Biometrics and Bioinformatics

C. Vijayalakshmi ¹, K. Ramya ²

Affiliations
1 Department of Mathematics, Sathyabama University, Chennai, IN
2 Department of Mathematics, Kingston Engineering College, Vellore, IN

Abstract

The systematic growth of vacation queueing model in recent part is described in this paper .An M/G/1 queue with probability association is also analyzed in this paper. A two phase service queueing system with multiple server vacation is the subject matter. Service to customer starts with a batch mode service in the phase-I followed by individual mode service in phase – II. Each customer may or may not balk on the arrival at the queue. As soon as the system becomes empty, the server starts taking sequence of different distributed vacations. The number of Poisson arrivals during the time interval is distributed as the forward recurrence time of vacation and the number of customers present in the standard M/G/1 queueing system is random. Based on the numerical values of service rate and mean system time is analyzed in a graphical manner.

Keywords

Busy Cycle, Distribution Function Server Idle Time, System Size, Utilization Factor, Waiting Time.

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C. Vijayalakshmi ¹, K. Senthamarai Kannan ²

Affiliations
1 Department of Mathematics, Sathyabama University, Chennai-119, IN
2 Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli, IN

Abstract

This paper mainly deals with the recent advances in DNA Micro array technologies and the abundance of Genomic information which plays a vital role for analyzing the molecular mechanisms. Statistical and Machine Learning Algorithms are used to analyze the biological implications in order to discover complex gene expression patterns. A Hidden Markov model (HMM) is designed and the maximum penalized likelihood is used to estimate the parameters in this model. This method is applied to lung cancer micro array experiment. Several regions identified through the HMM are consistent with known recurrent regions of amplifications or deletions in cancer. The association of these abnormal expression regions with the measures of disease status, such as tumor stage, differentiation, and survival are being analyzed. Numerical calculations and graphical representations reveals that genes in these regions may play a major role in the process of carcinogenesis of the lungs.

Keywords

DNA, Molecular Information, HMM, Machine Learning Algorithm, Lung Cancer, Markov.

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