Namur Institute For Complex Systems

Jérémy Rekier (Royal Observatory of Belgium)
2025-03-20 13:00 - 14:00 (Europe/Brussels)
Title : The Tidal Flows in Ocean Worlds
Abstract :
Planet Earth is one of a handful of ocean worlds in the solar system. Others include Jupiter’s moons Europa, Ganymede and Callisto, as well as Saturn’s moons Titan and Enceladus. Other such worlds might also exist in orbit around Uranus and Neptune. In all of these bodies, tidal heating plays a crucial role in keeping the water ocean from freezing, thereby extending the habitable zone beyond its classical circumstellar (aka Goldilocks) limit. Some authors even consider that such worlds orbiting exoplanets might be more habitable than analogues to the Earth. This makes exploration of the ocean worlds that are closer to us crucial in order to understand the conditions for extraterrestrial life, and this involves paying close attention to the process of tidal heating.
Exploration of the fluid dynamics of icy moons is a complicated matter, in large part due to the subsurface nature of their oceans. We present some of the methods developed to this end, inspired by previous work focusing on the study of the Earth’s and planet’s deep interior. We show how tidal flows can be resonantly amplified by inertial modes (restored by the Coriolis force) in liquid oceans, and how these modes are affected by density stratification.
The seminar will take place in Room S08 at the Faculty of Sciences.

Hélène Verhaeghe (UCLouvain)
2025-03-13 13:00 - 14:00
Title : The best of both worlds: when constraint programming and machine learning help each other
Abstract : Constraint programming is well known to be performant at finding the solutions of combinatorial optimization problems and can provide guarantees about these solutions. However, as problems tend to grow in size and complexity, the limits of such methods tend to show. Machine learning, on the other hand, is very good at extracting statistical patterns and dealing with uncertainty. However, they are really bad at reasoning, even on simple tasks. This talk is about how, by combining the two families of techniques, they can benefit one another. This talk will start with an introduction to constraint programming for those not knowledgeable about the technique.
The seminar will take place in Room S08 at the Faculty of Sciences.

Thomas Robiglio (IT-U University, Linz)
2025-02-28 13:00 - 14:00
Title : Mechanisms and behaviors in complex systems with group interactions
Abstract :

The interplay between causal mechanisms and emerging collective behaviors is a central aspect of understanding, controlling, and predicting complex networked systems.
Existing methods to study each of the two facets mostly adopt lower-order descriptions: pairwise network representations for mechanisms, and low-order information-theoretic metrics for behaviors. Despite their success, these low-order methods often fail to fully capture the intricate nuances inherent to many complex systems, thus beyond-pairwise methods are being developed: higher-order network representations and higher-order behavorial metrics.
As both low-order and higher-order mechanisms can determine the observation of both low and higher-order behaviors, the connection between behavioral observables and microscopic mechanisms in systems with pairwise and group interactions is not trivial; a systematic investigation of this complex relationship across different orders of interactions is needed.
In this talk, I will present recent work exploring the link between higher-order mechanisms and higher-order behavioral observables in two representative models with group interactions: a simplicial Ising model and a social contagion model. Our findings reveal that group (higher-order) interactions give rise to emergent synergistic (higher-order) behaviors in both systems.
Finally, I will argue that fully disentangling behaviors and mechanisms in complex systems—especially those with group interactions—requires principled approaches based on generative models and statistical inference.
REFERENCES:

Robiglio, T., Neri, M., Coppes, D., Agostinelli, C., Battiston, F., Lucas, M., & Petri, G. (2024). Synergistic signatures of group mechanisms in higher-order systems. arXiv preprint arXiv:2401.11588.
Peel, L., Peixoto, T. P., & De Domenico, M. (2022). Statistical inference links data and theory in network science. Nature Communications, 13(1), 6794.

The seminar will take place in Room S08 at the Faculty of Sciences.

Benoît Legat (UCLouvain)
2025-02-27 13:00 - 14:00
Title : Hidden convexity in linear neural networks
Abstract :
Training neural networks involves minimising a loss function that is nonconvex with respect to the network’s weights. Despite this nonconvexity, when the optimization converges to a local minimum, it is often close to globally optimal. This transfer from local properties to global properties is often achieved through convexity in optimization which neural networks seem to lack, or is it hidden ? There are two sources of nonconvexity in neural networks : 1) the nonlinear activation functions and 2) the multilinear product of the weight matrices.
Interestingly, recent research has demonstrated that the second source does not, on its own, lead to local minima that are not global when paired with a mean squared error loss. Although this result is promising, the complexity of the proof limits its generalization to more complex models, such as those with nonlinear activation functions or other loss structures. In this talk, we reveal the convexity hidden in the problem and show how it allows for a simpler and more insightful proof. By exposing this underlying structure, we aim to open the door to recognizing which types of models are more likely to train well and to extend this understanding to other machine learning architectures.
The seminar will take place in Room S08 at the Faculty of Sciences.

Women and Girls in Science
2025-02-13, 2024-02-08
The International Day of Women and Girls in Science takes place every 11th of February, following the declaration by the General Assembly of the United Nations on 22nd of December 2015.
This annual event aims at promoting the access of women and girls to science and technology as well as their full and fair participation. It reminds the important role of women in the scientific community and constitutes a great opportunity to encourage girls and young women to participate in the scientific developments.

Jeff Arnoldi (CNRS)
2025-02-06 13:00 - 14:00
Title : Linear Functional Ecology – Rethinking species contributions to ecosystem functions
Abstract :
Ecosystem functions describe processes like biomass production, respiration, or nutrient cycling, that can be key to the livelihood of humans and other life forms.
These functions are collectively performed by the many species that constitute an ecosystem; trees is a forest, plants in a grassland, or bacterial strains in a microbiome.
Here, I will use linear algebra to show that generically, there is a sense in which a rare species can have as much importance as an abundant one.

The reason why this claim is not obvious comes from the fact that in functional ecology, under the mass ratio hypothesis, species contributions should be well predicted by their traits and abundance. I will illustrate using soil-microbiome data that this is indeed true, even for complex functions related to nutrient cycling. Yet the mass-ratio hypothesis has an awkward corollary: functions are typically performed by just a few dominant species, so that most of an ecosystem diversity appears useless. This a description of the state of the system, but says nothing of its dynamics. To understand why rare species can be important, one has to take a perturbative approach, looking at the sensitivity of a function to say, added mortality (a pathogen) on a given species. In doing so, we reveal a completely different picture than the one the mass-ratio hypothesis depicts. Via direct and indirect interactions between them, species can have large impacts on a given function, even if those species are rare or if they do not possess traits that relate to the function.

The seminar will take place in Room S08 at the Faculty of Sciences.

Corentin Bisot (VU Amsterdam)
2025-02-04 13:00 - 14:00
Title : Transport logistics in a growing fungal network
Abstract :
Branching forms are ubiquitous in nature and evolved repeatedly throughout evolution. An example are mycorrhizal fungi, that have, for nearly 450 million years, constructed networks to collect and trade nutrient resources with plant roots. Because of their dependence on host-derived carbon, these fungi face conflicting trade-offs in building networks that balance construction costs against geographic coverage and long-distance resource transport to and from roots. How they navigate these design challenges is unknown. Using data from fungal colonies at the scale of individual filament growth but also internal cytoplasmic flows our lab investigates intimate relationships between growth, transport and trade.

We found a consistant pattern of colony propagation that emerges through the combination of branching and fusion of individual hyphae. The exact balance of these two ingredients can be adapted depending on fungal strategy. I will show how the necessity of transport within the colony, and trade with the plant, constrain the space of possible propagation patterns. I will conclude discussing how intracellular flows could be organizing to allow coherent trade patterns explaining the stability of the symbiosis accross such a wide timescale.

The seminar will take place in Room S08 at the Faculty of Sciences.

Gauvain Leconte-Chevillard and Andrea Roselli (UNamur)
2024-12-12 13:00 - 14:00
Title : Did the laws of physics emerge at t=10-34 s?
Abstract :
According to the vast majority of the inflationary models of the universe, the exponential expansion of space ends ≃10-34 s after the Big Bang with a phase of reheating during which the inflation field decays into the particles of the Standard Model. In this talk, we do not address issues regarding the empirical adequacy of this cosmological scenario; we rather focus on the two following questions:
– According to this scenario, can we argue that the particles of the Standard Model emerged from the inflation field, and in which sense?
– If we claim that the interaction carriers of the Standard Model (e.g. gluons) emerged during the reheating, does it mean that thelaws describing or governing these interactions (e.g. the strong nuclear force) emerged at the same time?
In the first part of the talk, we give a brief overview of the physics underlying the reheating of the universe at the end of inflation. Then, in the second part, we claim that the models of reheating are sufficiently developed to answer unambiguously to the first question – if and only if we are careful to distinguish two kinds of emergence: synchronic and diachronic. However, such a precise answer might not be available for the second question, which depends on our metaphysical conception of physical laws. In the last part, we will present a metaphysical conception that could elegantly accommodate the physical claims made above, we will show how things would “hang together” in such a metaphysics, and make some more general philosophical remarks.
The seminar will take place in Room S08 at the Faculty of Sciences.

Yusuke Kato (University of Tokyo)
2024-11-28 13:00 - 14:00
Title : Introduction of two studies: (1) analysis of oscillation quenching by periodic perturbation and (2) parameter estimation of Kuramoto model
Abstract :
I will talk about the two different projects that I am working on in Japan. (1) In the first part, I will present the oscillation quenching (annihilation of oscillation) in a bistable oscillator model [1]. We find that multiplicative periodic forces combined with feedback induce quenching and perform the bifurcation analysis using an averaging approximation. (2) The second part would be about the parameter estimation of the Kuramoto model, which is a mathematical model that describes synchronization phenomena. We use the time series of the order parameter (a macroscopic quantity that characterizes how the whole population is synchronized) as given data and estimate the model parameters. The estimation is performed by the Bayesian approach, using the exchage Monte Carlo method for computation.

[1] Y. Kato and H. Kori. Periodic forces combined with feedback induce quenching in a bistable oscillator. Chaos 34, 103125 (2024).

The seminar will take place in Room S08 at the Faculty of Sciences.

Hidemasa Ishii (University of Tokyo)
2024-11-26 13:00 - 14:00
Title : Employing dynamical modeling to understand complex phenomena: from interacting bistable systems to football ball possession
Abstract :
I have been motivated to employ dynamical modeling to understand complex phenomena in social sciences and biology.
In this seminar, I would like to introduce two projects I have worked on.
The first involves a system of diffusively coupled bistable elements, which have been utilized to study abrupt transitions in complex systems.
We analysed the influence of coupling strength over the mean escape time.
We numerically found that weak coupling facilitates escape on average, while strong coupling impedes escape [1].
We argue, although diffusive coupling both facilitates and impedes escape, the facilitating effect is dominant under weak coupling.
The second topic concerns dynamical modelling for three-versus-one ball possession in football.
In our model, motion of the players and ball is governed by a system of ODEs during a single pass.
The model is nevertheless stochastic, because the initial condition and parameters of the ODEs depend probabilistically on the final state of the previous pass.
We aim to utilize this approach to quantify the difference between high- and lower-level football teams.
[1] H. Ishii and H. Kori, Diffusive coupling facilitates and impedes noise-induced escape in interacting bistable elements, Sci Rep 14, 11019 (2024).
The seminar will take place in Room S07 at the Faculty of Sciences.

Maxime Lucas (UNamur/UCLouvain)
2024-11-21 13:00 - 14:00
Title : Of higher-order interactions, whales, and fungi
Abstract :
The strength of dynamical systems and network models lies in their ability to represent diverse systems that, despite their apparent differences, rely on common mechanisms. In this talk, I will share insights from three of my primary research areas. First, we will explore how higher-order interactions—those involving any number of units—extend beyond traditional networks to impact the synchronisation of oscillators. In particular, I will discuss how the two most common representations of higher-order interactions, hypergraphs and simplicial complexes, can have opposing effects on synchrony stability. We will also see how these interactions can reduce the basin of attraction for synchronised states while enhancing their linear stability, resulting in more stable yet narrower basins. Second, I will introduce Project CETI, a multi-disciplinary collaboration focused on understanding sperm whale communication. Here, we will look at how factors like kinship and shared territories influence their communicative behaviors and social interactions. Finally, we will discuss underground fungal networks, specifically those of arbuscular mycorrhizal fungi. These fungi form extensive hyphal networks that connect to plant roots, facilitating resource exchanges and enhancing ecosystem resilience. We are interested in characterising the structural properties and robustness of these vital networks.
The seminar will take place in Room S07 at the Faculty of Sciences.

Serge Gratton (Toulouse INP)
2024-11-15 13:00 - 14:00
Title : Adaptive regularization algorithms for Objective-Function-Free Optimization
Abstract :
This work is about the fastest known optimization method in terms of complexity, which does not require the evaluation of the objective function. Such methods, termed Objective-Function-Free Optimization (OFFO), have gained popularity recently, especially in noisy problem contexts, including deep learning applications. We present an adaptive regularization OFFO algorithm for unconstrained nonconvex optimization. This algorithm is part of the adaptive regularization methods family, which is known for its optimal worst-case complexity results in the conventional framework where the objective function is evaluated. We demonstrate that these outstanding complexity bounds are maintained with the new algorithm, even though it relies on significantly less information. Specifically, we show that using derivatives of degree one to p, the algorithm will find an 𝛆1-approximate first-order minimizer in at most O(𝛆-(p+1)/p) iterations, and an (𝛆1, 𝛆2)-approximate second-order minimizer in at most O(𝛆-(p+1)/p, 𝛆-(p+1)/(p-1)}) iterations. As a particular case, the algorithm, when using first and second derivatives and applied to functions with Lipschitz continuous Hessian, will find an iterate xk where the gradient’s norm is less than 𝛆1 in at most O(𝛆-3/2) iterations. Numerical experiments demonstrate the excellent performance of this method for noisy problems, highlighting its robustness and efficiency across various scenarios.
The seminar will take place in Room S08 at the Faculty of Sciences.

Christian Bick (VU Amsterdam)
2024-09-19 13:30 - 14:00
Title : Higher-order Interaction Networks: Phase Reduction, Synchronization, and Global Dynamics
Abstract : Synchronization is a fascinating effect of the interaction between coupled oscillatory units and is ubiquitous in many real-world systems. If the coupling between units is sufficiently weak, phase reductions provide an adequate description of the dynamics. We discuss phase reductions beyond first order that yield phase oscillator networks with higher-order interactions. Specifically, we discuss how the nonpairwise higher-order phase interactions depend on the shape of the limit cycles and the underlying network structure. If time permits, we also discuss how higher-order interactions influence the emergence of metastable (synchronization) dynamics induced by heteroclinic cycles.
The seminar will take place in Room S08 at the Faculty of Sciences.

Riccardo Muolo (Tokyo Institute of Technology)
2024-09-19 13:00 - 13:30
Title : A general theory of phase reduction for systems with higher-order interactions
Abstract:

Synchronization is a ubiquitous emergent phenomenon in which an ensemble of elementary units behaves in unison due to their interactions [1]. Given the pervasiveness of synchronization, understanding how it is achieved is a fundamental question. In particular, the nature of the interactions among oscillators has strong consequences on the transition to synchronization. To tackle this issue, it is convenient to consider phase models in which each oscillator is described solely in terms of a phase variable. According to phase reduction theory, the phase model captures the dynamics completely when the coupling among the oscillators is sufficiently weak [2]. If one considers only pairwise interactions, the synchronization transition is described by the Kuramoto-type model. Despite the versatility of such an approach, the classical theory of synchronization is solely based on pairwise interactions, while, in many natural systems, the interactions are intrinsically higher-order (many-body) rather than pairwise [3]. In fact, many examples show that a pairwise description is sufficient not to match the theory with observations and, additionally, higher-order interactions appear naturally when phase reduction is performed up to higher orders [4]. It was also shown that extensions of the Kuramoto model including higher-order interactions exhibit an explosive transition and other interesting dynamics [5].

This seminar will be divided in two parts. In the first part, I will introduce the phase reduction theory and highlight the universality of phase models and the generality of the approach, especially when compared to the Master Stability Function [6]. Then, after discussing the basics of higher-order interactions, I will present a recent work where we analyzed the collective dynamics of the simplest minimal extension of the Kuramoto-type phase model for identical globally coupled oscillators subject to two- and three-body interactions and showed how the many-body interactions greatly enriches the behaviors of the system [7]. Lastly, I will show some preliminary results for some general cases, one where the coupling is not constrained to the all-to-all case [8] and the other in which the phase reduction cannot be performed analytically [9].
This is a joint work with Hiroya Nakao (Tokyo Institute of Technology, Japan), Iván León (Universidad de Cantabria, Spain) and Shigefumi Hata (Kagoshima University, Japan)

References
[1] Kuramoto Y., Chemical Oscillations, Waves, and Turbulence. Springer-Verlag, 1984.
[2] Nakao H., Phase reduction approach to synchronisation of nonlinear oscillators. Cont. Phys., 57(2): 188-214, 2016.
[3] Battiston F. et al., Networks beyond pairwise interactions: Structure and dynamics. Phys. Rep., 84: 1-92, 2020.
[4] León I. and Pazó D., Phase reduction beyond the first order: The case of the mean-field complex Ginzburg-Landau equation. Phys. Rev. E, 100(1): 012211, 2019.
[5] Skardal P.S. and Arenas A., Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplexes. Phys. Rev. Lett., 122(84): 248301, 2019.
[6] Fujisaka, H., and Yamada, T., Stability theory of synchronized motion in coupled-oscillator systems. Prog. Theor. Phys., 69(1), 32-47, 1983.
[7] León I., Muolo R., Hata S. and Nakao H., Higher-order interactions induce anomalous transitions to synchrony. To appear in Chaos, Dec 2023.
[8] Muolo R., León I., Hata S. and Nakao H., Phase Reduction Analysis of Collective Dynamics in Systems of Coupled Oscillators with Higher-Order Interactions. In preparation.
[9] Muolo R. and Nakao H., A general framework to study spiking neurons coupled through higher-order interactions. In preparation.

The seminar will take place in Room S08 at the Faculty of Sciences.

Keisuke Taga (Waseda University)
2024-09-18 13:00 - 14:00
Title : Nonlinear pattern formation of tape peeling
Abstract :
When we look closely at the peel front of the adhesives, we can ﬁnd two kinds of structures. One of them is a tunnel structure which can be found in slow peeling. Then for fast peeling, the tunnel structure collapses and a without tunnel structure occurs . And at the intermediate peel speed, these two structures switch chaotic. From the experimental observation,this chaotic switching gives Sierpinski-gasket like fractal random patterns in the peel trace of the adhesive tapes[1].

In this talk, I introduce a model for the pattern formation of the peel trace by considering the deformation of the peel front based on the Newton equation, then we compare its scaling properties to the previous experimental result [2].

[1] Y. Yamazaki and A. Toda, Physica D 214 120 (2006).
[2] K. Taga and Y. Yamazaki, J. Phys. Soc. Jpn., 92, 4, 043001 (2023).

The seminar will take place in Room S08 at the Faculty of Sciences.

WIVACE Workshop 2024
2024-09-11 - 2024-09-13
XVIII International Workshop on Artificial Life and Evolutionary Computation
Namur, Belgium, 11-13 September 2024
The International Workshop on Artificial Life and Evolutionary Computation aims at bringing together researchers to present and share their results and ideas in a multidisciplinary context. The workshop provides a forum for the discussion of new research directions and applications in Artificial Life, Evolutionary Computation and in related fields, where different disciplines and research areas could effectively meet.
More information : https://events.info.unamur.be/wivace2024/index.html

Mathematics for Industry 2024
2024-09-09 - 2024-09-13
Study week Mathematics for Industry 2024
From 9 to 13 September 2024, the Belgian network BE-MATHS-IN on applied mathematics for industry and innovation, which gathers applied mathematical researchers at all Belgian universities, organizes its third Belgian study week “Mathematics for Industry”, which will be held at the TRAKK co-working center in Namur.
The Mathematics for Industry study week is an intensive problem-solving workshop that brings together young researchers, postdocs, scientists and industrialists. In the course of one week, small groups of researchers of different backgrounds will intensively brainstorm and work together to model and solve real-world challenges provided by industry. On Monday, each company representative presents their problem, after which the participants choose a problem to work on for the remainder of the week along with the industrial partner. On Friday morning, each group presents their solution to the chosen problem.
The study week warmly welcomes a broad scientific audience: from applied and computational sciences (applied mathematics, engineering, statistics, …) to pure sciences (mathematics, physics, chemistry, biology, …).
More information : https://be-maths-in.be/mfi24/

naXys Research Day
2024-09-05
The naXys Research Day takes place at La Bergerie de Lives (100 rue de Mosanville, 5000 Namur).
Schedule
13.00-13.30 Welcome and words of the President, A.-S. Libert
13.30-13.45 Meet Jeanick Pignolet, Executive assistant
13.45-14.30 Flash talks (3 minutes / 3 slides) by naXys PhD students
14.30-15.15 Design the research poles – SPACE | BIO | OPTICS | AI | ECO | ROBUST
15.15-15.30 Feedback
COFFEE BREAK (15.30 – 16.10)
16.10-17.50 Interdisciplinary talks (15′ + 5′) by naXys post-docs and PI
17.50-18.00 Conclusion
COCKTAIL DINNER (18.00)
Program
FLASH TALKS

Alexandru Caliman, Long-term stability of planetary systems
Arunima Sidker, Stress echoes: how past environments shape population responses to future stress
Antoine Hubermont, Predictive maintenance as a multi label classification problem
Baptiste Perez Riaza, Empirical insights into crypto-assets using network inference
Charles Modera, Generation of High-Frequency Gravitational Waves Using Resonant Cavities
Davoud Alahvirdi, Traffic monitoring and management by swarm of drone
François-Grégoire Bierwart, Koopman-based framework for stability analysis of dynamical systems
Julien Pietquin, Urban traffic networks with unmanned aerial vehicules
Loic Warscotte, Weighing vehicules with piezo material
Marie Dorchain, Turing patterns on higher-order structures
Martin Moriamé, Control of synchronization in Higher-order networks
Nemanja Antonic, BABOTS: the design and control of biological animal robots
Nicolas Roy, Surrogate-Assisted Heuristic Optimization in Photonic Device Engineering
Williams Dhelonga, Probing the universe with the light sail or the Einstein Dirac fermions
Yun Li, Biodiversity shifts mediate global change effects on trophic pyramids

INTERDISCIPLINARY TALKS

Alexis Coyette, JUICE – Constraining the interior of the Galilean Moons
Gonzalo Marcello Ramirez-Avila, Modeling posible chronobiological strategies for improving radiotherapy treatments
Jean-Yves Gnabo, Climate Risk Exposure : A Comparative Analysis of Sustainable and Conventional Funds
Maxime Boucher, On directional runs and their local and asymptotic properties
Mohammed Alkhateeb, Tunneling time problem in relativistic quantum field theory

Corbinian Schlösser (INRIA Paris)
2024-06-13 13:00 - 14:00
Title : Identifying low dimensional systems from high dimensional observations
Abstract : Motivated by the increasing availability of motion data through multiple sensors and cameras, we address the problem of identifying low-dimensional autonomous systems for which only high-dimensional measurements are observed. We do not assume prior knowledge on the latent dimension or its dynamics. However, we assume that the observation map is injective which implies that the observations follow an autonomous system. This is our starting point for reducing a general and non-linear identification problem towards a (tractable) convex optimization problem. We discuss different obstacles that came across our route, several limiting factors, and situations for which our approach provides feasible solutions to the identification problem. This is joint and ongoing work with Francis Bach and Alessandro Rudi.
The seminar will take place in Room S08 at the Faculty of Sciences.

Interdisciplinary Training School for Doctoral students (EFID 2024)
2024-05-24

Williams Dhelonga (UNamur)
2024-05-21 13:00 - 14:00
Title : Exploring Weak measurements within the Einstein-Dirac Cosmological framework.
Abstract : Our study applies the Two-State Formalism alongside weak measurements within a spatially homogeneous and isotropic cosmological framework, wherein Dirac spinors are intricately coupled to classical gravity. To elucidate this, we provide detailed formulations for computing the weak values of the energy-momentum tensors, the Z component of spin, and the characterization of pure states. Weak measurements appear to be a generalization and extension of the computation already made by Finster an Hainzl, in A spatially homogeneous and isotropic Einstein-Dirac cosmology. Our analysis reveals that the acceleration of the Universe expansion can be understood as an outcome of postselection, underscoring the effectiveness of weak measurement as a discerning approach for gauging cosmic acceleration. https://arxiv.org/abs/2405.02108

The seminar will take place in Room S08 at the Faculty of Sciences.

Jean-François de Kemmeter (UNamur)
2024-04-25 13:00 - 14:00
Title : Random walks on networks with limiting nodes carrying capacities
Abstract :
Over the last years, network science has emerged as an efficient tool to model complex systems composed of numerous interconnected entities. In particular, the interplay between network structure and dynamics on networks has long been recognized as a cornerstone of network science and is at the core of various applications such as community detection. Among those dynamical processes on networks, random walks are ubiquitous stochastic processes that describe, in their “standard” formulation, the displacement of an entity that hops from node to node following at random the available connections.
In this talk, we will focus on a class of random walks in which multiple random walkers travel across the network under the constraint of limiting nodes carrying capacities, a feature of most real-life networks. We will discuss how the outcomes of the dynamics differ from the “standard” random walk and depend on the network structure.
This is based on joint work with Malbor Asllani and Timoteo Carletti.
More information: https://arxiv.org/abs/2112.02549 https://arxiv.org/abs/2307.14083
The seminar will take place in Room S08 at the Faculty of Sciences.

Benoît Bonnet-Weill (CNRS)
2024-04-15 13:00 - 14:00
Title : A Set-Valued Approach to Koopman Operators for Control Systems

Abstract : In this talk, I will present a new approach that we recently put forth together with Milan Korda (LAAS-CNRS) to define and study the properties of Koopman operators for general nonlinear control systems, based on the theory of set-valued analysis. In this framework, the Koopman operators at some given time are defined as the multi-mappings which, to a given function observable, associate the collection of its evaluations along all possible flows of the control systems.
Starting from this general construct, we were able to obtain relevant set-valued counterparts of all the basic results of Koopman theory, namely the existence of an infinitesimal generator, whose dynamics precisely encodes a rich subclass of observables, an adapted version of the spectral mapping theorem relating their respective point spectra, and a characterisation of the dual (also known as Perron-Frobenius) semigroup as a family of time-dependent operators acting on measures.
Besides its conceptual soundness, our approach provides theoretical grounding for a class of practical methods used for solving control problems by leveraging the Koopman framework, which revolve around the idea of bundling together the classical Koopman operators stemming from a collection of fixed control inputs.
The seminar will take place in Room S08 at the Faculty of Sciences.

Valentin Delchevalerie (UNamur)
2024-04-04 13:00 - 14:00
Title : SO(2) and O(2) Equivariance in Image Recognition with Bessel-Convolutional Neural Networks
Abstract : For many years, it has been shown how much exploiting equivariances can be beneficial when solving image analysis tasks. For example, the superiority of convolutional neural networks (CNNs) compared to dense networks mainly comes from an elegant exploitation of the translation equivariance. Patterns can appear at arbitrary positions and convolutions take this into account to achieve translation invariant operations through weight sharing. Nevertheless, images often involve other symmetries that can also be exploited. It is the case of rotations and reflections that have drawn particular attention and led to the development of multiple equivariant CNN architectures. Among all these methods, Bessel-convolutional neural networks (B-CNNs) exploit a particular decomposition based on Bessel functions to modify the key operation between images and filters and make it by design equivariant to all the continuous set of planar rotations, and also include the incorporation of reflection and multi-scale equivariances.
More information: https://arxiv.org/abs/2304.09214 https://proceedings.neurips.cc/paper/2021/hash/f18224a1adfb7b3dbff668c9b655a35a-Abstract.html
The seminar will take place in Room S08 at the Faculty of Sciences.

Jean-Charles Delvenne (UCLouvain)
2024-03-21 13:00 - 14:00
Title : Markov chains, transport theory and statistical physics
Abstract :
We look at the following motivating problem: how to move an electronic memory from a ‘zero’ state to a ‘one’ state, at minimal energy cost?

Mathematically, this amounts to design a Markov chain that drives a certain probability measure (encoding a ‘zero’) towards another one (a ‘one’) through an ‘optimal’ path — an avatar of Gaspard Monge’s so-called ‘earth mover problem’, at the core of transport theory.

We explore various recent results and conjectures around this theme at the interface of statistical physics and Markov chain theory. We support these by illustrations on realistic simulations on electronic memories.

The seminar will exceptionally take place in Room S06 (and not S08) at the Faculty of Sciences.

Michaël Fanuel (Université de Lille)
2024-03-14 13:00 - 14:00
Title : Sparsification of the magnetic Laplacian with statistical guarantees
Abstract :

Laplacian matrices are discrete analogues of Laplacian differential operators, which have applications in several areas of applied mathematics such as network science, machine learning, control, etc.
A Laplacian matrix is in general associated with a graph.
In this talk, we consider the problem of finding a controlled approximation of a Laplacian matrix — called a sparsifier — which only has a few non-zero entries.
This (sparse) matrix is associated with a graph with fewer edges, and is often cheaper to inverse.
More specifically, we consider a U(1)-connection graph, that is, a graph where each oriented edge is endowed with a unit modulus complex number which is simply conjugated under orientation flip. A natural replacement for the usual graph Laplacian is then the so-called magnetic Laplacian, a Hermitian matrix which includes information about the graph’s connection. Connection graphs and magnetic Laplacians appear, e.g., in the problem of angular synchronization (signal processing).In the context of large and dense graphs, we study spectral sparsifiers of the magnetic Laplacian, i.e., spectral approximations based on subgraphs with few edges. Our approach relies on sampling variants of spanning forests using a custom determinantal point process, a distribution over edges that favours diversity (and which originates from quantum physics).
In a word, the connected components of our spanning forests are either trees or cycle-rooted trees. The latter partially capture the angular inconsistencies of the connection graph, and thus provide a way to compress information contained in the connection.
One of our contributions is to provide statistical guarantees for a choice of natural estimators of the connection Laplacian based on batches of spanning forests.
Interestingly, when the connection graph has weakly inconsistent cycles, samples of this distribution can be obtained by using a loop-erased random walk.
This sampling algorithm is called CyclePopping and is actually rather performant in practice. The law of the number of steps to complete CyclePopping is also known exactly if the connection graph has weakly inconsistent cycles.
We shall briefly discuss our contribution in the analysis of this algorithm.
This is a joint work with Rémi Bardenet (CNRS & ULille) https://arxiv.org/abs/2208.14797.

The seminar will take place in Room S08 at the Faculty of Sciences.

Morine Delhelle (UCLouvain)
2024-02-29 13:00 - 14:00
Title : Copula based dependent censoring in cure models with covariates
Abstract : In survival data analysis, datasets with both a cure fraction (individuals who will never experience the event of interest) and dependent censoring (loss to follow-up for a reason related to the event of interest before the occurrence of that event) are not scarce, and appropriate models and methods must be considered to avoid biased estimators of the survival function or incorrect conclusions in clinical trials. Delhelle and Van Keilegom proposed a fully parametric model for the bivariate distribution of survival (T) and censoring (C) times, that takes these features into account. The model depends on a parametric copula (with an unknown association parameter) and on parametric marginal distributions for T and C. An advantage is that it allows one to estimate the strength of the dependence and the cure rate.

This talk presents an improvement of this model. Administrative censoring is considered separately from dependent censoring, and covariates are included in the model.

Authors : Morine Delhelle (Institute of Statistics, Biostatistics and Actuarial Science, UCLouvain, Belgium) and Ingrid Van Keilegom (ORSTAT, KU Leuven, Belgium)
The seminar will take place in Room S08 at the Faculty of Sciences.

Johan Barthélemy (University of Wollongong, NVIDIA)
2024-02-01 13:00 - 14:00
Title : Accelerating Simulations with NVIDIA Modulus
Abstract : High-fidelity simulations in science and engineering are computationally expensive and time-prohibitive for quick iterative use cases, from design analysis to optimization.
NVIDIA Modulus, the open source physics machine learning platform, turbocharges such use cases by building physics-based deep learning models that are order of magnitudes. faster than traditional methods and offer high-fidelity simulation results. Once trained, the model can perform quick forward passes, making it ideal for applications that demand fast responses, such as real-time simulations of large complex systems.
Modulus is a offers a suite Physics-ML model architectures, including Fourier neural operators. It provides an end-to-end pipeline for training models, from geometry ingestion to training and inference, with explicit parameter specifications for a wide range of applications. The framework is also integrated with NVIDIA Omniverse for enhanced visualization and is tailored for high-performance, leveraging technologies for multi-GPU computing and multinode scaling.
This seminar will present the key features, use cases, and performance aspects of NVIDIA Modulus, providing attendees with a understanding of its capabilities and applications.
The seminar will take place in Room S07 at the Faculty of Sciences.

André Füzfa (UNamur)
2023-12-14 13:00 - 14:00
Title: Fundamentals of relativistic astrodynamics and rocketry
Abstract:
Astrodynamics traditionally denotes the study of controlled flight paths of human-made spacecraft (Kaplan, 1976). This term originates from the prehistory of the space age, at a time where only archaic Newtonian dynamics were used for determining interplanetary spaceflights at extremely low velocities (in the km/s range).
After briefly reviewing basic rocketry in this primitive language, we will introduce space cadets to the modern geometric formalism that is now state-of-the-art for interstellar navigation. Relativistic trajectories in curved space-time are described by non-geodesic worldlines of particles submitted to the action of an external four-force. We will show how to use your relativistic inertial guidance system to monitor the evolution of both the rest mass of your starship and the apparent weight inside it, through the space-time orientation of the total four-force. Then, several well-known models of deep space propulsion will be reviewed: Ackeret’s rocket and the relativistic Tsiolkowsky equation, thermal and radiation rockets, Bussard’s ramjet and finally lightsails. We will end the course by two relativistic astrodynamical applications : basic interstellar transfer and ascent trajectories from a compact object.
The seminar will take place in Room S08 at the Faculty of Sciences.
