Hierarchical neural networks, \(p\)-adic PDEs, and applications to image processing
type: Item
instance of: scholarly article
title: Hierarchical neural networks, \(p\)-adic PDEs, and applications to image processing
author: W. A. Zúñiga-Galindo
author: B. A. Zambrano-Luna
author: Baboucarr Dibba
published in: Journal of Nonlinear Mathematical Physics
publication date: 2024-11-04T00:00:00Z
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 37M05
zbMATH DE Number: 7938337
zbMATH Keywords: \(p\)-adic analysis
zbMATH Keywords: cellular neural networks
zbMATH Keywords: Wilson-Cowan models
zbMATH Keywords: hierarchical neural networks
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: delay
zbMATH Keywords: stationary states
zbMATH Keywords: image processing
zbMATH Keywords: edge detection
zbMATH Keywords: denoising
MaRDI profile type: Publication
cites work: \(p\)-adic cellular neural networks
cites work: \(p\)-adic cellular neural networks: applications to image processing
cites work: Cellular neural networks: theory
cites work: Q4706964
cites work: Neural Fields
cites work: A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
cites work: Dynamics of pattern formation in lateral-inhibition type neural fields
cites work: Multiple Bumps in a Neuronal Model of Working Memory
cites work: A mathematical theory of visual hallucination patterns
cites work: Stochastic Neural Field Theory and the System-Size Expansion
cites work: Ultrametric Pseudodifferential Equations and Applications
cites work: Information dynamics in cognitive, psychological, social and anomalous phenomena.
cites work: Learning of \(p\)-adic neural networks.
cites work: p-Adic statistical field theory and convolutional deep Boltzmann machines
cites work: \(p\)-adic statistical field theory and deep belief networks
cites work: Ultrametric diffusion, rugged energy landscapes and transition networks
cites work: Reaction-diffusion equations on complex networks and Turing patterns, via \(p\)-adic analysis
cites work: Non-Archimedean reaction-ultradiffusion equations and complex hierarchic systems
cites work: Q5306363
cites work: Q5283909
cites work: Fourier Analysis on Local Fields. (MN-15)
cites work: Fractal geometry for images of continuous embeddings of \(p\)-adic numbers and solenoids into Euclidean spaces
cites work: Q5799972
cites work: Ultrametric diffusion, exponential landscapes, and the first passage time problem
cites work: p-adic description of characteristic relaxation in complex systems
cites work: p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes
cites work: Heat kernels for isotropic-like Markov generators on ultrametric spaces: a survey
cites work: Theory and applications of partial functional differential equations
cites work: Q4220655
cites work: Pseudo-differential equations and stochastics over non-Archimedean fields
cites work: Pseudodifferential equations over non-Archimedean spaces
cites work: \(p\)-adic analogue of the porous medium equation
cites work: Mathematical image processing. Translated from the German
cites work: Existence and uniqueness of travelling waves for a neural network
cites work: Q4804243
cites work: Waves in neural media. From single neurons to neural fields
cites work: Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation
cites work: Existence and stability of local excitations in homogeneous neural fields
cites work: Heaviside World: Excitation and Self-Organization of Neural Fields
cites work: PDE Methods for Two-Dimensional Neural Fields
cites work: Iterative schemes for bump solutions in a neural field model
cites work: Adaptive control for fractional order induced chaotic fuzzy cellular neural networks and its application to image encryption
cites work: ADVANCED IMAGE PROCESSING CELLULAR NEURAL NETWORKS
DOI: 10.1007/S44198-024-00229-6
description: scientific article; zbMATH DE number 7938337