Nonlinear-dynamics theory of up-down transitions in neocortical neural networks

2012 ◽  
Vol 85 (2) ◽  
Author(s):  
Maryam Ghorbani ◽  
Mayank Mehta ◽  
Robijn Bruinsma ◽  
Alex J. Levine
Keyword(s):  
Nonlinear Dynamics ◽  
Neural Networks

Nonlinear dynamics and machine learning of recurrent spiking neural networks

2021 ◽  
Author(s):  
Oleg V. Maslennikov ◽  
Mechislav M. Pugavko ◽  
Dmitrii S. Shchapin ◽  
Vladimir I. Nekorkin
Keyword(s):  
Nonlinear Dynamics ◽  
Machine Learning ◽  
Neural Networks ◽  
Spiking Neural Networks

Nonlinear dynamics and machine learning of recurrent spiking neural networks

2021 ◽  
Author(s):  
Oleg V. Maslennikov ◽  
Mechislav M. Pugavko ◽  
Dmitrii S. Shchapin ◽  
Vladimir I. Nekorkin
Keyword(s):  
Nonlinear Dynamics ◽  
Machine Learning ◽  
Neural Networks ◽  
Spiking Neural Networks

The secret is at the crossways: Hodotopic organization and nonlinear dynamics of brain neural networks

2013 ◽  
Vol 36 (6) ◽  
pp. 623-624 ◽  
Author(s):  
Tobias A. Mattei
Keyword(s):  
Nonlinear Dynamics ◽  
Neural Networks ◽  
Cognitive Neuroscience ◽  
State Of The Art ◽  
Current State

AbstractBy integrating the classic psychological principles of ancient art of memory (AAOM) with the most recent paradigms in cognitive neuroscience (i.e., the concepts of hodotopic organization and nonlinear dynamics of brain neural networks), Llewellyn provides an up-to-date model of the complex psychological relationships between memory, imagination, and dreams in accordance with current state-of-the-art principles in neuroscience.

Predicting service request in support centers based on nonlinear dynamics, ARMA modeling and neural networks

2008 ◽  
Vol 34 (1) ◽  
pp. 665-672 ◽  
Author(s):  
Emili Balaguer ◽  
Alberto Palomares ◽  
Emilio Soria ◽  
Jose David Martín-Guerrero
Keyword(s):  
Nonlinear Dynamics ◽  
Neural Networks ◽  
Service Request ◽  
Arma Modeling

A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science Part II: Universal Neuron

2003 ◽  
Vol 13 (09) ◽  
pp. 2377-2491 ◽  
Author(s):  
Leon O. Chua ◽  
Valery I. Sbitnev ◽  
Sook Yoon
Keyword(s):  
Nonlinear Dynamics ◽  
Neural Networks ◽  
Cellular Automata ◽  
Explicit Formula ◽  
Double Helix ◽  
Gene Families ◽  
Value Functions ◽  
Local Rule ◽  
Absolute Value ◽  
Science Part

Wolfram's celebrated three-input Cellular Automata is further developed and extended from the perspective of neural networks. A single explicit formula involving two nested absolute-value functions and eight adjustable parameters called synaptic weights, is presented. Such a neuron is proved to be universal by specifying the synaptic weights of all 256 local rules. Applying the nonlinear dynamics concepts developed from Part I of this multipart series of papers, we present the rational for partitioning the entire set of 256 local rules into 16 distinct gene families, each composed of 16 gene siblings. Such a partitioning allows us to explain, if not predict, the pattern features generated from each local rule. Finally, these 16 gene families of Cellular Automata rules are encoded onto a new compact and insightful representation called the "double-helix torus."

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