Efficient Sensor Node Selection for Observability Gramian Optimization.

Optimization approaches that determine sensitive sensor nodes in a large-scale, linear time-invariant, and discrete-time dynamical system are examined under the assumption of independent and identically distributed measurement noise. This study offers two novel selection algorithms, namely an approximate convex relaxation method with the Newton method and a gradient greedy method, and confirms the performance of the selection methods, including a convex relaxation method with semidefinite programming (SDP) and a pure greedy optimization method proposed in the previous studies. The matrix determinant of the observability Gramian was employed for the evaluations of the sensor subsets, while its gradient and Hessian were derived for the proposed methods. In the demonstration using numerical and real-world examples, the proposed approximate greedy method showed superiority in the run time when the sensor numbers were roughly the same as the dimensions of the latent system. The relaxation method with SDP is confirmed to be the most reasonable approach for a system with randomly generated matrices of higher dimensions. However, the degradation of the optimization results was also confirmed in the case of real-world datasets, while the pure greedy selection obtained the most stable optimization results.

A Case of Successful Pregnancy and Delivery in a Chronic Renal Failure Patient with Membranoproliferative Glomerulonephritis and Preeclampsia-related Nephrotic Syndrome.

A 37-year-old woman with chronic kidney disease stage (CKD) G4 with membranoproliferative glomerulonephritis was hospitalized for nephrotic syndrome and hypertension due to superimposed preeclampsia at 27 weeks into her third pregnancy. Proteinuria did not worsen significantly after pulse steroid therapy. Delivery was induced at 30 weeks' gestation due to the maternal renal function and fetal growth. No obvious fetal complications other than preterm delivery were observed. In this case, we successfully managed a high-risk patient with membranoproliferative glomerulonephritis complicated by advanced CKD, nephrotic syndrome, and hypertension, which are independent risk factors for pregnancy complications.