Iterative Methods for the Solution of Semi-Nonlinear Systems with Linear Diagonals

We discuss Jacobi, Gauss-seidel and SOR methods for the solution of semi-nonlinear systems with linear diagonals in this paper. A Comparison of these methods is done through an example.

TIVO-3: Age-related tolerability outcomes of tivozanib versus sorafenib in metastatic relapsed or refractory renal cell carcinoma, a subgroup analysis of the TIVO-3 clinical trial.

e16553 Background: Tivozanib (TIVO) is a potent and selective VEGF receptor (R) tyrosine kinase inhibitor with a long half-life designed to optimize the VEGF blockade while minimizing off-target toxicities. The TIVO-3 trial demonstrated improved progression-free survival (PFS) when compared to sorafenib (SOR; 5.6 mo. vs 3.9 mo., respectively) with a hazard ratio (HR) of 0.73. TIVO showed better tolerability with reduced need for dose interruptions (p = 0.0164) and dose reductions (p = 0.0147) as compared to SOR. Methods: Data was analyzed to identify relationships between and age or prior use of immune checkpoint inhibitors (CPI). Results: Of the 343 patients treated on study, 120 (35%) were between age 65 and 75 and 34 (10%) were over 75. Adverse events were less frequent for TIVO compared to SOR in all age groups and drug exposure was consistently greater in the TIVO arm. Of particular interest, the tolerability advantages noted in the total population are also observed in the patients 75 and over with almost half the rate of the adverse drug reactions leading to dose reduction or discontinuation compared to SOR. Patients treated with prior CPI had an increased need for dose adjustment, but dose adjustments were less common with TIVO than SOR in CPI exposed and naïve patients. Conclusions: Tivozanib was better tolerated than sorafenib regardless of age or prior CPI treatment. Dose adjustments and interruptions are more common after prior CPI. Clinical trial information: NCT02627963. [Table: see text]

An optimized AOR iterative method for solving absolute value equations

In recent years, the AOR iterative method has been proposed for solving absolute value equations. This method has two parameters ? and ?. In this paper, we intend to find the optimal parameters of this method to improve convergence rate by suitable optimization techniques. Meanwhile, the convergence of the optimized AOR iterative method is discussed. It is both theoretically and experimentally demonstrated efficiency of the optimized AOR iterative method in contrast with the AOR and SOR methods.

An Exploratory Study Testing Autonomic Reactivity to Pain in Women with Sensory Over-Responsiveness

Background: Difficulty modulating sensory input related to multi-sensory integration dysfunction, specifically the sensory over-responsive (SOR) type, is associated with psychological distress and hyperalgesia in children and adults. Scares reports suggest atypical autonomic nervous system (ANS) reactivity to innocuous sensory stimuli in children with SOR. Thus, the ANS may contribute to sensory stimuli responses and psychological distress. This exploratory study aimed to characterize the ANS reactivity to single and dual pain stimulation, and in relation to psychological distress in adults with SOR. Methods: Healthy women with SOR (n = 9) vs. without SOR (n = 9) underwent two runs of single pain stimulation and a third run comprised of dual pain stimulation. Pain was self-rated, while heart rate variability was measured and analyzed in the time and frequency domains. In addition, questionnaires assessing anxiety and somatization were utilized. Results: While controls demonstrated a vagal tone withdrawal (root mean square of successive differences in R-R-intervals; (RMSSD)) p = 0.029 from base-line to the third run, this was absent in the SOR group. However, no group differences were found in pain ratings. Furthermore, groups differed in the correlations between R-R mean and the level of both anxiety (p = 0.006) and somatization (p < 0.001); while in the SOR group, higher levels of anxiety and somatization correlated with shorter R-R intervals, the opposite was found in the control group. Conclusions: This is the first study to demonstrate in women with SOR atypical vagal tone reactivity to challenging pain load. Vagal tone reactivity is related to both pain ratings and psychological distress.

Parallel Iterative Solution Schemes for the Analysis of Air Foil Bearings

In an air foil bearing analysis the model is usually solved iteratively due in part to the nonlinearity of the modeling Reynolds equation and the compliance of the bearing surface. The solution procedure requires a multiple-level-deep nested iteration, which involves extended solution time and convergence difficulty. In this study, a simple air foil bearing model is used and the compressible-fluid Reynolds equation for modeling gas lubrication is linearized by Newton's method. The discretized equation is solved by one of the two parallel iterative methods, red-black or strip partition successive-over-relaxation (SOR) method. The parallel programming is conducted using OpenMP programming in an eight-core work-station. Then, a numerical damping scheme for the film-profile convergence is presented. Finally, a root-finding process is conducted to iteratively attain the eccentricity of the bearing for a given load. It is found that the numerical damping step is crucial, which allows the use of a larger relaxation factor to have a fast rate of convergence. Both the parallel SOR methods are easy to implement and the red-black SOR method exhibits better efficiency in the studied cases. This study presents a parallel computing scheme for analyzing air foil bearing of bump-type by today's shared-memory multicore platforms.