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We report the generation of a stable, broadband frequency comb, covering more than 10 THz, using a normal dispersion fiber Fabry-Perot resonator with a high quality factor of 69 millions. This platform ensures robust and easy integration into photonic devices via FC/PC connectors, and feature quality factors comparable to those of microresonators. We demonstrate a passive mode-locking phenomenon induced by the coherent interaction of the Kerr effect and Brillouin scattering, which generates a frequency comb with a repetition rate exceeding the free spectral range of the cavity. This parametric process modulates the continuous wave (CW) pump and can then be transformed into a train of almost square-wave pulses thanks to the generation of switching waves. Our results are supported by advanced numerical simulations, and theoretical derivations that include the Brillouin effect in the Fabry-Perot configuration. The very high stable feature of this optical frequency comb lying in the GHz range is critical to several applications ranging from telecommunication, spectroscopy and advanced microwave generation.

A capillary jet plunging into a quasi-2D slab of monodisperse foam of the same solution is studied experimentally. We show that the jet can have a drastic impact on the foam. At small speeds it inflates the channels separating the bubbles. At intermediate speeds, impact with channels creates very small bubbles. At higher speeds, the jet thins the foam films, which can result in bubble rupture. We study the mechanisms behind these processes using an elementary foam formed by three soap films in contact through a Plateau border. We obtain scaling laws, which transfer quantitatively from the elementary foam to the 2D foam.

We propose a general approach for quantitative convergence analysis of non-reversible Markov processes, based on the concept of second-order lifts and a variational approach to hypocoercivity. To this end, we introduce the flow Poincar{\'e} inequality, a space-time Poincar{\'e} inequality along trajectories of the semigroup, and a general divergence lemma based only on the Dirichlet form of an underlying reversible diffusion. We demonstrate the versatility of our approach by applying it to a pair of run-and-tumble particles with jamming, a model from non-equilibrium statistical mechanics, and several piecewise deterministic Markov processes used in sampling applications, in particular including general stochastic jump kernels.

We report on a combined structural and magnetotransport study of Hall bar devices of various lateral dimensions patterned side-by-side on epitaxial PdCoO$_2$ thin films. We study the effects of both the thickness of the PdCoO$_2$ film and the width of the channel on the electronic transport and the magnetoresistance properties of the Hall bar devices. All the films with thicknesses down to 4.88 nm are epitaxially oriented, phase pure, and exhibit a metallic behavior. At room temperature, the Hall bar device with the channel width $\text{W}=2.5\, \mu\text{m}$ exhibits a record resistivity value of $0.85\,\mu\Omega$cm, while the value of $2.70\,\mu\Omega$cm is obtained in a wider device with channel width $\text{W}=10\, \mu\text{m}$. For the 4.88 nm thick sample, we find that while the density of the conduction electrons is comparable in both channels, the electrons move about twice as fast in the narrower channel. At low temperatures, for Hall bar devices of channel width $2.5\,\mu\text{m}$ fabricated on epitaxial films of thicknesses 4.88 and 5.21 nm, the electron mobilities of $\approx$ 65 and 40 cm$^2$V$^{-1}$s$^{-1}$, respectively, are extracted. For thin-film Hall bar devices of width $10\,\mu\text{m}$ fabricated on the same 4.88 and 5.21 nm thick samples, the mobility values of $\approx$ 32 and 18 cm$^2$V$^{-1}$s$^{-1}$ are obtained. The magnetoresistance characteristics of these PdCoO$_2$ films are observed to be temperature dependent and exhibit a dependency with the orientation of the applied magnetic field. When the applied field is oriented 90{\deg} away from the crystal $c$-axis, a persistent negative MR at all temperatures is observed; whereas when the field is parallel to the $c$-axis, the negative magnetoresistance is suppressed at temperatures above 150K., Comment: 5 figures in Maintext and 8 figures in supplementary

We consider a process $X^\varepsilon$ solution of a stochastic Volterra equation with an unknown parameter $\theta^\star$ in the drift function. The Volterra kernel is singular and given by $K(u)=c u^{\alpha-1/2} \mathbb{1}_{u>0}$ with $\alpha \in (0,1/2)$. It is assumed that the diffusion coefficient is proportional to $\varepsilon \to 0$. From an observation of the path $(X^\varepsilon_s)_{s\in[0,T]}$, we construct a Trajectory Fitting Estimator, which is shown to be consistent and asymptotically normal. We also specify identifiability conditions insuring the $L^p$ convergence of the estimator.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

In this work celebrating the centenary of quantum mechanics, we rewiev the principles of de Broglie Bohm theory, also known as pilot-wave theory and Bohmian mechanics. We assess the most common reading of it (the Nomological interpretation based on the notion of primitive ontology in tridimensional space) and defend instead a more causal and pluralistic approach, drawing on classical analogies with optics and hydrodynamics. Within this framework, we review some of the approaches exploiting mechanical analogies to overcome the limitations of current Bohmian theory and perhaps quantum mechanics itself., Comment: Review article, submitted for publication

Our approach to training 3D vision-language understanding models is to train a feedforward model that makes predictions in 3D, but never requires 3D labels and is supervised only in 2D, using 2D losses and differentiable rendering. The approach is new for vision-language understanding. By treating the reconstruction as a ``latent variable'', we can render the outputs without placing unnecessary constraints on the network architecture (e.g. can be used with decoder-only models). For training, only need images and camera pose, and 2D labels. We show that we can even remove the need for 2D labels by using pseudo-labels from pretrained 2D models. We demonstrate this to pretrain a network, and we finetune it for 3D vision-language understanding tasks. We show this approach outperforms baselines/sota for 3D vision-language grounding, and also outperforms other 3D pretraining techniques. Project page: https://liftgs.github.io., Comment: Project page: https://liftgs.github.io

Machine learning programs, such as those performing inference, fine-tuning, and training of LLMs, are commonly delegated to untrusted compute providers. To provide correctness guarantees for the client, we propose adapting the cryptographic notion of refereed delegation to the machine learning setting. This approach enables a computationally limited client to delegate a program to multiple untrusted compute providers, with a guarantee of obtaining the correct result if at least one of them is honest. Refereed delegation of ML programs poses two technical hurdles: (1) an arbitration protocol to resolve disputes when compute providers disagree on the output, and (2) the ability to bitwise reproduce ML programs across different hardware setups, For (1), we design Verde, a dispute arbitration protocol that efficiently handles the large scale and graph-based computational model of modern ML programs. For (2), we build RepOps (Reproducible Operators), a library that eliminates hardware "non-determinism" by controlling the order of floating point operations performed on all hardware. Our implementation shows that refereed delegation achieves both strong guarantees for clients and practical overheads for compute providers.

In recent years, following tremendous achievements in Reinforcement Learning, a great deal of interest has been devoted to ML models for sequential decision-making. Together with these scientific breakthroughs/advances, research has been conducted to develop automated functional testing methods for finding faults in black-box Markov decision processes. Pang et al. (ISSTA 2022) presented a black-box fuzz testing framework called MDPFuzz. The method consists of a fuzzer whose main feature is to use Gaussian Mixture Models (GMMs) to compute coverage of the test inputs as the likelihood to have already observed their results. This guidance through coverage evaluation aims at favoring novelty during testing and fault discovery in the decision model. Pang et al. evaluated their work with four use cases, by comparing the number of failures found after twelve-hour testing campaigns with or without the guidance of the GMMs (ablation study). In this paper, we verify some of the key findings of the original paper and explore the limits of MDPFuzz through reproduction and replication. We re-implemented the proposed methodology and evaluated our replication in a large-scale study that extends the original four use cases with three new ones. Furthermore, we compare MDPFuzz and its ablated counterpart with a random testing baseline. We also assess the effectiveness of coverage guidance for different parameters, something that has not been done in the original evaluation. Despite this parameter analysis and unlike Pang et al.'s original conclusions, we find that in most cases, the aforementioned ablated Fuzzer outperforms MDPFuzz, and conclude that the coverage model proposed does not lead to finding more faults., Comment: Author's version. 12 pages, 7 figures

Learned denoisers play a fundamental role in various signal generation (e.g., diffusion models) and reconstruction (e.g., compressed sensing) architectures, whose success derives from their ability to leverage low-dimensional structure in data. Existing denoising methods, however, either rely on local approximations that require a linear scan of the entire dataset or treat denoising as generic function approximation problems, often sacrificing efficiency and interpretability. We consider the problem of efficiently denoising a new noisy data point sampled from an unknown $d$-dimensional manifold $M \in \mathbb{R}^D$, using only noisy samples. This work proposes a framework for test-time efficient manifold denoising, by framing the concept of "learning-to-denoise" as "learning-to-optimize". We have two technical innovations: (i) online learning methods which learn to optimize over the manifold of clean signals using only noisy data, effectively "growing" an optimizer one sample at a time. (ii) mixed-order methods which guarantee that the learned optimizers achieve global optimality, ensuring both efficiency and near-optimal denoising performance. We corroborate these claims with theoretical analyses of both the complexity and denoising performance of mixed-order traversal. Our experiments on scientific manifolds demonstrate significantly improved complexity-performance tradeoffs compared to nearest neighbor search, which underpins existing provable denoising approaches based on exhaustive search.

We consider the verification of parameterized networks of replicated processes whose architecture is described by hyperedge-replacement graph grammars. Due to the undecidability of verification problems such as reachability or coverability of a given configuration, in which we count the number of replicas in each local state, we develop two orthogonal verification techniques. We present a counting abstraction able to produce, from a graph grammar describing a parameterized system, a finite set of Petri nets that over-approximate the behaviors of the original system. The counting abstraction is implemented in a prototype tool, evalutated on a non-trivial set of test cases. Moreover, we identify a decidable fragment, for which the coverability problem is in 2EXPTIME and PSPACE-hard.

We report on the angle-resolved polarized Raman spectroscopy and estimation of the Raman tensor elements using both classical and quantum treatments to analyse the polarized Raman spectra of single crystal Bismuth Telluride. The observed polar patterns and systematic variations in the relative intensities of four characteristic Raman active modes indicate a higher differential polarizability along the c-axis, accompanied by anisotropic photon-phonon interactions. This interplay of electron-photon-phonon interactions is crucial for understanding the lattice dynamics of Bismuth Telluride, which underpin its thermoelectric performance and topological properties., Comment: 15 Pages, 4 Figures

In this paper, we investigate how weakening the classical hydrostatic balance hypothesis impacts the well-posedness of the stochastic LU primitive equations. The models we consider are intermediate between the incompressible 3D LU Navier-Stokes equations and the LU primitive equations with standard hydrostatic balance. As such, they are expected to be numerically tractable, while accounting well for phenomena within the grey zone between hydrostatic balance and non-hydrostatic processes. Our main result is the well-posedness of a low-pass filtering-based stochastic interpretation of the LU primitive equations, with rigid-lid type boundary conditions, in the limit of ``quasi-barotropic'' flow. This assumption is linked to the structure assumption proposed in the work of Agresti et al., which can be related to the dynamical regime where the primitive equations remain valid. Furthermore, we present and study two eddy-(hyper)viscosity-based models.

Delafossites, comprised of noble metal (A+) and strongly correlated sublayers (BO2-), form natural superlattices with highly anisotropic properties. These properties hold significant promise for various applications, but their exploitation hinges on the successful growth of high-quality thin films on suitable substrates. Unfortunately, the unique lattice geometry of delafossites presents a significant challenge to thin-film fabrication. Different delafossites grow differently, even when deposited on the same substrate, ranging from successful epitaxy to complete growth suppression. These variations often lack a clear correlation to obvious causes like lattice mismatch. Unidentified stabilization mechanisms appear to enable growth in certain cases, allowing these materials to form stable thin films or act as buffer layers for subsequent delafossite growth. This study employs advanced scanning transmission electron microscopy techniques to investigate the nucleation mechanism underlying the stable growth of PdCoO2 films on Al2O3 and LaAlO3 substrates, grown via molecular-beam epitaxy. Our findings reveal the presence of a secondary phase within the substrate surface that stabilizes the films. This mechanism deviates from the conventional understanding of strain relief mechanisms at oxide heterostructure interfaces and differs significantly from those observed for Cu-based delafossites.

The topological Hall effect (THE) is a hallmark of a non-trivial geometric spin arrangement in a magnetic metal, originating from a finite scalar spin chirality (SSC). The associated Berry phase is often a consequence of non-coplanar magnetic structures identified by multiple k-vectors. For single-k magnetic structures however with zero SSC, the emergence of a finite topological Hall signal presents a conceptual challenge. Here, we report that a fluctuation-driven mechanism involving chiral magnons is responsible for the observed THE in a low-symmetry compound, monoclinic Fe3Ga4. Through neutron scattering experiments, we discovered several nontrivial magnetic phases in this system. In our focus is the helical spiral phase at room temperature, which transforms into a transverse conical state in applied magnetic field, supporting a significant THE signal up to and above room temperature. Our work offers a fresh perspective in the search for novel materials with intertwined topological magnetic and transport properties., Comment: 20 pages, 4 figures

In this paper, we model the plasma environment of Ganymede by means of a collisionless test particle simulation. By coupling the outputs from a DSMC simulation of Ganymede's exosphere (i.e. number density profiles of neutral species such as $\mathrm{H}$, $\mathrm{H_2}$, $\mathrm{O}$, $\mathrm{HO}$, $\mathrm{H_2O}$, $\mathrm{O_2}$ for which we provide parametrisation) with those of a MagnetoHydroDynamic simulation of the interaction between Ganymede and the Jovian plasma (i.e. electric and magnetic fields), we perform a comparison between simulated ion plasma densities and ion energy spectra with those observed in-situ during 6 close flybys of Ganymede by the Galileo spacecraft. We find that not only our test particle simulation sometimes can well reproduce the in-situ ion number density measurement, but also the dominant ion species during these flybys are $\mathrm{H_2^+}$, $\mathrm{O_2^+}$, and occasionally $\mathrm{H_2O^+}$. Although the observed ion energy spectra cannot be reproduced exactly, the simulated ion energy spectra exhibit similar trends to those observed near the closest approach and near the magnetopause crossings but at lower energies. We show that the neutral exosphere plays an important role in supplying plasma to Ganymede's magnetised environment and that additional mechanisms may be at play to energise/accelerate newborn ions from the neutral exosphere., Comment: accepted for publication in MNRAS

Anomaly Detection is a crucial step for critical applications such in the industrial, medical or cybersecurity domains. These sectors share the same requirement of handling differently the different types of classification errors. Indeed, even if false positives are acceptable, false negatives are not, because it would reflect a missed detection of a quality issue, a disease or a cyber threat. To fulfill this requirement, we propose a method that dynamically applies a trustworthy approximated partial AUC ROC loss (tapAUC). A binary classifier is trained to optimize the specific range of the AUC ROC curve that prevents the True Positive Rate (TPR) to reach 100% while minimizing the False Positive Rate (FPR). The optimal threshold that does not trigger any false negative is then kept and used at the test step. The results show a TPR of 92.52% at a 20.43% FPR for an average across 6 datasets, representing a TPR improvement of 4.3% for a FPR cost of 12.2% against other state-of-the-art methods. The code is available at https://github.com/ArnaudBougaham/tapAUC.

This study examines the growth characteristics and structural properties of $\alpha$-MoO$_3$ thin films with thicknesses ranging from 2.5 to 160 nm, deposited on f-mica and c-sapphire substrates at 400 {\deg}C. X-ray diffraction analysis reveals that the films are predominantly orthorhombic $\alpha$-MoO$_3$ with a preferred 0k0 orientation along the out-of-plane direction on both substrates. The d-spacing for the 060 reflection shows a slight reduction with increased thickness, particularly on f-mica, which suggests minimal out-of-plane strain in the film and a stabilization of lattice parametes over larger thicknesses. Furthermore, full-width at half maximum measurements indicate improved stacking and crystal quality on f-mica compared to c-sapphire. The films on f-mica exhibit epitaxial growth with specific orientation relationships, while films on c-sapphire display a fiber texture. The near-thickness-independent nature of the peak positions on f-mica suggests stable lattice parameters and reduced strain accumulation, could be attributed to the van der Waals epitaxy. These results highlight the role of substrate choice in $\alpha$-MoO$_3$ film growth and minimizing strain, providing valuable insights into the tuning of thin-film properties.

Molybdenum oxide films are attractive for diverse applications due to properties offered by multiple phases and polymorphs, which also makes exclusive synthesis of desired phases a major challenge. Here, we demonstrate that oxygen flow ratio pO2 is key to phase selection, the type and extent of preferred orientation and epitaxy. Exclusive formation of non-layered monoclinic MoO2 crystals is supported on both mica and sapphire substrates at 500 {\deg}C within much of the 0.1 \le pO2 \le 0.25 range, outside which the films are amorphous. At 400 {\deg}C, the behavior is qualitatively similar, except for layered orthorhombic MoO3 formation at high pO2 and greater sensitivity of phase selection to pO2 due to the presence of a larger number of other phases. Increasing the pO2 tends to enhance preferred orientation and epitaxy, with fine-grained petal-like microstructure forming at low pO2, and large thin-sheeted crystals for at high pO2; however, MoO2 grows epitaxially on both f-mica and c-sapphire substrates while layered \alpha-MoO3 grows epitaxially on f- mica but not on sapphire These findings should facilitate the rationale synthesis of MoOx thin films with control over preferred orientation and microstructure to access and tune properties for applications. The research highlights the critical role of control over deposition parameters in tailoring the properties of MoOx films for applications such as electrochromic coatings and gas sensing.

Parallel Tempering (PT) is a classical MCMC algorithm designed for leveraging parallel computation to sample efficiently from high-dimensional, multimodal or otherwise complex distributions via annealing. One limitation of the standard formulation of PT is the growth of computational resources required to generate high-quality samples, as measured by effective sample size or round trip rate, for increasingly challenging distributions. To address this issue, we propose the framework: Generalised Parallel Tempering (GePT) which allows for the incorporation of recent advances in modern generative modelling, such as normalising flows and diffusion models, within Parallel Tempering, while maintaining the same theoretical guarantees as MCMC-based methods. For instance, we show that this allows us to utilise diffusion models in a parallelised manner, bypassing the usual computational cost of a large number of steps to generate quality samples. Further, we empirically demonstrate that GePT can improve sample quality and reduce the growth of computational resources required to handle complex distributions over the classical algorithm.

Super-resolution (SR) is a promising tool for generating high-fidelity simulations of physical systems from low-resolution data, enabling fast and accurate predictions in engineering applications. However, existing deep-learning based SR methods, require large labeled datasets and lack reliable uncertainty quantification (UQ), limiting their applicability in real-world scenarios. To overcome these challenges, we propose a probabilistic SR framework that leverages the Statistical Finite Element Method and energy-based generative modeling. Our method enables efficient high-resolution predictions with inherent UQ, while eliminating the need for extensive labeled datasets. The method is validated on a 2D Poisson example and compared with bicubic interpolation upscaling. Results demonstrate a computational speed-up over high-resolution numerical solvers while providing reliable uncertainty estimates.

This study explores the impact of boron carbide (B4C) addition on magnetic domains within Fe/Si multilayers through off-specular neutron scattering with polarization analysis. The incorporation of B4C induces amorphization in layers, disrupting magnetic domain structures. Analysis of the scattering patterns reveals that magnetic domains in pure Fe/Si multilayers exhibit no significant correlation between layers, resulting in a specific diffuse off-specular scattering signal, while the B4C incorporated Fe/Si multilayers revealed no diffuse off-specular scattering. We offer a qualitative interpretation of these scattering phenomena and accurately model the observed diffuse patterns using the distorted wave Born approximation. Low-energy {\mu}+SR measurements further reveal that local magnetic fields in Fe/Si and Fe/Si + B4C multilayers are more easily manipulated by external fields in B4C-containing layers, with enhanced field uniformity in the muon length-scale. Our findings provide insights into the role of B4C in altering magnetic domain arrangements within Fe/Si multilayers, contributing to advances in the design of magnetic materials and neutron polarization coatings.

This paper presents a novel approach to dual-frequency comb generation utilizing a single fiber Fabry-Perot resonator, advancing the implementation of these sources in fiber-based systems. Dual-comb applications such as spectroscopy, ranging, and imaging, known for their high-resolution and rapid data acquisition capabilities, benefit significantly from the stability and coherence of optical frequency comb sources. Our method leverages the birefringent property of the resonator induced by the optical fiber to generate two orthogonally polarized optical frequency combs in a monolitic resonator. This approach allows for the generation of two different frequency combs with slightly different repetition rates, exhibiting excellent mutual coherence, making it highly relevant for dual-comb applications. The 40 nm bandwidth generated combs are induced by switching-waves in a normal dispersion fiber Fabry-Perot resonator. These comb types have the advantage of being easily generated by a pulse pumping scheme, which is employed in this study. Finally, the potential of the source is demonstrated by a proof-of-concept spectroscopy measurement.

As waves propagate through a complex medium, they undergo multiple scattering events. This phenomenon is detrimental to imaging, as it causes a full blurring of the image beyond a transport mean free path. Here, we show how to detect, localize, and characterize any scattering target through the reflection matrix of the complex medium in which this target is embedded and thus hidden from direct view. More precisely, we introduce a fingerprint operator that contains the specific signature of the target with respect to its environment. Applied to the recorded reflection matrix, this operator provides a likelihood index of the target in any given state, despite the scattering fog induced by the surrounding environment. This state can be the target position for localization purposes, its shape for characterization, or any other parameter that influences the target response. Our concept is versatile and broadly applicable to different type of waves for which multi-element technology allows a reflection matrix to be measured. We demonstrate this here explicitly by performing different proof-of-concept experiments with ultrasound on targets buried inside a strongly scattering granular suspension, on lesion markers for clinical applications, and on the architecture of muscle tissue., Comment: 47 pages, 19 figures, 2 tables

Model validity is key to the accurate and safe behavior of autonomous vehicles. Using invalid vehicle models in the different plan and control vehicle frameworks puts the stability of the vehicle, and thus its safety at stake. In this work, we analyze the validity of several popular vehicle models used in the literature with respect to a real vehicle and we prove that serious accuracy issues are encountered beyond a specific lateral acceleration point. We set a clear lateral acceleration domain in which the used models are an accurate representation of the behavior of the vehicle. We then target the necessity of using learned methods to model the vehicle's behavior. The effects of model validity on state observers are investigated. The performance of model-based observers is compared to learning-based ones. Overall, the presented work emphasizes the validity of vehicle models and presents clear operational domains in which models could be used safely.

Convergent Cross Mapping (CCM) is a powerful method for detecting causality in coupled nonlinear dynamical systems, providing a model-free approach to capture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced as an extension of CCM to address indirect causality in three-variable systems by comparing cross-mapping quality between direct cause-effect mapping and indirect mapping through an intermediate conditioning variable. However, PCM remains limited to univariate delay embeddings in its cross-mapping processes. In this work, we extend PCM to the multivariate setting, introducing multiPCM, which leverages multivariate embeddings to more effectively distinguish indirect causal relationships. We further propose a multivariate cross-mapping framework (MXMap) for causal discovery in dynamical systems. This two-phase framework combines (1) pairwise CCM tests to establish an initial causal graph and (2) multiPCM to refine the graph by pruning indirect causal connections. Through experiments on simulated data and the ERA5 Reanalysis weather dataset, we demonstrate the effectiveness of MXMap. Additionally, MXMap is compared against several baseline methods, showing advantages in accuracy and causal graph refinement., Comment: Accepted by CLeaR 2025; Main manuscript 18 pages, appendix 24 pages, 30 tables

Let $v$ be a finite place of a number field $K$ and write $K^{nr,v}$ for the maximal field extension of $K$ in which $v$ is unramified. The purpose of this paper is split up into two parts. The first one generalizes a theorem of Pottmeyer, which states that if $E$ is an elliptic curve defined over $K$ with split-multiplicative reduction at $v$, then the N\'eron-Tate height of a non-torsion point $P\in E(\overline{K})$ is bounded from below by $C / e_v(P)^{2 e_v(P)+1}$, where $C>0$ is an absolute constant and $e_v(P)$ is the maximum of all ramification indices $e_w(K(P) \vert K)$ with $w\vert v$. We improve this lower bound by replacing the denominator with $9^{e_v(P)}$ and we will also show that it remains valid for all abelian varieties defined over $K$ which are totally degenerate at $v$. Next, we will provide general examples of polynomials $\phi\in K[X]$ of degree at least $2$ so that the canonical height $\hat{h}_\phi$ of any point in $\mathbb{P}^1(K^{nr,v})$ is either $0$ or bounded from below by an absolute constant.

We address the problem of solving a system of linear equations via the Quantum Singular Value Transformation (QSVT). One drawback of the QSVT algorithm is that it requires huge quantum resources if we want to achieve an acceptable accuracy. To reduce the quantum cost, we propose a hybrid quantum-classical algorithm that improves the accuracy and reduces the cost of the QSVT by adding iterative refinement in mixed-precision A first quantum solution is computed using the QSVT, in low precision, and then refined in higher precision until we get a satisfactory accuracy. For this solver, we present an error and complexity analysis, and first experiments using the quantum software stack myQLM.

Lugiato-Lefever equation (LLE) is a nonlinear Schr\"odinger equation with damping, detuning and driving terms, introduced as a model for Kerr combs generation in ring-shape resonators and more recently, in the form of a variant, in Fabry-Perot (FP) resonators. The aim of this paper is to present some numerical methods that complement each other to solve the LLE in its general form both in the dynamic and in the steady state regimes. We also provide some mathematical properties of the LLE likely to help the understanding and interpretation of the numerical simulation results.

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises" a Gaussian sample into a sample from the data distribution. However, generating high-quality outputs requires many discretization steps to obtain a faithful approximation of the reverse process. This is expensive and has motivated the development of many acceleration methods. We propose to accomplish sample generation by learning the posterior {\em distribution} of clean data samples given their noisy versions, instead of only the mean of this distribution. This allows us to sample from the probability transitions of the reverse process on a coarse time scale, significantly accelerating inference with minimal degradation of the quality of the output. This is accomplished by replacing the standard regression loss used to estimate conditional means with a scoring rule. We validate our method on image and robot trajectory generation, where we consistently outperform standard diffusion models at few discretization steps.

A temporal graph is a graph whose edges are available only at certain points in time. It is temporally connected if the nodes can reach each other by paths that traverse the edges chronologically (temporal paths). In general, temporal graphs do not always admit small subsets of edges that preserve connectivity (temporal spanners). In the case of temporal cliques, spanners of size $O(n\log n)$ are guaranteed. The original proof by Casteigts et al. [ICALP 2019] combines a number of techniques, one of which is dismountability. In a recent work, Angrick et al. [ESA 2024] simplified the proof and showed, among other things, that a one-sided version of dismountability can be used to replace the second part of the proof. In this paper, we revisit the dismountability principle. We characterizing the structure that a temporal clique has if it is not 1-hop dismountable, then not {1,2}-hop dismountable, and finally not {1,2,3}-hop dismountable. It turns out that if a clique is k-hop dismountable for any other k, then it must also be {1,2,3}-hop dismountable. Interestingly, excluding only 1-hop and 2-hop dismountability is already sufficient for reducing the spanner problem from cliques to bi-cliques. Put together with the strategy of Angrick et al., the entire $O(n \log n)$ result can now be recovered using only dismountability. An interesting by-product of our analysis is that any minimal counter-example to the existence of $4n$ spanners must satisfy the properties of non {1,2,3}-hop dismountable cliques. In the second part, we discuss connections between dismountability and pivotability. We show that recursively k-hop dismountable cliques are pivotable (and thus admits $2n$ spanners, whatever k). We define a family of labelings (called full-range) which force both dismountability and pivotability and that gives some evidence that large lifetimes could be exploited more generally.

The SPIRAL2 superconducting linear accelerator (LINAC), which has been operational since 2019, employs superconducting, independently phased RF resonators to deliver a wide range of particle beams. Designed for flexibility in particle types, intensities, and energies, it utilizes superconducting quarter-wave resonators (QWRs), whose performances are critically dependent on the reliability of the cryogenic operation. This paper reviews the evolution from commissioning to the routine operation of the SPIRAL2 cryogenic system, initially commissioned in 2017. It highlights the key challenges encountered, including thermo-acoustic oscillations, thermal management, and abnormal behavior of cavities. Furthermore, it explores the integration of thermodynamic modeling and machine learning techniques to enhance system control and diagnose issues. This work serves as a comprehensive resource for advancing the cryogenic operation and performance of superconducting LINACs.

In population genetics and other application fields, models with intractable likelihood are common. Approximate Bayesian Computation (ABC) or more generally Simulation-Based Inference (SBI) methods work by simulating instrumental data sets from the models under study and comparing them with the observed data set, using advanced machine learning tools for tasks such as model selection and parameter inference. The present work focuses on model criticism, and more specifically on Goodness of fit (GoF) tests, for intractable likelihood models. We introduce two new GoF tests: the pre-inference \gof tests whether the observed dataset is distributed from the prior predictive distribution, while the post-inference GoF tests whether there is a parameter value such that the observed dataset is distributed from the likelihood with that value. The pre-inference test can be used to prune a large set of models using a limited amount of simulations, while the post-inference test is used to assess the fit of a selected model. Both tests are based on the Local Outlier Factor (LOF, Breunig et al., 2000). This indicator was initially defined for outlier and novelty detection. It is able to quantify local density deviations, capturing subtleties that a more traditional k-NN-based approach may miss. We evaluated the performance of our two GoF tests on simulated datasets from three different model settings of varying complexity. We then illustrate the utility of these approaches on a dataset of single nucleotide polymorphism (SNP) markers for the evaluation of complex evolutionary scenarios of modern human populations. Our dual-test GoF approach highlights the flexibility of our method: the pre-inference \gof test provides insight into model validity from a Bayesian perspective, while the post-inference test provides a more general and traditional view of assessing goodness of fit

The meaning of the wave function has been a subject of intense debate in the foundations of quantum mechanics. In Bohmian Mechanics, the prevailing view is the nomological interpretation, which regards the wave function as a nomological entity. To make this abstract notion more concrete, the wave function is often compared to the classical Hamiltonian - another high-dimensional field whose gradient determines particle motion. However, unlike the wave function, the Hamiltonian is not the solution to a differential equation. Furthermore, while the Hamilton-Jacobi formalism offers a pilot-wave formulation of classical mechanics, it has been largely overlooked in contemporary discussions about the physical meaning of the wave function. Nonetheless, in the classical limit, there is a clear mathematical connection between the quantum wave function and the guiding field in this formalism, specifically the action function S. On the basis of these mathematical parallels, we initially intended to argue that the action function is a more appropriate classical analogue of the wave function, which, when combined with a clear conceptual distinction between laws of nature and nomological entities, could strengthen the nomological interpretation. We thought it could address some of the criticisms levelled at the nomological interpretation without resorting to the speculative realm of quantum gravity. However, contrary to our initial expectations, a closer comparison of the roles played by the action function and the wave function in their respective formalisms suggests a departure from the nomological interpretation in favour of the so-called sui generis interpretation of the wave function.

Due to rich rheological properties, dispersions of attractive colloidal particles are ubiquitous in industries. Specifically, upon experiencing a sudden reduction in shear rate, these dispersions may exhibit transient behaviors such as thixotropy-where viscosity increases over time-and anti-thixotropy, characterized by an initial viscosity decrease before reaching a steady state. While thixotropy has been described as a competition between structure buildup and disruption, the mechanisms of anti-thixotropy remain poorly understood. Here, we investigate the anti-thixotropic dynamics of carbon black particles dispersed in oil-a system known for exhibiting anti-thixotropy-through flow step-down experiments. Using a multi-technique approach combining rheology with velocimetry and structural characterizations, we show that viscosity decrease results from a decrease in wall slip concomitant to shear-induced structural rearrangements, indicating a transition from a dynamical network of fractal clusters into a network of loosely connected dense agglomerates. Additionally, after a characteristic anti-thixotropic time $\tau$, a steady flow is reached. This time $\tau$ diverges with increasing shear rate at a critical value corresponding to a Mason number of one, indicating that anti-thixotropy occurs only when colloidal attraction outweighs viscous forces. More precisely, we show that the structural rearrangement underpinning the viscosity decrease is mediated by elastic stresses $\sigma_e$, such that $\tau \propto \sigma_e^{-3}$. Finally, on long time scales, the steady state is linked to a microstructure with nearly zero yield stress, indicating a loss of flow memory. These findings provide a mechanism for anti-thixotropy and suggest pathways for controlling viscosity and yield stress in attractive colloidal dispersions.

We present an analytical model for density-split correlation functions, that probe galaxy clustering in different density environments. Specifically, we focus on the cross-correlation between density-split regions and the tracer density field. We show that these correlation functions can be expressed in terms of the two-point probability density function (PDF) of the density field, or equivalently, its bias function. We derive analytical predictions using three levels of approximation for the two-point PDF: a bivariate Gaussian distribution, a bivariate shifted log-normal distribution, and a prediction based on the Large Deviation Theory framework. Under spherical symmetry $\unicode{x2013}$ where spherical collapse dynamics apply, such as for count-in-cell densities with spherical top-hat smoothing $\unicode{x2013}$ LDT predicts the density two-point PDF in the large-separation regime relative to the smoothing radius. We validate our model against dark matter N-body simulations in real space, incorporating Poisson shot noise. Our results show that the LDT predictions outperform the log-normal approximation, and agrees with simulations on large scales within the cosmic variance of a typical DESI DR1 sample, despite relying on only one degree of freedom., Comment: 28 pages, 12 figures

For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the expectation of the logarithm of an importance sampling estimate of the likelihood with respect to both the latent variable model parameters and the importance distribution parameters, the expectation being itself with respect to the importance samples. Despite its great empirical success in machine learning, a theoretical analysis of the limit properties of the resulting estimates is still lacking. We fill this gap by establishing consistency when both the Monte Carlo and the observed data sample sizes go to infinity simultaneously. We also establish asymptotic normality and efficiency under additional conditions relating the rate of growth between the Monte Carlo and the observed data samples sizes. We distinguish several regimes related to the smoothness of the importance ratio., Comment: 25 pages, 2 figures

Repeated waves of emerging variants during the SARS-CoV-2 pandemics have highlighted the urge of collecting longitudinal genomic data and developing statistical methods based on time series analyses for detecting new threatening lineages and estimating their fitness early in time. Most models study the evolution of the prevalence of particular lineages over time and require a prior classification of sequences into lineages. Such process is prone to induce delays and bias. More recently, few authors studied the evolution of the prevalence of mutations over time with alternative clustering approaches, avoiding specific lineage classification. Most of the aforementioned methods are however either non parametric or unsuited to pooled data characterizing, for instance, wastewater samples. In this context, we propose an alternative unsupervised method for clustering mutations according to their frequency trajectory over time and estimating group fitness from time series of pooled mutation prevalence data. Our model is a mixture of observed count data and latent group assignment and we use the expectation-maximization algorithm for model selection and parameter estimation. The application of our method to time series of SARS-CoV-2 sequencing data collected from wastewater treatment plants in France from October 2020 to April 2021 shows its ability to agnostically group mutations according to their probability of belonging to B.1.160, Alpha, Beta, B.1.177 variants with selection coefficient estimates per group in coherence with the viral dynamics in France reported by Nextstrain. Moreover, our method detected the Alpha variant as threatening as early as supervised methods (which track specific mutations over time) with the noticeable difference that, since unsupervised, it does not require any prior information on the set of mutations., Comment: 45 pages, 19 figures and tables

Speculative sampling is a popular technique for accelerating inference in Large Language Models by generating candidate tokens using a fast draft model and accepting or rejecting them based on the target model's distribution. While speculative sampling was previously limited to discrete sequences, we extend it to diffusion models, which generate samples via continuous, vector-valued Markov chains. In this context, the target model is a high-quality but computationally expensive diffusion model. We propose various drafting strategies, including a simple and effective approach that does not require training a draft model and is applicable out of the box to any diffusion model. Our experiments demonstrate significant generation speedup on various diffusion models, halving the number of function evaluations, while generating exact samples from the target model.

This paper is a continuation of previous work of the author. We use the categorical trace formalism to give a construction of the categorical Jordan decomposition for representations of finite groups of Lie type. As a second application, we study the endomorphism algebra of the Gelfand-Graev representation and recover a result of Li and Shotton-Li., Comment: Comments welcome !

Density Functional Theory (DFT) calculations not only allow to predict the vibrational and optical properties of solids but also to understand and disentangle the mechanisms playing a key role in the generation of coherent optical phonons. Recent experiments performed on a Bi$_2$Te$_3$ nanofilm have shown that a THz pulse launches at least a coherent $A_{1g}^1$ phonon as the transient transmittance measured using an isotropic detection scheme displays oscillations with a frequency matching the frequency of the $A_{1g}^1$ mode measured in Raman experiments. Such an observation can be explained by invoking either a sum frequency process or cubic/quartic phonon-phonon couplings as considered for Bi$_2$Se$_3$, a parent compound of Bi$_2$Te$_3$. By resorting to group theory and calculating energy surfaces from first-principles, the main phonon-phonon couplings can be identified. Furthermore, a minimal model can be built to compute the dynamics of the Raman active modes coupled to the infrared active mode driven by the experimental THz pulse. Our model firmly establishes that cubic phonon-phonon interactions are relevant as the agreement between the computed and experimental transmittance is noteworthy., Comment: 6 pages, 3 figures, submitted to Physical Review Letters

The pressure function is a fundamental object in various areas of mathematics. Its regularity is studied to derive insights into phase transitions in certain physical systems or to determine the Hausdorff dimension of self-affine sets. In this paper, we prove the analyticity of the pressure function for products of non-invertible matrices satisfying an irreducibility and a contractivity assumptions. Additionally, we establish a variational principle for the pressure function, thereby generalizing previous results., Comment: arXiv admin note: text overlap with arXiv:2402.03879 by other authors

Let X be a smooth cubic hypersurface. We prove that a general cubic surface is isomorphic to a hyperplane section of X .

Continuous gravitational waves (CWs) emission from neutron stars carries information about their internal structure and equation of state, and it can provide tests of General Relativity. We present a search for CWs from a set of 45 known pulsars in the first part of the fourth LIGO--Virgo--KAGRA observing run, known as O4a. We conducted a targeted search for each pulsar using three independent analysis methods considering the single-harmonic and the dual-harmonic emission models. We find no evidence of a CW signal in O4a data for both models and set upper limits on the signal amplitude and on the ellipticity, which quantifies the asymmetry in the neutron star mass distribution. For the single-harmonic emission model, 29 targets have the upper limit on the amplitude below the theoretical spin-down limit. The lowest upper limit on the amplitude is $6.4\!\times\!10^{-27}$ for the young energetic pulsar J0537-6910, while the lowest constraint on the ellipticity is $8.8\!\times\!10^{-9}$ for the bright nearby millisecond pulsar J0437-4715. Additionally, for a subset of 16 targets we performed a narrowband search that is more robust regarding the emission model, with no evidence of a signal. We also found no evidence of non-standard polarizations as predicted by the Brans-Dicke theory., Comment: main paper: 12 pages, 6 figures, 4 tables

The goal of this article is to study quantitatively the localisation/delocalisation properties of the discrete Gaussian chain with long-range interactions. Specifically, we consider the discrete Gaussian chain of length $N$, with Dirichlet boundary condition, range exponent $\alpha \in (1 , \infty)$ and inverse temperature $\beta \in (0,\infty)$, and show that: - For $\alpha \in (2 ,3)$ and $\beta \in (0 , \infty)$, the fluctuations of the chain are at least of order $N^{\frac{1}{2}(\alpha - 2)}$; - For $\alpha = 3$ and $\beta \in (0 , \infty)$, the fluctuations of the chain are of order $\sqrt{N / \ln N}$ (sharp upper and lower bounds up to multiplicative constants are derived). Combined with the results of Kjaer-Hilhorst, Fr\"{o}hlich-Zegarlinski and Garban, these estimates provide an (almost) complete picture for the localisation/delocalisation of the discrete Gaussian chain. The proofs are based on graph surgery techniques which have been recently developed by van Engelenburg-Lis and Aizenman-Harel-Peled-Shapiro to study the phase transitions of two dimensional integer-valued height functions (and of their dual spin systems). Additionally, by combining the previous strategy with a technique introduced by Sellke, we are able extend the method to study the $q$-SOS long-range chain with exponent $q \in (0 , 2)$ and show that, for any inverse temperature $\beta\in (0, \infty)$ and any range exponent $\alpha \in (1 , \infty)$: - The fluctuations of the chain are at least of order $N^{\frac{1}{q}(\alpha -2) \wedge \frac{1}{2}}$; - The fluctuations of the chain are at most of order $N^{\left( \frac{1}{q}\alpha - 1 \right) \wedge \frac 12}$., Comment: 44 pages, 25 Figures. Comments are welcome

In this paper, we present a method based on a modal decomposition to quantify the efficiency of photonic lanterns (PL) based free space optical (FSO) communication receivers. We fabricate a seven port PL and we evaluate numerically the free space to fiber coupling efficiency based on a reconstruction of the fields at the PL FSO multimode port. We validate the numerical approach with an experimental characterization of the PL. Then we compare the PL to a commercial multiplane light converter spatial demultiplexer. The PL shows better coupling efficiency for low order spatial modes with orders of magnitude of demultiplexer size reduction. Finally we evaluate the PL receiver with a simulation of received optical wavefront in a FSO communication