*Correspondence:
This article was submitted to Fractal Physiology, a section of the journal Frontiers in Physiology.
Edited by: Richard E. Moon, Duke University, USA
Reviewed by: Nicola Scafetta, Duke University, USA; James Andrew Dixon, University of Connecticut, USA; Damian Kelty-Stephen, Grinnell College, USA; Sebastian Wallot, Aarhus University, Denmark
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Multifractal formalism and analysis have been described many times (Lopes and Betrouni,
Ihlen's presentation of MFDFA stands out from others in a number of respects. The article presents a recent and advanced concept, but it manages to do so at a level which anyone with basic MATLAB skills, independent of scientific background, should be able to follow. A similar paper would likely be found in the documentation of an MFDFA software library. However, Ihlen's paper appeared in a scientific journal. Thanks to this fact, and a proper peer-review, this “tutorial page” from a package's documentation offers a manual that is informative, easy to digest, yet is scientifically correct and elucidates a useful mathematical method of signal analysis to researchers without experience with complex mathematical notation.
Scientific method should not be a black box. The purpose of software in science is similar to the purpose of mathematics: it is a tool for the communication of ideas. Often, mathematics and software complement each other: while mathematics is more abstract and general, software is the choice for practical applications. Both methods of communication fulfill their roles in science only if their products are well understood. Understanding mathematical descriptions requires brainpower, years of education and practical application. In the case of software, many of the requirements can be “downloaded.” The download approach, however, opens up a new space for errors due to inappropriate application of the method. Such errors can often be avoided if the workings of a method are clear and well explained.
Is there a better way to teach a method than by demonstrating it, and its crucial properties, with real examples? The paper of Ihlen perhaps did not aim to follow the ideas of literate programming proposed by Knuth (
The tutorial approach worked well and helped me not only to adopt MFDFA in my analyses, but also to apply it across implementation language boundaries. To this end I have reproduced some of Ihlen's results in the Python programming language in the form of an interactive notebook (
The approach of notebooks and literate programming has one important benefit for any single author who offers scientific software for reuse: the access to a proper code review. No serious business releases code without a proper review; its reputation and potential for customers depend on it. In research backed by software, it seems that only the correctness of results matter; how we get them is secondary. Very few reviews will ever venture beyond the proverbial double click and a visual confirmation of expected results. However, if the method is reused, currently it is most often reused through the software. It is thus the software, not just its verbal or mathematical description, which should be reviewed. This can be facilitated by making software code into an intrinsic part of an article, following Ihlen's approach or Knuth's suggestions. Interactive reviews are already possible, for example through interactive notebooks (Shen,
The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
I would like to thank Z. Struzik for introduction of the methods and helpful comments during writing of this article.