Papers

Many results in categorical algebra rely fundamentally on pointedness, yet numerous categories of mathematical interest are not pointed. Building on ideas from the theory of ideally exact categories, recently introduced by G. Janelidze, we investigate the extent to which constructions and results from pointed contexts can be extended to categories admitting suitable forgetful functors to pointed categories. We introduce the notion of a propointed category, described as a category admitting a conservative right-adjoint functor to a pointed lex category, and give an intrinsic characterisation of this notion. We then investigate and characterise the cases in which the target of the given functor is pointed protomodular, homological, or normal, and establish within these settings generalisations of classical results - including the short five lemma, the nine lemma, and Noether's isomorphism theorems - as well as a well-behaved notion of ideal of an object. We also prove that the 2-category of pointed lex categories is 2-reflective in the 2-category of lex categories with an initial object, the reflection being given by the slice over the initial object, which thus provides a universal 'pointification'.

We describe a simple, visually compelling demonstration/laboratory of astronomical interferometry using a standard planetary telescope and a thin piece of opaque plastic punched with two small holes. By observing the disappearance of interference fringes as the hole spacing is increased, students can directly estimate the angular diameter of Venus. The demonstration is a tabletop analogue of the landmark 1921 Michelson-Pease measurement of Betelgeuse and scales naturally from that measurement: where Michelson and Pease required a 6.1 m baseline to resolve a disk 47 mas (milli-arcsecond) across, a 15 mm baseline suffices for Venus, when it is approximately 10-15$''$ (arc seconds). The lab works reliably in ordinary atmospheric seeing conditions, and a side-by-side comparison of Venus (or Jupiter) with a bright star such as Sirius provides an immediate visual demonstration of the difference between extended and point sources. It works equally well as a laboratory at a variety of difficulty levels. Furthermore, it does not require advanced knowledge or skills with optical telescopes. While the underlying ideas are well known, we are unaware of any source that presents them in an accessible, unified form.

Usually in semiconductor heterostructures, such as quantum wells, the quantum confinement is realized by means of heterobarriers, which are simply the band offsets in adjacent materials. Here the arguments are provided, that the energy dispersions in materials (in simple case determined by effective masses) are important as well. Using a simple model system, such as quantum well with an additional heterojunction, it is shown the predominant localization of the carrier density in the regions with higher effective mass. The possibility of different spatial localization of wave function for different subbands is predicted. This can be applied in semiconductor structures such as quantum cascade lasers.

Employing problem-specific non-universal Variational Quantum Circuits aligned with a suitable state preparation has become a standard approach to counter the difficulty in training universal ansätze. However, due to their non-universality, diagnosing their reachability and trainability remains reference-state-specific. In this work, we establish the equivalence of maximal reachability and generic reachability over arbitrary reference states as a consequence of the principal orbit-type theorem. Thereafter, assuming that the global minimum of the cost function is achieved on a subset that can be described as the image of a smooth function, we derive necessary and sufficient conditions for non-zero probability of reachability under generically sampled reference states. Furthermore, when the solution set is assumed to be realised through a real analytic map that embeds a solution manifold, we show that local surjectivity is generically obtained on the entire solution manifold if it is attained at a single point. As a practical design rule, the need for local surjectivity automatically translates to a necessary dimensional criterion: reachability requires the target set's topological dimension to be at least as large as the co-dimension of the generic orbit. Numerical simulations show that finite-depth optimisation consistently fails when the dimensional obstruction applies, while unobstructed cases show improved convergence.

The increasing adoption of the Internet of Things (IoT) and cloud computing has accelerated the evolution of edge computing paradigms [1]. Industry forecasts estimate that the number of connected IoT devices will reach approximately 50 billion by 2030, following an estimated 38 billion connections by 2025 [34], resulting in an unprecedented growth in data generation. This trend necessitates efficient, scalable, and secure data processing mechanisms at the network edge. Consequently, ensuring the reliable management and protection of IoT applications and devices has become a critical challenge. In this context, KubeEdge extends cloud-native capabilities to edge environments, enabling distributed orchestration while introducing new security concerns. This paper investigates the security of container images in IoT-driven and distributed edge architectures. Specifically, we analyze the impact of major security threats, including Denial of Service (DoS) attacks and malicious container deployments, on the availability and operational stability of KubeEdge-based systems. To address these challenges, we propose a lightweight Recommended Intrusion Detection Rule Set (RIDRS) tailored for resource-constrained edge environments. The proposed approach improves system resilience by enabling timely detection and mitigation of security threats. We define system stability as the ability to maintain consistent operational behavior and to recover autonomously under adversarial conditions. Experimental results demonstrate that RIDRS significantly reduces system downtime and enhances service availability, particularly in scenarios involving code injection and malicious pod deployment attacks.

Language-model agents now run the whole of quantitative factor research: they propose investment factors, backtest them, select the survivors and retire them. We ask which of those jobs an agent should keep. Our answer is governed self-evolution: the agent may propose, and a frozen statistical referee that the agent cannot touch must judge. The referee scores each candidate only on market outcomes revealed after submission, by betting, so its false-discovery guarantee holds at every stopping time for any proposal policy. We cross three proposers (a script, a bandit and a language model) with this referee and with three deliberately leaky ones, in a synthetic world with planted truth, a probe-authoring environment and a ten-year walk-forward on the CSI 500. Who judges sets the number of false admissions: the frozen referee admits 5-11 times fewer sub-threshold factors than the leaky referees under a scripted proposer, and no proposer closes that gap. Who proposes sets the yield: the language model beats the script, matches the bandit, and adds the one capability a bandit lacks, writing its own diagnostic probes. The certificate's price is time: an admitted true factor waits about 500 trading days, and the certified portfolio's Sharpe ratio therefore trails an ungated one. Judging belongs to the procedure; proposing and instrument-making belong to the agent.

Electric vehicle (EV) battery performance is strongly coupled with driver behavior, yet human intent is typically expressed semantically rather than numerically. This paper proposes a hybrid physics-artificial intelligence framework that integrates a Large Language Model (LLM) as a high-level behavioral reasoning layer within a physics-driven supervisory architecture. The LLM interprets textual user intent and structured battery feedback to generate bounded behavioral parameters that shape a discharge current envelope. A physics-driven safety filter then enforces physical safety constraints before computing feasible velocity recommendations. Lyapunov-based analysis establishes bounded recommendation error under battery model and prompt inaccuracies. Simulation results demonstrate adaptive, user-aware operation without compromising physical safety. The proposed reasoning-enforcement architecture provides a principled pathway for safe AI integration in EV energy management.

A substantial body of results is known for curves of degree $d=3$, namely elliptic curves, including the theorems of Siegel, Mazur, and Mordell, among others. More generally, Faltings established comprehensive results for all algebraic curves of degree $d \ge 2$. However, these results do not, in general, furnish an explicit or systematic procedure for classifying algebraic curves that fail to admit solutions over a prescribed set such as $\mathbb{Z}^{+}$. The principal aim of the present work is accordingly to develop a method for classifying families of algebraic curves having no solutions in $\mathbb{Z}^{+}$. We begin by establishing a correspondence between algebraic geometry and linear algebra, from which we develop a classification procedure grounded in linear-algebraic constructions and tools. Specifically, let $S:Ax=b$ be a linear system, where $A \in M_{3k \times m}(\mathbb{Z})$ satisfies suitable conditions on its entries, and let $S=\{s_{1},s_{2},\dots,s_{N}\} \subset \mathbb{Z}^{m}$ denote the solution set of the system, with $A=(a_{ij})$, and $s_{i}=(c_{1},c_{2},\dots,c_{n+1})$. From such a solution we construct algebraic curves of degree $n \le m$, nonsingular curves $C_{js_i}$ of genus $g \ge 0$, of the form $C_{js_{i}}:Y^{2}=a_{3j1}c_{1}X^{n}+a_{3j2}c_{2}X^{n-1}+\dots+a_{3jn}c_{n}$. If $Y \ge 1, X > 1$ and $\forall(X,Y) \in C_{js_{i}}(\mathbb{Z}^{+})$ holds then $[C_{js_{i}}(\mathbb{Z}^{+})]_{1 \le j \le k}^{N}=\emptyset$ and if the system $S$ admits infinitely many solutions, then $[C_{js_{i}}(\mathbb{Z}^{+})]_{1 \le j \le k}^{\infty}=\emptyset$ as $N \longrightarrow \infty$.

Recent observations of the nearby Seyfert galaxy Mrk 573 found that the galactic nucleus and bicone regions surrounding the jet are significantly metal-enriched. In this paper, we develop a simple model for the observed metal enrichment, assuming a population of stars in the $10 - 30 \, M_{\odot}$ range formed in-situ in the accretion disk. We assume the stars form according to a Salpeter initial mass function and generate the typical metal yields expected of field stars of the same mass. We find that in the thick disk ($H/r \sim 0.1$) case, a Salpeter population of stars can easily explain the observed metal enrichment and provide limits on the formation model; we also argue that a thin disk ($H/r \lesssim 0.01$) is incompatible with the observed metal enrichment. In our model, AGN metallicity scales most strongly with disk thickness, implying a potentially powerful observable diagnostic.

We develop a unified defect theory for embedded algebraic vector bundles which places several classical constructions within a common framework. The theory recovers tangential, dual, join, and secant defects. We first prove an effective numerical criterion characterizing defectivity by the vanishing of a bidegree. This also allows us to recover the exact defect from the vanishing pattern of the bidegrees, extending a theorem of Holme. Using van der Waerden's theorem on bidegrees, we obtain a formula that decomposes the geometric degree of an embedded vector bundle into contributions from the direction varieties of its general linear restrictions. This leads to a characterization of embedded algebraic vector bundles of minimal degree. As a main application, we establish the sharp universal bound $\operatorname{deg}(TV) \leq \operatorname{deg}(V)^2$ for every smooth irreducible affine variety $V \subseteq \mathbb{A}^n$ and $TV\subseteq \mathbb{A}^{2n}$ its tangent bundle. Finally, under suitable regularity assumptions, we apply the quadratic bound to prolongation varieties of differential algebraic systems, obtaining uniform degree estimates and thereby providing a partial answer to an open problem in differential algebra posed by Pogudin.

An eigenvalue of a signed graph is called main if there exists a corresponding eigenvector non-orthogonal to the all-ones vector. An important result of O'Rourke and Touri (2016) states that almost all (unsigned) graphs have all main eigenvalues. Akbari, França, Ghasemian, Javarsineh, and de Lima (2021) considered main eigenvalues of signed graphs and conjectured that for any unsigned connected graph $G \notin\{ K_2, K_4 - e\}$, there is a switching $\mathbf{s}$ such that all eigenvalues of the signed graph $G^{\mathbf{s}}$ are main. We prove two incomparable asymptotic versions of this conjecture. We show that for any graph $G$ of order $n$, there exists a switching $\mathbf{s}\in\{\pm1\}^n$ such that $G^{\mathbf{s}}$ has $n - O\!\left(\frac{n}{(\log n)^{1/4}}\right)$ main eigenvalues counted with multiplicity. Using a similar proof strategy, we also show that if $G$ has $d$ distinct eigenvalues, then there exists a switching $\mathbf{s}\in\{\pm1\}^n$ such that $G^{\mathbf{s}}$ has $d - O\!\left(\frac{d}{(\log d)^{1/4}}\right)$ main eigenvalues.

We prove power-loss results for some variants of Stein's Weighted $L^2$ Conjecture for Bochner-Riesz means. The variants concern multipliers by convex bodies with $C^k$ boundaries in every dimension $n$. The counterexamples are related to recently-constructed counterexamples to the Mizohata-Takeuchi Conjecture. Related results like logarithmic blowups for the endpoint case of the original conjecture are also discussed.

The slice rank method gives exponential bounds for sets with no three-term arithmetic progression in finite vector spaces of odd characteristic and for three-sunflower-free families of subsets of a fixed ground set. We show that for $k\ge4$, every tensor that is nonzero exactly on the $k$-term arithmetic progression relation or the $k$-sunflower relation has maximal slice rank over every coefficient field. When the support is prescribed only on pairwise distinct inputs, we obtain comparable lower bounds, which likewise rule out exponential savings.

Large language models have enabled rapid deployment of language classification and analysis, allowing users to describe complex constructs in natural language, such as pedagogical moves or expressions of learning and engagement, and label them in conversational datasets such as classroom or tutoring transcripts. However, because LLM reasoning is opaque, we have no verifiable, mechanistic insight into why a model chose a label for an utterance, and output differences over time or across models challenge replication. We introduce the EduBehaviors framework to generate interpretable, reliable, and scalable construct annotations in educational dialogue data that retain human agency while leveraging the strengths of generative AI, encoders, and machine learning models. We evaluate the framework on the TalkMoves dataset, predicting the Teacher TalkMoves labels. Our best configuration results in a macro-F1 of 0.764 and 0.756 Cohen's kappa, demonstrating improvements over direct prompting approaches and showing competitiveness with fine-tuned classifiers while gaining the benefit of greater transparency and comparability. To facilitate adoption and operationalization of the EduBehaviors framework in educational dialogue data by other researchers, we also release the EduBehaviors Toolkit with two complementary open-source tools based on the TalkMoves application.

We present a computational framework to verify a refinement of the McKay conjecture, proposed by E. Giannelli, for sporadic simple groups and their universal covers. This refinement asserts the existence of a bijection between the $p'$-characters of a finite group and those of the normalizer of its Sylow $p$-subgroup that does not increase character degrees. Our verification enforces stricter conditions, ensuring equivariance under the relevant outer automorphism group, preservation of the $p$-part of the character conductor, and compatibility with central characters. We establish theoretical reductions that limit the relevant outer automorphism action to an order of at most 2, allowing us to leverage Clifford theory and precomputed character tables to circumvent expensive explicit group constructions. Finally, we provide algorithms for classifying characters and constructing bijections that strictly satisfy these conditions.

Mathematical reasoning benchmarks are typically organized by topic, but language models may organize their internal computation by reusable reasoning approach instead. In this paper, we investigate whether open math-capable LLMs organize internally by topical sub-skill or by reasoning approach, and we present evidence that the approach is the key. We introduce a generation-replay protocol: a model first generates a solution, after which we replay the exact prompt-plus-generation trajectory and extract activation-importance signatures over the reasoning tokens. We cluster these signatures without supervision across eight models and five mathematical reasoning sources, then evaluate the recovered structure with structural, semantic, and intervention tests. Across all 40 model-source cells, the recovered clusters outperform matched-size random baselines. Two independent frontier-LLM judges find approach-level coherence in 77-82% of real clusters versus 6-11% in within-source controls, and topic-pure clusters usually receive labels finer than the topic itself. In approach-controlled prompting, changing the requested reasoning approach shifts cluster assignment in seven of eight model conditions, whereas paraphrases largely preserve it. These results indicate that math-capable LLMs organize internal mathematical computation by reasoning approach rather than benchmark topic. The implication is that topic-stratified benchmarks and topic-balanced training corpora can still miss the axis that matters: even deliberately topic-balanced corpora may remain imbalanced over reasoning approaches.

Multi-GPU servers have become the standard building block of modern data centers, providing aggregated capacity through high-bandwidth interconnects. At the same time, workloads such as LLM inference exhibit highly dynamic memory demands, which can cause one GPU to exhaust its local memory while others remain underutilized. This mismatch motivates a model of elastic resource sharing across GPUs. We present EMA, a memory sharing system that allows GPUs within a server to borrow and reclaim memory from each other, forming an elastic pool of capacity. EMA ensures performance transparency for both borrowers and lenders. For borrowers, prefetching hides remote access costs so that applications experience remote and local memory as indistinguishable in performance. For lenders, borrowed resources remain reclaimable on demand, guaranteeing that performance never falls below that of static partitioning. While our design focuses on memory, the same principle naturally extends to other GPU resources. Our evaluation shows that EMA improves individual user throughput by up to 52%, achieves 96% of the throughput of a system provisioned with 2X capacity, and maintains latency similar to the static local baseline.

Multiwavelength surveys of the Galactic midplane enable the identification of infrared-excess sources, signatures of circumstellar material, though high extinction and crowding hinder detection. We construct a homogeneous catalog of infrared-excess candidates in a $\sim$7.0 deg$^2$ field of the Vela-Carina region, characterizing their excess emission via spectral energy distribution (SED) analysis. We combine optical photometry from DECaPS, near-infrared photometry from VVVX, and mid-infrared photometry from Spitzer/GLIMPSE using hierarchical positional cross-matching. Candidates are selected via photometric quality and MIR color diagnostics, and their SEDs are analyzed with VOSA using theoretical atmosphere model grids. Photogeometric distances are adopted, while Gaia DR3 and NEOWISE variability provide complementary diagnostics. From the matched 249,719-source VVVX-GLIMPSE-DECaPS catalog, we identify 1,512 MIR-excess objects, of which 191 have complete 12-band photometry with S/N > 10, enabling detailed SED analysis. Photogeometric distances are statistically consistent with geometric distances for nearly the entire sample. SED analysis independently supports the MIR-excess nature of most sources, indicating emission beyond stellar photospheres. About 15% of sources are flagged variable by Gaia, while NEOWISE light curves reveal MIR variability of a few tenths of a magnitude. Comparisons with published YSO and variability-selected catalogs show limited overlap, particularly with variability-selected samples, indicating that MIR-excess selection complements other approaches to identifying candidate YSOs in the Vela-Carina region. The resulting catalog provides a well-defined MIR-excess sample with homogeneous multiband photometry, SED characterization, distances, and variability diagnostics, forming a foundation for future spectroscopic and time-domain studies.

Chain-of-thought (CoT) monitoring assumes that the reasoning a model writes reflects the computation that directly produces its answer. Previous faithfulness metrics have been predominantly behavioral, as they simply edit the reasoning text and observe the resulting answer. However, our methodology aims to measure faithfulness causally at the activation level, specifically on self-generated reasoning. Unlike previous causal audits, which measure degradation, our interventions carry a known predicted target. In this way, each patch should switch the answer to a specific counterfactual entity derivable by construction. Specifically, we use synthetic multi-hop lookup tasks (2-6 hops). We patch the residual stream at the token span where the model states each intermediate step with the corresponding activations from a counterfactual run. For Qwen3-4B, 76.9% +/- 2.8% of stated steps are causally load-bearing (CLB) at the most responsive mid-network layer (random-position null: 11.3%; patching the underlying prompt fact: 83%, so stated steps carry approximately 96% of the achievable effect). Moreover, the standard behavioral test on the same items yields 88.2%, which overstates causal faithfulness by 11.4 percentage points (item-matched; 111:14 discordant pairs, p < 1e-15) and, for the easiest items, by up to 20 percentage points. This gap also has a clear capability dimension. Qwen3-1.7B is far less causally faithful overall (54.8%), with its faithfulness collapsing as reasoning depth increases (68% at 2 hops to 30% at 6), while Qwen3-4B remains relatively flat. Although stated reasoning can be causally meaningful, standard behavioral tests tend to overestimate its causal faithfulness, particularly on easier examples where model reasoning appears most fluent.

Wake word detection is a critical component of virtual assistants, serving as the gateway to seamless user interactions. This paper introduces a novel wake-up system that extends traditional direct keyword detection with contextual trigger detection. After an initial wake word activation, the system uses reasoning to distinguish between user commands and unrelated speech, ensuring efficient and context-aware engagement. We present a data generation architecture that produces a 62.3-hour corpus of controllable multi-speaker conversations containing direct invocations, contextual follow-ups, and non-addressed speech. Experimental results demonstrate the effectiveness of the proposed approach across diverse synthetic conversational scenarios. We release the code, dataset and trained models to promote reproducibility and further advancements in intelligent assistant technologies.

Polymer property prediction lacks open, standardized benchmarks that enable rigorous comparison of machine-learning methods, with existing resources covering only a narrow fraction of polymer architectures, such as homopolymers. We introduce Polymer Benchmark 2026 (PolyBench26), an open dataset comprising nearly 250,000 polymer-property datapoints across eight physical properties, including data from experimental measurements, density functional theory, and molecular dynamics. The benchmark supports four evaluation tasks across homopolymers and alternating, random, and block copolymers: in-distribution property prediction, dataset-size scaling, repeat-unit complexity, and transfer to held-out polymer architectures. We compare language model, graph-based, and descriptor-based approaches and find graph-based models provide the lowest errors in property prediction, retain their advantage across the evaluated training-set sizes, and remain robust to increasing repeat-unit complexity. PolyBench26 provides a reproducible foundation for developing models for the increasingly complex polymer design space. The PolyBench26 benchmark is available open-source at https://github.com/rlearsch/PolymerBenchmark2026.

Group Relative Policy Optimization (GRPO) and related policy-gradient methods for training language model agents collapse an entire multi-turn rollout into a single scalar trajectory reward before it enters the policy update. When the task composes distinct skills, especially under sparse and delayed environmental feedback, this collapsing is lossy: the optimizer must implicitly infer which competency drove the outcome and how that should change behavior. We argue the right primitive is not a better scalar but a decomposition: trajectory reward should be split along subtasks before it enters the policy update. We introduce Reinforcement Learning with Decomposed Subtasks (RLDS), whose core is Subtask-Decomposed Advantage Estimation (SDAE): a replacement for the scalar GRPO advantage that splits trajectory reward into per-subtask shares on a fixed taxonomy, computes a group-relative advantage per subtask, and distributes per-token credit by weighting each subtask's advantage by its importance, concentrating it around the step where a reflection marks that subtask's execution as consequential. We evaluate on four agentic benchmarks: FrozenLake (sparse grid navigation), HotpotQA (multi-hop QA, one retrieval tool), ScienceWorld (long-horizon embodied science), and DeepResearch (long-form research, four tools, composite rubric reward). Heterogeneity diagnostics emitted during training show where decomposition pays off - gains scale with subtask heterogeneity, largest on the high-heterogeneity tasks ScienceWorld (+11.5 points, paired-bootstrap 95% CI [+9.8, +13.3]) and FrozenLake (+9.8 points, [+7.0, +12.8]), and within noise on HotpotQA and DeepResearch, where the diagnostics predicted little to recover. ScienceWorld is also more compute-efficient under RLDS than scalar GRPO (-10.9% wall-clock per step), as long rollouts amortize the fixed reflect-and-grade overhead.

We study prediction in new environments when the training data contains rare, large distribution shifts. Anchor regression penalizes the average of the squared mean residual across environments. It protects against shifts in an ellipsoid determined by the second moment of the training shifts. Covering rare shifts may therefore require a large penalty $\gamma \gg 1$, expanding the ellipsoid in every direction and reducing accuracy on common environments. We propose CVaR anchor regression, which replaces the average of the squared mean residuals with a tail average. We prove an exact worst-case risk guarantee under a linear structural model that allows for heteroscedastic noise. CVaR anchor regression protects against shifts in a union of ellipsoids determined by second moments of the shifts in the worst $\alpha$-fraction of environments. For $\alpha$ small enough, this is the scaled convex hull of the training shifts and their negatives. It therefore covers all training shifts when $\gamma \geq 1$. Unlike CVaR or GroupDRO applied directly to prediction risks, CVaR anchor regression does not give environments more weight solely because their noise levels are high. Examples show how the method can improve protection against rare shifts while retaining accuracy on common environments. We illustrate the method on the New York City taxi dataset.

Reward fine-tuning aims to update a pre-trained flow-based generative model to improve the downstream reward of its generated samples. Existing methods typically formulate this problem as sampling from a reward-tilted distribution, the solution to a KL-regularized reward-maximization problem. Here, we introduce an optimal transport regularizer built directly from the pre-trained drift. Unlike KL reward tilting, the resulting objective transports individual samples toward higher reward rather than reweighting the base distribution. We show that the resulting problem is equivalent to a deterministic optimal control problem on the flow. Given a pre-trained flow map, this equivalence yields a simulation-free reinforcement learning algorithm for fine-tuning generative flows. We call the resulting framework Wasserstein-Tilted Flow Maps (WTF), the first end-to-end fine-tuning recipe native to flow maps. The output is a fine-tuned flow map that retains strong reward-aligned performance at few-step inference budgets without post-hoc distillation. Experiments on ImageNet-256 and text-to-image show that WTF achieves higher reward with comparable or higher diversity than baselines, while requiring up to $280\times$ less training compute. More broadly, we argue that accelerated samplers such as flow maps are essential infrastructure for efficient post-training, and that the dominant KL-regularized formulation is only one of many choices worth revisiting.

Faithfulness is a central concern in legal text summarization, which motivates extractive approaches that select verbatim content traceable to its source. Such methods typically rank paragraphs or other structural units in isolation, yet give little attention to consolidating evidence that is distributed across, and shares salience between, distant parts of a document. We introduce LexLattice, an extractive summarizer that reifies a legal act's hierarchy as a two-dimensional semantic lattice and consolidates over it with a masked 2D neural cellular automata before selection. LexLattice attains state-of-the-art ROUGE across all 24 languages of EUR-Lex-Sum in both multilingual and cross-lingual settings, surpassing instruction-tuned baselines with billions of parameters, despite concentrating all trainable capacity in a 1.8M parameter consolidator over a frozen multilingual encoder. A consolidator trained only on high-resource languages further transfers to unseen languages with near-lossless retention (0.99), indicating that the model operates on language-agnostic semantic geometry rather than surface form. Our results position explicit consolidation over document structure as a compact and traceable alternative to scale for multilingual legal summarization.

Complex organic molecules are widely detected in star-forming regions and are important precursors to prebiotic species. Because these molecules are thought to form primarily within icy grain mantles, their desorption is assumed to be regulated by the sublimation of the surrounding H$_2$O ice matrix. However, observations increasingly reveal gas-phase abundances of methyl formate (MF) at temperatures well below the sublimation temperature of water ice (T ~ 100K), challenging this view. To investigate how ice composition and phase influence MF desorption, we present laboratory temperature-programmed desorption measurements of MF from four astrophysically relevant substrates: amorphous and crystalline H$_2$O and CH$_3$OH. Desorption kinetics were analyzed using pre-exponential factors derived from transition-state theory with leading-edge analysis and non-negative least-squares inversion to recover binding-energy distributions. We find that MF binds more weakly to CH$_3$OH ice than to H$_2$O-rich substrates, with representative binding energies of ~6247K for amorphous H$_2$O, ~6213K for crystalline H$_2$O, and ~5469K for amorphous CH$_3$OH. MF deposited on crystalline CH$_3$OH exhibits coverage-independent leading edges consistent with multilayer or island desorption, yielding an effective binding energy of 5333K. Enhanced surface mobility and reduced trapping efficiency on methanol ice, combined with weaker MF binding, provide a natural explanation for the early appearance of gas-phase MF observed in star-forming environments, with characteristic desorption temperatures of ~85K on CH$_3$OH and ~95-100K on H$_2$O. Together, these effects support a two-step thermal desorption pathway in which MF associated with CH$_3$OH-rich ice can be released prior to bulk H$_2$O sublimation.

Kubernetes is widely used to orchestrate cloud-native applications, yet its declarative configuration model often introduces security misconfigurations that threaten system reliability. Despite available detection tools, misconfiguration patterns and scalable remediation remain insufficiently understood. This paper presents an empirical study of Kubernetes security misconfigurations based on 2,662 developer-reported Stack Overflow issues. We derive a taxonomy of recurring security weaknesses across configuration objects and categories. We analyze severity variations and investigate how misconfigurations evolve between incubator and stable project stages. Findings show that while some operational issues decrease as projects mature, critical security misconfigurations often persist or reappear. We then evaluate Large Language Models (LLMs) for automated remediation under progressively enriched contextual conditions. Contextual grounding improves correction accuracy, with the best standalone model achieving 89.06%. To enhance structural correctness and schema compliance, we introduce Kubecurity, a schema-guided validation framework based on official Kubernetes specifications. Combining contextual LLM reasoning with deterministic schema enforcement achieves 98.50% correction accuracy while substantially reducing newly introduced misconfigurations. This work advances the understanding of Kubernetes security misconfigurations and demonstrates a hybrid approach to more reliable automated remediation.

YZ Ret is a well observed nova from the first detection of an X-ray flash phase in classical novae until the end of a supersoft X-ray source phase. We have reanalyzed multiwavelength light curves of YZ Ret over the total duration of the outburst. Our fully self-consistent nova outburst model, a 1.25 $M_\odot$ white dwarf (WD) and a mass accretion rate of $1\times 10^{-9} ~M_\odot$ yr$^{-1}$ on to the WD, reasonably reproduced $V$/$g$ light curves as well as the very early X-ray flash and late supersoft X-ray light curves. This model explains the emergence epoch of the GeV gamma-ray emission because a shock naturally arises far outside the nova (WD) photosphere just after the optical maximum. In our model, before optical maximum, later ejected matter has a smaller velocity than that of earlier ejecta and therefore the ejecta expands while, after optical maximum, later ejected matter has a larger velocity than that of earlier ejecta and collision with the earlier ejecta makes a shock.

The dark matter halo profile in galaxies holds key information about the nature of dark matter and galaxy formation. Constraining the dark matter profile of galaxies beyond the Milky Way traditionally requires expensive spectroscopic observations for kinematic information. In this paper, we explore a conditional generative model framework to map the dark matter profile of Milky Way-mass galaxies from stellar density profiles, more easily obtainable through large photometric imaging surveys. As a proof of concept, we train the model to learn a stochastic bridge between instrument systematics-free baryonic stellar distributions and underlying dark matter density maps from the DREAMS hydrodynamics simulation suite. We recover 2D dark matter density profiles with a typical accuracy of $\sim0.1$ dex ($\sim1.5$% of the truth in log scale). The stochastic sampling procedure provides uncertainty estimates of the predicted dark matter map, with typical values $\sim0.1$ dex. Out-of-domain tests with Milky Way-mass galaxies from IllustrisTNG and FIRE simulations show that, while the model can qualitatively be generalized to TNG50 galaxies from IllustrisTNG, the model is sensitive to the galaxy formation model, with $\sim0.2$-$0.4$ dex over-prediction for the inner profiles ($r\lesssim5$ kpc) of the FIRE test galaxies. Future work will explore training with additional suites of simulations and/or conditioning on additional information, such as multi-band images. Our results are a first step towards using generative models as a flexible, uncertainty-aware framework for turning forthcoming data from large imaging surveys into spatially resolved dark matter maps.

Coherent multidimensional spectroscopy will benefit greatly from near single-cycle pulses through the spectral breadth of states that can be accessed and the high frequency oscillations that can be resolved. However, the necessary cost of working with such pulses is the spectral structure arising from efficient self-phase modulation, which imparts into the signal and complicates interpretation of the molecular response. In this paper, we develop an in-operando approach to characterize and remove pump spectral features from two-dimensional spectroscopic signals. The pump spectrum is retrieved via an interferometric integrated autocorrelation measurement that runs concurrently with the experiment and thereby inherits the same time and frequency domain properties. A deconvolution procedure then suppresses noise and extracts the third-order response from the total signal. The analysis enables correction of spectral intensities and unambiguous assignment of spectral features to the molecular response. This work pushes multidimensional spectroscopy toward the impulsive limit and enables integration with other nonlinear spectroscopies such as attosecond spectroscopy - all without compromising few-cycle pulse properties.