The correlation coefficients of certain time series pairs.

<p>In each table cell, the first value is the Spearman’s rank correlation coefficient, and the second value is the Pearson product-moment correlation coefficient.</p><p>The correlation coefficients of certain time series pairs.</p

Certain quantitative indicators for the interdisciplinarity of disciplines.

<p>The degree, PageRank and betweenness centrality of the nodes in the unweighted (weighted) discipline network are denoted by <i>K</i> (<i>K</i>_<i>W</i>), <i>P</i> (<i>P</i>_<i>W</i>), and <i>B</i> respectively. The interdisciplinary strength is <i>S</i> = <i>M</i>/<i>N</i> and the cross indicator is <i>C</i> = <i>SK</i>, where <i>N</i> is the number of the papers and <i>M</i> is the number of the interdisciplinary papers of a certain discipline in PNAS 1999–2013.</p><p>Certain quantitative indicators for the interdisciplinarity of disciplines.</p

The quarterly proportions of the papers containing a certain topic word.

<p>The topic words respectively represent four research paradigms, viz. model, experiment, simulation, and data-driven, and three transdisciplinary topics, viz. system, network, and control.</p

Quantitative Analysis of the Interdisciplinarity of Applied Mathematics

<div><p>The increasing use of mathematical techniques in scientific research leads to the interdisciplinarity of applied mathematics. This viewpoint is validated quantitatively here by statistical and network analysis on the corpus PNAS 1999–2013. A network describing the interdisciplinary relationships between disciplines in a panoramic view is built based on the corpus. Specific network indicators show the hub role of applied mathematics in interdisciplinary research. The statistical analysis on the corpus content finds that algorithms, a primary topic of applied mathematics, positively correlates, increasingly co-occurs, and has an equilibrium relationship in the long-run with certain typical research paradigms and methodologies. The finding can be understood as an intrinsic cause of the interdisciplinarity of applied mathematics.</p></div

The slopes of the linear fitting of certain time series.

<p>The time series are the annual proportion of papers containing “algorithm” and a certain topic word (the column heading) amongst papers containing that word (the first row), and amongst all of the papers (the second row).</p><p>The slopes of the linear fitting of certain time series.</p

The discipline information given by PNAS.

<p>The panels (a,b) respectively come from <a href="http://www.pnas.org/content/110/18.toc" target="_blank">http://www.pnas.org/content/110/18.toc</a>, <a href="http://www.pnas.org/content/110/18.toc#PhysicalSciences" target="_blank">http://www.pnas.org/content/110/18.toc#PhysicalSciences</a>.</p

The discipline network.

<p>It contains 42 nodes and 354 edges. Two disciplines are connected if there is a paper in PNAS 1999-2013 belonging to them simultaneously.</p

The quarterly proportions of the papers containing “algorithm” and a certain topic word amongst the papers containing that word (Panels (a,b)), and amongst all of the papers (Panels (c,d)).

<p>The quarterly proportions of the papers containing “algorithm” and a certain topic word amongst the papers containing that word (Panels (a,b)), and amongst all of the papers (Panels (c,d)).</p

The boolean decisions of the Johansen test on certain time series pairs.

<p>When doing the test, we let the scalars of nominal significance levels be 0.05, choose the lagged difference in {1, …, 3} by AIC, and assume that there are intercepts and linear trends in the cointegrating relations and there are quadratic trends in the data. The values equal to 1 indicate cointegration, and 0 indicate not.</p><p>The boolean decisions of the Johansen test on certain time series pairs.</p

Empirical citation networks.

<p>Empirical citation networks.</p