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Decisiveness for Countable MDPs and Insights for NPLCSs and POMDPs
No full textInternational audienceMarkov chains and Markov decision processes (MDPs) are well-established probabilistic models. While finite Markov models are well-understood, analyzing their infinite counterparts remains a significant challenge. Decisiveness has proven to be an elegant property for countable Markov chains: it is general enough to be satisfied by several natural classes of countable Markov chains, and it is a sufficient condition for simple qualitative and approximate quantitative model-checking algorithms to exist.In contrast, existing works on the formal analysis of countable MDPs usually rely on ad hoc techniques tailored to specific classes. We provide here a general framework to analyze countable MDPs by extending the notion of decisiveness. Compared to Markov chains, MDPs exhibit extra non-determinism that can be resolved in an adversarial or cooperative way, leading to multiple natural notions of decisiveness. We show that these notions enable the approximation of reachability and safety probabilities in countable MDPs using simple model-checking procedures.We then instantiate our generic approach to two concrete classes of models inducing countable MDPs: non-deterministic probabilistic lossy channel systems and partially observable MDPs. This leads to an algorithm to approximately compute safety probabilities in each of these classes
Analysis of an optimal control problem for the Navier-Stokes system with Tresca boundary conditions
No full textInternational audienceWe consider an optimal control problem for the Navier-Stokes system with Tresca boundary conditions. With such boundary conditions, the weak formulation of the system is a variational inequality. We approximate this system and the optimal control problem by regularizing the boundary conditions leading to a variational equality. We show that for the approximate system, there exists an optimal control and we derive the first optimality condition by using an adjoint system. We also prove that the approximate optimal controls converge towards an optimal control for the Navier-Stokes system with Tresca boundary conditions. Finally we show that as the threshold of the Tresca law goes to infinity, the corresponding optimal controls converge towards an optimal control for the Navier-Stokes system with the Dirichlet boundary condition
CLIP's Visual Embedding Projector is a Few-shot Cornucopia
No full textInternational audienceWe consider the problem of adapting a contrastively pretrained vision-language model like CLIP [30] for few-shot classification. The literature addresses this problem by learning a linear classifier of the frozen visual features, optimizing word embeddings, or learning external feature adapters. This paper introduces an alternative way for CLIP adaptation without adding "external" parameters to optimize. We find that simply fine-tuning the last projection matrix of the vision encoder leads to performance better than all baselines. Furthermore, we show that regularizing training with the distance between the fine-tuned and pretrained matrices adds reliability for adapting CLIP. This simple approach, coined ProLIP, yields state-of-the-art performance on 11 few-shot classification benchmarks, fewshot domain generalization, cross-dataset transfer, base-tonew class generalization, and test-time adaptation. Code will be made available at: https://github.com/ astra-vision/ProLI
Try-Mopsa: Relational Static Analysis in Your Pocket
No full textInternational audienceStatic analyzers are complex pieces of software with large dependencies. They can be difficult to install, which hinders adoption and creates barriers for students learning static analysis. This work introduces Try-Mopsa: a scaled-down version of the Mopsa static analysis platform, compiled into JavaScript to run purely as a client-side application in web browsers. Try-Mopsa provides a responsive interface that works on both desktop and mobile devices. Try-Mopsa features all the core components of Mopsa. In particular, it supports relational numerical domains. We present the interface, changes and adaptations required to have a pure JavaScript version of Mopsa. We envision Try-Mopsa as a convenient platform for onboarding or teaching purposes
Exotic traveling waves for a quasilinear Schrödinger equation with nonzero background
No full textInternational audienceWe study a defocusing quasilinear Schrödinger equation with nonzero conditions at infinity in dimension one. This quasilinear model corresponds to a weakly nonlocal approximation of the nonlocal Gross-Pitaevskii equation, and can also be derived by considering the effects of surface tension in superfluids. When the quasilinear term is neglected, the resulting equation is the classical Gross-Pitaevskii equation, which possesses a well-known stable branch of subsonic traveling waves solution, given by dark solitons. Our goal is to investigate how the quasilinear term affects the traveling-wave solutions. We provide a complete classification of finite energy traveling waves of the equation, in terms of the two parameters: the speed and the strength of the quasilinear term. This classification leads to the existence of dark and antidark solitons, as well as more exotic localized solutions like dark cuspons, compactons, and composite waves, even for supersonic speeds. Depending on the parameters, these types of solutions can coexist, showing that finite energy solutions are not unique. Furthermore, we prove that some of these dark solitons can be obtained as minimizers of the energy, at fixed momentum, and that they are orbitally stable
Prescribing the best decay rate of the wave equation using internal delayed feedback damping
No full textInternational audienceIn this paper, we investigate the stabilization of the damped wave equation through the use of an internal feedback mechanism incorporating time delay. This work builds upon the partial pole placement paradigm, a recent theoretical framework originally developed for functional differential equations, which enables the selective assignment of eigenvalues within a prescribed region of the complex plane. Using this approach, we design an internal delayed feedback law that guarantees the exponential stabilization of the resulting closed-loop system. A distinctive feature of our control strategy lies in its ability to prescribe the optimal exponential decay rate for each modal cluster, thereby achieving the fastest possible stabilization consistent with the system's spectral limitations. This can be achieved regardless of the stabilizability domain being delay-independent or delay-dependent. This allows for a highly efficient control mechanism tailored to the specific dynamical behavior of the wave equation. To illustrate the practical relevance of our theoretical findings, we apply the proposed method to the control of transverse vibrations in a taut string. Numerical simulations confirm the robustness and effectiveness of the feedback design, underscoring its potential for broader applications in the control of distributed parameter systems with delay effects
Interpretation of a Discrete de Rham method as a Finite Element System
No full textWe show that the DDR method can be interpreted as defining a computable consistent discrete L2 product on a conforming FES defined by PDEs. Without modifying the numerical method itself, this point of view provides an alternative approach to the analysis. The conformity and consistency properties we obtain are stronger than those previously shown, even in low dimensions. We can also recover some of the other results that have been proved about DDR, from those that have already been proved, in principle, in the general context of FES. We also bring VEM, the Virtual Element Method, into the discussion
An all-Mach cell-centered multi-dimensional nite volume numerical scheme for the Euler equations
No full textInternational audienceIn the context of the numerical approximation of Euler equations, great efforts have been devoted to developing schemes that can accurately reproduce solutions in low Mach number ows. Solutions of classic Finite Volume (FV) schemes are usually plagued by an excessive diusion as the numerical scheme is not consistent with the limit equations for the Mach number that tends to zero. Instead, a numerical scheme that satises such a property is called Asymptotic-Preserving (AP). In this paper, we propose an AP FV scheme for the multi-dimensional Euler equations. In classic FV methods, the numerical approximation of the face ux is obtained by means of a two-state 1D approximate Riemann Solver (RS) in the normal direction to the face. Here, we rely on a node-based ux approximation that exploits a particular RS involving a nodal quantity which depends on all the cells around a given node. Such an idea has been exploited by Barsukow et al. (2023) for the linear acoustic equations. Their method is vorticity-preserving, but its extension to the Euler equations proved to be far from trivial. For such a reason, a change of perspective is needed in the denition of the RS
Investigating the Effects of Augmented Reality on Message Credibility When Visualizing Environmental Impacts
No full textInternational audienceAugmented reality (AR) has increasingly been used to communicate environmental impacts, offering greater engagement than conventional displays. However, its effect on message credibility—how much people believe in the content of the communication—remains unclear. In a preregistered study, we compared the perceived credibility of environmental information presented via visualizations on an AR headset or a desktop display. We created display-specific visual encodings (3D concrete for AR, 2D bar charts for desktop) and added two control conditions to cross display and encoding. We found no difference in message credibility between AR and desktop, though concrete AR was rated most engaging. Supplementary material is available at https://osf.io/n4p5c/