This paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main feature of our approach is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of it) does not appear in our formulas. Another aspect of our analysis is that it emphasizes the relationship with the subdifferential of the supremum of finite subfamilies, or equivalently, finite weighted sums. Some specific results are given in the setting of reflexive Banach spaces, showing that the subdifferential of the supremum can be reduced to the supremum of a countable family. ; ANID-Fondecyt 1190012 Proyecto/Grant PIA AFB-170001 MICIU of Spain Universidad de Alicante (Contract Beatriz Galindo) BEA-GAL 18/00205 Spanish Government PGC2018-097960-B-C21 Australian Research Council DP 180100602 ; Versión publicada - versión final del editor
Gastric cancer (GC) is a leading cause of cancer death in Chile. Although recommended in international guidelines since 2006, perioperative chemotherapy was not available to patients in the public health system in Chile until 2016. We conducted an observational study to assess the feasibility of this strategy in public hospitals in Chile (Observational Study of Perioperative Chemotherapy in Locally Advanced Gastric Cancer – PRECISO). Patients with locally advanced, operable GC were offered to receive preoperative chemotherapy with Epirubicin + Cisplatin + Capecitabine (ECX) for three cycles followed by curative surgery. Staging included abdominal CT scan and laparoscopy if peritoneal carcinomatosis was suspected. Postoperative ECX for three cycles was recommended. Between August 2010 and March 2013, 110 patients were screened and 61 enrolled. Median age was 62 years (23–76 years) and most patients had good performance status at baseline (Eastern Cooperative Oncology Group performance status score (ECOG) 0: 42, ECOG 1: 19). Tumour site was proximal in 32 (52%) and medial and distal in 29 (48%) patients. All but four patients (n = 57, 93%) completed three cycles of preoperative chemotherapy. Fifty-six patients were operated and 54 (89%) had a curative resection. Thirty-three patients (54%) had pT0-2, and 18 (30%) had pN0 tumours, with two patients achieving a complete response. As of 20 December 2020, 39 patients died, 32 due to GC, one within 30 days of surgery, two due to intestinal obstruction at 5 and 3 months after surgery and four due to other causes. Five-year survival rate was 38%. We conclude that perioperative chemotherapy is feasible in public hospitals in Chile and should be offered to patients with locally advanced GC. ; National Agency for Research and Development ICN09_015 PIA/ACT192015 Corporacion de Fomento de la Produccion (CORFO) 16CTTS-66390 Deutscher Akademischer Austausch Dienst (DAAD) 57220037 57168868 Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) CONICYT FONDAP 1513001 Fondo Nacional de Desarrollo Cientifico y Tecnologico (FONDECYT) from the National Agency for Research and Development (ANID), Government of Chile 1191928 ; Versión publicada - versión final del editor
