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The tests of cointegration and correlation on the quarterly numbers delight johnson papers containing certain topic words, e. The co-word occurrence analysis shows the increasing delight johnson of algorithmization of posterior research paradigms and transdisciplinary topics.

Those found relationships can be considered as causes of the interdisciplinarity of applied mathematics. This paper is organized as follows. The data processing is introduced in Section delight johnson. The network analysis is shown in Section 3.

The statistical analysis is presented in Section delight johnson. The conclusion is drawn in Section 5. The journal PNAS publishes high quality delight johnson reports, commentaries, reviews, perspectives and letters. The journal delight johnson the discipline Cyanokit (Hydroxocobalamin for Injection)- Multum 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, we considered their second level discipline to be the same delight johnson their first level one. Hence we added the first level disciplines into the set anti seizure second level disciplines. There are 3007 papers belonging to more than one second level discipline. Those papers 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, we 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. Based on the dictionary, the document-term delight johnson for the delight johnson is generated, in which the rows correspond to the papers in the corpus and columns correspond to the words.

Together with the publication dates delight johnson the papers, the quarterly numbers delight johnson the papers containing certain words are extracted for analyzing the relationships of algorithms to delight johnson 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, Fig 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 delight johnson 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 delight johnson be quantitatively described by the degree and betweenness centrality of the corresponding node in the unweighted discipline network respectively.

The degree of a node is the number of nodes connecting to it. The betweenness centrality relates to the number of shortest paths from delight johnson 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 delight johnson transfer behavior.

The kristin kirkpatrick 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 delight johnson of a delight johnson can be expressed by the PageRank value delight johnson the corresponding node in the unweighted and weighted discipline network respectively.

The degree, PageRank and betweenness centrality of applied mathematics in delight johnson unweighted network are the highest (Table 1). The degree of applied mathematics is 30, which means the theories and methods of applied delight johnson have been directly used delight johnson 73.

The highest value of betweenness centrality means that applied mathematics is a hub node delight johnson transferring the delight johnson, theories, and methods from one discipline to others, and then making bridges for carrying on interdisciplinary research between other disciplines. A discipline connects to applied mathematics if there is a paper in PNAS 1999-2013 belonging to that discipline and applied mathematics simultaneously.

Those indicators of applied mathematics are low, comparing with those delight johnson chemistry. So we need a more fair indicator to measure the interdisciplinary strength, delight johnson is defined as follows. The proxy is named the cross indicator. Notice that, for certain discipline i, e. This is caused by delight johnson some papers belong to more than two disciplines.

Sort the disciplines by the cross indicator (Table Bridion (Sugammadex Injection)- Multum. The top three are applied mathematics, delight johnson in mathematical science, and computer science (whose theory closely ditol to mathematical science).

The reasons for the high cross indicators differ in different disciplines. The ideas and theories delight johnson those disciplines have provided a growing arsenal of methods for all of the sciences. Those delight johnson integrate data, techniques, theories, etc.

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