We consider exponent equations in finitely generated groups. These are equations, where the variables appear as exponents of group elements and take values from natural numbers. Solvability such (systems of) has been intensively studied for various classes groups recent years. In many cases, it turns out that set all solutions on an equation is a semilinear can be constructed effectively. Such ...

The success of an ensemble of classifiers depends on the diversity of the underlying features. If a classifier can address more different aspects of the analyzed objects, this allows to improve an ensemble. In this paper we propose an ensemble using as classifier members a Hopfield Neural Network (HNN) that uses Haar-like features as an input template. We analyse the HNN as the only classifier ...

Among the large number of possible optimization algorithms, Hopfield Neural Networks (HNN) propose interesting characteristics for an in-line use. Indeed, this particular optimization algorithm can produce solutions in brief delay. These solutions are produced by the HNN convergence which was originally defined for a sequential evaluation of neurons. While this sequential evaluation leads to lo...

This paper proposes a novel method based on Hopfield neural networks (HNNs) for solving job-shop scheduling problems (JSPs). The JSP constraints are analyzed and their permutation matrix express is developed. A new calculation energy function is also proposed, which includes all JSP constraints. A novel Hopfield neural network for such JSP problems is constructed and the effect of its weights f...

We investigate the application of Hopfield neural networks (HNN's) to the problem of multiuser detection in spread spectrum/CDMA (code division multiple access) communication systems. It is shown that the NP-complete problem of minimizing the objective function of the optimal multiuser detector (OMD) can be translated into minimizing an HNN "energy" function, thus allowing to take advantage of ...

We present the ACID/HNN framework, a principled approach to hierarchical connectionist acoustic modeling in large vocabulary conversational speech recognition (LVCSR). Our approach consists of an Agglomerative Clustering algorithm based on Information Divergence (ACID) to automatically design and robustly estimate Hierarchies of Neural Networks (HNN) for arbitrarily large sets of context-depend...

A sufficient condition for the existence of HNN-extensions in the class of groups of odd exponent n ≫ 1 is given in the following form. Let Q be a group of odd exponent n > 2 and G be an HNN-extension of Q. If A ∈ G then let F(A) denote the maximal subgroup of Q which is normalized by A. By τA denote the automorphism of F(A) which is induced by conjugation by A. Suppose that for every A ∈ G, wh...

This paper is intended to provide an alternative approach for the design of FIR filters by using a Hopfield Neural Network (HNN). The proposed approach establishes the error function between the amplitude response of the desired FIR filter and the designed one as a Lyapunov energy function to find the HNN parameters. Using the framework of HNN, the optimal filter coefficients can be obtained fr...

This paper presents a general framework for hybrids of Hidden Markov models (HMM) and neural networks (NN). In the new framework called Hidden Neural Networks (HNN) the usual HMM probability parameters are replaced by neural network outputs. To ensure a probabilistic interpretation the HNN is normalized globally as opposed to the local normalization enforced on parameters in standard HMMs. Furt...