Distance-based analysis of dynamical systems and time series by optimal transport
Muskulus, M.
Citation
Muskulus, M. (2010, February 11). Distance-based analysis of
dynamical systems and time series by optimal transport. Retrieved from https://hdl.handle.net/1887/14735
Version: Corrected Publisher’s Version License:
Licence agreement concerning inclusion of doctoral thesis in the Institutional Repository of the University of Leiden
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Prologue
Of course this limits me to being there in my being only in so far as I think that I am in my thought; just how far I actually think this concerns only myself and if I say it, interests no one.
Jacques Lacan1
T
he scientific endeavour has grown enormously in recent decades, with many new scientific journals being set up to accomodate the continuing flood of re- search papers. It is a sobering fact that many of these articles are never read at all, or more precisely, are never being cited in a research context (Meho,2007). Some of the reasons for this development are probably the rising popularity of quantitative eval- uations of the research output of scientists, measured in the number of publications produced, by university administrations and research agencies.In my experience, the majority of journal articles belong to three distinct cate- gories. Depending on whether to locate the subject of the research on either the methodological or the experimental side, many scientific publications describe mi- nor modifications of existing methods or, on the other hand, report empirical find- ings obtained under minor modifications of experimental protocol. These modifica- tions are necessary to guarantee the status of a truly innovative work or, put differ- ently, to avoid the vice of double publication, but apart from a limited set of experts working on the same subject the value of these findings is often questionable to a broader scientific public. More frightening is the thought that most of these find- ings might actually be false: Methodological improvements do not always merit the effort to realize them in practice, and empirical findings might be purely coinciden- tal (Ioannidis,2005). Even in mathematics, where rigorous proofs can be had, and which consequently does not belong under the general heading of science, technical improvements do sometimes not lead to further our understanding of the subject matter (e.g., as in the computer-assisted proof of the four-colour theorem by Appel and Haken). The third major category of publications are of a secondary nature and
1 On “’cogito ergo sum’ ubi cogito, ibi sum” [Where I think ’I think, therefore I am’, there I am].
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Prologue
consist of editorials, commentaries, letters and review articles. These do not present new findings, and although of occasional interest to readers most of these, disregard- ing the latter, never find themselves being cited. Review articles are often highly valued, however, since they not only lend themselves as introductions to a specific research trend, but offer advice and insight that goes beyond mere exposition, and in the best case combine relevant publications that would otherwise go unnoticed in a focussed way.
Regarding the above, it is my opinion that there is much value in reviewing and combining seemingly unrelated fields of research and their tools, which might be one way to define the ubiquitious term interdisciplinary research. Indeed, I think that many important methods and ideas do already exist in the large scientific literature, but experience seems to confirm that these are often less well known in other areas of science where they might be favourably used. This transfer of knowledge across boundaries of scientific disciplines is usually not easy. The scientific conservation- ism exposed by Thomas Kuhn in 1962 seems not to have diminished over time, and it is still difficult to convince scientists from other disciplines about the value of tech- niques they are not already familiar with. To overcome such scepticism it is neces- sary to concentrate on essential and proven methods, and to exhibit their advantages (and disadvantages) in as clear a way as possible.
In this thesis I have therefore tried to use well known tools from a variety of distinct (sub-) disciplines in statistics, physics and the theory of dynamical systems to derive new and nontrivial insights in various fields of application, by combining long established and robust ideas in a general framework. To be convincing appli- cations, this involved a lot of time implementing these methods as actually useable computer code, closing quite a few gaps in existing software and collecting the nec- essary tools in one central place. The text of this thesis follows the same idea of mak- ing essentially all of the necessary methods understandable and accessible, even to non-experts. As the reader might imagine, a lot of ideas and results that did not fit into this presentation have been left out (but many of these are discussed cursorily in notes), and, to a mathematician, quite a frightening amount of redundancy might have crept into the text.
I hope the reader will appreciate this effort.
Michael Muskulus Leiden, January 2010
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