Gel electrophoresis (GE) is a widely used technique to separate DNA sequence according to their size and weight, GE results are presented using images. In this paper, we present a scheme that aims to detect and segment the lanes in DNA gel images without any human interventions. We have successfully implemented an image processing scheme to automatically detect and segment the lanes in DNA gel images, applying this scheme to several DNA fingerprint gel images ,all the lanes are successfully segmented. Also we have obtained up to 99.5% accuracy for the segmentation of lanes in good quality images. The proposed scheme is compared with other techniques and the comparison shows that it has a minimum error rate.

The steepest decent method is proposed by French mathematician Cauchy and it is one of the simplest and oldest methods for solving unconstrained optimization problems. The steepest descent method, negative gradient direction is chosen as the search direction, also known as the gradient method. Usually, the step length α(cid:2921) of the steepest decent method can be computed by some inexact line search. In this paper, we will use a Wolfe type line search to evaluate the step length and its convergence property will be given under mild assumptions. From the numerical results, we can see that the steepest descent method with this Wolfe type line search is very promising. Finally, we give an application of the method to solve the nonlinear complementarity problem.

Since hippocampal volume measurement is often used in studying Alzheimer’s disease to assess disease progression, automatic hippocampus segmentation is an important task in clinical applications. However, it is a challenging task due to its small size, complex shape, fuzzy boundaries, partial volume effects, and anatomical variability. In this paper we propose a new segmentation method to segment the hippocampus from brain MRI images automatically.This proposed method presents a new region-based signed pressure force function, which can efficiently stop the contours at weak boundary. Experimental results show that the model can fast and effectively segment the intensity inhomogeneous images.

In this paper, we propose a smoothing Newton method to find the minimum norm solution of linear program problems. By using the smoothing technique, we reformulate the problem as an unconstrained minimization problem with a twice continuous differentiable objective function. The minimization of this objective function can be carried out by the classical Newton-type method which is shown to be globally convergence.

K-means algorithm is one of the most popular clustering algorithms that has been survived for more than 4 decades. Despite its inherent flaw of not knowing the number of clusters in advance, very few methods have been proposed in the literature to overcome it. The paper contains a fast heuristic algorithm for guessing the number of clusters as well as cluster center initialization without actually performing K-means, under the assumption that the clusters are well separated in a certain way. The proposed algorithm is experimented on various synthetic data. The experimental results show the effectiveness of the proposed approach over the existing.

Intuitionistic fuzzy set has proven interesting and useful in providing a flexible framework or model to elaborate uncertainty and vagueness involved in decision making. In this paper, we proposed the application of intuitionistic fuzzy sets (IFS) in career determination. Solution is obtained by looking for the smallest distance between each student and each career.

In this paper, we present a method for numerical solution of linear Volterra integro - differential equations with boundary conditions. First, we obtain variational form of the problem, and then, finite element method and basis functions will be used. Also, the error analysis of the method is considered. Furthermore, the efficiency of the proposed method will be considered through numerical examples.

In this paper, a numerical technique is presented for the solution of a parabolic partial differential equation with a time-dependent coefficient subject to an extra measurement. For solving the discussed inverse problem, at first we transform it into a nonlinear direct problem and then use the proposed method. This method is a combination of collocation method and radial basis functions. The radial basis functions (RBFs) method is an efficient meshfree technique for the numerical solution of partial differential equations. The main advantage of numerical methods which use radial basis functions over traditional techniques is the meshless property of these methods. The accuracy of the method is tested in terms of maximum and RMS errors. Illustrative examples are included to demonstrate the validity and applicability of the technique.

In this paper, the homotopy perturbation method (HPM) is proposed to solve an inverse problem of finding an unknown function in parabolic equation with an extra measurement. For solving the discussed inverse problem, at first we transform it’s into a nonlinear direct problem then uses the proposed method. Also an error analysis is presented for the method and prior and posterior error bounds of the approximate solution are estimated. Application of the HPM to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution.