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This study is motivated through the interesting non-Arcchimedean stability results of ρ-inequalities and ρ-equations arising from linear, second power, third power and fourth power mappings. The aim of this paper is to determine the solutions of new multiplicative inverse µ-inequalities and µ-equations arising from multiplicative inverse mapping. Further, their stabilities involved with various superior limits are proved in the context of non-Archimedean complete normed spaces.

Abstract There is an urgent need to fully understand the biology of third generation EGFR‐tyrosine kinase inhibitors (EGFR‐TKIs), particularly osimertinib, and to develop mechanism‐driven strategies to manage their acquired resistance. Transient receptor potential melastatin‐2 (TRPM2) functions as an important regulator of Ca2+ influx, but its role in mediating therapeutic efficacies of EGFR‐TKIs and acquired resistance to EGFR‐TKIs has been rarely studied. This study has demonstrated a previously undiscovered role of suppression of TRPM2 and subsequent inhibition of Ca2+ influx and induction of ROS and DNA damage in mediating apoptosis induction and the therapeutic efficacy of osimertinib against EGFR mutant NSCLC. The rebound elevation represents a key mechanism accounting for the emergence of acquired resistance to osimertinib and other third generation EGFR‐TKIs. Accordingly, targeting TRPM2 is a potentially promising strategy for overcoming and preventing acquired resistance to osimertinib, warranting further study in this direction including the development of cancer therapy‐optimized TRPM2 inhibitors.

Introduction: The JAVELIN Lung 101 phase 1b/2 trial evaluated avelumab (immune checkpoint inhibitor) combined with lorlatinib or crizotinib (tyrosine kinase inhibitors) in ALK-positive or ALK-negative advanced NSCLC, respectively. Methods: Starting doses of lorlatinib 100 mg once daily or crizotinib 250 mg twice daily were administered with avelumab 10 mg/kg every 2 weeks. Primary objectives were assessment of maximum tolerated dose (MTD) and recommended phase 2 dose in phase 1 and objective response rate in phase 2. Primary end points were dose-limiting toxicity (DLT) and confirmed objective response per Response Evaluation Criteria in Solid Tumors, version 1.1. Results: In the avelumab plus lorlatinib group (ALK-positive; n = 31; 28 in phase 1b; three in phase 2), two of 28 assessable patients (7%) had DLT, and the MTD and recommended phase 2 dose was avelumab 10 mg/kg every 2 weeks plus lorlatinib 100 mg once daily. In the avelumab plus crizotinib group (ALK-negative; n = 12; all phase 1b), five of 12 assessable patients (42%) had DLT, and the MTD was exceeded with avelumab 10 mg/kg every 2 weeks plus crizotinib 250 mg twice daily; alternative crizotinib doses were not assessed. Objective response rate was 52% (95% confidence interval, 33%–70%) with avelumab plus lorlatinib (complete response, 3%; partial response, 48%) and 25% (95% confidence interval, 6%–57%) with avelumab plus crizotinib (all partial responses). Conclusions: Avelumab plus lorlatinib treatment in ALK-positive NSCLC was feasible, but avelumab plus crizotinib treatment in ALK-negative NSCLC could not be administered at the doses tested. No evidence of increased antitumor activity was observed in either group. ClinicalTrials.gov identifier: NCT02584634

Objective Immune checkpoint inhibitors (ICI) that block the programmed cell death 1 (PD-1) pathway have shown promise with limited benefit. We and others have shown in small patient cohorts that an early proliferative CD8 T-cell response in the blood may be predictive of clinical response. However, these studies lack detailed analyses and comparisons between monotherapy and combination therapies.Methods and analysis We analysed longitudinal blood samples from 103 patients with cancer who received αPD-1 monotherapy or combined with anti-cytotoxic T lymphocyte-associated protein 4 (αCTLA-4) or chemotherapy. Transcriptional analysis of CD8 T cells after the first treatment cycle with effector cells generated following yellow fever virus (YFV-17D) vaccine-induced infection was also compared.Results An early proliferative (Ki-67+) CD8 T-cell response was observed after cycle 1 in 60 patients (58.3%). Patients with early-and-sustained proliferative responses (cycle 1 and beyond) had better clinical responses and survival than patients with an early-but-limited response (p=0.02). The proliferating cells had an effector-like phenotype. The transcriptional profiles of the effector-like CD8 T cells were similar irrespective of treatment type or clinical response but distinct from that of YFV-specific effector CD8 T cells.Conclusions Our data suggest that early proliferative CD8 T-cell response in the blood is predictive, and that an early-and-sustained proliferative response may further identify patients with prolonged survival. The ICI-induced effector-like CD8 T cells are transcriptionally distinct from highly functional YFV-specific cells, suggesting opportunities for improved T-cell effector function with combination therapies for better clinical outcome.