Hodge Laplacian of Brain Networks

Area of Science:

• Neuroscience
• Network Science
• Computational Mathematics

Background:

• Brain networks exhibit complex structures, including closed loops or cycles.
• These cycles are crucial for higher-order signal transmission and understanding brain function.
• Existing methods for analyzing network cycles are limited.

Purpose of the Study:

• To develop an efficient algorithm for the systematic identification and modeling of cycles in brain networks.
• To introduce novel statistical inference procedures for analyzing these cycles.
• To validate the proposed methods using simulations and real-world brain imaging data.

Main Methods:

• Utilizing persistent homology to identify topological features (cycles) in brain networks.
• Employing the Hodge Laplacian operator for cycle analysis and modeling.
• Applying statistical inference techniques to characterize identified cycles.

Main Results:

• Successfully identified and modeled cycles in simulated and resting-state functional magnetic resonance imaging (fMRI) brain networks.
• Demonstrated the efficiency and robustness of the proposed algorithm.
• Developed and validated statistical procedures for cycle analysis.

Conclusions:

• The proposed algorithm provides an effective approach for analyzing cycles in brain networks.
• This work offers fundamental insights into the role of network topology in brain functioning.
• The computational codes are publicly available for further research.