From Synaptic Interactions to Collective Dynamics in Random Neuronal Networks Models: Critical Role of Eigenvectors and Transient Behavior

DOI10.1162/neco_a_01253zbMath1445.92006arXiv1805.03592OpenAlexW2995436804WikidataQ91960260 ScholiaQ91960260MaRDI QIDQ5131178

Maciej A. Nowak, Wojciech Tarnowski, Jeremi K. Ochab, Dante R. Chialvo, Ewa Gudowska-Nowak

Publication date: 2 November 2020

Published in: Neural Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.03592

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20)

Related Items (3)

Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities ⋮ Condition numbers for real eigenvalues in the real elliptic Gaussian ensemble ⋮ Spectral theory of sparse non-Hermitian random matrices

Uses Software

• Eigtool

Cites Work

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• Erratum to: Outliers in the spectrum of iid matrices with bounded rank perturbations
• Free probability and random matrices
• Spectral radii of large non-Hermitian random matrices
• Spectrum estimation for large dimensional covariance matrices using random matrix theory
• Statistical eigen-inference from large Wishart matrices
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Stable laws and domains of attraction in free probability theory
• Non-Gaussian non-Hermitian random matrix theory: phase transition and addition formalism
• Infinite products of large random matrices and matrix-valued diffusion
• Brown's spectral distribution measure for \(R\)-diagonal elements in finite von Neumann algebras
• Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach
• Mastering the master field
• On statistics of bi-orthogonal eigenvectors in real and complex Ginibre ensembles: combining partial Schur decomposition with supersymmetry
• Stochastic spike synchronization in a small-world neural network with spike-timing-dependent plasticity
• The distribution of overlaps between eigenvectors of Ginibre matrices
• Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles
• “Single ring theorem” and the disk-annulus phase transition
• Random Matrix Methods for Wireless Communications
• Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem
• Applying free random variables to random matrix analysis of financial data. Part I: The Gaussian case
• Full Dysonian dynamics of the complex Ginibre ensemble
• Free Random Variables
• Lectures on the Combinatorics of Free Probability
• A random matrix approach to VARMA processes
• Collective dynamics of ‘small-world’ networks
• Some Applications of the Mellin Transform in Statistics
• Free random Lévy variables and financial probabilities

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