Quantitative characterisation of an engineering write-up using random walk analysis

Abstract

This contribution reports on the investigation of correlation properties in an English scientific text (engineering write-up) by means of a random walk. Though the idea to use a random walk to characterise correlations is not new (it was used e.g. in the genome analysis and in the analysis of texts), a random walk approach to the analysis of an English scientific text is still far from being exploited in its full strength as demonstrated in this paper. A method of high-dimensional embedding is proposed. Case examples were drawn arbitrarily from four engineering write-ups (Ph.D. synopsis) of three engineering departments in the Faculty of Technology, University of Ibadan, Nigeria. Thirteen additional analyses of non-engineering English texts were made and the results compared to the engineering English texts. Thus, a total of seventeen write-ups of eight Faculties and sixteen Departments of the University of Ibadan were considered. The characterising exponents which relate the average distance of random walkers away from a known starting position to the elapsed time steps were estimated for the seventeen cases according to the power law and in three different dimensional spaces. The average characteristic exponent obtained for the seventeen cases and over three different dimensional spaces studied was 1.42 to 2-decimal with a minimum and a maximum coefficient of determination (R2 ) of 0.9495 and 0.9994 respectively. This is found to be 284% of the average characterising exponent value (0.5), as supported by the literature for random walkers based on the pseudo-random number generator. The average characteristic exponent obtained for the four cases that were engineering-based and over the three different dimensional studied spaces was 1.41 to 2-decimal (closer by 99.3% to 1.42) with a minimum and a maximum coefficient of determination (R2 ) of 0.9507 and 0.9974 respectively. This is found to be 282% of the average characterising exponent value (0.5), as supported by the literature for random walkers based on the pseudo-random number generator. In view of the range of the average characterising exponent across Faculties and the closeness of the average characterising exponent in the engineering-based cases in particular, it can be concluded that the engineering writing is strongly correlated. This study recommends that a very high characterising exponent value (e.g 1.42) is a mark of a very good engineering write-up.