All Years Seminars
[INMA] 2024-10-08 (14h) : Expanding Inductive Functional Proofs: Beyond Barrier Certificates
At Euler building (room A.002)
Speaker :
Majid Zamani (University of Colorado Boulder, USA)
Abstract :
A prominent approach to ensuring the safety of cyber-physical systems is through the use of barrier certificates—real-valued functions that serve as inductive proofs of safety. In this talk, we explore generalizations of barrier certificates, inspired by alternative notions of induction, to verify discrete-time dynamical systems against a wide range of specifications, from safety to more complex logic-based and security specifications. We introduce several new concepts, including k-inductive barrier certificates, closure certificates, and augmented barrier certificates, to verify systems against safety, ω-regular, and hyperproperty specifications. Drawing from k-induction in software verification, we propose k-inductive barrier certificates for system safety verification, allowing simpler functions to serve as proofs of safety compared to traditional barrier certificates. Building on the concept of transition invariants, we introduce closure certificates for verifying systems against ω-regular properties—temporal specifications described by ω-regular automata, which extend beyond safety to encompass a broader class of system behaviors. Finally, we present augmented barrier certificates for verifying systems against hyperproperties, which describe relationships between system traces and often address security-related concerns.
[INMA] 2024-10-01 (14h) : Newcomers seminars (PhDs)
At Euler building (room a.002)
Section 1:Tools for measuring and quantifying neurodegenerative diseases. Quantitative approach applied to essential tremor and Parkinson disease
Speaker :
François Lessage (PhD UCLouvain/INMA)
Abstract : To develop quantitative measures and assess pathologies affecting movement control, we will study populations with essential tremor (ET) and Parkinson disease (PD) in tasks at the forefront of current knowledge on these pathologies. For essential tremor, we will study the mechanism of sensory attenuation in relation to recent laboratory results suggesting delay compensation errors. For Parkinson disease, we will study Long-Range Autocorrelation (LRA) and adaptation to better understand how this pathology affects gait control. In both cases, we hope to expand knowledge and identify complementary measures that could be useful to quantify these deficits.
Section 2:A computational framework to study the integration of mechanical and thermal inputs during tactile interactions
Speaker :
Louis Lovat (PhD UCLouvain/INMA)
Abstract : A computational framework to study the integration of mechanical and thermal inputs during tactile interactions"
Abstract : "The study of somatosensation has made significant strides, with numerous models developed to simulate either mechanical or thermal responses of the skin. These models have provided valuable insights into the response of the skin under various conditions, such as stress, deformation, and temperature changes. However, most existing models tend to focus on either mechanical or thermal stimuli in isolation, bypassing proven interactions between the different somatosensory submodalities and often overlooking the fine-scale interactions that occur at the level of fingerprint ridges and small topographic features of objects. Here, we aim to develop a comprehensive computational framework capable of simulating the complex interactions between mechanical and thermal stimuli at the fingertip. The core of this work being to create a detailed model of the fingertip accurately predicting the mechanical and thermal responses of the skin at both macro and micro scales. This model will be integrated with artificial neurons representing somatosensory afferents which will allow precise simulation of the sensory system’s responses to various combined stimuli. Understanding how the human somatosensory system captures these intricate dynamics will provide a tool to design, predict and interpret future psychophysical and neurophisiological experiment, and contribute to practical applications in the development of haptic interfaces, neuroprosthetics and virtual reality technologies
Section 3:Tight analysis and design of online optimization algorithms
Speaker :
Erwan Meunier (PhD UCLouvain/INMA)
Abstract : Online optimization algorithms aim at minimizing on average over time a function that can change every time it is sampled. Crucially, the value of the function often has to be “paid” each time it is sampled, e.g. in terms of energy, money, prediction error, etc. Preliminary results in my master‘s thesis show that (i) the currently available performance bounds are conservative, which can lead to a suboptimal use and tuning of online methods and higher costs, and (ii) tight performance bounds can be understood by analyzing highly structured low-dimensional functions. In my thesis, I will be to analyze and exploit this structure to develop general worst-case performance bounds, and to use these bounds and the insights gained to design novel more efficient online optimization algorithms.
Specifically, I will begin by analyzing online settings with unstructured (arbitrary) changes of functions. I will then move to several contexts where changes are structured, with applications in control and stochastic optimization. Finally, I will generalize my results to distributed online optimization, where a group of interconnected computers each own a part of the functions and collaborate towards the global minimization. Based on recent results in standards optimization, potential gains in the decentralized settings are suspected to be tremendous. A key enabler of my project and my preliminary works, is the recently developed performance estimation problem (PEP) methodology, which allows computing the exact worst-case behavior of a wide class of deterministic optimization algorithms, by formulating this analysis itself as a tractable optimization problem. I will exploit it both as a guide in my exploration, and as a method for theoretical developments
.
[INMA] 2024-09-24 (14h) : Newcomer seminar (postdocs)
At Euler building (room a.002)
Section 1:Synchronization Analysis, Control and Verification of Complex Networked Systems
Speaker :
Shuyuan Zhang
Abstract : Synchronization is a kind of common collective phenomenon in nature, which has a quite wide range of applications for various subjects, including physics, biology, control science, social science. A typical way of analyzing synchronization of complex networked systems is to establish the synchronization criteria based on quadratic Lyapunov functions. Beyond the challenge of obtaining quadratic Lyapunov functions, the serious challenge is no guarantee of Lyapunov functions of the quadratic form for some systems. However, for these systems, there may exist general Lyapunov functions. Inspired by this fact, we propose several less conservative synchronization criteria by using general Lyapunov functions beyond quadratic ones. Then, the synchronization problem is transformed into a sum-of-squares optimization problem. The resulting sum-of-squares-based optimization algorithm efficiently generates polynomial Lyapunov functions, facilitating automatic synchronization verification. The obtained results are less conservative and are applicable for more systems, not only homogeneous networked systems but also heterogeneous networked systems.
Section 2:A coarse view on dynamical systems, control and optimization
Speaker :
Wouter Jongeneel
Abstract : It is not clear if our field would be in this state without early efforts towards understanding stability of the solar system. At that time---as explicit integration turned out to be overly complicated, the key insight was not to approximate, but to move away from the quantitative. The result was the inception of a more qualitative study of dynamical systems, with the overall philosophy being nicely captured by Conley: "... if such rough equations are to be of use it is necessary to study them in rough terms ...".
Now, flash-forward to 2024, with the advent of computational power and data storage, the focus shifted again to the quantitative. It is hard to find papers without sample complexities, probabilistic bounds and a statistical analysis of extensive simulations. This viewpoint is evidently very important towards safe and practical algorithms, for instance, regarding a control system. So is there still room for something qualitative?
In this talk we discuss open homotopy questions (and partial resolutions) in dynamical systems, topological insights in control systems and we comment on some optimization problems. With these examples we hope to show that there is indeed room---and arguably a need, for more qualitative work in a quantitative age.
[INMA] 2024-09-17 (14h) : Emergence and control of synchronization patterns in systems with higher-order interactions
At Maxwell building (Shannon room)
Speaker :
Riccardo Muolo (Tokyo Institute of Technology)
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 a Kuramoto-type model. Despite the versatility of such an approach, the classical theory of synchronization is solely based on pairwise interactions, while, in many systems, the interactions are intrinsically higher-order (many-body) rather than pairwise [3]. In fact, many examples show that a pairwise description is not sufficient 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 to synchrony and other rich behaviors [5].
I will start by introducing the phase reduction theory and highlight the universality of phase models. 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 enrich the synchronization patterns of the system [6]. In the last part of the seminar, I will briefly introduce an intriguing synchronization pattern in which coherent and incoherent oscillators coexist, called chimera states [7]. Such patterns are known to be elusive and characterized by a very short life-time when the interactions are pairwise, but are enhanced by the presence higher-order interactions [9]. This fact can be exploited by using a pinning control approach: in fact, controlling the emergence of chimera states in systems with higher-order interactions is much easier and efficient if compared with the classic network framework [10].
This is joint work with Hiroya Nakao (Tokyo Institute of Technology, Japan), Shigefumi Hata (Kagoshima University, Japan), Iván León (University of Cantabria, Spain), Lucia Valentina Gambuzza and Mattia Frasca (University of Catania, Italy)
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] León I., Muolo R., Hata S. and Nakao H., Higher-order interactions induce anomalous transitions to synchrony. Chaos 34, 013105, 2024.
[7] Zakharova A., Chimera Patterns in Networks. Interplay between Dynamics, Structure, Noise, and Delay. Springer, 2020.
[8] Kuramoto Y. and Battogtokh D, Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Nonlinear Phenom. Complex Syst. 5, 2002.
[9] Muolo R., Njougouo T., Gambuzza L.V., Carletti T. and Frasca M., Phase chimera states on nonlocal hyperrings. Phys. Rev. E 109, L022201, 2024.
[10] Muolo R., Gambuzza L.V., Nakao H. and Frasca M., Pinning control of chimera states on nonlocal hyperrings. In preparation.
.
[INMA] 2024-08-22 (14h) : Exact Continuous Relaxations of L0-Regularized Generalized Linear Models
At Euler building (room A.002)
Speaker :
Emmanuel Soubies (IRIT, CNRS, Université de Toulouse)
Abstract :
Sparse generalized linear models are widely used in fields such as statistics, computer vision, signal/image processing and machine learning. The natural sparsity promoting regularizer is the l0 pseudo-norm which is discontinuous and non-convex. In this talk, we will present the l0-Bregman relaxation (B-Rex), a general framework to compute exact continuous relaxations of such l0-regularized criteria. Although in general still non-convex, these continuous relaxations are qualified as exact in the sense that they let unchanged the set of global minimizer while enjoying a better optimization landscape. In particular, we will show that some local minimizers of the initial functional are eliminated by these relaxations. Finally, these properties will be illustrated on both sparse Kullback-Leibler regression and sparse logistic regression problems. This is joint work with M'hamed Essafri and Luca Calatroni.
Seminars
Subscribe (ICS)
INMA Contact Info
Mathematical Engineering (INMA)
L4.05.01
Avenue Georges Lemaître, 4
+32 10 47 80 36
secretaire-inma@uclouvain.be
Mon – Fri 9:00A.M. – 5:00P.M.
JOIN US