Philippe Toint (University of Namur)
2022-10-27 13:00 - 14:00 (Europe/Brussels)
Title: Recent topics in complexity for nonconvex optimization problems
Abstract: The talk will review results on the evaluation complexity of algorithms for nonlinear (nonconvex) optimization problems. The focus is on unconstrained and “simply constrained” cases and will consider obtaining high-order optimality conditions. Algorithms using inexact information will also be covered.
The seminar will take place in room S08 at the Faculty of Sciences

Christian Mugisho Zagabe (University of Namur)
2022-11-10 13:00 - 14:00
Title: Lie-algebraic condition for uniform stability of switched nonlinear systems: Construction of a common Lyapunov function by the Koopman operator approach.
Abstract: Switched systems consist of a finite set of dynamical systems and a switching signal indicating which system is activated. Their interest is due to the fact that many phenomena in nature, engineering,… are represented by different models depending on the change of some parameters. Their stability properties are not intuitive. Indeed, for two individually stable (or unstable) systems one can construct a signal that makes the whole system unstable (or stable). In the uniform stability theory, the main goal is to find sufficient (and/or necessary) conditions that make the whole system stable for all possible switching laws.
In 1999, Daniel Liberzon and co-workers proved that for a switched linear system, the solvability property of the Lie algebra generated by Hurwitz matrices is a sufficient condition for uniform stability.
In 2004, Daniel Liberzon formulated an open problem to find which condition of the Lie algebra (of vector fields) can be used to guarantee the global uniform asymptotic stability (GUAS) of switched nonlinear systems.
Using the Koopman operator approach, we propose an answer to the open Liberzon problem. Our result is related to the dynamics on the polydisc and shows that a sufficient condition for GUAS follows from the solvability of the Lie algebra generated by the Hurwitz Jacobian matrices of the vector fields.
More precisely, we construct a common Lyapunov function for switched nonlinear systems, which is convergent in a specific region of the state space. This is done by defining the Koopman operator on the Hardy space on the polydisc where the reproducing kernel property allows us to obtain a Lyapunov function via the evolution of the evaluation functional. We then infer the GUAS property of switched nonlinear systems on a specific invariant set.
The seminar will take place in room S08 at the Faculty of Sciences

Ariane Courtot (IMCCE, France)
2022-11-17 13:00 - 14:00
Title: Chaos in the Geminid Meteoroid stream
Abstract: Meteor showers originate from a parent body (an asteroid or a comet). This parent body ejects several meteroids, forming a meteoroid stream, which will meet the Earth. From Earth, several meteors can then be observed. To prove they actually form a shower, we need to show whether they come from the same source.
But dynamically linking a meteor shower with its parent body can be challenging. This is in part due to the complex dynamics of meteoroid streams and the influence of non-gravitational forces (FNG).
We develop a method to study chaos in meteoroid streams and apply it to the Geminid meteoroid stream. We choose to draw chaos maps, which relies on chaos indicator. We show that the best one is the Orthogonal Fast Lyapunov Indicator, after comparison with the Fast Lyapunov Indicator, the FLI for close encounters and the Mean Exponential Growth factor for Nearby Orbits.
We apply this method on the Geminids, a well-known meteoroid stream. We show the influence of mean-motion resonances with the Earth and with Venus, which tend to trap the largest particles. The chaos maps present 3 distinct regimes in eccentricity, reflecting close encounters with the planets. We also study the effect of NGFs and we determine a first approximation of the particle size needed to counterbalance the resonances with the diffusion created by NGFs.
The seminar will take place in room S08 at the Faculty of Sciences

Johan SEGERS (UCLouvain)
2022-12-01 13:00 - 14:00
Title: Graphical and uniform consistency of estimated optimal transport plans
Abstract: A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based on the identification of such a mapping with a closed subset of a Cartesian product of Euclidean spaces and leveraging tools from random set theory. Weak convergence in the appropriate Fell space together with the maximal cyclical monotonicity then automatically yields local uniform convergence of the associated mappings. Viewing such mappings as optimal transport plans between probability measures with respect to the squared Euclidean distance as cost function yields consistency results for notions of multivariate ranks and quantiles based on optimal transport, notably the empirical center-outward distribution and quantile functions.
The seminar will take place in room S08 at the Faculty of Sciences

Victor Pessanha (Mathematical Institute of the Federal University of Rio de Janeiro, Brazil)
2022-12-15 13:00 - 14:00
Title: A quick introduction to knots and braids
Abstract: In this talk I will do an overview on the theory of knots and braids. The idea is to define what these objects are and to present two major theorems relating them by just giving an intuition behind their proof. If possible, I will also talk about how these objects can naturally appear in the dynamics of point masses.
The seminar will take place in Room S08 at the Faculty of Sciences.

Stefanella Boatto (Department of Applied mathematics, Institute of Mathematics, Federal University of Rio de Janeiro, Brazil)
2023-01-24 10:30 - 11:30
Title: A journey into the mathematical universe: Topological Data Analysis. A briefintroduction and some applications.
Abstract: Data Science is a highly evolving discipline that presents many challenges. Forexample, in the case of an epidemic, how can we identify which socio–economic and socialparameters, tourist mobility, prevention and control measures have the greatest impact onthe dynamics of an epidemic? In recent years Topological Data Analysis has proved to be apowerful tool, a lens to highlight some dominant features of collective phenomena andexplore large and complex data sets. In this lecture we will see a brief introduction and howthis new discipline is highly multidisciplinary within mathematics itself, bringing togetherareas such as Space–Time Analysis, Algebraic Topology, Complex Networks, Alg. Linear andComputation.
The seminar will take place in Room S08 at the Faculty of Sciences.

Sylvério Pool Marquez (University of Namur)
2023-02-16 13:00 - 14:00
Title: Impact of mixed-variable management by probability features in an Evolutionary Algorithm
Abstract: The management of mixed variables, i.e., of different natures (continuous, integer, discrete, categorical) in optimization problems is a challenge, especially in the presence of categorical variables since there is no concept of order between their possible “values”. In a black-box optimization context, a way to handle categorical variables has been proposed within a particle swarm algorithm to improve its performance. It consists in defining a probability feature for each “value” of each categorical variable which will evolve during the optimization process. These probabilities are then used to update the population of the algorithm.In this talk, we present an adaptation of this method to be used in the evolutionary algorithm (EA) implemented in Minamo, the in-house design space exploration and multi-disciplinary optimization platform developed in the applied research center Cenaero. More specifically, we propose several ways to use these probabilities inside the genetic operators of the EA and we compare them in order to get a modified version of the EA which is more efficient in the presence of categorical variables.
The seminar will take place in Room S08 at the Faculty of Sciences.

Ramachandran CHITTUR ANANTHARAMAN (University of Namur)
2023-03-09 13:00 - 14:00
Title: Inverses of polynomials over finite fields – A Koopman operator based approach
Abstract: Any map (linear or non-linear) from a finite field to itself can be represented as a polynomial with coefficients over the finite field. When the map is invertible (under composition), the inverse map will also have a polynomial representation. Verifying invertibility and computing the inverse of the non-linear maps over finite fields have significant applications in cryptography and coding theory. In this talk, I discuss a Koopman operator-based approach to test invertibility, compute the inverse of polynomials, and define a linear representation for non-linear maps. This approach can be extended to a parametric family of maps over finite fields (such as Dickson polynomials), and the parametric inverse is computed (when the parametric map is invertible). Further, I shall discuss how this linear representation defined through the Koopman operator leads to a group representation for a group generated by multiple invertible maps under composition.
The seminar will take place in Room S08 at the Faculty of Sciences.

Lorena Ballesteros Ferraz (University of Namur)
2023-03-16 13:00 - 14:00
Title: Geometrical and non–normal properties of weak values
Authors: Lorena Ballesteros Ferraz, Dominique Lambert, Timoteo Carletti, Riccardo Muolo,and Yves Caudano
Abstract: Quantum measurements are essential to all quantum experiments and are key to developing new quantum technologies. In particular, weak measurements have attracted much interest, for both theoretical and experimental reasons. When performing a weak measurement with preselection (which consists of choosing the initial state) and post–selection (which requires a projective measurement after the weak measurement and corresponds to choosing the final state), weak values appear. In that case, the ancilla’s wavefunction is shifted in position by a quantity that is proportional to the real part of the weak value.
Its wavefunction is also shifted in momentum by a quantity that is proportional to the imaginary part of the weak value. Even though weak values are regularly studied in terms of their real and imaginary parts, we focus our analysis in terms of their modulus and argument. In this work, we have studied the geometrical interpretation of the argument of weak values of general observables in N–level systems. This argument corresponds to a geometric phase (Berry phase) that is associated to the symplectic area generated by the geodesic triangle spanned by the three normalized vectors representing the initial state, the application of the observable over the initial state and the postselected state. These vectors represent quantum pure states in complex projective space CP^(N–1) and they can be mapped to a subspace of the (𝑁² − 2)–sphere, a generalization of the Bloch sphere (the usual S² sphere, used to describe qubits).
The argument of the weak value of an N–level system observable can also be mapped to the sum of N–1 arguments of weak values of two–level projectors up to a phase that specifies the quadrant. Each of these arguments is associated to the solid angle on the Bloch sphere spanned by three vectors representing the pre–selected state, the observable and the post–selected state. To obtain this decomposition, we employ the Majorana representation to factor the weak value of the N–level system observable into the product of N–1 weak values of qubit projectors and a real constant.
Studying the modulus of the weak value provides information on the ability of weak values toamplify minute phenomena as well as their role in improving the estimation of small physicalparameters. Weak values can be written as the expectation value of a non–normal operator.Investigating the non–normal properties of the operator, we found a direct link with theamplitude of the modulus of the weak value. This paves the way for a deeper understanding of these values from an energetics point of view and links the fields of weak measurements and non–normality.
The seminar will take place in Room S08 at the Faculty of Sciences.

Fabian Bastin (University of Montreal (Canada)) - Cinzia Cirillo (University of Maryland (USA))
2023-04-06 13:00 - 14:00
Title: Large-scale transport model systems: from synthetic population generation to agent-based simulation
Abstract:
1. Generation of synthetic populations exploiting dependency structure transfer (Fabian Bastin)
The generation of synthetic populations consists of producing a realistic representation of a target population for modeling and behavioral simulation purposes, a task that can be tricky when the available multivariate samples are small. Starting from the idea that combining various sources of information makes it possible to design more realistic population generators, we introduce a new framework based on copulas to generate synthetic data for a population whose only empirical marginal distributions are known, using a sample from another population sharing a similar dependency structure. We compare the proposed scheme to common methods such as Iterative Proportional Fitting and to modern probabilistic approaches such as Bayesian networks, variational auto-encoders and generative adversarial networks. We illustrate on American Community Survey data that the method proposed allows to study the structure of the data at different geographical levels in a way that is robust to the peculiarities of the marginal distributions.
2. Large scale transportation model systems: an agent-based simulator for the State of Maryland (Cinzia Cirillo)
The talk will introduce the architecture of a large-scale microsimulation model that combines population synthesis, land use models, transportation choices, and agent-based transport simulation. This modeling suite overcomes limitations of aggregate four step models and is completely open source. Application of this type of tools will be illustrated in the context of transportation and equity; the first considers the problem of evacuating low-income carless populations during an emergency, the second evaluates the effects of complete streets on the willingness to walk and bike under different levels of traffic stress.
The seminar will take place in Room S08 at the Faculty of Sciences.

Hilda A. CERDEIRA (Instituto de Física Teórica, UNESP, São Paulo, Brazil)
2023-04-13 13:00 - 14:00
Title: Phase transition to Synchronization in a system of Swarmalators
Abstract: Systems of oscillators called Swarmalators,whose phase and spatial dynamics are coupled, have been used to describe the dynamics of some living systems. Their collective behavior presents simultaneous aggregation in space and synchronization in phase which in turn leads in some cases to explosive synchronization in a finite population as a function of the coupling parameter between the phases of the internal dynamics. This phenomenon is described using the order parameter and the Hamiltonian formalism. Near the synchronization transition the phase energy of the particles are represented by the XY model, and they undergo a transition which can be of the first order or second depending on the distribution of natural frequencies of the internal dynamics of the swarmalators.
The seminar will take place in Room S08 at the Faculty of Sciences.

Philippe Naveau (Laboratoire des Sciences du Climat et de l'Environnement (LSCE) CNRS, France)
2023-04-20 13:00 - 14:00
Title: Records Analysis in Climate Attribution
Abstract: Numerical climate models are complex and combine a large number of physical processes. They are key tools in quantifying the relative contribution of potential anthropogenic causes (e.g., the current increase in greenhouse gases) on high-impact atmospheric variables like heavy rainfall or temperatures. These so-called climate extreme event attribution problems are particularly challenging in a non-stationary context. In addition, global climate models like any in sillico numerical experiments are affected by different types of bias. In this talk, I will discuss about how to combine to different statistical concepts to assess records changes in the context of extreme event attribution. In addition, the question of uncertainties quantification that remains a challenge in any climate attribution analysis will be explored from various directions. In particular, a simple model bias correction step for records will described in detail. To illustrate our approach, we infer emergence times in precipitation from the CMIP5 and CMIP6 archives. This is joint work with Paula Gonzalez, Soulivanh Thao and Julien Worms.
The seminar will take place in Room S08 at the Faculty of Sciences.

Daniele Avitabile (Vrije Universiteit Amsterdam, The Netherlands)
2023-04-25 13:00 - 14:00
Title: Bump Attractors and Waves in Networks of Integrate-and-Fire Neurons

Abstract: Bump attractors are localised patterns observed in in vivo experiments of neurobiological networks. They are important for the brain’s navigational system and specific memory tasks. A bump attractor is characterised by a core in which neurons fire frequently, while those away from the core do not fire. We uncover a relationship between bump attractors and travelling waves in a classical network of excitable, leaky integrate-and-fire neurons. This relationship bears strong similarities to the one between complex spatiotemporal patterns and waves at the onset of pipe turbulence. We define and study analytical properties of the voltage mapping, an operator transforming a solution’s firing set into its spatiotemporal profile. This operator allows us to construct localised travelling waves with an arbitrary number of spikes at the core, and to study their linear stability. A homogeneous “laminar” state exists in the network, and it is linearly stable for all values of the principal control parameter. We show that one can construct waves with a seemingly arbitrary number of spikes at the core; the higher the number of spikes, the slower the wave, and the more its profile resembles a stationary bump. As in the fluid-dynamical analogy, such waves coexist with the homogeneous state, are unstable, and the solution branches to which they belong are disconnected from the laminar state. We provide evidence that the dynamics of the bump attractor displays echoes of the unstable waves.

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

Ludovic Ducobu (Transilvania University of Brasov, Romania)
2023-06-01 13:00 - 14:00
Title: Compact objects and scalar fields in theories of gravity with torsion, ep. 1 : modelisation
Abstract:
General Relativity [GR] offers an extremely successful framework to describe the gravitational interaction. That being said, the necessity to question the framework of GR is clear at both the experimental (origin and composition of dark matter and dark energy) and theoretical (search for quantum gravity) levels.
Since not all these puzzles can be purely reduced to quantum correction problems, this motivates the study of alternative theories of gravitation already at the classical level.

To this purpose, one can follow two distinct but complementary routes. On the one hand, one can try to modify Einstein’s equations by introducing new fields while maintaining the assumptions related to the geometrical structure of spacetime. On the other hand, one can precisely question the framework of pseudo-Riemannian geometry as being adapted to the full description of spacetime (typically, at cosmological scales).
In the first case, scalar-tensor theories of gravity (and especially Horndeski gravity), where the new degrees of freedom are encoded by means of a scalar field, have been extensively investigated in the litterature.
In the later case, a minimal generalisation of GR’s framework consist in relaxing the hypothesis linking the connection to the metric, leading to the framework of metric-affine gravity. This reveals new starting points to generalise GR through, for instance, an examination of the so-called geometrical trinity of gravity.

The aim of this talk is to present the main motivations and features of modified theories of gravity involving scalar fields in both the usual (GR) and metric-affine approaches.

I will first propose a quick overview of Horndeski gravity and of the metric-affine approach of GR; focussing on the so-called Teleparallel theories of gravity and on the Teleparallel equivalent to GR.
Then, “unifying” the two approaches, I will advocate for the interest of modified theories of gravity involving scalar fields in the metric-affine framework.
I will then present recent results from my own research and discuss the first study of assymptotically flat black holes endowed with scalar hair in a teleparallel generalisation of Horndeski gravity.
Our study provides an explicit demonstration of how scalar-torsion gravity (and possibly other non-Riemaniann models) provides a richer canvas for the study of phenomenology beyond GR and open the way for novel studies regarding scalarized black hole solutions in non-Riemannian theories of gravity.

This presentation is based on the work done in [arXiv:2201.11445 [gr-qc]] (https://arxiv.org/abs/2201.11445) and [arXiv:2212.07653 [gr-qc]] (https://arxiv.org/abs/2212.07653) in collaboration with Sebastian Bahamonde, Daniela Doneva, Christian Pfeifer and Stoytcho Yazadjiev.

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

Enoch Yeung (UC Santa Barbara (UCSB), USA)
2023-06-30 13:00 - 14:00
Title: Data-Driven State Criticality and Observability with Koopman
Operator Methods
Abstract: I will present two major results to show the use of data-
driven Koopman methods to identify critical states and observable
subspaces to solve problems in synthetic biology. In the first, I
present the use of dynamic mode decomposition (DMD) to model the
transcriptome-wide response of a root-isolate bacterium to a novel
chemical compound. By solving an observability maximization problem
for the DMD model, we find a panel of biomarkers that can act as
effective biosensors for the compound, even in field studies with the
bacterium. This study establishes a new precedent for reasoning about
state criticality and system observability, even without prior
knowledge of a network model. Second, I present new theoretical
results that show how Koopman methods can be used to evaluate
criticality of states to optimize performance of a nonlinear system.
Historically, this problem is solved using either direct sensitivity
analysis on a known model or by generating local function
distributions that span the nonlinear observable subspace of a system.
In the absence of a known model, I present a new Koopman-based method
for estimating the observable subspace of a nonlinear system purely
from data. Our results provide a route for data-driven discovery of
critical states that affect an output-based performance measure.
The seminar will take place in Room S08 at the Faculty of Sciences.

Stefanella Boatto (Federal University of Rio de Janeiro)
2023-10-19 13:00 - 14:00
Title: Vortex and gravitational modeling : A long journey with a rich mathematical history
Abstract:
Vortex and gravitational dynamics have long fascinating and interwoven histories, both for the modeling and for the different areas of mathematics needed to study the corresponding models. Philosophical questions reside behind the modeling part, as for example how do we define gravity beyond our Euclidean R3 perception?
Are the laws we are so familiar with, universal ? What is the geometry of our universe? As for vortices within the boundary of our Solar systems we witness fascinating images of vortex dynamics. Recent beautiful observations of polygonal configurations of vortices present in the atmosphere of Jupiter and Saturn, and of polygonal jets in the Earth’s atmosphere have revived the interest in the subject.
The seminar will take place in Room S08 at the Faculty of Sciences.

Guillermo Garcia-Sanchez (Spanish National Research Council, Spain)
2023-10-26 13:00 - 14:00
Title: From Chaos to Clarity: Revealing Oceanic Transport Pathways In Real-World Applications Through Dynamical Systems
Abstract: Finding order in the apparent chaos that seems to govern transport processes in the ocean is a challenge. Dynamical system tools, such as Lagrangian Descriptors reveal time dependent geometries in the ocean that comprise an efficient underlying transport network. In this talk, I will show how these theoretical approaches are now being applied to address various marine problems, including oil spills, harmful algae, marine litter and search and rescue operations, bridging the gap between academic theory and real-world applications.
The seminar will take place in Room S08 at the Faculty of Sciences.

Tamas Kovács (Institute of Physics, Eötvös University, Hungary)
2023-11-09 13:00 - 14:00
Title: Stability of exoplanetary systems retrieved from scalar time series
Abstract: In this talk I propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time series are used to reconstruct the high-dimensional phase space trajectory representing the dynamical evolution of planetary motion. The framework of nonlinear time series analysis and Poincaré recurrences allows us to transform the obtained univariate signals into complex networks whose topology carries the dynamical properties of the underlying system. The proposed scheme does not require neither n-body integration nor best fitting planetary model to perform the stability investigation, therefore, the computation time can be reduced drastically compared to those of the standard numerical methods.
The seminar will take place in Room S08 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.
