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International audience; Precision medicine allows the extraction of information from complex datasets to facilitate clinical decision-making at the individual level. Topological Data Analysis (TDA) offers promising tools that complement current analytical methods in precision medicine studies. We introduce the fundamental concepts of the TDA corpus (the simplicial complex, the Mapper graph, the persistence diagram and persistence landscape). We show how these can be used to enhance the prediction of clinical outcomes and to identify novel subpopulations of interest, particularly applied to understand remission of depression in data from the GENDEP clinical trial.

Understanding the biological function of knots in proteins and their folding process is an open and challenging question in biology. Recent studies classify the topology and geometry of knotted proteins by analysing the distribution of a protein's planar projections using topological objects called knotoids. We approach the analysis of proteins with the same topology by introducing a topologically inspired statistical metric between their knotoid distributions. We detect geometric differences between trefoil proteins by characterising their entanglement and we recover a clustering by sequence similarity. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for proteins forming open-ended trefoil knots. Interestingly, our pipeline reveals that the folding pathway of shallow knotted Carbonic Anhydrases involves the creation of a double-looped structure, differently from what was previously observed for deeply knotted trefoil proteins. We validate this with Molecular Dynamics simulations., 5 figures, Supplementary information contained as an appendix

The 3rd Annual European Alternative Finance Report presents the most comprehensive analysis of the status of alternative finance industry in Europe, covering more countries, alternative finance models, as well as industry trends and developments than was available in its predecessors. Much effort has been placed on data quality verifications and clarifications in an ongoing productive and collaborative dialogue with all platform informants and research partners. Here, we wish to acknowledge their invaluable contributions, without which this report could not have been written. Overall, the data collected shows that 2016 saw European alternative finance doubling its volumes from 2015, and continuing an impressive growth. When placed into its short historical perspective, an impression emerges of an industry progressing from an introduction stage catering to innovators, into the growth stage catering to a growing number of early adopters. This growth phase is characterized by entry of new platforms and service providers, overall increasing competition, emergence of first cases of consolidation, diversification of products, and investments in process effectivization and streamlining. Despite exhibiting continuous healthy growth, Europe still punches well below its potential in most countries. Challenges remain both in terms of market education, and amendments of regulation. In Europe regulatory challenges are faced with two barriers. First, most countries have relatively mature and well-established regulatory systems. And, second, these vary significantly across countries. In this respect, our study provides initial evidence that more favorable regulation at national level is associated with higher volumes per capita, as well as with higher share of funding reaching businesses. Accordingly, one can expect that if regulatory conditions will continue to improve at both national and international levels, the industry will be able to maintain and enhance its growth. Nevertheless, one should acknowledge that the story of European alternative finance sector growth, more importantly, is the story of the democratization of access to finance and investment opportunities for people and ventures in Europe. When we present that the industry has generated EUR 2 Billion in 2016, it implies that close to 95% of this sum was actually invested in European venturing reaching businesses, entrepreneurs, artists, and social activists. All aim at creating value to consumers, investors and society via ventures made possible thanks to the support of the crowd. Accordingly, and by extension, more accommodating regulation for the industry, also implies greater access to finance for multiple stakeholders in the economy and more opportunities for value creation. Here, our findings leave much room for optimism for the coming years. Not only are volumes growing strongly, but platforms are investing actively in innovative solutions towards improving performance and customer service. Moreover, evidence suggests that a greater share of platforms engage in cross-border transactions, although, in most cases, these still represent a relatively modest share of overall volumes (thanks to limitations mentioned above). Finally, we hope this report, and the insights emerging form it, will be of help to all stakeholders interested in the development of alternative finance in Europe. And we look forward to a continued cooperation with all our partners in monitoring industry developments in the future.

This report presents the research findings from the 3rd Annual European Alternative Finance Industry Survey, which systematically records the development of this industry during 2016. This research was carried out by the Cambridge Center for Alternative Finance at the University of Cambridge Judge Business School, with the support of 29 major European industry associations and research partners, in partnership with BBVA.

We obtain a simple and complete characterisation of which matchings on the Tait graph of a knot diagram induce a discrete Morse function (dMf) on $S^2$, extending a construction due to Cohen. We show these dMfs are in bijection with certain rooted spanning forests in the Tait graph. We use this to count the number of such dMfs with a closed formula involving the graph Laplacian. We then simultaneously generalise Kauffman's Clock Theorem and Kenyon-Propp-Wilson's correspondence in two different directions; we first prove that the image of the correspondence induces a bijection on perfect dMfs, then we show that all perfect matchings, subject to an admissibility condition, are related by a finite sequence of click and clock moves. Finally, we study and compare the matching and discrete Morse complexes associated to the Tait graph, in terms of partial Kauffman states, and provide some computations., Comment: 31 pages, 44 figures, comments are welcome! This version accepted by the Electronic Journal of Combinatorics