# Independent simultaneous discoveries visualized through network analysis: the case of linear canonical transforms

## Abstract

We describe the structural dynamics of two groups of scientists in relation to the independent simultaneous discovery (i.e., definition and application) of linear canonical transforms. This mathematical construct was built as the transfer kernel of paraxial optical systems by Prof. Stuart A. Collins, working in the ElectroScience Laboratory in Ohio State University. At roughly the same time, it was established as the integral kernel that represents the preservation of uncertainty in quantum mechanics by Prof. Marcos Moshinsky and his postdoctoral associate, Dr. Christiane Quesne, at the Instituto de Física of the Universidad Nacional Autónoma de México. We are interested in the birth and parallel development of the two follower groups that have formed around the two seminal articles, which for more than two decades did not know and acknowledge each other. Each group had different motivations, purposes and applications, and worked in distinct professional environments. As we will show, Moshinsky–Quesne had been highly cited by his associates and students in Mexico and Europe when the importance of his work started to permeate various other mostly theoretical fields; Collins’ paper took more time to be referenced, but later originated a vast following notably among Chinese applied optical scientists. Through social network analysis we visualize the structure and development of these two major coauthoring groups, whose community dynamics shows two distinct patterns of communication that illustrate the disparity in the diffusion of theoretical and technological research.

## Keywords

Psychology of science Simultaneous discoveries Network analysis Scientific communication Linear canonical transforms## Mathematical Subject Classification

91D30 01A65 65R10## Notes

### Acknowledgments

The work of the first author has been supported by the project DGAPA-PAPIIT Nº IN305013_2014, of the Universidad Nacional Autónoma de México; the work of the second author has been supported by DGAPA-PAPIIT Nº101115. The authors also acknowledge the very useful comments of two anonymous reviewers.

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