The existence of EFX allocations is a fundamental question in fair division. In this paper, we construct a three-agent, eight-good instance with monotone subadditive valuations such that no allocation satisfies $α$-EFX for any $α> \frac{1}{\sqrt[6]{2}} \approx 0.89$. We also provide a closely related three-agent, eight-good instance with submodular (in fact weighted coverage) valuations for which no EFX allocation exists. A key feature of our construction is its symmetry: the agents' valuations are identical up to a relabeling of the goods. Thus, EFX can fail even when agents differ only in how the goods are labeled. This symmetry makes the counterexamples compact and human-verifiable, yielding simple combinatorial obstructions to the existence of EFX.

Electron spins in single molecules are a promising platform for quantum information processing. However, their practical implementation as qubits requires reliable control at the single-entity level, including an efficient state initialization. Here, we demonstrate the remote, all-electrical initialization of the electron spin in single molecules: Using electron spin resonance scanning tunneling microscopy, we investigate coupled pairs of S=1/2 molecules (Fe-FePc), where one molecule serves as a readout and pumping unit for the neighboring one. We show that the exchange interaction between them enables angular momentum transfer, which allows for the control of the remote spin state via the direction and magnitude of the spin-polarized tunneling current and the exchange coupling strength. These results establish a general, all-electrical approach for remote spin initialization that is readily transferable to a wide range of spin-based quantum architectures.

Accurate characterization of atmospheric optical turbulence is essential for evaluating astronomical sites and optimizing adaptive optics systems. The Multistar Turbulence Monitor (MTM) infers the vertical distribution of the refractive-index structure constant Cn2(z) from differential image motion measured between multiple stellar pairs in short-exposure frames. We present a comprehensive investigation of the MTM method, combining theoretical analysis, instrument-performance assessment, numerical simulations, and on-sky observations obtained at the Daocheng Astronomical Site. Simulations based on a standard HV turbulence model demonstrate that the inversion pipeline robustly recovers both the integrated seeing and the vertical turbulence profile under realistic centroiding noise and varying pixel scales. The Markov Chain Monte Carlo (MCMC) inversion achieves stable results with thirteen discrete height nodes and provides reliable uncertainties. Three nights of MTM measurements at the Daocheng Astronomical Site show that MTM-derived seeing closely tracks simultaneous Differential Image Motion Monitor (DIMM) results, accurately reproducing both short-term fluctuations and nightly averages. These results confirm that MTM provides a simple, portable, and versatile solution for atmospheric turbulence profiling and routine seeing monitoring.

Model predictive control (MPC) is widely used in industries but implementing it poses challenges due to hardware or time constraints. A promising solution is to approximate the MPC policy using function approximators like neural networks. Existing methods focus on minimizing the error between the approximators outputs and the MPC optimal control actions on training data, which is called error guided learning approach in this paper. However, the goals of control law design is not to minimize the fitting error but to minimize the operation cost. This paper proposes a novel cost-guided learning approach that utilizes the cost sensitivity information from the MPC problem to directly minimize the loss in closed-loop performance. A theoretical analysis shows cost-guided learning provides tighter guarantees on optimality loss compared to traditional error-guided learning. Experiments on a continuous stirred tank reactor (CSTR) benchmark demonstrate that the proposed technique results in approximate MPC policies that achieve substantially better closed-loop performance. This work makes an important contribution by connecting the fitting errors with operational objectives, overcoming key limitations of existing approximation methods. The core idea could be applied more broadly for data-driven control.

Precoding is a key technique for interference management and performance improvement in multi-antenna wireless systems. However, existing precoding methods are typically developed for specific system models, objectives, and constraint sets, which limits their adaptability to the heterogeneous and evolving scenarios expected in future 6G networks. To address this limitation, we propose AgenticPrecoding, a universal multi-agent framework that automates end-to-end precoding derivation directly from user-level communication requirements. Specifically, AgenticPrecoding decomposes the derivation process into four coordinated stages: problem formulation, solver selection, prompt upsampling, and code generation, assigning each stage to a specialized agent tailored to its specific reasoning demands. We employ two LoRA-adapted reasoning agents to inject precoding-specific domain knowledge for problem formulation and solver selection, while two general-purpose Large Language Models (LLMs) handle prompt refinement and executable code generation. Furthermore, a feedback-driven refinement mechanism is incorporated to enhance code executability, constraint feasibility, and solution quality. Extensive experiments across 10 representative precoding scenarios demonstrate that AgenticPrecoding achieves superior cross-scenario adaptability compared to conventional optimization-based and LLM-based baselines.

The increasing uncertainty in modern power systems, driven by the integration of intermittent energy sources and variable loads, underscores the need for probabilistic transient stability assessment. However, existing assessment methods primarily focus on average system stability behavior and may struggle or incur high computational cost when identifying rare transient instability events, which in turn are critical for ensuring system resilience. To address this, the paper proposes a Kriging-based active learning framework to accurately characterize rare instability regions within the input uncertainty space and estimate the associated small instability probability, while requiring only a limited number of expensive time-domain simulations. The proposed active learning (AL) framework is tested on a modified IEEE 59-bus system with simulated load and wind uncertainties, and a WECC 240-bus system incorporating real-world wind and solar generation data. Comparative studies with the existing random forest-based active learning method and three non-AL methods demonstrate that the proposed AL framework achieves superior accuracy and computational efficiency.

Deep recommender systems (DRS) often face challenges in balancing computational efficiency and model accuracy, especially when handling high-dimensional input features. Existing methods either focus on improving accuracy while neglecting training efficiency or prioritize efficiency at the cost of suboptimal accuracy across tasks. We propose Light-FMP: Lightweight Feature and Model Pruning for Enhanced DRS, a lightweight framework that addresses the challenges through three key phases: \textit{pretraining}, \textit{pruning}, and \textit{continued training}. Using a hard concrete distribution, a masking layer is efficiently pretrained on a small data subset to identify important features. The model and features are then pruned, and training continues on the remaining dataset with domain-adapted parameters. Experiments on benchmark datasets from real-world recommender systems demonstrate that Light-FMP outperforms existing methods in both efficiency and accuracy while maintaining scalability and robustness.

6G industrial in-X subnetworks are expected to support highly time-critical alarm reporting in large-scale environments characterized by mobility, bursty event-driven traffic, and limited radio resources. In such settings, conventional medium access solutions are ill-suited to guarantee reliable delivery of critical traffic, e.g., emergency alarms, within strict deadlines, especially when multiple subnetworks become simultaneously active after a common alarm event, a scenario widely referred as medium access with a shared message. This paper proposes a distributed deep reinforcement learning (DRL)-based medium access control protocol for timely alarm transmission in time-critical industrial subnetworks. The proposed method enables each local access point (LAP) to learn, in an online manner, to infer contention conditions from a broadcast contention-signature signal and to autonomously select a transmission pattern over the available channels using a lightweight deep neural network and an (ephsilon)-greedy policy. Simulation results demonstrate that the proposed approach consistently achieves a higher probability of in-time alarm delivery than benchmark random-access schemes, while exhibiting better scalability with increasing network density. For instance, the proposed method improves probability of in-time alarm delivery by at least 7% with a network size of 40 subnetworks, while the gain increases to 21% when the number of subnetworks increases to 60.

This paper studies second-order methods for nonconvex-strongly-convex bilevel optimization. We propose a novel fully second-order bilevel approximation method (FSBA) that achieves an iteration complexity of $\tilde{\mathcal{O}}(ε^{-1.5})$ for finding the $(ε, \mathcal{O}(\sqrtε))$ second-order stationary point of the hyper-objective function. Our results demonstrate that second-order methods can achieve an accelerated convergence rate than first-order methods in bilevel optimization. To address the heavy computational cost associated with the second-order oracle, we introduce a lazy variant of FSBA, called LFSBA, which reuses second-order information across several iterations. We prove that LFSBA exhibits better computational complexity than FSBA by a factor of $\sqrt{d}$, where $d$ is the dimension of the problem. We also apply a similar idea to nonconvex strongly-concave minimax optimization and propose the lazy minimax cubic-regularized Newton (LMCN) method with better computational complexity compared to existing second-order methods.

In this work, we revisit the idea of using an interferometer of pairs of Josephson junctions as a protected rhombus qubit. Unlike in the original proposal, where the qubit states are encoded into odd and even parity charge states, here, we intentionally alter the energy of one of the junctions to investigate the soft version of the rhombus qubit. This approach allows us to directly probe the qubit transitions over several GHz and reduce the potential drawbacks of the interferometer-based protection. Away from a half flux quantum external field, the large shunting capacitors of the circuit ensure localized qubit states in different phase valleys, leading to a biased-noise qubit. In the realized circuit, we measure an average $T_1\approx500\,μ$s relaxation time in the biased-noise regime (with a Ramsey dephasing time of $T^{R}_φ\approx90\,$ns), while an average $T_1\approx27\,μ$s relaxation time at frustration (with $T^{R}_φ\approx670\,$ns). Our loss analysis on this multi-mode circuit indicates that at low frequencies, flux noise and quasiparticle tunneling limit the relaxation times, pointing toward the presence of an optimal operating regime of around a few GHz.

We construct the full edge scaling limit of the singular values of Brownian motion on the general linear group $\mathsf{GL}_N(\mathbb{C})$ starting from general conditions. We show that the limiting paths solve an infinite system of SDE with log-interaction and have a Gibbs resampling property with exponential Brownian bridges. Moreover, we show that the evolution of the limiting rescaled reverse characteristic polynomial solves a stochastic partial differential equation with a non-linear multiplicative noise and linear drift. From a special initial condition the resulting line ensemble coincides, in logarithmic coordinates, with a line ensemble constructed by Ahn which arises as a universal scaling limit of singular values of products of random matrices. We prove some analogous results on the evolution of limiting characteristic polynomials for two models whose stationary measures are given by the Hua-Pickrell and Bessel stochastic zeta functions respectively.

The Baikal-GVD neutrino telescope is the largest neutrino detector of its kind in the Northern Hemisphere. Muons produced in neutrino interaction in the vicinity of the detector leave track-like response in the detector allowing to reconstruct the neutrino arrival direction with the precision up to 0.2 degree. The Baikal-GVD collaboration has developed a variety of methods for the track-like event analysis. Methods for track-like event direction and energy reconstruction and neutrino cadidate event selection are discussed in this report. Preliminary results of application of analysis pipeline to the data-taking seasons from 2019 to 2021 are shown.

We investigate the presence of memory in the sequential measurement statistics of an open quantum system, as witnessed by the departure from the quantum regression theorem (QRT), that is, the possibility to predict multitime probabilities from the one-time reduced dynamical map. For factorized initial states, we identify an exact decomposition of the two-time propagator into a QRT-like contribution, fully determined by the reduced dynamical map, and a memory term encoding system--environment correlations across the intervention; in the weak-coupling regime, the memory term yields an explicit second-order correction expressed in terms of the reduced map and bath correlation functions. Furthermore, we introduce an operational quantifier of QRT violations based on the distance between exact and QRT-predicted joint probabilities. Benchmarking the framework on a spin--boson model and using a pseudomode embedding as nonperturbative reference, we comprehensively analyze the impact of spectral-density parameters, environmental temperature, and measurement protocols on the non-Markovianity of the multitime statistics. Comparison with a one-time quantifier shows that reduced-state non-Markovianity and multitime memory are related but inequivalent: the latter, as probed through sequential statistics, is intrinsically protocol dependent and can become visible at higher temporal order even when two-time statistics remain compatible with QRT predictions.

The optimal control of passive systems in equilibrium typically favours quasistatic (infinite-time) protocols. We show that a breakdown of quasistatic optimality occurs when the controller itself is dissipative. Concretely, we study a Brownian particle confined by a harmonic trap with stochastically fluctuating stiffness, driven by an external protocol. When these fluctuations violate detailed balance, the probe-controller coupling continuously exchanges work with the system, altering the optimisation landscape. In this regime, optimal protocols are characterised by a finite duration which vanishes above a critical fluctuation strength. This transition can be directly observed in a short-time expansion of the mean work functional. When imposing an endpoint constraint, the transition to zero duration disappears and finite duration protocols remain optimal for all values of the controller fluctuations. These results demonstrate that finite-time optimality can emerge in passive systems under nonequilibrium control.

Large language models (LLMs) show strong performance across many applications, but their ability to memorize and potentially reveal training data raises serious privacy concerns. We introduce the PopQuiz Attack, a black-box membership inference attack that tests whether a model can recall specific training examples. The core idea is to turn target data into quiz-style multiple-choice questions and infer membership from the model's answers. Across six widely used LLMs (GPT-3.5, GPT-4o, LLaMA2-7b, LLaMA2-13b, Mistral-7b, and Vicuna-7b) and four datasets, our method achieves an average ROC-AUC of 0.873 and outperforms existing approaches by 20.6%. We further analyze factors affecting attack success, including query complexity, data type, data structure, and training settings. We also evaluate instruction-based, filter-based, and differential privacy-based defenses, which reduce performance but do not eliminate the risk. Our results highlight persistent privacy vulnerabilities in modern LLMs.

We investigate the electronic phases of an effective Hubbard model on the body-centered-cubic lattice, motivated by alkali-doped fulleride molecular solids. The model incorporates renormalized on-site interactions and an effective inverted Hund's coupling originating from electron-phonon interactions. To access complementary interaction regimes, we employ two theoretical approaches. In the intermediate-coupling regime, the on-site repulsive interaction is approximated by a long-range interaction in momentum space, yielding an exactly solvable Hatsugai-Kohmoto model supplemented by a BCS-type pairing term. Within this framework, we analyze the superconducting instability and demonstrate a first-order normal-superconducting phase transition, characterized by a discontinuous jump of the order parameter. In the strong-coupling regime, where pairing fluctuations are suppressed, we apply the spin rotationally invariant slave-boson formalism to map out the temperature-interaction phase diagram. This analysis reveals first-order transitions between a Fermi-liquid phase, an antiferromagnetic phase, and a Mott insulating phase, with a narrow intermediate region where all three phases compete. The resulting phase diagram captures the interplay of itinerancy, magnetic order, and Mott localization in three dimensions and provides a unified perspective on superconducting and correlation-driven phenomena in fulleride-inspired lattice systems.

Brain-DNN alignment is usually assessed through stimulus-level correspondence or stimulus-set geometry. Inspired by category theory, we operationalize a different question: do brain and model preserve the same candidate transformations among stimuli? We formalize this as approximate naturality: if a proxy-defined stimulus change is propagated through the brain side and then translated to the model side, the result should match translating first and then propagating, so that the naturality square approximately commutes. We quantify deviations from commutativity by a Naturality Violation Score (NVS) normalized to a permutation null, shifting alignment from per-stimulus sameness to preservation of structure under an explicitly chosen comparison map. As a proof of concept, a controlled five-factor synthetic setting shows that NVS separates complementary alignment failures that aggregate object- and geometry-level scalars cannot resolve. Applied to fMRI responses from the GOD dataset (5 subjects), 3 vision DNNs, and 3 World-Model proxy embeddings, the axis-resolved analysis reveals a hierarchy crossover: semantic axes align most strongly toward HVC and deeper DNN layers (NVS^animacy = 0.39 vs 0.52 for the next-best axis and 1.0 for the permutation-null baseline), whereas low- and mid-level visual axes align toward earlier visual cortex and shallower layers. Supporting analyses (a 15-axis appendix atlas, dissociation tests against RSA/CKA and encoding/decoding accuracy, and a W-less anchor-ablation control) confirm that the alignment is selective over candidate morphism families rather than uniform. NVS thereby turns brain-DNN comparison into a test of jointly preserved candidate transformations, relative to an explicit proxy space and permutation null, and opens a path to richer proxy spaces and controlled world-side transformations.

Accurate terminal-voltage prediction underpins model-based battery management, yet low-order equivalent-circuit models (\ecm{}) lack expressiveness under transient conditions, whereas purely data-driven predictors sacrifice interpretability and may degrade under operating-condition shift. This paper introduces a residual-corrected hybrid formulation in which a first-order Thevenin \ecm{} (\ecmrc{}) provides the dominant voltage structure, and a compact neural network embedded as a universal differential equation (\ude{}) corrects only the latent polarization mismatch. The \ecmrc{} parameters identified by nonlinear least squares warm-start the hybrid model so that the learned component operates in a low-residual regime. Experiments on a public Panasonic 18650PF dataset compare the proposed \ecmude{} with standalone \ecmrc{} and Long Short-Term Memory (\lstm{}) baselines across four axes: matched-condition prediction on UDDS at \SI{25}{\celsius}, inference-time perturbation of the supplied state-of-charge (\SOC{}, denoted $z$) input, zero-shot temperature transfer (\SI{25}{\celsius} to \SI{-20}{\celsius}), and zero-shot drive-cycle transfer to US06, LA92, and HWFET. The proposed \ecmude{} achieves the lowest voltage error in every setting, reducing mean absolute error (\mae{}) by 48\% relative to the \lstm{} under matched conditions and showing an order-of-magnitude lower inter-seed variability (coefficient of variation: 0.44\% vs.\ 6.20\%). Substantial gains persist under challenging distribution shifts, indicating that the physical model anchors prediction where a purely learned model is most vulnerable. These results position residual-corrected \ecmude{} as a lightweight and interpretable enhancement of low-order circuit models for voltage prediction in battery management systems (\bms{}).

Non-radial oscillation modes of neutron stars serve as diagnostics of their internal composition and relativistic structure. In this work, we investigate the perturbations of static and spherically symmetric neutron stars characterized by an anisotropic pressure. Given the background symmetry, perturbations decouple into polar and axial modes. To date, axial modes have remained less explored, primarily because matter and metric perturbations decouple in the isotropic limit. In this work, we provide a consistent treatment of axial modes and demonstrate that pressure anisotropy induces a direct coupling between matter and metric perturbations. We employ parameterized anisotropy models that ensure consistency with the treatment of matter perturbations. We numerically integrate the linearized Einstein field equations for the axial modes, employing a diverse set of realistic equations of state. Our results indicate that as the stellar mass grows, the frequency of the lower $w$-mode generally decreases, while its damping time increases. Softer equation of states typically yield slightly higher oscillation frequencies. Furthermore, larger anisotropy (i.e., when the tangential pressure exceeds the radial pressure) allows for more massive equilibrium configurations, which correspondingly leads to lower oscillation frequencies and prolonged damping times. Finally, we demonstrate that the frequency and damping time, both scaled by the stellar mass, exhibit a nearly universal quadratic dependence on the stellar compactness, remaining largely insensitive to both the underlying equation of state and the specific anisotropy model.

We study the minimax estimation of covariance eigenfunctions and eigenvalues in functional principal component analysis when $n$ trajectories are observed at $p$ common grid points with additive noise. We consider covariance kernels with arbitrary Hölder smoothness and no prescribed parametric decay of the eigenvalues. In this setting, kernel smoothness and local spectral separation play distinct roles: a minimax inconsistency result over the smoothness-only class shows that kernel regularity alone is not sufficient for minimax-consistent eigenfunction estimation. To capture this interplay, we introduce a class of processes that jointly controls the Hölder smoothness of the covariance kernel and a local relative inverse eigengap quantity at the target index $\ell$. Over this class, we derive non-asymptotic minimax lower bounds for eigenfunction estimation that disentangle sampling variability, discretization and spectral effects, revealing rates of order $δ_\ell n^{-1}+p^{-2α}$, where $δ_\ell$ quantifies the spectral difficulty. We also obtain non-asymptotic lower bounds for eigenvalue estimation under a relative squared-error loss. We then construct a computable wavelet projection estimator based on Coiflet scaling functions and a quadrature scheme designed to accommodate arbitrary Hölder smoothness. For eigenfunction estimation, this estimator matches the minimax dependence on the sample size and grid resolution, up to the natural spectral factor, for any Hölder index $α>0$. Finally, we show that the proposed framework covers several classical Gaussian processes and Karhunen--Loève constructions. In particular, a Karhunen--Loève based criterion links spectral decay, eigenfunction regularity and covariance-kernel smoothness, and yields controlled simulation settings illustrating the predicted phase transitions and least-favourable discretization effects.

Quantum linear-system algorithms (QLSAs) have rigorous worst-case complexity guarantees, but their runtimes are often chosen from spectral information assumed in advance. What is largely lacking is an a posteriori progress flag: most QLSA workflows, unlike the classical counterparts, do not provide a built-in mechanism to signal whether a particular instance has already converged. For discretizations of elliptic PDEs $-\nabla\cdot(a(x)\nabla u(x))=f(x),$ with divergence--gradient structure \[ -\nabla\cdot \big(a(x)\nabla) \approx A_h=G_h^\dagger G_h, \] we formulate a stable first-order ODE whose limiting solution block is the desired Galerkin solution. The PDE-dependent scale is then \(\norm{G_h}=\bigO(h^{-1})\), comparable to factorized QLSA constructions with square-root condition-number scaling. We design an augmented dynamics with residual variables, in which measuring a residual register gives an on-the-fly convergence indicator without reconstructing the solution vector. For smooth right-hand sides, dynamic stopping can reduce the evolution time and gate count relative to a fixed worst-case schedule, and may also reduce exposure to accumulated hardware errors. Numerical experiments for a two-dimensional finite element Poisson problem show that the residual-register probability follows the actual error decay and, for some right-hand sides, can stop the quantum circuit well before a conservative worst-case runtime estimate is reached.

The leading Generalized Transverse Momentum Dependent parton distributions (GTMDs) are studied in the bag model. The model description is shown to be theoretically consistent. The orbital angular momentum is studied in terms of the GTMD $F_{1,4}^q$ and Ji sum rule. Analytical proofs of the associated sum rules are given. A deeper relationship between orbital angular momentum and the pretzelosity TMD is established in this model.

Global food security depends on tightly coupled international supply chains including natural gas, mineral fertilizers, and staple crops. Earlier research has examined potential consequences of disruptions in each of these domains separately but not from a systemic perspective. Here we integrate bilateral trade in natural gas, nitrogen, phosphorus and potassium fertilizers, and eleven staple crops accounting for approximately 70% of plant-based calories into a cascading-impact model spanning 208 countries, 20 geopolitical blocs, and the period 1992-2023. Under complete trade isolation, up to 22% of global caloric consumption would be lost, with a peak in the most recent evaluated years. Structural vulnerabilities vary greatly. Regions largely lacking some parts of the supply chain face near-total crop supply collapse, while few countries can cover the whole nexus through domestic resource endowments and production capacities. Temporal trends highlight a substantial increase in vulnerability globally, most prominently in the EU with a near two-fold increase since the 1990s. Market power is most concentrated and most volatile in the upstream gas and mineral-fertilizer layers, from which shocks propagate downstream. Food stocks provide only limited resilience with half of humanity living in countries disposing of stock lasting less than three months. Our results identify the upstream supply chains as the structural bottlenecks of the global agrifood system and propose leverage points to enhance resilience.

We study the large-$c$ expansion of general relativity in ADM variables. Using a unified even $ω$-expansion, the ADM formulation gives a common starting point for Galilean and Carrollian limits. We focus on the Galilean branch and derive the ADM action and field equations up to NNLO. We then construct stationary vacuum solutions in weak and strong branches. In the weak branch, we find NLO Kerr-type, Hartle-Thorne-type and mixed-type solutions. The NLO weak equations also allow a simple extension to higher mass multipoles. At NNLO, the weak Kerr-type and extended Hartle-Thorne-type sectors solve the equations separately, but their naive sum is not a solution. The nonlinear NNLO equations generate mixed $J^2Q$ source terms, which require additional corrections to the NNLO lapse and NNLO spatial tensor field. This gives a mixed weak-branch Galilean solution in the ADM gauge. In the strong branch, Kerr-type data solve the equations through NNLO while the strong Hartle-Thorne-type data solve the NLO equations. We also explain how the ADM data can be reconstructed into approximate spacetime metrics. Since these metrics include spin, quadrupole and mixed spin-quadrupole effects, they may be useful for studying the spacetime around rotating compact objects such as black holes and neutron stars.

In this paper we address the existence and uniqueness of entire spacelike hypersurfaces in the Lorentz--Minkowski space $\mathbb{L}^{m+1}$ with prescribed mean curvature that are star-shaped with respect to a point and asymptotic to a light cone. We also establish a Willmore-type inequality and prove a non-existence result for spacelike radial graphs asymptotic to the light cone whose mean curvature belongs to $L^p$ for $1 \leq p\leq m$, in particular in the case of compactly supported mean curvature.

Voronoi diagrams, and their more general weighted counterpart, power diagrams, are fundamental geometric constructs with wide-ranging applications. Recently, they have gained renewed attention in mesh-based neural rendering. Despite being extensively studied, the construction of 3D Voronoi diagrams for large-scale point sets remains computationally expensive, limiting their adoption in large-scale applications. Existing CPU-based approaches typically rely on computing its dual, the Delaunay tetrahedralization, but are prohibitively slow for large diagrams, while GPU-based methods either struggle to scale efficiently to large point sets or assume homogeneous point distributions. The weighted case, power diagrams, is even less explored in this context. Existing approaches are typically tailored to the application at hand, assuming homogeneous point distributions and small weight variations, making them unsuitable for general use in more complex heterogeneous data. In this paper, we present a highly parallelizable GPU algorithm for the fast construction of large-scale 3D Voronoi and power diagrams. Our approach constructs each convex cell from a weighted 3D point by progressively clipping an initial cell volume against bisecting planes induced by candidate neighboring points. To efficiently identify candidate neighbors under arbitrary spatial distributions, we introduce a culling criterion based on directional geometric bounds of the evolving cell, combined with a hierarchical best-first traversal of bounding volumes. We achieve performance on par with state-of-the-art Delaunay tetrahedralization methods on small and moderate problem sizes, while exhibiting robust scalability to large point sets and diverse spatial distributions. Moreover, our method naturally generalizes to power diagrams without additional assumptions. See https://research.zenseact.com/publications/paragram .

We present Very Large Telescope/Xshooter spectrophotometric observations of eleven low-redshift (z<0.085) compact star-forming galaxies (`high O32 sample'). These galaxies are characterised by extremely high emission-line ratios [OIII]$λ$5007/[OII]3727, ranging from 11 to 42. Galaxies with such high ratios are thought to be promising candidates for leaking large amounts of Lyman continuum radiation. They are characterized by low oxygen abundances 12+log(O/H)\,=7.5-8.0 and low stellar masses M*~10^6-10^8 Msun. Strong emission lines of various ions in all spectra are used to derive helium and oxygen abundances, and N/O, Ne/O, S/O, Cl/O, Ar/O and Fe/O abundance ratios. We also derived macroscopic velocity dispersions sigma(lambda) from various emission lines of different ions. We find that sigma(4861) of the Hbeta emission line is increased with increasing stellar mass and decreasing O32 ratio. On the other hand, sigma(lambda)/sigma(4861) ratios for various lines are close to 1. Exceptions are sigma(lambda)/sigma(4861) of two lines, HeII 4686 and HeI 10830, which are considerably higher than unity and of four lines, [OII] 3726,3729, [SII] 6717,6731, with sigma(lambda)/sigma(4861) lower than unity. The two former lines are likely produced in the inner parts of HII regions and are broadened by dynamical processes generated by massive stars, and by radiative scattering in the case of the HeI 10830 emission line. Emission in the four latter lines is produced mainly in the outer and likely more quiet parts of HII regions.

This paper studies optimal liquidity provision for perpetual contracts when the funding rate is a stochastic state variable. The core extension to classical market making is the coupling between inventory and funding payments: inventory creates both mark-to-market exposure and a state-dependent funding cash flow. A reduced inventory-funding control problem is formulated, solved with a monotone finite-difference Hamilton-Jacobi-Bellman scheme, and bid and ask quote offsets are recovered from discrete inventory value differences. Funding is calibrated on Hyperliquid ETH, BTC, and SOL perpetual data. Gaussian OU funding is retained as a tractable diffusion baseline, while OU-plus-jump diagnostics document the heavy-tailed funding innovations that should enter a future extension. In 100-seed holdout simulations under two official-fill proxy calibrations, the funding-aware HJB improves mean ETH/BTC performance while lowering inventory RMS relative to classical Avellaneda-Stoikov. SOL gains are positive versus unscaled AS but are not a Pareto improvement once a risk-scaled AS diagnostic is included.

The interpretation of the SN1987A neutrino data continues to be hindered by significant absolute timing uncertainties and a well-known tension in the angular distributions. We perform a quantitative, high-precision alignment of the Kamiokande-II and Baksan data with the IMB clock, using for the first time the relative time offset (RTO) and reducing the temporal uncertainty by two orders of magnitude to the sub-second level. The chi-square analysis shows that Baksan's absolute timestamps require an advancement of 30.4 s, while those of Kamiokande-II require a delay of about 6.4 s. The knowledge of the unified timeline provides a necessary and rigorous basis for testing whether the first Kamiokande-II event arose from the neutronization burst - a possibility motivated by its angular properties. Our analysis favors an accretion phase electron anti-neutrino origin over a neutronization-burst origin, with a likelihood ratio of 3-6, depending on the specific MSW oscillation scenario. This result corroborates the standard interpretation - that only inverse beta decay events were detected. Our framework yields the most stringent constraints to date on the SN1987A chronology and establishes a precision benchmark for future Galactic supernova observations.

The third data release of the LOFAR Two-metre Sky Survey provides an unprecedented view of the northern sky at 144 MHz. While compact sources can be efficiently identified with automated software packages, the detection of diffuse radio emission associated with galaxy clusters still requires dedicated processing and visual inspection. Given the scale of current and forthcoming radio surveys, automated approaches based on artificial intelligence are becoming essential to the identification of the most interesting targets. We aim to develop an automated pipeline to construct a catalogue of galaxy clusters hosting diffuse radio emission from LoTSS-DR3 20arcsec images. The pipeline is designed to provide both the probability that a cluster hosts diffuse radio emission and an interpretable image of its shape and morphology. We employed Radio U-Net, a convolutional neural network optimised for image segmentation (i.e. pixel-level identification) of diffuse radio emission. To associate detected emission with individual clusters, we combined the network output with positional, mass, and redshift information from four X-ray- and Sunyaev-Zeldovich-selected cluster catalogues, resulting in a merged sample of 3822 clusters covered by the LoTSS-DR3. We produced a pixel-level segmentation map of the full LoTSS-DR3 and a quantitative indicator for the presence of diffuse emission in each cluster. This enables the selection of sub-samples with specific properties for targeted follow-up or statistical studies. As a demonstration of the first application, we identified a sub-sample of 357 clusters selected at the highest network accuracy (76%), and we showed some examples of newly detected systems. For the second, using a larger statistical sample, we verified that the detection fraction of diffuse radio sources in the four catalogues increases with the mass and redshift of the clusters. [Abridged]