Imagine dozens of robots sent into a disaster zone to search for victims, monitor a fragile ecosystem, or respond to a chemical spill. In these environments that are difficult or dangerous for humans, swarms of robots could one day play a valuable role. 

But to operate independently, they must first be able to agree on a course of action. And the task becomes more complicated when the information they exchange isn’t always reliable: a robot might malfunction, a sensor might provide incorrect data, or a message might be tampered with during a cyberattack.

Andreagiovanni Reina of the University of Konstanz, Marco Dorigo and Raina Zakir of the Free University of Brussels, and Timoteo Carletti of UNamur sought to understand how robots can reach agreement when they receive conflicting information. To find a solution, the researchers turned to nature and to a champion of collective decision-making: the honeybee. 

Indeed, when a colony needs to find a new place to build its nest, bees set out to explore the surroundings and return to advocate for different locations. Those supporting one location can then send a signal to deter the bees advocating for another. Gradually, certain options are abandoned, and the colony eventually agrees on a single destination. 

Researchers have replicated this logic in robots. When a robot receives information that contradicts its current choice, it does not immediately change its mind. It first goes through a brief moment of hesitation, during which it no longer supports any option, before being able to make a new choice. This brief hesitation makes all the difference. Even when some information is false or unreliable, robots generally manage to reach agreement more quickly and clearly. 

Even more surprising, researchers discovered that a limited amount of unreliable information could sometimes improve the outcome. These disruptions can prevent the swarm from agreeing too quickly on a poor option and increase its chances of ultimately choosing the best one. 

Similar mechanisms exist at various levels in nature, from neural networks to the mechanisms that regulate cells. This research thus bridges the gap between biology and robotics: living organisms inspire the design of more efficient robots, while experiments conducted with these robots provide a better understanding of certain mechanisms found in nature. 

Ultimately, this approach could help swarms of robots determine which area to explore first after a disaster or which environmental threat to address first. Congratulations to Timoteo Carletti and the entire team on this publication in *Nature Communications*! 

On Tuesday, June 23, the state visit began with an official banquet at the Château de Laeken. Among the approximately 150 guests was Alexandre Mauroy, a professor in the Department of Mathematics at the Faculty of Sciences of UNamur. Invited at the request of the Vice-Rector for International Relations and Cooperation, he represented the University of Namur due to his scientific collaborations with Japanese researchers, particularly in connection with a future Erasmus+ project with Kyoto University. “It was a wonderful opportunity to raise awareness of UNamur,” he explains.

At the Castle of Laeken, Alexandre Mauroy encountered a highly formalized protocol and an evening attended by numerous prominent figures. “At the cocktail reception, Prime Minister Bart De Wever was right next to me. At the end of the evening, the King was having his coffee just a few meters away. The next morning, I almost felt like I’d been dreaming.”

The next day, the imperial procession stopped at the Castle of Namur for a visit focused on water management. On this occasion, Isabelle Parmentier, a professor in the Department of History at the Faculty of Philosophy and Letters and a specialist in environmental history, was invited by the Governor of the Province of Namur to present a scholarly lecture on the province’s hydrological history. This topic was chosen because of Emperor Naruhito’s interest in issues related to water and the environment.

“It’s a truly special experience,” she explains. “I never would have imagined going through this a few years ago. I was very happy to be able to present my area of expertise to the monarchs.” After the presentations, she shared lunch at the table of the Emperor of Japan and King Philippe. “Protocol dictated that we not speak to them spontaneously, but the Emperor showed great interest in my presentation and asked me several questions.” 

Although their experiences were very different, Alexandre Mauroy and Isabelle Parmentier both share the same feeling: pride in having represented the University of Namur at an event that highlights the strength of relations between Belgium and Japan, as well as the international reach of the research conducted at UNamur. 

Cooperation lies at the heart of many human societies, ecosystems, and microbial communities. Yet it is constantly threatened by individuals who benefit from collective efforts without contributing themselves. A new study driven by an international collaboration between the teams lead by, Professor Dibakar Ghosh (ISI, Kolkata, India), Professor Matjaž Perc (University of Maribor, Slovenia) and Professor Timoteo Carletti (UNamur, naXys institute, Belgium) shows that the way individuals move within a network can play a decisive role in sustaining cooperation.

For decades, scientists have sought to understand why cooperation persists even though selfish behaviour often appears more advantageous in the short term. Classical theoretical models generally predict that “defectors” — individuals who benefit from a common resource without contributing to it — should eventually dominate.

Reality, however, tells a different story. In nature as well as in human societies, cooperation remains remarkably widespread. To investigate this apparent paradox, the researchers developed a mathematical model describing populations organized in groups modelled as nodes of a network, where cooperators and defectors can move between groups. Their analysis reveals an unexpected phenomenon: when defectors move faster than cooperators, their advantage can actually diminish. Because cooperators are less mobile, they tend to remain clustered together. These clusters create favourable conditions for mutual support and allow cooperation to persist despite the presence of opportunistic individuals.

The researchers also found that the structure of the network itself plays an important role. Highly connected nodes — comparable to transportation hubs or highly influential individuals in a social network — are particularly effective at sustaining cooperation. By contrast, more peripheral areas remain more vulnerable to defection.

These findings highlight a simple yet powerful mechanism: differences in mobility can promote the spontaneous emergence of stable cooperative communities. The results offer new insights into the dynamics of collective behaviour across a wide range of systems, from ecosystems and human societies to microbial populations.

The journal "Proceedings of the National Academy of Sciences" (PNAS), a peer-reviewed publication of the National Academy of Sciences (NAS), is a leading venue for high-impact original research spanning the biological, physical, and social sciences. The journal has a global reach and welcomes submissions from researchers around the world.

Congratulations to the researchers on this publication!

Alexandre Mauroy trained as a civil engineer. With a passion for mathematics, he embarked on an academic career that led him to specialize in the study of dynamic systems. A choice that reflects his taste for solving complex problems: "Dynamic systems are phenomena that evolve over time in a non-linear fashion, and do not obey the laws of proportionality. They therefore represent a real challenge for mathematicians, as their equations cannot be solved directly. And yet, non-linear systems are all around us, starting with the weather, our biological clock, road traffic or even the movement of a simple pendulum. So it's a very rich subject."

In his work, Alexandre Mauroy develops methods to better understand these dynamical systems. His stint at the University of Santa Barbara in California from 2011 to 2013 introduced him to operator theory, and in particular the Koopman operator, an original method for studying these unsolvable equations : "The idea may seem counter-intuitive, because we transform a finite-dimensional system into an infinite-dimensional one. It is then described by an infinite number of variables, but it becomes linear and can therefore be solved more easily. It's like using a kind of mathematical magic wand", he explains.

Koopman's operator is not new, however: it was first demonstrated in the 1930s before falling into oblivion. It was only revived in the 2000s. "It was the very beginning of the renaissance of this approach, we were pioneers", recalls Alexandre Mauroy. "Today, the Koopman operator has become very trendy in the scientific community."

And for good reason, many applications are possible thanks to this method. Among those studied by Alexandre Mauroy:

• The study of global stability of equilibria.
• The identification of network structure from observed data (e.g. connections between neurons in the brain or interactions between people).
• Control theory, halfway between mathematics and engineering sciences, which aims to impose the behavior of the dynamic system (e.g. car cruise control).

In this last field, Alexandre Mauroy is collaborating with Elio Tuci (Faculty of Computer Science) on the ARC "AUTOMATic" project, which aims to develop an intelligent urban traffic management system, thanks to data collected by drones. This project illustrates the interdisciplinary dimension of the naXys Institute's research and the "applied math" specificity of the teaching at UNamur's Mathematics Department, which is unique in the Wallonia-Brussels Federation.

In addition to his research activities, Alexandre Mauroy is involved in outreach work with secondary school students. The aim? To show that a world "without maths" would be very different from our own.

His message is clear: mathematics is everywhere, and mathematicians have a role to play alongside engineers and computer scientists, particularly in meeting the technological challenges of today and tomorrow.