Connecting Islands: Bridging zbMATH and DLMF with Scholix, a blueprint for connecting expert knowledge systems

This paper reports on the recently launched zbMATH Links API. We discuss its potential based on the initial link partner, the National Institute of Standards and Technology Digital Library of Mathematical Functions. As the API provides machine readable data in the links, we show how one can use data from both sources for further analysis. To exemplify the simplicity, we also show how one can use zbMATH’s link data in Jupyter notebooks.


Introduction
As reported in the last EMS Magazine (formerly Newsletter of the European Mathematical Society) [7], zbMATH Open provides application programming interfaces (API) to make zbMATH data machine accessible. We described the OAI-PMH API which enables the harvesting of zbMATH Open metadata. In contrast, this issue focuses on links between zbMATH Open and third parties. Our zbMATH Links API, available from http://purl.org/zb/14, provides a machine-readable interface for links between academic literature and other resources. To make this API interoperable with various information systems, we rely on the Scholix API standard [2]. Scholix, which is short for A Framework for Scholarly Link eXchange, is a long-running initiative supported by partners such as the Research Data Alliance, Crossref, and DataCite amongst many others, which aims to exchange information on research data and related scholarly articles. By exporting our data in a Scholix-compliant manner, we ensure that our data gets integrated into the worldwide ecosystem of open data. In this regard, it is not only important to export individual data sets, but also to explicitly annotate the links between different data sets in a standardized, machine readable format.
The zbMATH Open team is currently in the process of linking zbMATH Open reviews and abstracts with various partners such as  [4], 5. and many others.
The first step, establishing links between zbMATH Open and DLMF has now been completed.
In [6] we described the details of the zbMATH Links API interface and analyzed the current links in the DLMF; statistical analysis of metadata was obtained by combining both data sources. For instance, we can analyze the distribution of Mathematics Subject Classification (MSC) classes in DLMF chapters, or the average age of the referenced publications. Let us now explain how one can proceed to generate any similar analysis in a very short time, using simple tools.

Jupyter notebook demonstration
One way to use data from the zbMATH Links API is via Jupyter notebooks jupyter.org. Jupyter notebooks are interactive notebooks that can be run in the browser and thus do not require any setup or configuration. In contrast to other interactive notebooks by commercial publishers, Jupyter notebooks are based on free and open source software, which implies that one is not bound to a specific vendor. Recently, Jupyter notebooks have become increasingly popular and are being used to create easily reproducible scientific workflows [1]. For this demonstration, we use Jupyter with Python and employ the library pandas pandas.pydata.org for data aggregations as well as plotly to create plotly.com interactive visualizations.
In Figure 1, we create an interactive version of the MSC distribution of the articles linked in the DLMF as described in [6]. As shown, the visualization can be created in eight lines of code and fetches Figure 1. Jupyter notebook running on https://mybinder.org fetching and visualizing data from the zbMATH Links API data online from our API. In pandas there is built-in support to read from our API endpoint. Thus one can use real-time results from our API without any more effort than loading any other resource from the local file system. The source code with additional examples and further links to the interactive visualization is available from https://github.com/zbMATHOpen/LinksApiJupyterDemo.

Conclusion and outlook
We have shown how easy it is to use the data obtained from our zbMATH Links API. While currently, DLMF links are only accessible via this API, additional links are currently in the process of being generated. Moreover, trusted third parties will be able to add new links to their respective services. Additionally, conformity with the Scholix scheme ensures that content aggregators such as OpenAIRE, DataCite, and others can integrate our data into their systems and workflows.
As of the publication of this article, the zbMATH Links data is not yet displayed on the zbMATH Open user-interface. The integration of the data and the API within our user-interface is scheduled for the second half of 2021.