A degree reduction method for an efficient QUBO formulation for the graph coloring problem

We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional methods. The simulated results show that our new method produces reduced quadratic polynomials that contains less variables than the reduced quadratic polynomials produced by the conventional methods

Efficacy and safety of standard dose triple combination of telmisartan 80 mg/amlodipine 5 mg/chlorthalidone 25 mg in primary hypertension: A randomized, double‐blind, active‐controlled, multicenter phase 3 trial

Abstract The authors evaluated the efficacy, safety, and characteristics of patients who respond well to standard dose triple combination therapy including chlorthalidone 25 mg with telmisartan 80 mg plus amlodipine 5 mg in hypertensive patients. This is a multicenter, double‐blind, active‐controlled, phase 3, randomized trial. Patients are randomized to triple combination (telmisartan 40 mg/amlodipine 5 mg/chlorthalidone 12.5 mg, TEL/AML/CHTD group) or dual combination (telmisartan 40 mg/amlodipine 5 mg, TEL/AML group) treatment and then dose up titration to TEL 80/AML5/CHTD25mg and TEL80/AML5, respectively. The primary endpoint is the change of mean sitting systolic blood pressure (MSSBP) at week 8. A Target BP achievement rate, a response rate, and the safety endpoints are also evaluated. Total 374 patients (mean age = 60.9 ± 10.7 years, male = 78.3%) were randomized to the study. The baseline MSSBPs/diastolic BPs were 149.9 ± 12.2/88.5 ± 10.4 mm Hg. After 8 weeks treatment, the change of MSSBPs at week 8 are −19.1 ± 14.9 mm Hg (TEL/AML/CHTD) and −11.4 ± 14.7 mm Hg (TEL/AML) (p < .0001). The achievement rates of target BP (53.8% vs. 37.8%, p = .0017) and responder rate (54.8% vs. 35.6%, p = .0001) at week 8 were significantly higher in TEL/AML/CHTD. There are no serious adverse event and no one discontinued medication due to adverse event. Among the TEL 80/AML5/CHTD25mg treatment group, patients of female or age ≥ 65 years old showed higher rate of target BP achievement than relatively young male. (61.4 vs. 46.8%, p = .042) Our study showed standard dose triple combination of telmisartan 80 mg/amlodipine 5 mg/chlorthalidone 25 mg is efficacious and safe in treatment of primary hypertension. Target BP achievement with triple therapy would be facilitated in female or old age