Concentration places, concentration evolutions and online information retrieval techniques for caculating them

Abstract

Suppose we have N unordered classes to which objects can belong (i.e., articles dealing primarily with a certain broad topic; we have then N topics). We define the concentration place relative to a certain permutation σ of the set {1,….,N}. We show that the concept is good in different ways. We then give a theory of concentration evolution resulting in a nontrivial problem in operations research. We calculate levels of evolutions as well as directions of evolutions. Once they are calculated, these data give valuable information on how interests in certain topics can change along the years. Comparisons between the evolution of a journal and the evolution of the whole subject can be made as well as comparisons between the evolution of two journals. Also, the velocity of evolution can be measured with this theory.

An explicit examination is done for the Transactions of the American Mathematical Society, in comparison with mathematics as a whole.