Kω — Open-source library for the shifted Krylov subspace method of the form (zI−H)x=b

We develop Kω, an open-source linear algebra library for the shifted Krylov subspace methods. The methods solve a set of shifted linear equations (zkI−H)x(k)=b(k=0,1,2,…) for a given matrix H and a vector b, simultaneously. The leading order of the operational cost is the same as that for a single equation. The shift invariance of the Krylov subspace is the mathematical foundation of the shifted Krylov subspace methods. Applications in materials science are presented to demonstrate the advantages of the algorithm over the standard Krylov subspace methods such as the Lanczos method. We introduce benchmark calculations of (i) an excited (optical) spectrum and (ii) intermediate eigenvalues by the contour integral on the complex plane. In combination with the quantum lattice solver HΦ, Kω can realize parallel computation of excitation spectra and intermediate eigenvalues for various quantum lattice models

Subsequent chemotherapy with paclitaxel plus cetuximab-based chemotherapy following immune checkpoint inhibitor in recurrent or metastatic squamous cell carcinoma of the head and neck

BackgroundImmune checkpoint inhibitors (ICIs) are essential in treating recurrent/metastatic squamous cell carcinoma of the head and neck (R/M SCCHN). However, the overall response rate (ORR) is limited to 10-20%, and subsequent chemotherapy is critical to maximizing the subjects’ prognosis.MethodsWe retrospectively reviewed 59 patients with R/M SCCHN treated with paclitaxel+cetuximab (PE)-based chemotherapy (PCE, paclitaxel+carboplatin+cetuximab; or PTX+Cmab, paclitaxel+cetuximab) following disease progression after either pembrolizumab or nivolumab monotherapy.ResultsOf 59 patients, 15 were treated with pembrolizumab, with an ORR of 13.3%, and the remaining 44 with nivolumab, with an ORR of 11.4%. All patients in the pembrolizumab cohort had platinum-sensitive disease. Following ICI treatment, 19 patients were treated with PCE and the remaining 40 with PTX+Cmab. PE-based chemotherapy induced favorable and prompt tumor shrinkage even in cases where ICI was not effective, with a median change in the summed dimensions of target lesions of -43.4%, resulting in an ORR of 62.7%. Median time to response was 1.8 months. The patients in the pembrolizumab cohort appeared to have a numerically higher response rate than those receiving nivolumab (80.0% vs. 56.8%). For the 59 patients, progression-free survival and overall survival, calculated from the initiation of PE-based chemotherapy, were 4.6 months and 17.1 months, respectively. Grade ≥3 adverse events occurred in 40.7%, and no treatment-related death was observed.ConclusionPE-based chemotherapy following ICI is encouraging for its robust antitumor efficacy in R/M SCCHN