This survey paper presents a collection of the most important algorithms for the well-known Traveling Salesman Problem (TSP) using Self-Organizing Maps (SOM). Each one of the presented models is characterized by its own features and advantages. The modes are compared to each other to find their differences and similarities. The models are classified in two basic categories, namely the enriched and hybrid models. For each model we present information regarding its performance, the required number of iterations, as well as the number of neurons that are capable of solving the TSP problem. Based on the experimental results, the best model is identified for different occasions. The paper is a good starting point for anyone who is interested in solving TSP with SOM and desires to grasp a lot about this renowned problem.

Optimization is a concept, a process, and a method that all people use on a daily basis to solve their problems. The source of many optimization methods for many scientists has been the nature itself and the mechanisms that exist in it. Neural networks, inspired by the neurons of the human brain, have gained a great deal of recognition in recent years and provide solutions to everyday problems. Evolutionary algorithms are known for their efficiency and speed, in problems where the optimal solution is found in a huge number of possible solutions and they are also known for their simplicity, because their implementation does not require the use of complex mathematics. The combination of these two techniques is called neuroevolution. The purpose of the research is to combine and improve existing neuroevolution architectures, to solve time series problems. In this research, we propose a new improved strategy for such a system. As well as comparing the performance of our system with an already existing system, competing with it on five different datasets. Based on the final results and a combination of statistical results, we conclude that our system manages to perform much better than the existing system in all five datasets.

This paper proposes a neural network architecture for solving systems of non-linear equations. A back propagation algorithm is applied to solve the problem, using an adaptive learning rate procedure, based on the minimization of the mean squared error function defined by the system, as well as the network activation function, which can be linear or non-linear. The results obtained are compared with some of the standard global optimization techniques that are used for solving non-linear equations systems. The method was tested with some well-known and difficult applications (such as Gauss–Legendre 2-point formula for numerical integration, chemical equilibrium application, kinematic application, neuropsychology application, combustion application and interval arithmetic benchmark) in order to evaluate the performance of the new approach. Empirical results reveal that the proposed method is characterized by fast convergence and is able to deal with high-dimensional equations systems.

The objective of this research is the presentation of a neural network capable of solving complete nonlinear algebraic systems of n equations with n unknowns. The proposed neural solver uses the classical back propagation algorithm with the identity function as the output function, and supports the feature of the adaptive learning rate for the neurons of the second hidden layer. The paper presents the fundamental theory associated with this approach as well as a set of experimental results that evaluate the performance and accuracy of the proposed method against other methods found in the literature.

This paper presents an MLP‐type neural network with some fixed connections and a backpropagation‐type training algorithm that identifies the full set of solutions of a complete system of nonlinear algebraic equations with n equations and n unknowns. The proposed structure is based on a backpropagation‐type algorithm with bias units in output neurons layer. Its novelty and innovation with respect to similar structures is the use of the hyperbolic tangent output function associated with an interesting feature, the use of adaptive learning rate for the neurons of the second hidden layer, a feature that adds a high degree of flexibility and parameter tuning during the network training stage. The paper presents the theoretical aspects for this approach as well as a set of experimental results that justify the necessity of such an architecture and evaluate its performance. Copyright © 2015 John Wiley & Sons, Ltd.

The objective of this review paper, is the presentation of the basic features of the well known class of elliptic filters. Even though this is not a new subject, the theory of the elliptic filters found in most books is restricted only to a few resulting equations, due to the great complexity associated with the Jacobian elliptic functions. The aspects of the elliptic filters described in this paper include the detailed estimation of the minimum filter order, the construction of the filter transfer function via the identification of its poles and zeros in the complex plane, as well as the application of the resulting design procedure for the construction of an elliptic filter that meets prescribed specifications.

The objective of this research is to construct parallel implementations of the Jacobi algorithm used for the solution of linear algebraic systems, to measure their speedup with respect to the serial case and to compare each other, regarding their efficiency. The programming paradigm used in this implementation is the message passing model, while, the used MPI implementation is the MPICH implementation of the Argonne National Laboratory.

The objective of this paper is the short description of the LAM (Local Area Multicomputer) implementation of MPI that can be used for the development of parallel applications based on the message passing interface. The paper describes the main aspects of the LAM environment such as the LAM architecture, configuration and use. A comparison between the LAM and the MPICH implementation (another very popular and commonly used MPI implementation) with respect to their performance is also presented.

The objective of this research is the presentation of a feed‐forward neural network capable of estimating the 2‐cycle fixed points of Henon map by solving their defining nonlinear algebraic system. The network uses the back propagation algorithm and solves the aforementioned system for a set of values of the parameters α and β of Henon map. Besides the estimation of the fixed points, the paper includes the study of the network convergence and its speed for many different initial conditions. Copyright © 2013 John Wiley & Sons, Ltd.

The objective of this paper is to present a suite of applications that allow the simulation and study of chaotic systems, as well as the estimation of the most important properties associated with them.These applications implement fundamental algorithms from the field of chaotic system dynamics, such as the reconstruction of the system trajectory in the appropriate embedding space, and the estimation of the Lyapunov exponents and the fractal dimension.Furthermore, they provide additional features such as the study of bifurcation diagrams and the detection of chaotic regions in the parameter space.The current version of the applications has been developed in the programming framework of Visual C++ 6.0 and they can be used under the operating system of Microsoft Windows.

The objective of this research is the description of a feed-forward neural network capable of solving nonlinear algebraic systems with polynomials equations. The basic features of the proposed structure, include among other things, product units trained by the back-propagation algorithm and a fixed input unit with a constant input of unity. The presented theory is demonstrated by solving complete 3x3 nonlinear algebraic system paradigms, and the accuracy of the method is tested by comparing the experimental results produced by the network, with the theoretical values of the systems roots.

The objective of this research is the numerical estimation of the roots of a complete 2 × 2 nonlinear algebraic system of polynomial equations using a feed forward back-propagation neural network. The main advantage of this approach is the simple solution of the system, by building a structure—including product units—that simulates exactly the nonlinear system under consideration and find its roots via the classical back-propagation approach. Examples of systems with four or multiple roots were used, in order to test the speed of convergence and the accuracy of the training algorithm. Experimental results produced by the network were compared with their theoretical values.

The objective of this paper is the concise presentation of the most important and recent lemmas and theorems associated with the global asymptotic and exponential stability of the equilibrium point of time delayed cellular neural networks. For each theorem a short proof is given, so that the reader can understand its features and its relationships to other theorems. In the last section, the presented theorems are grouped according to their characteristics and the way they relate to one another, and some of them are demonstrated, in order to draw conclusions about their use.

The objective of this work is to present the application of back propagation neural networks for the experimental identification of fixed points of chaotic maps. The results presented here, are associated with the Henon map but the same algorithm can be applied without modification for the estimation of the fixed points of any chaotic attractor. The type of neural network presented in this paper, is a powerful general purpose neural network architecture, capable of solving nonlinear algebraic systems with an arbitrary complexity. The next sections describe the main theory associated with this field, the structure of the neural networks used for this purpose as well as the experimental results for the case of the Henon map.

This paper is an attempt to test for nonlinear structure and chaos indicators on the returns of bank stocks listed in Athens Exchange (ATHEX) as well as the indices: ATHEX Composite index. FTSE/ASE 20 and FTSE/ASE mid 40.

The objective of this paper is the review of the log file formats that allow the performance visualization of parallel applications based on the usage of message passing interface (MPI) standard. These file formats have been designed by the LANS (Laboratory for Advanced Numerical Software) group of the Argonne National Laboratory and they are distributed together with the corresponding viewers as part of the MPE (multipurpose environment) library of the MPICH implementation of the MPI. The formats studied in this paper is the ALOG, CLOG, SLOG1 and SLOG2 file formats—the formats are studied in chronological order and the main features of their structures are presented.

The objective of this paper is the analytical presentation of the Alan Wolf's Algorithm with the derivation of the equations needed to implement BASGEN and fixed evolution time algorithms, used for the numerical calculation of the largest positive Lyapunov exponent of an unknown time series. An improvement of the above algorithm is proposed by introducing a new stability criterion to make the algorithm more robust and improve its reliability.

Education and learning is undergoing a worldwide change from the didactic model towards a learner-centred approach more sensitive to the needs of both the learners and the context in which learning takes place. Advances in Information and Communication Technologies (ICTs) have increasingly enabled global asynchronous interactive learning and teaching, thus offering greater flexibility and easier access to information in a life-long learning context. Also the Bologna Process for European Higher Education integration and various Quality Assurance procedures, as well as the emerging globalisation bring virtual networked academic courses into the scene. As a result of these prevailing requirements in combination with emphasis on specification of objectives and learning outcomes, pressure on teachers to rethink and redesign their courses has emerged. Through active, adaptive and cognitive project-based learning, including authentic activities, problem solving and reflective thinking, networked learning can facilitate a supportive and affordable model of learning that can benefit many groups in society. The department of Informatics at Alexander Technological Educational Institution of Thessaloniki responds to the new challenges by adopting a blended learning model that combines traditional classroom teaching and user-centred networked learning. This paper reports experiences and findings from different blended courses in the department revealed in a first assessment of the teaching-and-learning practices. The aim of the assessment was to identify strengths and weaknesses of the current practices. The assessment was carried out by using a questionnaire completed by 119 students. Emphasis is put on students’ views regarding the current teaching-and-learning practices. The findings reveal that the students consider that the most important advantages of e-learning environments are studies at own time followed by studies at own place. Concerning the disadvantages the most important factors are considered to be the student’s dependency on internet and technology in general. All students who take part in e-learning environments consider that their learning activities and outcome are improved and that e-learning provides independence and free choice of their personal learning strategy. The ultimate outcome of the assessment aims at creating guidelines for the best practice in networked learning. A first set of guidelines for the best practice in networked blended learning presented in this paper was created based on the results from the student survey and experiences from discussions between educators. The guidelines aim at serving as a roadmap and initiating the development of a list of relevant best practices. Continuous improvement of the research instruments together with regular assessments will ensure continuous improvement of processes and practices regarding networked blended learning.