International Journal of Applied Mathematics and Informatics

ISSN: 2074-1278
Volume 12, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of NAUN Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

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Volume 12, 2018

Title of the Paper: An Improved Method for Obtaining Optimal Polygonal Approximations


Authors: A. Carmona-Poyato, F. J. Madrid-Cuevas, N. L. Fernández-García, R. Medina-Carnicer

Pages: 46-50

Abstract: In computer vision, polygonal approximations of digital planar curves are important for a great number of applications. Given N ordered points on a Euclidean plane, an optimal method to obtain M points that defines a polygonal approximation with the minimum distortion is proposed. Some of the state-of-the-art methods solve optimally this problem, however a high computational burden is required. In order to reduce the computational time of the state-of-art-methods, a new improved method for obtaining optimal polygonal approximations in closed curves is proposed. The authors present an improved version of a method proposed by them in 2017. The original method is an iterative method that uses the improved Salotti method for obtaining many local optimal polygonal approximations with a prefixed starting point, where each iteration improves to the previous iteration. Thus, the original method obtains the global optimal polygonal approximation by using the number of iterations required to reach the global optimum. In the new proposal, only three iterations by using the improved Salotti method are required. Tests have shown that the global optimal polygonal approximation is obtained in more than 98% of cases and the computation time is significantly reduced compared with the original method.

Title of the Paper: Two-Stage Feature Selection Algorithm Based on Supervised Classification Approach for Automated Epilepsy Diagnosis


Authors: Slim Mechmeche, Ridha Ben Salah, Noureddine Ellouze

Pages: 40-45

Abstract: Epileptic diagnosis is generally achieved by visual scanning of Interictal Epileptiform Discharges (IEDs) using EEG recordings. The main objective of this research is to select a smallest relevant feature subset from the original dataset in order to reduce the diagnosis time and increase classification accuracy by removing irrelevant and redundant features. For this purpose we suggest a two-stage feature selection algorithm based on supervised classification approach adopting successively a wrapper feature selection and a wrapper feature subset selection method. Matlab simulation results illustrate that through comparing the two classifiers, the highdimensionality is reduced at only one relevant feature that showed classification metrics of 100%. The epilepsy diagnosis is successfully tested in the discriminant Fisher-space with the single-best relevant feature.

Title of the Paper: Fetal-Maternal ECG Signal Separation from Two Channels based on the Continuous Wavelet Transform and the JADE Algorithm


Authors: Said Ziani, Atman Jbari, Larbi Belarbi

Pages: 29-39

Abstract: This paper presents a new approach based on the continuous wavelet transform CWT and JADE algorithm for the blind source separation. The JADE algorithm has been widely used to separate the fECG and mECG signals from 8 recordings or channels, while not all of this number is needed. The present work will show that it isn’t the number of channels that counts but rather the quality of the channel used in terms of the energy or the information that it carries. That’s why before introducing the 8 channels to the JADE algorithm we will make a selection by the mathematical microscope Continuous Wavelet Transform CWT and we will show that the number of channels will be reduced to 5 or 3 or even to 2 channels. This algorithm has been validated on several real data.

Title of the Paper: Emergence of Power Law Behavior in Threshold Based Neuron Model with Stochastic Membrane Decay Constant


Authors: Saket Kumar Choudhary

Pages: 21-28

Abstract: A new phenomenon to obtain the power-law behavior in neuronal properties for a threshold based neuron model is proposed. Membrane decay constant in leaky integrate-and-fire neuron model is considered to be a stochastic process which results a new model, the LIFSD neuron model (leaky integrate-and-fire neuron model with stochastic membrane decay constant). Two neuronal activities, namely, stationary state membrane potential and ISI (inter-spike-interval) distribution for the LIFSD model is investigated. In order to obtain the stationary state membrane potential, Fokker-Planck equation (FPE) with reflecting boundary condition, associated with LIFSD neuron model is solved which results the power-law behavior. ISI distribution depicts the power-law behavior during Monte Carlo simulation based study of proposed model. To mathematically complete LIFSD model, explicit expressions for membrane potential and its first two moments; mean and variance for membrane potential are also calculated. The LIFSD neuron model is found capable to generate the power law behavior for stationary state membrane potential distribution and ISI distribution. However a number of other neuronal activities are still left to investigate in context of the power law behavior. These findings suggest the robustness of proposed model for input-output relationship prediction and also prove that the development of the net membrane potential and the spiking activity in the single neuron are due to the aggregate effort of group of ions and molecules.

Title of the Paper: Numerical Solutions of Non Linear Parabolic PDE by Discrete Adomian Decomposition Method


Authors: Nadia Amel Messaoudi, Salah Manseur Mostafa Blidia

Pages: 14-20

Abstract: In this paper, a discrete Adomian decomposition method (DADM) is developed in avoid to …nd the solution of non linear parabolic partial differential equation (PDE) with Dirichlet boundary conditions. The method converts the nonlinear boundary value problem into a system of ordinary di¤erential equations. By solving the system by Adomian method, the solution can be determined. Compary the methodology for some examples where the exact solution are known and with the classical technique : finite difference method shows that the present approach is easy to use and reliable.

Title of the Paper: Multi-layer Thermal Analysis for VLSI Chips: A New Technique and its Mathematical Foundations


Authors: Keiji Nakabayashi

Pages: 1-13

Abstract: We present a new technique of multi-layer thermal analysis for VLSI chips. It performs two dimensional, steady-state analysis of thermal conduction and heat generation. Its key component is a new direct method of solving huge systems of linear equations derived from thermal conduction equations. We implemented our technique in C and compared its performance to that of the most effective iterative method of ICCG of LASPACK. Our experimental results demonstrate the superiority of our program by the factors of 3.25 and 6.4 while keeping smaller residuals by 5 and 1 order(s) of magnitude, respectively.