Assessing Coupling Dynamics from an Ensemble of Time Series

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17.04.2014 (02.04.2015)

Assessing Coupling Dynamics from an Ensemble of Time Series, Gérman Gómez-Herrero, Wei Wu, Kalle Rutanen, Miguel C. Soriano, Gordon Pipa, Raul Vicente, Entropy 2015, 17, 1958-1970.

Official paper

Arxiv preprint


Finding interdependency relations between time series provides valuable knowledge about the processes that generated the signals. Information theory sets a natural framework for important classes of statistical dependencies. However, a reliable estimation from information-theoretic functionals is hampered when the dependency to be assessed is brief or evolves in time. Here, we show that these limitations can be partly alleviated when we have access to an ensemble of independent repetitions of the time series. In particular, we gear a data-efficient estimator of probability densities to make use of the full structure of trial-based measures. By doing so, we can obtain time-resolved estimates for a family of entropy combinations (including mutual information, transfer entropy and their conditional counterparts), which are more accurate than the simple average of individual estimates over trials. We show with simulated and real data generated by coupled electronic circuits that the proposed approach allows one to recover the time-resolved dynamics of the coupling between different subsystems.

Publication process

This paper was left unpublished in 2010, and placed into Arxiv to wait for some of the authors to do something about it.


One of the authors submitted the paper to the Entropy journal of MDPI.

I was uncomfortable with this choice, because a quick search revealed that Jeffrey Beall had added MDPI into its list of “questionable publishers”. As a direct reaction, OASPA carried out its own investigation, and cleared MDPI of the accusations. I still felt conflicted about the matter, since I had no ways to check on any of the facts, by either Beall or OASPA. Since the other authors did not raise an issue, I decided to see the review process through.


The first reviews arrived, requiring minor revisions. The reviewers of the papers were knowledgable of the topic, and also familiar with the paper in Arxiv beforehand.


The revised paper was sent to MDPI.


The paper was accepted. The communication between us and MDPI did not differ from other journals. We were charged 1200 CHF (1152 EUR) for an open-access publication of the paper.


The paper was published.

Open Access

This is my second experience on open-access publishing. It battles against my thoughts that authors should pay anything to get papers published, especially when the review is done by voluntary peers. However, I also do not think that the traditional model of artificially restricting access to publications is any good. I am imagining a future where papers are reviewed publicly and free-of-charge in collaborative sites similar to Stack Exchange.