Hierarchical neural networks, \(p\)-adic PDEs, and applications to image processing
DOI10.1007/s44198-024-00229-6MaRDI QIDQ6632335
Wilson A. Zuniga-Galindo, B. A. Zambrano-Luna, Baboucarr Dibba
Publication date: 4 November 2024
Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)
delayimage processingcellular neural networksstationary statesdenoisingreaction-diffusion equationsedge detection\(p\)-adic analysishierarchical neural networksWilson-Cowan models
Neural networks for/in biological studies, artificial life and related topics (92B20) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Simulation of dynamical systems (37M05)
Cites Work
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- Pseudodifferential equations over non-Archimedean spaces
- Waves in neural media. From single neurons to neural fields
- Dynamics of pattern formation in lateral-inhibition type neural fields
- Existence and stability of local excitations in homogeneous neural fields
- A mathematical theory of visual hallucination patterns
- Ultrametric diffusion, exponential landscapes, and the first passage time problem
- \(p\)-adic analogue of the porous medium equation
- Theory and applications of partial functional differential equations
- Fractal geometry for images of continuous embeddings of \(p\)-adic numbers and solenoids into Euclidean spaces
- Information dynamics in cognitive, psychological, social and anomalous phenomena.
- Mathematical image processing. Translated from the German
- Ultrametric diffusion, rugged energy landscapes and transition networks
- Reaction-diffusion equations on complex networks and Turing patterns, via \(p\)-adic analysis
- Adaptive control for fractional order induced chaotic fuzzy cellular neural networks and its application to image encryption
- Iterative schemes for bump solutions in a neural field model
- Heat kernels for isotropic-like Markov generators on ultrametric spaces: a survey
- \(p\)-adic statistical field theory and deep belief networks
- \(p\)-adic cellular neural networks: applications to image processing
- \(p\)-adic cellular neural networks
- Stochastic Neural Field Theory and the System-Size Expansion
- Multiple Bumps in a Neuronal Model of Working Memory
- ADVANCED IMAGE PROCESSING CELLULAR NEURAL NETWORKS
- Cellular neural networks: theory
- Fourier Analysis on Local Fields. (MN-15)
- Existence and uniqueness of travelling waves for a neural network
- p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes
- p-adic description of characteristic relaxation in complex systems
- Non-Archimedean reaction-ultradiffusion equations and complex hierarchic systems
- Ultrametric Pseudodifferential Equations and Applications
- A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
- Heaviside World: Excitation and Self-Organization of Neural Fields
- Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation
- PDE Methods for Two-Dimensional Neural Fields
- Neural Fields
- p-Adic statistical field theory and convolutional deep Boltzmann machines
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