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This study introduces pseudocumulants to analyze heterogeneous systems, overcoming limitations of Lorentzian distributions. This new method enables exact results for complex neural network models with various fluctuations.

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Area of Science:

  • Statistical mechanics
  • Computational neuroscience

Background:

  • Lorentzian distributions are common in statistical mechanics for heterogeneous systems.
  • Analytic continuation of Lorentzian distributions is limited by moment divergence.

Purpose of the Study:

  • To overcome limitations in analyzing heterogeneous systems using Lorentzian distributions.
  • To develop a unified mean-field formulation for spiking neural networks with disorder.

Main Methods:

  • Introduction of a "pseudocumulants" expansion.
  • Development of a reduction methodology for heterogeneous spiking neural networks.
  • Analysis of systems subject to extrinsic and endogenous fluctuations.

Main Results:

  • Solved the problem of analytic continuation for deformed Lorentzian distributions.
  • Achieved a unified mean-field formulation for neural networks.
  • Successfully encompassed quenched and dynamical sources of disorder.

Conclusions:

  • Pseudocumulant expansion provides a novel approach for analyzing complex systems.
  • The methodology offers exact results for heterogeneous spiking neural networks.
  • Unified formulation advances understanding of neural network dynamics under disorder.