Continuous Energy Landscape Model for Analyzing Brain State Transitions

Energy landscape models characterize neural dynamics by assigning energy values to each brain state that reflect their stability or probability of occurrence. The conventional energy landscape models rely on binary brain state representation, where each region is considered either active or inactive based on some signal threshold. However, this binarization leads to significant information loss and an exponential increase in the number of possible brain states, making the calculation of energy values infeasible for large numbers of brain regions. To overcome these limitations, we propose a novel continuous energy landscape framework that employs Graph Neural Networks (GNNs) to learn a continuous precision matrix directly from functional MRI (fMRI) signals, preserving the full range of signal values during energy landscape computation. We validated our approach using both synthetic data and real-world fMRI datasets from brain tumor patients. Our results on synthetic data generated from a switching linear dynamical system (SLDS) and a Kuramoto model show that the continuous energy model achieved higher likelihood and more accurate recovery of basin geometry, state occupancy, and transition dynamics than conventional binary energy landscape models. In addition, results from the fMRI dataset indicate a 0.27 increase in AUC for predicting working memory and executive function, along with a 0.35 improvement in explained variance (R2) for predicting reaction time. These findings highlight the advantages of utilizing the full signal values in energy landscape models for capturing neuronal dynamics, with strong implications for diagnosing and monitoring neurological disorders.

MSGCN: Multiplex Spatial Graph Convolution Network for Interlayer Link Weight Prediction

Graph Neural Networks (GNNs) have been widely used for various learning tasks, ranging from node classification to link prediction. They have demonstrated excellent performance in multiple domains involving graph-structured data. However, an important category of learning tasks, namely link weight prediction, has received less emphasis due to its increased complexity compared to binary link classification. Link weight prediction becomes even more challenging when considering multilayer networks, where nodes can be interconnected across multiple layers. To address these challenges, we propose a new method named Multiplex Spatial Graph Convolution Network (MSGCN), which spatially embeds information across multiple layers to predict interlayer link weights. The MSGCN model generalizes spatial graph convolution to multiplex networks and captures the geometric structure of nodes across multiple layers. Extensive experiments using data with known interlayer link information show that the MSGCN model has robust, accurate, and generalizable link weight prediction performance across a wide variety of multiplex network structures.

Discovering Governing equations from Graph-Structured Data by Sparse Identification of Nonlinear Dynamical Systems

The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered dynamical models could be used to address challenges in climate science, neuroscience, ecology, finance, epidemiology, and beyond. However, most existing sparse identification methods for discovering dynamical systems treat the whole system as one without considering the interactions between subsystems. As a result, such models are not able to capture small changes in the emergent system behavior. To address this issue, we developed a new method called Sparse Identification of Nonlinear Dynamical Systems from Graph-structured data (SINDyG), which incorporates the network structure into sparse regression to identify model parameters that explain the underlying network dynamics. SINDyG discovers the governing equations of network dynamics while offering improvements in accuracy and model simplicity.