The classical origin of modern mathematics

The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database includes a large number (N~200K) of advisor-student relationships, with affiliations and keywords on their research topic, over several centuries, from the 14th century until today. We focus on two different topics, the evolving importance of countries and of the research disciplines over time. Moreover we study the database at three levels, its global statistics, the mesoscale networks connecting countries and disciplines, and the genealogical level

Pollen, women, war and other things : reflections on the history of palynology

I am grateful to the Royal Swedish Academy of Sciences (Kungliga Vetenskapsakademien; KVA), Stockholm, for hosting the conference at which the themes in this paper were presented. For archival material, I appreciate access to (and the assistance of): Gunnar Erdtman papers, Center for History of Science, KVA (Maria Asp); Thomas Woodhead papers, Kirklees Museums and Galleries (Tolson Memorial Museum, Huddersfield; Chris Yates); Harold Hyde papers, Botany Section Correspondence, Amgueddfa Cymru National Museum Wales (Heather Pardoe); Kathleen Blackburn papers, Natural History Society of Northumbria Archive, Great North Museum (Hancock), Newcastle upon Tyne (Alan Hart); material concerning Florence Campbell James, Aberystwyth University (Julie Archer). Richard Bradshaw, Paul Buckland, Andrew Cameron, Peter Coxon, Egill Erlendsson, Michael Grant, Alan Hart, Angus Lunn, Limi Mao, Heather Pardoe, Ed Schofield and Richard West are thanked for advice and assistance. I appreciate the constructive comments on a draft of this paper by John Birks. Jenny Johnston assisted with artwork.Peer reviewedPublisher PD

Eigenvector-Based Centrality Measures for Temporal Networks

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NTxNT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.Comment: 38 pages, 7 figures, and 5 table

The global migration network of sex-workers

Differences in the social and economic environment across countries encourage humans to migrate in search of better living conditions, including job opportunities, higher salaries, security and welfare. Quantifying global migration is, however, challenging because of poor recording, privacy issues and residence status. This is particularly critical for some classes of migrants involved in stigmatised, unregulated or illegal activities. Escorting services or high-end prostitution are well-paid activities that attract workers all around the world. In this paper, we study international migration patterns of sex-workers by using network methods. Using an extensive international online advertisement directory of escorting services and information about individual escorts, we reconstruct a migrant flow network where nodes represent either origin or destination countries. The links represent the direct routes between two countries. The migration network of sex-workers shows different structural patterns than the migration of the general population. The network contains a strong core where mutual migration is often observed between a group of high-income European countries, yet Europe is split into different network communities with specific ties to non-European countries. We find non-reciprocal relations between countries, with some of them mostly offering while others attract workers. The GDP per capita is a good indicator of country attractiveness for incoming workers and service rates but is unrelated to the probability of emigration. The median financial gain of migrating, in comparison to working at the home country, is 15.9%. Only sex-workers coming from 77% of the countries have financial gains with migration and average gains decrease with the GDPc of the country of origin. Our results shows that high-end sex-worker migration is regulated by economic, geographic and cultural aspects.Comment: Comments and feedback welcomed. Two tables and 6 figures including S

Random walks on hypergraphs

In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but involve larger sets of nodes, at a time. These systems are thus better described in the framework of hypergraphs, whose hyperedges effectively account for multi-body interactions. We hereby propose a new class of random walks defined on such higher-order structures, and grounded on a microscopic physical model where multi-body proximity is associated to highly probable exchanges among agents belonging to the same hyperedge. We provide an analytical characterisation of the process, deriving a general solution for the stationary distribution of the walkers. The dynamics is ultimately driven by a generalised random walk Laplace operator that reduces to the standard random walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings. We illustrate our results on synthetic models for which we have a full control of the high-order structures, and real-world networks where higher-order interactions are at play. As a first application of the method, we compare the behaviour of random walkers on hypergraphs to that of traditional random walkers on the corresponding projected networks, drawing interesting conclusions on node rankings in collaboration networks. As a second application, we show how information derived from the random walk on hypergraphs can be successfully used for classification tasks involving objects with several features, each one represented by a hyperedge. Taken together, our work contributes to unveiling the effect of higher-order interactions on diffusive processes in higher-order networks, shading light on mechanisms at the hearth of biased information spreading in complex networked systems

Learning network embeddings using small graphlets

Techniques for learning vectorial representations of graphs (graph embeddings) have recently emerged as an effective approach to facilitate Machine Learning on graphs. Some of the most popular methods involve sophisticated features such as graph kernels or convolutional networks. In this work, we introduce two straightforward supervised learning algorithms based on small-size graphlet counts, combined with a dimension reduction step. The first relies on a classic feature extraction method powered by Principal Component Analysis (PCA). The second is a feature selection procedure also based on PCA. Despite their conceptual simplicity, these embeddings are arguably more meaningful than some popular alternatives and at the same time are competitive with state-of-the-art methods. We illustrate this second point on a downstream classification task. We then use our algorithms in a novel setting, namely to conduct an analysis of author relationships in Wikipedia articles, for which we present an original dataset. Finally, we provide empirical evidence suggesting that our methods could also be adapted to unsupervised learning algorithms

Local peer communities and future academic success of Ph.D. candidates

Compared to senior scientists, early-career scientists have largely been neglected in the literature on academic success. This study aims to identify the effects of local peer communities of Ph.D. candidates on their future careers. We argue that local communities of Ph.D. candidates may offer both supportive and competitive environments depending on the nature of the relationships between its members. While Ph.D. candidates generally learn from and support each other in their local peer communities, they may also compete for their mentor's attention and future academic positions. We analyse such complex peer effects for 90,264 Ph.D. candidates in the field of mathematics in a genealogical way, by measuring a candidate's academic career success by the number of next-generation Ph.D. candidates supervised later on. To capture both the supportive and competitive peer effects, we distinguish between local peers who share mentors (co-mentees) and other local peers. Our result suggests that competition exists primarily among peers who share mentors, and only at the start of one's career. We also find supportive effects among peers who do not share mentors, particularly those from the same cohort. Our results highlight the importance of universities supporting informal interactions among Ph.D. candidates