Athanasios Margaris

Finding all real roots of 3×3 nonlinear algebraic systems using neural networks

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.

Log file formats for parallel applications: a review

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.

A detailed study of the Wolf's algorithm

The objective of this paper is the analytical presentation of the Alan Wolfs 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.

Simulation and Visualization of Chaotic Systems

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.

Blind system identification: instantaneous mixtures of n sources

Blind signal processing deals with the outputs of unknown systems excited by unknown sources. In the current work, the case of instantaneous mixtures of n binary antipodal sources that are linearly combined by an unknown system is examined. The parameters of the system can be easily calculated, given the output constellation. The method proposed is based on the geometrical properties of the system output set. In the current method, there is no need to work out any system deflation, since a solvable linear system of equations can be directly formed in order to compute the systems parameters.

Investigation of the determinism of complex dynamical systems using simple back propagation neural networks

In this paper the deterministic manner of complex systems from which a time series of one variable is known, is investigated by the use of neural networks. The idea on which the method is based is that back propagation neural networks with sigmoid nodes can simulate deterministic systems. This means that when a neural network is able to learn a system successfully, the system is deterministic, but when it is not, no such statement can be directly asserted. In this case simple criteria are proposed, presuming that when the proper amount of information feeds the network its performance is improved. This improvement indicates the networks effort to capture, in some way, the deterministic properties of the simulated system. This consideration is confirmed by the observation that random systems do not satisfy any of the criteria proposed in this work. The neural method of investigating determinism is simpler than methods proposed in previous research work, since no pre-calculated parameter values, such as the delay time or the embedding dimension of the dynamical system, are necessary for its implementation.

A Survey on the Design of Lowpass Elliptic Filters

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.

Local Area Multicomputer (LAM -MPI)

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.

Logistic map neural modelling: A theoretical foundation

The aim of this paper is to establish a theoretical framework for the modelling and simulation of chaotic attractors using neural networks. The attractor paradigm in this paper is the logistic map, which is modelled via neural networks in the convergence, periodic and chaotic regions. It is proved that, under certain conditions, the function simulated by the neural model is actually the logistic map with a different value of the λ parameter from the theoretical value. A two-dimensional system is defined and studied, facilitating the generation of the theoretical time series and the associated simulation error. The fixed points of periods p = 1 and p = 2 are identified and studied with respect to their stability. For higher period values, a theorem concerning the periodicity of the simulation error is postulated and proved. The minimum simulation error value is calculated using analytical methods, and the chaotic nature of the system with respect to Lyapunov exponents is described. Conclusions are discussed with respect to the experimental results obtained by the simulation models.