Estimation of sample spacing in stochastic processes

Motivated by applications in electron microscopy, we study the situation where a stationary and isotropic random field is observed on two parallel planes with unknown distance. We propose an estimator for this distance. Under the tractable, yet flexible class of Lévy-based random field models, we derive an approximate variance of the estimator. The estimator and the approximate variance perform well in two simulation studies

Hvordan kan matematiklæreres refleksionssamtaler om undervisningspraksis karakteriseres?

At reflektere over undervisning er centralt i nye former for lærersamarbejder som fx lektionsstudier hvor lærere udforsker egen og andres praksis. Vores formål er at karakterisere sådanne fagdidaktiske refleksionssamtaler når danske matematiklærere reflekterer over deres observationer af praksis. Analytisk er vi inspirerede af en japansk diskursmodel som vi videreudvikler til en refleksionsmodel der gør det muligt for os at indfange bredden og variationerne i samtalerne set som helheder. To refleksionsformer viser sig at dominere: beskrivende og problemløsende refleksioner. Vi foreslår lærere og andre at bruge refleksionsmodellen som redskab til at diskutere og udvikle kvalitet i refleksionssamtaler om matematikundervisning og -læring

Tumor volume and cancer stem cell expression as prognostic markers for high-dose loco-regional failure in head and neck squamous cell carcinoma - A DAHANCA 19 study

BACKGROUND AND PURPOSE: Reliable and accessible biomarkers for patients with Head and Neck Squamous Cell Carcinoma (HNSCC) are warranted for biologically driven radiotherapy (RT). This study aimed to investigate the prognostic value of putative cancer stem cell (CSC) markers, hypoxia, and tumor volume using loco-regional high-dose failure (HDF) as endpoint.MATERIALS AND METHODS: Tumor tissue was retrieved from patients treated with primary chemo-(C-)RT and nimorazole for HNSCC in the Danish Head and Neck Cancer Study Group (DAHANCA) 19 study. Tumor volume, hypoxic classification, and expression of CSC markers CD44, SLC3A2, and MET were analyzed. For patients with eligible data on all parameters (n = 340), the risk of HDF following primary chemo-(C-)RT were analyzed by these biomarkers as a whole and stratified for p16-positive oropharynx (p16 + OPSCC) vs p16-negative (p16-) tumors (oral cavity, p16- oropharynx, hypopharynx and larynx).RESULTS: Higher risk of HDF was seen for patients with larger primary and nodal volume (&gt;25 cm3, Hazard Ratio (HR): 3.00 [95 % CI: 1.73-5.18]), high SLC3A2 (HR: 2.99 [1.28-6.99]), CD44 (&gt;30 % positive, HR: 2.29 [1.05-5.00]), and p16- tumors (HR: 2.53 [1.05-6.11]). p16- tumors had a higher CSC marker expression than p16 + OPSCC. The factors associated with the highest risk of HDF were larger volume (HR: 3.29 [1.79-6.04]) for p16- tumors (n = 178) and high SLC3A2 (HR: 6.19 [1.58-24.23]) for p16 + OPSCC (n = 162).CONCLUSION: Tumor volume, p16, and CSC markers are potential biomarkers for HDF for patients with HNSCC treated with (C-)RT. Lower expression of CSC in p16 + OPSCC may contribute to better tumor control.</p