Wall-crossing formulae and strong piecewise polynomiality for mixed Grothendieck dessins d'enfant, monotone, and double simple Hurwitz numbers

We derive explicit formulae for the generating series of mixed Grothendieck dessins d'enfant/monotone/simple Hurwitz numbers, via the semi-infinite wedge formalism. This reveals the strong piecewise polynomiality in the sense of Goulden–Jackson–Vakil, generalising a result of Johnson, and provides a new explicit proof of the piecewise polynomiality of the mixed case. Moreover, we derive wall-crossing formulae for the mixed case. These statements specialise to any of the three types of Hurwitz numbers, and to the mixed case of any pair

Special cases of the orbifold version of Zvonkine's rr-ELSV formula

We prove the orbifold version of Zvonkine's $r$-ELSV formula in two special cases: the case of $r=2$ (complete $3$-cycles) for any genus $g\geq 0$ and the case of any $r\geq 1$ for genus $g=0$

PD-L1 testing for lung cancer in the UK: recognizing the challenges for implementation.

A new approach to the management of non-small-cell lung cancer (NSCLC) has recently emerged that works by manipulating the immune checkpoint controlled by programmed death receptor 1 (PD-1) and its ligand programmed death ligand 1 (PD-L1). Several drugs targeting PD-1 (pembrolizumab and nivolumab) or PD-L1 (atezolizumab, durvalumab, and avelumab) have been approved or are in the late stages of development. Inevitably, the introduction of these drugs will put pressure on healthcare systems, and there is a need to stratify patients to identify those who are most likely to benefit from such treatment. There is evidence that responsiveness to PD-1 inhibitors may be predicted by expression of PD-L1 on neoplastic cells. Hence, there is considerable interest in using PD-L1 immunohistochemical staining to guide the use of PD-1-targeted treatments in patients with NSCLC. This article reviews the current knowledge about PD-L1 testing, and identifies current research requirements. Key factors to consider include the source and timing of sample collection, pre-analytical steps (sample tracking, fixation, tissue processing, sectioning, and tissue prioritization), analytical decisions (choice of biomarker assay/kit and automated staining platform, with verification of standardized assays or validation of laboratory-devised techniques, internal and external quality assurance, and audit), and reporting and interpretation of the results. This review addresses the need for integration of PD-L1 immunohistochemistry with other tests as part of locally agreed pathways and protocols. There remain areas of uncertainty, and guidance should be updated regularly as new information becomes available

The tautological ring of Mg,n via Pandharipande-Pixton-Zvonkine r-spin relations

We use relations in the tautological ring of the moduli spaces Mg,n derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the r-spin Witten class in order to obtain some restrictions on the dimensions of the tautological rings of the open moduli spacesMg,n. In particular, we give a new proof for the result of Looijenga (for n = 1) and Buryak et al. (for n > 2) that dimRg-1(Mg,n) ≤ n. We also give a new proof of the result of Looijenga (for n = 1) and Ionel (for arbitrary n > 1) that Ri(Mg,n) = 0 for i > g and give some estimates for the dimension of Ri(Mg,n) for i ≤ g - 2

Neoadjuvant chemotherapy and trastuzumab versus neoadjuvant chemotherapy followed by post-operative trastuzumab for patients with HER2-positive breast cancer

Neoadjuvant chemotherapy plus trastuzumab (NCT) increases the rate of pathological complete response (pCR) and event-free survival (EFS) compared to neoadjuvant chemotherapy (NC) alone in women with HER2 positive breast cancer (BC). pCR in this setting is associated with improved EFS. Whether NCT preferentially improves EFS in comparison to NC followed by adjuvant trastuzumab initiated postoperatively (NCAT) has not been addressed. Using clinical data from women with HER2 positive BC treated at 7 European institutions between 2007 and 2010 we sought to investigate the impact on breast cancer outcomes of concomitant (NCT) versus sequential (NCAT) treatment in HER2 positive early BC. The unadjusted hazard ratio (HR) for event free survival with NCT compared with NCAT was 0.63 (95% CI 0.37–1.08; p = 0.091). Multivariable analysis revealed that treatment group, tumour size and ER status were significantly associated with EFS from diagnosis. In the whole group NCT was associated with a reduced risk of an event relative to NCAT, an effect that was confined to ER negative (HR: 0.25; 95% CI, 0.10–0.62; p = 0.003) as opposed to ER positive tumours (HR: 1.07; 95% CI, 0.46–2.52; p = 0.869). HER2 positive/ER negative BC treated with NC gain greatest survival benefit when trastuzumab is administered in both the neoadjuvant and adjuvant period rather than in the adjuvant period alone. These data support the early introduction of targeted combination therapy in HER2 positive/ER negative BC

Clinical translation of [18F]ICMT-11 for measuring chemotherapy-induced caspase 3/7 activation in breast and lung cancer

Background: Effective anticancer therapy is thought to involve induction of tumour cell death through apoptosis and/or necrosis. [18F]ICMT-11, an isatin sulfonamide caspase-3/7-specific radiotracer, has been developed for PET imaging and shown to have favourable dosimetry, safety, and biodistribution. We report the translation of [18F]ICMT-11 PET to measure chemotherapy-induced caspase-3/7 activation in breast and lung cancer patients receiving first-line therapy. Results: Breast tumour SUVmax of [18F]ICMT-11 was low at baseline and unchanged following therapy. Measurement of M30/M60 cytokeratin-18 cleavage products showed that therapy was predominantly not apoptosis in nature. While increases in caspase-3 staining on breast histology were seen, post-treatment caspase-3 positivity values were only approximately 1%; this low level of caspase-3 could have limited sensitive detection by [18F]ICMT-11-PET. Fourteen out of 15 breast cancer patients responded to first–line chemotherapy (complete or partial response); one patient had stable disease. Four patients showed increases in regions of high tumour [18F]ICMT-11 intensity on voxel-wise analysis of tumour data (classed as PADS); response was not exclusive to patients with this phenotype. In patients with lung cancer, multi-parametric [18F]ICMT-11 PET and MRI (diffusion-weighted- and dynamic contrast enhanced-MRI) showed that PET changes were concordant with cell death in the absence of significant perfusion changes. Conclusion: This study highlights the potential use of [18F]ICMT-11 PET as a promising candidate for non-invasive imaging of caspase3/7 activation, and the difficulties encountered in assessing early-treatment responses. We summarize that tumour response could occur in the absence of predominant chemotherapy-induced caspase-3/7 activation measured non-invasively across entire tumour lesions in patients with breast and lung cancer

Randomized trial of erlotinib plus whole-brain radiotherapy for NSCLC patients with multiple brain metastases

Background: Median survival of non-small cell lung cancer (NSCLC) patients with brain metastases is poor. We examined concurrent erlotinib and whole brain radiotherapy (WBRT) followed by maintenance erlotinib in patients with untreated brain metastases, given the potential radiosensitizing properties of erlotinib and its direct effect on brain metastases and systemic activity.Methods: Eighty NSCLC patients with KPS of 70 and greater and multiple brain metastases were randomly assigned to placebo (n = 40) or erlotinib (100mg, n = 40) given concurrently with WBRT (20 Gy in 5 fractions). Following WBRT, patients continued with placebo or erlotinib (150mg) until disease progression. The primary end point was neurological progression-free survival (nPFS); hazard ratios (HRs) were calculated using Cox regression. All P values were two-sided.Results: Fifteen patients (37.5%) from each arm were alive and without neurological progression 2 months after WBRT. Median nPFS was 1.6 months in both arms; nPFS HR 0.95 (95% CI = 0.59 to1.54; P = .84). Median overall survival (OS) was 2.9 and 3.4 months in the placebo and erlotinib arms; HR 0.95 (95% CI = 0.58 to 1.55; P = .83). The frequency of epidermal growth factor receptor (EGFR) mutations was low with only 1 of 35 (2.9%) patients with available samples had activating EGFR-mutations. Grade 3/4 adverse event rates were similar between the two groups (70.0% in each arm), except for rash 20.0% (erlotinib) vs 5.0% (placebo), and fatigue 17.5% vs 35.0%. No statistically significant quality of life differences were found.Conclusions: Our study showed no advantage in nPFS or OS for concurrent erlotinib and WBRT followed by maintenance erlotinib in patients with predominantly EGFR wild-type NSCLC and multiple brain metastases compared to placebo. Future studies should focus on the role of erlotinib with or without WBRT in patients with EGFR mutations.Up to 40% of patients with non-small cell lung cancer (NSCLC) develop brain metastases (BM), which are associated with poor outcome (median survival <5 months) (1–3). Treatment options include whole-brain radiotherapy (WBRT) with or without corticosteroids. Modifying the radiation dose or fractionation or combining radiotherapy with radiosensitizers have not substantially improved prognosis (4–10). More than half of patients treated with WBRT ultimately die of progressive systemic disease (11–13).Erlotinib, an epidermal growth factor receptor (EGFR) pathway inhibitor, is currently approved as first-line treatment for advanced NSCLC patients harboring EGFR mutations, and, as maintenance, second-line or third-line treatments following chemotherapy (14–17). Pre-clinical data show that erlotinib enhances the inhibitory effect of ionizing radiation in lung cancer, and it crosses the blood-brain barrier, so it could be used to provide sufficient radiosensitizing and therapeutic level in the brain (18–22).To exploit the potential radiosensitizing properties, the direct effect on brain metastases, and systemic activity of erlotinib, we examined the role of erlotinib given concurrently with WBRT, then as maintenance