Mean field mutation dynamics and the continuous Luria-Delbr\"uck distribution

The Luria-Delbr\"uck mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics. Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they correspond to generalized Fokker-Planck equations for the mutants distribution whose solutions are given by the corresponding Luria-Delbr\"uck distribution. Numerical results confirming the theoretical analysis are also presented

Mathematical Methods and Models in Biomedicine

XI, 427 p. 94 illus.online resource

Repeatability analysis of airborne electromagnetic surveys

Purpose: We provide methods for determining the repeatability of airborne electromagnetic surveys when conducted at different altitudes over a number of repeated flights. Our data arise from the TELLUS project carried out by the Geological Surveys of Ireland and Northern Ireland and we examine the repeatability of the apparent resistivity at different frequencies. Methods: After considering a number of issues with the data, we propose two different models from the functional data analysis literature; a Weiner process with random effects, and a penalised spline smoother. Results: Both methods arrive at the same conclusion regarding repeatability of the data; results obtained are more repeatable for flights at lower altitudes. Conclusions: The target altitude for aircraft carrying out airborne electromagnetic surveys should be as low as possible

Estimating the conditional probability of developing human papilloma virus related oropharyngeal cancer by combining machine learning and inverse bayesian modelling

The epidemic increase in the incidence of Human Papilloma Virus (HPV) related Oropharyngeal Squamous Cell Carcinomas (OPSCCs) in several countries worldwide represents a significant public health concern. Although gender neutral HPV vaccination programmes are expected to cause a reduction in the incidence rates of OPSCCs, these effects will not be evident in the foreseeable future. Secondary prevention strategies are currently not feasible due to an incomplete understanding of the natural history of oral HPV infections in OPSCCs. The key parameters that govern natural history models remain largely ill-defined for HPV related OPSCCs and cannot be easily inferred from experimental data. Mathematical models have been used to estimate some of these ill-defined parameters in cervical cancer, another HPV related cancer leading to successful implementation of cancer prevention strategies. We outline a “double-Bayesian” mathematical modelling approach, whereby, a Bayesian machine learning model first estimates the probability of an individual having an oral HPV infection, given OPSCC and other covariate informatio