We aim to visualise the current state of collaborations between the Texas A&M Departments of Mathematics, Statistics and Computer Science and identify sub-fields of each where these collaborations occur. Cornell University’s arXiv is an open-access archive of scholarly articles from each of these three areas which classifies articles by a refined system of tags. We gathered arXiv submissions published by Texas A&M University authors and grouped articles according to their corresponding tags. This data was then visualised to show connections between sub-fields of each field and which sub-fields may benefit from future collaborations with neighbouring areas.

   As stated on their website, the arXiv is an open-access archive of over 2 million scholarly articles in the fields of Mathematics, Computer Science, Statistics, etc. Mathematics has significant collaborations with every other field that is featured on arXiv and so we studied the collaborations that Mathematicians at Texas A&M University have among its own sub-fields and with other fields. Therefore, our problem statement is:

How can we visualise the collaborations at Texas A&M University that occur between sub-fields of mathematics and non-mathematical fields?

   Our goal was to collect research publication data for papers published by the Mathematics, Statistics, and Computer Science departments of Texas A&M University which included the subfields of each discipline that the papers in our data set correspond to. Initially, we used data from Dimensions (https://app.dimensions.ai), a competition dataset, to find publications with authors from Texas A&M University. This data did not include subfield information, however. The data from arXiv (https://arxiv.org), an outside dataset, includes which subfields its publications correspond to, but it does not consistently keep track of the institutions that its publications are affiliated with. To collect our data, then, we cross-referenced each paper from the Dimensions database to see if it had a corresponding entry on arXiv from which we could collect its subfield data. We used arXiv’s free API to conduct this step. The data we collected this way required some cleaning: a paper could have multiple drafts on arXiv, or authors could publish under different names, for instance. Our data set is made up of all Texas A&M publications that we found listed on arXiv.

   Following is a timeline of our project:

• Initial Steps: At the beginning of our project we had our initial meetings and discussed what is expected from us. We set up VOSViewer and (in the interest of time) agreed upon the fact that we want to focus on the data for the publications from Mathematics, Statistics and Computer Science at Texas A&M University. The first thing that came to mind was arXiv, as it is the most popular website for pre-prints in our department and we decided to use the python API provided by arXiv (https://arxiv.org/help/api/). Initially, we wanted to include the data from the Physics department too, but we later decided not to. At this point, we didn’t decide what problem we wanted to focus on, but we started the data collection.
• Data Collection and Problem Statement: Once we decided that we wanted to focus on the arXiv publication data from the Mathematics, Statistics and Computer Science departments, we first had to come up with a script that could filter out publications from Texas A&M University. We used data from Dimensions to cross reference publishers at Texas A&M University. Due to the volume of data and the nature of the arXiv API, the script had to run over a long period of time, which required us to divide the task of collecting the data from different fields among ourselves. At this point, we also noticed that a significant number of pre-prints on arXiv have one or more cross-lists to other categories (in addition to a primary category), which reflect subfields. We decided to look at collaborations among subfields of Mathematics, Computer Science, and Statistics as our primary goal. Once we had the data from different fields, we compared them and tried to decide on which datasets we wanted to use. We compared the data from many sources and found the data from Dimensions and arXiv are most useful for us and comparatively cleaner.
• Data Manipulation and Exploration: This has been the most crucial and time consuming step in our project. After we decided on the datasets we divided the task of cleaning up the data. Then we started exploratory data analysis with those datasets and tried to see hidden relations we could draw in there. We generated many visualisations with those datasets and tried to see different aspects those datasets represent.
• Modelling and Analysis: After exploratory data analysis we found few interesting relations we could see in the data and decided to establish some of them through graphics and further analysis. We have described our analysis in the next few sections.

Figure 1: Heat map of the popularity of different subfields of Mathematics, Statistics and Computer Science. Figure 2: Collaboration network among different subfields of Mathematics, Statistics and Computer Science. The link width is proportional to the amount of collaborative publications between those two areas. Figure 3: This picture above visualises the collaboration among different subfields of Mathematics, Statistics and Computer Science and also colours them depending on time. There are three clusters of areas from the departments of Mathematics, Statistics and Computer Science. An interesting observation about this data is that the cluster for the department of Mathematics is larger and has more publications compared to other two departments, but most of the collaborations are among different subfields of Mathematics. One other thing we notice is that the Mathematics department has some popular and relatively old sub areas like Combinatorics, Algebraic Geometry, Functional Analysis etc. but the Computer Science department has the areas such as Machine Learning and AI, which are also popular but relatively new. Another interesting observation we made is that emerging popular areas such as Machine Learning and AI have comparatively more collaborations with different subfields and other fields. Figure 4: This bar graph represents the inter departmental collaborations between Mathematics and Computer Science over a period of about the last 30 years. We would like to point out a few interesting observations that we made from this. The amount of collaborative work between Mathematics and Computer Science has an overall increasing trend. The number of collaborations reached a sort of plateau around 2011-2016 but it saw a strong increase in around 2017 onwards. This, we believe, is due to the popularity of emerging fields like Machine Learning and AI. Figure 5: This bar graph represents the inter departmental collaborations between Mathematics and Statistics over a period of about the last 30 years. As the broad field of data science incorporates elements of statistics and several subfields of applied mathematics, this graph may show a correlation with the rise in popularity of data science itself. Since, in the past decade, most Fortune 100 companies have taken an interest in, if not invested heavily into, data mining and analysis for the purposes of strategy refinement (among others), this rise may be a response to the increased demand for employees who specialise in such fields. Figure 6: This bar graph here represents the inter departmental collaborations between Statistics and Computer Science over a period of about the last 30 years. One interesting thing we observe from this graph is that Statistics and Computer Science did not used to have too many collaborative works but the amount of collaborations between CS and Stats have started to grow in recent times. One reason for this we think is that the Statistics department here is comparatively new and have started to expand only recently and another reason we think is the popularity of ML and AI. These two research areas have become increasingly popular recently and it is around the same time when the collaborations between CS and Stats started picking up.

   We saw from the data that mathematicians at Texas A&M University are collaborating more among subfields than with collaborators in Computer Science and Statistics. Moreover, we see that collaborations with Computer Science and Statistics have increased over the past few years, especially with the more newly emerging fields such as machine learning. Even so, we can identify that some subfields of mathematics such as Numerical Analysis are more active collaborators with other fields.

   During the collection of our datasets, we noticed that arXiv does not have “institution name” as one of the required fields when submitting preprints, so we had to go through a very time consuming process to filter out researchers at Texas A&M University. We would recommend APIs and scholarly databases to include institution names. Moreover, the arXiv API has several bugs that required us to include a mandatory sleep time between two consecutive calls, which made collecting the data slow. We didn’t use an API for the Dimensions data as it was downloadable, but it didn’t keep track of subfields.

   Initially, we wanted to collect data for more scientific fields and include Physics, Biology, Material Sciences, et cetera, however due to the slow speed of our data collection and filtering process, we had to scrap those plans. We must also note that many of the papers we found on Dimensions did not have corresponding entries on arXiv. In particular, arXiv seems more popular in Mathematics than it does in other disciplines, and older papers show up less often on arXiv as well. This means that we cannot reliably conclude which fields of Mathematics have more or less collaborations with non-Mathematical fields as our collaboration data is incomplete. For future work, we would like to explore APIs and databases that have field labels like arXiv, but also allow for a more smooth data collection so we can visualise our networks better.