Open Access Original Research Article

Recurrent Neural Network Based Modeling of Gene Regulatory Network Using Bat Algorithm

Sudip Mandal, Goutam Saha, Rajat K. Pal

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/JAMCS/2017/34916

Correct inference of genetic regulations inside a cell is one of the greatest challenges in post genomic era for the biologist and researchers. Several intelligent techniques and models were already proposed to identify the regulatory relations among genes from the biological database like time series microarray data. Recurrent Neural Network (RNN) is one of the most popular and simple approach to model the dynamics as well as to infer correct dependencies among genes. In this paper, Bat Algorithm (BA) is applied to optimize the model parameters of RNN model of Gene Regulatory Network (GRN). Initially the proposed method is tested against small artificial network without any noise and the efficiency is observed in term of number of iteration, number of population and BA optimization parameters. The model is also validated in presence of different level of random noise for the small artificial network and that proved its ability to infer the correct inferences in presence of noise like real world dataset. In the next phase of this research, BA based RNN is applied to real world benchmark time series microarray dataset of E. coli. The results prove that it can able to identify the maximum number of true positive regulation but also include some false positive regulations. Therefore, BA is very suitable for identifying biological plausible GRN with the help RNN model.

Open Access Original Research Article

Structure of Some Pregroups and Length Functions

Faisal H. Nesayef

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/JAMCS/2017/34918

The concept of Pregroups was introduced by Stallings in 1971.  Subsequently the concept of Pregroups was developed by many other researchers. Stallings originally defined a set with a binary operation satisfying five axioms, namely, P1, P2, P3, P4, and P5. It has been proved later that P3 is a consequence of the other axioms. Stallings has also linked this construction of a Pregroup to Free Product of Groups.

This construction is developed to include a new axiom called P6, which enabled to define a length function on the universal group of Pregroups. Applications of Pregroups with length functions led to direct proof of many other problems in combinatorial group theory.

Open Access Original Research Article

On Skew Circulant Type Matrices Involving any Continuous Pell Numbers

Jinjiang Yao, Zhaolin Jiang, Jixiu Sun

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/JAMCS/2017/34959

In this paper, the invertibility of the skew circulant type matrices are discussed, the determinants and the inverse matrices of them are given. We present the four kinds of norms and bounds for the spread of these special matrices, respectively.

Open Access Original Research Article

Open Access Original Research Article

Optimal Control Model of Malaria Disease with Standard Incidence Rate

Sacrifice Nana-Kyere, Richmond Hede Doe, Francis Agyei Boateng, James Kwabena Odum, Seth Marmah, Desmond Titus Banon

Journal of Advances in Mathematics and Computer Science, Page 1-21
DOI: 10.9734/JAMCS/2017/35011

In this research article, an optimal control model of malaria disease with standard incidence rate is proposed. Maximum Principle was employed to derive the necessary conditions for the existence of optimal control. Numerical solution of the optimality was derived and computed to investigate the optimum control strategy that would be efficacious to be implemented in reducing the number of exposed and infected humans.