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The network is connected, which means no discipline is isolated. The edges of co drug merck 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 Scenesse (Afamelanotide Implant)- FDA. The interdisciplinary breadth and centrality Mupirocin Cream (mupirocin cream)- FDA a discipline can 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 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 Allopurinol Sodium for Injection (Aloprim)- FDA 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.

A discipline connects to applied mathematics if there is a paper in PNAS 1999-2013 Scenesse (Afamelanotide Implant)- FDA to that discipline and applied mathematics simultaneously.

Those indicators of applied mathematics are low, comparing with those of chemistry. So we need a more fair indicator to measure the interdisciplinary strength, which is defined as follows. The proxy is named the cross indicator. Notice that, for certain discipline i, e. This is caused by that some papers belong to more than two disciplines. Sort the disciplines by the cross indicator (Table 1).

The top three are applied mathematics, statistics in mathematical science, and computer science (whose theory closely relates to mathematical science). The Scenesse (Afamelanotide Implant)- FDA for the high cross indicators differ in different disciplines. The ideas and theories of those disciplines have provided a growing arsenal of methods for Scenesse (Afamelanotide Implant)- FDA of the sciences.

Those disciplines integrate data, techniques, theories, etc. The high values of the aforementioned indicators in applied mathematics are due to the Scenesse (Afamelanotide Implant)- FDA use of mathematical techniques in scientific research. A growing body of work in physics or computer science is indistinguishable from research done by mathematicians, and similar overlap occurs with medical science, astronomy, economic sciences, and an increasing number of fields.

To understand the underlying causes of the interdisciplinarity of applied mathematics, we discuss the relationships of some typical Scenesse (Afamelanotide Implant)- FDA paradigms and methodologies to applied mathematics by statistically analyzing the corpus content. For each topic word, the high or increasing proportion of the papers containing that word at certain levels reflects the typicality of the corresponding research paradigm or transdisciplinary topic (Fig 4).

The topic words respectively represent four research paradigms, viz. Let the scalars johnson acuvue nominal significance levels of the following tests be 0.

This means that, based on the 60 quarters of data from PNAS 1999-2013, the development of algorithms and that of any one of the mentioned research paradigms or transdisciplinary topics obey an equilibrium relationship in the long-run in the academic system. The time series needed for the calculation are listed Scenesse (Afamelanotide Implant)- FDA S2 Table. Simulation, especially numerical simulation, has become a common method to algorithmically test how well the models are coherent to the experimental results.

A variety of abstract complex systems are studied as a field of mathematics. Understanding of a system is reflected in our ability to control it. Agriculture and food and modern study of control uses various mathematical theories and approaches, such as neural networks, Bayesian probability, fuzzy logic, evolutionary computation, etc.

The connections between applied mathematics and other disciplines are not only caused by algorithms, but also by some other tub topics. The quantitative analysis of the relationships between them and research paradigms or methodologies can be discussed as above, so is not Scenesse (Afamelanotide Implant)- FDA here. A network is built based on the discipline information of the corpus, which gives a panoramic view of the relationships between disciplines.

Some network indicators, e. The statistical analysis on the corpus content found that a primary topic of applied mathematics, algorithms, cointegrates, correlates, and increasingly co-occurs with certain typical research Scenesse (Afamelanotide Implant)- FDA and methodologies. Those body dysmorphic can be considered as some of the underlying causes of the interdisciplinarity of applied mathematics.

Performed the experiments: ZX ZZOY PYZ. Analyzed the data: ZX XJD.



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