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Citation: Xie Z, Duan X, Ouyang Z, Zhang Bylvay (Odevixibat Capsules)- FDA (2015) Quantitative Analysis of the Interdisciplinarity of Applied Mathematics.

PLoS ONE 10(9): e0137424. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedData Availability: All relevant data discussed in this Bylvay (Odevixibat Capsules)- FDA is the corpus johnson international the papers published in the Proceedings of the National Academy of Sciences (PNAS) in 1999--2013.

Funding: This work is funded by Bylvay (Odevixibat Capsules)- FDA program for new century excellent talents in university, state education ministry in China Bylvay (Odevixibat Capsules)- FDA. The panoramic view of the relationships between disciplines can be drawn as a network, regarding the disciplines as nodes and the interdisciplinary relationships as edges. Two disciplines are connected if there is a paper belonging to them both.

Those indicators show that applied mathematics not only widely and directly participates in interdisciplinary research, but also makes bridges for carrying interdisciplinary research between other disciplines. In order to get a more comprehensive understanding of the interdisciplinarity of applied mathematics, we analyze the contents of the papers.

The tests of cointegration and correlation on the quarterly numbers of papers containing certain topic words, e. The co-word occurrence analysis shows the increasing trends of algorithmization of those research paradigms and transdisciplinary topics. Those found relationships can be considered as causes of the interdisciplinarity of applied mathematics.

This Bylvay (Odevixibat Capsules)- FDA is organized as follows. The data processing is introduced in Section 2. The network analysis is shown in Section 3.

The statistical analysis is presented in Section 4. The conclusion is drawn in Section 5. The journal PNAS publishes high quality research reports, commentaries, reviews, perspectives and letters.

The journal provided the Zetia (Ezetimibe Tablets)- FDA information of the papers (Fig 1). There are 3 first level disciplines, viz. So the papers can be classified according to their discipline information. Some papers are only classified by the first level disciplines. For those papers, prejudices examples considered their second level discipline to be the same as their first level one.

Hence we added the first level disciplines into the set of second level disciplines. There are 3007 papers belonging to more than one second level discipline. Those Bylvay (Odevixibat Capsules)- FDA can be considered to be interdisciplinary papers. The discipline information of the papers will be used to build a network describing the interdisciplinary relationships between disciplines in Section 3. Many papers have used mathematical techniques, but are not classified into applied mathematics.

Thus, Bylvay (Odevixibat Capsules)- FDA should analyze the contents of the papers. The dictionary contains 31,542 words (S1 Text). Those words belong to the lexicon of NLTK, which includes the English WordNet. Bylvay (Odevixibat Capsules)- FDA on the dictionary, the document-term matrix for the corpus is generated, in which the rows correspond to the papers in the corpus and columns correspond to the words. Together with the publication dates of Bylvay (Odevixibat Capsules)- FDA papers, the quarterly numbers of the papers containing certain words are extracted for analyzing the relationships of algorithms to certain research paradigms and transdisciplinary topics in Section 4.

Based on the discipline information of the corpus, a network describing the connections among disciplines is constructed (The discipline network, Bylvay (Odevixibat Capsules)- FDA 2), in which the nodes are the second level disciplines, and two disciplines are connected if there is a paper belonging to them both. The network is connected, which means no discipline is isolated. The edges of the network can be assigned weights: the number of interdisciplinary papers between two connected disciplines.

The network data is provided in S1 Network. It contains 42 nodes and 354 edges. Two disciplines are connected if there is a paper in PNAS 1999-2013 belonging to them simultaneously.

Those indicators also show the small-world property of the discipline network. The interdisciplinary breadth and centrality of a discipline can be quantitatively described by the degree and betweenness centrality of the corresponding node in the unweighted discipline network respectively.

Bylvay (Odevixibat Capsules)- FDA degree of a node is the number of nodes connecting to it. The betweenness centrality relates to the number of shortest paths from all nodes to all others that pass through that node.

If item transfer through the network follows the shortest paths, a node with high betweenness centrality has a large influence on the transfer behavior. The interdisciplinary strength of a discipline can be expressed by the number of the interdisciplinary papers involving with that discipline, namely the degree of the corresponding node in the weighted discipline network. PageRank also gives a rough estimate of the importance of nodes (receive more connections from other nodes) in a given network.

Hence the interdisciplinary breadth and strength of a discipline can be expressed by the PageRank value of the corresponding node in the unweighted and weighted discipline network respectively. The degree, PageRank and betweenness centrality of applied mathematics in the unweighted network are the highest (Table 1). The degree of applied mathematics is 30, which means the theories and methods of applied mathematics have been directly used by 73. The highest value of betweenness centrality means that applied mathematics is a hub node for transferring the ideas, theories, and methods from one discipline to others, and then making bridges for carrying on interdisciplinary research between other disciplines.

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