MDPI Entropy | Complex Networks and Their Applications—in Memory of Prof. Erik Bollt

Dr. Paul Laurienti and Dr. Jeremie Fish invite submissions for a special number on "Complex Networks and Their Applications—in Memory of Prof. Erik Bollt" that they are editing for the journal MDPI Entropy.

Posted Jul 25, 2026

By Amahury J. L. Díaz

5 min read

Special Issue Information

Dear Colleagues,

Professor Erik Bollt (born 24 April 1967, died 7 December 2025) was born in Bethesda Maryland. He was an applied mathematician, though his interests and reach spread to many other fields. Erik completed a B.A. in Applied Mathematics at the University of California Berkeley in 1990, followed by an M.S. (in 1992) and Ph. D. in Applied Mathematics (in 1995) at the University of Colorado at Boulder under the supervision of Professor James Meiss, becoming the first student to complete his Ph.D. in the new program there. Following his Ph.D., Erik joined the United States Military Academy as an Assistant Professor in 1995 and joined the Army Research Labs in 1996. He moved to the United States Naval Academy as an Assistant Professor in 1997, was promoted to Associate professor in 2000 and became a consultant to Los Alamos National Laboratories in 2001. In 2002, Erik joined Clarkson University as an Associate professor and was promoted to full professor in 2006. He earned a named professorship, the W. Jon Harrington Professor of Mathematics, in 2010. In 2017, Erik founded the Clarkson Center for Complex Systems Science (C3S2), becoming the founding director, a role he maintained until his death. Erik served as a mentor to dozens Ph.D. students and postdocs, organized several conferences and workshops and published a book titled “Applied Computational Measurable Dynamics” along the way.

Erik’s impact is far reaching due to his work in dynamical systems, chaos theory, network theory, dynamics on networks, the theoretical underpinnings of machine learning, data-driven science and much more. Erik began in dynamical systems, working on the Kolmogorov–Arnold–Moser theory (K.A.M theory), where he focused on controlling chaos, an interest that carried with him throughout much of his early career. During this time, he demonstrated how a variety of nonlinear, chaotic dynamical systems could be controlled, both discrete (such as the logistic and tent maps) and continuous (such as the Lorenz system).

It was during this early stage of his career that Erik developed a substantial interest in the Shannon information theory and complexity, which he would carry with him throughout the entirety of his career. This began with encoding and decoding messages in chaotic dynamical systems, but would eventually lead to the development of optimal causation entropy, which he used both for data-driven inference of network structure from time series, as well as sparse identification with his work developing entropic regression.

Erik also was deeply interested in complex networks, particularly in synchronization on complex networks. He was an early entrant into the field of temporal networks, contributing several papers on the topic, specifically working on synchronization on temporal networks. He also demonstrated interest in the structure of networks, often tied to how dynamical processes operated on them, including works on cycles in networks, network growth processes, discovering the “backbones” of networks and more.

Machine learning, specifically an understanding of theoretical underpinnings, was also a passion of Erik’s. For instance, he demonstrated the relationship between reservoir computers and nonlinear vector autoregression, allowing for a technique called next generation reservoir computers, which strips out the random nature of the reservoir computer while maintaining its surprising success at forecasting chaotic systems. He also began work on expanding the frontier of the powerful Kolmogorov–Arnold networks (KANs). Both the data-driven discovery of KANs and widening the use case of KANs to things like auto-encoders and physics-informed learning happened under his purview.

As can be seen, Erik’s work was highly interdisciplinary, including people from numerous scientific fields and was always searching catchy paper titles such as “How famous is a scientist?—Famous to those who know us.” Several of his works were highlighted in the popular press on a variety of topics, including one on the synchronization of cows and another on reservoir computing, displaying how his impact spilled over beyond just the scientific community. The field of complex systems has been shaped and influenced by his work. He will be missed by us all and the field will now miss one of its leaders and innovating thinkers.

This Special Issue, in honor of the memory of Erik, focuses on the structure and function of complex networks and their applications across fields ranging from biology to economics. We are interested in new methodologies to infer network structure or to assess network topology. Studies are also welcome that apply advanced methods to understand network organization. We encourage the use of methods from information theory or dynamical systems as these were key topics of interest for Dr. Bollt. Submissions can be focused on social networks, brain connectomes, biological networks, economic networks or other systems that can be modeled and studied using network science methods.

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI’s English editing service prior to publication or during author revisions.