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Partially Hyperbolic Compact Complex Manifolds
No full textWe propose and investigate two types, the latter with two variants, of notions of partial hyperbolicity accounting for several classes of compact complex manifolds behaving hyperbolically in certain directions, defined by a vector subbundle of the holomorphic tangent bundle, but not necessarily in the other directions. A key role is played by certain entire holomorphic maps, possibly from a higher-dimensional space, into the given manifold X. The dimension of the origin C p of these maps is allowed to be arbitrary, unlike both the classical 1-dimensional case of entire curves and the 1-codimensional case introduced in previous work of the second-named author with S. Marouani. The higher-dimensional generality necessitates the imposition of certain growth conditions, very different from those in Nevanlinna theory and those in works by de Thélin, Burns and Sibony on Ahlfors currents, on the entire holomorphic maps f : C p -→ X. The way to finding these growth conditions is revealed by certain special, possibly non-Kähler, Hermitian metrics in the spirit of Gromov's Kähler hyperbolicity theory but in a higher-dimensional context. We then study several classes of examples, prove implications among our partial hyperbolicity notions, give a sufficient criterion for the existence of an Ahlfors current and a sufficient criterion for partial hyperbolicity in terms of the signs of two curvature-like objects introduced recently by the second-named author.</div
On the Private Estimation of Smooth Transport Maps
No full textInternational audienceEstimating optimal transport maps between two distributions from respective samples is an important element for many machine learning methods. To do so, rather than extending discrete transport maps, it has been shown that estimating the Brenier potential of the transport problem and obtaining a transport map through its gradient is near minimax optimal for smooth problems. In this paper, we investigate the private estimation of such potentials and transport maps with respect to the distribution samples.We propose a differentially private transport map estimator achieving an error of at most up to poly-logarithmic terms where is the sample size, is the desired level of privacy, is the smoothness of the true transport map, and is the dimension of the feature space. We also provide a lower bound for the problem
E-compagnion:Decomposition methods for the beam-layout optimization problem
No full textIn this article, we study an optimization problem related to the design of a telecommunication satellite, namely the beam-layout optimization problem in which the goal is to define the beams emitted by the antennas of a geostationary satellite to cover regions on Earth. Four key features of the application tackled are that (1) the regions to cover are defined as polygons, (2) there is a very large number of candidate beams, (3) the selected beams need to be colored (actually, allocated to an antenna reflector) and two close beams cannot have the same color, and (4) the candidate beams have heterogeneous sizes and the sizes of the selected beams must be minimized for efficiency reasons. We provide a complexity analysis, showing that the problem is NP-hard. To solve this challenging problem, we introduce two decomposition methods based on column generation and logic-based Benders decomposition, to go beyond the existing heuristic approaches. The experimental results show that these decomposition methods provide high-quality solutions within limited computational times, and that the logic-based Benders decomposition approach finds the optimal solution for many instances.Dans cet article, nous étudions un problème d'optimisation lié à la conception d'un satellite de télécommunications, à savoir le problème d'optimisation de la disposition des faisceaux dans lequel l'objectif est de définir les faisceaux émis par les antennes d'un satellite géostationnaire pour couvrir des régions sur Terre. Quatre caractéristiques clés de l'application traitée sont que (1) les régions à couvrir sont définies comme des polygones, (2) il y a un très grand nombre de candidats faisceaux, (3) les faisceaux sélectionnés doivent être colorés (en réalité, alloués à un réflecteur d'antenne) et deux faisceaux rapprochés ne peuvent pas avoir la même couleur, et (4) les candidats faisceaux ont des tailles hétérogènes et la taille des faisceaux sélectionnés doit être minimisée pour des raisons d'efficacité. Nous fournissons une analyse de complexité, ce qui montre que le problème est NP-difficile. Pour résoudre ce problème difficile, nous introduisons deux méthodes de décomposition basées sur la génération de colonnes et la décomposition de Benders basée sur la logique, afin d'aller au-delà des approches héuristiques existantes. Les résultats expérimentaux montrent que ces méthodes de décomposition fournissent des solutions de haute qualité dans des temps de calcul limités et que l'approche de décomposition de Benders basée sur la logique trouve la solution optimale pour de nombreux échantillons
3D CORNEAL MORPHO-GEOMETRIC PARAMETERS IN HEALTHY PATIENTS MEASURED WITH AN OPTICAL COHERENCE TOMOGRAPHER AND A SCHEIMPFLUG TOMOGRAPHER: A COMPARATIVE STUDY
No full textInternational audienceThe increasing advancement of ophthalmic procedures such as refractive surgeries, phakic lens implantations, and the management of corneal diseases has emphasized the critical nature of obtaining precise measurements of morpho-geometric parameters associated with the anterior eye segment, particularly the cornea. Despite the availability of numerous devices capable of measuring these parameters, none of them can be designated as a “gold standard”, making it particularly important to objectively characterize the differences in measurement between different devices, and the potential causes that generate them. This study seeks to evaluate possible interchangeability between measurements of the same morphological parameter in human corneas taken with two distinct technologies: the Scheimpflug Sirius tomographer and the Optical Coherence Tomographer (OCT) MS-39, both manufactured by CSO Italy. Ten healthy eyes from five adult males were selected for the study. Each eye underwent three tomographic measurements, with only those passing the devices' self-diagnostic quality test being recorded. Various morpho-geometric parameters related to the anterior and posterior corneal surfaces, as well as corneal volume, were then measured and extracted according to a validated method. Subsequently, a descriptive analysis was conducted to determine the distribution and variability of the data, followed by tests for normality and statistical comparisons. The findings suggest that while some parameters, such as anterior corneal area, demonstrate agreement between the devices, others such posterior corneal area or total corneal volume do not. In conclusion, results suggest possible interchangeably for some 3D morpho-geometrical parameters, but further study using a higher sample would be needed to confirm this evidence. Keywords: Volume, Elevation Maps, Thickness, Cornea
Euclid Quick Data Release (Q1). The role of cosmic connectivity in shaping galaxy clusters
No full textInternational audienceThe matter distribution around galaxy clusters is distributed over several filaments, reflecting their positions as nodes in the large-scale cosmic web. The number of filaments connected to a cluster, namely its connectivity, is expected to affect the physical properties of clusters. Using the first Euclid galaxy catalogue from the Euclid Quick Release 1 (Q1), we investigate the connectivity of galaxy clusters and how it correlates with their physical and galaxy member properties. Around 220 clusters located within the three fields of Q1 (covering ), are analysed in the redshift range 0.2 < z < 0.7. Due to the photometric redshift uncertainty, we reconstruct the cosmic web skeleton, and measure cluster connectivity, in 2-D projected slices with a thickness of 170 comoving and centred on each cluster redshift, by using two different filament finder algorithms on the most massive galaxies (M_*\ > 10^{10.3} \ M_\odot). In agreement with previous measurements, we recover the mass-connectivity relation independently of the filament detection algorithm, showing that the most massive clusters are, on average, connected to a larger number of cosmic filaments, consistent with hierarchical structure formation models. Furthermore, we explore possible correlations between connectivities and two cluster properties: the fraction of early-type galaxies and the Sérsic index of galaxy members. Our result suggests that the clusters populated by early-type galaxies exhibit higher connectivity compared to clusters dominated by late-type galaxies. These preliminary investigations highlight our ability to quantify the impact of the cosmic web connectivity on cluster properties with Euclid
General reproducing properties in RKHS with application to derivative and integral operators
No full textIn this paper, we consider the reproducing property in Reproducing Kernel Hilbert Spaces (RKHS). We establish a reproducing property for the closure of the class of combinations of composition operators under minimal conditions. This allows to revisit the sufficient conditions for the reproducing property to hold for the derivative operator, as well as for the existence of the mean embedding function. These results provide a framework of application of the representer theorem for regularized learning algorithms that involve data for function values, gradients, or any other operator from the considered class.Dans cet article, nous considérons la propriété reproduisante dans les espaces de Hilbert à noyaux reproduisants (RKHS). Nous établissons une propriété de reproduction pour l'adhérence de la classe des combinaisons d'opérateurs de composition sous des conditions minimales. Cela nous permet de revisiter les conditions suffisantes pour que la propriété de reproduction soit valable pour l'opérateur dérivé, ainsi que pour l'existence de la fonction mean embedding. Ces résultats donnent un cadre d'application du théorème du représentant pour les algorithmes d'apprentissage régularisés qui impliquent des données sur les valeurs de fonctions, les gradients ou tout autre opérateur de la classe considérée
Monopole excitations in the U(1) Dirac spin liquid on the triangular lattice
No full textInternational audienceThe U(1) Dirac spin liquid might realize an exotic phase of matter whose low-energy properties are described by quantum electrodynamics in 2+1 dimensions, where gapless modes exist but spinons and gauge fields are strongly coupled. Its existence was proposed in frustrated Heisenberg models in the presence of frustrating superexchange interactions by the (Abrikosov) fermionic representation of the spin operators [Wen, Phys. Rev. B 65, 165113 (2002)], supplemented by the Gutzwiller projection. Here, we construct charge-Q monopole excitations in the Heisenberg model on the triangular lattice with nearest-neighbor (J1) and next-nearest-neighbor (J2) couplings. In the highly frustrated regime, singlet and triplet monopoles with Q=1 become gapless in the thermodynamic limit; in addition, the energies for generic Q agree with field-theoretical predictions, obtained for a large number of gapless fermion modes. Finally, we consider localized gauge excitations, in which magnetic π fluxes are concentrated in the triangular plaquettes (in analogy with Z2 visons), showing that these kinds of states do not play a relevant role at low energies. All our findings lend support to a stable U(1) Dirac spin liquid in the J1-J2 Heisenberg model on the triangular lattice
Multivariate Self-Exciting Processes with Dependencies
No full textThis paper introduces the class of multidimensional self-exciting processes with dependencies (MSPD), which is a unifying writing for a large class of processes: counting, loss, intensity, and also shifted processes. The framework takes into account dynamic dependencies between the frequency and the severity components of the risk, and therefore induces theoretical challenges in the computations of risk valuations. We present a general method for calculating different quantities related to these MSPDs, which combines the Poisson imbedding, the pseudo-chaotic expansion and Malliavin calculus. The methodology is illustrated for the computation of explicit general correlation formula
Expanding the Diversity of Nitroxide‐Based Paramagnetic Probes Conjugated to Non‐Canonical Amino Acids for Sdsl‐Epr Applications
No full textInternational audienceUnderstanding protein structure requires studying its dynamics, which is critical to elucidating its functional role. Biophysical techniques have revolutionized this field over time, providing remarkable insights into structure‐function relationships. Among these, Site‐Directed Spin Labelling (SDSL) combined with Electron Paramagnetic Resonance (EPR) is a powerful method delivering structural data at the residue level, irrespective of protein size or environment. Traditional nitroxide labels targeting cysteine residues face limitations when these residues are essential for protein structure or function. To address this, alternatives have been proposed as the use of non‐canonical amino acids (ncaa) coupled with specific nitroxide labels. This study introduces 14 N‐HO‐5223, a novel nitroxide label specific to the p AzPhe ncaa, along with its 15 N‐derivative. These labels were grafted at two sites of the model protein, the diflavin cytochrome P450 reductase. For comparative purpose, two already reported labels were also used. Continuous wave (cw) EPR spectroscopy confirmed the HO‐5223 label as an effective reporter of protein dynamics. Additionally, Double Electron‐Electron Resonance (DEER) measurements provided distance distributions between the semi‐quinone FMNH⋅ state of the CPR and all nitroxide labels. These results expand the toolkit of the ncaa‐nitroxide pairs, enabling EPR‐based structural studies of proteins where cysteine modification is impractical, further advancing our ability to decode protein dynamics and function
On random classical marginal problems with applications to quantum information theory
No full textInternational audienceAbstract In this paper, we study random instances of the classical marginal problem. We encode the problem in a graph, where the vertices have assigned fixed binary probability distributions, and edges have assigned random bivariate distributions having the incident vertex distributions as marginals. We provide estimates on the probability that a joint distribution on the graph exists, having the bivariate edge distributions as marginals. Our study is motivated by Fine’s theorem in quantum mechanics. We study in great detail the graphs corresponding to CHSH and Bell–Wigner scenarios providing rations of volumes between the local and non-signaling polytopes