Papers

Passive Acoustic Monitoring of bats generates massive ultrasonic datasets (>27 GB/night per node), straining edge storage and battery life. Legacy triggers fail against acoustic confusers, while deep models exceed microcontroller limits. We present a hardware-aware Bat Activity Detector (BAD) specifically designed to discriminate bat calls from hard biological and environmental confusers across variable sampling rates (192-384 kHz). Tailored for the Silicon Labs EFM32PG26 (MVP) in 8-bit integer precision, our model achieves 100 percent hardware offload across all 14 layers (17.2 KB Flash, 73.1 KB RAM). End-to-end preprocessing (74.00 ms for 76 frames) and inference (30.00 ms) of 100 ms clips at 192 kHz require 104.00 ms per clip. On spatially out-of-domain recordings under a realistic low-prevalence regime (r_pos = 0.05), BAD achieves an AUC-ROC of 0.9748 and suppresses 99.4% of non-target noise frames while retaining 65.3% of bat calls - delivering a >33x precision gain over classical Goertzel baselines.

Subgiant stars represent a critical phase in stellar evolution, offering an opportunity to investigate how planetary systems respond to the early stages of post-main-sequence expansion. Despite their importance, systematic occurrence-rate studies of this population remain sparse compared with those of main-sequence and red-giant hosts. In this paper, we present a uniform analysis of planet occurrence around a sample of 282,904 subgiant stars selected from the Gaia Data Release 3 (DR3) catalogue. We performed an independent re-analysis of Transiting Exoplanet Survey Satellite (TESS) light curves for transit-signal detection and refinement, followed by multi-stage vetting including a visual inspection and statistical false-positive assessment. We quantified the detection sensitivity of the survey through injection-and-recovery experiments, with 565,808 synthetic transit signals injected across the stellar sample. Over the period range of 1–10 days and the planet-radius range for which the detection completeness is well characterised, we measure a completeness-corrected planet occurrence rate of $0.644^{+0.048}_{-0.041}\%$. The occurrence rate is strongly dependent on planet radius, with the highest occurrence contributed by planets in the $1$–$4\,R_{\oplus}$ range and a secondary enhancement at $12$–$15\,R_{\oplus}$. These results provide a demographic baseline for studying the population of close-in planets around stars undergoing early post-main-sequence evolution.

Device-to-device and sample-to-sample variability remains a major obstacle to the reliable implementation of hafnia-based ferroelectrics, even in nominally identical structures fabricated under similar processing conditions. This highlights the need for operando diagnostic probes that provide process-relevant feedback beyond conventional structural phase analysis. Here, we demonstrate that operando nanoscale surface measurements serve as sensitive probe of the local electrochemical processes governing reliability in hafnia ferroelectric devices. Using epitaxial rhombohedral Y:HfO2 films grown on La0.67Sr0.33MnO3 (LSMO)-buffered SrTiO3 as a model system, we combine operando atomic force microscopy, conductive AFM, piezoresponse force microscopy, and correlative STEM-EELS to directly link surface evolution with interfacial electrochemistry. Devices exhibiting wake-up show a spatially uniform increase in surface height, arising from homogeneous oxidation of the LSMO electrode followed by oxygen migration into the ferroelectric layer during polarization switching. In contrast, leaky devices display pronounced surface roughening and blister formation, originating from spatially inhomogeneous oxidation states in the pristine LSMO electrode that promote competing oxygen evolution reactions at the LSMO/Y:HfO2 interface. The accompanying electron generation produces leakage which is transient. Guided by these mechanistic insights, we introduce simple modifications to the processing conditions, without altering the optimized ferroelectric phase, that suppress the competing electrochemical pathways and reproducibly yield 100% ferroelectric devices. More broadly, this work establishes operando surface evolution as a powerful nanoscale diagnostic of hidden electrochemical processes and provides a practical route for improving the reliability and reproducibility of hafnia-based ferroelectric devices.

Thorough evaluation of vision-language models (VLMs) has become prohibitively expensive, as benchmarks span an ever-broader spectrum of capabilities and new models arrive at a relentless pace. Benchmark compression methods that preserve model rankings at a fraction of the cost are well studied for language models, but for VLMs the question remains under-explored. We present PRIMEBench (Pruning Redundant Items for Multimodal Evaluation), a vision-aware hierarchical benchmark compression framework that substantially reduces evaluation cost while preserving model rankings. This hierarchical framework operates in four stages: data cleaning to remove items answerable without the image and all-correct items, category representative selection to pick one benchmark per capability category, item pruning with Vision-Aware Variance (VAW), and category-count pruning. VAW combines inter-model variance with a vision-dependence score computed from multimodal embeddings alone, while encouraging coverage of diverse items within each benchmark. On models held out from item selection, it has the highest mean fidelity at the released 5% retention. The hierarchical design lets practitioners stop at any stage to match their compute budget; the released suite removes over 97% of items while preserving model rankings. Beyond compression, our analyses show how VLM evaluation behaves as model panels grow and evolve, providing guidance for designing future benchmarks that are more efficient, robust to model turnover, and explicit about the limits of evaluation-side pruning.

Spontaneous parametric down-conversion is a primary resource for generating non-classical light, yet phase mismatch fluctuations from temperature drift, angular misalignment, and domain fabrication errors reduce pair-generation efficiency and phase stability. Here, we analyze error mitigation in spontaneous parametric down-conversion using composite segmentation governed by SU(1, 1) spatial dynamics. We show that odd spatial Fourier harmonics preserve error-cancellation flatness with pair-generation rates scaling asymptotically as $m^{-2}$, while a coordinate-dilation symmetry provides a design prescription for translating configurations across distinct operating wavelengths (405, 532, and 775 nm). Furthermore, an open-loop thermo-optic bias counteracts off-axis angular drift to broaden the 90%-efficiency angular acceptance half-width by 3.46x, and up to two missing poling domains are tolerated with no numerically resolved loss in relative conversion efficiency. Across a 5$^\circ$C thermal window, the generated pairs sustain a relative conversion efficiency of $\eta \ge 0.954$ with the modeled phase-coherence metric remaining above 0.95, providing a structurally robust approach for entangled photon generation without requiring continuous closed-loop feedback stabilization.

We prove that any Fano orbifold admits a free Campana curve in the sense of Campana. Moreover, assuming that any klt log Fano pair admits a very free rational curve in its smooth locus, we prove that any Fano orbifold is Campana rationally connected. As an application, we prove the finiteness of the orbifold fundamental groups for Fano orbifolds.

We study spin-current fluctuations of the folded XXZ chain, which describes the strong-anisotropy limit of the XXZ chain. We obtain an exact expression for the moment-generating function of the time-integrated spin current at infinite temperature. A long-time asymptotic analysis establishes that the rescaled time-integrated current converges to a non-Gaussian distribution described by the M-Wright function. The derivation relies on a nonlocal map to the one-dimensional t-0 model and its exact spin-charge separation. By extending this approach, we also show that the dynamical correlation function of the spins summed over two adjacent sites exhibits a diffusive Gaussian profile at long times.

We construct a five-dimensional generalization of the swirling universe and embed in it the Myers-Perry black hole and the rotating black ring. We prove that both solutions are free of conical singularities, analyze their geometrical properties, compute their mass and angular momentum, and discuss their uniqueness.

On-policy distillation (OPD) trains a student on its own reasoning trajectories using feedback from a stronger teacher. Teacher interventions can improve these trajectories, but also change the distribution on which the student learns. Our controlled studies show that rollout quality alone is an incomplete criterion for allocating teacher guidance. Deeper intervention yields diminishing gains in rollout accuracy while increasing off-policy load. In a training probe with a restricted rollout horizon, peak student accuracy and performance retention favor different intervention strengths. The preferred intervention depth and placement also vary across benchmarks. These findings motivate MAESTRO, which uses local policy disagreement to jointly adapt when the teacher takes over and how long it generates. Its {policy disagreement score} combines teacher-weighted candidate coverage with local distribution similarity and is aggregated within reasoning paragraphs. Across eight mathematical reasoning benchmarks, MAESTRO achieves the highest macro-average accuracy among the compared methods for both 0.6B and 1.7B Qwen3 students, with the 1.7B student leading on every benchmark. MAESTRO also reduces average training response length by 67.3% relative to standard OPD. The code is available at https://github.com/yhao-wang/MAESTRO.

The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains. By restricting the discretization to the domain boundaries, it substantially reduces computational complexity. The procedure first consists in determining the solution trace on the boundaries of the domain by solving a boundary integral equation. Then, the volumetric solution can be recovered at low computational cost using a boundary integral representation. As the first step of the BEM represents the main computational bottleneck, we present ScaGNN, a learning-based approach designed to approximate the solution trace. It relies on a graph neural network architecture that incorporates a dynamic adaptive edge sampling mechanism for selecting the most relevant interactions to model. Guided by intermediate predictions of expected error and edge length, this mechanism selects, at various stages of the forward pass, the most relevant distant interactions to model. The proposed method is tailored to achieve linear complexity with the number of nodes in the input graph. To train and evaluate our network, we present a benchmark consisting of several datasets with different types of multiple scattering problems. Our experiments show that our approach surpasses existing state-of-the-art learning-based methods on the considered tasks and investigate the generalization capabilities to settings with an increased number of obstacles and out-of-distribution obstacle shapes. github.com/LARIAD/ScaGNN

Supervised causal discovery learns to infer causal structure for a new dataset from training datasets paired with structural labels. These training pairs are typically simulated, making the simulator both a source of supervision and a carrier of assumptions about causal graphs, mechanisms, and noise. Understanding the resulting predictions therefore requires examining how these assumptions supplement the information available in observational data, which may be compatible with multiple causal graphs. This paper examines that relationship across representative methods available through June 2026. We organize these methods by prediction target, prediction granularity, encoder, structural decoder, and training regime to relate what each method predicts to how it uses data and simulator-based supervision. Using this framework, we distinguish two questions: whether the target is identifiable under the assumed model class, and whether a trained predictor generalizes beyond its training distribution. Restrictions on mechanisms and noise can make otherwise ambiguous causal directions identifiable, but predictive accuracy under those restrictions does not establish transfer when they change. This distinction motivates evaluation that matches metrics to the identifiable graph target and tests changes in graphs, mechanisms, and noise between training and deployment. Extending such evaluation to real data also requires documenting the external causal evidence and uncertainty behind benchmark reference graphs. Together, these analyses guide method comparison and identify open questions in transfer, test-time adaptation, and uncertainty assessment.

Extended Ly$\alpha$ emission is commonly detected around luminous quasars at $z\sim2$-3 and traces cold gas in the circumgalactic environment of the AGN. Together with the spatial distribution of galaxies, Ly$\alpha$ probes gas and galaxy assembly in high-redshift overdensities. We use deep KCWI wide-field spectroscopy and HST/F140W imaging to investigate the assembling cluster CARLA J0800+4029 at $z=1.986\pm0.014$. No robust extended Ly$\alpha$ emission is detected at the radio-loud quasar position. Instead, the dominant Ly$\alpha$ emission is offset from the AGN and coincides with a disturbed structure composed of galaxies, tidal features, and diffuse intra-halo light (IHL). The detected structure has $L_{\rm Ly\alpha}=1.42\times10^{43}$ erg/s and reaches surface-brightness levels of $\sim10^{-17}$ erg/s/cm$^2$/arcsec$^2$. At the quasar position, a matched $3\sigma$ limit gives $L_{\rm Ly\alpha}<4.20\times10^{42}$ erg/s, a factor of $\sim3.4$ below the detected offset emission and among the most stringent constraints at similar redshift. The Ly$\alpha$ emission is dominated by one extended region near systemic velocity, with FWHM $\sim300$-500 km/s. The associated tidal structure has an IHL fraction of 18.8%, and contains a spatially coherent absorption-like decrement at $\sim+1000$ km/s. The offset and alignment between Ly$\alpha$ emission and IHL suggest that gas and stars have been redistributed together during assembly. The lack of a comparable Ly$\alpha$ halo around the quasar further suggests that gas in the immediate AGN environment is ionized, depleted, or suppressed, while the offset region remains favorable for Ly$\alpha$ emission. CARLA J0800+4029 reveals baryon redistribution during cluster assembly, with the dominant observable Ly$\alpha$ reservoir decoupled from the central AGN and linked to ongoing tidal assembly.

Greedy box splitting reads gradient signs at the centre and retains one smaller box. Its summable travel budget makes an incorrect exclusion irreversible. We determine when this geometry is safe. Halving is minimax optimal in the sign-vector oracle model on a coordinatewise sign-consistent class that need not be convex. A dimensionless sign defect yields a sharp scalar envelope, attained by one smooth convex potential; a three-dimensional trajectory ends farther from the target than its initial radius. For quadratics, universal convergence with aspect $w$ and contraction beta holds exactly when the weighted absolute row defect is at most $(2 \beta - 1)$. Perron weights minimise this defect. Adaptive half-sizes avoid initial enlargement and, under persistent error, converge to an exact capped fixed-point limit. For binary comparisons, an independent probe fraction $q$ permits universal localisation on common-target monotone sections exactly when $(q \leq 2 \beta - 1)$; coupled probes give the sharp threshold $2/3$. Matching information bounds distinguish comparisons from sign-vector queries. Error bands give finite-time guarantees and sharp residual floors. Extensions and reproducible experiments identify the assumptions and costs of freezing, smoothing, voting, multistart and random-matrix certificates.

Long-term memory enables language models to use past interactions in future conversations. However, evidence needed to answer a question may be scattered across distant turns, while the question itself omits clues needed to locate it. Retrieved facts can reveal these clues, motivating retrieval decisions conditioned on evidence already found. We introduce MERA (Missing-Evidence Retrieval Augmentation), which separates globally searchable memory from a question-specific evidence state. Verified evidence guides subsequent retrieval without restricting access to the global memory. We train a lightweight planner through reinforcement learning, rewarding queries that recover previously missing evidence. MERA achieves strong answer accuracy across Qwen3-30B and GPT-4o-mini backbones. With Qwen3-30B for evidence processing and answer generation, the trained 0.6B planner achieves 77.40% accuracy on LoCoMo and 71.29% on LongMemEval-S, exceeding a 30B planner without retrieval-grounded training by 4.10% and 3.96%, respectively. On LoCoMo, later retrieval rounds increase cumulative evidence recall from 55.5% to 80.5%.

Certifying Bell correlations in increasingly larger multipartite quantum systems is challenging because conventional Bell inequalities rely on many-body correlations, which become experimentally demanding to estimate as system size grows. Here we demonstrate that multipartite Bell correlations can be certified using few-body permutation-invariant (PI) correlations with a fixed maximal correlation order. We experimentally test few-body PI Bell correlation witnesses tailored for six- and eight-photon postselected Dicke states. The addition of a few four-body correlators is found to significantly enhance the noise tolerance compared with previously studied two-body witnesses: for instance, for six qubits, the selected witness tolerates a white-noise fraction of $p_c\approx0.301$, compared with $p_c\approx0.048$ for the best two-body PI inequality with the same two settings per party. For six and eight photons respectively, we observe violations of the witness bounds by $32$ and $8.9$ standard deviations, arising from postselected polarisation states with fidelities of $0.933(4)$ and $0.916(11)$ to the corresponding half-excitation Dicke states. The witnesses for the six- and eight-photon cases use the same symmetric two- and four-body correlators, just with different coefficients. These results demonstrate an experimentally accessible approach for certifying multipartite Bell correlations in larger systems without requiring full-body correlation measurements.

Latent world models learn action-conditioned dynamics in representation space and often score candidate actions by Euclidean distance to a goal representation. Joint training typically regularizes the representation to prevent collapse, but the resulting representation geometry also determines how terminal errors are weighted during planning. We show that accurate prediction and noncollapsed representations do not guarantee a task-aligned latent planning cost: isotropic Gaussian regularization can induce a geometry that ranks feasible outcomes differently from the task cost. To address this mismatch, we introduce AnisoWM with $\Lambda$Reg, which replaces the fixed isotropic Gaussian target with a learnable diagonal covariance under fixed-trace and anisotropy constraints. The prediction objective, predictor architecture, and Euclidean planner remain unchanged; the target is used only during training. Our analysis characterizes the prediction-driven allocation of target variance, its dependence on the training distribution, and the conditions under which the induced metric reduces planning regret. Across four visual control environments, AnisoWM improves planning success over LeWorldModel in all four. Its latent planning cost also shows better agreement with task outcomes. Project website: https://rkdrn79.github.io/AnisoWM-page/

This paper proposes a calculus for Dynamic Epistemic Logic (DEL) based on dynamic hypersequents, a new framework for capturing the dynamics of epistemic models in a purely structural and natural way. We enrich dynamic hypersequents with agent indices and an event store, yielding a uniform representation of epistemic events. The resulting calculus enjoys a set of logical rules that are provably invertible. Moreover, all structural rules, including the contraction rules, as well as the cut-rule, are shown to be admissible. Finally, the calculus constitutes, to the best of our knowledge, the only proof-theoretic calculus for DEL that is both grounded in a classical S5 framework and inherently dynamic.

We prove that the Ehrhart $h^*$-polynomial of a rank-two matroid with exactly three parallel classes is real-rooted whenever its smallest parallel class has size at most three. This bound is sharp: the loopless rank-two matroids with parallel-class sizes $(4,561,600)$ and $(4,a,a+29)$, for all sufficiently large integers $a$, have $h^*$-polynomials that are not real-rooted. By matroid duality, these examples disprove Ferroni's real-rootedness conjecture even for cycle matroids of theta graphs. Nevertheless, every matroid of rank two or corank two has a positive $h^*$-coefficient sequence that is ultra log-concave of order equal to the polynomial's degree. In particular, the unimodality conjecture holds in both cases.

We supply the details of the subcritical dry Ten Martini statement announced in [6, Remark 1.3]: for every irrational frequency, every subcritical Type I energy with resonant rotation number is an endpoint of an open spectral gap. The proof combines the all-frequency Puig argument developed there with quantitative almost reducibility. A different proof was recently given by Li [7].

Recent baryon acoustic oscillation measurements from the Dark Energy Spectroscopic Instrument (DESI), combined with supernova observations, show a mild preference for an evolving dark-energy equation of state, in which dark energy remains phantom-like at higher redshift while a transition toward the quintessence regime emerges around $z\lesssim0.5$. Beyond the monotonic evolution of the equation of state, an oscillatory dark-energy scenario provides a potential alternative realization of dynamical dark energy. We study such an oscillatory scenario within the Einstein-scalar-Gauss-Bonnet gravity framework, where a scalar field with a hybrid exponential-quadratic potential couples nonminimally to the Gauss-Bonnet (GB) invariant. We choose a Gaussian GB coupling function localized around the minimum of the potential. During the late-time epoch, the field thereby oscillates around the potential minimum and eventually exits toward a stable de Sitter attractor phase. In the minimally coupled limit, the effective equation of state oscillates in the quintessence regime at low redshift, $z\sim0$, without crossing the phantom divide. The nonminimal coupling amplifies the oscillations and drives the effective equation of state across the phantom divide multiple times. Although a sufficiently strong coupling can induce negative scalar and tensor sound speeds, rendering the perturbation modes unstable. We identify a region of parameter space in which the model undergoes multiple phantom crossings while remaining free of ghost and gradient instabilities and approaching a stable de Sitter attractor in the future.

We study the three-dimensional active Potts model (APM) on a cubic lattice with 2, 4, and 6 orientational states. The steady-state phase diagrams exhibit low-density gaseous, high-density polar liquid, and liquid–gas coexistence phases, with the phase behavior controlled by density, temperature, and propulsion speed and retaining the main features of the previously studied two-dimensional APM. At weak propulsion, the dense phase forms a slab perpendicular to its direction of motion. With increasing propulsion speed, this morphology persists for the 2-state model, whereas the dense phases for 4 and 6 states reorient and propagate along their longitudinal direction. For the 6-state model, the reoriented dense phase further develops a cylindrical morphology. We also examine the stability of polar liquids against artificially introduced droplets using microscopic simulations and coarse-grained hydrodynamic equations. At high propulsion speeds, counter-propagating droplets can partially modify the initial polar state, while transverse droplets can completely alter it, demonstrating the metastable nature of polar liquids in the three-dimensional active Potts model.

Neural Koopman autoencoder models have been shown to successfully build a latent embedding with linear dynamics for arbitrary dynamical systems, enabling strong performance in long-term time series forecasting. However, these models usually work in a deterministic setting, which does not allow the quantification of the uncertainty of their predictions. Thus, we propose the new Variational Augmented Invertible Koopman AutoEncoder (VAIKAE), in which the latent embedding follows a Gaussian distribution instead of being deterministic. A key property of the VAIKAE architecture is that it leverages normalizing flow models, enabling the use of likelihood computations in the state space of dynamical systems for training a model. We further propose new strategies for uncertainty-aware latent data assimilation with a trained VAIKAE model. The effectiveness of our methods is demonstrated in a series of experiments on long-term time series forecasting benchmarks.

Erdős, Odlyzko and Sárközy conjectured that every reduced residue class modulo $q$ contains a product of two primes not exceeding $q$; their conjecture remains open even under the GRH. We prove that its analogue holds, unconditionally and in the wider range $q^{\Theta}$ for any fixed $\Theta > 3/4$, in Granville's random model of the primes. Almost surely, every reduced class modulo every sufficiently large modulus is representable, and the number of representations is asymptotic to its expected order. The choice of the model is decisive; the corresponding statement in the random prime model of Banks, Ford and Tao fails with positive probability, an elementary local defect that Granville's discard step removes.

Robotic foundation models (RFMs) are increasingly capable of general-purpose manipulation, yet reliable physical interaction remains challenging in contact-rich settings. We present FP2, a lightweight downstream interface that equips task-adapted RFMs with explicit force control while preserving their action-generation capability. FP2 adopts an action-regulation decomposition: the task-adapted RFM serves as a foundation policy responsible for task-level action generation, while a high-frequency force control policy focuses solely on interaction regulation. To condition force regulation on the ongoing manipulation, FP2 compresses foundation-policy contextual representations and combines them with wrench and proprioceptive histories to predict structured force-control parameters. We evaluate FP2 with four RFM backbones across four real-world contact-rich manipulation tasks. FP2 consistently improves task performance and force regulation quality over the corresponding foundation policies, while comparing favorably with representative force-aware and force-control baselines. Ablations further show that foundation-policy context and physical feedback are complementary for effective force regulation, while preserving foundation-policy action generation improves both efficiency and novel-object generalization. Project website: http://force-policy.github.io/fp2

Looped reasoning models repeatedly apply a shared set of parameters, enabling more computation without increasing the model size. These models also support input-dependent computation by dynamically deciding when to stop looping. Motivated by the recent success of looped transformers in language modeling and reasoning, we investigate whether dynamic looping can similarly benefit sequential decision-making. We provide a complexity-theoretic motivation for this approach by showing that there exist Markov decision processes in which a state-adaptive policy achieves the optimal return with asymptotically less expected computation than any optimal fixed-runtime policy. To learn compute-adaptive policies in practice, we introduce Looped Actor, a transformer-based policy that repeatedly refines a latent representation toward a fixed point using a shared computational block. This allows the model to allocate computation adaptively by varying the number of loops based on the current state. We evaluate Looped Actor on 22 tasks across six environments, ranging from combinatorial puzzles to robotic manipulation and spanning online and offline reinforcement learning (RL) with discrete and continuous actions. Looped Actor matches or exceeds the performance of an untied baseline with 16$\times$ more parameters, with the largest gains in environments where action selection requires substantial multistep planning. For the Boxoban environment, we find that the computation allocation is structured: the number of loops increases with the number of remaining pushes and future optimal pushes become increasingly predictable from the latent state over successive loops. Together, these results highlight actor looping as a simple and efficient way to equip RL agents with adaptive computation and improve their planning capabilities. Code is available at https://github.com/camail-official/LoopedActor

We study the query complexity of testing membership in structured string languages, focusing on Dyck languages and natural generalizations. A tester receives query access to a word and must distinguish valid inputs from words that are far in Hamming distance, while inspecting only a sublinear number of positions. Our results sharpen the boundary between constant-query testability and polynomial query complexity. First, we prove an $\Omega(n^{2/5})$ lower bound for testing Dyck languages $D_m$ with any fixed number $m\ge2$ of parenthesis types, improving the previous $\Omega(n^{1/5})$ lower bound of Fischer, Magniez, and Starikovskaya (SODA `18) and nearly matching their upper bound of $O(n^{2/5+o(1)})$. Furthermore, we show that all nonadaptive algorithms for these problems require $\Omega(n^{1/2})$ queries. Our lower bounds use a Pólya-urn process to construct the hard distribution; Second, we identify a broad class of weighted-parenthesis languages, which we call excursion languages, that remain constant-query testable. These languages encode bounded-step walks that stay nonnegative and return to zero. For every fixed excursion language, we give a nonadaptive tester with query complexity $O(1/\varepsilon^2)$, and we prove this dependence on $\varepsilon$ is optimal, even for adaptive algorithms. As a special case, we obtain the tight $\Theta(1/\varepsilon^2)$ query complexity of testing $D_1$, improving the previous $O(\log(1/\varepsilon)/\varepsilon^2)$ upper bound and giving the first matching two-sided-error lower bound. Third, we construct a simple hard language, Hidden String, that is generated by a deterministic linear grammar but nevertheless requires $\Omega(n^{2/5})$ adaptive queries and $\Omega(n^{1/2})$ nonadaptive queries to test. This shows that polynomial query complexity appears even for highly restricted string languages.

The construction of absolutely irreducible $KG$-modules for a field $K$ and a finite group $G$ is a basic problem in representation theory. For the symmetric group $\operatorname{S}_n$, Gordon James gave an explicit solution using subgroup data associated to a $\mu$-tableau $t$ for partitions $\mu\vdash n$. Here, we want to investigate in which way James's method can be extended beyond symmetric groups. We identify suitable subgroup data from a finite group and use it to construct a module such that an associated factor module is absolutely irreducible or zero.

Succinct arguments are a fundamental cryptographic primitive for verifying computational claims with small communication. In the classical setting, succinct arguments for NP can be constructed from unstructured hardness alone (e.g., hash functions) by compiling probabilistically checkable proofs (PCPs) or interactive oracle proofs (IOPs) for NP via the commit-and-open paradigm. In contrast, known succinct arguments for QMA rely on “structured” cryptographic primitives, or on the quantum PCP conjecture. We construct the first succinct argument for QMA in the quantum random oracle model (QROM) without relying on additional cryptographic assumptions or unproven conjectures. This yields succinct arguments for QMA from unstructured hardness alone, showing that ideal hash functions not only suffice for succinct arguments for NP but also for QMA. Underlying our result is an efficiency-preserving transformation that compiles quantum interactive oracle proofs (QIOPs), a recently introduced interactive generalization of quantum PCPs, into quantum arguments for the same language, via a natural quantum commit-and-open paradigm. Our transformation applies to every QIOP with public-query soundness, a notion that we formalize to capture a natural requirement of the commit-and-open paradigm and is satisfied by a known QIOP for QMA. As a key ingredient in our transformation, we formalize and construct extractable vector commitments for quantum states with local openings in the QROM, which may be of independent interest.

We investigate how particle stiffness governs length-scale-dependent relaxation dynamics in dense suspensions of thermoresponsive PNIPAM microgels subjected to temperature variations and large amplitude oscillatory shear. By combining dielectric spectroscopy with rheometric measurements, we directly correlate microscopic polarization fluctuation dynamics with macroscopic mechanical relaxation. Highly crosslinked, stiffer microgels exhibit longer dielectric relaxation times across a broad temperature range and strain-induced slowing down, whereas softer, open-network microgels exhibit nearly strain-independent dielectric dynamics. Below the volume phase transition temperature (VPTT), macroscopic bulk stress relaxation experiments reveal that suspensions of the softest particles relax most rapidly. For the stiffer microgel suspensions, however, the dynamics decouple: bulk stress relaxation speeds up with increasing stiffness even as dielectric relaxation slows down. Above the VPTT, softer particles undergo greater volume collapse, leading to very rapid bulk stress relaxation. Besides exhibiting slower stress decay, stiffer microgel suspensions also undergo shear-induced structural regeneration during the later stages of deformation. These findings demonstrate that particle stiffness and internal architecture govern relaxation pathways across microscopic and macroscopic length scales, thereby providing a framework for designing adaptive soft metamaterials, stress-dissipative coatings, and self-healing robotic materials.

We prove that (n + 1)-dimensional de Sitter spacetime is locally the unique $(\Lambda > 0)$-vacuum spacetime whose Killing horizons intersect the conformal boundary $\mathscr{I}$. The intersection occurs at the isolated essential zeros of the extension of the Killing vector field to $\mathscr{I}$. We then reconstruct all de Sitter Killing vector fields from their boundary value and obtain a characterization of those admitting a Killing horizon in terms of a conformal invariant $\sigma$: $\sigma<0$ characterizes non-degenerate bifurcate horizons, whereas $\sigma = 0$ yields degenerate non-bifurcate horizons. Finally, we derive an intrinsic, conformally invariant formula for the surface gravity of the horizons in de Sitter, $\kappa^2 = |\sigma|$.