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Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. © 2019 Howison et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Quantifying and comparing the scientific output of researchers has become critical for governments, funding agencies and universities. Comparison by reputation and direct assessment of contributions to the field is no longer possible, as the number of scientists increases and traditional definitions about scientific fields become blurred. The h-index is often used for comparing scientists, but has several well-documented shortcomings. In this paper, we introduce a new index for measuring and comparing the publication records of scientists: the pagerank-index (symbolised as π). The index uses a version of pagerank algorithm and the citation networks of papers in its computation, and is fundamentally different from the existing variants of h-index because it considers not only the number of citations but also the actual impact of each citation. We adapt two approaches to demonstrate the utility of the new index. Firstly, we use a simulation model of a community of authors, whereby we create various ‘groups’ of authors which are different from each other in inherent publication habits, to show that the pagerank-index is fairer than the existing indices in three distinct scenarios: (i) when authors try to ‘massage’ their index by publishing papers in low-quality outlets primarily to self-cite other papers (ii) when authors collaborate in large groups in order to obtain more authorships (iii) when authors spend most of their time in producing genuine but low quality publications that would massage their index. Secondly, we undertake two real world case studies: (i) the evolving author community of quantum game theory, as defined by Google Scholar (ii) a snapshot of the high energy physics (HEP) theory research community in arXiv. In both case studies, we find that the list of top authors vary very significantly when h-index and pagerank-index are used for comparison. We show that in both cases, authors who have collaborated in large groups and/or published less impactful papers tend to be comparatively favoured by the h-index, whereas the pagerank-index highlights authors who have made a relatively small number of definitive contributions, or written papers which served to highlight the link between diverse disciplines, or typically worked in smaller groups. Thus, we argue that the pagerank-index is an inherently fairer and more nuanced metric to quantify the publication records of scientists compared to existing measures.