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Analyse et simulation numérique de schémas décalés pour les écoulements à bas nombre de Mach
No full textThis thesis focuses on the simulation of flows in nuclear reactors with the aim of improving safety conditions. The objective of a simulation is, by definition, to faithfully preserve the properties of the underlying model. In fact, since flows in these reactors are considered to be low Mach number under nominal conditions, it is essential to have a numerical tool capable of adequately capturing this type of flow. On the other hand, the fluid mechanics equations that govern these flows are fundamentally derived from conservation principles. It is possible to replicate this conservation property numerically, in particular using the very popular finite volume methods. However, it is well known that these methods are generally not accurate at low Mach numbers. There is, however, a special case where this limitation disappears: on simplicial meshes, these methods can recover this valuable accuracy without correction. One possible interpretation of this unexpected property is that in this particular case there is a Hodge-Helmholtz decomposition on the discrete velocity space. Furthermore, there are methods, known as staggered methods, which seem to be ideal candidates for preserving this structure on more varied meshes, but for which the notion of conservation is poorly defined. Thus, our proposal is twofold: on the one hand, we seek to extend the conservation properties of classical schemes to staggered formalism; on the other hand, we introduce a methodology for obtaining accurate numerical schemes at low Mach numbers, which we apply to the case of staggered discretization. In practice, there is a well-established link between the low Mach number limit and the long time limit of a wave system, via an asymptotic analysis in Mach number. This link allows us to reduce the problem of accuracy at low Mach numbers to the simpler problem of capturing the long-time limit of a linear system. This limit, at the continuous level, is characterized by a Hodge–Helmholtz decomposition, which itself comes from a more general framework: de Rham complexes. The first step is to introduce a staggered discretization of the wave system based on a discrete de Rham complex. Although this structure may seem far removed from classical numerical analysis problems, it preserves the fundamental properties of partial differential equations at the discrete level. We show that it leads to the identification of a long-time limit corresponding to a particular discrete Hodge-Helmholtz decomposition. This discretization is then extended to the barotropic Eulerian system. Conservation is achieved by working directly on this system, while accuracy at low Mach numbers results from the long-time consistency of the staggered scheme on the wave system. Finally, implementations on the C++ SolverLab platform allow the validity of the proposals for the wave system and the barotropic Euler system to be illustrated numerically.Cette thèse s'intéresse à la simulation d'écoulements dans des réacteurs nucléaires dans un but d'améliorer les conditions de sûreté. L'objectif d'une simulation est, par définition, de préserver fidèlement les propriétés du modèle sous-jacent. De fait, puisqu'en régime nominal de ces réacteurs les écoulements sont considérés comme étant à bas nombre de Mach, il est essentiel d'avoir un outil numérique capable de capturer convenablement ce type d'écoulements. D'un autre côté, les équations de la mécanique des fluides, qui régissent ces écoulements, dérivent fondamentalement de principes de conservation. Répliquer cette propriété de conservation numériquement est possible, notamment grâce aux très populaires méthodes de volumes finis. Cependant, il est bien connu que ces dernières ne sont généralement pas précises à bas nombre de Mach. Il existe toutefois un cas particulier où cette limitation disparaît : sur des maillages simpliciaux, ces dernières peuvent récupérer sans correction cette précieuse précision. Une interprétation possible de cette propriété inattendue est qu'il existe dans ce cas particulier une décomposition de Hodge-Helmholtz sur l'espace des vitesses discrètes. Par ailleurs, il existe des méthodes, dites décalées, qui semblent être les candidates idéales pour préserver sur des maillages plus variés cette structure, mais pour lesquelles la notion de conservation est mal définie. Ainsi, notre proposition est double : d'une part nous cherchons à étendre les propriétés de conservation de schémas classiques au formalisme décalé, d'autre part, nous introduisons une méthodologie permettant d'obtenir des schémas numériques précis à bas nombre de Mach que nous appliquons au cas d'une discrétisation décalée. En pratique, un lien bien établi relie la limite à bas nombre de Mach et la limite en temps long d'un système d'ondes, via une analyse asymptotique en nombre de Mach. Ce lien permet de ramener le problème de la précision à bas nombre de Mach à celui, plus simple, de la capture de la limite en temps long d'un système linéaire. Cette limite, au niveau continu, est caractérisée par une décomposition de Hodge–Helmholtz, elle-même issue d'un cadre plus général : les complexes de de Rham. La première étape consiste à introduire une discrétisation décalée du système d'ondes fondée sur un complexe de de Rham discret. Cette structure, bien qu'a priori éloignée des problématiques classiques d'analyse numérique, permet de préserver au niveau discret des propriétés fondamentales des équations aux dérivées partielles. Nous montrons qu'elle conduit à l'identification d'une limite en temps long correspondant à une décomposition de Hodge-Helmholtz discrète particulière. Cette discrétisation est ensuite étendue au système d'Euler barotrope. La conservation est obtenue en travaillant directement sur ce système, tandis que la précision à bas nombre de Mach résulte de la consistance en temps long du schéma décalé sur le système d'ondes. Enfin, des implémentations sur la plateforme C++ SolverLab permettent d'illustrer numériquement la validité des propositions pour le système d'ondes et le système d'Euler barotrope
The Quantum Approximate Optimization Algorithm Can Require Exponential Time to Optimize Linear Functions
No full textInternational audienc
Serverless Computing
No full textThis special issue covers emerging research and development challenges in serverless computing, ranging from the development of an allocation and scheduling simulator to evaluate various orchestration policies, to support for scalable and cost-effective deployment of serverless machine learning models in heterogeneous edge environments. The articles also demonstrate how the serverless computing paradigm has been deployed across different system architectures, from edge-only deployments to those that make use of a combination of edge and cloud environments. There is clear enthusiasm in the systems community in utilizing this paradigm for a wide range of applications
Exchanging and updating opinions and beliefs reinforces echo chambers
No full textkataoka2025aInternational audienceEcho chamber, the state in which agents are split into groups sharing the same opinions, is a well-known phenomenon in social networks. Opinion dynamics models have been proposed to explain how the phenomenon occurs through agents revising their opinions. However, social network users also exchange beliefs supporting their opinions. This has not been taken into account. In this paper, we extend an existing opinion dynamics model by allowing agents to exchange and update both beliefs and opinions. The process of updating beliefs is described based on the classical belief revision theory. Beliefs and opinions can influence each other guided by values that agents share. We compare opinion propagation with respect to belief influence. Simulation results show that echo chambers are reinforced by interactions between opinions and beliefs
Unified Privacy Guarantees for Decentralized Learning via Matrix Factorization
No full textDecentralized Learning (DL) enables users to collaboratively train models without sharing raw data by iteratively averaging local updates with neighbors in a network graph. This setting is increasingly popular for its scalability and its ability to keep data local under user control. Strong privacy guarantees in DL are typically achieved through Differential Privacy (DP), with results showing that DL can even amplify privacy by disseminating noise across peer-to-peer communications. Yet in practice, the observed privacy-utility trade-off often appears worse than in centralized training, which may be due to limitations in current DP accounting methods for DL. In this paper, we show that recent advances in centralized DP accounting based on Matrix Factorization (MF) for analyzing temporal noise correlations can also be leveraged in DL. By generalizing existing MF results, we show how to cast both standard DL algorithms and common trust models into a unified formulation. This yields tighter privacy accounting for existing DP-DL algorithms and provides a principled way to develop new ones. To demonstrate the approach, we introduce MAFALDA-SGD, a gossip-based DL algorithm with user-level correlated noise that outperforms existing methods on synthetic and real-world graphs
Ask and Remember: A Questions-Only Replay Strategy for Continual Visual Question Answering
No full textInternational audienceContinual Learning in Visual Question Answering (VQACL) requires models to learn new visual-linguistic tasks (plasticity) while retaining knowledge from previous tasks (stability). The multimodal nature of VQACL presents unique challenges, requiring models to balance stability across visual and textual domains while maintaining plasticity to adapt to novel objects and reasoning tasks. Existing methods, predominantly designed for unimodal tasks, often struggle to balance these demands effectively. In this work, we introduce QUestion-only replay with Attention Distillation (QUAD), a novel approach for VQACL that leverages only past task questions for regularisation, eliminating the need to store visual data and addressing both memory and privacy concerns. QUAD achieves stability by introducing a question-only replay mechanism that selectively uses questions from previous tasks to prevent overfitting to the current task's answer space, thereby mitigating the out-of-answer-set problem. Complementing this, we propose attention consistency distillation, which uniquely enforces both intra-modal and inter-modal attention consistency across tasks, preserving essential visual-linguistic associations. Extensive experiments on VQAv2 and NExT-QA demonstrate that QUAD significantly outperforms state-of-the-art methods, achieving robust performance in continual VQA.ICCV 2025, 8 pages. Code: https://github.com/IemProg/QUA
Understanding the new distinguisher of alternating codes at degree 2
No full textInternational audienceDistinguishing Goppa codes or alternant codes from generic linear codes [?] has been shown to be a first step before being able to attack McEliece cryptosystem based on those codes [?]. Whereas the distinguisher of [?] is only able to distinguish Goppa codes or alternant codes of rate very close to 1, in [?] a much more powerful (and more general) distinguisher was proposed. It is based on computing the Hilbert series tHFpdq, d P Nu of a Pfaffian modeling. The distinguisher of [?] can be interpreted as computing HFp1q. Computing HFp2q still gives a polynomial time distinguisher for alternant or Goppa codes and is apparently able to distinguish Goppa or alternant codes in a much broader regime of rates as the one of [?]. However, the scope of this distinguisher was unclear. We give here a formula for HFp2q corresponding to generic alternant codes when the field size q satisfies q ě r, where r is the degree of the alternant code. We also show that this expression for HFp2q provides a lower bound in general. The value of HFp2q corresponding to random linear codes is known and this yields a precise description of the new regime of rates that can be distinguished by this new method. This shows that the new distinguisher improves significantly upon the one given in [?]. Reed-Solomon and alternant codes.Definition 1 (Generalized Reed-Solomon code). Let n ď q be an integer, x " px1, . . . , xnq be a vector of pairwise-distinct elements of Fq,</div
Error floor prediction with Markov models for QC-MDPC codes
No full textInternational audienceQuasi-cyclic moderate-density parity check (QC-MDPC) codebased encryption schemes under iterative decoders offer highly-competitive performance in quantum-resistant cryptography, but their IND-CCA2 security is an open question because the decoding failure rate (DFR) of these algorithms is not well-understood. The DFR decreases extremely rapidly as the blocklength increases, then decreases much more slowly in regimes known as the waterfall and error floor, respectively. The waterfall behavior is rather well predicted by a Markov model introduced by Sendrier and Vasseur [SV19b] but it does not capture the error floor behavior. Assessing precisely for which blocklength this error floor begins is crucial for the low DFRs sought in the context of cryptography. By enriching the Markov model [SV19b] with information about near codewords we are able to capture this error-floor behavior for a step-bystep decoder. This decoder displays worse decoding performance than the parallel decoders used in practice but is more amenable to a Markov chain analysis. We already capture the error floor with a simplified model. A refined model taking into account certain structural features of the secret key is even able to give accurate key dependent predictions both in the waterfall and error floor regimes. We show that error floor behavior is governed by convergence to a near codeword when decoding fails. We ran this model for the BIKE cryptosystem with this simpler stepby-step decoder to better ascertain whether the DFR is low enough to achieve IND-CCA2 security. Our model gives a DFR below 2 -131.2 , using a block length r = 13477 instead of the BIKE parameter r = 12323. This paper gives some strong evidence that the IND-CCA2 requirement can be met at the cost of a modest increase of less than 10% in the key size
Learning-based pricing policy for substitute itineraries
No full textInternational audienceIn airline revenue management, dynamic pricing for substitutable itineraries presents significant challenges due to the stochastic nature of customer choices. The dynamic pricing problem can be conceptualized as a Markov Decision Process with the objective of maximizing the total expected revenue over a finite selling horizon. However, the complexity of this model, characterized by its multi-dimensional state and action spaces, makes it computationally prohibitive to solve exactly, even for small-to-medium-sized instances. As a result, classic methods such as dynamic programming (DP) prove inefficient in addressing the dynamic pricing problem for larger instances. In this work, we introduce learning-based policies tailored to the dynamic pricing problem of substitute itineraries. We proposed two different machine learning (ML) pipelines to encode pricing policy and designed tailored training processes for each of them
Don’t Forget Your Inverse DDIM for Image Editing
No full textInternational audienceThe field of text-to-image generation has undergone significant advancements with the introduction of diffusion models. Nevertheless, the challenge of editing real images persists, as most methods are either computationally intensive or produce poor reconstructions. This paper introduces SAGE (Self-Attention Guidance for image Editing) - a novel technique leveraging pre-trained diffusion models for image editing. SAGE builds upon the DDIM algorithm and incorporates a novel guidance mechanism utilizing the self-attention layers of the diffusion U-Net. This mechanism computes a reconstruction objective based on attention maps generated during the inverse DDIM process, enabling efficient reconstruction of unedited regions without the need to precisely reconstruct the entire input image. Thus, SAGE directly addresses the key challenges in image editing. The superiority of SAGE over other methods is demonstrated through quantitative and qualitative evaluations and confirmed by a statistically validated comprehensive user study, in which all 47 surveyed users preferred SAGE over competing methods. Additionally, SAGE ranks as the top-performing method in seven out of 10 quantitative analyses and secures second and third places in the remaining three.12 pages, 12 figures, code available at https://guillermogotre.github.io/sage