Quantifying the rise and fall of scientific fields

Science advances by pushing the boundaries of the adjacent possible. While the global scientific enterprise grows at an exponential pace, at the mesoscopic level the exploration and exploitation of research ideas is reflected through the rise and fall of research fields. The empirical literature has largely studied such dynamics on a case-by-case basis, with a focus on explaining how and why communities of knowledge production evolve. Although fields rise and fall on different temporal and population scales, they are generally argued to pass through a common set of evolutionary stages. To understand the social processes that drive these stages beyond case studies, we need a way to quantify and compare different fields on the same terms. In this paper we develop techniques for identifying scale-invariant patterns in the evolution of scientific fields, and demonstrate their usefulness using 1.5 million preprints from the arXiv repository covering 175 research fields spanning Physics, Mathematics, Computer Science, Quantitative Biology and Quantitative Finance. We show that fields consistently follows a rise and fall pattern captured by a two parameters right-tailed Gumbel temporal distribution. We introduce a field-specific rescaled time and explore the generic properties shared by articles and authors at the creation, adoption, peak, and decay evolutionary phases. We find that the early phase of a field is characterized by the mixing of cognitively distant fields by small teams of interdisciplinary authors, while late phases exhibit the role of specialized, large teams building on the previous works in the field. This method provides foundations to quantitatively explore the generic patterns underlying the evolution of research fields in science, with general implications in innovation studies.Comment: 18 pages, 4 figures, 8 SI figure

Transport collapse in dynamically evolving networks

Transport in complex networks can describe a variety of natural and human-engineered processes including biological, societal and technological ones. However, how the properties of the source and drain nodes can affect transport subject to random failures, attacks or maintenance optimization in the network remain unknown. In this paper, the effects of both the distance between the source and drain nodes and of the degree of the source node on the time of transport collapse are studied in scale-free and lattice-based transport networks. These effects are numerically evaluated for two strategies, which employ either transport-based or random link removal. Scale-free networks with small distances are found to result in larger times of collapse. In lattice-based networks, both the dimension and boundary conditions are shown to have a major effect on the time of collapse. We also show that adding a direct link between the source and the drain increases the robustness of scale-free networks when subject to random link removals. Interestingly, the distribution of the times of collapse is then similar to the one of lattice-based networks

Correlation Networks from Flows. The Case of Forced and Time-Dependent Advection-Diffusion Dynamics

Acknowledgments We would like to thank Henk Dijkstra, Frank Hellman, Alexis Tantet for helpful and interesting discussions. Also we would like to acknowledge EC-funding through the Marie-Curie ITN LINC project (P7-PEOPLE-2011-ITN, grant No.289447), and FEDER and MINECO (Spain) through project ESCOLA (TM2012-39025-C02-01) Funding: The authors would like to acknowledge EC-funding through the Marie-Curie ITN LINC project (P7-PEOPLE-2011-ITN, grant No.289447, http://climatelinc.eu/home/), and FEDER and MINECO (Spain) through project ESCOLA (TM2012-39025-C02-01, http://ifisc.uib-csic.es/). Thanks to LINC and ESCOLA projects, the interaction between groups was possible; as the result, the collaborators developed methods together and analyzed the methods applications.Peer reviewedPublisher PD

Edge anisotropy and the geometric perspective on flow networks

ACKNOWLEDGMENTS This work was financially supported by the German Research Foundation (DFG) via the DFG Graduate School 1536 (“Visibility and Visualization”), the European Commission via the Marie-Curie ITN LINC (P7-PEOPLE-2011-ITN, Grant No. 289447), the German Federal Ministry for Education and Research (BMBF) via the BMBF Young Investigator's Group CoSy-CC2 (“Complex Systems Approaches to Understanding Causes and Consequences of Past, Present and Future Climate Change, Grant No. 01LN1306A”) and the project GLUES, the Stordalen Foundation (via the Planetary Boundary Research Network PB.net), the Earth League's EarthDoc program, and the Volkswagen Foundation via the project “Recurrent extreme events in spatially extended excitable systems: Mechanism of their generation and termination” (Grant No. 85391). The presented research has greatly benefited from discussions with Emilio Hernández-Garcia and Cristóbal López. Parts of the network calculations have been performed using the Python package pyunicorn56 (see http://tocsy.pik-potsdam.de/pyunicorn.php). pyunicorn is freely available for download at https://github.com/pik-copan/pyunicornPeer reviewedPublisher PD

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

Temporal and Spatial Aspects of Correlation Networks and Dynamical Network Models: Analytical Approaches and Physical Applications

In der vorliegenden Arbeit untersuchte ich die komplexen Strukturen von Netzwerken, deren zeitliche Entwicklung, die Interpretationen von verschieden Netzwerk-Massen und die Klassen der Prozesse darauf. Als Erstes leitete ich Masse für die Charakterisierung der zeitlichen Entwicklung der Netzwerke her, um räumlich Veränderungsmuster zu erkennen. Als Nächstes führe ich eine neue Methode zur Konstruktion komplexer Netzwerke von Flussfeldern ein, bei welcher man das Set-up auch rein unter Berufung Berufung auf das Geschwindigkeitsfeld ändern kann. Diese Verfahren wurden für die Korrelationen skalarer Grössen, z. B. Temperatur, entwickelt, welche eine Advektions-Diffusions-Dynamik in der Gegenwart von Zwingen und Dissipation. Die Flussnetzwerk-Methode zur Zeitreihenanalyse konstruiert die Korrelationsmatrizen und komplexen Netzwerke. Dies ermöglicht die Charakterisierung von Transport in Flüssigkeiten, die Identifikation verschiedene Misch-Regimes in dem Fluss und die Anwendung auf die Advektions-DiffusionsDynamik, Klimadaten und anderen Systemen, in denen Teilchentransport eine entscheidende Rolle spielen. Als Letztes, entwickelte ich ein neuartiges Heterogener Opinion Status Modell (HOpS) und Analysetechnik basiert auf Random Walks und Netzwerktopologie Theorien, um dynamischen Prozesse in Netzwerken zu studieren, wie die Verbreitung von Meinungen in sozialen Netzwerken oder Krankheiten in der Gesellschaft. Ein neues Modell heterogener Verbreitung auf einem Netzwerk wird als Beispielssystem für HOpS verwendent, um die vergleichsweise Einfachheit zu nutzen. Die Analyse eines diskreten Phasenraums des HOPS-Modells hat überraschende Eigenschaften, welches sensibel auf die Netzwerktopologie reagieren. Sie können verallgemeinert werden, um verschiedene Klassen von komplexen Netzwerken zu quantifizieren, Transportphänomene zu charakterisieren und verschiedene Zeitreihen zu analysieren