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Finite convergence of the Moment-SOS hierarchy under hidden convexity
No full textInternational audienceOne considers polynomial optimization problems with compact feasible set Ω defined by SOS-concave polynomials gj, and with a globally non-convex polynomial objective f . We show that if f is strongly convex on Ω, or SOS-convex on Ω when the constraints gj are at most quadratic, then the Moment-SOS hierarchy converges in finitely many steps, without à priori knowledge of this hidden (local) convexity. In addition, in the latter case, the exact order for which the relaxation is exact is provided by the degree of a Putinar-like certificate of convexity. This demonstrates that a general-purpose hierarchy can adapt to favorable hidden properties of a specific instance without being informed of them, yielding certified global minimizers
Set-point regulation of perturbed switched affine systems based on a nonlinear observer with application to DC-DC converters
No full textWe address robust set-point output regulation of continuous switched affine systems in the presence of constant unknown perturbations. We first prove the existence of at least one perturbed equilibrium point, which is well defined thanks to a rank condition pertaining the unperturbed (nominal) equilibrium. Then we introduce two nonlinear observers for estimating the perturbation and an optimality-based selection of the perturbed equilibrium. The switching stabilizer, driven by such estimates, is then proven to induce local asymptotic stability of the optimal equilibrium, via the application of reduction theorems. The effectiveness of the proposed approach is demonstrated through application to a non-inverting buck-boost converter, simulated with the electrical engineering software PLECS integrated in MATLAB/Simulink
Pourquoi mon filtre antispam fonctionne-t-il si mal ?
No full textLes filtres antispam restent poreux car les attaquants conçoivent en permanence des contenus adversariaux (obfuscation textuelle, images, homoglyphes, segmentation) qui contournent les modèles statistiques et d’apprentissage automatique, exploitant leurs limites de généralisation et de robustesse
On the dynamics of viscoelastic cantilever beams under arbitrary base motion and eccentric damped tip mass via integral transform
No full textInternational audienc
A Scaled Poisson Bayesian Model for Viral Epidemic Monitoring
No full textInternational audienceMonitoring an ongoing epidemic requires accurate, trustworthy and easy to use tools, capable of handling low quality data. Extending existing epidemiological models quantifying the propagation intensity via a time-varying reproduction number, this work proposes a scaled Poisson model, accounting for large intrinsic variability in infection counts. The associated scaled likelihood is plugged into a Bayesian model with a quasi-noninformative prior. A carefully designed Markov Chain Monte Carlo algorithm yields a point estimate and credibility intervals of the reproduction number. The accuracy and robustness to model misspecification and to scale parameter selection of the proposed estimator is demonstrated through intensive numerical experiments on COVID-19 case counts in different countries and during various phases of the pandemic
Orchestrating on-board sensors for global hybrid robust stabilization of unicycles
No full textWe consider mobile robots described through unicycle dynamics equipped with on-board range sensors and cameras, one facing forward and one facing backward, providing measurements of the distance and misalignment to a target. We propose a hybrid control law combining the two on-board measurements and discuss stability results for the closed-loop expressed in the on-board camerabased coordinates, using Lyapunov-based arguments. We prove robustness of the stability properties to uncertainties affecting the sensors and external perturbations acting on the robot. The results are illustrated via simulations
Computing Approximate Nash Equilibria for Integer Programming Games
No full textInternational audienceWe propose a framework to compute approximate Nash equilibria in integer programming games with nonlinear payoffs, i.e., simultaneous and non-cooperative games where each player solves a parametrized mixed-integer nonlinear program. We prove that using absolute approximations of the players' objective functions and then computing its Nash equilibria is equivalent to computing approximate Nash equilibria where the approximation factor is doubled. In practice, we propose an algorithm to approximate the players' objective functions via piecewise linear approximations. Our numerical experiments on a cybersecurity investment game show the computational effectiveness of our approach
Token-Efficient Change Detection in LLM APIs
No full textRemote change detection in LLMs is a difficult problem. Existing methods are either too expensive for deployment at scale, or require initial white-box access to model weights or grey-box access to log probabilities. We aim to achieve both low cost and strict black-box operation, observing only output tokens.Our approach hinges on specific inputs we call Border Inputs, for which there exists more than one output top token. From a statistical perspective, optimal change detection depends on the model's Jacobian and the Fisher information of the output distribution. Analyzing these quantities in low-temperature regimes shows that border inputs enable powerful change detection tests.Building on this insight, we propose the Black-Box Border Input Tracking (B3IT) scheme. Extensive in-vivo and in-vitro experiments show that border inputs are easily found for non-reasoning tested endpoints, and achieve performance on par with the best available grey-box approaches. B3IT reduces costs by 30× compared to existing methods, while operating in a strict black-box setting
Laser self-injection locking to fiber Fabry-Perot resonator for frequency comb generation
No full textInternational audienceThis study demonstrates that self-injection locking (SIL) of a distributed feedback (DFB) laser to a high-Q fiber Fabry Perot (FFP) resonator, fabricated with highly nonlinear fiber, allows optical frequency combs (OFC) generation with a laser power as low as 100 mW. More precisely, cavity soliton (CS) regime has been observed in this configuration, along with other types of combs. The laser stabilization using SIL is described. Then the system's behavior is analyzed through modeling the laser's dynamics and comparing the model results to experimental tuning curve measurements. Our findings highlight the critical role of the initial phase of the fiber link between laser and FFP in determining the stability and effectiveness of the locking process. We explore the dynamics of the nonlinear SIL process while varying the laser current, revealing the transition from modulation instability to chaotic comb states, and eventually to soliton formation as the system moves from an effective blue-detuned to an effective red-detuned regime. Notably, the inclusion of self-phase modulation (SPM) in the SIL model predicts accessibility of the narrow soliton existence range. These results highlight the potential of SIL in FFP resonators for low-power, stable OFC generation, offering a promising path forward for practical applications
Fast and Reliable Evaluation of the Distribution of Quadratic Forms of Gaussian Random Variables
No full textQuadratic forms in Gaussian random variables yield generalized noncentral chisquare distributions which appear in many test statistics. Classical cdf methods (e.g., characteristic-function inversion, saddlepoint approximations) can be effective but are not designed for reliable finite-precision computation and offer limited structural or complexity insight. We study finite-precision cdf evaluation and its binary complexity.Building on earlier low-dimensional results, we note that relevant modified Laplace transforms of the cdf are available in closed-form and are D-finite functions. This reduces the general d dimensional cdf evaluation problem to evaluating a truncated holonomic power series with positive coefficients, together with explicit tail bounds. Next, we develop a reduced-rounding-error evaluation by switching from the standard alternating-sign scalar recurrence to an equivalent coupled recurrence in which all update coefficients are nonnegative. This "positivity feature" supports a sharper forward-error analysis and improves robustness of the finiteprecision evaluation.Finally, we propose an accelerated coefficient-generation algorithm. Using a transposed multipoint-evaluation primitive, it computes collectively-via a transposed Vandermonde/remainder-tree construction-the truncated contributions in-duced by the rational factors of the holonomic equation. The remaining step, which assembles the solution by exponentiating a truncated series formed from these aggregated transforms, is carried out with FFT-based power-series exponentiation. Overall, the method achieves quasi-linear complexity in the maximum between the number of Gaussian random variables and the truncation order