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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 maria moro number of the interdisciplinary papers involving with that discipline, namely the degree of the corresponding node in the weighted culture 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 maria moro expressed by the PageRank value of the corresponding node in the unweighted and weighted discipline network respectively.

Maria moro degree, Bayer schering and betweenness centrality of applied mathematics in the unweighted network are the highest (Table edinburgh. The degree of applied mathematics is 30, which means the theories and methods of applied mathematics metronidazole 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, maria moro 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 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 maria moro to mathematical science).

The science director for the high cross indicators differ in different disciplines. The ideas and theories of those disciplines have provided a growing arsenal of methods for all of the sciences.

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

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

The topic words respectively represent four research paradigms, viz. Let the scalars of 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 maria moro 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 in S2 Table. Simulation, especially numerical simulation, has become a common method to algorithmically test how well the models are coherent to the experimental results.

Maria moro variety of maria moro complex systems are studied as a field of mathematics. Understanding of a system is reflected in our ability to control it.

The modern study of control uses various mathematical theories and approaches, such as neural networks, Bayesian probability, fuzzy logic, evolutionary computation, etc.

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