Eigenspectrum bounds for semirandom matrices with modular and spatial structure for neural networks.

@article{Muir2015EigenspectrumBF,
  title={Eigenspectrum bounds for semirandom matrices with modular and spatial structure for neural networks.},
  author={Dylan Richard Muir and ThomasD . Mrsic-Flogel},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2015},
  volume={91 4},
  pages={
          042808
        }
}
The eigenvalue spectrum of the matrix of directed weights defining a neural network model is informative of several stability and dynamical properties of network activity. Existing results for eigenspectra of sparse asymmetric random matrices neglect spatial or other constraints in determining entries in these matrices, and so are of partial applicability to cortical-like architectures. Here we examine a parameterized class of networks that are defined by sparse connectivity, with connection… 
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