HAL-INSA Toulouse
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Observed-based exponential stability of the fractional heat equation
No full textInternational audienceIn this work, the exponential stability of the nonlocal fractional heat equation is studied. The fractional Laplacian is defined via a singular integral. Using the spectral properties of the fractional Laplacian and a state-decomposition. The feedback control is build taking account the first N modes and an observer defined via a bounded operator. Different kind of configurations are studied to mention, interior controller and interior observation, interior controller and exterior observation. Using the recent result about simplicity of the eigenvalues \cite{fall2023generic}, some of our stabilization results are valid for s ∈ (0, 1), in particular for s ∈ (0, 1/2) in which case the fractional heat equation is not null controllable
Modeling ballistic aggregation by time stepping approaches
No full textInternational audienceThis paper deals with the problem of simulating dense dispersed systems composed by large numbers of particles undergoing ballistic aggregation. The most classical approaches for dealing with such problems are represented by the so-called event-driven methods. Despite being more accurate, these methods become computationally very expensive as the number of particles increases. Typically, their computational cost is proportional to the square of the number of particles and thus they become extremely demanding as soon as this number becomes sufficiently large. An alternative approach, called time-stepping, consists in evolving the problem over small time-intervals and to handle all collisions occurring during each time interval simultaneously. In this work, we follow this second direction and we introduce a new time stepping method which recasts the problem of the multiple collisions in a minimization framework. The objective of this work is twofold, first to show that the statistical description of the resulting aggregates obtained with this new time stepping method is sufficiently close to that of the event driven methods. The second goal consists in showing that the computational performance considerably improve when the number of particles becomes sufficiently large. Numerical results obtained in the case of spherical particles moving in a two dimensional box show that these two properties are indeed satisfied by this new method
Impulsive switching signals with functional inequalities: Stability analysis using hybrid systems framework
No full textInternational audienceIn this work, we introduce a class of impulsive switching signals described via functional inequalities which govern the switching among different modes with state resets. By choosing the parameters of the inequalities appropriately, we can recover several known classes of switching signals and also allow for signals that depend on time, mode or state of the system. Signals from this class can also be generated online via the use of an auxiliary timer while the dynamical system is running. Via a multiple Lyapunov functions approach, we provide sufficient conditions on the functional parameters of the switching signal which ensure that the equilibrium is globally asymptotically stable (GAS) for autonomous impulsive switched system. In case of inputs, similar methodology is used to provide sufficient conditions for input-to-state stability (ISS) and integral-input-tostate stability (iISS) uniformly over the proposed class of impulsive switching signals. As case studies, we consider switched systems which do not satisfy ISS (respectively, iISS) property for switching signals with arbitrarily large dwell-times but they are shown to be ISS (resp. iISS) for our proposed class of impulsive switchings signals described via functional inequalities.</div
Exponentially fast selection of sectors for quantum trajectories beyond non demolition measurements
No full textInternational audienceWe show that, in long time, quantum trajectories select an invariant subspace of the Hilbert space of the system being indirectly measured. This selection is shown to be exponentially fast in an almost sure sense and in average. This result generalizes a known result for non demolition measurements to arbitrary repeated indirect measurements. Our proofs are based on the introduction of a deformation of the original instrument to an equivalent one with a unique invariant state
Taming the Triangle: On the Interplays between Fairness, Interpretability and Privacy in Machine Learning
No full textInternational audienceMachine learning techniques are increasingly used for high-stakes decision-making, such as college admissions, loan attribution or recidivism prediction. Thus, it is crucial to ensure that the models learnt can be audited or understood by human users, do not create or reproduce discrimination or bias, and do not leak sensitive information regarding their training data. Indeed, interpretability, fairness and privacy are key requirements for the development of responsible machine learning, and all three have been studied extensively during the last decade. However, they were mainly considered in isolation, while in practice they interplay with each other, either positively or negatively. In this survey paper, we review the literature on the interactions between these three desiderata. More precisely, for each pairwise interaction, we summarize the identified synergies and tensions. These findings highlight several fundamental theoretical and empirical conflicts, while also demonstrating that jointly considering these different requirements is challenging when one aims at preserving a high level of utility. To solve this issue, we also discuss possible conciliation mechanisms, showing that a careful design can enable to successfully handle these different concerns in practice
Body-attitude coordination in arbitrary dimension
No full textInternational audienceWe consider a system of self-propelled agents interacting through body attitude coordination in arbitrary dimension n ≥ 3. We derive the formal kinetic and hydrodynamic limits for this model. Previous literature was restricted to dimension n = 3 only and relied on parametrizations of the rotation group that are only valid in dimension 3. To extend the result to arbitrary dimensions n ≥ 3, we develop a different strategy based on Lie group representations and the Weyl integration formula. These results open the way to the study of the resulting hydrodynamic model (the "Self-Organized Hydrodynamics for Body orientation (SOHB)") in arbitrary dimensions
How to Study the Mechanobiology of Intestinal Epithelial Organoids? A Review of Culture Supports, Imaging Techniques, and Analysis Methods
No full textInternational audienceMechanobiology studies how mechanical forces influence biological processes at different scales, both in homeostasis and in pathology. Organoids, 3D structures derived from stem cells, are particularly relevant tools for modeling tissues and organs in vitro. They currently constitute one of the most suitable models for mechanobiology studies. This review provides an overview of existing or applicable approaches to organoids for mechanical studies. We first present the different types of culture supports, including hydrogels and organ‐on‐chip. We then discuss advanced imaging techniques, particularly suitable for studying the physical properties of cells, allowing the visualization of mechanical forces and cellular responses. We also describe the approaches and tools available to observe the organoids by microscopy. Finally, we present analytical methods, including computational models and biophysical measurement approaches, which facilitate the quantification of mechanical interactions. This review aims to provide the most comprehensive overview possible of the methods, instrumentations, and tools available to conduct a mechanobiological study on organoids
Experimental and Detonation-Shock Dynamics analyses of cellular detonations in diverging channels: the effects of the cross-sectional shape
No full textInternational audienceThis experimental study examines the transients of cellular detonations during weak diffraction from straight to diverging channels. First, we analyze the effects of the cross-sectional shapes (square or round) on the 3D transients of the detonation cells using parietal and head-on soot recordings. The diverging channels have the same initial cross-sections (shape and area) as the straight channels, with their area increasing linearly at an equal moderate expansion rate. The cell mean widths first increase from starting values dependent on the channel shape and then decrease to stabilize at the same higher value independent of the channel shape. Then, we use a relationship between velocity, acceleration, and total curvature of the average detonation front which qualitatively explains the experimental trends, particularly the non-monotonic variation in the mean cell widths. This sensitivity makes the experimental data reliable for high-resolution numerical simulations that can handle three-dimensionality and detailed chemical kinetic mechanisms
Icosahedra CoPd Bimetallic Nanoparticles for Magnetically Induced Aromatic Ketone Hydrodeoxygenation
No full textInternational audienceThe development of bimetallic nanomaterials with precisely controlled size, shape and composition has emerged as a cornerstone of sustainable catalysis, offering innovative solutions for chemical valorization processes. In this work, CoPd bimetallic nanoparticles (NPs) were prepared via an organometallic approach using Co[N(SiMe3)2]2(thf) and Pd(acac)2 (acac: acetylacetonate) as metal sources. Advanced structural characterization techniques including high-resolution transmission electron microscopy (HR-TEM), X-ray diffraction (XRD) and wideangle X-ray scattering (WAXS) revealed an icosahedral Pd-rich core with a less crystalline Co rich shell. Thanks to a large magnetic anisotropy, these 10 nm particles are ferromagnetic at room temperature and thus can be used as efficient heating agents under alternative magnetic field (AMF). This nanomaterial was successfully tested as a catalyst in hydrodeoxygenation (HDO) reactions using induction heating (IH) for energy-efficient activation. The CoPd catalyst demonstrates the synergistic potential of non-noble/noble metal combination, achieving challenging chemical transformations at relatively low temperatures, while keeping an optimal balance between their heating capability and surface-to-volume ratio. This study underscores the potential of CoPd systems for advancing sustainable catalysis through magnetically induced reactions
Improved learning theory for kernel distribution regression with two-stage sampling
No full textThe distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method of choice. Indeed, kernel distribution regression is both computationally favorable, and supported by a recent learning theory. This theory also tackles the two-stage sampling setting, where only samples from the input distributions are available. In this paper, we improve the learning theory of kernel distribution regression. We address kernels based on Hilbertian embeddings, that encompass most, if not all, of the existing approaches. We introduce the novel near-unbiased condition on the Hilbertian embeddings, that enables us to provide new error bounds on the effect of the two-stage sampling, thanks to a new analysis. We show that this near-unbiased condition holds for three important classes of kernels, based on optimal transport and mean embedding. As a consequence, we strictly improve the existing convergence rates for these kernels. Our setting and results are illustrated by numerical experiments