Average synaptic activity and neural networks topology: a global inverse problem

Area of Science:

• Computational neuroscience
• Complex systems analysis
• Network dynamics

Background:

• Neural networks exhibit collective behavior and quasi-synchronous firing events, crucial for brain function.
• These dynamics are highly sensitive to network topology and connectivity fluctuations.

Purpose of the Study:

• To develop a heterogeneous mean-field approach for analyzing neural dynamics on random networks.
• To provide an analytical description of microscopic and large-scale temporal signals in neural systems.
• To investigate the role of network topology in shaping neural activity patterns.

Main Methods:

• Proposed a heterogeneous mean-field approach that preserves topological disorder in growing random networks.
• Derived a set of self-consistent equations to model neural dynamics.
• Utilized a leaky integrate-and-fire model with short-term plasticity.
• Formulated and solved a global inverse problem to reconstruct in-degree distribution from average activity.

Main Results:

• Successfully described quasi-synchronous events arising from neural network dynamics.
• Provided a clear analytical picture of neural dynamics, distinguishing contributions from periodic and aperiodic neurons.
• Demonstrated the ability to reconstruct network in-degree distribution from average activity data.

Conclusions:

• The heterogeneous mean-field approach offers a general framework for understanding neural dynamics on random networks.
• The method effectively captures the interplay between network topology and emergent collective behaviors.
• This approach provides valuable tools for analyzing and predicting temporal signals in complex neural systems.