The grapheme-valued Wright-Fisher diffusion with mutation.

In Athreya et al. (2021), models from population genetics were used to define stochastic dynamics in the space of graphons arising as continuum limits of dense graphs. In the present paper we exhibit an example of a simple neutral population genetics model for which this dynamics is a Markovian diffusion that can be characterized as the solution of a martingale problem. In particular, we consider a Markov chain in the space of finite graphs that resembles a Moran model with resampling and mutation. We encode the finite graphs as graphemes, which can be represented as a triple consisting of a vertex set (or more generally, a topological space), an adjacency matrix, and a sampling (Borel) measure. We equip the space of graphons with convergence of sample subgraph densities and show that the grapheme-valued Markov chain converges to a grapheme-valued diffusion as the number of vertices goes to infinity. We show that the grapheme-valued diffusion has a stationary distribution that is linked to the Griffiths-Engen-McCloskey (GEM) distribution. In a companion paper (Greven et al. 2023), we build up a general theory for obtaining grapheme-valued diffusions via genealogies of models in population genetics.

A scoring system to quantify late effects in children after treatment for medulloblastoma/ependymoma and its correlation with quality of life and neurocognitive functioning.

BACKGROUND: The aim of this study was to quantify the severity of late effects by a simple numerical score (late effects severity score, LESS) in patients who received radiochemotherapy for medulloblastoma or ependymoma. The LESS was correlated with neurocognitive and quality of life (QoL) outcomes. PATIENTS AND METHODS: The LESS was calculated by assigning 0, 1, or 2 points within each of four different categories (neurology, endocrine, visual/auditory, others). Twenty-three patients with medulloblastoma (n = 18) or ependymoma (n = 5) underwent extensive neurocognitive and QoL testing at a median of 56 months (range, 1-174) after the end of treatment. Eight patients with low-grade glioma (LGG) who underwent tumor resection only served as control group. RESULTS: Patients with medulloblastoma/ependymoma had significantly higher LESS and significantly lower Wechsler Adult Intelligence Scale (WAIS)/Wechsler Intelligence Scales for Children (WISC) scores compared to patients with LGG. There was no statistically significant correlation between neurocognitive performance and QoL. The total LESS was negatively correlated with WAIS/WISC, attention, concentration, and verbal learning scores. Comparison of QoL and late effects in patients with medulloblastoma/ependymoma demonstrated a significant negative correlation only for neurological late effects and the KINDL score suggesting that younger patients with more severe late effects reported on a worse QoL. CONCLUSIONS: This LESS seems to be a simple and practical tool to quantify late effects in former brain tumor patients. Although both groups differ significantly with regard to neurocognitive parameters and severity of late effects, this does not apply for all QoL outcomes. Neurological late effects seem to be most predictive for an impaired QoL in younger children.