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Laurent Michel

Publications and source records attributed to Laurent Michel.

At least 37 records · Page 2Linked to original sources
arXiv2020

Bringing freedom in variable choice when searching counter-examples in floating point programs

Program verification techniques typically focus on finding counter-examples that violate properties of a program. Constraint programming offers a convenient way to verify programs by modeling their state transformations and specifying searches that seek counter-examples. Floating-point computations present additional challenges for verification given the semantic subtleties of floating point arithmetic. % This paper focuses on search strategies for CSPs using floating point numbers constraint systems and dedicated to program verification. It introduces a new search heuristic based on the global number of occurrences that outperforms state-of-the-art strategies. More importantly, it demonstrates that a new technique that only branches on input variables of the verified program improve performance. It composes with a diversification technique that prevents the selection of the same variable within a fixed horizon further improving performances and reduces disparities between various variable choice heuristics. The result is a robust methodology that can tailor the search strategy according to the sought properties of the counter example.

cs.AI↗
arXiv2019

Applications of resonance theory without analyticity assumption

We prove that the results in scattering theory that involve resonances are still valid for non-analytic potentials, even if the notion of resonance is not defined in this setting. More precisely, we show that if the potential of a semiclassical Schrödinger operator is supposed to be smooth and to decrease at infinity, the usual formulas relating scattering quantities and resonances still hold. The main ingredient for the proofs is a resolvent estimate of a new type, relating the resolvent of an operator with the resolvent of its cut-off counterpart.

math.AP↗
arXiv2019

DOCSDN: Dynamic and Optimal Configuration of Software-Defined Networks

Networks are designed with functionality, security, performance, and cost in mind. Tools exist to check or optimize individual properties of a network. These properties may conflict, so it is not always possible to run these tools in series to find a configuration that meets all requirements. This leads to network administrators manually searching for a configuration. This need not be the case. In this paper, we introduce a layered framework for optimizing network configuration for functional and security requirements. Our framework is able to output configurations that meet reachability, bandwidth, and risk requirements. Each layer of our framework optimizes over a single property. A lower layer can constrain the search problem of a higher layer allowing the framework to converge on a joint solution. Our approach has the most promise for software-defined networks which can easily reconfigure their logical configuration. Our approach is validated with experiments over the fat tree topology, which is commonly used in data center networks. Search terminates in between 1-5 minutes in experiments. Thus, our solution can propose new configurations for short term events such as defending against a focused network attack.

cs.CR↗
arXiv2018

About small eigenvalues of Witten Laplacian

We study the eigenvalues of the semiclassical Witten Laplacian $Δ_ϕ$ associated to a potential $ϕ$. We consider the case where the sequence of Arrhenius numbers $S_1\leq \ldots\leq S_n$ associated to $ϕ$ is degenerated, that is the preceding inequality are not necessarily strict.

math.AP↗
arXiv2018

A semiclassical approach to the Kramers--Smoluchowski equation

We consider the Kramers--Smoluchowski equation at a low temperature regime and show how semiclassical techniques developed for the study of the Witten Laplacian and Fokker--Planck equation provide quantitative results. This equation comes from molecular dynamics and temperature plays the role of a semiclassical paramater. The presentation is self-contained in the one dimensional case, with pointers to the recent paper \cite{Mi16} for results needed in higher dimensions. One purpose of this note is to provide a simple introduction to semiclassical methods in this context.

math.AP↗
arXiv2017

IVOA Recommendation: HiPS - Hierarchical Progressive Survey

This document presents HiPS, a hierarchical scheme for the description, storage and access of sky survey data. The system is based on hierarchical tiling of sky regions at finer and finer spatial resolution which facilitates a progressive view of a survey, and supports multi-resolution zooming and panning. HiPS uses the HEALPix tessellation of the sky as the basis for the scheme and is implemented as a simple file structure with a direct indexing scheme that leads to practical implementations.

astro-ph.IM↗
arXiv2015

IVOA recommendation: IVOA DataLink

This document describes the linking of data discovery metadata to access to the data itself, further detailed metadata, related resources, and to services that perform operations on the data. The web service capability supports a drill-down into the details of a specific dataset and provides a set of links to the dataset file(s) and related resources. This specification also includes a VOTable-specific method of providing descriptions of one or more services and their input(s), usually using parameter values from elsewhere in the VOTable document. Providers are able to describe services that are relevant to the records (usually datasets with identifiers) by including service descriptors in a result document.

astro-ph.IM↗
arXiv2015

Around supersymmetry for semiclassical second order differential operators

Let $P(h),h\in]0,1]$ be a semiclassical scalar differential operator of order $2$. The existence of a supersymmetric structure given by a matrix $G(x;h)$ was exhibited in \cite{HeHiSj13} under rather general assumptions. In this note we give a sufficient condition on its coefficient so that the matrix $G(x;h)$ enjoys some nice estimates with respect to the semiclassical parameter.

math.AP↗
arXiv2014

Building an Archive with Saada

Saada transforms a set of heterogeneous FITS files or VOTables of various categories (images, tables, spectra ...) in a database without writing code. Databases created with Saada come with a rich Web interface and an Application Programming Interface (API). They support the four most common VO services. Such databases can mix various categories of data in multiple collections. They allow a direct access to the original data while providing a homogenous view thanks to an internal data model compatible with the characterization axis defined by the VO. The data collections can be bound to each other with persistent links making relevant browsing paths and allowing data-mining oriented queries.

astro-ph.IM↗
arXiv2014

A Microkernel Architecture for Constraint Programming

This paper presents a microkernel architecture for constraint programming organized around a number of small number of core functionalities and minimal interfaces. The architecture contrasts with the monolithic nature of many implementations. Experimental results indicate that the software engineering benefits are not incompatible with runtime efficiency.

cs.AI↗
arXiv2014

Domain Views for Constraint Programming

Views are a standard abstraction in constraint programming: They make it possible to implement a single version of each constraint, while avoiding to create new variables and constraints that would slow down propagation. Traditional constraint-programming systems provide the concept of {\em variable views} which implement a view of the type $y = f(x)$ by delegating all (domain and constraint) operations on variable $y$ to variable $x$. This paper proposes the alternative concept of {\em domain views} which only delegate domain operations. Domain views preserve the benefits of variable views but simplify the implementation of value-based propagation. Domain views also support non-injective views compositionally, expanding the scope of views significantly. Experimental results demonstrate the practical benefits of domain views.

cs.AI↗
arXiv2013

Spectral Analysis of hypoelliptic random walks

We study the spectral theory of a reversible Markov chain associated to a hypoelliptic random walk on a manifold M. This random walk depends on a parameter h which is roughly the size of each step of the walk. We prove uniform bounds with respect to h on the rate of convergence to equilibrium, and the convergence when h goes to zero to the associated hypoelliptic diffusion.

math.AP↗
arXiv2011

IVOA Recommendation: Observation Data Model Core Components and its Implementation in the Table Access Protocol Version 1.0

This document defines the core components of the Observation data model that are necessary to perform data discovery when querying data centers for observations of interest. It exposes use-cases to be carried out, explains the model and provides guidelines for its implementation as a data access service based on the Table Access Protocol (TAP). It aims at providing a simple model easy to understand and to implement by data providers that wish to publish their data into the Virtual Observatory. This interface integrates data modeling and data access aspects in a single service and is named ObsTAP. It will be referenced as such in the IVOA registries. There will be a separate document to cover the full Observation data model. In this document, the Observation Data Model Core Components (ObsCoreDM) defines the core components of queryable metadata required for global discovery of observational data. It is meant to allow a single query to be posed to TAP services at multiple sites to perform global data discovery without having to understand the details of the services present at each site. It defines a minimal set of basic metadata and thus allows for a reasonable cost of implementation by data providers. The combination of the ObsCoreDM with TAP is referred to as an ObsTAP service. As with most of the VO Data Models, ObsCoreDM makes use of STC, Utypes, Units and UCDs. The ObsCoreDM can be serialized as a VOTable. ObsCoreDM can make reference to more complete data models such as ObsProvDM (the Observation Provenance Data Model, to come), Characterisation DM, Spectrum DM or Simple Spectral Line Data Model (SSLDM).

astro-ph.IM↗
arXiv2011

Gibbs/Metropolis algorithms on a convex polytope

This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a fixed, finite set of directions, needs some new tools. We get useful bounds on the spectrum and eigenfunctions using Nash and Weyl-type inequalities. The top eigenvalues of the Markov chain are closely related to the Neuman eigenvalues of the polytope for a novel Laplacian.

math.SP↗
arXiv2010

Spectral analysis of random walk operators on euclidian space

We study the operator associated to a random walk on $\R^d$ endowed with a probability measure. We give a precise description of the spectrum of the operator near $1$ and use it to estimate the total variation distance between the iterated kernel and its stationary measure. Our study contains the case of Gaussian densities on $\R^d$.

math.SP↗
arXiv2010

Random walk on surfaces with hyperbolic cusps

We consider the operator associated to a random walk on finite volume surfaces with hyperbolic cusps. We study the spectral gap (upper and lower bound) associated to this operator and deduce some rate of convergence of the iterated kernel towards its stationary distribution.

math.SP↗