Open Access Original Research Article

A Recommendation for Classical and Robust Factor Analysis

Ying-Ying Zhang, Teng-Zhong Rong, Man-Man Li

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2017/31936

Considering the factor analysis methods (classical or robust), the data input (data or scaled data), and the running matrix (covariance or correlation) all together, there are 8 combinations. The objective of the study is to give a recommendation for classical and robust factor analysis. First, when the variables have different units, it is common to standardize the variables, and thus it is common to use the correlation matrix as the running matrix. Second, we need to explain the factors from the loading matrix. The entries of the loading matrix from the sample covariance matrix are not limited between 0 and 1, which makes the explanations of the factors hard. Third, we may not be able to compute the robust covariance matrix, and thus the robust correlation matrix of the original data, as the stocks data example illustrates. Consequently, we recommend classical and robust factor analysis using the correlation matrix of the scaled data as the running matrix for theoretical and computational reasons. The hbk data and the stock611 data illustrate our recommendation.

Open Access Original Research Article

Solving Multi-level Multi-objective Fractional Programming Problem with Rough Intervals in the Objective Functions

Mohamed S. Osman, Kamal R. Raslan, Osama E. Emam, Farahat A. Farahat

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/BJMCS/2017/30626

In this paper multi-level multi-objective fractional programming problem (ML-MOFP) is considered where some or all of its coefficients in the objective function are rough intervals. At the first phase of the solution approach and to avoid the complexity of the problem, two FP problems with interval coefficients will be constructed. One of these problems was a FP problem where all of its coefficients are lower approximations of the rough intervals and the other problem was a FP problem where all of its coefficients are upper approximations of rough intervals. At the second phase, a membership function was constructed to develop a fuzzy goal programming model for obtaining the satisfactory solution of the multi-level multi-objective fractional programming problem. The linearization process introduced by Pal et al. [1] will be applied to linearize the membership functions.. Finally, a numerical example will be introduced to illustrate the theoretical results.

Open Access Original Research Article

Multicyclic Codes and Algebraic Dynamical Systems

R. M. Lalasoa, R. Andriamifidisoa, T. J. Rabeherimanana

Journal of Advances in Mathematics and Computer Science, Page 1-22
DOI: 10.9734/BJMCS/2017/31510

We present the structures within group algebras constructed from commutative groups and finite fields. Then we define and construct multicyclic codes in these group algebras. At the end, in the frame of the decoding process, we give a characterization of the locator ideal to the multidimensional case. All of this is done using algebraic dynamical systems, which explains the underlying mathematical objects.

Open Access Original Research Article

A Comparative Analysis of Jellyfish Attacks and Black Hole Attack with Selfish Behavior Attack under AODV Routing Protocol

Bhawna Singla, A. K. Verma, L. R. Raheja

Journal of Advances in Mathematics and Computer Science, Page 1-18
DOI: 10.9734/BJMCS/2017/31430

The applications of mobile adhoc network (MANET) are increasing day-by-day due to the flexibility they provide to seamless communication. However MANETS are vulnerable to number of attacks because of properties like non-existing infrastructure, dynamic topology, multihop network etc. Lot of previous works have focused on the impact of various attack on routing protocol. Some attacks like jellyfish attack even follow all the rules and regulations of routing protocol then also they may cause damage to the communication. On the other hand, some attacks like blackhole attack have malicious intentions and causes destruction by dropping the sent packets. There also exist one other category of attack called selfish node attack that do not causes any destruction by modifying the field of the packet rather they do not cooperate in forwarding the packet. In a typical MANET scenario which may be in use for few minutes or even hours, the attacking node will have time to intervene in to the routing process, and able to make some destruction. But, if the network under consideration will be in use for limited short time for a particular military like quick rescue scenario, then how a malicious node will intervene in to the routing process and make considerable damage to the network within that short duration – this is the research question addressed in this work. In this work we study the impacts of some of the attacks on network under a short term military rescue mission like scenario. We will do a comparative analysis of above discussed attacks under AODV routing protocol. The analysis will be made with respect to different network sizes and under the presence of different number of attackers in the network. The impact on the performance will be measured with suitable metrics to understand the nature of different attacks.

Open Access Review Article

Hellinger Distance Between Generalized Normal Distributions

C. P. Kitsos, T. L. Toulias

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/BJMCS/2017/32229

A relative measure of informational distance between two distributions is introduced in this paper. For this purpose the Hellinger distance is used as it obeys to the definition of a distance metric and, thus, provides a measure of informational “proximity” between of two distributions. Certain formulations of the Hellinger distance between two generalized Normal distributions are given and discussed. Motivated by the notion of Relative Risk we introduce a relative distance measure between two continuous distributions in order to obtain a measure of informational “proximity” from one distribution to another. The Relative Risk idea from logistic regression is then extended, in an information theoretic context, using an exponentiated form of Hellinger distance.