# A 12-year Analysis of Malmquist Total Factor Productivity in by Kontodimopoulos N., Niakas D.

By Kontodimopoulos N., Niakas D.

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Extra info for A 12-year Analysis of Malmquist Total Factor Productivity in Dialysis Facilities

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Adapting our approach to this problem is straightforward - instead of using the ”random surfer” model (which goes uniformly at random from a web page to one of the pages it points to) [14] we use a ”content biased surfer”. This new ”surfer” simply goes from one page to another one it points to with a probability that is proportional to the relevance of its content to the query. 3 Method Let us recall the deﬁnitions of eigenvector centrality and PageRank centrality, and rephrase the last paragraph of section 2 with more rigor.

And then somehow combine ci and si to get a ﬁnal rank ri . Here we ask the following question: why should the surfer keep clicking on links completely at random? What happens if he chooses a link with a probability that is proportional to the relevance of its destination to the topic of the surfer’s interest?

2 Related Work In [4] the authors modeled the spread of information in an email correspondence network essentially as a random branching process with oﬀspring distributed as the number of individuals to whom a person sends emails. The underlying premise in [4] was that if and only if the branching process is supercritical then a large fraction of the population will receive the information (see [8] for an introduction to branching processes). A more advanced approach was taken by [3] which presented a descriptive analysis of a cellular-phone network of oneto-one human communication.