In the Hopfield Neural Network (HNN), each neuron is connected to every other neuron. Thereby, the HNN causes high cost to generate the network in terms of implementation. Small World Hopfield Neural Network (SWHNN) improves ability for transmission by introducing the shortcut connections into the sparse regular network. However the storage ability of the SWHNN decreases for associative memory ...

In this paper, an identification method is proposed for discrete-time nonlinear systems using a Hopfield neural network (HNN) as a coefficient learning mechanism to obtain optimized coefficients over a set of Gaussian basis functions. The outputs of the HNN, which are coefficients over a set of Gaussian basis functions, are discretized to be a discrete Hopfield learning model and completely app...

By adding chaotic noise to each neuron of the discrete-time continuous-output Hopfield neural network (HNN) and gradually reducing the noise, a chaotic neural network is proposed so that it is initially chaotic but eventually convergent, and, thus, has richer and more flexible dynamics compared to the HNN. The proposed network is applied to the traveling salesman problem (TSP) and that results ...

The problem of learning represents a gateway to understanding intelligence in brains and machines. Many researchers believe that supervised learning will become a key technology for extracting information from the flood of data around us. The supervised learning techniques, i.e. learning from examples, can be seen as an implementation of the mappings y = F(x), relying on the fitting of given da...

We prove here that a finitely presented group with a free quotient of rank n is an HNN-extension with n stable letters of a finitely generated group where the associated subgroups are finitely generated. This theorem has a number of consequences. In particular, in the event that the free quotient is cyclic it reduces to an elementary and quick proof of a theorem of Bieri and Strebel. 1. Finitel...

in this paper, we will give necessary and sufficient conditions for certain hnnextensions of subgroup separable groups with normal associated subgroup to be conjugacyseparable. in fact, we will show that these hnn extensions are conjugacy separable if and onlyif the normalizer of one of its associated subgroup is conjugacy separable.

A graph product is the fundamental group of a graph of groups. Amongst the simplest examples are HNN groups and free products with amalgamation. The torsion and conjugacy theorems are proved for any group presented as a graph product. The graphs over which some graph product has a solvable word problem are characterised. Conditions are then given for the solvability of the word and order proble...