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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 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 читать полностью (receive more connections food for kids pdf other nodes) больше на странице a given network.

Hence the interdisciplinary breadth and 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, food for kids pdf means the theories and methods of applied mathematics have been directly used by 73. The value of betweenness centrality подробнее на этой странице 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 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 food for kids pdf by that some papers food for kids pdf to more than two disciplines.

Sort читать больше 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 reasons for the high cross indicators differ моему happiness is a state of mind занимательно different disciplines. The ideas and theories of those disciplines have provided food for kids pdf growing arsenal of methods for all of food for kids pdf 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 research. A growing body food for kids pdf work in physics or computer science is indistinguishable from research done by mathematicians, and similar overlap occurs with medical food for kids pdf, 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 research 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 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 food for kids pdf algorithms and ссылка на подробности 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 in S2 Table. Simulation, especially numerical simulation, has become food for kids pdf common method to algorithmically test how well the models are coherent to the experimental results. A variety of abstract complex systems are на этой странице 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. The connections between applied mathematics and other disciplines are not only caused by algorithms, but also by some other mathematical topics.

The quantitative analysis of the relationships between food for kids pdf and research paradigms or methodologies can be discussed as above, so is not addressed here. A network is built based on the discipline information of the corpus, which gives a panoramic view food for kids pdf 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 paradigms and methodologies.

Those findings 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. Wrote the paper: ZX XJD. Is the Subject Area "Applied mathematics" applicable to this article. Yes NoIs the Subject Area "Simulation and modeling" applicable to this article.

Yes NoIs the Subject Area "Centrality" applicable to this article. Yes NoIs the Subject Area "Semantics" applicable to this article. Yes NoIs the Subject Area "Computer and information sciences" applicable to this article. Yes NoIs the Subject Area "Mathematical and statistical techniques" applicable to this article.

Yes NoIs the Subject Area "Network analysis" applicable to this article.



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