Papers

MnBi$_2$Se$_4$, MnSb$_2$Se$_4$, and MnSb$_2$Te$4$ are layered magnetic quantum materials of interest for spintronic and topological electronic applications, where control of magnetic order at the atomic scale is essential. These materials are particularly sensitive to strain. We investigate their strain-dependent magnetism in the monolayer limit using first-principles calculations across the full two-dimensional strain space spanned by independent variations of the two in-plane strain components. Our results show that the Mn-projected local moments depend primarily on the volumetric strain, whereas the magnetic ground state, exchange interactions, magnetocrystalline anisotropy, and ordering temperature show pronounced directional and composition-dependent responses. We also observe strain-induced competition between the phases, with MnBi$_2$Se$_4$, and MnSb$_2$Se$_4$ monolayers exhibiting a more diverse range of competing magnetic states, while MnSb$_2$Te$_4$ monolayer remains ferromagnetic over a larger portion of strain space. MnSb$_2$Te$_4$ also exhibits a substantially larger out-of-plane magnetocrystalline anisotropy, while showing a weaker dependence on strain than the Se-based materials. The calculated magnetic ordering temperature maps further highlight the role of two-dimensional strain to tune thermal magnetic stability in these materials. These results establish magnetoelastic trends across this family of Mn-based chalcogenide monolayers.

We describe the design and characterization of a neutron scatter camera specifically developed for the study of neutron fields (flux, energy, direction) in experimental areas of spallation facilities, where multiple neutron sources can simultaneously contribute. A combination of hardware and logic triggers provides the isotropic response required for this application. Neutron source locations are accurately reconstructed on images from a built-in 360$^\circ$ panoramic camera. The full understanding of neutron fields that the device provides can be used for site selection and abatement of neutron backgrounds affecting sensitive instruments such as coherent elastic neutrino-nucleus scattering (CE$\nu$NS) detectors to be located at the upcoming European Spallation Source.

We show that all normal covers of a fixed finite graph $G$ sitting between the universal and maximal abelian covers share the same atomic part of their spectral measures. We give an explicit double formula for the mass of atoms which generalises and unifies known results on universal covering trees and maximal abelian covers. It also proves an extension of a conjecture in physics literature on hyperbolic lattices. Moreover, we also establish the logarithmic Hölder regularity of the continuous part of the spectral measures. Our proof combines techniques from von Neumann algebras, matching theory and the monotone labelling method. In an appendix, we prove a converse generalised Gallai-Edmonds structural theorem which might be of independent interest.

High-stakes advisory domains such as medical aesthetics, legal consultation, and educational planning exhibit a two-phase structure. The early phase requires empathetic elicitation and emotional support, and the late phase requires authoritative specialist judgment. Neither fully automated agents nor human junior consultants adequately address this structure at scale. We formalize the core design challenge as dynamic decoupling, asking how an AI advisory agent should decide what to ask, when to stop, what to resolve autonomously, and what to forward to the specialist. We present ThuRunel, an advisory agent combining a finite-state belief management framework, a chain-of-thought teacher synthesis protocol, and learned generation adapters. Against eleven baselines, ThuRunel achieves consistent improvements in elicitation completeness and specialist brief quality. ThuRunel is publicly deployed as a bilingual web application in which the same decoupling decisions operate from the client's side, grounded in a curated knowledge base that cites its sources in every answer.

Purpose: Adaptive proton therapy (APT) relies on routine offline CT simulations for updated anatomy. We present a modality-agnostic regularized Brownian bridge (rBBrg) framework to deterministically predict stopping power ratio (SPR) maps from CBCTs or MRIs. Methods: rBBrg consisted of (1) generation mapping where a Brownian bridge predicted SPR from input and (2) reconstruction mapping where a cGAN reconstructed input from predicted SPR. Class embedding was adopted for modality conditioning. Efficient, deterministic prediction was achieved via one-step sampling. Unimodality rBBrg and ResNet were implemented for comparison. Matched-pair planning CT-CBCT (n=37) and CT-MRI (n=21) from head-and-neck cancer patients were evaluated. A calibration phantom was scanned to establish Hounsfield look-up table for real SPR. Predicted SPR maps were evaluated via mean absolute error (MAE), peak-signal-to-noise ratio and structural similarity against ground truth with demonstration of dosimetric performance. Results: For CBCT-SPR synthesis, most metrics were comparable across models (p>=0.05). Modality-agnostic rBBrg outperformed ResNet in MAEbone (0.059 vs 0.067, difference=11%, p<0.05) and showed lower MAEexternal than ResNet (0.038 vs 0.040, p=0.05). Modality-agnostic and unimodality rBBrg were comparable (p>0.05). Qualitatively, both rBBrg better preserved anatomical fidelity than ResNet. For MRI-SPR synthesis, performance was overall comparable across models (p>0.05). Modality-agnostic rBBrg obtained MAEexternal=0.057. Dose calculation comparisons between real and CBCT-predicted SPR were higher in modality-agnostic rBBrg predictions compared to ResNet with gamma pass rate=98.8%/99.3% vs 94.5%/96.9% at 2 mm/2%, respectively. Conclusion: A novel modality-agnostic rBBrg model was developed to generate high fidelity, deterministic SPR from CBCT or MRI to support efficient and flexible APT workflow.

We introduce the T-Adaptive Segment Routing, a multi-period optimization problem that emerges in the traffic engineering of core IP/MPLS networks when scheduled maintenance operations are involved. The problem seeks a sequence of Segment Routing (SR) configurations that can adapt to a multi-period scheduled maintenance, while allowing limited number of path reconfigurations between successive time steps. Instead of only minimizing the classical Maximum Link Utilization (MLU) criteria, we propose a more refined lexicographic objective that minimizes the sorted vector of link loads in its entirety, thereby enabling a more efficient resource utilization across all links. To tackle this problem, we develop three exact formulations for solving the resulting lexicographic optimization problem. Among these, the Stela and Carla formulations provide the most favorable computational basis for trajectory-based optimization. We thus develop a trajectory column-generation scheme for these formulations, using pricing oracles that vary from heuristic to exact. Exact pricing gives an exact solution of the LP relaxation of the trajectory master, but it does not itself give a certificate of integer optimality: solving the integer master over the columns generated at the root node only certifies optimality within the generated column pool. To overcome this gap, we incorporate trajectory column generation into a Branch-and-Price framework. The branching rule operates on aggregate variables representing segment usage, which correspond to the original compact routing variables. Thus, Branch-and-Price guarantees global integer optimality for every Stela and Carla rank, and when all ranks are solved to exactness, it guarantees lexicographic optimality of the final solution.

Tabular foundation models achieve strong performance by conditioning on labelled examples in context, but softmax attention limits their use on large datasets. Existing linear-time alternatives, however, are mostly causal, and their potential for tabular in-context learning (ICL) remains underexplored. To address this, we (1) revisit causal training setups, (2) compare linear sequence mixers, and (3) investigate their ICL generalisation beyond the pretraining context length. First, we show that the best training setup for causal models resembles next-token prediction. Then, perhaps surprisingly, the most promising linear sequence mixer is causal: DeltaNet outperforms even non-causal linear attention. However, it degrades beyond $2$-$4\times$ the pretraining context length, and existing mitigation strategies such as bidirectionality defer the problem at best. A hidden-state oracle shows that this is not a capacity problem. Instead, our analysis points to an instability in the recurrent state, which drifts in deeper layers of causal models. Since DeltaNet's learned write rates overfit to the pretraining regime, we modulate them with a time-dependent decay schedule intervention to stabilise length generalisation. Finally, re-introducing non-causality by reading out from the final state allows us to closely match a controlled softmax attention baseline on OpenML-CC18 and TabArena.

We prove a separability rigidity theorem for finite-mode Gaussian states. Let $\rho_G$ be Gaussian and let $\mathcal I$ be a fixed partition of the modes. If $\rho_G$ dominates a nonzero positive operator $T$ that is separable across $\mathcal I$, $0\neq T\preccurlyeq \rho_G$, then $\rho_G$ itself is separable across $\mathcal I$. The dominated operator is arbitrary and need not be Gaussian. The theorem has three applications. First, any Gaussian channel admitting a nonzero entanglement-breaking completely positive subchannel is itself entanglement breaking, even when that subchannel is non-Gaussian. Second, if a resource state dominates a positive multiple of a faithful separable state, no finite-copy, postselected separability-preserving protocol can prepare an entangled Gaussian state exactly with nonzero success probability. Third, a connected graph of entangled Gaussian two-mode marginals certifies genuine multipartite entanglement of every compatible global state, even if the global state is non-Gaussian; the certification is robust to sufficiently small trace-norm errors in the marginals. As a structural corollary, mixing states separable across different partitions cannot produce new Gaussian states, so full inseparability and genuine multipartite entanglement coincide for finite-mode Gaussian states and identical copies of a biseparable Gaussian state cannot activate genuine multipartite entanglement.

Quantum fire consists of quantum states that can be efficiently functionally cloned but cannot be transmitted using one-way classical communication. Whereas all previous quantum-fire constructions with proven untelegraphability are relative to an oracle, ours, based on one-shot signatures, is in the standard model. Our construction achieves two further notions that we introduce: (a) keyless untelegraphability, a strengthening of untelegraphability; and (b) conversability, meaning that a flame, though not telegraphable via one-way classical communication, can be transmitted via classical interaction. Hence one-way and two-way classical communication differ qualitatively in their power to transmit this quantum fire. We use these two novel properties of quantum fire, along with its clonability, to give one of the first cryptographic applications of quantum fire. Keyless untelegraphability forces the distribution of serial numbers of valid flames to have high min-entropy, while conversability and clonability allow the corresponding flame to be cloned and transferred using only classical communication. We present two variants of our conversable quantum-fire construction. The first, based on one-shot signatures (instantiable from subexponential iO, subexponentially secure one-way functions, and LWE), supports polynomially many flames, and super-logarithmic min-entropy of the serial-number distribution. The second, under the stronger assumption of exponentially unforgeable one-shot signatures (instantiable relative to a classical oracle), supports exponentially many flames, and linear min-entropy.

While nonlinear systems can be generally described as infinite-dimensional linear systems via their Koopman semigroups, the direct synthesis of state observers on the premise of learned Koopman operator models, in an analogous manner to finite-dimensional linear systems, remains an open problem. In this paper, the concepts of Koopman observability (exact and approximate), Koopman detectability (exponential and strong), and Koopman–Luenberger observer of nonlinear systems are provided. By defining the Koopman semigroup on a reproducing kernel Hilbert space (RKHS), the conditions for Koopman exponential detectability are established, which involves solving an operator Lyapunov inequality that only implicitly involves the the infinitesimal generator of the Koopman semigroup. Through the use of a finite-horizon Yosida approximation of the Koopman generator and an empirical sampling operator, the data-driven solution of the observer gain can be reduced to a finite-dimensional subspace specified by the sample and hence fulfilled by convex semidefinite programming. The state observation error is guaranteed to be bounded in mean squares, under closed-loop dissipation conditions on the sampling operator and its empirical operator.

Latent world models rely on representation geometry for planning, yet regularizing the latent marginal alone does not determine the state-to-state relationships used for action selection. We show that this can cause planning-relevant novelty structure to be weakened as representations are transformed into the final latent used by the planner. We introduce Aligned Transport of Latent Structure (ATLAS), a training objective that explicitly preserves relational geometry while calibrating the global latent distribution. ATLAS transfers normalized pairwise structure from an informative encoder representation to the planning latent and uses Wasserstein embedding matching (WEMReg) to calibrate its marginal through one-dimensional Wasserstein-2 transport. Our analysis shows that relational preservation and marginal calibration impose non-redundant constraints, and connects finite-candidate planning stability to relational distortion, latent-scale mismatch, and prediction error. Instantiated in LeWM, ATLAS improves mean goal-reaching success across PushT, TwoRoom, and OGBench-Cube on both lower- and higher-novelty evaluation subsets, with the largest gain on higher-novelty TwoRoom episodes. Representation and rollout diagnostics further show stronger novelty-related structure in the planning latent, improved marginal calibration, and lower multi-step prediction error. Together, these results highlight preservation of planning-relevant latent geometry as an important ingredient for reliable world-model planning. Code is available at https://anonymous.4open.science/r/atlas-world-model-72C4/.

The order $m$ antisymmetrised matrix product ensemble is represented by the product $X_1^T\cdots X_m^TJX_m\cdots X_1$, where $X_1,\ldots,X_m$ are independent real Ginibre matrices and $J$ is the elementary antisymmetric matrix, while the order $m$ Hermitised matrix product ensemble is represented by $X_1^\dagger\cdots X_m^\dagger HX_1\cdots X_m$, where $X_1,\ldots,X_m$ are now independent complex Ginibre matrices and $H$ is a Hermitian matrix drawn from the Gaussian unitary ensemble. These ensembles have recently been shown to be related to certain Muttalib–Borodin ensembles and integrals of Harish-Chandra–Itzykson–Zuber type, thereby motivating further investigation into their eigenvalue statistics. In this work, we construct ribbon graphs and constellations that are enumerated by the mixed cumulants of these ensembles and give loop equation characterisations for the generating functions of said cumulants when $m=1$.

The state-of-the-art Membership Inference (MI) methods calibrate their signal separately for each example using reference models, auxiliary models trained to exclude the target. This paradigm scales poorly to modern large models, however, whose training is too expensive to replicate. This has motivated one-round settings, where only a single trained model is available; but without reference models the per-example calibration that drives the strongest attacks can no longer be estimated, leaving the membership signal weak. We ask whether neighbors of the target point can recover this calibration without training any additional model. Our key observation is that reference models serve only to reveal how an example behaves under models not trained on it, and that querying the target model on nearby samples yields the same information. We propose two complementary ways to obtain such neighbors, and show that querying them against an early training checkpoint further sharpens the signal. We evaluate across three image classification datasets and three training setups, showing that neighbors yield strong membership signals and competitive attack performance at no additional training cost.

Decentralized Federated Learning (DFL) eliminates the central aggregation server, reducing the single point of observation that traditional defenses against attacks rely on. As a result, peer-to-peer networks become exposed to malicious updates containing backdoors or semantic poisoning, since such updates can remain close to benign ones in the parameter space while behaving very differently. This may evade defenses based on passive parameter inspection. However, existing deception-based defenses have mainly been designed for centralized FL and do not jointly address local observation, poisoning propagation, source attribution, and containment in strictly serverless DFL. To address these limitations, this paper presents DecoyTrace, a proactive cyber deception-based defense for strictly serverless DFL environments. DecoyTrace deploys a mobile DecoyNode that generates decoy challenges using chaotic maps, disseminates a dual model (clean vs. decoy) based on neighbor trust, and evaluates them using three-state semantic metrics. Upon confirmation, a distributed protocol isolates the source and performs a model reset or recovery to preserve training progress. Evaluated across sixty configurations on the NEBULA platform (five datasets, three topologies, and four attack/defense scenarios), DecoyTrace systematically restores lost utility. The F1-score remains within 0.03 of the baseline on MNIST/FashionMNIST (mitigating drops of up to 0.37), matches or exceeds the baseline on EMNIST and CIFAR-100, and remains between 0.05 and 0.10 below the baseline on CIFAR-10, the most visually complex convolutional scenario evaluated. Furthermore, containment reduces CPU and network usage by up to two-thirds. These results demonstrate the feasibility of unifying deception, identification, and containment in DFL, while also identifying its limitations in complex tasks and multi-attractor threat models.

Parameter-efficient fine-tuning (PEFT) determines not only how many parameters are trained, but also which local directions a model can move in, so similar adapters can affect subgroup losses differently. Since curvature matrices are infeasible to form at adapter scale, scalar summaries such as the Fisher trace are often used instead. We study what the trace reveals and what it loses through the reachable Fisher: each subgroup's full-model Fisher pulled back through the adapter Jacobian. Under likelihood losses, it represents the Gauss-Newton curvature accessible to the adapter, and its trace can be computed from score-gradient norms without forming the full matrix. Under matched subgroup gradients, a positive-definite reachable-Fisher difference, with a margin exceeding the Hessian-Fisher defect, implies that every sufficiently small nonzero model-changing update increases the signed gap. In contrast, the restricted operator norm determines worst-case quadratic change, while a matrix-free Frobenius discrepancy bounds its reachable-Fisher component. Trace alone cannot certify definiteness or control matrix mismatch. Equal traces rule out a positive-definite difference but can still hide large operator discrepancies. Across 306 single-seed models, higher trace accompanies greater subgroup difficulty in 75.7 percent of 1,218 eligible evaluations, while trace matching reduces the best-worst subgroup gap in all 30 dataset-encoder-adapter combinations. However, held-out audits show that operator discrepancy decreases in 23 of 30 combinations, while the unbiased squared-Frobenius statistic decreases in only 16 of 30. Fisher trace is therefore a scalable diagnostic and training heuristic, but not a certificate of local gap behavior or matrix alignment.

We propose a Bayesian regression tree model fit within a multilevel structure and apply it to historic wildfire data in the western United States. Sharing of information between related groups (ecoregions) combined with highly interpretable regression trees allows for better predictions and understanding of climate and land cover variables predictive of wildfires. By doing a simulation study with a range of performance metrics, we demonstrate our method produces tree posteriors most structurally similar to assumed true trees, while simultaneously achieving good out-of-sample predictive performance. Applied to a large wildfire data set, we explore variable splits within regression trees corresponding to each ecoregion in detail, taking into account known features of each location. Shared hyperparameters between trees provide highly useful understanding of both variable and split value importance in predicting wildfires among all ecoregions, with no direct parallel in comparable models. Namely, we highlight potential evaporation, temperature, and evergreen forest land cover as variables most associated with historic wildfires, with some observable patterns in split values most commonly chosen across the groups. We propose a new algorithm based on parallel tempering, conditioning on shared hyperparameters at the true posterior temperature, improving Markov chain mixing, a known bottleneck in Bayesian CART models.

Precise strong-gravity models describing the evolution of bound compact binary systems provide important information about the gravitational radiation such binaries generate and how they evolve due to the radiation's backreaction. The limit of very high eccentricity, $e \to 1$, is challenging to model: frequency-domain techniques require many harmonics to accurately describe radiation in this limit, and time-domain techniques can be slow to converge due to the systems' long timescales. Many recent astrophysical analyses have nonetheless emphasized the importance of understanding gravitational-wave emission in this regime, highlighting the fact that many systems may evolve through $e \simeq 1$ en route to becoming detectable sources, and may enter the sensitive band of detectors with substantial eccentricity. In this paper, we show how to adapt frequency-domain methods for computing gravitational radiation in the small-mass-ratio limit to effectively handle high eccentricity. The key piece of this analysis is an integral over the source of the frequency-domain Teukolsky equation. We examine features of this integral that make it difficult to evaluate as $e \to 1$, and study methods to circumvent these difficulties. We find a simple fix which allows us to compute gravitational-wave amplitudes and the associated fluxes of energy and angular momentum with ease up to eccentricities $e = 0.99$; with patience (and stamina), we have pushed to $e = 0.999$, though numerical accuracy appears to degrade for such extreme cases. Interestingly, we find that the well-known and often used classic formulas of Peters and Mathews are subject to a systematic error which persists at quite wide separation. This has implications for models of compact binary formation which evolve through $e \simeq 1$.

Retrieval-augmented generation (RAG) hands the user's query to whoever hosts the corpus. We propose PILLAR, a Privacy-Preserving RAG (PPRAG) system based on Private Information Retrieval (PIR) in which a client utilizes the k documents most similar to their query from a server-held and publicly known corpus to respond to their query, while the server learns nothing about the query, either its terms or its access pattern. Prior PPRAG constructions rely on dense retrieval alone, translating approximate nearest-neighbor search into many query-dependent rounds of PIR, and pay for it in both latency and retrieval quality. PILLAR instead performs private hybrid retrieval in two stages. A sparse stage issues a small, fixed number of PIR queries against a carefully designed index of precomputed BM25 scores, filtering the corpus down to candidates that share terms with the query without the server ever seeing which terms these are. A dense stage then fetches only those candidates' document embeddings and re-ranks them locally, avoiding the many costly PIR queries that private dense retrieval typically requires. We instantiate PILLAR with two protocols that trade latency against retrieval quality, each built on a different private rendering of lexical search. PILLAR-Bin bins posting lists into a hash table and is a single-round design that achieves lower latency than state-of-the-art private retrieval schemes. PILLAR-Tree turns block-max pruning into an oblivious tree traversal combined with cuckoo hash tables and achieves the highest retrieval quality at lower latency than state-of-the-art schemes.

Varying coefficient (VC) regression models have become indispensable tools in spatial data analysis, providing unmatched flexibility in capturing complex, nonlinear relationships and spatially-varying effects of predictors on responses. Although hierarchical Bayesian approaches offer a rigorous probabilistic framework for uncertainty quantification in VC modeling, their practical application to large-scale spatial datasets remains severely hindered by the scalability limitations of Markov chain Monte Carlo (MCMC) algorithms. In response, the past decade has seen substantial advances in developing more efficient hierarchical Bayesian VC models, primarily through substituting traditional Gaussian processes (GP) with computationally efficient stochastic surrogates for estimating unknown coefficient functions. This article introduces a fundamentally different approach: the Geostatistical Variational Auto-Encoder (GeoVAE), a hierarchical deep generative framework built specifically for joint estimation of multiple spatially varying coefficient functions. GeoVAE departs from both classical GP-based Bayesian models and standard variational auto-encoders (VAEs) in two key ways. First, it constructs a coefficient-specific auto-encoder for each coefficient function, allowing each to capture its own spatial resolution and smoothness. Second, a hierarchical synthesis layer integrates information across these auto-encoders to a shared auto-encoder, explicitly modeling cross-coefficient dependencies arising from the shared spatial domain. This design enables GeoVAE to recover complex spatial patterns at computational cost that scales favorably with sample size, without MCMC or explicit GP covariance representations. We characterize the advantages and limitations of GeoVAE relative to hierarchical Bayesian spatial models, demonstrating its strong potential for large-scale spatial analysis.

Flow-matching text-to-speech (TTS) models achieve high synthesis quality but require many neural function evaluations (NFEs) to integrate their generative trajectories. Recent few-step flow-map distillation approaches for TTS construct targets from numerically integrated teacher trajectories, creating a trade-off between target accuracy and training cost. We propose Local Flow-Map Distillation (LFMD), which adapts Eulerian Map Distillation to conditional TTS and avoids teacher trajectory integration during target construction. For inference, we derive a sampling schedule (TD-DP) from teacher dynamics and consistency of the learned maps, with a single cost graph supporting multiple NFE budgets without external audio-metric evaluation. Because scheduling offers no flexibility at one NFE, we refine this regime with alignment-aware temporal self-distillation using soft-DTW. Across Seed-TTS and LibriSpeech-PC, LFMD improves low-NFE synthesis over a matched integral-distillation baseline. On Seed-TTS, the refined student reaches 1.80% WER with 1-NFE, compared with 1.76% for its 32-NFE teacher.

AI-assisted coding tools deliver significant acceleration of coding, but only limited impact across the end-to-end software development lifecycle (SDLC)–an Amdahl's law effect! In this paper, we discuss our progress towards building an AI SW Factory that accelerates all the stages of SDLC-Targeting, Coding, Reviewing, and Ops. The AI SW Factory produces a metadata exhaust that enables self-improvement by fine-tuning model weights and updating our World Model (a rich data substrate). We focus on Data Systems and the important class of Evolutionary Coding Tasks (i.e., those with a measurable objective to hill-climb) and report on 1) scaled deployments at Microsoft (tens of repositories) leading to 3x engineering efficiency above agentic coding and up to 22x token efficiency, and 2) several open challenges.

Chunked KV-cache compression reduces the memory and attention costs of long-context inference by compressing windows of consecutive tokens into fewer cache entries at a fixed stride. Such compression also introduces a new positional coordinate: a token's phase, or its position relative to compression-window boundaries. We uncover a systematic asymmetry in models using such compression: the same information can be easy to retrieve at one phase and difficult at another. We call this periodic variation in retrieval performance phase sensitivity. In large open-weight models with such compression, long-context retrieval accuracy can differ by up to 40 percentage points across phases, revealing periodic weak spots that average benchmark scores can conceal. To investigate this behavior, we pretrain a family of transformers from scratch across multiple KV-compression designs, reproducing phase sensitivity across the variants. Mechanistic analysis using causal interventions in these models reveals phase specialization: different attention components contribute asymmetrically to retrieving information at different source phases. We further analyze idealized retrieval models, showing how gradient flow dynamics may favor sharp phase specialization. Evaluating models with chunked KV-cache compression thus requires measuring across compression phases: high average accuracy can coexist with systematic positional failures.

We define and study the $F$-signature of big divisors on projective varieties in positive characteristics. For a normal projective variety $X$, we show that the $F$-signature function defines a continuous function on the big cone of $X$, extending our previous results on the ample cone. By studying the the Frobenius-alpha invariant on the big cone, we prove that the positivity of the $F$-signature of any big $\mathbb{R}$-divisor on $X$ is equivalent to the global $F$-regularity of $X$. As applications, we prove a birational transformation rule for the $F$-signature in terms of the $F$-signature of certain graded ideal sequences. We also prove that in a reduction modulo $p$ situation, a characteristic independent lower bound for the $F$-signature of $X$ with respect to any ample divisor $L$ spreads out to a similar bound for arbitrary big divisors on $X$.

In the present study, we explore the existence and characteristics of a rotating vibrational mode in a discrete buckled ring that manifests under transverse harmonic forcing. The study is conducted through mathematical analysis complemented by numerical simulations. The ring is composed of uniformly distributed concentrated masses connected by linear and torsional springs and supported by an elastic foundation. The buckled state of interest results from homogeneous in-plane compression and is characterized by vibrational modes that have a rotating nature because of the rotational symmetry of the system. The resulting vibrational mode, called a rotational soft mode, is characterized by large amplitude rotations of the ring deformation while keeping its angular momentum zero. It is shown that rotational soft modes can be activated via transverse harmonic forcing through parametric resonance, which is possible only when nonlinearities are introduced to the foundation. In the absence of nonlinear behavior, transverse vibrations of the ring cannot lead to excitation of the rotational mode. Analysis of a constrained kinematics model shows that linear stiffness of the foundation leads to decoupling of the rotational mode from transverse vibrations. When the foundation is considered piecewise linear, with different stiffness values in compression and in extension, it is shown that three different behaviors are possible for the dynamic response of the forced ring: i) no rotation, ii) a limit cycle within a limited finite rotation angle range, iii) induced rotation between subsequent equilibrium angles. The present study contributes to the understanding of the activation and control of soft modes in buckled structures and may lead to actuation applications in soft robotics, as well as advanced manipulation strategies of molecular systems in the context of nanomechanics.

Despite the recent success of coding agents built on large language models, it remains challenging to run them over long horizons, since every observation is appended to the context and the context grows with each one. History-based maintenance is a common remedy, which masks or summarizes old observations, or prunes what a model reads as useless, and bounds the context at little cost. However, it decides from the text of the history alone and sees nothing of how the code is connected. Since a coding agent edits code many times over a single task, and each write can change what code elsewhere means, such maintenance may keep records a write has falsified, drop ones that still hold, and miss code the agent needs next. To overcome these challenges, this paper proposes StateTape, a novel and scalable framework that rewrites a coding agent's context as the repository changes rather than as the context grows. The key idea of StateTape is to model the repository as a symbol-level code graph, whose dependencies and language rules expose which symbols a write can affect. Upon this graph, a tape marks the symbols each write changed, which turns staleness from an inference about text into an observation of the agent's writes. We propose a per-write procedure in which the tape nominates the records a write could have falsified while a small manager model settles what the write log cannot, and further provide a theoretical analysis and TraceBench, a benchmark that labels what an agent is holding against what is actually needed. Empirically, we demonstrate that StateTape can effectively clear falsified records and retrieve what is needed, and thus achieve a higher resolve rate in all experiments spanned by six coding agents and three edit-heavy benchmarks with little computational overhead.

We report on JWST/MIRI low-resolution spectroscopy ($5$-$12 \mu$m) and imaging ($15$-$25 \mu$m) of the black hole X-ray binary XTE~J1118+480 in quiescence, at an X-ray luminosity nine orders of magnitude sub-Eddington, together with contemporaneous optical monitoring and a radio upper limit of $4.5~\mu$Jy at 6 GHz. With the donor subtracted, the $5$-$12 \mu$m continuum is curved, turning over near $6~\mu$m; a single power law is rejected in favor of a $764\pm 9$ K blackbody. Longward of the turnover the spectral index is $\alpha = +1.21\pm0.36$, steeper at the $2\sigma$ level than the flat to slightly inverted spectrum of a compact jet. Interpreted as synchrotron, the turnover implies equipartition fields of $\sim$$10^{4}$ G on scales of tens of gravitational radii, but the MIRI photometry at $15$-$21~\mu$m-taken $2.6$ hr before the spectrum-lies $30$-$90$ per cent above its extrapolation, suggesting a second self-absorbed zone. A single partially self-absorbed jet spectrum can reach the photometry only at the expense of the spectral curvature and the $25.5~\mu$m upper limit, so a steady compact jet is disfavored, although not excluded. Representative self-consistent irradiated-disk models instead reproduce the principal features of the $5$-$25~\mu$m spectral energy distribution, with a directly illuminated dust wall at $\simeq 5$ binary separations, outside the tidal-truncation radius, and a minimum dust mass of order $10^{22}$ g. This is the first spectroscopic evidence, though not yet conclusive, favoring circumbinary dust over a jet in a quiescent black hole X-ray binary.

We introduce frustrated triangular networks that mix two different beam thicknesses. The two thicknesses separate the energetic costs of second-order buckling and angular deformation into four competing contributions. Using scaling arguments and mapping to an effective Ising description, we construct the system's phase diagram in terms of its dimensionless geometric parameters. Selected beam arrangements exhibit local bistability: hexagonal motifs switch independently between opposite twisting states, while linear motifs support independently switchable beam states. In both cases, the number of mechanically stable configurations grows exponentially with system size. Experiments on fabricated silicone metamaterials confirm the predicted bistability and local switching. More generally, the allowed beam arrangements map onto rhombus tilings, producing a large combinatorial space of architectures. The system thus combines multiplicity in both architecture and stable deformation states, establishing beam-thickness patterning as a route for programming frustration, multistability, and extensive degeneracy in triangular mechanical metamaterials.

Evaluation awareness (EA) can cause large language models (LLMs) to behave differently during audits than in deployment, yet measuring and accounting for EA remains challenging. We introduce verbalization training (VT), a method for making LLMs less reticent about verbalizing evaluation awareness while avoiding to supervise the latent belief itself. VT uses a model's spontaneous verbalizations as evidence that awareness is present and truncates each rollout immediately before the verbalization, producing training prefixes at which the model is presumed to be aware. The model is then trained with an RL objective designed to increase verbalization in a calibrated way. Across Qwen3.6-35B-A3B, Kimi K2.6, and Inkling, VT increases verbalized EA by 2.4-2.9 times and transfers to held-out agentic settings, while measured latent EA and behavior remain largely stable. In a causal experiment, we independently implant meta-knowledge about evaluations through synthetic-document fine-tuning and show that VT-induced verbalizations reflect the richer knowledge acquired by the model.

Wildfires are an increasing hazard to ecosystems, air quality, and human systems, creating a growing need for datasets that support systematic development and evaluation of models for predicting fire spread across diverse landscapes. Effective prediction requires integrating meteorological conditions, fuels, vegetation, and topography at spatial and temporal resolutions suitable for both physical simulation and data-driven approaches. However, existing datasets often lack the resolution and coverage needed to capture these interacting controls. The PyroStack dataset addresses this gap by providing a harmonized, event-based collection of wildfire and environmental data across the contiguous United States and Alaska. It integrates satellite-derived fire observations with atmospheric reanalysis, vegetation, fuel characteristics, and topographic information into a unified framework spanning 6994 wildfires that occurred between 2012 and 2024 across a wide range of ecosystems and climate conditions. PyroStack offers spatial resolutions ranging from 30 m to 9 km and hourly temporal resolution, along with fire progression data at 12-hour intervals to support model initialization and evaluation. By combining broad spatial coverage with fine spatial and temporal detail, the dataset enables systematic analysis of wildfire dynamics and supports both physics-based and machine learning approaches, providing a foundation for benchmarking and improving fire spread models, with future extensions aimed at incorporating additional regions and fire suppression data streams to further advance wildfire prediction.

State Space Models (SSMs) compress sequence history into a bounded recurrent state, making the resulting memory law a central architectural choice for long-context performance. Most modern SSMs rely on ODE-based dynamics that lead to exponential forgetting, limiting their ability to retain information over broad temporal ranges. We introduce FRAC, a selective SSM architecture derived from fractional dynamics that replaces this exponential decay with power-law long memory. To make fractional dynamics practical, FRAC approximates the heavy-tailed target kernel with a finite-state, log-spaced sum of exponential modes. This construction turns fractional memory into an efficient recurrent module with parallel training and prefill, while retaining bounded-state autoregressive decoding. Extensive experiments, including 1.3B-parameter language modeling, demonstrate that FRAC consistently improves long-context performance over state-of-the-art SSM baselines while staying competitive on short-context. These results show that fractional dynamics provide a practical and effective prior for long-context SSMs.