Interview with Remco van der Hofstad and Henk Nijmeijer

Mathematics for complexity

Mathematics for complexity

Remco van der Hofstad and Henk Nijmeijer present new plans for the ICMS focus area Grip on Complexity. At the heart will be a mathematics inspired approach that combines Network Theory with expertise from the field of Dynamics and Control. And it’s not only about gaining understanding; the design and synthesis of new complex systems will be an integral part. The first such system is in the exciting new field of Biological Computing.

What is to be expected when complex molecular systems are studied from the proposed viewpoint? Remco van der Hofstad, the younger and more outspoken of the two mathematicians, explains: “The essence of complex systems is the large number of components that are all connected to each other. Although these mutual interactions can in themselves be simple and predictable, on the scale of the entire system they can lead to emergent and unpredictable behavior. By applying mathematics we want to discover how to deal with such phenomena. Not just to understand them, but also to use the knowledge for the sensible design of novel complex systems”.



Van der Hofstad contributes with his expertise in stochastic Network analysis, his elder and more cautiously speaking colleague Henk Nijmeijer has extensive experience in the field of Dynamics and Control. Working at the department of Mechanical Engineering, Nijmeijer approaches complexity from a ‘systems of systems’ perspective where mathematics complements experiments and systems design. “We are for instance concerned with developments in vehicle automation, such as cooperative driving. There you create a new driving entity, a new system consisting of individual systems – the cars. Each has its own characteristics in vehicle dynamics, but you want them to synchronize their driving and operate as a new, composed entity. We think that knowledge developed in the field of Dynamics and Control will benefit multiple other systems, for instance human tissue consisting of individual cells.” Van der Hofstad is excited about cooperating with Nijmeijer: “Put bluntly, in Henk’s field you have complex dynamic entities in a relatively simple network, in my field the network is complex and the dynamics are fairly simple. It is exciting to bring these two approaches together to investigate complex networks consisting of complex dynamic entities. We want to explore what can still be modelled then, and how.”



The question of course is what these mathematical explorations of complexity might bring the field of complex molecular systems. Van der Hofstad: “At the celebration of the 10th anniversary of ICMS I have sort of jokingly said that we might consider the future use of the abbreviation ‘ICMS’ for ‘Institute of Complex and Molecular Systems’. But jokes aside, at the ICMS focus area Grip on Complexity we explicitly expand our scope beyond molecular systems. We set out to further develop this focus area from a broad fundamental perspective, which after all is the forte of ICMS.” Nijmeijer adds: “Complex systems are all around us: large ones, such as the climate, the Internet and the global economy, and smaller ones, such as a platoon of cooperative vehicles, drones or mobile robots. We think that by combining the strength of TU/e both in Dynamics and Control and in Network analysis we will be able to contribute to the broader field of complexity. This will, in the end, also be of relevance to molecular systems, of course. For instance, if complexity research helps to understand how thousands of biomolecules in our bodies react to each other in networks, we will be able to develop new drugs for serious diseases such as cancer. And we will learn to design biochemical molecules that assemble themselves into new, smarter materials that would otherwise not be produced.”



Approaching complexity from a thorough mathematical viewpoint perfectly fits the TU/e, the professors argue. Being a University of Technology, mathematics is widely supported and appreciated. After all, it is the language of engineers, and of engineering sciences. Nijmeijer: “As mathematicians, or rather as researchers having a mathematics background, at TU/e we are comfortable being in touch with other disciplines. Which perfectly fits another main aspect of ICMS, that of interdisciplinarity. We live in an era where the developments will really take place in multidisciplinary fields. We do not have to abandon disciplinary approaches, certainly not, as these form our core competencies. But I think that many disciplines will see the need to work in a multidisciplinary way.” Van der Hofstad adds: “In fact, throughout TU/e the theme of complexity has a rather strong presence, even though it is not always very visible as such. Whether you develop molecular systems, photonic systems, software systems and so forth, very often there is a complexity aspect to it.” On the other hand, cooperating with researchers from other disciplines is not always easy. Nijmeijer: “Every expertise area is full of jargon, so it might take quite some time before you really understand each other. I have run projects with IT specialists, with mechanical engineers, with electrical engineers. It could take a year before it was perfectly clear what exactly was meant by the term ‘system’ or ‘model’. But there is always a strong feeling that mathematical language has a connecting role.”



An explicit goal of the focus area Grip on Complexity is to not only increase the understanding of complexity itself, but also to design and synthesize complex systems based on the findings. A concrete example of this aspect of ‘engineering complexity’ is the research of ICMS scientist, Tom de Greef, towards biological computing. This rapidly growing research field includes biological programs that store data in (and retrieve data from) living cells, or memory devices that can record molecular events directly onto DNA. Exciting applications of biological computing devices are emerging in the area of cancer immunotherapy and biosensing, but can also be expected in other areas such as tissue engineering or chemical biology. The investigation of biological computing from a complexity perspective is a quite promising approach, since complexity research worldwide is predominantly aimed at acquiring understanding. Van der Hofstad: “Most complexity research does little work regarding synthesis: building systems, generating data and trying to understand the system through mathematical modeling. I expect ICMS to really stand out in this perspective.”



Van der Hofstad and Nijmeijer expect to build future bridges reaching out from the Grip on Complexity focus area towards other ICMS focus areas. All ICMS researchers will at one time or another experience issues that touch the theme of complexity, whether their research is about molecular devices, regenerative materials, novel polymers or artificial cells. Van der Hofstad: “We are more than willing to help by complementing their efforts with our theoretical framework. As a matter of fact that does not have to be limited to theories of Networks or Dynamics and Control, but can be much broader. We can help formulate the right model for what people are building or observing. I would not go so far as to call our focus area a ‘help desk’, but we will for certain make an inventory of the complexity issues within ICMS by means of seminars and workshop. We really think this will be very exciting.”