolkits often rely on non-standardized and closed-source vendor software optimizations, creating challenges in software-hardware co-design at scale. Our goal is to support a variety of distributed-memory sparse matrix operations and helper functions in the newly created Sparse Global Arrays (SGA), such that it is possible to build portable and productive Machine Learning scenarios for algorithm/software and hardware codesign purposes. Contemporary data-parallel schemes for training/inference are undergoing a major overhaul since model replication limits scalability and causes resource inefficiencies. As such, we have adopted tensor parallelism in decomposing the model and inputs, to mitigate memory issues. Current implementation is built on top of MPI and uses CPUs to maximize the portability across the platforms.

Distributed computing, machine learning

Graph neural network for neutrino physics event reconstruction

Liquid argon time projection chamber (LArTPC) detector technology offers a wealth of high-resolution information on particle interactions, and leveraging that information to its full potential requires sophisticated automated reconstruction techniques. Here, this article describes NUGRAPH 2, a graph neural network for low-level reconstruction of simulated neutrino interactions in a LArTPC detector. Simulated neutrino interactions in the MicroBooNE detector geometry are described as heterogeneous graphs, with energy depositions on each detector plane forming nodes on planar subgraphs. The network utilizes a multihead attention message-passing mechanism to perform background filtering and semantic labeling on these graph nodes, identifying those associated with the primary physics interaction with 98.0% efficiency and labeling them according to particle type with 94.9% efficiency. The network operates directly on detector observables across multiple two-dimensional representations but utilizes a three-dimensional-context-aware mechanism to encourage consistency between these representations. Model inference takes 0.12 s / event on a CPU and 0.005 s / event batched on a GPU. This architecture is designed to be a general-purpose solution for particle reconstruction in neutrino physics, with the potential for deployment across a broad range of detector technologies, and offers a core convolution engine that can be leveraged for a variety of tasks beyond the two described in this paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

CRADA Number NFE-24-10110 with Qubit Engineering Inc. (CRADA Final Report)

Over the past year, the Qubit Engineering team has pushed the frontiers of power‑grid optimization, working in close collaboration with Oak Ridge National Laboratory (ORNL) and the Tennessee Valley Authority (TVA). Their progress is reflected in three newly submitted conference papers, “Unified Relational GNN Architecture for AC Optimal Power Flow Calculations in Electric Grids,” “Graph‑Based Attention Mechanisms for Solving the AC Optimal Power Flow Problem in Electrical‑Power Networks,” and “Enhanced Power‑Grid Maintenance Planning and Quantum‑Inspired Combinatorial Prospects.” These publications showcase state‑of‑the‑art graph‑neural‑network methods for AC‑OPF and novel quantum‑inspired heuristics for maintenance scheduling. Beyond the academic results, the Qubit team has converted the research into two production‑grade tools built on TVA data: Neuro‑Grid, an AI‑driven power‑flow simulator that provides instant, interactive full‑grid load‑flow visualizations, and Quanta‑Grid, a quantum‑inspired maintenance‑scheduling engine to support logistics optimization for power utilities. Together, these advances demonstrate how Qubit’s partnership with ORNL and TVA is delivering practical, physics‑grounded analytics for next‑generation grid management.

24 POWER TRANSMISSION AND DISTRIBUTION

Portable Parallel Algorithms and Frameworks for Exascale Graph Analytics

Graphs (or networks) are a tool used to model the interactions among various entities. Efficiently processing large graphs has recently attracted significant attention due to the applications of graphs in various domains, such as biology, chemistry, and cyber-security. Analyzing the structure and properties of these graphs is an important component of many scientific computing pipelines. With the explosion in the volume of data, graphs have become very large and can contain hundreds of billions of vertices and trillions of edges. Therefore, it is crucial to develop high-performance methods to enable graph analysis to be done quickly and energy-efficiently. Furthermore, these solutions should be highly parallel in order to take advantage of modern parallel machines. However, designing efficient solutions is not enough. With the wide variety of computing environments available, each with different programmability and performance characteristics, it is necessary to develop solutions that are portable in terms of both performance (i.e., provide theoretical guarantees) and programmability (i.e., provide high level abstractions).

97 MATHEMATICS AND COMPUTING

Knowledge Oriented Graph Unified Transformer (KOGUT) v0.1

KOGUT — Knowledge Oriented Graph Unified Transformer KOGUT implements the Relational Graph Transformer (RelGT) architecture for knowledge graph link prediction in biological domains, with a primary focus on microbial growth media prediction. While the original RelGT (arXiv:2505.10960) targets relational tables, time series, and multi-table databases, KOGUT adapts this architecture for heterogeneous biological knowledge graphs, providing first-in-class AI predictive models for microbial cultivation. Key Adaptations Beyond Original RelGT: - Knowledge Graph Focus: Applied to biological KGs with semantic node types (taxa, chemicals, media, phenotypes, environments) versus generic relational database tables, trained on the KG-Microbe knowledge graph (1.3M entities, 2.9M edges, 24 relation types). - Multimodal Node Encoding: Integrates node labels, categories, descriptions, and synonyms from KG metadata through learned embedding layers—adapting relational column features to graph node attributes with textual semantics. - Extended K-Hop Subgraph Strategy: Optimized neighborhood sampling (3-hop default, configurable up to 200 nodes) tuned for sparse biological networks, building on the original local-global attention framework with biological relation preservation. - Biolink Predicate Preservation: Type-specific transformations for 24 biological edge semantics (occurs_in, consumes, produces, has_phenotype, subclass_of) beyond standard relational foreign keys, enabling multi-relation link prediction. - Inductive Learning Support: Enables zero-shot predictions for novel taxa through feature-based embeddings (temperature, oxygen requirements, gram stain, cell shape), extending the original transductive relational benchmark scope to uncultured microorganisms. CheapSOTA Performance Optimizations (This Distribution): - VQ-EMA Centroid Attention: Vector quantization with exponential moving average for improved global context modeling (+5-10% MRR improvement). - HDF5 Precomputed Data Loading: One-time preprocessing of k-hop subgraphs to eliminate redundant graph traversals (2-5× training speedup). - Distributed Data Parallel Training: Multi-GPU support for scaling to larger knowledge graphs (tested on 4× NVIDIA A100 GPUs at NERSC Perlmutter). - Mixed Precision Training: Automatic mixed precision (AMP) for memory efficiency and faster training. Advantages Over Standard Knowledge Graph Embedding Models: Combines RelGT's proven multi-element tokenization (features, type, hop, structure) with graph-native biological representations, enabling interpretable link prediction across heterogeneous entities that standard embedding models (TransE, RotatE, ComplEx) and table-based transformers cannot directly model. Achieves near-perfect performance on microbial growth media prediction (MRR: 0.9966, Precision@1: 0.9932, Hit@10: 1.0000) while maintaining explainability through attention-based reasoning over biological pathways. Training Data: - KG-Microbe merged knowledge graph: 1,379,337 nodes, 2,960,472 edges - 24 biological relation types including taxonomic hierarchies, metabolic interactions, phenotype associations, and environmental relationships - Primary prediction task: Growth media suitability for microbial taxa (biolink:occurs_in, 50K edges) - Multi-relation capability: Predicts links for any of the 24 relation types, including chemical consumption/production, phenotype associations, and taxonomic classification Citation: Original RelGT Architecture: Dwivedi et al., "Relational Graph Transformer", arXiv:2505.10960, 2025 KOGUT Implementation: Knowledge Oriented Graph Unified Transformer for Microbial Growth Media Prediction Developed at Lawrence Berkeley National Laboratory (LBNL) Trained on NERSC Perlmutter supercomputer

Joachimiak, Marcin [Lawrence Berkeley National Lab

Search for Stable and Low-Energy Ce–Co–Cu Ternary Compounds Using Machine Learning

Cerium-based intermetallics have garnered significant research attention as potential new permanent magnets. In this study, we explore the compositional and structural landscape of Ce−Co−Cu ternary compounds using a machine learning (ML)- guided framework integrated with first-principles calculations. We employ a crystal graph convolutional neural network (CGCNN), which enables efficient screening for promising candidates, significantly accelerating the material discovery process. With this approach, we predict five stable compounds, Ce 3 Co 3 Cu, CeCoCu 2 , Ce 12 Co 7 Cu, Ce 11 Co 9 Cu, and Ce 10 Co 11 Cu 4 , with formation energies below the convex hull, along with hundreds of low-energy (possibly metastable) Ce−Co−Cu ternary compounds. Firstprinciples calculations reveal that several structures are both energetically and dynamically stable. Notably, two Co-rich low-energy compounds, Ce 4 Co 33 Cu and Ce 4 Co 31 Cu 3 , are predicted to have high magnetizations.

Chemical structure

Continuous system modeling

A comprehensive and systematic introduction is presented for the concepts associated with 'modeling', involving the transition from a physical system down to an abstract description of that system in the form of a set of differential and/or difference equations, and basing its treatment of modeling on the mathematics of dynamical systems. Attention is given to the principles of passive electrical circuit modeling, planar mechanical systems modeling, hierarchical modular modeling of continuous systems, and bond-graph modeling. Also discussed are modeling in equilibrium thermodynamics, population dynamics, and system dynamics, inductive reasoning, artificial neural networks, and automated model synthesis.

Cellier, Francois E.

Knowledge Graph of RB-Tnseq Data from Fitness Browser (KP-DP1)

Motivation: Predicting microbial gene fitness across environmental conditions remains a central challenge for predictive phenomics and autonomous experimentation. Fitness assays generate large volumes of genotype–phenotype measurements difficult to integrate with experimental metadata and biological function in a form that supports mechanistic reasoning. Knowledge graphs offer a semantic framework for unifying modalities and enabling context-aware inference. Results: We build GIMME (Graph Inference for Microbial Metabolism Exploration), a semantically grounded knowledge graph that unifies gene fitness measurements spanning 10 Pseudomonas species with experimental metadata and biological context. Media are decomposed into chemical components and experiments carry structured links to natural-language descriptions. The resulting graph supports two inference modes: (1) symbolic graph traversal to surface candidate gene–environment and gene–chemical associations, and (2) learned inference using heterogeneous graph neural networks that propagate information across neighborhoods. We formulate link regression over (gene, media, experiment) triplets, combining learned gene embeddings with pretrained LLM sourced text embeddings of node descriptions to predict gene fitness. We then augment a baseline MLP with an auxiliary message-passing encoder (GraphSAGE/GAT) that propagates information over gene–protein–function and media–chemical subgraphs, and fuse the two pathways with a gated residual connection. This approach produces strong agreement with held-out fitness measurements (GraphSAGE Pearson r 0.74) while also highlighting inference challenges in extreme-fitness regimes. We aggregate GAT edge-attention weights by relation type and layer to estimate which biological and environmental relations most influence fitness predictions. Conclusion: This work explores using knowledge graphs as “context graphs” for microbial phenotype prediction. They provide a rich substrate which enables explainable retrieval of supporting evidence, and provides a natural bridge to autonomous workflows that prioritize the next experiment.

59 BASIC BIOLOGICAL SCIENCES

NuGraph2: A Graph Neural Network for Neutrino Event Reconstruction

Neutrino experiments are set to probe some of the most important open questions in physics, from CP violation and the nature of dark matter. The technology of choice for many of these experiments is the liquid argon time projection chamber (LArTPC). In current LArTPC experiments, reconstruction performance often represents a limiting factor for the sensitivity. New developments are therefore needed to unlock the full potential of LArTPC experiments. NuGraph2 is a state of the art Graph Neural Network for reconstruction of data in LArTPC experiments. NuGraph2 utilizes a heterogeneous graph structure, with separate subgraphs of 2D nodes (hits in each plane) connected across planes via 3D nodes (space points). The model provides a consistent description of the neutrino interaction across all planes. NuGraph2 is a multi-purpose network, with a common message-passing attention engine connected to multiple decoders with different classification or regression tasks. These include the classification of detector hits according to the particle type that produced them (semantic segmentation) and the separation of hits from the neutrino interaction from hits due to noise or cosmic-ray background. Additional decoders are being developed, performing tasks such as the regression of the neutrino interaction vertex position. Performance results will be presented based on publicly available samples from MicroBooNE. These include both physics performance metrics, achieving 95% accuracy for semantic segmentation and 98% classification of neutrino hits, as well as computational metrics for training and for inference on CPU or GPU. The status of the NuGraph integration in the LArSoft software framework will be presented, as well as initial studies about model interpretability and injection of domain knowledge.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

NuGraph2: A Graph Neural Network for Neutrino Event Reconstruction

Neutrino experiments are set to probe some of the most important open questions in physics, from CP violation and the nature of dark matter. The technology of choice for many of these experiments is the liquid argon time projection chamber (LArTPC). In current LArTPC experiments, reconstruction performance often represents a limiting factor for the sensitivity. New developments are therefore needed to unlock the full potential of LArTPC experiments. NuGraph2 is a state of the art Graph Neural Network for reconstruction of data in LArTPC experiments. NuGraph2 utilizes a heterogeneous graph structure, with separate subgraphs of 2D nodes (hits in each plane) connected across planes via 3D nodes (space points). The model provides a consistent description of the neutrino interaction across all planes. NuGraph2 is a multi-purpose network, with a common message-passing attention engine connected to multiple decoders with different classification or regression tasks. These include the classification of detector hits according to the particle type that produced them (semantic segmentation) and the separation of hits from the neutrino interaction from hits due to noise or cosmic-ray background. Additional decoders are being developed, performing tasks such as the regression of the neutrino interaction vertex position. Performance results will be presented based on publicly available samples from MicroBooNE. These include both physics performance metrics, achieving 95% accuracy for semantic segmentation and 98% classification of neutrino hits, as well as computational metrics for training and for inference on CPU or GPU. The status of the NuGraph integration in the LArSoft software framework will be presented, as well as initial studies about model interpretability and injection of domain knowledge.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

NuGraph2: A Graph Neural Network for Neutrino Event Reconstruction

Neutrino experiments are set to probe some of the most important open questions in physics, from CP violation and the nature of dark matter. The technology of choice for many of these experiments is the liquid argon time projection chamber (LArTPC). In current LArTPC experiments, reconstruction performance often represents a limiting factor for the sensitivity. New developments are therefore needed to unlock the full potential of LArTPC experiments. NuGraph2 is a state of the art Graph Neural Network for reconstruction of data in LArTPC experiments [https://arxiv.org/abs/2403.11872]. NuGraph2 utilizes a heterogeneous graph structure, with separate subgraphs of 2D nodes (hits in each plane) connected across planes via 3D nodes (space points). The model provides a consistent description of the neutrino interaction across all planes. NuGraph2 is a multi-purpose network, with a common message-passing attention engine connected to multiple decoders with different classification or regression tasks. These include the classification of detector hits according to the particle type that produced them (semantic segmentation) and the separation of hits from the neutrino interaction from hits due to noise or cosmic-ray background. Additional decoders are being developed, performing tasks such as the regression of the neutrino interaction vertex position. Performance results will be presented based on publicly available samples from MicroBooNE. These include both physics performance metrics, achieving 95% accuracy for semantic segmentation and 98% classification of neutrino hits, as well as computational metrics for training and for inference on CPU or GPU. The status of the NuGraph integration in the LArSoft software framework will be presented, as well as initial studies about model interpretability and injection of domain knowledge.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Performance evaluation of a simulated data-flow computer with low-resolution actors

Basic problems related to the exploitation of parallelism in a program include sequencing of the instructions and communication of the data. It is pointed out that the data-flow approach offers an elegant solution to the sequencing problem, since all data dependencies are automatically handled and only instructions with ready input sets are activated. It is shown that a change in the level of subcomputations (actors) affects communications costs. The concept of variable resolution is discussed, and the testbed environment is examined. Attention is given to the architecture of the processing elements, the communication network, and the simulators. A description of the analytical model is also provided. Simulation and results are discussed, taking into account test programs and allocation, the variation of the number of processing elements, the variation of the resolution in directed acyclic graphs, performance in processing loops, and array handling.

Gaudiot, J. L.

Optimal Network Reconfiguration and Scheduling With Hardware-in-the-Loop Validation for Improved Microgrid Resilience

With the increased occurrence of various major extreme weather events, power outages and prompt power system restorations have recently drawn more attention to the resilience and recovery of power systems. From the perspective of a more resilient power delivery at the distribution grid, system restoration using network topology reconfiguration together with optimal scheduling of distributed energy resources are adopted in this paper. The proposed optimization model aims at minimizing the total load shedding cost and other operational costs, in which linearized topological constraints borrowed from graph theory and linearized DistFlow models are respectively used to maintain the radial network topology and power flow balance after system contingencies. To demonstrate the applicability of the proposed strategy, a real-world case study of a networked three-microgrid system in Adjuntas, Puerto Rico, is used with the consideration of different independent/interconnected microgrid scenarios, contingencies, and fairness settings. Furthermore, hardware-in-the-loop testing is conducted for the same three-microgrid network, where the closely matched results with the simulated ones have validated the effectiveness of the proposed restoration strategy, which is now ready to move one step forward towards field deployment. Finally, to test the proposed restoration strategy in a larger networked system, the modified IEEE-33 bus test distribution system is considered, and the results show a more resilient power delivery for critical loads under three and four line outages.

24 POWER TRANSMISSION AND DISTRIBUTION

Perturbations in Brain Functional Connectivity Patterns After Waking From Slow Wave Sleep Under Different Cognitive States

Sleep inertia refers to the state of transition between sleep and wake characterized by impaired alertness, confusion, and reduced cognitive and behavioral performance. While the behavioral symptoms of sleep inertia are well described, the neurological changes that lead to this state remain elusive. Here, to understand the state of sleep inertia and the reorganization that the brain undergoes, we took a graph theoretical approach and compared the EEG derived brain connectivity patterns before sleep and after waking up while participants (n = 10) performed multiple tasks that differed in cognitive complexities. We focused on how the degree and the clustering coefficient of brain regions (EEG sensors) change immediately after participants wake up from slow wave sleep. During a psychomotor vigilance task (PVT), designed to assess vigilant attention, we find that the brain regions with strong network connectivity (degree) before sleep show a reduction in connectivity after waking. In contrast, those with low connectivity before sleep have greater connectivity after waking. The regions that undergo these changes are specific to each participant and these findings are unique to the beta frequency range, which plays a key role in sensorimotor functioning and preserving the current state of the brain. Moreover, in tasks that required inhibitory control and arithmetic reasoning, we found that only regions with weak connectivity before sleep exhibited more connections after waking, but regions with high connectivity prior to sleeping remained unchanged, highlighting task specific effects. Furthermore, we find that during the PVT, the clustering coefficient within low frequency oscillations of the brain is reduced upon waking while it remains unchanged during other tasks. These results suggest that the connections between regions that are lost after abrupt awakening can be reallocated to other regions in order to renormalize the brain. However, this response may only be evident during specific cognitive states and may be more nuanced during complex task performance.

sleep inertia