We evaluate the self-diffusion and transport diffusion of interacting particles in a discrete geometry consisting of a linear chain of cavities, with interactions within a cavity described by a free-energy function. Exact analytical expressions are obtained in the absence of correlations, showing that the self-diffusion can exceed the transport diffusion if the free-energy function is concave. The effect of correlations is elucidated by comparison with numerical results. Quantitative agreement is obtained with recent experimental data for diffusion in a nanoporous zeolitic imidazolate framework material, ZIF-8.

Background: Disability progression is a key milestone in the disease evolution of people with multiple sclerosis (PwMS). Prediction models of the probability of disability progression have not yet reached the level of trust needed to be adopted in the clinic. A common benchmark to assess model development in multiple sclerosis is also currently lacking. Methods: Data of adult PwMS with a follow-up of at least three years from 146 MS centers, spread over 40 countries and collected by the MSBase consortium was used. With basic inclusion criteria for quality requirements, it represents a total of 15, 240 PwMS. External validation was performed and repeated five times to assess the significance of the results. Transparent Reporting for Individual Prognosis Or Diagnosis (TRIPOD) guidelines were followed. Confirmed disability progression after two years was predicted, with a confirmation window of six months. Only routinely collected variables were used such as the expanded disability status scale, treatment, relapse information, and MS course. To learn the probability of disability progression, state-of-the-art machine learning models were investigated. The discrimination performance of the models is evaluated with the area under the receiver operator curve (ROC-AUC) and under the precision recall curve (AUC-PR), and their calibration via the Brier score and the expected calibration error. All our preprocessing and model code are available at https://gitlab.com/edebrouwer/ms_benchmark, making this task an ideal benchmark for predicting disability progression in MS. Findings: Machine learning models achieved a ROC-AUC of 0⋅71 ± 0⋅01, an AUC-PR of 0⋅26 ± 0⋅02, a Brier score of 0⋅1 ± 0⋅01 and an expected calibration error of 0⋅07 ± 0⋅04. The history of disability progression was identified as being more predictive for future disability progression than the treatment or relapses history. Conclusions: Good discrimination and calibration performance on an external validation set is achieved, using only routinely collected variables. This suggests machine-learning models can reliably inform clinicians about the future occurrence of progression and are mature for a clinical impact study.

Wearable technology will become available and allow prolonged electroencephalography (EEG) monitoring in the home environment of patients with epilepsy. Neurologists analyse the EEG visually and annotate all seizures, which patients often under-report. Visual analysis of a 24-h EEG recording typically takes one to two hours. Reliable automated seizure detection algorithms will be crucial to reduce this analysis. We investigated such algorithms on a dataset of behind-the-ear EEG measurements. Our first aim was to develop a methodology where part of the data is deferred to a human expert, who performs perfectly, with the goal of obtaining an (almost) perfect detection sensitivity (DS). Prediction confidences are determined by temperature scaling of the classification model outputs and trust scores. A DS of approximately 90% (99%) can be achieved when deferring around 10% (40%) of the data. Perfect DS can be achieved when deferring 50% of the data. Our second contribution demonstrates that a common modelling strategy, where predictions from several short EEG segments are combined to obtain a final prediction, can be improved by filtering out untrustworthy segments with low trust scores. The false detection rate shows a relative decrease between 21% and 43%, and the DS shows a small increase or decrease.