A best online algorithm for scheduling on two parallel batch machines

AbstractWe consider the online scheduling on two parallel batch machines with infinite batch size to minimize makespan, where jobs arrive over time. That is, all information of a job is not available until it is released. For this online scheduling problem, Nong et al. [Q.Q. Nong, T.C.E. Cheng, C.T. Ng, An improved online algorithm for scheduling on two unrestrictive parallel batch processing machines, Operations Research Letters, 36 (2008) 584–588] have provided an online algorithm with competitive ratio no greater than 2. We show that this bound is tight for the problem. Furthermore we give a new best possible online algorithm with a tighter structure

Electrocardiographic characteristics of bladder cancer patients receiving preoperative chemotherapy combined with immunotherapy.

Objective Patients treated with preoperative chemotherapy and immunotherapy for bladder cancer may be at increased risk of cardiotoxicity and electrophysiological abnormalities. This study aimed to analyze their electrocardiographic (ECG) alterations. Methods Patients with bladder cancer who were hospitalized and receiving tislelizumab plus nab-paclitaxel (TnP) were enrolled prospectively. ECG, cardiac biomarkers, and echocardiography were performed at baseline and the end of TnP. Results A total of 60 patients (76.7% males), including 30 muscle-invasive and 30 non-muscle-invasive bladder cancer, received three or four cycles of TnP, respectively. Hypertension was the commonest comorbidity (41.7%), and 25 patients (41.7%) were prescribed cardiovascular drugs. In comparison with baseline characteristics, cardiac troponin I (cTnI) and N-terminal pro-brain natriuretic peptide (NT-proBNP) were within normal ranges after TnP. However, echocardiographic parameter of left ventricular ejection fraction slightly decreased after TnP (62.81 ± 3.81% to 61.10 ± 4.37%, p = .011). The incidence of abnormal ECG increased from 65.0% at baseline to 76.7%, of which only a higher prevalence of fragmented QRS (fQRS) was observed (33.3% to 50.0%, p = .013; mainly in inferior leads). ECG parameters of QT dispersion (QTd) were prolonged significantly after the regimen (39.50 ± 11.37 to 44.20 ± 15.85 ms, p = .019). Conclusion In bladder cancer patients receiving preoperative chemotherapy combined with immunotherapy, the main ECG abnormality was fQRS and QTd, with relatively normal cardiac biomarkers and echocardiographic parameters. Regular ECG screening should be carried out carefully to detect potential cardiotoxicity in the long-term follow-up