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Three-dimensional microphone array for the reconstruction of compact dipole aeroacoustic sources with spatially varying orientation
No full textInternational audienceThis work investigates, using a microphone array, the localization of aeroacoustic sources resulting from the interaction of a flow with rods. In similar investigations in the literature, arrays often have a planar geometry and the spatial region in which acoustic sources are searched is a plane parallel to that of the array. However, the sources are not always distributed in such a plane. Moreover, aeroacoustic sources resulting from flow-obstacle interaction are often dipoles, and for some complex geometries, the dipoles' orientation can vary in space, such as for curved obstacles or arrangements of rods with different orientations. In order to identify such dipoles, this work uses a three-dimensional array composed of four flat arrays, forming a tunnel of 1024 microphones around the open vein of an anechoic wind tunnel. Microphone signals are processed by an inverse beamforming technique to identify equivalent dipole sources producing the measured sound field at the array, using classical Tikhonov regularization. Taking advantage of the acoustic compactness of the cross-section of the rods located in the flow, the dipoles are sought along the axis of the rods, with a spacing of the order of the vortex shedding coherence length. The technique does not require any prior assumption on dipole orientation. Results from simulated or experimental data are presented to assess the effectiveness of the method, in the cases of a rectilinear rod and a bended rod forming a ring
GW/DT Invariants and 5D BPS Indices for Strips from Topological Recursion
No full textInternational audienceTopological string theory partition function gives rise to Gromov-Witten invariants, Donaldson-Thomas invariants and 5D BPS indices. Using the remodeling conjecture, which connects Topological Recursion with topological string theory for toric Calabi–Yau threefolds, we study a more direct connection for the subclass of strip geometries. In doing so, new developments in the theory of topological recursion are applied as its extension to Logarithmic Topological Recursion (Log-TR) and the universal -- duality. Through these techniques, our main result in this paper is a direct derivation of all free energies from topological recursion for general strip geometries. In analyzing the expression of free energy, we shed some light on the meaning and the influence of the -- duality in topological string theory and its interconnection to GW and DT invariants as well as the 5D BPS index
An equation for the kinetic energy balance in homogeneous turbulence
No full textInternational audienceWe derive a two-equation model for the energy balance in statistically homogeneous turbulence. The present formulation is expressed in terms of the energy flux, unlike the classical approach, where the dissipation rate appears in the kinetic energy equation. This enables a unified description of both forced and decaying turbulence with a single set of model constants. The model also captures the time lag between the evolution of the kinetic energy and the dissipation rate. Reformulating the system as an equation for the dissipation rate further clarifies how non-equilibrium effects can be incorporated into existing turbulence models
Generalization and Scaling Laws for Mixture-of-Experts Transformers
No full textWe develop a theory of generalization and scaling for Mixture-of-Experts (MoE) Transformers that cleanly separates active per-input capacity from routing combinatorics. Conditioning on fixed routing patterns and union-bounding across them, we obtain a sup-norm coveringnumber bound whose metric entropy scales with the active parameter budget and incurs a MoE-specific overhead. Combining this with a standard ERM argument for squared loss we provided a generalization bound under a d-dimensional manifold model (d is the intrinsic dimension of the training data) and C β targets, showing that approximation and estimation trade off in the same way as in dense networks once active parameters are counted appropriately. We further prove a constructive approximation theorem for MoE architectures, demonstrating that accuracy can be improved either by scaling active capacity or by increasing the number of available experts, with the better of the two mechanisms prevailing. From these results we derive neural scaling laws, covering model scaling, data scaling and compute-optimal tradeoffs. The theory highlights that enlarging the expert pool at fixed sparsity influences performance only through a mild logarithmic routing term, whereas increasing active capacity per input drives the main gains in generalization and approximation. These insights provide principled guidance for the design of efficient sparse Transformer systems and clarify the fundamental tradeoffs underlying their empirical scaling behavior.</div
-structures through quotient by torus actions
No full textWe show that if is a Kähler manifold with an -structure and a Hamiltonian holomorphic action of a compact torus , then the usual symplectic quotient inherits an -structure provided the existence of special 1-forms on X, called twist forms. We then give several applications of our results: on complex projective spaces, on cones over Fano Kähler-Einstein manifold and on toric bundles. We also study the geometry behind these structures in the case of
FNOPT: Resolution-Agnostic, Self-Supervised Cloth Simulation using Meta-Optimization with Fourier Neural Operators
No full textInternational audienceWe present FNOPT, a self-supervised cloth simulation framework that formulates time integration as an optimization problem and trains a resolution-agnostic neural optimizer parameterized by a Fourier neural operator (FNO). Prior neural simulators often rely on extensive ground truth data or sacrifice fine-scale detail, and generalize poorly across resolutions and motion patterns. In contrast, FNOPT learns to simulate physically plausible cloth dynamics and achieves stable and accurate rollouts across diverse mesh resolutions and motion patterns without retraining. Trained only on a coarse grid with physics-based losses, FNOPT generalizes to finer resolutions, capturing fine-scale wrinkles and preserving rollout stability. Extensive evaluations on a benchmark cloth simulation dataset demonstrate that FNOPT outperforms prior learning-based approaches in out-ofdistribution settings in both accuracy and robustness. These results position FNO-based meta-optimization as a compelling alternative to previous neural simulators for cloth; thus reducing the need for curated data and improving cross-resolution reliability.</div
Strong asymptotic freeness of Haar unitaries in quasi-exponential dimensional representations
No full text53 pagesInternational audienceWe prove almost sure strong asymptotic freeness of i.i.d. random unitaries with the following law: sample a Haar unitary matrix of dimension and then send this unitary into an irreducible representation of . The strong convergence holds as long as the irreducible representation arises from a pair of partitions of total size at most and is uniform in this regime. Previously this was known for partitions of total size up to by a result of Bordenave and Collins
A Comparative Optimal Control Study of Protecting Susceptibles and Isolating Infecteds in SIR Models
No full textThere are several approaches to controlling the spread of infectious diseases. Among the most widely used measures are the protection of susceptible individuals and the isolation of infected ones. This raises a critical question: which strategy — protecting susceptible individuals, isolating infected ones, or combining both — most effectively mitigates disease transmission? The work proposed here, address this question by analyzing protection and isolation strategies within the framework of the classical SIR (Susceptible-Infected-Recovered) epidemic model. Three scenarios are considered: (i) combined protection and isolation, (ii) protection alone, and (iii) isolation alone. Using Optimal Control Theory, we show that, in the short-term context of epidemic control, combining protection and isolation generally provides the most effective and robust strategy. However, when the combination is unavailable or unnecessary, isolation tends to outperform protection, particularly under challenging conditions such as high transmission rates or low recovery rates. Protection alone can still be effective, but primarily in settings where recovery rates are sufficiently high.These results contrast with those obtained from autonomous models, in which, in the long-term dynamics, protecting susceptible individuals proved to be more effective than isolating the infected
Model selection for extremal dependence structures using deep learning: Application to environmental data
No full textAlthough the CLIC-based model selection approach is widely used to identify spatial extreme models, the complexity of the associated statistical inference limits the reliability of this criterion. In addition, the strong spatial dependence in small or moderate regions may lead to substantial overlap among the spatial extremes models. This potential overlap increases the risk of model misidentification. In this paper, we exploit the ability of Convolutional Neural Networks (CNNs) to extract spatial patterns in order to develop a CNN-based model selection framework. The proposed approach evaluates how well the dependence structure observed in the data matches the dependence patterns implied by competing models. Two identification strategies are considered. In the first strategy, both the max-stable model and its associated covariance function are identified simultaneously by a single CNN in a one-step procedure. In the second strategy, model identification is performed hierarchically. First, a CNN identifies the class of max-stable model, and then additional CNNs are trained for each model to determine the corresponding covariance function. The performance of the two strategies is evaluated through an extensive simulation study designed to reproduce the spatial dependence structure of 2-m air temperature data over Iraq, where strong dependence and model overlap are observed. The results demonstrate that the proposed CNN-based approach provides an effective alternative for model selection in spatial extremes
EcoViz: a tool for visual analysis and photorealistic rendering of forest landscape model simulations
No full textInternational audienceSimulation outputs from forest landscape models are complex, and tools for their visual analysis and effective communication are often limited. In this paper, we present EcoViz, a novel, open‐source visualisation platform designed to complement existing forest models by providing advanced 3D visualisation capabilities. EcoViz facilitates the exploration of simulation results through two primary modes: symbolic rendering, designed for analytical tasks, such as pattern recognition and model evaluation, and photorealistic rendering, leveraging physically based rendering (Mitsuba 3) and a custom library of European 3D tree models for communication purposes. The platform imports spatially explicit individual tree or cohort data and employs a temporally coherent sampling technique to visualise individual trees derived from cell‐based density maps. Key features include: interactive side‐by‐side comparison of different simulation scenarios or time points, with synchronised navigation (viewpoint, timeline, transects), a mini‐map overview, timeline controls with linked ecological metric graphs, and transect analysis tools. The practical application of EcoViz is demonstrated by visualising simulations of the Berchtesgaden National Park under baseline and climate change scenarios exported from a forest landscape model. This case study showcases EcoViz's utility for comparative scenario analysis across spatial scales and how it aids model evaluation through visual inspection. While symbolic views support detailed analysis, the photorealistic output offers a compelling tool for science communication with diverse audiences, including scientific peers, forest managers, and the public