Papers

Code-switching (CS) speech, characterized by language alternation within a single utterance, is prevalent in multilingual communities and poses challenges to automatic speech recognition (ASR) due to rapid language transitions. We propose LLM-HB, a language-aware large language model-guided hotword biasing framework for code-switching ASR (CS-ASR). The framework incorporates a mixture-of-experts (MoE) adaptor and an auxiliary language prediction head to better capture and differentiate multilingual representations, while hotwords are injected through LLM-based prompting. Experiments on the ASRU2019 code-switching challenge test set demonstrate that LLM-HB achieves a 20.30% relative reduction in mixed error rate (MER) over the baseline, reaching 5.85% MER under a 15-distractor hotword setting. To the best of our knowledge, this is the first work to integrate LLM-guided biasing into code-switching ASR. We further release the extracted ASRU2019 hotword list to support future research.

Modern deep classifiers trained by gradient descent need many passes over the data to become accurate, and even then are not always well calibrated; post-hoc temperature scaling corrects calibration after training but cannot influence training-time accuracy or convergence. We propose a variational filtering algorithm for the last layer of deep classifiers, whose parameters are treated as the latent state of a linear-Gaussian state-space model. Each mini-batch is assimilated by an exact prediction step followed by a closed-form variational update, made conjugate by an independent binary probit (IBProbit) surrogate for the categorical likelihood. The filter's process noise stabilises the updates under feature drift and keeps the predictive distribution from collapsing to a point estimate, allowing the same procedure to be used for linear probing on a frozen backbone and for full-network fine-tuning. We evaluate on DINOv3 backbones against two baselines tuned under an identical protocol: AdamW with cross-entropy and post-hoc temperature scaling, and Variational Bayesian Last Layers (VBLL). As a linear probe on frozen features, IBProbit attains the best accuracy and negative log-likelihood on all five downstream tasks at the largest backbone, and on two of the five at the smallest. In out-of-distribution detection with CIFAR probes on the largest backbone, IBProbit reduces the false-positive rate at 95% true-positive rate by a factor of 1.4 to 3.2 relative to the better of the two baselines, on all three dataset pairs. When the whole network is fine-tuned on ImageNet-1k, IBProbit reaches the final performance of the cross-entropy baseline in half the wall-clock time.

Reconstructing reference videos as editable dynamic 3D scenes is an important path toward controllable video generation for filmmaking: these scenes provide modifiable, renderable visual proxies that enable explicit control over scene layout, subject actions, and camera behavior. To evaluate agents' ability to reconstruct editable dynamic 3D scenes from dynamic reference videos, we introduce CineRecon, a benchmark comprising 50 reference videos and 360 annotated evaluation clips. The reference videos span film, real-world footage, and games. Given a complete video, an agent uses tools to construct, animate, render, and refine its reconstruction. We evaluate this task under three representation settings: Proxy, Simplified, and Detailed. These settings increase geometric and appearance requirements while retaining the same requirements for spatial relations, camera behavior, and subject dynamics. This design tests whether agents can reproduce the events in a video when detailed appearance is unnecessary, and how performance changes as representation requirements increase. For evaluation, we construct checklists that associate observable properties and events with specific entities and times. A vision-language judge compares timestamp-aligned reference and rendered frames across 11 categories, grouped into camera, static, and dynamic consistency dimensions. We evaluate 12 models using their corresponding agent harnesses and find failures across all three dimensions. Subject motions and interactions remain difficult to reproduce even under the Proxy setting.

Conventional Gaussian filtering typically approximates nonlinear models or their statistical moments and retains the Kalman update structure. The resulting approximation errors can affect both state estimates and their uncertainty. This paper presents the Natural Gradient Gaussian Approximation (NANO) framework for nonlinear filtering. Both prediction and measurement update are formulated as optimization problems over Gaussian distributions, with the entire Gaussian distribution serving as the optimization variable. The framework integrates observation losses, distributional discrepancies, natural-gradient optimization, and finite-step update rules, providing a unified formulation for constructing different filters. Natural-gradient iterations account for the geometry of the Gaussian family and jointly update the distribution parameters. The framework incorporates the existing NANO-P method using the Kullback-Leibler divergence and introduces NANO-W using the Wasserstein distance. NANO-P maintains covariance positive definiteness through a positive-semidefinite curvature approximation, while NANO-W uses a covariance transport update that accommodates indefinite curvature. Their update rules and sufficient conditions for covariance positive definiteness are established within the common framework. Through these two realizations, the proposed framework achieves the best estimation accuracy among the evaluated methods on each of six benchmarks. Runtime evaluations further assess its computational feasibility for practical applications.

We give a deterministic distributed algorithm for $(\Delta+1)$-coloring an $n$-node graph of maximum degree $\Delta$ in $O(\sqrt\Delta+\log^* n)$ rounds in both the LOCAL and CONGEST models. More generally, $(\deg+1)$-list coloring with lists from a color space of size $C\geq\Delta+1$ can be solved in $O(\sqrt\Delta\log(1+C/\Delta)+\log^* n)$ rounds; in CONGEST, we assume $C\leq n^{O(1)}$. The algorithm combines Barenboim's polynomial coloring procedure with arbdefective decompositions, degree reduction, and a short family of hash functions. Using the polynomial procedure in the degree-reduction framework already gives an $O(\sqrt\Delta\log\Delta+\log^* n)$-round algorithm when $C=O(\Delta)$. Hashing adapts the color space to the current degree and removes the logarithmic factor. We prove the existence of the hash family by the probabilistic method and compute it by deterministic exhaustive search, using unrestricted local computation. We also give an explicit variant based on lossless expanders that avoids this search and achieves $O(\sqrt\Delta+\log^* n)$ rounds for $C=O(\Delta)$.

Accurately assessing the convergence of Monte Carlo Markov Chains is crucial for ensuring their validity in Bayesian inference problems. However, convergence assessment in high dimensions is known to be difficult, due to most convergence diagnostics becoming insensitive beyond a few dozen parameters. Conventional convergence statistics analyze marginal distributions which in high dimensions neglects increasing levels of information from the joint and conditional probability distributions. Thus we propose $\texttt{NFDiag}$, which taps into the information of the full multivariate joint posterior with a normalizing flow (NF). Our convergence diagnostic thereby also analyzes information from conditional distributions. In other words, by working in the full multivariate space, it is sensitive with respect to the geometry of the chain in high dimensions. Our diagnostic utilizes that NFs assume independent and identically distributed (iid) training samples, which is a testable assumption that will be violated by a non-converged or strongly correlated chain. Our diagnostic trains NFs on separate parts of a chain, and then assesses whether these correspond to the same multivariate target distribution. We test our diagnostic in up to 250 dimensions, and demonstrate it is universal and unbiased, and detects problematic chain quality also when Gelman-Rubin $\hat{R}$ and the multivarite effective sample size do not.

We present an overview of the MSHT family of global PDF fits. We describe the underlying methodology, including parameterisation choice, theoretical inputs and datasets included in the fit. We describe the impact of recent theoretical advances in the inclusion of higher order QCD and EW corrections on the fit and their implications for phenomenology. We discuss recent methodological improvements and ongoing studies relating to closure tests of the parameterisation flexibility and the inclusion of errors on errors for experimental data. We in addition discuss recent results on the determination of the strong coupling from the MSHT fits.

We introduce hybrid expanders, sparse graphs which combine sublinear expansion across all scales with strong constant-factor expansion on smaller, polylogarithmic sets. We show that every $n$-vertex graph of average degree at least $2^{\omega(\log^*n)}$ contains such a subgraph, and use this local expansion to bring into the sparse setting tree-embedding and rollback tools more commonly associated with random or pseudorandom graphs. As an application, for fixed $k\in\mathbb N$, we prove that every graph satisfying this average-degree condition contains $k$ pairwise edge-disjoint cycles with nested vertex sets and compatible cyclic orders, resolving up to a quasi-constant factor a problem of Thomassen, originating in work of Erdős.

We present a comprehensive analysis of the complex subpulse modulation in PSR J1901-0906 using data from the Thousand-Pulsar-Array (TPA) programme. Our analysis reveals the coexistence of three distinct periodicities in the subpulse modulation of both profile components, which obey a beat relation. We also detect additional spectral beat features caused by the modulation of these co-existing periodicities by investigating the Fourier phase correlation in two-dimensional fluctuation spectra. Moreover, the single-pulse polarization states are shown to be modulated and synchronized with the three co-existing periodicities observed in total intensity. Such synchronization has been reported for only a small number of pulsars, but this discovery marks the only one where this synchronization involves multiple co-existing periodicities. The modulation beats are similar to, yet more complex than, the beat system previously identified in PSR J1514-4834 with higher-order harmonics playing a significant role. The coexistence of the observed beat-like periodicities in PSR J1901-0906 implies that they are not independent, but rather originate from an underlying, interconnected physical system within the pulsar magnetosphere. Building upon the same geometric framework previously applied to PSR J1514-4834, we demonstrate that a feedback system with interacting rotating carousels successfully reproduces the complex subpulse modulations observed in PSR J1901-0906 and naturally explains the beat relations.

Bronchoscopy inserts a camera through the airways to diagnose endoluminal disease. Locating the camera along the airway usually requires additional equipment, such as an electromagnetic tracker and a preoperative CT scan. In this paper, we investigate the use of the monocular camera stream to localise the bronchoscope without requiring additional sensing. We introduce a monocular SLAM system that localises the tip of a bronchoscope and reconstructs the airway surface around it from RGB video alone. A Depth Anything 3 backbone, fine-tuned on over a million photorealistic airway renderings, returns metric per-pixel depth and is the system's only source of scale. DINOv3 features routed through a custom cross-attention matcher supply sub-pixel correspondences on mucosa where classical descriptors fail. Both enter a factor graph alongside a dense constraint from projective iterative closest point (ICP) registration against the system's own running reconstruction, so surface evidence stabilises the directions the visual factors leave weakly observable. On six airways rendered from patient CT scans, the system reaches 26.1 mm mean absolute trajectory error and 77.5% mean surface F-score. Its mean surface accuracy exceeds that of five recent monocular SLAM and feed-forward baselines. MASt3R-SLAM, which fits a free scale to the ground truth, has a lower mean trajectory error (22.0 mm). ORB-SLAM3 completes only two of the six airways, whereas our system completes all six and also reconstructs two ex vivo specimens.

Relevance prediction between user queries and items is a fundamental component of e-commerce search systems. Traditionally, high-quality relevance labels are obtained through human judgment, which is reliable but expensive, slow, and difficult to scale. Recent advances in large language models (LLMs) enable automated relevance judgment at scale, achieving performance comparable to human annotators. However, such systems often rely on large commercial LLMs with complex prompts, resulting in high inference costs and limited throughput. In this work, we propose a framework that bridges this gap by distilling a high-performing LLM-based relevance judgment system into efficient multimodal student models. We first curate a small, high-quality human-annotated dataset to serve as ground truth. Using this dataset, we develop a reliable LLM-as-a-judge pipeline through careful prompt engineering and iterative refinement. This pipeline is then used to generate large-scale relevance labels, which serve as training data for compact multimodal models. Our distilled models achieve performance close to the teacher system while significantly improving latency, cost, and scalability. This approach enables practical deployment of high-quality relevance prediction systems in production environments.

We determine the minimal observation time for the heat equation on a closed almost-Riemannian surface, for a class of observation sets leaving sufficiently thin collars around simple Baouendi-Grushin circles. The structure and density are analytic near these circles, and the coefficients may depend on both variables. The formula is expressed through a complex phase describing concentration near the singular set and extends the thresholds known for separated models. Regular unobserved regions away from the circles do not change this time, provided all other singularities are observed. For singular circles of constant bracket step greater than two, local analyticity implies failure of observability at every time for observation sets at positive distance. We also construct quasimodes concentrated near simple singular circles, with exponentially small errors. Their superpositions give a lower bound for the Schrödinger observation time.

Vision-Language-Action models (VLAs) have achieved high success rates on familiar manipulation tasks, yet it remains unclear whether such scores reflect genuine zero-shot generalization and perturbation robustness. Existing evaluation frameworks provide limited capability-level diagnosis and combinatorial perturbation coverage, often without connecting diagnosis to targeted model refinement. We introduce VLA-GAUGE, a diagnostic framework that unifies both evaluations under a shared executable task representation. It combines (1) paired in-distribution and out-of-distribution tasks across six capability suites, (2) single-factor sensitivity analysis with combinatorial perturbation screening and evaluation, and (3) diagnosis-driven refinement through targeted data augmentation and model fine-tuning. We evaluate 12 VLAs spanning different model sizes and action-modeling paradigms under a unified protocol. We find that (1) The mean Zero-Shot Score on VLA-GAUGE is only 22.3%, with SimpleVLA-RL scoring 8.0% and ranking second to last among the evaluated models. (2) Under three representative combinatorial perturbation configurations, the mean R-Score is 9.3. (3) Diagnosis-driven fine-tuning improves $\pi_{0.5}$'s zero-shot generalization and robustness under a selected perturbation combination on held-out scenarios by 72.4 and 31.8 scoring points, respectively; the latter exceeds the 10.9-point gain from LIBERO-Plus single-factor fine-tuning despite fewer successful training trajectories. These results show that high reported success rates on familiar manipulation tasks do not guarantee strong zero-shot generalization to unseen tasks or robustness to combinatorial perturbations, while diagnostic evaluation provides actionable signals for targeted model improvement.

Coherently driven phonons are conventionally described classically. Nonlinear phonon-phonon interactions, however, allow an infrared drive to reshape the fluctuation spectrum and generate substantial nonthermal enhancement of phonon fluctuations, motivating a description beyond the coherent displacement alone. We benchmark classical and semiclassical approximations against the full quantum theory and find that the semiclassical treatment substantially improves agreement with the quantum dynamics. We propose nonequilibrium spontaneous Raman scattering as a sensitive probe of these effects and apply our framework to recent experiments suggesting quantum nonlinear phononics involving the $\mathrm{E}_{1u}$ and $\mathrm{E}_{2g}$ modes in multilayer graphene. At very strong pump fields, driving the $\mathrm{E}_{1u}$ mode significantly modifies the $\mathrm{E}_{2g}$ Raman spectrum; however, reproducing the reported response at experimental field strengths requires accounting for pump-induced Raman matrix element dynamics or alternative energy pathways into the $\mathrm{E}_{2g}$ mode. Our findings extend nonlinear phononics beyond average atomic displacements to the dynamics of lattice fluctuations, highlighting the interplay between coherent motion and quantum correlations in driven materials.

Human gaze is the primary high-bandwidth interface through which we parse the semantics of our environment. While often modeled as a sequence, the degree to which gaze exhibits transferable local structure across domains remains underexplored. Using motion tokenization as a diagnostic lens across four diverse datasets, we investigate the transferability of local sequence structure. We demonstrate that while gaze can share a reusable motion-token vocabulary, identical motion tokens are organized into different local transition patterns depending on the dataset and task context. Our results show the limitations of naive data-pooling under low-semantic motion-token representations and provide a framework for evaluating behavioral sequences through information-theoretic diagnostics.

The focusing coupled Kundu-Eckhaus (CKE) equation extends the coupled nonlinear Schrödinger (CNLS) equation by adding quintic and derivative nonlinearities. We study the Cauchy problem for the focusing CKE equation with Schwartz initial data under the assumption of no discrete spectrum and no spectral singularities on the real axis. Based on the gauge equivalence between the focusing CKE and CNLS equations, we analyze the associated $3\times3$ matrix Riemann-Hilbert problem by the Deift-Zhou nonlinear steepest descent method. By establishing joint error estimates for the CNLS solution and the gauge phase, we obtain a uniform long-time asymptotic formula for the dispersive radiation of the CKE equation with an $O(t^{-1}\log t)$ remainder in bounded velocity cones.

We study Ricci pinching problem on complete Kähler manifolds. For complete noncompact manifolds with Euclidean volume growth, we prove flatness under nonnegative bisectional curvature and Ricci pinching, and Ricci flatness under nonnegative Ricci curvature, quadratic curvature decay, and the same pinching condition. In both cases, the pinching constant may tend to zero at a logarithmic rate. Examples show that the logarithmic exponent is sharp in complex dimension two. Second part of the paper proves that a complete Kähler manifold of complex dimension at least two with positive holomorphic bisectional curvature is compact if its sectional curvature is nonnegative and its Ricci curvature is uniformly pinched outside a compact set. No volume-growth assumption or curvature upper bound is needed. Heat smoothing of the Busemann function supplies a strictly plurisubharmonic exhaustion with bounded gradient, so the general top Ricci-mass theorem of Datar–Pingali–Seshadri applies. The new ingridents are integral estimates for the Ricci form. The analytic arguments use scalar curvature gap theorems and a critical-$L^n$ vanishing theorem for closed real $(1,1)$-forms under nonnegative Ricci curvature and nonnegative quadratic orthogonal bisectional curvature. The Hodge-Laplace heat eqution deformation conserves the signed top-degree integral, including its initial value, while norm domination and scalar heat-semigroup decay force this integral to vanish. For semipositive initial forms this gives pointwise vanishing of the top wedge power.

In this paper, we study the maximal length of a minimal zero-sum sequence over $\left[\!\left[ -m,m \right]\!\right]^d$ having a support of size $d+1$. When $d=2$, we find the exact value of this maximal length for all $m \ge 2$, as well as the exact structure of all extremal sequences for this problem. When $d=3$, we obtain lower and upper bounds that asymptotically match each other as $m$ tends to infinity. This allows us to improve on the best known lower bounds for the Davenport constant of low-dimensional boxes.

The central object in this work is the Boolean network, a function $f:\{0,1\}^V \to \{0,1\}^V$. Often identified with $f$ is its dynamics $D_f$, the digraph with exactly $\{x \to y : f(x)=y\}$ as its arcs. The interaction graph of $f$ is the digraph $G$ on $V$ which can be thought of as representing the dependencies of the components of $f$ on one another. On the other hand, model-checking is a major field of study in graph algorithms and complexity. We consider problems at the intersection of these paradigms: for a given property $\phi$, we say that a digraph $G$ is $\phi$-dynamic if $G$ is the interaction graph of some Boolean network $f$ such that $D_f \models \phi$. The corresponding decision problem $\phi$-DYNAMIC asks whether $G$ is $\phi$-dynamic. Problems of this form are well-studied in the Boolean networks community. For example, it is a well-known result that, letting $\phi$ be 'No fixed points' (i.e. $\nexists x:x\to x$), $\phi$-DYNAMIC is equivalent to the structural digraph problem NON-ACYCLIC, which is solvable in linear time. We establish, for the first time, properties $\phi$ for which $\phi$-DYNAMIC is computationally hard. These include the 'Unique fixed point' property $\exists!x:x\to x$, and a range of properties concerning the periodic points of $f$ (i.e. vertices of $D_f$ which lie on a cycle). More widely, we exhibit an infinite family of natural properties $\phi$ such that $\phi$-DYNAMIC is $\mathrm{NEXPTIME}$-complete, which we call PERIOD PIECE. As a special case, these include all properties of the form 'Unique cycle of length $k$' and 'Exactly $k$ fixed points' for any $k \ge 1$. On the other hand, we show that if the input digraph has bounded in-degree, then for those same problems $\phi$-DYNAMIC collapses down to $\mathrm{NP}^{\mathrm{NP}}$, the second level of the polynomial hierarchy, though it remains $\mathrm{NP}^{\mathrm{NP}}$-complete.

PAC-Bayesian generalization bounds are among the strongest distribution-dependent guarantees in statistical learning and are typically expressed in terms of the Kullback-Leibler (KL) divergence between a prior and posterior distribution. While analytically convenient, the KL divergence requires the posterior to be absolutely continuous w.r.t. the prior, imposing support constraints that can substantially restrict the choice of posterior. Moreover, the KL divergence does not account for the underlying geometry of the probability space. In this work, we derive new PAC-Bayesian bounds replacing the KL divergence with general optimal transport (OT) distances, including the total variation and Wasserstein-$p$ distances.

We present a scalable method for identifying nonlinear dynamics from partial measurements, supporting physics-based, neural-network, and gray-box models. We use the Prediction Error Method (PEM) coupled with state estimation performed by a Moving Horizon Estimation (MHE) scheme, which can account directly for general nonlinear dynamics. This results in a bi-level optimization problem that scales poorly with increasing model parameters. To improve computational efficiency, we derive a reformulation that avoids explicit parameter-wide sensitivity matrices and exploits the temporal structure of the underlying optimization problem. Numerical comparisons show up to a $215\times$ speedup in hypergradient evaluation. Racing-vehicle simulations demonstrate accurate prediction and physical-parameter recovery in tire-force identification. Real-world data show that the gray-box model improves prediction accuracy with a neural residual while retaining physical interpretability.

World models capture environment dynamics and support counterfactual reasoning for planning. In image-goal navigation, where the target often lies beyond the current field of view, the agent must not only model environmental dynamics but also maintain a persistent spatial memory of the scene. Existing approaches either introduce spatial context by fine-tuning pretrained models on the target task, which underexploits their spatial priors, or rely on external 3D reconstruction, which is computationally expensive for real-world deployment. In this paper, we propose the Geometry Grounded World Action Model (G$^2$WAM) for image-goal navigation. G$^2$WAM encodes spatial cues through a learned scene-coordinate localization module that anchors the current, goal, and history frames in a common reference frame, yielding a stable and consistent spatial context that enables efficient navigation without explicit 3D reconstruction. Following the world-action-model paradigm, G$^2$WAM jointly predicts future states and actions, eliminating the need for costly cross-entropy method (CEM) style planning. In addition, G$^2$WAM operates entirely in latent space, avoiding the computational burden of pixel-level reconstruction and substantially reducing inference cost. Across four trajectory prediction benchmarks, G$^2$WAM reduces average ATE and RPE by 40.1% and 35.2%, respectively. In closed-loop navigation experiments, it improves the success rate from 54.0% to 63.0% and the success weighted by path length (SPL) from 36.4% to 59.2%, while maintaining high efficiency.

Feedback from massive stars regulates the formation of next-generation stars and planets and thus shapes the evolution of galaxies, yet observational evidence capable of determining which mechanism dominates the feedback process has long been lacking. Here,we present a large-scale HI survey toward Orion A$.$ With an unprecedented sensitivity and superior resolution, FAST (Five-hundred-meter Aperture Spherical radio Telescope) reveals a well-defined heart-shaped expanding HI bubble, enshrouding the well-known "Veil" bubble of ionized gas. The photoionization-driven and wind-driven gas expands at 10.9 and 13.8 kilometers per second, respectively, with a kinetic energy ratio of 1:2 assuming a spherical symmetry and a uniform HI-to-H2 ratio. This first direct comparison within a single bubble shows that radiation does not dominate the feedback process as predicted by classical theories; instead, stellar winds contribute a comparable share of the injected kinetic energy.

State estimation is widely used in networked dynamical systems, but released estimates may inadvertently reveal sensitive information about private state variables. Existing privacy-preserving estimation frameworks often do not explicitly account for adversarial prior knowledge. Motivated by this gap, we study privacy-preserving state estimation for discrete-time linear stochastic systems under prior information exposure using pointwise maximal leakage (PML). We first reveal a privacy anti-optimality property of the Kalman filter: in the absence of additive release noise, the steady-state Kalman filter maximizes PML privacy leakage among the considered class of stable linear estimators. We further establish a nontrivial lower bound on the steady-state estimation error enforced by $(\varepsilon,\delta)$-PML privacy. We then derive sufficient release-noise conditions that guarantee $(\varepsilon,\delta)$-PML privacy, first for the Kalman filter and then for stable linear estimators. Finally, a convex semidefinite program is formulated for a joint design of the estimator gain and release noise covariance, providing a tractable privacy-preserving estimator with an explicit upper bound on the steady-state estimation error. Simulations on a source–load power system demonstrate the proposed privacy–utility tradeoff.

We introduce $qt$Bench, a benchmark of 29 open problems in algebraic combinatorics. These problems ask for a simple combinatorial algorithm that explains given polynomial coefficients or identities. To help AI agents search for such algorithms, we provide a scaffold for playing with combinatorial objects, countering cheating attempts, and testing candidate solutions. To explore how far frontier AI systems can go on these problems, we collaborated with OpenAI, whose researchers obtained proposed solutions to several of them. This highlights bigger meta-problems: is AI discovery at scale ethical? How should these results be released? How should proof digestion be organized? We discuss these questions and give our views.

We study order convergence in ordered vector spaces that are not necessarily lattices. In this setting, we consider two generalizations of order convergence on vector lattices, a directed and an undirected variant. We show that these notions agree for the class of pervasive spaces and extend several results concerning atomicity and order convergence in vector lattices to this class. In particular, we prove that a pervasive JB-algebra is associative, which strengthens a result of Sherman for C*-algebras. We also establish a number of new characterizations of pervasive spaces. Additionally, we systematically study a class of order unit spaces associated to Banach spaces, called ice cream spaces. We provide descriptions of both directed and undirected order convergences in these spaces, yielding examples where the two notions differ. We also consider other order-theoretic aspects of ice cream spaces, such as atoms and lattice operations, relating them to the geometry of the underlying Banach spaces. We demonstrate that ice cream spaces exhibit behavior very different from vector lattices and can serve as a rich source of counterexamples in the theory of ordered vector spaces.

Active gels are intrinsically non-equilibrium materials whose structural and dynamical heterogeneity emerges from the interplay of attractive interactions, thermal fluctuations, and self-propulsion. We investigate a model active gel, simulated using large-scale Brownian dynamics simulations, to explore the effects of temperature $T$, active force strength $f_0$, persistence timescale $\tau_p$, and active particle concentration $\rho_a$. We characterize the structure of the evolving gel network through morphological analysis, while dynamical changes are quantified by the relaxation timescale and dynamical heterogeneity (DH). We show that an optimal choice of activity parameters yields a percolating gel network with faster gelation and larger voids and clusters, enhancing mechanical stability. Conversely, the structural relaxation timescale and DH decrease with increasing activity, indicating enhanced particle rearrangements and reduced spatial correlations of mobile and immobile regions. An effective temperature ($T_\text{eff}$) framework for colloidal gels maps structural quantities and relaxation timescales in an active gel onto those of a passive gel. More interestingly, the growth of DH with increasing swim force can also be described by the same effective-temperature framework, in stark contrast to observations in active glasses. Our findings show that, in colloidal gels, temperature and active force compete, giving rise to similar structural ordering and, consequently, similar DH at the same $T_\text{eff}$. These findings highlight the crucial role of structural ordering in governing DH in active colloidal gels, as compared to active glasses.

An ordered visual code lets a short prefix stand in for an image, and the training loss decides what that prefix contains. Under pixel reconstruction the first bits go to the directions of highest variance, and we prove that a caption can then be independent of the entire first half of a code that is rate-optimal for pixels at every length. In the rate-distortion sense a caption is therefore not the low-rate code of its image, unless the code is built to make it one. We study that construction and what it costs. We cast captioning and text-to-image generation as successive refinement under a distortion measure that changes along the code, from caption log-loss in the early stages to pixel distortion in the last, so that each stage is compared with its own optimum. Putting words first then costs nothing among the caption stages exactly when the captions form a summarization chain, and it costs the pixels at most the caption uncertainty left in a pixel-optimal reconstruction, which is large for short prefixes and small at full length. We build RUNG, an ordered code whose prefixes are supervised by a summarization ladder of captions and whose full length reconstructs the image; generation extends the code past the prompt and captioning truncates it. With data and capacity held fixed, ordering by language instead of reconstruction raises prefix-caption information 2.9 times and GenEval from 0.76 to 0.83, at a measured cost of 2.8 dB PSNR at a quarter of the code and 0.1 dB at full length. RUNG-XL (3.4B) reaches 0.88 GenEval and 87.6 DPG-Bench in 32 network evaluations and 0.91 GenEval when errors are redrawn at the rung where they appear; its coarse and fine captions agree 94.1% of the time, and it edits images without inversion.

We study a long-duration, confined X2.0-class solar flare exhibiting three distinct episodes of HXR emission, along with an accompanying EUV late phase. A key highlight of this work is the novel observations from the high-resolution solar X-ray spectrometers SoLEXS and HEL1OS onboard Aditya-L1, providing insights into the evolution of thermal and non-thermal emissions. Simultaneous EUV observations from AIA/SDO in hot channels, combined with multi-band X-ray light curves, reveal a two-stage confined eruption of a large MFR, separated by $\sim$10~minutes. The first stage corresponds to an M4.6 flare, while the overall event reaches X2.0 on the GOES scale. During the first phase, magnetic reconnection beneath the large EUV hot channel causes plasma heating to $\sim$19~MK, with a non-thermal spectral index of $\sim$4.3. In the second phase, characterized by external reconnection and confinement of the MFR hot channel, the temperature increases to $\sim$22~MK, accompanied by further hardening of the spectral index to $\sim$3.9. Despite pronounced non-thermal signatures and enhanced particle acceleration, the MFR fails to erupt through the overlying coronal loops because of the strong strapping force exerted by the large overlying coronal loops. Importantly, the stalled eruption, together with reconnection in the higher overlying loops, results in enhanced heating within a closed magnetic configuration, with temperatures peaking at up to $\sim$15~MK during the late phase. The paper also provides the first observations of detectable non-thermal X-ray emission during the early EUV late phase, albeit briefly, providing direct evidence for reconnection-induced heating, likely occurring in the higher overlying coronal loops.

General-purpose frontier models are large, expensive to run, and increasingly reluctant to engage with authorised defensive- and offensive-security work. We ask the opposite question: how small can a cybersecurity-specialist transformer be while remaining genuinely useful to a security practitioner? We introduce CT0, a Cybersecurity Transformer architecture, and CT0-Micro, its first incarnation: a compact (~4B-parameter) model built on the open base model, whose backbone is specialised by two-phase on-policy distillation on our Cybersecurity AI (CAI) dataset. CT0 serves two modes from one set of weights: System 1 answers typed security decisions (is this file suspicious, is this request an attack, did the model just refuse) in a single forward pass without generating a token, System 2 is the usual tool-using agent, and a confidence gate spends generation only where the fast path is unsure. Specialisation lifts the agentic path: CT0-Micro solves 21.1% of cybench-subtask against 7.6% for its base, above every open model of comparable footprint and the densest cybersecurity capability per parameter we measured. The fast path is what the architecture buys: CT0-Micro screens eighty files per second for indicators of compromise, catches its own refusals at 96.5% accuracy in 47 ms where the model judging itself reaches 76.5% in 254 ms and misses half of them, flags jailbreak requests at AUROC 0.966 in 8 ms, and, generating only for the facts it is unsure about, extracts vulnerability facts more accurately than either mode alone at a fifth of the generative cost. All of it is built in about 314 RTX PRO 6000 GPU-hours and served from one workstation GPU, with no policy layer between operator and target. Across eighteen benchmarks and use cases run with one checkpoint and head, we report where the design helps, where it does not, and what it still lacks.