FACULTY OF SCIENCE

It has been observed over the years that real life data are usually non-conforming to the classical linear regression assumptions. One of the stringent assumptions that is unlikely to hold in many applied settings is that of homoscedasticity. When homogenous variance in a normal regression model is not appropriate, invalid standard inference procedure may result from the improper estimation of standard error when the disturbance process in a regression model present heteroscedasticity. When both outliers and heteroscedasticity exist, the inflation of the scale estimate can deteriorate. This study identifies outliers under heteroscedastic errors and seeks to study the performance of four methods; ordinary least squares (OLS), weighted least squares (WLS), robust weighted least squares (RWLS) and logarithmic transformation (Log Transform) methods to estimate the parameters of the regression model in the presence of heteroscedasticity and outliers. Real life data obtained from the Central Bank of Nigeria Bulletin and Monte Carlo simulation were carried out to investigate the performances of these four estimators. The results obtained show that the transformed logarithmic model proved to be the best estimator with minimum standard error followed by the robust weighted least squares. The performance of OLS is the least in this order

Proteins are polymers of Amino Acid (AA) which are constructed after translation of genetic code in DNA of organisms, and have functionality that depends on their Native Structure (NS). Experimental methods for protein NS determination are complicated, expensive and time-consuming. Consequently, Computational Methods (CM), including Monte Carlo (MC), aim to circumvent these challenges. However, the MC is complex and inconsistent in NS Prediction (NSP). This study was designed to develop a Move-Biased MC (MBMC) simulation algorithm that may simplify the complexity of existing MC and makes it consistent for NSP. Protein was described as a coarse-grained structure and folding as Self-Avoiding Walks (SAW) on square lattices. Relative Probability Parameters (RPP) were introduced to determine natural probabilities of protein conformations from SAW and to simulate the desired sequence length from RPP optimal combination. Thereafter, a graphical algorithm was developed to group the SAW steps into hydrophobic and polar AA units according to the Hydrophobic-Polar (HP) model. The MBMC method was developed as a coupling of diagonal-pull Move-Biased (MB) on the lowest energy SAW conformation. The materials for testing the MBMC method included eight Benchmark Sequences (BMS) from the protein data bank such as SI-1, SI-2, SI-3, SI-4, SI-5, SI-6, SI-7, and SI-8 with sequence lengths 20, 24, 25, 36, 48, 60, 64, and 85 nm, respectively. The lowest energy (consistency in prediction of NS), computation time and algorithmic steps of the MBMC method was compared with some existing methods [such as Conventional MC (CMC), Genetic Algorithm (GA), Evolutionary MC (EMC), Ant Colony Optimization (ACO), Hybrid Elastic Net Algorithm (ENA)]. Data were analysed using inferential statistics. The optimal combination of the RPP for the MBMC algorithm were 0.71, 0.02, 0.25 and 0.02 for up, down, left and right orientations, respectively. The energies of the NS obtained from the MBMC method were -9, -9, -8, -14, -23, -35, -42 and -52 J for the BMS, respectively. In contrast, for GA energies derived were -9, -9, -8, -12, -22, -34, -37, and no record for eighth BMS; for ACO they were -9, -9, -8, -14, -23, -34, -32, -53; for EMC they were -9, -9, -8, -14, -23, -35, -39 and -52; for ENA they were -9, -9, -8, -14, -23, -36, -39, and no record for eighth BMS; for CMC they were -9, -9, -7, -12, -20, -33, -35, and no record for the eighth BMS. Also, MBMC method consistently predicted the NS of the BMS in 8.90, 8.51, 8.37, 9.14, 9.45, 9.46, 9.52, and 12.85 seconds, respectively. In contrast the computation times for GA were only reported for the first four BMS as 5.60, 6.00, 3.66, 54.60 seconds, and no record of computational time for the CMC and EMC Benchmark sequences, respectively. Moreover, MBMC has fewer algorithmic steps and simpler simulation procedure than CMC, GA, EMC and ENA methods. The developed Move-Biased Monte Carlo method had simpler algorithmic steps than the existing Monte Carlo methods and consistently predicted the native structure of proteins faster than existing algorithms.

FACULTY OF SCIENCE

Browse

Filters

Settings

Sort By

Results per page

Search Results