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!

Heritage sciences are experiencing a resurgence at UNamur. This field of research—which involves applying techniques and expertise from the exact sciences (physics, chemistry, biology) to study ancient heritage objects—is reinventing itself thanks to the PHOENIX project, led by seven researchers from the Faculties of Science (Department of Physics) and Philosophy and Letters (Departments of History and Classical Languages and Literatures). 

“PHOENIX emerged from the collaboration of several researchers from different backgrounds, yet all driven by the same desire to study the materiality of heritage objects. One notable figure is Julien Colaux, whose predecessor had led the first heritage science projects at UNamur’s Laboratory of Analysis by Nuclear Reactions (LARN). It’s a sort of return to our roots,” recalls Nicolas Ruffini-Ronzani, a researcher in the Department of History, president of the PaTHs Institute, and one of the project’s leaders. 

With PHOENIX, researchers aim to “make” two types of objects speak: ancient coins and medieval parchments (see box). More specifically, their research is guided by three objectives:

• To understand the composition of the artifacts being studied. For the parchments, to identify the animal species (sheep, goat, or calf); and for the coins, to characterize the metal alloy.
• Gain a better understanding of the production and processing workflow. For example, determine which parts of the animal were used in the production of a parchment.
• To propose the most precise dating possible. 

It is in this last objective that the main challenge lies. “We won’t be able to date these objects to within a year,” warns Olivier Deparis, a professor in the Department of Physics and a member of the NISM research institute. “The idea is to provide a time frame that is as precise, if not more so, than that already provided by paleography (the study of ancient scripts) or textual analysis. If we can narrow it down to a quarter-century, that will already be a significant step forward.”

To achieve this, the PHOENIX team uses various non-invasive techniques, in particular infrared and Raman spectroscopy, time-of-flight secondary ion mass spectrometry (ToF-SIMS), and ion beam analysis (IBA). These approaches—which utilize UNamur’s state-of-the-art tools such as the ALTAÏS particle accelerator (see Omalius #36)—provide detailed information on the physicochemical composition of materials, such as the animal origin and ink formulations for parchments or the type of metal alloy for coins. “The use of the exact sciences will enrich our studies and thus allow us to better understand how these objects were produced in the past,” explains Nicolas Ruffini-Ronzani. “Contrary to what one might think, collaboration between the humanities and the exact sciences has a long history, dating back to the 19^th century, and even much earlier in the case of coins.”

These tools will make it possible to examine parchments and coins down to the finest detail, at the pixel level. These in-depth analyses therefore generate a colossal volume of raw data to process. This is where artificial intelligence comes into play to speed up the processing and reveal the information “hidden” in the data, identifying major trends invisible to the naked eye. 

Above all, it will provide a boost in meeting the challenge of dating the objects under study. Dated documents, such as charters, will thus be used as references to test the model’s robustness by comparing the results obtained with already known dates. “If the results are convincing, the technique could be applied to undated documents,” says Nicolas Ruffini-Ronzani. This would represent a significant breakthrough in historical research.

“The use of machine learning methods is not a panacea,” Olivier Deparis qualifies, however. “We wanted to explore it as an open-ended question to assess its benefits.”

PHOENIX could thus herald a new era for heritage sciences, where artificial intelligence—much like the phoenix after which the project is named—opens up new ways to analyze and understand materials from the past.

• Francesca Cecchet (Department of Physics – NISM and NARILIS Institutes)
• Lucas Baseil (Department of Physics – NISM Institute)
• Julien Colaux (Department of Physics – NISM and PaTHs Institutes)
• Olivier Deparis (Department of Physics – NISM, naXys, and PaTHs Institutes)
• Christophe Flament (Department of Classical Languages and Literatures – PaTHs Institute)
• Louise Fauchier (Department of Classical Languages and Literature – PaTHs Institute)
• Laurent Houssiau (Department of Physics – NISM Institute)
• Alexandre Mayer (Department of Physics – NISM and naXys Institutes)
• Giulia Morabito (Department of Physics – NISM and PaTHs Institutes)
• Nicolas Ruffini-Ronzani (Department of History – PaTHs Institute)
• Nicolas Gros (Department of Physics – NISM and PaTHs Institutes)
• Manon Bart (Department of Physics – NISM and naXys Institutes)

The PHOENIX project is funded by the Concerted Research Action (ARC) program from September 2024 to August 2029. It is a continuation of the interdisciplinary Pergamenum21 project, launched in 2014 by the Moretus Plantin University Library (BUMP) under the leadership of Professor Olivier Deparis and dedicated to the scientific study of parchment with a view to improving conservation practices.

Young people from Rochefort showcased the PHOENIX project at the international First Lego League competition, a robotics contest open to students aged 10 to 16. To align with the annual theme focused on new technologies in the field of archaeology, this team from the Rochefort Youth and Culture Center drew inspiration from IBA technology to develop a research game designed to identify the origin of Ancient Greek coins modeled using a 3D printer. Their project caught the jury’s eye and earned them a spot in the national finals, which took place last March. Beyond the competition, this original game will be presented during Family Day at the Malagne Archaeological Park (Rochefort). 

In his research, Antoine Hubermont, a member of naXys (Namur Institute for Complex Systems), focuses specifically on the infrastructure that enables the operation of Galileo, the European satellite navigation system. 

“We use it every day, but few people know that we have a European GPS, Galileo, based on a constellation of satellites orbiting more than 23,000 kilometers above Earth,” he explains. 

Using artificial intelligence methods, Antoine Hubermont is developing tools capable of predicting the onset of failures. 

More specifically, the Monsater project aims to create a platform that allows for visualizing and predicting the status of this equipment, assessing the risk of failure, and identifying anomalies in order to initiate a process to restore their functions. The platform integrates and combines the detection and prediction capabilities of artificial intelligence-based solutions with the technical capabilities of robotic solutions. 

In this work, Antoine Hubermont is supervised by Professor Elio Tuci, a member of naXys and professor at the Faculty of Computer Science at UNamur. 

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.