Due to the existence of membrane potential differences, electromagnetic induction flows can be induced in interconnected neurons Hopfield neural network (HNN). To express flows, this paper presents a unified memristive HNN model using hyperbolic-type memristors link neurons. By employing theoretical analysis along with multiple numerical methods, we explore effects on three Three cases are clas...

Introduction. If d is a positive square-free integer let Id be the ring of integers in Q(\Jd). Id is a Euclidean domain if d = 1, 2, 3, 7, 11. The groups PSL2(/d) = Fd over these Euclidean rings have recently been investigated. Methods for generating presentations as well as actual presentations were given in [2], [3] and [8], while these groups were shown to be describable in terms of generali...

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...

In my lecture I report on a joint work with Alexei G. Myasnikov. Non-Archimedean words have been introduced as a new type of infinite words which can be investigated through classical methods in combinatorics on words due to a length function. The length function, however, takes values in the additive group of polynomials Z[t] (and not, as traditionally, in N), which yields various new properti...