NAXYS Newsletter November 2017


Newsletter - November 2017


  • Alternative expression of the Bloch wave group velocity using the Sturm-Liouville formalism applied to electromagnetic wave propagation in periodic dielectric media, Olivier Deparis (UNamur), November 10, 13:00 - 14:00, E22
  • The influence of the network connectivity in the spatial patterns of chimera states, Astero Provata (National Center for Scientific Research Demokritos, Athens), November 16, 13:00 - 14:00, E25
  • Language as a signature of collective identity: Wikipedia editing across twelve languages, Yeralica Gandica (UNamur), November 23, 13:00 - 14:00, E25
  • On the continuation of degenerate periodic orbits via normal form: full dimensional resonant tori, Marco Sansottera (University of Milan), November 30, 13:00 - 14:00, E25

More information can be found on our website:


The new scientific committee of naXys has been elected:
Anne-Sophie Libert (Director) - Timoteo Carletti - Frederik De Laender -
Jean-Yves Gnabo - Renaud Lambiotte - Alexandre Mayer.

In October, three naXys PhD theses were defended:
  • Etude de populations observées ou synthétiques de débris spatiaux depuis les données jusqu'aux modèles, Alexis Petit, October 13,
  • Formation of non-coplanar planetary systems, Sotiris Sotiriadis, October 25,
  • Invariant Stabilization of Discretized Boundary Control Systems, Jonathan Dehaye, October 25.

Virtual Belgium in Health Workshop. In the framework of the WB-Health program, Wallonia (DGO 6) funds the VBIH project led by a naXys team (E. Cornelis & T. Carletti with M. Dumont and W. Henrotin) with collaboration from the DEMO team from UCL. This project aims at developing a synthetic population platform as decision-support tool for planifying and forecasting health cares needed by elderly people. Since this project reaches its final step, a workshop has been organized last Monday to present its results and the developed software tool allowing health professionals to achieve forecasting exercices. As well all the health professionals attending this event as the invited foreign experts (Arnaud Banos and Alain Trugeon) stated all the potential of the developed methodology and of the provided tool and encouraged the researchers to go further in future developments.


Quantifying the degree of average contraction of Collatz orbits,
Carletti, T. & Fanelli, D., Bollettino dell'Unione Matematica Italiana, 2017
Arithmetics is the branch of mathematics dealing with integer numbers; additions, subtraction, multiplications, divisions, even numbers (divisible by 2) and odd numbers (not divisible by 2), are all souvenirs of our primary school years. Everything seems so evident and simple that one could not expect unsolved problems still exist in arithmetics, even more if their statements do not involve complicated expressions. But look at this intriguing problem.

Let n_0 be any integer number, if it is even divide it by 2 and call the result n_1=n_0/2, otherwise let n_1=3n_0+1; do the same for n_1 and so on obtaining new integer numbers, the trajectory starting from n_0. To warm up, let us take n_0=1, it is odd then n_1=3x1+1=4, which is even and so n_2=4/2=2, which is also even and thus n_3=2/2=1. We are back to our initial number. The case n_0=2 is straightforward, so let us do the same with n_0=3; then one easily get: n_1=10, n_2=5, n_3=16, n_4=8, n_5=4, n_6=4, n_7=2 and n_8 =1. Wow! We end up again at 1.

The natural question is thus: does any initial integer n_0 will end up at 1 after a finite number of operations (division by 2 and multiplication by 3 followed by adding 1)? Despite its simplicity, this is an open question since almost a century; mathematicians believe it is true and named it the Collatz conjecture. In this paper, we provide a novel argument to support the validity of the Collatz conjecture.

More information:

Theory of Turing Patterns on Time Varying Networks,
Petit, J.,В Lauwens, B., Fanelli, D. & Carletti, T., Physical Review Letters, 119, 148301, 2017
Networks are everywhere. The brain, Internet and the cyberworld, foodwebs, social contacts and commuting fall within the vast realm of network science. Networks are often dynamical entities, and their ability to change in time drastically affects the behaviour of a scrutinized system (e.g. how constitutive elements diffuse and interact), in terms of resilience, vulnerability to attacks or degree of synchronization. As rigorously demonstrated in the paper by Petit et al, self-organized motifs (e.g. non uniform distribution across the nodes) can indeed emerge from noise, as follows a spontaneous drive triggered by the inherent network dynamics. This observation translates in a new route to pattern formation that bears applied and fundamental interests, from neuroscience to biology, via chemistry and physics, to ecology and social systems.Relevant is for instance the application to epidemics spreading, as mediated by the rapidly evolving networks of pairwise social contacts. Pathogens need in fact some time to settle and eventually reach the virulent stage. During this latent period, individuals carrying the virus experience a multitude of interactions [in the bus/underground, at work/shops/sport…], so contributing to reshape the underlying networks of contacts. As discussed in the paper, the unavoidable variability of the network structure [an ingredient so far largely omitted in the relevant literature] can shape the response of the system and possibly impact on the propagation of the infection. The theory developed covers a wide range of possible settings, from periodic to random modulation of the network structure and allows for quite general interactions terms.

More information:

Shifts of community composition and population density substantially affect ecosystem function despite invariant richness,
Spaak, J. W., Baert, J. M., Baird, D. J., Eisenhauer, N., Maltby, L., Pomati, F., Radchuk, V., Rohr, J. R., Van den Brink, P. J., De Laender, F., Ecology Letters 20, 10, 1315–1324, 2017
Impacts of environmental change are typically measured by comparing the observed number of species with some reference no impact' value.
We show that this approach severely underestimates such impacts, because environmental change can affect population sizes and the composition of biological communities, even if does not affect the number of species.

Our results, which are based on mathematical analyses of a mechanistic model and statistical modelling of phytoplankton data both sustain the same conclusion: When solely relying on the number of species present as an indicator of environmental quality, effects of up to 80% can go unnoticed. Our findings have far-reaching implications for the field of Biodiversity-Ecosystem Function research and environmental monitoring and assessment.

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