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• Re-casting of the P 3 neutron transport equations as an exterior differential system. • Conditional symmetry analysis of the P 3 equations. • Identification of admissible scaling and translation groups. • Construction of similarity variables and an example solution. This work explores conditional translation and scaling symmetries of a P 3 approximation to the one-dimensional (1D) Boltzmann neutron transport equation with arbitrary material properties. The principal outcomes of this analysis are twofold: 1) the identification of symmetries using Lie group theory is exhaustive, and thus provides definitive insight into scenarios where the differential equation(s) under consideration are expected to hold across phase space position or dimensional scale; and 2) invariance under transformations may be leveraged to construct changes of variables under which reduced-order structures or exact solutions with special properties may be derived. In support of these goals, this work includes the application of Lie group theory to the aforementioned neutron transport model. A variety of conditional translation and scaling symmetries are obtained (e.g., depending on the functional form of various macroscopic cross section functions), and an example scaleinvariant numerical solution of the 1D spherical P 3 equations is provided. [ABSTRACT FROM AUTHOR]

Background: Pembrolizumab (PD-1 inhibitor) and cetuximab (EGFR inhibitor) are active as single agents and in combination with cytotoxic chemotherapy for recurrent or metastatic head and neck squamous cell carcinoma (HNSCC). Given each drug's single agent activity and unique mechanism of action, we aimed to evaluate the anti-tumour activity of PD-1 blockade with EGFR inhibition in recurrent or metastatic HNSCC.Methods: This study is an open-label, non-randomised, multi-arm, phase 2 trial done at four academic centres in the USA. Participants were required to have platinum-resistant or platinum-ineligible, recurrent or metastatic HNSCC, be at least 18 years old, have an Eastern Cooperative Oncology Group performance status 0-1, have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1, and to have received no previous immunotherapy or EGFR inhibition. All participants received pembrolizumab 200 mg intravenously every 3 weeks, combined with an initial loading dose of cetuximab 400 mg/m2 intravenously followed by 250 mg/m2 intravenously weekly (21 day cycle). The primary endpoint was overall response rate defined as the proportion of participants with a partial or complete responses (per RECIST version 1.1) by 6 months in the intention-to-treat population. The safety population included all participants who received at least one dose of pembrolizumab. Herein, the final analysis of cohort 1 (no previous PD-1, PD-L1, or EGFR inhibition for recurrent or metastatic HNSCC) is reported. Three additional cohorts (two for participants with a previous response to immunotherapy followed by relapse or progression, with or without previous cetuximab exposure, and one for cutaneous HNSCC) will be reported separately once fully accrued. This study is registered with ClinicalTrials.gov, NCT03082534, and remains open as the three additional cohorts are actively accruing participants.Findings: Between March 22, 2017, and July 16, 2019, 33 participants were enrolled to cohort 1. All 33 participants received at least one dose of pembrolizumab. Median follow-up duration was 7·3 months (IQR 3·9-10·9). By 6 months, the overall response rate was 45% (95% CI 28-62), with 15 of 33 participants achieving a partial response. The most common grade 3-4 treatment-related adverse event was oral mucositis (three [9%] of 33 participants), and serious treatment-related adverse events occurred in five (15%) participants. No treatment-related deaths occurred.Interpretation: Pembrolizumab combined with cetuximab shows promising clinical activity for recurrent or metastatic HNSCC, and merits further investigation.Funding: Merck Sharp & Dohme. [ABSTRACT FROM AUTHOR]

Objectives: We aimed to test the safety of the CDK4/6 inhibitor palbociclib in combination with the EGFR inhibitor cetuximab and the PD-L1 inhibitor avelumab in recurrent/metastatic head and neck squamous cell carcinoma (R/M HNSCC).Materials and Methods: This phase I study enrolled eligible adult patients with R/M HNSCC into three sequential single dose-escalation cohorts of palbociclib (75, 100, and 125 mg) PO daily on days 1 to 21 of a 28-day cycle in combination with avelumab 10 mg/kg IV every 2 weeks and cetuximab 400 mg/m2IV on day 1, then 250 mg/m2weekly thereafter. The study followed a 3 + 3 design with no intra-patient escalation. The primary objective was to identify the recommended phase II dose (RP2D); secondary objectives included overall response rate (ORR), duration of response (DOR), progression free survival (PFS), and overall survival (OS).Results: Palbociclib in combination with avelumab and cetuximab was well tolerated, with rash and fatigue being the most common adverse events. A single dose-limiting toxicity was observed at the 125 mg dose of palbociclib: a grade 3 infusion reaction related to cetuximab. The RP2D of palbociclib is 125 mg, with avelumab and cetuximab at standard doses. The ORR by RECIST v1.1 was 42 %, the median DOR and OS have not been reached. Median PFS was 6.5 months.Conclusions: The combination of avelumab, cetuximab, and palbociclib was well tolerated and supports further evaluation in patients with R/M HNSCC.Clinical Trial Registration Number: NCT03498378. [ABSTRACT FROM AUTHOR]