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Scaling limit of random plane quadrangulations with a simple boundary, via restriction
No full textInternational audienceThe main purpose of this work is to provide a framework for proving that, given a family of random maps known to converge in the Gromov--Hausdorff sense, then some (suitable) conditional families of random maps converge to the same limit. As a proof of concept, we show that quadrangulations with a simple boundary converge to the Brownian disk. More precisely, we fix a sequence of even positive integers with for some . Then, for the Gromov--Hausdorff topology, a quadrangulation with a simple boundary uniformly sampled among those with inner faces and boundary length weakly converges, in the usual scaling , toward the Brownian disk of perimeter
Scaling limit of graph classes through split decomposition
No full text47 pagesInternational audienceWe prove that Aldous' Brownian CRT is the scaling limit, with respect to the Gromov--Prokhorov topology, of uniform random graphs in each of the three following families of graphs: distance-hereditary graphs, -connected distance-hereditary graphs and -leaf power graphs. Our approach is based on the split decomposition and on analytic combinatorics
On the stability of the invariant probability measures of McKean-Vlasov equations
No full textInternational audienceWe study the long-time behavior of some McKean-Vlasov stochastic differential equations used to model the evolution of large populations of interacting agents. We give conditions ensuring the local stability of an invariant probability measure. Lions derivatives are used in a novel way to obtain our stability criteria. We obtain results for non-local McKean-Vlasov equations on and for McKean-Vlasov equations on the torus where the interaction kernel is given by a convolution. On , we prove that the location of the roots of an analytic function determines the stability. On the torus, our stability criterion involves the Fourier coefficients of the interaction kernel. In both cases, we prove the convergence in the Wasserstein metric with an exponential rate of convergence.On étudie le comportement en temps long d’équations non-linéaires au sens de McKean–Vlasov. Ces équations sont utilisées pour modéliser les comportements de grandes populations d’agents en interaction. On donne des critères garantissant la stabilité locale d’une mesure de probabilité invariante. Pour ce faire, on utilise de manière novatrice les dérivées de Lions. On obtient des résultats pour des équations de McKean–Vlasov non locales sur , ainsi que pour des équations de McKean–Vlasov sur le tore pour lesquelles le noyau d’interaction est donné par une convolution. Sur , on montre que la stabilité est déterminée par l’emplacement des zéros d’une fonction holomorphe. Sur le tore, notre critère de stabilité fait intervenir les coefficients de Fourier du noyau d’interaction. Dans les deux cas, on montre la convergence vers la mesure de probabilité invariante à vitesse exponentielle pour la métrique de Wasserstein
Measurement of the top-quark production cross-section and charge asymmetry at LHCb
No full textInternational audienceThe first measurements of the top- and antitop-quark differential production cross-sections and the top-quark charge asymmetry in the forward region are presented, using proton-proton collision data collected by the LHCb experiment at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 5.4 . The total production cross-sections of top and antitop quarks are also determined. Measurements are performed using the final state within a fiducial region defined by a p_{\text{T, jet}}>50 GeV and pseudorapidity 2.2<η_{\text{jet}}<4.0,, with the muon from the -boson decay required to have p_{\text{T},μ}>25 GeV and pseudorapidity 2.0<η_μ<4.5. The muon and -jet system must satisfy p_{T}(μ+\text{jet}) > 20 GeV. The measured integrated production cross-sections for the top and antitop quarks are pb, pb, where the first uncertainty is statistical, the second systematic, and the third accounts for the luminosity uncertainty. The top-quark charge asymmetry is measured to be , where the first uncertainty is statistical and the second is systematic. These results are consistent with next-to-leading-order Standard Model predictions
Minimax spectral estimation of weighted Laplace operators
No full textGiven n i.i.d. observations, we study the problem of estimating the spectrum of weighted Laplace operators of the form ∆ f = ∆ + α∇ log f • ∇, where f is a positive probability density on a known compact d-dimensional manifold without boundary and α ∈ R is a hyperparameter. These operators arise as continuum limits of graph Laplacian matrices and provide valuable geometric information on the underlying data distribution. We establish the exact minimax rates of estimation for this problem, by exhibiting two different rates of convergence for eigenfunctions and eigenvalues. When f belongs to a Hölder-Zygmund class C s of regularity s 2, the eigenfunctions can be estimated with respect to the L q -norm (q 1) via plug-in methods at the minimax rate n -s+1 2s+d for d 3 (with different rates for d 2). Moreover, eigenvalues can be estimated at the minimax rate n -4s 4s+d + n -1 2 . In the regime s > d 4 , we further show that asymptotically efficient estimators exist.We also present a general framework for estimating nonlinear functionals over Hölder-Zygmund spaces, with potential applications to a broad class of statistical problems
Shadowgraphy measurements of bubble jet coupled with surface oscillations
No full textInternational audienceWe present an image processing method to track and characterize the motion of air–liquid interfaces occurring in aerated liquid baths. In a rectangular tank filled with water, an immersed sparger injects air vertically at a constant flow rate and creates well-defined sloshing oscillations of the free surface. The phenomenon is referred to as self-induced sloshing.We retrieve the positions of both the surface and the jet position using a tailored image processing method based on shadowgraphy. Using Complex Orthogonal Decomposition (COD), we reveal the main spatial and temporal dynamics of the oscillations
Experimental evidence of stimulated Raman rescattering in laser-plasma interaction
No full textInternational audienceWe present the first experimental evidence of stimulated Raman re-scattering of a laser in plasma: The scattered light produced by the Raman instability is intense enough to scatter again through the same instability. Although never observed, re-scattering processes have been studied theoretically and numerically for many years in the context of inertial confinement fusion (ICF), since the plasma waves they generate could bootstrap thermal electrons to high energies [Phys. Rev. Lett. \textbf{110}, 165001 (2013)], preheating the fuel and degrading ignition conditions. Our experimental results are obtained with a spatially smoothed laser beam consisting of many speckles, with an average intensity around W/cm and close to W/cm in the speckles, such as those usually used in direct-drive ICF. Kinetic and hydrodynamic simulations show good agreement with the observations
Deciphering the intermolecular interactions between G-quadruplex (G4)-forming sequences
No full textInternational audienceInteractions between biomolecules govern cellular biology. While protein/protein and protein/nucleic acid (DNA, RNA) interactions-and, to a lesser extent, RNA/RNA and RNA/DNA interactions-ha v e been e xtensiv ely described, a question remains as to whether and how non-canonical DNA str uct ures might interact with each other. This is of particular interest for guanine (G)-rich sequences that can fold into G-quadruplex (G4) str uct ures: Individual G4s are currently studied for their involvement in a myriad of cellular events (mostly pertaining to the control of gene expression), and, more recently, the interactions between two G4s have been scrutinized as being part of a novel gene expression regulatory mechanism in v olving chromatin remodeling through G4-mediated loop f ormation. T he question that needs to be answered is whether G4s or their corresponding G-rich sequences are in v olv ed. We present here a series of results collected using a combination of sequences, experimental conditions, and tec hniques, whic h led us to the conclusion that G4/G4 intermolecular interactions are mostly go v erned b y primary sequence interactions in vitro.</div
Measurements of electroweak production of a photon in association with two jets in proton-proton collisions at = 13 TeV
No full textInternational audienceThe first observation of electroweak production of a photon in association with two forward jets in proton-proton collisions is presented. The measurement uses data recorded by the CMS experiment at the LHC during 20162018 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb. The analysis is performed in a region enriched in photon production via vector boson fusion, with a requirement on the transverse momentum of the photon to exceed 200 GeV. The cross section is measured to be 202 fb, at a significance with respect to the null hypothesis that exceeds five standard deviations. This is in agreement with the standard model prediction of 177 fb. Differential cross sections are measured as a function of various observables. Limits are set on dimension-6 effective field theory operators that contribute to the WW interaction. The observed 95% confidence intervals for the corresponding Warsaw basis Wilson coefficients and are [0.11, 0.16] and [1.6, 1.5], respectively
Conceptual design report of the Super Tau-Charm Facility: the accelerator
No full textInternational audienceAbstract Electron–positron colliders operating in the GeV center-of-mass range, or tau-charm energy region, have been proved to enable competitive frontier research due to several unique features. With the progress of high-energy physics in the last two decades, a new-generation Tau-Charm factory, called the Super Tau-Charm Facility (STCF), has been actively promoted by the particle physics community in China. STCF has the potential to address fundamental questions such as the essence of color confinement and the matter–antimatter asymmetry within the next decades. The main design goals of the STCF are a center-of-mass energy ranging from 2 to 7 GeV and a luminosity surpassing 5 × 10 34 cm −2 s −1 that is optimized at a center-of-mass energy of 4 GeV, which is approximately 50 times that of the currently operating Tau-Charm factory—BEPCII. The STCF accelerator has two main parts: a double-ring collider with a crab-waist collision scheme and an injector that provides top-up injections for both electron and positron beams. As a typical third-generation electron–positron circular collider, the STCF accelerator faces many challenges in both accelerator physics and technology. In this paper, the conceptual design of the STCF accelerator complex is presented, including the ongoing efforts and plans for technological research and development, as well as the required infrastructure. The STCF project aims to secure support from the Chinese central government for its construction during the 15th Five-Year Plan (2026–2030)