Sur quelques problèmes de stabilisation de systèmes à paramètres distribués

This work is devoted to feedback stabilization of some distributed parameters systems. The first part deals with the boundary feedback stabilization of a rotating body-beam system. This one consists of a disk with a beam attached to its center and perpendicular to its plan. We propose a local boundary feedback laws, (force and/or moment applied on the free end of the beam, and a torque control applied on the disk). We show that these feedback laws exponentially stabilize the system so that the beam vibrations are suppressed and the whole structure rotates about the axis with a given, sufficiently small, angular velocity. We illustrate this results by some numericals simulations. In the second part, we study the problem of boundary feedback stabilization of a hybrid system. This one is composed of an elastic beam linked to a rigid antenna. The vibrations of this system are governed by a partial differential equation and two ordinary differential equations. In our model, the moment of inertia of the antenna in neglected. Our purpose is to stabilize this system by only a bending moment feedback. We show that this can be achieved by using a simple feedback law. Finally, in the third part, we study the spectre assignment, by bounded linear feedback, for two examples of distributed parameters systems. For the wave equation, we show that the best stability result achievable by continuous feedback is strong stability. For the cantilever beam equation, we show that it is possible to assign the spectrum uniformly by continuous feedback, this garantees the exponential stabilization of the system with an arbitrary decay rateDans ce travail, on s'intéresse à la stabilisation par retour d'état, pour certains systèmes à paramètres répartis. La première partie concerne la stabilisation d'un système rigide-flexible en rotation. Ce système est composé d'un disque au centre duquel est encastrée une poutre flexible, l'autre extrémité étant libre. Nous avons proposé des lois de commande locales (force et/ou moment appliqués à l'extrémité libre de la structure flexible) et couple appliqué sur le disque. Nous avons montré que ces lois de commande stabilisent exponentiellement le système autour d'une configuration à vitesse constante, suffisamment petite, ou les vibrations du système sont supprimées. Les résultats obtenus ont été illustrés par des simulations numériques. La deuxième partie traite du problème de stabilisation, par feedback frontière, d'un système constitue d'une poutre encastrée en l'une de ses extrémités, à l'autre extrémité est fixée une antenne rigide de masse m. Dans le modèle considéré on néglige le moment d'inertie de la masse m. Les vibrations de ce système sont régies par une équation aux dérivées partielles et deux équations différentielles ordinaires. L'objectif est de stabiliser ce système par le seul feedback de moment appliqué sur la masse m. Nous avons proposé une loi de commande locale qui rend l'énergie dissipative, puis nous avons établi la stabilité uniforme du système. Dans la dernière partie, on a étudié le problème de placement du spectre, par feedback linéaire borne, pour deux systèmes à paramètres répartis. Le premier système décrit les vibrations d'une corde, pour celui-ci nous avons montré que, par feedback linéaire borné appliqué sur la frontière, seule la stabilité forte peut être assurée. Pour le second système, qui décrit les vibrations d'une poutre encastrée, nous avons établi que le spectre du système peut être déplacé uniformément vers la gauche, ce qui garantit la stabilisation exponentielle avec un taux de décroissance arbitrair

Certification of Deep Learning Models for Medical Image Segmentation

International audienceIn medical imaging, segmentation models have known a significant improvement in the past decade and are now used daily in clinical practice. However, similar to classification models, segmentation models are affected by adversarial attacks. In a safety-critical field like healthcare, certifying model predictions is of the utmost importance. Randomized smoothing has been introduced lately and provides a framework to certify models and obtain theoretical guarantees. In this paper, we present for the first time a certified segmentation baseline for medical imaging based on randomized smoothing and diffusion models. Our results show that leveraging the power of denoising diffusion probabilistic models helps us overcome the limits of randomized smoothing. We conduct extensive experiments on five public datasets of chest X-rays, skin lesions, and colonoscopies, and empirically show that we are able to maintain high certified Dice scores even for highly perturbed images. Our work represents the first attempt to certify medical image segmentation models, and we aspire for it to set a foundation for future benchmarks in this crucial and largely uncharted area

Deep Reinforcement Learning for L3 Slice Localization in Sarcopenia Assessment

International audienceSarcopenia is a medical condition characterized by a reduction in muscle mass and function. A quantitative diagnosis technique consists of localizing the CT slice passing through the middle of the third lumbar area (L3) and segmenting muscles at this level. In this paper, we propose a deep reinforcement learning method for accurate localization of the L3 CT slice. Our method trains a reinforcement learning agent by incentivizing it to discover the right position. Specifically, a Deep Q-Network is trained to find the best policy to follow for this problem. Visualizing the training process shows that the agent mimics the scrolling of an experienced radiologist. Extensive experiments against other state-of-the-art deep learning based methods for L3 localization prove the superiority of our technique which performs well even with a limited amount of data and annotations

Towards Better Certified Segmentation via Diffusion Models

International audienceThe robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached production-level accuracy. However, like classification models, segmentation models can be vulnerable to adversarial perturbations, which hinders their use in critical-decision systems like healthcare or autonomous driving. Recently, randomized smoothing has been proposed to certify segmentation predictions by adding Gaussian noise to the input to obtain theoretical guarantees. However, this method exhibits a trade-off between the amount of added noise and the level of certification achieved. In this paper, we address the problem of certifying segmentation prediction using a combination of randomized smoothing and diffusion models. Our experiments show that combining randomized smoothing and diffusion models significantly improves certified robustness, with results indicating a mean improvement of 21 points in accuracy compared to previous state-of-the-art methods on Pascal-Context and Cityscapes public datasets. Our method is independent of the selected segmentation model and does not need any additional specialized training procedure

Towards Better Certified Segmentation via Diffusion Models

International audienceThe robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached productionlevel accuracy. However, like classification models, segmentation models can be vulnerable to adversarial perturbations, which hinders their use in criticaldecision systems like healthcare or autonomous driving. Recently, randomized smoothing has been proposed to certify segmentation predictions by adding Gaussian noise to the input to obtain theoretical guarantees. However, this method exhibits a trade-off between the amount of added noise and the level of certification achieved. In this paper, we address the problem of certifying segmentation prediction using a combination of randomized smoothing and diffusion models. Our experiments show that combining randomized smoothing and diffusion models significantly improves certified robustness, with results indicating a mean improvement of 21 points in accuracy compared to previous state-of-the-art methods on Pascal-Context and Cityscapes public datasets. Our method is independent of the selected segmentation model and does not need any additional specialized training procedure

Towards Better Certified Segmentation via Diffusion Models

International audienceThe robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached productionlevel accuracy. However, like classification models, segmentation models can be vulnerable to adversarial perturbations, which hinders their use in criticaldecision systems like healthcare or autonomous driving. Recently, randomized smoothing has been proposed to certify segmentation predictions by adding Gaussian noise to the input to obtain theoretical guarantees. However, this method exhibits a trade-off between the amount of added noise and the level of certification achieved. In this paper, we address the problem of certifying segmentation prediction using a combination of randomized smoothing and diffusion models. Our experiments show that combining randomized smoothing and diffusion models significantly improves certified robustness, with results indicating a mean improvement of 21 points in accuracy compared to previous state-of-the-art methods on Pascal-Context and Cityscapes public datasets. Our method is independent of the selected segmentation model and does not need any additional specialized training procedure

Assessment of Functional and Nutritional Status and Skeletal Muscle Mass for the Prognosis of Critically Ill Solid Cancer Patients

Simple and accessible prognostic factors are paramount for solid cancer patients experiencing life-threatening complications. The aim of this study is to appraise the impact of functional and nutritional status and skeletal muscle mass in this population. We conducted a retrospective (2007–2020) single-center study by enrolling adult patients with solid cancers requiring unplanned ICU admission. Performance status, body weight, and albumin level were collected at ICU admission and over six months. Skeletal muscle mass was assessed at ICU admission by measuring muscle areas normalized by height (SMI). Four-hundred and sixty-two patients were analyzed, mainly with gastro-intestinal (34.8%) and lung (29.9%) neoplasms. Moreover, 92.8% of men and 67.3% of women were deemed cachectic. In the multivariate analysis, performance status at ICU admission (CSH 1.74 [1.27–2.39], p < 0.001) and the six month increase in albumin level (CSH 0.38 [0.16–0.87], p = 0.02) were independent predictors of ICU mortality. In the subgroup of mechanically ventilated patients, the psoas SMI was independently associated with ICU mortality (CSH 0.82 [0.67–0.98], p = 0.04). Among the 368 ICU-survivors, the performance status at ICU admission (CSH 1.34 [1.14–1.59], p < 0.001) and the six-month weight loss (CSH 1.33 [1.17–2.99], p = 0.01) were associated with a one-year mortality rate. Most cancer patients displayed cachexia at ICU admission. Time courses of nutritional parameters may aid the prediction of short- and long-term outcomes