From Euclidean Geometry to Knots and Nets

This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe

A method for comprehensive proteomic analysis of human faecal samples to investigate gut dysbiosis in patients with cystic fibrosis

BACKGROUND: This chapter reports the evaluation of two shotgun metaproteomic workflows. The methods were developed to investigate gut dysbiosis via analysis of the faecal microbiota from patients with cystic fibrosis (CF). We aimed to set up an unbiased and effective method to extract the entire proteome, i.e. to extract sufficient bacterial proteins from the faecal samples in combination with a maximum of host proteins giving information on the disease state.; METHODS: Two protocols were compared; the first method involves an enrichment of the bacterial proteins while the second method is a more direct method to generate a whole faecal proteome extract. The different extracts were analysed using denaturing polyacrylamide gel electrophoresis followed by liquid chromatography-tandem mass spectrometry aiming a maximal coverage of the bacterial protein content in faecal samples.; RESULTS AND CONCLUSIONS: In all extracts, microbial proteins are detected, and in addition, nonbacterial proteins are detected in all samples providing information about the host status. Our study demonstrates the huge influence of the used protein extraction method on the obtained result and shows the need for a standardised and appropriate sample preparation for metaproteomic analysis. To address questions on the health status of the patients, a whole protein extract is preferred over a method to enrich the bacterial fraction. In addition, the method of the whole protein fraction is faster, which gives the possibility to analyse more biological replicates