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In this article, we address the problem of determining a domain in $\mathbb{R}^N$ that minimizes the first eigenvalue of the Lam\'e system under a volume constraint. We begin by establishing the existence of such an optimal domain within the class of quasi-open sets, showing that in the physically relevant dimensions $N = 2$ and $3$, the optimal domain is indeed an open set. Additionally, we derive both first and second-order optimality conditions. Leveraging these conditions, we demonstrate that in two dimensions, the disk cannot be the optimal shape when the Poisson ratio is below a specific threshold, whereas above this value, it serves as a local minimizer. We also extend our analysis to show that the disk is nonoptimal for Poisson ratios $\nu$ satisfying $\nu \leq 0.4$.

Post-alignment of large language models (LLMs) is critical in improving their utility, safety, and alignment with human intentions. Direct preference optimisation (DPO) has become one of the most widely used algorithms for achieving this alignment, given its ability to optimise models based on human feedback directly. However, the vast number of DPO variants in the literature has made it increasingly difficult for researchers to navigate and fully grasp the connections between these approaches. This paper introduces a unifying framework inspired by mutual information, which proposes a new loss function with flexible priors. By carefully specifying these priors, we demonstrate that many existing algorithms, such as SimPO, TDPO, SparsePO, and others, can be derived from our framework. This unification offers a clearer and more structured approach, allowing researchers to understand the relationships between different DPO variants better. We aim to simplify the landscape of DPO algorithms, making it easier for the research community to gain insights and foster further advancements in LLM alignment. Ultimately, we hope our framework can be a foundation for developing more robust and interpretable alignment techniques.

The Compact Muon Solenoid (CMS) detector at the Large Hadron Collider at CERN is used to study the production of new particles in proton-proton collisions at a center of mass energy of 13.6 TeV. The detector includes a magnet based on a 6 m diameter superconducting coil operating at a current of 18.164 kA. This current creates a central magnetic flux density of 3.8 T that allows for the high-precision measurement of the momenta of the produced charged particles using tracking and muon subdetectors. The CMS magnet contains a 10,000 ton flux-return yoke made from the construction steel blocks. These blocks are magnetized, with the coil returned magnetic flux and wrap the muons escaping the hadronic calorimeters. To describe the distribution of the magnetic flux in the magnet yoke layers, a three-dimensional computer model of the CMS magnet is used. To validate the calculations, special measurements are performed, with the flux loops wound in 22 cross-sections of the flux-return yoke blocks. The measured voltages induced in the flux loops during the CMS magnet current variations, are integrated over time to obtain the initial magnetic flux densities in the flux loop cross-sections. In the last time, three fast discharges occurred during the standard ramp-downs of the magnet. This allows us to single out the contributions of the eddy currents, induced in steel, to the flux loop voltages. Accounting for these contributions to the flux loop measurements during intentionally triggered fast discharges in 2006 allows us to perform the validation of the CMS magnet computer model with better precision. The technique for the flux loop measurements and the obtained results are presented and discussed. The method for measuring magnetic flux density in steel blocks described in this study is innovative., Comment: 14 pages, 12 figures, 2 equations, 18 references

A summary of recent contributions in the field of rough partial differential equations is given. For that purpose we rely on the formalism of ``unbounded rough driver''. We present applications to concrete models including Landau-Lifshitz-Gilbert, Navier-Stokes and Euler equations.

Partial differential equation (PDE) is an important math tool in science and engineering. This paper experimentally demonstrates an optical neural PDE solver by leveraging the back-propagation-free on-photonic-chip training of physics-informed neural networks.

This paper describes RHP Friends, a social humanoid robot developed to enable assistive robotic deployments in human-coexisting environments. As a use-case application, we present its potential use in nursing by extending its capabilities to operate human devices and tools according to the task and by enabling remote assistance operations. To meet a wide variety of tasks and situations in environments designed by and for humans, we developed a system that seamlessly integrates the slim and lightweight robot and several technologies: locomanipulation, multi-contact motion, teleoperation, and object detection and tracking. We demonstrated the system's usage in a nursing application. The robot efficiently performed the daily task of patient transfer and a non-routine task, represented by a request to operate a circuit breaker. This demonstration, held at the 2023 International Robot Exhibition (IREX), conducted three times a day over three days., Comment: IEEE Robotics and Automation Magazine, In press

We introduce a canonical way of performing the joint lift of a Brownian motion $W$ and a low-regularity adapted stochastic rough path $\mathbf{X}$, extending [Diehl, Oberhauser and Riedel (2015). A L\'evy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations]. Applying this construction to the case where $\mathbf{X}$ is the canonical lift of a one-dimensional fractional Brownian motion (possibly correlated with $W$) completes the partial rough path of [Fukasawa and Takano (2024). A partial rough path space for rough volatility]. We use this to model rough volatility with the versatile toolkit of rough differential equations (RDEs), namely by taking the price and volatility processes to be the solution to a single RDE. We argue that our framework is already interesting when $W$ and $X$ are independent, as correlation between the price and volatility can be introduced in the dynamics. The lead-lag scheme of [Flint, Hambly, and Lyons (2016). Discretely sampled signals and the rough Hoff process] is extended to our fractional setting as an approximation theory for the rough path in the correlated case. Continuity of the solution map transforms this into a numerical scheme for RDEs. We numerically test this framework and use it to calibrate a simple new rough volatility model to market data.

Obtaining the classification of 3d $\mathcal{N}=4$ quivers whose Coulomb branches have an isolated singularity is an essential step in understanding moduli spaces of vacua of supersymmetric field theories with 8 supercharges in any dimension. In this work, we derive a full classification for such Abelian quivers with arbitrary charges, and identify all possible Coulomb branch geometries as quotients of $\mathbb{H}^n$ by $\mathrm{U}(1)$ or a finite cyclic group. We give two proofs, one which uses the decay and fission algorithm, and another one relying only on explicit computations involving 3d mirror symmetry. In the process, we put forward a method for computing the 3d mirror of any $\mathrm{U}(1)^r$ gauge theory, which is sensitive to discrete gauge factors in the mirror theory. This constitutes a confirmation for the decay and fission algorithm., Comment: 31 pages + appendices

This paper presents an extension of a recently introduced multistage stochastic integer model designed for optimizing the deployment of charging stations under uncertainty. A key contribution of this work is incorporating additional constraints accounting for congestion management at charging stations. The solution approach combines a greedy heuristic with a branch-and-price algorithm, enabling the efficient handling of medium instances. In the branch-and-price algorithm, when the solution to the restricted master problem is not integer, a greedy heuristic and a local search procedure are conducted to obtain feasible solutions. Computational experiments illustrate the effectiveness of the proposed framework., Comment: 13 pages

Network reconstruction consists in retrieving the -- hidden -- interaction structure of a system from empirical observations such as time series. Many reconstruction algorithms have been proposed, although less research has been devoted to describe their theoretical limitations. To this end, we adopt an information-theoretical point of view and define the reconstructability -- the fraction of structural information recoverable from data. The reconstructability depends on the true data generating model which is shown to set the reconstruction limit, i.e., the performance upper bound for all algorithms. We show that the reconstructability is related to various performance measures, such as the probability of error and the Jaccard similarity. In an empirical context where the true data generating model is unknown, we introduce the reconstruction index as an approximation of the reconstructability. We find that performing model selection is crucial for the validity of the reconstruction index as a proxy of the reconstructability, and illustrate how it assesses the reconstruction limit of empirical time series and networks.

In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual ``pseudogap'' metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associated with strong electron correlations, still offers major computational challenges despite its simple formulation. In this context, ultracold atoms quantum simulators have provided invaluable insights into the microscopic nature of correlated quantum states. Here, we use a quantum gas microscope Fermi-Hubbard simulator to explore a wide range of doping levels and temperatures in a regime where a pseudogap is known to develop. By measuring multi-point correlation functions up to fifth order, we uncover a novel universal behaviour in magnetic and higher-order spin-charge correlations. This behaviour is characterized by a doping-dependent energy scale that governs the exponential growth of the magnetic correlation length upon cooling. Accurate comparisons with determinant Quantum Monte Carlo and Minimally Entangled Typical Thermal States simulations confirm that this energy scale agrees well with the pseudogap temperature $T^{*}$. Our findings establish a qualitative and quantitative understanding of the magnetic origin and physical nature of the pseudogap and pave the way towards the exploration of pairing and collective phenomena among charge carriers expected to emerge at lower temperatures.

Whole-body hemodynamics simulators, which model blood flow and pressure waveforms as functions of physiological parameters, are now essential tools for studying cardiovascular systems. However, solving the corresponding inverse problem of mapping observations (e.g., arterial pressure waveforms at specific locations in the arterial network) back to plausible physiological parameters remains challenging. Leveraging recent advances in simulation-based inference, we cast this problem as statistical inference by training an amortized neural posterior estimator on a newly built large dataset of cardiac simulations that we publicly release. To better align simulated data with real-world measurements, we incorporate stochastic elements modeling exogenous effects. The proposed framework can further integrate in-vivo data sources to refine its predictive capabilities on real-world data. In silico, we demonstrate that the proposed framework enables finely quantifying uncertainty associated with individual measurements, allowing trustworthy prediction of four biomarkers of clinical interest--namely Heart Rate, Cardiac Output, Systemic Vascular Resistance, and Left Ventricular Ejection Time--from arterial pressure waveforms and photoplethysmograms. Furthermore, we validate the framework in vivo, where our method accurately captures temporal trends in CO and SVR monitoring on the VitalDB dataset. Finally, the predictive error made by the model monotonically increases with the predicted uncertainty, thereby directly supporting the automatic rejection of unusable measurements.

Quantum $n$-qubit states that are totally symmetric under the permutation of qubits are essential ingredients of important algorithms and applications in quantum information. Consequently, there is significant interest in developing methods to prepare and manipulate Dicke states, which form a basis for the subspace of fully symmetric states. Two simple protocols for transforming Dicke states are considered. An algebraic characterization of the operations that these protocols induce is obtained in terms of the Weyl algebra $W(2)$ and $\mathfrak{su}(2)$. Fixed points under the application of the combination of both protocols are explicitly determined. Connections with the binary Hamming scheme, the Hadamard transform, and Krawtchouk polynomials are highlighted., Comment: 15 pages

In the era of exoplanet studies with JWST, the transiting, hot gas giant WASP-52 b provides an excellent target for atmospheric characterization through transit spectroscopy. WASP-52 b orbits an active K-type dwarf recognized for its surface heterogeneities, such as star-spots and faculae, which offers challenges to atmospheric characterization via transmission spectroscopy. Previous transit observations have detected active regions on WASP-52 through crossing events in transit light-curves and via the spectral imprint of unocculted magnetic regions on transmission spectra. Here, we present the first JWST observations of WASP-52 b. Our JWST NIRISS/SOSS transit observation, obtained through the GTO 1201 Program, detects two clear spot-crossing events that deform the 0.6-2.8 $\mu$m transit light-curves of WASP-52 b. We find that these two occulted spots combined cover about 2.4 % of the stellar surface and have temperatures about 400-500 K colder than the stellar photosphere. Our NIRISS/SOSS transmission spectrum is best-fit by an atmosphere with H$_2$O (10.8 $\sigma$), He (7.3 $\sigma$, with evidence of an escaping tail at $\sim$ 2.9 $\sigma$), hints of K (2.5 $\sigma$), and unocculted star-spots and faculae (3.6 $\sigma$). The retrieved H$_2$O abundance ($\log$ H$_2$O $\approx -4 \pm 1$) is consistent with a subsolar or solar atmospheric metallicity for two independent data reductions. Our results underscore the importance of simultaneously modelling planetary atmospheres and unocculted stellar heterogeneities when interpreting transmission spectra of planets orbiting active stars and demonstrate the necessity of considering different stellar contamination models that account for both cold and hot active regions., Comment: Submitted to MNRAS; 17 pages, 11 figures and 3 tables

This study investigates the behavior of model-integrated routers in Mixture of Experts (MoE) models, focusing on how tokens are routed based on their linguistic features, specifically Part-of-Speech (POS) tags. The goal is to explore across different MoE architectures whether experts specialize in processing tokens with similar linguistic traits. By analyzing token trajectories across experts and layers, we aim to uncover how MoE models handle linguistic information. Findings from six popular MoE models reveal expert specialization for specific POS categories, with routing paths showing high predictive accuracy for POS, highlighting the value of routing paths in characterizing tokens., Comment: Accepted at COLING 2025

There has been an ongoing race for the past couple of years to develop the best universal machine learning interatomic potential. This rapid growth has driven researchers to create increasingly accurate models for predicting energy, forces, and stresses, combining innovative architectures with big data. Here, these models are benchmarked for their performance in predicting phonon properties, which are critical for understanding the vibrational and thermal behavior of materials. Our analysis is based on around 10 000 ab initio phonon calculations, enabling us to assess performance across a range of phonon-related parameters while testing the universal applicability of these models. The results reveal that some models are already capable of predicting phonon properties with a high level of accuracy. However, others still exhibit substantial inaccuracies, even if they excel in the prediction of the energy and the forces for materials close to dynamical equilibrium. These findings highlight the importance of considering phonon-related properties in the development of universal machine learning interatomic potentials.

Direct-current resistivity is a key probe for the physical properties of materials. In metals, Fermi-liquid (FL) theory serves as the basis for understanding transport. A $T^2$ behavior of the resistivity is often taken as a signature of FL electron-electron scattering. However, the presence of impurity and phonon scattering as well as material-specific aspects such as Fermi surface geometry can complicate this interpretation. We demonstrate how density-functional theory combined with dynamical mean-field theory can be used to elucidate the FL regime. We take as examples SrVO$_{3}$ and SrMoO$_{3}$, two moderately correlated perovskite oxides, and establish a precise framework to analyze the FL behavior of the self-energy at low energy and temperature. Reviewing published low-temperature resistivity measurements, we find agreement between our calculations and experiments performed on samples with exceptionally low residual resistivity. This comparison emphasizes the need for further theoretical, synthesis, and characterization developments in these and other FL materials., Comment: 9 pages, 4 figures

The rise of the generative models quality during the past years enabled the generation of edited variations of images at an important scale. To counter the harmful effects of such technology, the Image Difference Captioning (IDC) task aims to describe the differences between two images. While this task is successfully handled for simple 3D rendered images, it struggles on real-world images. The reason is twofold: the training data-scarcity, and the difficulty to capture fine-grained differences between complex images. To address those issues, we propose in this paper a simple yet effective framework to both adapt existing image captioning models to the IDC task and augment IDC datasets. We introduce BLIP2IDC, an adaptation of BLIP2 to the IDC task at low computational cost, and show it outperforms two-streams approaches by a significant margin on real-world IDC datasets. We also propose to use synthetic augmentation to improve the performance of IDC models in an agnostic fashion. We show that our synthetic augmentation strategy provides high quality data, leading to a challenging new dataset well-suited for IDC named Syned1., Comment: This paper has been accepted for the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV) 2025

The processes that generate rogue waves on the sea surface remain a mystery. Despite their different natures, the nonlinear bending waves generated in a thin elastic plate share some similarities with waves on the surface of the sea. For instance, both involve four-wave interactions during energy exchange, but in bending waves, the number of waves is not conserved. Here, we present an experimental study to investigate extreme event statistics in random elastic bending waves forced by an electromagnetic shaker on a thin stainless steel plate. In our setup, the standard statistical criterion used to define extreme events, such as rogue waves on the sea surface, is insufficiently restrictive. We therefore apply a new criterion to determine the occurrence frequency of rare events, similar to those observed in wave tanks. With this new criterion, we examine correlations between extreme events amplitude and wave slopes, energy, and periods, raising questions about the links between statistically rare events and rogue waves.

Achieving high conversion efficiencies in second-order nonlinear optical processes is a key challenge in integrated photonics for both classical and quantum applications. This paper presents the first demonstration of Transverse Orientation-Patterned gallium phosphide (TOP-GaP) waveguides showing high-efficiency second harmonic generation. In such devices, first order modal phase matching is unlocked and optimized through the inversion of the nonlinear susceptibility along the vertical direction. We discuss here the theory behind modal phase matching in TOP structures, describe the fabrication process, and present linear and nonlinear characterizations of the TOP-GaP waveguides.

We analyze the French housing market prices in the period 1970-2022, with high-resolution data from 2018 to 2022. The spatial correlation of the observed price field exhibits logarithmic decay characteristic of the two-dimensional random diffusion equation -- local interactions may create long-range correlations. We introduce a stylized model, used in the past to model spatial regularities in voting patterns, that accounts for both spatial and temporal correlations with reasonable values of parameters. Our analysis reveals that price shocks are persistent in time and their amplitude is strongly heterogeneous in space. Our study confirms and quantifies the diffusive nature of housing prices that was anticipated long ago (Clapp et al. 1994, Pollakowski et al. 1997), albeit on much restricted, local data sets., Comment: 14 pages, 9 figures

The sparse and spatio-temporally discontinuous nature of precipitation data presents significant challenges for simulation and statistical processing for bias correction and downscaling. These include incorrect representation of intermittency and extreme values (critical for hydrology applications), Gibbs phenomenon upon regridding, and lack of fine scales details. To address these challenges, a common approach is to transform the precipitation variable nonlinearly into one that is more malleable. In this work, we explore how deep learning can be used to generate a smooth, spatio-temporally continuous variable as a proxy for simulation of precipitation data. We develop a normally distributed field called pseudo-precipitation (PP) as an alternative for simulating precipitation. The practical applicability of this variable is investigated by applying it for downscaling precipitation from \(1\degree\) (\(\sim\) 100 km) to \(0.25\degree\) (\(\sim\) 25 km).

The acceleration of material property calculations while maintaining ab initio accuracy (1 meV/atom) is one of the major challenges in computational physics. In this paper, we introduce a Python package enhancing the computation of (finite temperature) material properties at the ab initio level using machine learning interatomic potentials (MLIP). The Machine-Learning Assisted Canonical Sampling (MLACS) method, grounded in a self-consistent variational approach, iteratively trains a MLIP using an active learning strategy in order to significantly reduce the computational cost of ab initio simulations. MLACS offers a modular and user-friendly interface that seamlessly integrates Density Functional Theory (DFT) codes, MLIP potentials, and molecular dynamics packages, enabling a wide range of applications, while maintaining a near-DFT accuracy. These include sampling the canonical ensemble of a system, performing free energy calculations, transition path sampling, and geometry optimization, all by utilizing surrogate MLIP potentials, in place of ab initio calculations. This paper provides a comprehensive overview of the theoretical foundations and implementation of the MLACS method. We also demonstrate its accuracy and efficiency through various examples, showcasing the capabilities of the MLACS package.

Dynamically maintaining the minimum cut in a graph $G$ under edge insertions and deletions is a fundamental problem in dynamic graph algorithms for which no conditional lower bound on the time per operation exists. In an $n$-node graph the best known $(1+o(1))$-approximate algorithm takes $\tilde O(\sqrt{n})$ update time [Thorup 2007]. If the minimum cut is guaranteed to be $(\log n)^{o(1)}$, a deterministic exact algorithm with $n^{o(1)}$ update time exists [Jin, Sun, Thorup 2024]. We present the first fully dynamic algorithm for $(1+o(1))$-approximate minimum cut with $n^{o(1)}$ update time. Our main technical contribution is to show that it suffices to consider small-volume cuts in suitably contracted graphs., Comment: To appear at SODA2025

We present our calculation of the isospin-violating part of the hadronic vacuum polarisation (HVP) contribution to muon $(g-2)$ in lattice QCD at the $SU(3)_{\mathrm{f}}$ symmetric point. The computation of the contributing fully connected diagrams with one internal photon as well as the computation of the only (mass) counterterm are shown. The latter is determined from the charged-neutral kaon mass splitting. We employ coordinate-space methods and a photon propagator which is regulated \`a la Pauli-Villars with a cutoff scale $\Lambda$ well below the lattice cutoff. This regularization makes it possible for us to do crosschecks of individual contributions with calculations in the continuum. Our continuum extrapolated results show little to no dependence on $\Lambda$. This makes our final limit $\Lambda \rightarrow \infty$ straightforward.

The recent observation of superconductivity in the vicinity of insulating or Fermi surface reconstructed metallic states has established twisted bilayers of WSe$_2$ as an exciting platform to study the interplay of strong electron-electron interactions, broken symmetries and topology. In this work, we study the emergence of electronic ordering in twisted WSe$_2$ driven by gate-screened Coulomb interactions. Our first-principles treatment begins by constructing moir\'e Wannier orbitals that faithfully capture the bandstructure and topology of the system and project the gate-screened Coulomb interaction onto them. Using unbiased functional renormalization group calculations, we find an interplay between intervalley-coherent antiferromagnetic order and chiral, mixed-parity $d/p$-wave superconductivity for carrier concentrations near the displacement field-tunable van-Hove singularity. Our microscopic approach establishes incommensurate intervalley-coherent antiferromagnetic spin fluctuations as the dominant electronic mechanism driving the formation of superconductivity in $\theta = 5.08^{\circ}$ twisted WSe$_2$ and demonstrates that nesting properties of the Fermi surface sheets near the higher-order van-Hove point cause an asymmetric density dependence of the spin ordering as the density is varied across the van-Hove line, in good agreement with experimental observations. We show how the region of superconducting and magnetic order evolves within the two-dimensional phase space of displacement field and electronic density as twist angle is varied between $4^{\circ} \dots 5^{\circ}$., Comment: 11 pages, 6 figures

In this paper, we provide a combinatorial description of seminormal toric varieties. The corresponding combinatorial object is a fan equipped with a collection of groups assigned to each cone. This framework introduces a more general class of toric varieties than classical normal toric varieties, while having simpler combinatorial data compared to general non-normal toric varieties., Comment: 17 pages

Encoder-only transformer models such as BERT offer a great performance-size tradeoff for retrieval and classification tasks with respect to larger decoder-only models. Despite being the workhorse of numerous production pipelines, there have been limited Pareto improvements to BERT since its release. In this paper, we introduce ModernBERT, bringing modern model optimizations to encoder-only models and representing a major Pareto improvement over older encoders. Trained on 2 trillion tokens with a native 8192 sequence length, ModernBERT models exhibit state-of-the-art results on a large pool of evaluations encompassing diverse classification tasks and both single and multi-vector retrieval on different domains (including code). In addition to strong downstream performance, ModernBERT is also the most speed and memory efficient encoder and is designed for inference on common GPUs.

Deterministic regression-based downscaling models for climate variables often suffer from spectral bias, which can be mitigated by generative models like diffusion models. To enable efficient and reliable simulation of extreme weather events, it is crucial to achieve rapid turnaround, dynamical consistency, and accurate spatio-temporal spectral recovery. We propose an efficient correction diffusion model, TAUDiff, that combines a deterministic spatio-temporal model for mean field downscaling with a smaller generative diffusion model for recovering the fine-scale stochastic features. We demonstrate the efficacy of this approach on downscaling atmospheric wind velocity fields obtained from coarse GCM simulations. Our approach can not only ensure quicker simulation of extreme events but also reduce overall carbon footprint due to low inference times.

In this paper we design, analyze and simulate a finite volume scheme for a cross-diffusion system which models chemotaxis with local sensing. This system has the same gradient flow structure as the celebrated minimal Keller-Segel system, but unlike the latter, its solutions are known to exist globally in 2D. The long-time behavior of solutions is only partially understood which motivates numerical exploration with a reliable numerical method. We propose a linearly implicit, two-point flux finite volume approximation of the system. We show that the scheme preserves, at the discrete level, the main features of the continuous system, namely mass, non-negativity of solution, entropy, and duality estimates. These properties allow us to prove the well-posedness, unconditional stability and convergence of the scheme. We also show rigorously that the scheme possesses an asymptotic preserving (AP) property in the quasi-stationary limit. We complement our analysis with thorough numerical experiments investigating convergence and AP properties of the scheme as well as its reliability with respect to stability properties of steady solutions.

Collisionless shocks are complex nonlinear structures that are not yet fully understood. In particular, the interaction between these shocks and the particles they accelerate remains elusive. Based on an instability analysis that relates the shock width to the spectrum of the accelerated particle and the shock density ratio, we find that the acceleration process could come to an end when the fraction of accelerated upstream particles reaches about 30\%. Only unmagnetized shocks are considered., Comment: To appear in Laser and Particle Beams

For any integer $ p \geq 2 $, we construct a compact Riemannian manifold $ \mathcal{N} $, such that if $ \dim \mathcal{M} > p $, there is a map in the Sobolev space of mappings $ W^{1,p} (\mathcal{M}, \mathcal{N})$ which is not a weak limit of smooth maps into $ \mathcal{N} $ due to a mechanism of analytical obstruction. For $ p = 4n - 1 $, the target manifold can be taken to be the sphere $ \mathbb{S}^{2n} $ thanks to the construction by Whitehead product of maps with nontrivial Hopf invariant, generalizing the result by Bethuel for $ p = 4n -1 = 3$. The results extend to higher order Sobolev spaces $ W^{s,p} $, with $ s \in \mathbb{R} $, $s \geq 1 $, $ sp \in \mathbb{N}$, and $ sp \ge 2 $.

We give a complete solution of the linearization problem in the plane Cremona group over an algebraically closed field of characteristic zero.

We extend the classical coding of measured $\mathbb R$-trees by continuous excursion-type functions to c\`adl\`ag excursion-type functions through the notion of parametric representations. The main feature of this extension is its continuity properties with respect to the \textsc{Gromov-Hausdorff-Prokhorov} topology for $\mathbb R$-trees and \textsc{Skorokhod}'s $M_1$ topology for c\`adl\`ag functions. As a first application, we study the $\mathbb R$-trees $\mathcal T_{x^{(\alpha)}}$ encoded by excursions of spectrally positive $\alpha$-stable \textsc{L\'evy} processes for $\alpha \in (1,2]$. In a second time, we use this setting to study the large-scale effects of a well-known bijection between plane trees and binary trees, the so-called rotation. \textsc{Marckert} has proved that the rotation acts as a dilation on large uniform trees, and we show that this remains true when the rotation is applied to large critical \textsc{Bienaym\'e} trees with offspring distribution attracted to a Gaussian distribution. However, this does not hold anymore when the offspring distribution falls in the domain of attraction of an $\alpha$-stable law with $\alpha \in (1,2)$, and instead we prove that the scaling limit of the rotated trees is $\mathcal T_{x^{(\alpha)}}$., Comment: 45 pages, 20 figures

We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the single-particle eigenstates are related to discrete orthogonal polynomials of the Askey scheme. Due to the bispectral properties of these functions, one can construct an operator which commutes exactly with the entanglement Hamiltonian and corresponds to a linear or parabolic deformation of the physical one. We show that this deformation is interpreted as a local inverse temperature and can be obtained in the continuum limit via methods of conformal field theory. Using this prediction, the properly rescaled eigenvalues of the commuting operator are found to provide a very good approximation of the entanglement spectrum and entropy., Comment: 25 pages, 5 figures

Quantum simulators have the potential to solve quantum many-body problems that are beyond the reach of classical computers, especially when they feature long-range entanglement. To fulfill their prospects, quantum simulators must be fully controllable, allowing for precise tuning of the microscopic physical parameters that define their implementation. We consider Rydberg-atom arrays, a promising platform for quantum simulations. Experimental control of such arrays is limited by the imprecision on the optical tweezers positions when assembling the array, hence introducing uncertainties in the simulated Hamiltonian. In this work, we introduce a scalable approach to Hamiltonian learning using graph neural networks (GNNs). We employ the Density Matrix Renormalization Group (DMRG) to generate ground-state snapshots of the transverse field Ising model realized by the array, for many realizations of the Hamiltonian parameters. Correlation functions reconstructed from these snapshots serve as input data to carry out the training. We demonstrate that our GNN model has a remarkable capacity to extrapolate beyond its training domain, both regarding the size and the shape of the system, yielding an accurate determination of the Hamiltonian parameters with a minimal set of measurements. We prove a theorem establishing a bijective correspondence between the correlation functions and the interaction parameters in the Hamiltonian, which provides a theoretical foundation to our learning algorithm. Our work could open the road to feedback control of the positions of the optical tweezers, hence providing a decisive improvement of analog quantum simulators., Comment: 19 pages, 11 figures

In this paper, we present generalization bounds for the unsupervised risk in the Deep Contrastive Representation Learning framework, which employs deep neural networks as representation functions. We approach this problem from two angles. On the one hand, we derive a parameter-counting bound that scales with the overall size of the neural networks. On the other hand, we provide a norm-based bound that scales with the norms of neural networks' weight matrices. Ignoring logarithmic factors, the bounds are independent of $k$, the size of the tuples provided for contrastive learning. To the best of our knowledge, this property is only shared by one other work, which employed a different proof strategy and suffers from very strong exponential dependence on the depth of the network which is due to a use of the peeling technique. Our results circumvent this by leveraging powerful results on covering numbers with respect to uniform norms over samples. In addition, we utilize loss augmentation techniques to further reduce the dependency on matrix norms and the implicit dependence on network depth. In fact, our techniques allow us to produce many bounds for the contrastive learning setting with similar architectural dependencies as in the study of the sample complexity of ordinary loss functions, thereby bridging the gap between the learning theories of contrastive learning and DNNs., Comment: Accepted at AAAI 2025

In-context learning (ICL) enables Large Language Models (LLMs) to perform tasks using few demonstrations, facilitating task adaptation when labeled examples are hard to obtain. However, ICL is sensitive to the choice of demonstrations, and it remains unclear which demonstration attributes enable in-context generalization. In this work, we conduct a perturbation study of in-context demonstrations for low-resource Named Entity Detection (NED). Our surprising finding is that in-context demonstrations with partially correct annotated entity mentions can be as effective for task transfer as fully correct demonstrations. Based off our findings, we propose Pseudo-annotated In-Context Learning (PICLe), a framework for in-context learning with noisy, pseudo-annotated demonstrations. PICLe leverages LLMs to annotate many demonstrations in a zero-shot first pass. We then cluster these synthetic demonstrations, sample specific sets of in-context demonstrations from each cluster, and predict entity mentions using each set independently. Finally, we use self-verification to select the final set of entity mentions. We evaluate PICLe on five biomedical NED datasets and show that, with zero human annotation, PICLe outperforms ICL in low-resource settings where limited gold examples can be used as in-context demonstrations., Comment: Preprint

This study introduces a novel framework for joint reconstruction of the activity and attenuation (JRAA) in positron emission tomography (PET) using diffusion posterior sampling (DPS), which leverages diffusion models (DMs) to address activity-attenuation dependencies and mitigate crosstalk issues in non-time-of-flight (TOF) settings; experimental evaluations with 2-dimensional (2-D) XCAT phantom data show that DPS outperforms traditional maximum likelihood activity and attenuation (MLAA) methods, providing consistent, high-quality reconstructions even without TOF information., Comment: 5 pages, 4 figures

This study investigates students' perceptions of Generative Artificial Intelligence (AI), with a focus on Higher Education institutions in Northern Ireland and India. We collect quantitative Likert ratings and qualitative comments from 1,211 students on their awareness and perceptions of AI and investigate variations in attitudes toward AI across institutions and subject areas, as well as interactions between these variables with demographic variables (focusing on gender). We find that: (a) while perceptions varied across institutions, responses for Computer Sciences students were similar; and (b) after controlling for institution and subject area, we observed no effect of gender. These results are consistent with previous studies, which find that students' perceptions are predicted by prior experience. We consider the implications of this relation and some considerations for the role of experience.

Sympathetic solar flares are eruptions that occur nearby in space and time, driven by an apparent interaction between the active regions in which they are triggered. Their statistical existence on the Sun has yet to be firmly established. The main goal of this paper is to identify a statistical signature of sympathetic flares, characterize their properties and determine a potential mechanism driving their interaction. We perform a statistical analysis of a large number of flares observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO), the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and the Spectrometer Telescope for Imaging X-rays (STIX) on Solar Orbiter during solar cycle 24 and 25. We examine the spatiotemporal distribution of consecutive flare pairs across solar cycle phases and hemispheres, along with the propagation velocity of potential causal interactions and the relationship between flare magnitudes. We observe an excess of hemispheric flares separated by about 30 degrees of longitude and triggered in less than 1.5 hours from each other. This peak in angular separation varies with the solar cycle phase and hemisphere. Moreover, we identify a deficit of transequatorial events separated by 25-30 degrees in latitude and less than 5 degrees in longitude, a phenomenon we term unsympathetic flares. We provide strong statistical evidence for the existence of sympathetic flares on the Sun, demonstrating that their occurrence rate reaches approximately 5% across the three instruments used in this study. Additionally, we propose an interpretation of the observed angular scale of the sympathetic phenomenon, based on the separation between magnetic field line footpoints derived from potential field source surface extrapolations., Comment: Accepted for publication in Astronomy & Astrophysics, 14 pages, 16 figures, 2 tables

Spectroscopy and direct-imaging of ultra-faint targets such as Earth-like exoplanets and high redshift galaxies are among the primary goals of upcoming large scale astronomy projects like the Habitable World Observatory (HWO). Such objectives pose extreme instrumental challenges, in particular on detectors where dark currents lower than 1 e-/pixel/kilosecond and read noise less than 1 e-/pixel/frame will have to be achieved on large format arrays. Some technologies meet these requirements at optical wavelengths, but none do in the infrared. With this goal in mind, the University of Hawaii has partnered with Leonardo to develop linear-mode avalanche photodiodes (LmAPDs). In this paper, we report recent tests performed on LmAPDs, where we measure a ROIC glow of approximately 0.01 e-/pixel/frame, without which the intrinsic dark current is essentally zero (< 0.1 e- /pixel/kilosecond). We show that at high gain, these devices are capable of detecting single photons, Comment: Proceedings of SPIE Vol. 13103, 1310320 (2024)

The resilience problem for a query and an input set or bag database is to compute the minimum number of facts to remove from the database to make the query false. In this paper, we study how to compute the resilience of Regular Path Queries (RPQs) over graph databases. Our goal is to characterize the regular languages $L$ for which it is tractable to compute the resilience of the existentially-quantified RPQ built from $L$. We show that computing the resilience in this sense is tractable (even in combined complexity) for all RPQs defined from so-called local languages. By contrast, we show hardness in data complexity for RPQs defined from the following language classes (after reducing the languages to eliminate redundant words): all finite languages featuring a word containing a repeated letter, and all languages featuring a specific kind of counterexample to being local (which we call four-legged languages). The latter include in particular all languages that are not star-free. Our results also imply hardness for all non-local languages with a so-called neutral letter. We also highlight some remaining obstacles towards a full dichotomy. In particular, for the RPQ $abc|be$, resilience is tractable but the only PTIME algorithm that we know uses submodular function optimization., Comment: 47 pages, 17 figures

Generic pre-trained neural networks may struggle to produce good results in specialized domains like finance and insurance. This is due to a domain mismatch between training data and downstream tasks, as in-domain data are often scarce due to privacy constraints. In this work, we compare different pre-training strategies for LayoutLM. We show that using domain-relevant documents improves results on a named-entity recognition (NER) problem using a novel dataset of anonymized insurance-related financial documents called Payslips. Moreover, we show that we can achieve competitive results using a smaller and faster model., Comment: Coling 2025 workshop (FinNLP)

We present the results of the second commissioning phase of the short-focal-length area of the Apollon laser facility (located in Saclay, France), which was performed with the main laser beam (F1), scaled to a peak power of 2 PetaWatt. Under the conditions that were tested, this beam delivered on-target pulses of maximum energy up to 45 J and 22 fs duration. Several diagnostics were fielded to assess the performance of the facility. The on-target focal spot and its spatial stability, as well as the secondary sources produced when irradiating solid targets, have all been characterized, with the goal of helping users design future experiments. The laser-target interaction was characterized, as well as emissions of energetic ions, X-ray and neutrons recorded, all showing good laser-to-target coupling efficiency. Moreover, we demonstrated the simultaneous fielding of F1 with the auxiliary 0.5 PW F2 beam of Apollon, enabling dual beam operation. The present commissioning will be followed in 2025 by a further commissioning stage of F1 at the 8 PW level, en route to the final 10 PW goal.

Abstractive summarization has made significant strides in condensing and rephrasing large volumes of text into coherent summaries. However, summarizing administrative documents presents unique challenges due to domain-specific terminology, OCR-generated errors, and the scarcity of annotated datasets for model fine-tuning. Existing models often struggle to adapt to the intricate structure and specialized content of such documents. To address these limitations, we introduce DocSum, a domain-adaptive abstractive summarization framework tailored for administrative documents. Leveraging pre-training on OCR-transcribed text and fine-tuning with an innovative integration of question-answer pairs, DocSum enhances summary accuracy and relevance. This approach tackles the complexities inherent in administrative content, ensuring outputs that align with real-world business needs. To evaluate its capabilities, we define a novel downstream task setting-Document Abstractive Summarization-which reflects the practical requirements of business and organizational settings. Comprehensive experiments demonstrate DocSum's effectiveness in producing high-quality summaries, showcasing its potential to improve decision-making and operational workflows across the public and private sectors.

We present a general theory of multicolor soliton microcombs. These frequency combs require specially engineered dispersion and have an optical spectrum consisting of multiple spectral windows, centered at distinct frequencies. Our theory is based on a multiple-scale approach applied to the Lugiato-Lefever equation, and provides a framework to investigate different pumping configurations. For multi-frequency pumping, we predict a progressively lower pumping threshold as the number of spectral windows increases due to an enhancement of the effective nonlinear parameter. However, multi-frequency pumping is not a prerequisite for the formation of these combs and can emerge even with a single driving field. Our theoretical predictions are in excellent agreement with numerical simulations.

We present a novel appearance model that simultaneously realizes explicit high-quality 3D surface mesh recovery and photorealistic novel view synthesis from sparse view samples. Our key idea is to model the underlying scene geometry Mesh as an Atlas of Charts which we render with 2D Gaussian surfels (MAtCha Gaussians). MAtCha distills high-frequency scene surface details from an off-the-shelf monocular depth estimator and refines it through Gaussian surfel rendering. The Gaussian surfels are attached to the charts on the fly, satisfying photorealism of neural volumetric rendering and crisp geometry of a mesh model, i.e., two seemingly contradicting goals in a single model. At the core of MAtCha lies a novel neural deformation model and a structure loss that preserve the fine surface details distilled from learned monocular depths while addressing their fundamental scale ambiguities. Results of extensive experimental validation demonstrate MAtCha's state-of-the-art quality of surface reconstruction and photorealism on-par with top contenders but with dramatic reduction in the number of input views and computational time. We believe MAtCha will serve as a foundational tool for any visual application in vision, graphics, and robotics that require explicit geometry in addition to photorealism. Our project page is the following: https://anttwo.github.io/matcha/, Comment: Project Webpage: https://anttwo.github.io/matcha/

The creep behavior of an amorphous poly(etherimide) (PEI) polymer is investigated in the vicinity of its glass transition in a weakly non linear regime where the acceleration of the creep response is driven by local configurational rearrangements. From the time shifts of the creep compliance curves under stresses from 1 to 15~\si{\mega\pascal} and in the temperature range between $T_g -10K$ and $T_g$, where $T_g$ is the glass transition, we determine a macroscopic acceleration factor. The macroscopic acceleration is shown to vary as $e^{-(\Sigma/Y)^n} $ with $n=2 \pm 0.2$, where $\Sigma$ is the macroscopic stress and $Y$ is a decreasing function of compliance. Because at the beginning of creep, the stress is homogeneous, the macroscopic acceleration is thus similar to the local one, in agreement with the recent theory of Long \textit{et al.} (\textit{Phys. Rev. Mat.} (2018) \textbf{2}, 105601 ) which predicts $n=2$. For larger compliances, the decrease of the of $Y$ is interpreted as a signature of the development of stress disorder during creep., Comment: arXiv admin note: substantial text overlap with arXiv:2403.00355

We prove that measure-class-preserving non-amenable treeable equivalence relations of type III, meaning not preserving any equivalent $\sigma$-finite measure, are induced by free actions of non-abelian free groups of any given number of generators, including infinitely generated free groups, with the additional property that no ends of the induced Schreier graph are vanishing. This is done using a characterization of type III due to Hopf for transformations and Dang-Ngoc-Nghiem in general. This highlights the difference between the type III setting and the measure-preserving setting.