Direct Block Methods for Solving Special Second Order Ordinary Differential Equations and Their Parallel Implementations

This thesis focuses mainly on deriving block methods of constant step size for solving special second order ODEs. The first part of the thesis is about the construction and derivation of block methods using linear difference operator. The regions of stability for both explicit and implicit block methods are presented. The numerical results of the methods are compared with existing methods. The results suggest a significant improvement in efficiency of the new methods. The second part of the thesis describes the derivation of the r-point block methods based on Newton-Gregory backward interpolation formula. The numerical results of explicit and implicit r-point block methods are presented to illustrate the effectiveness of the methods in terms of total number of steps taken, accuracy and execution time. Both the explicit and implicit methods are more efficient compare to the existing method. The r-point block methods that calculate the solution at r-point simultaneously are suitable for parallel implementation. The parallel codes of the block methods for the solution of large systems of ODEs are developed. Hence the last part of the thesis discusses the parallel execution of the codes. The parallel algorithms are written in C language and implemented on Sun Fire V1280 distributed memory system. The fine-grained strategy is used to divide a computation into smaller parts and assign them to different processors. The performances of the r-point block methods using sequential and parallel codes are compared in terms of the total steps, execution time, speedup and efficiency. The parallel implementation of the new codes produced better speedup as the number of equations increase. The parallel codes gain better speedup and efficiency compared to sequential codes

Implicit block hybrid-like method for solving system of first order ordinary differential equations

The block hybrid-like method is presented and implemented in predictor-corrector mode to solve system of first order ordinary differential equations. The block method is applied to provide the approximation for both the main and off-step points concurrently. The stability properties of the method are investigated. Some illustrative examples are presented to demonstrate the efficiency of the block hybrid-like method

Block hybrid-like method for solving delay differential equations

The block hybrid-like method is presented and implemented in predictor-corrector mode to solve delay differential equations. The Lagrange interpolation polynomial is implemented to obtain the approximation for the delay terms. The Q-stability of the method is investigated. The illustrative examples are presented to demonstrate the efficiency of the block hybrid-like method

Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly.

This paper focused mainly on deriving explicit and implicit 3-point block methods of constant step size using linear difference operator for solving special second order ordinary differential equations (ODEs). The methods compute the solutions of the ODEs at three points simultaneously. Regions of stability for both the explicit and implicit block methods are presented. A standard set of problems are solved using the new methods and the numerical results are compared when the same set of problems are solved using existing methods. The results suggest a significant improvement in efficiency of the new methods in terms of number of steps and accuracy

An accurate block hybrid collocation method for third order ordinary differential equations

The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow

Ninth order block hybrid collocation method for second order ordinary differential equations

A ninth order block hybrid collocation method is proposed for solving general second order ordinary differential equations directly. The derivation involves interpolation and collocation of basic polynomial that generates the main and additional methods. These methods are applied simultaneously to provide approximate solutions at five main points and three off-step points. The stability properties of the block method are discussed. Some illustrative examples are given to demonstrate the efficiency of the method

Parallel implementation of explicit 2 and 3-point block methods for solving system of special second order ODEs directly

In this paper the explicit 2 and 3-point block method for solving large systems of special second order ODEs directly is discussed. Codes based on the methods are executed in sequential and parallel. The numerical results show that parallel to sequential counterpart for solving the large system of special second order ODEs

High negative predictive value of 68Ga PSMA PET-CT for local lymph node metastases in high risk primary prostate cancer with histopathological correlation

Background: Current guidelines highlight the importance of accurate staging in the management and prognostication of high risk primary prostate cancer. Conventional radiologic imaging techniques are insufficient to reliably detect lymph node metastases in prostate cancer. Despite promising results, there is limited published data on the diagnostic accuracy of PSMA PET-CT to assess local nodal metastases prior to radical prostatectomy. This study aims to assess the diagnostic efficacy of 68Ga PSMA PET-CT in local lymph node staging of high risk primary prostate cancer when compared to histopathological findings following radical prostatectomy with pelvic lymph node dissection. Methods: We retrospectively analysed consecutive patients with high risk primary prostate cancer referred by urologists for primary staging PSMA PET-CT using a 68Ga-labeled PSMA ligand, Glu-NH-CO-NHLys-(Ahx)-[HBEDDCC], from October 2015 to October 2017. The scans of patients who underwent radical prostatectomy with pelvic lymph node dissection were interpreted by the consensus reading of two experienced nuclear medicine physicians blinded to clinical and histopathological data. The contemporaneous records of the referring urologists were retrospectively reviewed for noteworthy unexpected PET findings that altered their personal preference for surgical management. Results: Seventy-one patients were recruited and analysed. PSMA PET-CT showed findings compatible with local disease in 47 patients (66.2%), lymph node metastases in 10 patients (14.1%) and distant metastases in 14 patients (19.7%). Twenty-eight patients (twenty-seven of whom had local disease only) underwent surgery yielding 214 lymph nodes, all of which were negative on histopathological analysis. On a node-based analysis, 213 of 214 lymph nodes were accurately identified as negative for disease with a negative predictive value of 100%. 11 patients had unexpected PET findings contemporaneously documented by urologists to alter their preference for surgical management. Conclusions: PSMA PET-CT appears to have a high negative predictive value for local lymph node metastases in high risk primary prostate cancer when compared to histopathological findings following radical prostatectomy with pelvic lymph node dissection

A Single Amino Acid of Human Immunodeficiency Virus Type 2 Capsid Protein Affects Conformation of Two External Loops and Viral Sensitivity to TRIM5α

We previously reported that human immunodeficiency virus type 2 (HIV-2) carrying alanine or glutamine but not proline at position 120 of the capsid protein (CA) could grow in the presence of anti-viral factor TRIM5α of cynomolgus monkey (CM). To elucidate details of the interaction between the CA and TRIM5α, we generated mutant HIV-2 viruses, each carrying one of the remaining 17 possible amino acid residues, and examined their sensitivity to CM TRIM5α-mediated restriction. Results showed that hydrophobic residues or those with ring structures were associated with sensitivity, while those with small side chains or amide groups conferred resistance. Molecular dynamics simulation study revealed a structural basis for the differential TRIM5α sensitivities. The mutations at position 120 in the loop between helices 6 and 7 (L6/7) affected conformation of the neighboring loop between helices 4 and 5 (L4/5), and sensitive viruses had a common L4/5 conformation. In addition, the common L4/5 structures of the sensitive viruses were associated with a decreased probability of hydrogen bond formation between the 97th aspartic acid in L4/5 and the 119th arginine in L6/7. When we introduced aspartic acid-to-alanine substitution at position 97 (D97A) of the resistant virus carrying glutamine at position 120 to disrupt hydrogen bond formation, the resultant virus became moderately sensitive. Interestingly, the virus carrying glutamic acid at position 120 showed resistance, while its predicted L4/5 conformation was similar to those of sensitive viruses. The D97A substitution failed to alter the resistance of this particular virus, indicating that the 120th amino acid residue itself is also involved in sensitivity regardless of the L4/5 conformation. These results suggested that a hydrogen bond between the L4/5 and L6/7 modulates the overall structure of the exposed surface of the CA, but the amino acid residue at position 120 is also directly involved in CM TRIM5α recognition

Gut microbiome of helminth-infected indigenous Malaysians is context dependent

Background: While microbiomes in industrialized societies are well characterized, indigenous populations with traditional lifestyles have microbiomes that are more akin to those of ancient humans. However, metagenomic data in these populations remains scarce, and the association with soil-transmitted helminth infection status is unclear. Here, we sequenced 650 metagenomes of indigenous Malaysians from fve villages with diferent prevalence of helminth infections. Results: Individuals from villages with higher prevalences of helminth infections have more unmapped reads and greater microbial diversity. Microbial community diversity and composition were most strongly associated with different villages and the efects of helminth infection status on the microbiome varies by village. Longitudinal changes in the microbiome in response to albendazole anthelmintic treatment were observed in both helminth infected and uninfected individuals. Inference of bacterial population replication rates from origin of replication analysis identifed specifc replicating taxa associated with helminth infection. Conclusions: Our results indicate that helminth efects on the microbiota were highly dependent on context, and efects of albendazole on the microbiota can be confounding for the interpretation of deworming studies. Furthermore, a substantial quantity of the microbiome remains unannotated, and this large dataset from an indigenous population associated with helminth infections is a valuable resource for future studie