Field-theoretic approach to fluctuation effects in neural networks

Area of Science:

• Theoretical neuroscience
• Statistical physics
• Computational neuroscience

Background:

• Understanding neural activity dynamics is crucial for theoretical neuroscience.
• Existing models often lack a comprehensive stochastic framework for analyzing neural fluctuations and responses.
• Field theoretic methods offer powerful tools for nonequilibrium statistical processes.

Purpose of the Study:

• To develop a well-defined stochastic theory for neural activity.
• To construct an effective spike model describing neural fluctuations and responses.
• To analyze dynamical phase transitions in neural networks and their universality classes.

Main Methods:

• Utilizing field theoretic methods for nonequilibrium statistical processes.
• Assuming Markovian dynamics for neural network activity.
• Constructing an effective spike model and performing systematic expansion of corrections to mean field theory.

Main Results:

• The effective spike model is a simplified version of the Wilson-Cowan equation.
• Neural activity exhibits a dynamical phase transition in the universality class of directed percolation.
• Higher-order terms in the expansion are small for highly connected networks, suggesting mean field exponents.

Conclusions:

• The developed stochastic theory provides a valuable tool for theoretical neuroscience.
• The effective spike model accurately describes neural dynamics and phase transitions.
• Experimental identification of dynamic universality classes in vivo remains an important future direction.