In this paper, we study the shortest $t$-dimensional hull embeddings of linear codes in both Euclidean and Hermitian cases, extending the existing research on the shortest LCD and self-orthogonal embeddings to arbitrary hull dimensions and arbitrary finite fields. We obtain the exact length of such embeddings by adopting tools from quadratic form theory over finite fields and classical group theory. Based on the congruence equivalence class of Gram matrices of linear codes, we classify linear codes into distinct ``types'' and present corresponding constructive algorithms. In particular, we improve the results of An et al. and fully determine the length of the shortest self-orthogonal embeddings for linear codes. Finally, applying these algorithms, we provide examples for various settings and obtain several optimal codes inequivalent to those in the BKLC database.

We present a validation of our recently proposed non-conventional method, Constant Acceleration Accounted Perspective (CAAP), for estimating the instantaneous expansion speed of coronal mass ejection (CMEs), even when only single-point in situ observations are available. This validation is enabled by the radial alignment of SolO and Wind spacecraft (0.13 AU radial and 2.3 deg angular separation), providing simultaneous observations of the center (at Wind) and trailing edge (at SolO) of a CME associated magnetic cloud (MC) during 3-5 November 2021, allowing a direct measurement of its instantaneous expansion speed. These measurements are compared with CAAP-derived instantaneous expansion speed estimates at both spacecraft. The favorable spacecraft configuration also enables tracking the temporal evolution of CME substructures, including the shock, sheath, and MC. A discrepancy is noted between the low-inclination MC axis estimated from minimum variance analysis (MVA) and the highly inclined ENW-type MC axis suggested by visual inspection of in situ measurements. We also observe an apparent increase in the magnetic flux within the MC from SolO to Wind, indicating a noticeable deviation from magnetic flux conservation. During the CME's propagation from SolO to Wind, the shock becomes unexpectedly stronger at Wind, while the sheath thickness remains nearly the same, likely due to MC acceleration from back compression by a high-speed stream and ambient solar wind variability. Our results demonstrate the applicability of the CAAP method and the importance of accounting for temporal evolution in CME substructures for space weather studies.

The hadron--quark crossover equation of state (EOS) of neutron star (NS) matter is investigated by combining relativistic mean-field (RMF) hadronic models with the Nambu--Jona-Lasinio (NJL) model for quark matter. The vector and diquark coupling constants of the NJL model are constrained using perturbative QCD (pQCD) calculations at high density through a scale-averaging likelihood approach, together with constraints from NS observations and the causality condition on the speed of sound. It is found that the diquark coupling is tightly constrained to $H \simeq 1.5G_s$, while the vector coupling is restricted to $G_v \lesssim 1.1G_s$ by the combined pQCD and astrophysical constraints. Crossover EOSs are constructed based on three hadronic RMF parameter sets, and their thermodynamic properties, sound speed behaviour, and trace anomaly are analysed. The resulting EOSs are applied to calculate NS global and dynamical properties, including mass--radius relations, tidal deformabilities, and fundamental radial oscillation frequencies. Compared with pure hadronic EOSs, the hadron--quark crossover is shown to significantly enhance the maximum NS mass, particularly for softer hadronic EOSs, while remaining consistent with observational bounds. It is further shown that the fundamental radial oscillation frequencies predicted by different EOSs exhibit pronounced differences, especially for intermediate-mass NSs, indicating that radial modes may provide a sensitive probe of the internal composition of NSs. These results indicate that quantitative NS observables may provide potential signatures of quark matter in NS interiors.

This paper proposes a mathematical model for the coevolution of actions and opinions for a population facing a social dilemma. In particular, we assume each person participates in a Public Goods Game (PGG), with their action being to cooperate or defect, and holds an opinion about which action they prefer. We propose a payoff function that combines the PGG with the Friedkin--Johnsen model from opinion dynamics to form a coevolutionary game. According to a discrete-time process, players asynchronously update their actions and opinions, aiming to maximise their individual payoff for the coevolutionary game using myopic best-response. We study the equilibria and provide conditions for the existence of the all-defection and all-cooperation consensus equilibria. We also establish conditions for global convergence to the all-defection equilibrium.

We establish two identities for Lambert series and double Lambert series, thereby resolving conjectures of Andrews, Dixit, Schultz and Yee (Acta Arith.~181:253--286, 2017), as well as Amdeberhan, Andrews and Ballantine (J Combin Theory Series A 221:106154, 2026). The proofs are based on classical transformations in the theory of infinite series together with a systematic rearrangement of double Lambert series.

In this paper we propose a new criterion for the Blind Source Separation (BSS) of antisparse bounded sources, based on the sum of the $\ell_\infty$-norm of the sources. Based on the observation that the mixing process of bounded sources with any mixing matrix with unitary Frobenius norm will increase the $\ell_\infty$-norm of the sources, unless it is the identity matrix, the minimization of the sum of the $\ell_\infty$-norm of the sources can be used for the estimation of a separation matrix. To that, a Principle Component Analysis technique followed by a Givens Rotations based optimization method can be used for the separation of independent bounded sources. Also, the Givens Rotations based optimization method can be used for the separation of correlated bounded sources mixed by a rotation matrix. We theoretically analyze the proposed criterion and assess its performance through numerical simulations involving three distinct types of bounded signals. Our theoretical and experimental findings underscore the efficacy of the $\ell_\infty$ norm as a suitable contrast function for antisparse bounded sources, showcasing its superior performance relative to a state-of-the-art algorithm.

High-resolution three-dimensional imaging under photon-starved conditions remains challenging. Here, we demonstrate a high-resolution long-range 3D single-photon imaging system based on a digital micromirror device (DMD) and a compact 64 multiply 64 single-photon avalanche diode (SPAD) array. By combining high-resolution spatial modulation with parallel time-resolved detection, the system extends the effective spatial sampling beyond the native detector format while preserving depth information through time-of-flight measurement. In outdoor experiments at a stand-off distance of 670 m, we achieved 3D reconstruction of natural targets with an effective spatial resolution of 256 multiply 256. These results validate the proposed method as an effective approach for high-resolution long-range 3D single-photon imaging using compact SPAD arrays.

Reasoning-intensive retrieval requires deep semantic inference beyond surface-level keyword matching, posing a challenge for current LLM-based rerankers limited by context constraints and order sensitivity. We propose \textbf{\BracketRank}, a framework that treats document reranking as a reasoning-driven competitive tournament. Our approach introduces three key innovations: (1) adaptive grouping based on model context limits, (2) reasoning-enhanced prompts that mandate step-by-step relevance explanations, and (3) a bracket-style elimination structure with winner and loser tracks. This design ensures robust document advancement while enabling parallel processing across competition stages. Evaluation on the BRIGHT reasoning benchmark shows that \BracketRank achieves \textbf{26.56 nDCG@10}, significantly outperforming state-of-the-art baselines including RankGPT-4 (17.0) and Rank-R1-14B (20.5). On TREC datasets, BracketRank achieves 77.90 nDCG@5 on DL 19 and 75.85 nDCG@5 on DL 20, exceeding all baselines, establishing that explicit reasoning within competitive elimination is a powerful paradigm for complex, multi-step retrieval tasks. https://github.com/DataScienceUIBK/BracketRank

Four axioms of immutable ledger, linear consent, payment irreversibility, and bounded credit manifest themselves as institutional facts codified by banking practice for the transfer of monetary value. These axioms certify the independence of 14 empirically observed and jurisdictionally invariant dimensions. Morphisms of the ambient category do not admit sections that would reconstruct one dimension from another, and every morphism admits epi-mono factorisation through the universal quotient Q_public. This factorisation is forced by definite causal order under classical realisation and echoes the factorisation theorem of Gogioso et al. Gaussian elimination across 4,590 endpoints from BIAN, CDR, and OBIE confirms rank 14 and witnesses the jurisdictional invariance of the quotient object. The axioms similarly constrain the monoidal structure. The information dominance preorder is a thin category; all five Szlachanyi conditions follow, establishing that Q_public carries left skew monoidal structure.

The Hayabusa2 extended mission, nicknamed Hayabusa2# (# is pronounced SHARP, which stands for the Small Hazardous Asteroid Reconnaissance Probe), is JAXA's small body explorer to conduct science and engineering investigations in space. After the successful return to the Earth with the samples from the carbonaceous asteroid (162173) Ryugu on December 6, 2020, Hayabusa2 diverted away from Earth to start its decade-long extended mission. The major scope includes engineering demonstration of long-term maintenance strategies for spacecraft and operation systems and scientific investigations during various mission phases. Major scientific investigations include spacecraft-based telescopic observations of exoplanets and zodiacal dust observations during the cruise phase, flyby observations of the near-Earth asteroid (98943) Torifune in July 2026, and rendezvous observations of near-Earth asteroid 1998 KY26 in 2031. This study overviews Hayabusa2#'s flyby and the physical properties of Torifune. Although the flyby operation planning is still ongoing, the mission will attempt to fly by the target at a distance (from the asteroid's center) of ~1-10 km. The flyby speed is planned to be 5.25 km/s, while the encounter location is 0.81 au from the sun. The mission plans to fix the spacecraft's orientation during the flyby, only allowing for a very limited pointing change to attain higher resolution imaging. The mission will attempt to obtain science and engineering returns during the flyby. The planned investigations will offer stronger insights into material transport mechanisms in the inner solar system and a demonstration of planetary defense technologies.

Safety-critical control systems, such as spacecraft performing proximity operations, must provide formal safety guarantees despite stochastic uncertainties from state estimation and unmodeled dynamics. Although Control Barrier Functions (CBFs) have been extended to stochastic systems, existing approaches typically face a trade-off between the tightness of probabilistic guarantees and computational tractability. This paper presents a particle-based probabilistic CBF framework that overcomes this limitation by exploiting the sub-Gaussian structure of the barrier function increment under Gaussian uncertainties. We establish that Gaussian uncertainties propagating through Lipschitz-continuous control-affine dynamics preserve sub-Gaussianity of the barrier function increment, with explicit tail bounds. Leveraging this structure, we derive finite-sample bounds on the approximation error between particle-based Conditional Value at Risk (CVaR) estimates and ground-truth probabilistic constraints; applying this yields a tractable optimization problem formulation with finite-sample safety certificates. We show through numerical experiments how the proposed approach provides tight yet provably valid probabilistic safety guarantees.

The present study investigated the formation of streamwise streaks in underexpanded jets from round sonic nozzles, based on direct experimental observation using high-speed schlieren imaging and PLIF methods. The effect of geometric perturbations of the nozzle exit on the streamwise flow structure was examined through a series of comparative experiments. Underexpanded jets were generated in a vacuum chamber using phi-4 mm nozzles of two different configurations: (a) a "smooth" nozzle, shaped and polished by a high-quality commercial lathe machine; and (b) nozzles with artificially introduced sinusoidal perturbation of various wavenumbers on the circular contour of the exit. In the case of the "smooth" nozzle, experiments were repeated following a 60-degree rotation of the nozzle along its axis, and a similar rotation in the streak patterns was observed. This suggests that the streamwise streaks most likely originated from geometric perturbations caused by the minute roughness at the nozzle exit. In the latter case, the effects of modal distribution of geometric perturbation on the streaks were further investigated. The results showed that the low-wavenumber (k < 5) perturbations exhibited much smaller growth rates of streamwise streaks - likely dominated by residual roughness similar to the "smooth" case - compared to higher-wavenumber (k = 6 and 7) perturbations, where the streak patterns were observed to correlate geometrically with the perturbed nozzle exit contour. Results from the present study should prove useful in enhancing the current understanding of noise patterns in supersonic wind tunnel tests, where nozzles are critical components.

Machine learning models and their applications, such as autonomous driving systems, are becoming increasingly common and are essential components of human daily life. However, due to their sensitivity to perturbed noise, these models are easily susceptible to adversarial attacks. Not only are classical machine learning models affected, but quantum machine learning (QML) models have also been proven to be vulnerable to adversarial attacks, which degrade their performance. To defend against these types of attacks, several classical methods have been proposed. Among these, a prominent approach uses various types of pseudo-noise during training to enhance the model's robustness against real-world attacks. One of the recently emerging solutions is to leverage the unique properties of quantum circuits to create quantum-based pseudo-noise similar to real perturbed noise to counter adversarial attacks. This paper proposes a solution that utilizes random quantum circuits (RQCs) as adversarial data to help QML models overcome these adversarial attacks. The results reported in this paper show that the data generated by RQC actually provides a similar effect to models trained with adversarial data on high-feature datasets. This quantum-based pseudo-noise resulted in a significant reduction in the attack rate in the CIFAR-10 data set, from \textbf{89. 8\%} to \textbf{68.45\%}. For the CINIC-10 dataset, the successful attack rate decreased from \textbf{94.23\%} to \textbf{78.68\%}. This research opens up avenues for applying unique quantum properties, such as superposition, entanglement, and even decoherence, to enhance the quality of machine learning models.

This study investigates the transmission of monetary policy narratives to Bitcoin prices, distinguishing the impact of ex-ante expectations from ex-post interest rate implementation. We introduce a high-frequency Monetary Policy Expectations (MPE) index, using a Large Language Model (LLM)-based classification of 118,000+ market messages to achieve a precise hawkish/dovish decomposition. Results from a framework combining Long Short-Term Memory (LSTM) networks with SHapley Additive exPlanations (SHAP) indicate that Bitcoin functions as a sensitive barometer of central bank signaling; specifically, hawkish narratives consistently trigger negative price responses independently of actual Federal Funds Rate adjustments. We demonstrate that the MPE index Granger-causes Bitcoin returns at short-to-medium horizons, establishing linear predictive causality, while the LSTM-SHAP framework reveals pronounced non-linear, macroeconomic regime-dependent interactions. These findings highlight Bitcoin's structural sensitivity to global monetary discourse, establishing LLM-derived sentiment as a potent leading macroeconomic indicator for the digital asset landscape.

The method of images (MoI) is a valuable technique for solving certain electrostatic boundary value problems consisting of charge density near conductor(s). We developed and validated an inquiry-based tutorial on MoI to help students learn to identify the problems related to the concept. We implemented the inquiry-based tutorial accompanied by pretest and posttest, across three instructors' classes to evaluate student learning. We also conducted think-aloud interviews with advanced physics students, which helped us gain insights into their problem-solving strategies, evaluate their understanding developed through the tutorial and make necessary refinements to the MoI tutorial. The study identified common student difficulties, which were subsequently integrated into the inquiry-based tutorial as a guide to provide support to students. We found that advanced students have common difficulties related to physics concepts similar to those found in introductory physics courses. The performance difference in the pretest administered after lecture-based instruction and the posttest administered after working through the tutorial reflects students' ability to apply what they learned from the inquiry-based tutorial compared to traditional lecture. Another important and unanticipated finding reveals how instructor's framing about inquiry-based instructional tasks can have a significant impact on student motivation, engagement, and performance. Overall, this iterative multi-year design-based comparative research with mixed-method triangulation provides valuable insights on the challenges involved in such studies that educators and researchers alike can greatly benefit from.

Modern supply chain networks involve spatially distributed flows that become difficult to interpret using traditional visualization techniques, producing visual clutter that obscures actionable patterns. We present a multi-scale visual analytics dashboard that combines Semantic Zooming with Skeleton-Based Edge Bundling (SBEB). The system dynamically adapts its representation based on zoom level: bundled aggregate flows at the macro-scale, hexagonal density heatmaps at the meso-scale, and hierarchical inventory sunbursts at the micro-scale. Built on Vue3 and Deck.gl, it reduces raw orders to 202 warehouse-to-state flows. We contribute (1)a semantic zoom implementation with animated transitions that unifies edge bundling, hexagonal density aggregation, and hierarchical inventory views into a single interface; and (2)an algorithmic adaptation of SBEB for geographic origin-destination flows, introducing directional-sector clustering and adaptive detour constraints to preserve cartographic plausibility.

We study statistical parameter estimation in the setting of data markets. A buyer seeks to estimate a parameter based on samples that can be purchased from competing providers that differ in their data quality and provision costs. When quality is known ex ante, we define a cost-per-information score that summarizes each provider's provision cost per unit of information about the buyer's estimation objective. We describe second-score procurement mechanism that ranks providers by this score, and endogenously chooses both a provider and a sample size while making truthful cost reports optimal. We then turn to the more realistic setting where data quality is private, and can only be indirectly observed via the delivered data. In this setting, we propose a simple mechanism that augments the second-score rule with a lenient ex post statistical test of the reported quality. We prove that under mild conditions, there exists an equilibrium in which sellers report costs truthfully and report quality up to deviations that vanish as the procured sample size grows. Our analysis highlights how the choice of verification test and the buyer's accuracy-cost tradeoff jointly shape participation and misreporting incentives in data markets.

The method of weighted least squares is widely used in parameter estimation problems such as asteroid orbit determination. A key difficulty is the treatment of observational uncertainties, especially when combining heterogeneous datasets with differing precision. We propose a simple reweighting scheme that adjusts the contribution of each measurement group to ensure a statistically consistent least-squares solution. It consists of three steps: (i) estimating error standard deviations for each observational subset, (ii) rescaling their weights by the corresponding variances, and (iii) a weighted least-squares fit with the adjusted weights. We apply this to heliocentric orbit fitting of asteroids using ground-based astrometry and high-precision Gaia measurements. We validated the method by fitting each orbit to a restricted set and comparing with the complete set of measurements. For 7 objects, the reweighted solutions provide significantly improved agreement with older data. The most dramatic case is asteroid (21) Lutetia, where increasing the effective uncertainty of Gaia observations by a factor of 17 yields a substantially better fit, indicating the importance of accounting for systematic biases in high-precision datasets. We further apply the scheme to near-Earth asteroid 2024 YR4, grouping observations by visual magnitude. The reweighted orbit produces smaller uncertainty regions and a more stable solution, reducing predicted impact probabilities by roughly an order of magnitude. All computed probabilities remain below 0.5%, under the 1% International Asteroid Warning Network (IAWN) alert threshold. This reweighting procedure provides a practical way to combine heterogeneous measurements, improving the reliability of orbit determination and impact-risk assessment. The method is general and can be readily applied to other parameter estimation problems involving mixed-precision data.

We prove that a prime Fano threefold of genus 8 over an algebraically closed field of positive characteristic is isomorphic to a linear section of the Grassmannian variety Gr(2, 6). As applications, it is shown that a prime Fano threefold of genus 8 is irrational and, if the characteristic is larger than two, then it is globally F-regular.

We propose a genetic algorithm powered evolution (GAPE) method to create deep learning solutions for energy and position estimation for reactor antineutrino interactions in the Precision Reactor Oscillation and Spectrum Experiment (PROSPECT) at the highly enriched High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory. We also apply GAPE to create classification models to distinguish signatures of inverse beta decay (IBD) interactions of reactor antineutrinos from common background types. The GAPE method can also be adopted for optimization of other types of problems that utilize machine learning (ML) models for particle physics applications. When applied in the PROSPECT context, we find that the models selected by GAPE can, in some cases, outperform the traditional models previously used for PROSPECT data analysis. In particular, when benchmarked against conventional PROSPECT neutrino identification pathways using the same underlying information, the classifier offers the promise of improving the signal-to-background ratio by nearly 2.8 times. Performance biases uncovered during initial IBD classifier validation were primarily caused by differences in time-dependent response between background and signal training datasets. Biases were effectively mitigated through a data-period-specific training regimen, offering a pathway towards realizing an unbiased IBD signal classifier for future reactor neutrino datasets.

Resonators and qubits with a niobium (Nb) base metal layer achieve some of the highest coherence times in superconducting quantum devices. The performance of such devices is often limited by loss associated with two-level systems, which are found primarily at material surfaces and interfaces. The metal-air (MA) interface is a major contributor to device loss. In this work, we develop a fast-sealing microwave cavity that enables devices to be placed under vacuum within five minutes of oxide removal, thereby significantly reducing the MA interface loss compared to common device processing and packaging approaches. Using coplanar stripline resonators, we demonstrate that devices sealed in such a cavity exhibit internal quality factors exceeding one million at single-photon power. After re-exposure to air, the devices show downward resonance frequency shifts and quality factor degradations, quantitatively consistent with a model of Nb oxide regrowth. The fast-sealing microwave cavity provides a practical and consistent method to mitigate MA interface loss and sustain high coherence in Nb devices, and establishes a controlled platform for studying metal oxide regrowth kinetics and dielectric properties, the understanding of which is critical to achieving high coherence in superconducting quantum devices.

Real-time tsunami early warning relies on distributed sensor networks to infer seismic sources and seafloor motion. Optimizing these networks via Bayesian optimal experimental design (OED) is exceptionally challenging for systems governed by hyperbolic partial differential equations, which lack the spectral decay required by standard low-rank approximations. We present a scalable Bayesian OED framework for linear time-invariant systems. By reformulating the inverse problem in the data space, we transform OED into dense matrix subset selection. We propose a multi-GPU, Schur-complement-update-based, greedy algorithm that solves the OED problem using a pipelined approach that fully overlaps I/O with GPU computations. Our framework achieves near-perfect weak and strong scaling across hundreds of GPUs on Perlmutter and Frontier. Applied to the 2025 Gordon Bell Prize-winning digital twin for tsunami forecasting in the Cascadia Subduction Zone, we optimize a 175-sensor network, minimizing the uncertainty of a parameter field with over one billion degrees of freedom.

We present the results of experiments probing the retention of CO2 in crystalline water ice, frozen sodium chloride (NaCl) brines, and flash-frozen carbonated water using diffuse reflectance infrared spectroscopy. Characteristic absorptions alluding to the formation of clathrate hydrates in crystalline ices and frozen brines are observed. NaCl in frozen brines does not affect qualitatively affect the formation of clathrate hydrates. Generation and stability of clathrates in crystalline ice transiently subjected to pressure-temperature (P-T) conditions in the stability region is observed, despite conditions being unviable at the onset of freezing. Retention of CO2 in flash-frozen carbonated water is observed to be dependent on the temperature of the substrate during freezing. The state of CO2 retained in the resulting ices differs from clathrate hydrates, as inferred from the respective infrared spectra. Both mechanisms of CO2 retention are stable up to 140 K and under evacuated conditions. In the context of Europa, the P-T states traversed by the samples plausibly represent the typical conditions around endogenous CO2 if it is indeed transported from the subsurface ocean to the surface while being retained in ice/frozen brines and/or liquid emerging on the surface. However, the absorptions of CO2 in the laboratory infrared spectra do not match those detected on the leading side of Europa by the NIRSpec instrument on board JWST. Therefore, it is unlikely that the endogenous CO2 observed at the surface of Europa is sourced directly from the ocean, unless additional processes affect the observed bands of CO2 on Europa.

Asymptotic properties of discrete, stochastic approximations to hybrid systems, modeled as hybrid inclusions, are studied. First, the internal chain transitivity of omega-limits of solutions is concluded, along with other properties related to chain recurrence and transitivity. A concept of an asymptotic solution is proposed to describe any mapping that, asymptotically, resembles a solution, and for which the chain transitivity properties also turn out to hold. The mentioned developments are carried out in an abstract setting of a generalized hybrid system defined by a set of hybrid curves, each defined on a hybrid time domain, and possibly consisting of all solutions to a given hybrid inclusion. Then, more specific kinds of perturbed solutions to a hybrid inclusion are proposed and shown to include the solutions of a discretization and of a stochastic approximation to the hybrid inclusion. Consequently, appropriate discretizations and stochastic approximations of a hybrid inclusion produce mappings whose omega limits are internally chain transitive for the underlying hybrid inclusion.

We study the Oppenheimer--Snyder (OS) collapse problem in metric $f(R)$ gravity by matching a homogeneous dust Friedmann--Lemaître--Robertson--Walker (FLRW) interior to a generalized Vaidya exterior across a timelike hypersurface. In metric $f(R)$ gravity, regular matching requires the continuity not only of the induced metric and extrinsic curvature, but also of the Ricci scalar and its normal derivative. These additional conditions generically exclude the usual Ricci-flat exteriors, such as the Schwarzschild solution. We show that, for an unrestricted generalized Vaidya exterior, the matching conditions fix the boundary data but do not uniquely determine the bulk extension, leaving open the possibility of a physical resolution of the collapse problem. However, once the exterior matter content is restricted to the generalized Vaidya form, the field equations impose a strong constraint, forcing $f_{,R}$ to be linear in the areal radius, $f_{,R}=A(v)\,r+B(v)$. For locally invertible $f_{,R}$ with $f_{,RR}\neq 0$, this sharply reduces the admissible class of exteriors, so that the matching data uniquely determine the exterior solution on each interval where the boundary map is locally invertible. We further show that, for generic viable $f(R)$ models, the branch with $A(v)\neq 0$ does not admit a global extension with finite asymptotic curvature, while the branch $A(v)=0$ places the interior on a constant-curvature sector. This excludes nontrivial dust collapse, although it does not rule out collapse for more general interior matter with constant trace. Thus, generalized Vaidya exteriors reopen the collapse problem at a formal level, but within the restricted matter sector considered here, the OS dust collapse problem remains unresolved and the physically acceptable branch is highly constrained.

We study identification of a structural group effect when the group indicator $G\in\{0,1\}$ is unobserved but the analyst observes a calibrated probability score $p\in[0,1]$ satisfying $\mathbb{E}[G|p,X]=p$. Under a constant-coefficient structural mean model, the latent-group coefficient $τ$ is point-identified from the joint law of observables $(Y,X,p)$ by a simple ratio of weighted moments: the covariance of the signed score $2p-1$ with the covariate-partialled outcome, divided by twice the residual variance of the score after conditioning on covariates. Identification fails if and only if the score is a deterministic function of $X$; we establish this by constructing an explicit continuum of observationally equivalent models indexed by arbitrary values of $τ$. The identified coefficient differs from the marginal latent mean gap by a compositional term that is unidentified without further assumptions; we give a necessary and sufficient condition for the two to coincide. The oracle estimator is $\sqrt{n}$-consistent and asymptotically normal with a closed-form sandwich variance. Under calibration error bounded uniformly by $δ$, the bias is bounded by $|τ|\,\mathbb{E}[|2p-1|]\,δ\,(2V^*)^{-1}$, a bound that is sharp over all calibration error functions of that magnitude. Hard-threshold classification at $p=1/2$ attenuates the estimated gap by a factor strictly less than one. Monte Carlo experiments confirm the asymptotic theory, trace the divergence of RMSE as $V^*\to 0$, illustrate the attenuation bias of hard-threshold classification, and verify identification of the variance-weighted estimand under heterogeneous effects.

Gravitational-wave detectors are affected by short-duration non-Gaussian noise transients, commonly referred to as glitches, which can obscure astrophysical signals and complicate downstream analyses. While recent work has demonstrated the effectiveness of deep learning models for glitch classification using image-based time-frequency representations, comparatively less attention has been given to systematic evaluations of machine-learning architectures operating directly on tabular glitch metadata. In this work, we present a comprehensive benchmark of classical and deep learning models for multiclass glitch classification using numerical features derived from the Gravity Spy dataset. We compare gradient-boosted decision trees with a diverse set of neural architectures, including multilayer perceptrons, attention-based models, and neural decision ensembles, and evaluate them in terms of classification performance, inference efficiency, parameter efficiency, data-scaling behavior, and cross-model interpretability alignment. We find that while tree-based methods remain strong baselines for tabular data, several deep learning models achieve competitive performance with substantially fewer parameters and exhibit distinct inductive biases and scaling behavior. A cross-model attribution analysis further reveals partially consistent feature-importance hierarchies across architectures, providing new insight into interpretability structure in tabular models. These results clarify trade-offs between performance, complexity, data efficiency, and interpretability in tabular gravitational-wave analyses and provide practical guidance for deploying machine-learning models in detector characterization pipelines.

We introduce a dynamical analogue of the lifting problem for Galois covers of algebraic curves and find a negative solution for the collection of additive, separable polynomials over $\overline{\mathbb{F}}_p$. We also explicitly compute the dimension of the space of linear conjugacy classes in $M_{p^m}(\overline{\mathbb{F}}_p)$ which contain an additive, separable polynomial.

Many bipartite networks exhibit hierarchical community structure, but existing community detection methods are not well-suited for detecting hierarchy. They also do not effectively handle weighted bipartite networks. In this work, we introduce a novel modularity-based objective function, called the generalized bipartite modularity density, Qbg, specifically designed for hierarchical community detection in bipartite systems. The framework incorporates a tunable resolution parameter that enables systematic exploration of community structure across multiple scales. It leverages resolution-limit behavior in bipartite networks as a tool to uncover hierarchical organization without projecting the network or altering its intrinsic bipartite topology. We evaluate the method using a hierarchical synthetic bipartite benchmark and apply it to two empirical networks. In all cases, Qbg recovers established mesoscale structure while revealing additional hierarchical and fine-scale organization beyond that detected by conventional bipartite approaches. These results establish Qbg as a flexible, interpretable, and resolution-aware framework for hierarchical community detection in bipartite networks.

High-level specifications of code are inherently ambiguous, and prior systems have explored interactive techniques to help users clarify their intent and resolve such ambiguities. However, most existing approaches elicit supervision through labeled examples, which are often error-prone and may fail to capture user intent. This paper introduces a new active learning paradigm for program disambiguation based on multiple-choice queries. In this paradigm, the system presents a small set of high-level behaviors as multiple-choice options, and the user simply selects the intended one. Technically, each answer option corresponds to a Hoare triple that characterizes a cluster of semantically similar candidate programs. This formulation enables formal reasoning about the informativeness and interpretability of queries, and supports systematic construction of optimal queries. Building on this insight, we develop a new active learning algorithm and implement it in a tool called Socrates, which automatically synthesizes informative multiple-choice queries for program disambiguation. We evaluate Socrates across four domains spanning both symbolic and neurosymbolic settings and show that it produces intuitive, easy-to-answer queries and achieves efficient convergence. Most importantly, Socrates identifies the intended program more reliably than existing methods, while maintaining competitive runtime performance.