Quantum metric learning enhances machine learning by mapping classical data to a quantum Hilbert space with maximal separation between classes. However, on current NISQ hardware, this mapping process itself is prone to errors and could be fundamentally incorrect. Verifying that a quantum embedding model successfully achieves its promised separation is essential to ensure the correctness and reliability. In this paper, we propose a practical black-box verification protocol to audit the performance of quantum metric learning models. We define a setting with two parties: a powerful but untrusted prover, who claims to have a parameterized unitary circuit that embeds classical data from different groups with a guaranteed angular separation, and a limited verifier, whose quantum capabilities are restricted to performing only basic measurements. The verifier has no knowledge of the implementation of the prover, including the structure of the model, its parameters, or the details of the prover measurement setup. To verify the separation between different data groups, the proposed algorithm must overcome two key challenges. First, the verifier is ignorant of the prover's implementation details, such as the optimization cost function and measurement setup. Consequently, the verifier lacks any prior information about the expected quantum embedding states for each group. Second, the destructive nature of quantum measurements prevents direct estimation of the separation angles. Our algorithm successfully overcomes these challenges, enabling the verifier to accurately estimate the true separation angles between the different groups. We implemented the proposed protocol and deployed it to verify the QAOAEmbedding models. The results from both theoretical analysis and practical implementation show that our proposal effectively assesses embedding quality and remains robust in adversarial settings.

The growing adoption of Rust for its memory safety and performance has increased the demand for effective migration of legacy C codebases. However, existing rule-based translators (e.g., \ctorust) often generate verbose, non-idiomatic code that preserves unsafe C semantics, limiting readability, maintainability, and practical adoption. Moreover, manual post-processing of such outputs is labor-intensive and rarely yields high-quality Rust code, posing a significant barrier to large-scale migration. To address these limitations, we present \tool, a program-structure-aware C-to-Rust translation approach that integrates program analysis with Large Language Models (LLMs). \tool extracts the multi-level program structure, including global symbols, function dependencies, and control- and data-flow information, and encodes these as structured textual representations injected into LLM prompts to guide translation and repair. Based on this design, \tool performs dependency-aware translation and adopts a multi-stage repair pipeline that combines rule-based and structure-guided LLM-based techniques to ensure syntactic correctness. For semantic correctness, \tool further integrates execution-based validation with structure-guided reasoning to localize and repair behavioral inconsistencies. Experimental results show that \tool achieves 100\% syntactic correctness on CodeNet and 97.78\% on GitHub, while significantly reducing code size (up to 43.70\%) and unsafe usage (to 5.75\%). At the project level, \tool achieves perfect syntactic correctness and an average semantic correctness of 78.87\%, demonstrating its effectiveness for practical and scalable C-to-Rust migration.

The PADME Experiment at Laboratori Nationali di Frascati is designed to search for the Dark Photon, a hypothetical gauge boson responsible for the interaction between the visible and the hidden sector. PADME explores the process of annihilation of beam positrons with the electrons in a fixed target, employing the missing mass technique: in case the annihilation results in the associate production of one visible and one Dark photon, the first can be registered by the experiment's electromagnetic calorimeter and the Dark Photon mass can be reconstructed knowing the beam energy. This paper presents the analysis techniques that are being employed for the PADME data, as well as the background composition and rejection procedure.

We present a fully automated framework for extracting interatomic force constants (IFCs) directly from X-ray thermal diffuse scattering (TDS) data. By formulating scattering intensity as a differentiable function of a symmetry-reduced IFC parameterization, we enable gradient-based optimization via direct, Cholesky-based sampling of correlated atomic displacements at thermal equilibrium. This approach bypasses the computational bottleneck of repeated Hessian matrix diagonalizations, significantly accelerating the inversion process. Benchmark tests demonstrate that the framework accurately recovers ground-truth IFCs and phonon dispersion relations, providing a robust, high-throughput pathway for studying lattice dynamics across diverse crystalline materials. This method bridges the gap between experimental observations and computational modeling, enabling the direct integration of TDS data into the refinement of high-fidelity inter-atomic potentials.

Overmassive black hole galaxies (OBGs) at redshifts $z \sim$ 10, or 450 Myr after the Big Bang, are one of the most puzzling discoveries by the James Webb Space Telescope to date because they formed by such early epochs and their black-hole to stellar mass ratios are a hundred times higher than those in galaxies today. Here we show that OBGs are simply the result of DCBH birth in primordial halos at early times. A 70,000 M$_{\odot}$ DCBH forming at $z =$ 25.7 in our cosmological simulation grows at about half the Eddington rate to $6.0 \times 10^6$ M$_{\odot}$ by $z =$ 10.1. Its host galaxy reaches a stellar mass of $4 \times 10^8$ M$_{\odot}$, a metallicity $Z =$ 0.1 Z$_{\odot}$, a star formation rate of 2 M$_{\odot}$ yr$^{-1}$, and $M_{\rm BH}/M_{\ast}$ $\sim$ 0.01, on par with OBGs like GN-z11, UHZ1, and GHZ9 at $z =$ 10.6, 10.1, and 10.2, respectively. Our simulation, the first to follow the coevolution of a DCBH and its host galaxy for several hundred Myr, shows that this ratio is a natural result of initial suppression of star formation by the DCBH and the later, violent blowout of metals by Pop III supernovae. Our models provide an excellent match to the spectra of UHZ1 and GHZ9 at $z =$ 10.1 and 10.4, respectively.

Introductory artificial intelligence (AI) courses present significant learning challenges due to abstract concepts, mathematical complexity, and students' diverse technical backgrounds. While active and collaborative pedagogies are often recommended, implementation can be difficult at scale due to large class sizes and the intensive design effort required of instructors. This paper presents a quasi-experimental case study examining the redesign of in-class instructional time in a university-level Introduction to Artificial Intelligence course. Inspired by CS Unplugged approaches, we redesigned the summer offering, integrating embodied, unplugged simulations, collaborative programming labs, and structured reflection to provide students with a first-person perspective on AI decision-making. We maintained identical assignments, exams, and assessments as the traditional lecture-based offering. Using course evaluation data, final grade distributions, and post-course interviews, we examined differences in student engagement, experiences, and traditional learning outcomes. Quantitative results show that students in the redesigned course reported higher attendance, stronger agreement that assessments measured their understanding, and greater overall course effectiveness, despite no significant differences in final grades or self-reported learning. Qualitative findings indicate that unplugged simulations and collaboration fostered a safe, supportive learning environment that increased engagement and confidence with AI concepts. These results highlight the importance of in-class instructional design in improving students' learning experiences without compromising rigor.

Context: Requirements prioritization is a challenging problem that is aimed to deliver the most suitable subset from a pool of candidate requirements. The problem is NP-hard when formulated as an optimization problem. Feedback from end users can offer valuable support for software evolution, and ReFeed represents a state-of-the-art in automatically inferring a requirement's priority via quantifiable properties of the feedback messages associated with a candidate requirement. Objectives: In this paper, we enhance ReFeed by shifting the focus of prioritization from treating requirements as independent entities toward interconnecting them. Additionally, we explore if interconnecting requirements provides additional value for search-based solutions. Methods: We leverage user feedback from mobile app store to group requirements into topically coherent clusters. Such interconnectedness, in turn, helps to auto-generate additional "requires" relations in candidate requirements. These "requires" pairs are then integrated into a search-based software engineering solution. Results: The experiments on 94 requirements prioritization instances from four real-world software applications show that our enhancement outperforms ReFeed. In addition, we illustrate how incorporating interconnectedness among requirements improves search-based solutions. Conclusion: Our findings show that requirements interconnectedness improves user feedback driven requirements prioritization, helps uncover additional "requires" relations in candidate requirements, and also strengthens search-based release planning.

Coarse-grained models of chaotic systems neglect unresolved degrees of freedom, inducing structured model error that limits predictability and distorts long-term statistics. Typical data-driven closures are trained to minimize error over a single time step, implicitly assuming Markovian dynamics and often failing to capture long-term behavior. Recent approaches instead optimize losses over finite trajectories. However, when such trajectory-based training is carried out with deterministic pointwise losses, it introduces a fundamental mathematical degeneracy. We prove that optimizing pointwise deterministic losses such as mean squared error over chaotic trajectories suppresses predictive variance, with corresponding loss of physical variability in long integrations. In contrast, strictly proper scoring rules avoid this degeneracy. By targeting forecast distributions rather than realized trajectories, they remove the penalty against predictive spread and align the long-lead optimum with the invariant measure. Using quasi-geostrophic turbulence as a canonical chaotic system, we validate this theory: one-step-trained closures fail to capture stable coarse-grained dynamics, while deterministic closures optimized over trajectories exhibit the variance-loss tendency predicted by our analysis. Stochastic closures calibrated over trajectories using the energy score, however, overcome both structural limitations, yielding skillful ensemble forecasts and realistic long-term statistics. Our results establish that both stochastic modeling and trajectory-based calibration are essential for faithfully representing the dynamics of coarse-grained systems.

The prospect of artificial superintelligence -- AI agents that can generally outperform humans in cognitive tasks and economically valuable activities -- will transform the legal order as we know it. Operating autonomously or under only limited human oversight, AI agents will assume a growing range of roles in the legal system. First, in making consequential decisions and taking real-world actions, AI agents will become de facto subjects of law. Second, to cooperate and compete with other actors (human or non-human), AI agents will harness conventional legal instruments and institutions such as contracts and courts, becoming consumers of law. Third, to the extent AI agents perform the functions of writing, interpreting, and administering law, they will become producers and enforcers of law. These developments, whenever they ultimately occur, will call into question fundamental assumptions in legal theory and doctrine, especially to the extent they ground the legitimacy of legal institutions in their human origins. Attempts to align AI agents with extant human law will also face new challenges as AI agents will not only be a primary target of law, but a core user of law and contributor to law. To contend with the advent of superintelligence, lawmakers -- new and old -- will need to be clear-eyed, recognizing both the opportunity to shape legal institutions as society braces for superintelligence and the reality that, in the longer run, this may be a joint human-AI endeavor.

We show that hadrons in QCD follow a spectrum determined by string dynamics characterized by a universal Hagedorn temperature linked to the string tension. While this behavior was recently established for light hadrons and glueballs, we demonstrate that the same dynamics describes the heavy-flavor sector. After separating the current quark masses, the resulting spectrum reproduces lattice QCD thermodynamics of charmed hadrons and the observed spectra of hadrons across quark flavors without additional parameters. These results reflect the universal confining dynamics of QCD through the string tension.

The Sourlas-Lechner-Hauke-Zoller (SLHZ) scheme for quantum annealing uses the parity to encode logical variables and has several advantages, but it has not been implemented for large-scale quantum annealers. If the SLHZ-based approach can be implemented on currently available quantum annealers, we can evaluate its performance. An efficient method to embed the parity-encoded model into the hardware graphs of available quantum annealers is one of the key elements for this approach. We propose a qubit-efficient embedding scheme for parity-encoded Hamiltonians on quantum annealers with the Zephyr connectivity. We give an explicit constructive embedding of the interaction graph of an intermediate Hamiltonian, which contains only one- and two-body interactions, into the Zephyr graph. Our embedding maps each spin to a two-qubit chain using systematic chain-assignment rules. Its validity is verified via the resulting chain-to-chain connectivity. Our embedding also offers practical flexibility. Chains assigned to ancillary spins allow reduction to a single physical qubit, leading to options to avoid inactive qubits. The number of required qubits per spin in the parity Hamiltonian is three, which is fewer than that for a known embedding scheme for the Pegasus graph.

We examine scattering amplitudes for an arbitrary number of photons in a class of non-null background electromagnetic fields, studying tree-level and one-loop amplitudes in scalar and spinor quantum-electrodynamics in backgrounds defined by a gauge field $A_μ(\mathfrak{n}\cdot x)$ for $\mathfrak{n}^2\neq 0$. Motivated to account for more physically realistic laser-plasma dispersive properties, our approach overcomes prior work studying such amplitudes in a constant background field and relaxes the familiar null criterion assumed for plane waves. Master Formulae for the $N$-photon amplitudes dressed by the non-null background are constructed using the first-quantised worldline formalism, which can systematically account for all orders in the non-null parameter, $\mathfrak{n}^2$, treated here as an expansion parameter. These are derived from worldline representations of the coordinate and momentum space propagators (and their LSZ-truncated amplitudes) and the effective action, each incorporating the non-null background non-perturbatively. We then outline a partial resummation of their expansions in $\mathfrak{n}^{2}$. A special exactly solvable case of non-null constant crossed fields without photon insertion in the effective action is explored to test the Master Formulae that result. The validity of the presented master formulae is further checked against known expressions for the wavefunction and non-linear Compton scattering in a non-null background to lowest order in the non-null parameter.

Quantum trajectories are Markov chains modeling quantum systems subjected to repeated indirect measurements. Their stationary regime depends on what observables are measured on the probes used to indirectly measure the system. In this article we explore the properties of quantum trajectories when the choice of probe observable is randomized. The randomization induces some regularization of the quantum trajectories. We show that non-singular randomization ensures that quantum trajectories purify and therefore accept a unique invariant probability measure. We furthermore study the regularity of that invariant measure. In that endeavour, we introduce a new notion of ergodicity for quantum channels, which we call multiplicative primitivity. It is a priory stronger than primitivity but weaker than positivity improving. Finally, we compute some invariant measures for canonical quantum channels and explore the limits of our assumptions with several examples.

We investigate the pushed-to-pulled transition for a minimal model for invasive fronts influence by ``aerotaxis,'' that is, when organisms follow oxygen gradients. We consider two singular reaction-advection-diffusion models for this. The version of primary interest arises as a hydrodynamic limit of a system of branching, rank-based interacting Brownian particles and features a nonlinear, nonlocal advection. The second version is introduced here as a local counterpart. We establish well-posedness for both models, with the local case requiring a novel use of the ``shape defect function.'' We further characterize the front location up to $O(1)$ precision in all cases, including the delicate boundary ``pushmi-pullyu'' case.

We revise the analysis of the acoustic wave equation, addressing the question whether the classical well-posedness implies the existence of an isomorphism between prescribed solution and data spaces. This question is of interest for the design and the analysis of discretization methods. Expanding on existing results, we point out that established choices of solution and data space in terms of classical Bochner spaces must be expected to be incompatible with the existence of such an isomorphism, because of resonant waves. We formulate this observation in the language of the so-called inf-sup theory, with the help of an eigenfunction expansion, which reduces the original partial differential equation to a system of ordinary differential equations. We further verify that an isomorphism can be established, for each equation in the system, upon equipping the data space with a suitable resonance-aware norm. In the appendix, we extend our results to other time-dependent linear PDEs.

We employed molecular dynamics simulations (MD) and Bennett's acceptance ratio method to compute the free energy of transfer (Delta G_trans) of phenol, methane, and 5-fluorouracil (5-FU) between bulk water and water-pNIPAM mixtures with different polymer volume fractions (phi_p). To this end, we first calculate the solvation free energies in both media to obtain Delta G_trans. Phenol and 5-FU (a drug used in cancer treatment) adsorb onto the pNIPAM surface and exhibit negative values of Delta G_trans irrespective of temperature, both above and below the lower critical solution temperature (T_c) of pNIPAM. In contrast, methane changes the sign of Delta G_trans, being positive below and negative above T_c. In all cases, and in contrast with some theoretical predictions, Delta G_trans shows a linear dependence on pNIPAM concentration up to high polymer densities. We also compute the diffusion coefficient (D) of phenol in water-pNIPAM mixtures as a function of phi_p in the dilute limit. Both Delta G_trans and D as functions of phi_p are key inputs to estimate the release halftime of hollow pNIPAM microgels using dynamic density functional theory (DDFT). Our scaling approach reproduces the experimental value of 2200 s for microgels of 50 micrometer radius without a cavity, at phi_p approximately 0.83 and 315 K.

The cross-lagged panel model (CLPM) has been widely used, particularly in psychology, to infer longitudinal relations among variables. At the same time, controlling for between-person heterogeneity and capturing within-person relations as processes of within-person change are regarded as key components to causal inference based on longitudinal data. Since Hamaker, Kuiper, and Grasman (2015) criticized the CLPM for its limitations in inferring within-person relations, the random intercept cross-lagged panel model (RI-CLPM), which incorporates stable trait factors representing stable individual differences, has rapidly spread, especially in psychology. At the same time, although many statistical models are available for inferring within-person relations, the distinctions among them have not been clearly delineated, and discussions over the interpretation and selection of statistical models remain active. In this paper, I position the RI-CLPM as one useful method for inferring within-person relations, explain its practical issues, and organize its mathematical and conceptual relationships with other statistical models, as well as potential problems that may arise in their application. In particular, I point out that a distinctive feature of the stable trait factors in the RI-CLPM, in representing between-person heterogeneity, is the assumption that they are uncorrelated with within-person variability, and that this point serves as an important link to the mathematical relationship with the dynamic panel model, another promising alternative.

AI-powered malware increasingly exploits cloud-hosted generative-AI services and large language models (LLMs) as analysis engines for reconnaissance and code generation. Simultaneously, enterprise uploads expose sensitive documents to third-party AI vendors. Both threats converge at the AI service ingestion boundary, yet existing defenses focus on endpoints and network perimeters, leaving organizations with limited visibility once plaintext reaches an LLM service. To address this, we present a framework based on steganographic canary files: realistic documents carrying cryptographically derived identifiers embedded via complementary encoding channels. A pre-ingestion filter extracts and verifies these identifiers before LLM processing, enabling passive, format-agnostic detection without semantic classification. We support two modes of operation where Mode A marks existing sensitive documents with layered symbolic encodings (whitespace substitution, zero-width character insertion, homoglyph substitution), while Mode B generates synthetic canary documents using linguistic steganography (arithmetic coding over GPT-2), augmented with compatible symbolic layers. We model increasing document pre-processing and adversarial capability for both modes via a four-tier transport-transform taxonomy: All methods achieve 100% identifier recovery under benign and sanitization workflows (Tiers 1-2). The hybrid Mode B maintains 97% through targeted adversarial transforms (Tier 3). An end-to-end case study against an LLM-orchestrated ransomware pipeline confirms that both modes detect and block canary-bearing uploads before file encryption begins. To our knowledge, this is the first framework to systematically combine symbolic and linguistic text steganography into layered canary documents for detecting unauthorized LLM processing, evaluated against a transport-threat taxonomy tailored to AI malware.

In this work we provide predictions for bottom-strange molecular states within the Hidden Gauge Formalism. We study the coupled-channel scattering of $B^{(*)}\bar{K}^{(*)}$ states and, by fixing only one free parameter to obtain the mass of a new excited $B_s^0$ state seen by the LHCb, we predict the pole parameters of six states in this sector. Concretely, we get that the masses of the flavor partners of the $D_{s0}(2317)$ and $D_{s1}(2460)$ states in the bottom sector are $5760$ and $5802$ MeV for the $B\bar{K}$ ($J^P=0^+$) and $B^{*}\bar{K}$ ($1^+$) states, respectively. Moreover, the recently seen states by the LHCb with masses around $6100$ and $6160$ MeV can be interpreted as $B\bar{K}^*$ and $B^*\bar{K}^*$ molecular states, according to reasonable values of the pole parameters and the splitting between these two states obtained in our calculation.

In light of major developments over the past decades in both quantum computing and simulations on classical hardware, it is a serious challenge to identify a real-world problem where quantum advantage is expected to appear. In quantum chemistry, electronic structure calculations of strongly correlated, i.e. multi-reference problems, are often argued to fall into such category because of their intractability with standard methods based on mean-field theory. Therefore, providing state-of-the-art benchmark data by classical algorithms is necessary to make a decisive conclusion when such competing development directions are compared. We report cutting-edge performance results together with high accuracy ground state energy for the Fe$_4$S$_4$ molecular cluster on a CAS(54,36) model space, a problem that has been included quite recently among the list of systems in the {\it Quantum Advantage Tracker} webpage maintained by IBM and RIKEN. Pushing the limits even further, we also present CAS-SCF based orbital optimizations for unprecedented CAS sizes of up to 89 electrons in 102 orbitals [CAS(89,102)] for the Fe$_5$S$_{12}$H$_4^{5-}$ molecular system comprising twenty five open shell orbitals in its sextet ground state and an active spaces size of 331 electrons in 451 orbitals. We have achieved our results via mixed-precision spin-adapted \textit{ab initio} Density Matrix Renormalization Group (DMRG) electronic structure calculations interfaced with the ORCA program package and utilizing the NVIDIA Blackwell graphics processing unit (GPU) platform. We argue that DMRG benchmark data should be taken as a classical reference when quantum advantage is reported. In addition, full exploitation of classical hardware should also be considered since even the most advanced DMRG implementations are still in a premature stage regarding utilization of all the benefits of GPU technology.

We describe a magnetically driven torsional oscillator that is well suited for teaching the physics of simple harmonic motion using a collection of hands-on, quantitative experiments. The mechanical Q of the system can be tuned using eddy-current damping, while optical read-outs provide electronic signals than can be recorded using nothing more than a basic digital oscilloscope. The 40-Hz oscillator is described by simple harmonic motion to high accuracy, providing many satisfying comparisons between theory and experiment.

As neural networks are known to efficiently represent classes of tensor-network states as well as volume-law-entangled states, identifying which properties determine the representational capabilities of neural quantum states (NQS) remains an open question. We construct NQS representations of ground states of medium-mass atomic nuclei, which typically exhibit significant entanglement and non-stabilizerness, to study their performance in relation to the quantum complexity of the target state. Leveraging a second-quantized formulation of NQS tailored for nuclear-physics applications, we perform calculations in active orbital spaces using a restricted Boltzmann machine (RBM), a prototypical NQS ansatz. For a fixed number of configurations, we find that states with larger non-stabilizerness are systematically harder to learn, as evidenced by reduced accuracy. This finding suggests that non-stabilizerness is a primary factor governing the compression and representational efficiency of RBMs in entangled regimes, and motivates extending these studies to more sophisticated network architectures.

Multidimensional loop kernels often suffer from control overhead that can dominate execution time on parallel loop accelerators. Tightly Coupled Processor Arrays (TCPAs) offload loop control to a global controller (GC), but existing approaches still require hundreds of control signals. We propose a method to derive and aggressively reduce these control conditions from a polyhedral representation of the iteration space, achieving reductions of 15x to 45x in control signals across several benchmarks. We introduce a lightweight GC architecture that evaluates conditions as unions of polyhedra using bounded evaluation units, requiring hardware comparable to a single processing element. Control signals are distributed throughout the array with a minimal number of delay elements resulting in zero-overhead loop control. Our evaluation on PolyBench kernels shows that the entire control flow requires < 10 % of the total array resources.

Preconditioning for overdetermined least-squares problems has received comparatively little attention, and designing methods that are both effective and memory-efficient remains challenging. We propose a class of ILU-based preconditioners built around a row-splitting strategy that identifies a well-conditioned square submatrix via an incomplete LU factorization and combines its incomplete factors with algebraic corrections from the remaining rows. This construction avoids forming the normal equations and is well suited to problems for which the normal matrix is ill-conditioned or relatively dense. Numerical experiments on test problems arising from practical applications illustrate the effectiveness of the proposed approach when used with a Krylov subspace solver and demonstrate it can outperform preconditioners based on incomplete Cholesky factorization of the normal equations, including for sparse-dense problems, where the splitting naturally isolates dense rows.

Cuprate HTSCs exhibit a dome-shaped dependence of the superconducting transition temperature on the charge carrier concentration, Tc(p), with a maximum at p = 0.16. Near the composition p = 1/8, a dip in Tc is observed (the "1/8 anomaly"), which is associated with charge and spin ordering in the CuO2 planes. By investigating the hydration process of La2-xBaxCuO4 and YBa2Cu3O6+delta conducted at room temperature (RT) and under the influence of a high-frequency magnetic field, we have discovered unusual weight changes in HTSC samples during the initial stage of hydration. For both studied compounds, the dependence of weight changes on the concentration p was found to almost exactly replicate the patterns of the corresponding Tc(p) dependencies, including the "1/8 anomaly". Such a manifestation of characteristic low-temperature features of HTSC systems at RT is intriguing. The results of this experimental work will be useful for the further development of HTSC theories.

In this paper, a class of linear evolution equations with time delay is studied in which the presence of continuous spectrum on the imaginary axis obstructs the analysis of long-time dynamics. To address it, a generalized spectral framework on a Gelfand triple is utilized. When the spectral measure of the unperturbed term (a skew-adjoint operator) admits some analyticity condition, the resolvent is extended to a generalized resolvent. Called generalized spectrum, the collection of singularities on the Riemann surface of the generalized resolvent may differ from the spectrum in the usual sense because of the change of topology via the Gelfand triple. It is shown that under some compactness assumption, the generalized spectrum consists only of isolated generalized eigenvalues (resonance poles). This structure allows contour deformation in the inverse Laplace representation and yields exponential decay in a weak topology. As an application, we analyze the continuum limit of the Kuramoto-Daido model with time delay and prove linear stability of the incoherent state in the weak coupling regime.

We introduce a novel reformulation of three-dimensional gravity in terms of divergenceless vector frames, inspired by the double copy for Chern-Simons theory. This formulation is on-shell equivalent to conventional 3D gravity and provides a transparent geometric interpretation of the double-copy construction. We relate the resulting theory to a Chern-Simons-like action, propose a higher-dimensional origin, and explore extensions that give rise to $AdS_3$

This paper studies the numerical approximation of divergence-free vector fields by linearized shallow neural networks, also referred to as random feature models or finite neuron spaces. Combining the stable potential lifting for divergence-free fields with the scalar Sobolev integral representation theory via ReLU$^k$ networks, we derive a core integral representation of divergence-free Sobolev vector fields through antisymmetric potentials parameterized by linearized ReLU$^k$ neural networks. This representation, together with a quasi-uniform distribution argument for the inner parameters, yields optimal approximation rates for such linearized ReLU$^k$ neural networks under an exact divergence-free constraint. Numerical experiments in two and three spatial dimensions, including $L^2$ projection and steady Stokes problems, confirm the theoretical rates and illustrate the effectiveness of exactly divergence-free conditions in computation.

Adapting Bauer and Furuta's constructions of the refinement of the Seiberg-Witten invariants, we establish the analogous stable cohomotopy refinement of the $Pin^{-}(2)$ monopole invariants proposed by Nakamura \cite{nakamura2015pin}, and give the corresponding connected sum formula.

Stochastic particle acceleration in magnetized turbulent plasmas has emerged as a key mechanism to explain multi-messenger signals from compact astrophysical environments. Self-consistent modelling remains challenging because it requires to treat simultaneously several non-linear kinetic processes, especially turbulence-driven acceleration and its feedback on the turbulent cascade, as well as the radiative and hadronic losses, including the reprocessing of electromagnetic radiation in radiatively dense environments. The present paper introduces the hybrid numerical code Turb-AM3 designed to this effect. This hybrid numerical code couples the state-of-the-art time-dependent lepto-hadronic radiative solver AM3 with a stochastic acceleration module that incorporates recent theoretical advances in turbulent acceleration and accounts for the dynamical damping of turbulence by accelerated particles. In a second part, we use this code to provide self-consistent time-dependent models of proton acceleration in the turbulent black hole corona of NGC~1068. We find that the IceCube neutrino signal is well reproduced for a standard set of physical parameters describing the black hole corona. The same template model accounts in a satisfactory way for IceCube observations of other active galactic nuclei. Furthermore, our exploration of parameter space allows us to predict detailed template spectral shapes for the TeV neutrino spectrum, which in turn help understand how future neutrino observations can constrain the properties of turbulent AGN coronae and the underlying acceleration mechanism. This Turb-AM3 framework provides a powerful tool to model multi-messenger emission in a broad variety of compact astrophysical environments.