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A two spaces extension of Cauchy-Lipschitz Theorem
No full textInternational audienceWe adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider ẋ = f (x, x) for a function f : V × E → E where E is a Banach space and V → E a normed vector space. This structure allows us to distinguish between the two dependencies of f in x and allows to generalize classical results. We also prove a similar results for partial differential equations
Provable non-accelerations of the heavy-ball method
No full textInternational audienceIn this work, we show that the heavy-ball (\HB) method provably does not reach an accelerated convergence rate on smooth strongly convex problems. More specifically, we show that for any condition number and any choice of algorithmic parameters, either the worst-case convergence rate of \HB on the class of -smooth and -strongly convex \textit{quadratic} functions is not accelerated (that is, slower than ), or there exists an -smooth -strongly convex function and an initialization such that the method does not converge. To the best of our knowledge, this result closes a simple yet open question on one of the most used and iconic first-order optimization technique. Our approach builds on finding functions for which \HB fails to converge and instead cycles over finitely many iterates. We analytically describe all parametrizations of \HB that exhibit this cycling behavior on a particular cycle shape, whose choice is supported by a systematic and constructive approach to the study of cycling behaviors of first-order methods. We show the robustness of our results to perturbations of the cycle, and extend them to class of functions that also satisfy higher-order regularity conditions
Finding meaningful paths in heterogeneous graphs with PathWays
No full textInternational audienceGraphs, and notably RDF graphs, are a prominent way of sharing data. As data usage democratizes, users need help figuring out the useful content of a graph dataset. In particular, journalists with whom we collaborate are interested in identifying, in a graph, the connections between entities, e.g., people, organizations, emails, etc. We present a novel method for exploring data graphs through their data paths connecting Named Entities (NEs, in short); each data path leads to a tabular-looking set of results. NEs are extracted from the data through dedicated Information Extraction modules. Our method builds upon the pre-existing ConnectionLens platform and follow-up work in the Abstra project, which builds simple, visual ER-style summaries of semi-structured data. The contribution of the present work, and its novelty, is twofold. First, we propose a novel analysis of entity-to-entity paths contained in datasets of any nature, and propose a new method for ranking paths, leveraging a novel Information Extraction (IE) module we built on top of ChatGPT. Second, we present an efficient approach to enumerate and compute NE paths, based on an algorithm which automatically recommends sub-paths to materialize, and rewrites the path queries using these subpaths. Our experiments demonstrate the interest of NE paths and the efficiency of our method for computing and ranking them
Amplitude analysis of decays
No full textInternational audienceThe first full amplitude analysis of decays is performed using proton-proton collision data corresponding to an integrated luminosity of recorded with the LHCb detector. The rich spectrum is studied and the branching fractions of the resonant substructure associated with the prominent contribution are measured. The data cannot be described by conventional strange and charmonium resonances only. An amplitude model with 53 components is developed comprising 11 hidden-charm exotic hadrons. New production mechanisms for charged charmonium-like states are observed. Significant resonant activity with spin-parity in the system is confirmed and a multi-pole structure is demonstrated. The spectral decomposition of the invariant-mass structure, dominated by decays, broadly resembles the spectrum observed in decays. Exotic resonances are observed for the first time
Triviality proof for mean-field -theories
No full textInternational audienceThe differential equations of the Wilson renormalization group are a powerful tool to study the Schwinger functions of Euclidean quantum field theory. In particular renormalization theory can be based entirely on inductively bounding their perturbatively expanded solutions. Recently the solutions of these equations for scalar field theory have been analysed rigorously without recourse to perturbation theory, at the cost of restricting to the mean-field approximation. In particular it was shown there that one-component -theory is trivial if the bare coupling constant of the UV regularized theory is not large. This paper presents progress w.r.t. Kopper's previous paper on asymptotically free solutions of the mean-field scalar flow equations: 1. The upper bound on the bare coupling is sent to infinity and the proof is extended to vector models. 2. The unphysical infrared cutoff used for technical simplicity is replaced by a physical mass
Skydiving to Bootstrap Islands
No full textInternational audienceWe study families of semidefinite programs (SDPs) that depend nonlinearly on a small number of "external" parameters. Such families appear universally in numerical bootstrap computations. The traditional method for finding an optimal point in parameter space works by first solving an SDP with fixed external parameters, then moving to a new point in parameter space and repeating the process. Instead, we unify solving the SDP and moving in parameter space in a single algorithm that we call "skydiving". We test skydiving on some representative problems in the conformal bootstrap, finding significant speedups compared to traditional methods
A geometric invariant of linear rank-metric codes
No full textInternational audienceRank-metric codes have been a central topic in coding theory due to their theoretical and practical significance, with applications in network coding, distributed storage, crisscross error correction, and post-quantum cryptography. Recent research has focused on constructing new families of rank-metric codes with distinct algebraic structures, emphasizing the importance of invariants for distinguishing these codes from known families and from random ones. In this paper, we introduce a novel geometric invariant for linear rank-metric codes, inspired by the Schur product used in the Hamming metric. By examining the sequence of dimensions of Schur powers of the extended Hamming code associated with a linear code, we demonstrate its ability to differentiate Gabidulin codes from random ones. From a geometric perspective, this approach investigates the vanishing ideal of the linear set corresponding to the rank-metric code
Kinetic theory and moment models of electrons in a reactive weakly-ionized non-equilibrium plasma
No full textInternational audienceWe study the electrons in a multi-component weakly-ionized plasma with an external electric field under conditions that are far from thermodynamic equilibrium, representative of a gas discharge plasma. Our starting point is the generalized Boltzmann equation with elastic, inelastic and reactive collisions. We perform a dimensional analysis of the equation and an asymptotic analysis of the collision operators for small electron-to-atom mass ratios and small ionization levels. The dimensional analysis leads to a diffusive scaling for the electron transport. We perform a Hilbert expansion of the electron distribution function that, in the asymptotic limit, results in a reduced model characterized by a spherically symmetric distribution function in the velocity space with a small anisotropic perturbation. We show that the spherical-harmonics expansion model, widely used in low-temperature plasmas, is a particular case of our approach. We approximate the solution of our kinetic model with a truncated moment hierarchy. Finally, we study the moment problem for a particular case: a Langevin collision (equivalent to Maxwell molecules) for the electron-gas elastic collisions. The resulting Stieltjes moment problem leads to an advection-diffusion-reaction system of equations that is approximated with two different closures: the quadrature method of moments and a Hermitian moment closure. A special focus is given along the derivations and approximations to the notion of entropy dissipation.</div
A strictly linear subatomic proof system
No full textInternational audienceWe present a subatomic deep-inference proof system for a conservative extension of propositional classical logic with decision trees that is strictly linear. In a strictly linear subatomic system, a single linear rule shape subsumes not only the structural rules, such as contraction and weakening, but also the unit equality rules. An interpretation map from subatomic logic to propositional classical logic recovers the usual semantics and proof theoretic properties. By using explicit substitutions that indicate the substitution of one derivation into another, we are able to show that the unit-equality inference steps can be eliminated from a subatomic system for propositional classical logic with only a polynomial complexity cost in the size of the derivation, from which it follows that the system p-simulates Frege systems, and we show cut elimination for the resulting strictly linear system