Splines can recover dynamic information contained in discrete data

摘要

We have shown why the use of splines is an interesting method to describe discrete, cumulative data, even if citation data can be connected directly by a polygonal line. Such a polygonal line contains no change in information because its first derivative is a constant and its second derivative is zero (in the points where these derivatives exist). A spline-fitted curve however can represent changing information. All information about change resides in the original data. Splines not only reflect this change, but keep this information. By integration and the use of differential calculus we can revive and reproduce the original information. In this sense, we like to say that splines behave like a hologram: both are able to recover the original information.