Isabelle/PIDE as Platform for Educational Tools

The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.Comment: In Proceedings THedu'11, arXiv:1202.453

Sparse Probit Linear Mixed Model

Linear Mixed Models (LMMs) are important tools in statistical genetics. When used for feature selection, they allow to find a sparse set of genetic traits that best predict a continuous phenotype of interest, while simultaneously correcting for various confounding factors such as age, ethnicity and population structure. Formulated as models for linear regression, LMMs have been restricted to continuous phenotypes. We introduce the Sparse Probit Linear Mixed Model (Probit-LMM), where we generalize the LMM modeling paradigm to binary phenotypes. As a technical challenge, the model no longer possesses a closed-form likelihood function. In this paper, we present a scalable approximate inference algorithm that lets us fit the model to high-dimensional data sets. We show on three real-world examples from different domains that in the setup of binary labels, our algorithm leads to better prediction accuracies and also selects features which show less correlation with the confounding factors.Comment: Published version, 21 pages, 6 figure

Retention of mouth-to-mouth, mouth-to-mask and mouth-to-face shield ventilation

Background: Retention of mouth-to-mouth, mouth-to-mask and mouth-to-face shield ventilation techniques is poorly understood.Methods: A prospective randomised clinical trial was undertaken in January 2004 in 70 candidates randomly assigned to training in mouth-to-mouth, mouth-to-mask or mouth-to-face shield ventilation. Each candidate was trained for 10 min, after which tidal volume, respiratory rate, minute volume, peak airway pressure and the presence or absence of stomach inflation were measured. 58 subjects were reassessed 1 year later and study parameters were recorded again. Data were analysed with ANOVA, \textgreekq2 and McNemar tests.Results: Tidal volume, minute volume, peak airway pressure, ventilation rate and stomach inflation rate increased significantly at reassessment with all ventilation techniques compared with the initial assessment. However, at reassessment, mean (SD) tidal volume (960 (446) vs 1008 (366) vs 1402 (302) ml; p<0.05), minute volume (12 (5) vs 13 (7) vs 18 (3) l/min; p<0.05), peak airway pressure (14 (8) vs 17 (13) vs 25 (8) cm H2O; p<0.05) and stomach inflation rate (63% vs 58% vs 100%; p<0.05) were significantly lower with mouth-to-mask and mouth-to-face shield ventilation than with mouth-to-mouth ventilation. The ventilation rate at reassessment did not differ significantly between the ventilation techniques.Conclusions: One year after a single episode of ventilation training, lay persons tended to hyperventilate; however, the degree of hyperventilation and resulting stomach inflation were lower when a mouth-to-mask or a face shield device was employed. Regular training is therefore required to retain ventilation skills; retention of skills may be better with ventilation devices