arXiv subjects

Laurent Michel

Publications and source records attributed to Laurent Michel.

At least 19 recordsLinked to original sources

arXiv2026

Semiclassical Schrödinger operators with purely imaginary potential

We consider Schrödinger operators with purely imaginary potential $P = - h^{2} Δ+ i V ( x )$ on a bounded domain. Assuming that near its critical points the potential $V$ can be approximated by an homogeneous polynomial, we show that in the limit $h \to 0$ the leftmost eigenvalues of $P$ are asymptotically given by the local model associated to the most degenerated critical points of $V$. We give applications of this result to the associated evolution problem including shear flows in fluid mechanics.

math.AP↗

arXiv2026

Towards Bound Consistency for the No-Overlap Constraint Using MDDs

Achieving bound consistency for the no-overlap constraint is known to be NP-complete. Therefore, several polynomial-time tightening techniques, such as edge finding, not-first-not-last reasoning, and energetic reasoning, have been introduced for this constraint. In this work, we derive the first bound-consistent algorithm for the no-overlap constraint. By building on the no-overlap MDD defined by Ciré and van Hoeve, we extract bounds of the time window of the jobs, allowing us to tighten start and end times in time polynomial in the number of nodes of the MDD. Similarly, to bound the size and time-complexity, we limit the width of the MDD to a threshold, creating a relaxed MDD that can also be used to relax the bound-consistent filtering. Through experiments on a sequencing problem with time windows and a just-in-time objective ($1 \mid r_j, d_j, \bar{d}_j \mid \sum E_j + \sum T_j$), we observe that the proposed filtering, even with a threshold on the width, achieves a stronger reduction in the number of nodes visited in the search tree compared to the previously proposed precedence-detection algorithm of Ciré and van Hoeve. The new filtering also appears to be complementary to classical propagation methods for the no-overlap constraint, allowing a substantial reduction in both the number of nodes and the solving time on several instances.

cs.AI↗

arXiv2025

Discovering periodic and repeating nuclear transients in the XMM-Newton archives

The regions around massive black holes can show X-ray variability on timescales from seconds to decades. Observing many black holes over different timescales can enhance our chances of detecting variability coming from (partial) tidal disruption events, massive black hole binaries, changing state AGN, blazar activity and much more. X-ray catalogues with hundreds of thousands of detections are treasure troves of such sources, which require innovative methods to identify these black holes. We present the current XMM-Newton catalogues available and describe several examples of tidal disruption events (TDEs) and quasi-periodic eruption sources that have been found whilst mining this data. We describe preliminary work on a search for periodic variables in the XMM-Newton EPIC archival data, with the example of finding new massive black hole binaries. We also describe the STONKS pipeline that is now in the XMM-Newton automatic reduction pipeline and the near real-time alert system that allows the follow-up of new and fading transients. We provide examples of fading sources that are newly identified candidate TDEs.

astro-ph.HE↗

arXiv2025

Eyring-Kramers formula for the mean exit time of non-Gibbsian elliptic processes: the non characteristic boundary case

In this work, we derive a new sharp asymptotic equivalent in the small temperature regime $h\to 0$ for the mean exit time from a bounded domain for the non-reversible process $dX\_t=b(X\_t)dt + \sqrt h \, dB\_t$ under a generic orthogonal decomposition of $b$ and when the boundary of $Ω$ is assumed to be \textit{non characteristic}. The main contribution of this work lies in the fact that we do not assume that the process $(X\_t,t\ge 0)$ is \textit{Gibbsian}. In this case, a new correction term characterizing the \textit{non-Gibbsianness} of the process appears in the equivalent of the mean exit time. The proof is mainly based on tools from spectral and semi-classical analysis.

math.AP↗

arXiv2025

Busting the Paper Ballot: Voting Meets Adversarial Machine Learning

We show the security risk associated with using machine learning classifiers in United States election tabulators. The central classification task in election tabulation is deciding whether a mark does or does not appear on a bubble associated to an alternative in a contest on the ballot. Barretto et al. (E-Vote-ID 2021) reported that convolutional neural networks are a viable option in this field, as they outperform simple feature-based classifiers. Our contributions to election security can be divided into four parts. To demonstrate and analyze the hypothetical vulnerability of machine learning models on election tabulators, we first introduce four new ballot datasets. Second, we train and test a variety of different models on our new datasets. These models include support vector machines, convolutional neural networks (a basic CNN, VGG and ResNet), and vision transformers (Twins and CaiT). Third, using our new datasets and trained models, we demonstrate that traditional white box attacks are ineffective in the voting domain due to gradient masking. Our analyses further reveal that gradient masking is a product of numerical instability. We use a modified difference of logits ratio loss to overcome this issue (Croce and Hein, ICML 2020). Fourth, in the physical world, we conduct attacks with the adversarial examples generated using our new methods. In traditional adversarial machine learning, a high (50% or greater) attack success rate is ideal. However, for certain elections, even a 5% attack success rate can flip the outcome of a race. We show such an impact is possible in the physical domain. We thoroughly discuss attack realism, and the challenges and practicality associated with printing and scanning ballot adversarial examples.

cs.CR↗

arXiv2024

Constraint Propagation on GPU: A Case Study for the Bin Packing Constraint

The Bin Packing Problem is one of the most important problems in discrete optimization, as it captures the requirements of many real-world problems. Because of its importance, it has been approached with the main theoretical and practical tools. Resolution approaches based on Linear Programming are the most effective, while Constraint Programming proves valuable when the Bin Packing Problem is a component of a larger problem. This work focuses on the Bin Packing constraint and explores how GPUs can be used to enhance its propagation algorithm. Two approaches are motivated and discussed, one based on knapsack reasoning and one using alternative lower bounds. The implementations are evaluated in comparison with state-of-the-art approaches on different benchmarks from the literature. The results indicate that the GPU-accelerated lower bounds offers a desirable alternative to tackle large instances.

cs.OH↗

arXiv2023

Real diffusion with complex spectral gap

The low-lying eigenvalues of the generator of a Langevin process are known to satisfy the Eyring-Kramers law in the low temperature regime under suitable assumptions. These eigenvalues are generically real. We construct generators whose spectral gap is given by non-real eigenvalues or by a real eigenvalue having a Jordan block.

math.AP↗

arXiv2023

XMM2ATHENA, the H2020 project to improve XMM-Newton analysis software and prepare for Athena

XMM-Newton, a European Space Agency observatory, has been observing the X-ray, ultra-violet and optical sky for 23 years. During this time, astronomy has evolved from mainly studying single sources to populations and from a single wavelength, to multi-wavelength or messenger data. We are also moving into an era of time domain astronomy. New software and methods are required to accompany evolving astronomy and prepare for the next generation X-ray observatory, Athena. Here we present XMM2ATHENA, a programme funded by the European Union's Horizon 2020 research and innovation programme. XMM2ATHENA builds on foundations laid by the XMM-Newton Survey Science Centre (XMM-SSC), including key members of this consortium and the Athena Science ground segment, along with members of the X-ray community. The project is developing and testing new methods and software to allow the community to follow the X-ray transient sky in quasi-real time, identify multi-wavelength or messenger counterparts of XMM-Newton sources and determine their nature using machine learning. We detail here the first milestone delivery of the project, a new online, sensitivity estimator. We also outline other products, including the forthcoming innovative stacking procedure and detection algorithms to detect the faintest sources. These tools will then be adapted for Athena and the newly detected or identified sources will enhance preparation for observing the Athena X-ray sky.

astro-ph.IM↗

arXiv2023

Exit time and principal eigenvalue of non-reversible elliptic diffusions

In this work, we analyse the metastability of non-reversible diffusion processes $$dX_t=\boldsymbol{b}(X_t)dt+\sqrt h\,dB_t$$ on a bounded domain $Ω$ when $\mathbf{b}$ admits the decomposition $\mathbf{b}=-(\nabla f+\mathbf{\ell})$ and $\nabla f \cdot \mathbf{\ell}=0$. In this setting, we first show that, when $h\to 0$, the principal eigenvalue of the generator of $(X_t)_{t\ge 0}$ with Dirichlet boundary conditions on the boundary $\partialΩ$ of $Ω$ is exponentially close to the inverse of the mean exit time from $Ω$, uniformly in the initial conditions $X_0=x$ within the compacts of $Ω$. The asymptotic behavior of the law of the exit time in this limit is also obtained. The main novelty of these first results follows from the consideration of non-reversible elliptic diffusions whose associated dynamical systems $\dot X=\mathbf{b}(X)$ admit equilibrium points on $\partialΩ$. In a second time, when in addition $÷\mathbf{\ell} =0$, we derive a new sharp asymptotic equivalent in the limit $h\to 0$ of the principal eigenvalue of the generator of the process and of its mean exit time from $Ω$. Our proofs combine tools from large deviations theory and from semiclassical analysis, and truly relies on the notion of quasi-stationary distribution.

math.PR↗

arXiv2022

FASHION: Functional and Attack graph Secured HybrId Optimization of virtualized Networks

Maintaining a resilient computer network is a delicate task with conflicting priorities. Flows should be served while controlling risk due to attackers. Upon publication of a vulnerability, administrators scramble to manually mitigate risk while waiting for a patch. We introduce FASHION: a linear optimizer that balances routing flows with the security risk posed by these flows. FASHION formalizes routing as a multi-commodity flow problem with side constraints. FASHION formulates security using two approximations of risk in a probabilistic attack graph (Frigault et al., Network Security Metrics 2017). FASHION's output is a set of software-defined networking rules consumable by Frenetic (Foster et al., ICFP 2011). We introduce a topology generation tool that creates data center network instances including flows and vulnerabilities. FASHION is executed on instances of up to 600 devices, thousands of flows, and million edge attack graphs. Solve time averages 30 minutes on the largest instances (seconds on the smallest instances). To ensure the security objective is accurate, the output solution is assessed using risk as defined by Frigault et al. FASHION allows enterprises to reconfigure their network in response to changes in functionality or security requirements.

cs.NI↗

arXiv2022

Metastable diffusions with degenerate drifts

We study the spectrum of the semiclassical Witten Laplacian $Δ_{f}$ associated to a smooth function $f$ on ${\mathbb R}^d$. We assume that $f$ is a confining Morse--Bott function. Under this assumption we show that $Δ_{f}$ admits exponentially small eigenvalues separated from the rest of the spectrum. Moreover, we establish Eyring-Kramers formula for these eigenvalues. Our approach is based on microlocal constructions of quasimodes near the critical submanifolds.

math.AP↗

arXiv2022

Eyring-Kramers type formulas for some piecewise deterministic Markov processes

In this work, we give sharp asymptotic equivalents in the small temperature regime of the smallest eigenvalues of the generator of some piecewise deterministic Markov processes (including the ZigZag process and the Bouncy Particle Sampler process) with refreshment rate $α$ on the one-dimensional torus T. These asymptotic equivalents are usually called Eyring-Kramers type formulas in the literature. The case when the refreshment rate $α$ vanishes on T is also considered.

math-ph↗

arXiv2022

Eyring-Kramers law for Fokker-Planck type differential operators

We consider Fokker-Planck type differential operators associated with general Langevin processes admitting a Gibbs stationary distribution. Under assumptions insuring suitable resolvent estimates, we prove Eyring-Kramers formulas for the bottom of the spectrum of these operators in the low temperature regime. Our approach is based on the construction of sharp Gaussian quasimodes which avoids supersymmetry or PT-symmetry assumptions.

math.AP↗

arXiv2022

Annotating TAP responses on-the-fly against an IVOA data model

With the success and widespread of the IVOA Table Access Protocol (1) for discovering and querying tabular data in astronomy, more than one hundred of TAP services exposing altogether 22 thousands of tables are accessible from the IVOA Registries at the time of writing. Currently the TAP protocol presents table data and metadata via a {TAP\_SCHEMA} describing the served tables with their columns and possible joins between them. We explore here how to add an information layer, so that values within table columns can be gathered and used to populate instances of objects defined in a selected IVOA data model like Photometry, Coords, Measure, Transform or the proposed MANGO container model. This information layer is provided through annotation tags which tell how the columns' values can be interpreted as attributes of instances of that model. Then when a TAP query is processed, our server add-on interprets the ADQL query string and produces on-the-fly, when possible, the TAP response as an annotated VOTable document. The FIELD elements in the table response are mapped to corresponding model elements templated for this service. This has been prototyped in Java, using the VOLLT package library and a template annotation document representing elements from the MANGO data model. This has been exercised on examples based on Vizier and Chandra catalogs.

astro-ph.IM↗

arXiv2021

TAP and the Data Models

The purpose of the "TAP and the Data Models" Bird of Feathers session was to discuss the relevance of enabling TAP services to deal with IVOA standardized data models and to refine the functionalities required to implement such a capability.

astro-ph.IM↗

arXiv2021

Spectral asymptotics for Metropolis algorithm on singular domains

We study the Metropolis algorithm on a bounded connected domain $Ω$ of the euclidean space with proposal kernel localized at a small scale $h > 0$. We consider the case of a domain $Ω$ that may have cusp singularities. For small values of the parameter $h$ we prove the existence of a spectral gap $g(h)$ and study the behavior of $g(h)$ when $h$ goes to zero. As a consequence, we obtain exponentially fast return to equilibrium in total variation distance.

math.AP↗

arXiv2020

Sharp spectral asymptotics for non-reversible metastable diffusion processes

Let $U_h:\mathbb R^{d}\to \mathbb R^{d}$ be a smooth vector field and consider the associated overdamped Langevin equation $$dX_t=-U_h(X_t)\,dt+\sqrt{2h}\,dB_t$$ in the low temperature regime $h\rightarrow 0$. In this work, we study the spectrum of the associated diffusion $L=-hΔ+U_h\cdot\nabla$ under the assumptions that $U_h=U_{0}+hν$, where the vector fields $U_{0}:\mathbb R^{d}\to \mathbb R^{d}$ and $ν:\mathbb R^{d}\to \mathbb R^{d}$ are independent of $h\in(0,1]$, and that the dynamics admits $e^{-\frac Vh}$ as an invariant measure for some smooth function $V:\mathbb{R}^d\rightarrow\mathbb{R}$. Assuming additionally that $V$ is a Morse function admitting $n_0$ local minima, we prove that there exists $ε>0$ such that in the limit $h\to 0$, $L$ admits exactly $n_0$ eigenvalues in the strip $\{0\leq \operatorname{Re}(z)< ε\}$, which have moreover exponentially small moduli. Under a generic assumption on the potential barriers of the Morse function $V$, we also prove that the asymptotic behaviors of these small eigenvalues are given by Eyring-Kramers type formulas.

math.SP↗

arXiv2020

An efficient constraint based framework forhandling floating point SMT problems

This paper introduces the 2019 version of \us{}, a novel Constraint Programming framework for floating point verification problems expressed with the SMT language of SMTLIB. SMT solvers decompose their task by delegating to specific theories (e.g., floating point, bit vectors, arrays, ...) the task to reason about combinatorial or otherwise complex constraints for which the SAT encoding would be cumbersome or ineffective. This decomposition and encoding processes lead to the obfuscation of the high-level constraints and a loss of information on the structure of the combinatorial model. In \us{}, constraints over the floats are first class objects, and the purpose is to expose and exploit structures of floating point domains to enhance the search process. A symbolic phase rewrites each SMTLIB instance to elementary constraints, and eliminates auxiliary variables whose presence is counterproductive. A diversification technique within the search steers it away from costly enumerations in unproductive areas of the search space. The empirical evaluation demonstrates that the 2019 version of \us{} is competitive on computationally challenging floating point benchmarks that induce significant search efforts even for other CP solvers. It highlights that the ability to harness both inference and search is critical. Indeed, it yields a factor 3 improvement over Colibri and is up to 10 times faster than SMT solvers. The evaluation was conducted over 214 benchmarks (The Griggio suite) which is a standard within SMTLIB.

cs.AI↗