Background: The most frequent cause of paediatric acute abdomen is acute appendicitis. If acute appendicitis is not treated promptly, one third of cases progress to complicated appendicitis. Complicated appendicitis is associated with significant morbidity and its management protocol differs significantly from that of uncomplicated appendicitis. In this study, we assessed the relationship between serum sodium levels and complicated appendicitis. Methods: We conducted a prospective observational study from July to December 2020 at the Department of Neonatal and Paediatric Surgery, The Children Hospital, Pakistan Institute of Medical Sciences, Islamabad, on a sample size of 140 patients who met inclusion and exclusion criteria. For this study, we divided the patients into two groups. Group 1 had uncomplicated appendicitis and Group 2 had complicated appendicitis. These findings were then compared to preoperative serum sodium (Na) levels. Results: The median serum sodium level in group 1 (uncomplicated appendicitis) was 137.81 mg/dl, while in group 2 it was 131.35 mg/dl (Complicated Appendicitis). The sensitivity and specificity of serum sodium levels at a cut-off point of less than 135 mg/dl were 84.80% and 89.40%, respectively. Conclusion: Hyponatremia is currently thought to be a new marker for differentiating between complicated and uncomplicated appendicitis. It is a low-cost, high-efficiency predictive marker for diagnosing and differentiating complicated appendicitis in children.

No abstract

No abstract

No abstract

This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fréchet or Gâteaux derivatives of the cost functional, which can be time consuming, but rather moves in a projected-gradient direction that is easily computable (for a class of problems) and does not require any explicit derivatives. The algorithm is applicable to a class of problems where a pointwise minimizer of the Hamiltonian is computable by a simple formula, and this includes many problems that arise in theory and applications. The natural setting for the algorithm is the space of continuoustime relaxed controls, whose special structure renders the analysis simpler than the setting of ordinary controls. While the space of relaxed controls has theoretical advantages, its elements are abstract entities that may not be amenable to computation. Therefore, a key feature of the algorithm is that it computes adequate approximations to relaxed controls without loosing its theoretical convergence properties. Simulation results, including cpu times, support the theoretical developments. arXiv:1609.03183v1 [math.OC]