Ordinal methods: Concepts, applications, new developments and challenges

The workshop, initially planned for spring 2021, was held from 28th February to 4th March in a hybrid format with 64 registered participants from five continents, of which 15 were on-site participants from Brazil, Germany, Greece, the Netherlands and Spain, and 49 were virtual participants from 15 countries incl. New Zealand, Australia, China, Japan, Cameroon, Argentina, to name a few. A total of 42 talks were given, 15 by the on-site participants and 27 by on-line participants.

In the center of the workshop were the application of the concept of ordinal pattern in different fields and theoretical aspects related to this concept. The topics discussed included permutation entropy, causality detection, ordinal networks, the entropy-complexity plane, and others. The workshop was highly interdisciplinary. It brought together researchers from different disciplines such as physics, mathematics, statistics, data analysis and computer sciences, interested in the theoretical aspects and practical applications of ordinal patterns, to discuss recent developments and challenges. The talks were supplemented by two discussion sessions, one on 'Ordinal Patterns and Machine Learning' and one on 'Statistical Aspects of Ordinal Pattern Distributions'.

With very few exceptions, the talks given in the workshop were of a high level, including those of newcomers who presented their work. A special highlight was the on-site colloquium lecture "Climate Meets Complex Systems: Exploring Predictability of Extreme Climate Events via a Complex Network Approach (on-site)" by Jürgen Kurths (Potsdam Institute for Climate Impact Research), presenting an overview of results of his working group. The on-site opening talk by Christoph Bandt (University of Greifswald) included interesting results and ideas for a further development of statistical methods based on ordinal pattern distributions. In some talks, the importance of ordinal networks to quantify complexity and coupling, as well as to detect causality was worked out. Moreover, impulses for new applications of ordinal patterns were given.

It is expected that this workshop will contribute to a further development of the field of ordinal patterns in the context of describing and investigating complex phenomena and data, particularly on the basis of newly established contacts and agreed collaborations. A Focus Issue of the journal Chaos on the topics of the workshop is being prepared to publish research papers and mini reviews, including work and ideas presented at the workshop.

Both from a scientific and social viewpoint, the workshop was very successful. This would not have been the case without the perfect organizational support provided by Dr. Michael Genkin and, particularly, Ms. Maria Voigt, and the perfect technical assistance by Mr. Ronny Börner regarding the virtual participation.