Papers

Trapdoor claw-free functions (TCFs) underpin much of classical-quantum cryptographic interaction, yet every TCF-based protocol states its guarantees relative to an honestly generated key. We give a family-agnostic abstraction of key certification for (noisy) TCF constructions, built on two notions: a certifiable key relation, an NP relation capturing a family's honest keys with witnesses recoverable from the trapdoor; and certified key generation, which emits with each key a certificate of membership satisfying completeness, certificate soundness with extractability, and key privacy. We instantiate certifiable key relations for different constructions, each met generically by a zero-knowledge argument of knowledge for the relation. As our main application, a generic compiler turns any TCF-based proof of quantumness into a zero-knowledge one, with each security property following from its counterpart in the certification scheme. Finally, we delimit the primitive's reach: for protocols resting on injective invariance, an accepting certificate is itself a family distinguisher, leaking exactly the bit such protocols must hide.

Pion production in intermediate-energy heavy-ion collisions (HICs) provides a sensitive probe of the nuclear equation of state and of the isospin dependence of reaction dynamics. In particular, pion production near threshold is strongly affected by the nucleon-nucleon ($NN$) inelastic cross sections and by the high-momentum components of the nucleon momentum distribution. To explore the influence of these two ingredients on pion production and charged-pion ratios, the in-medium $NN$ inelastic cross sections calculated within the relativistic Boltzmann-Uehling-Uhlenbeck transport theory and the short-range correlation induced high-momentum tail (HMT) are introduced into the Ultra-relativistic Quantum Molecular Dynamics model. By simulating Au+Au collisions at intermediate energies, we find that the in-medium modification of the $NN$ inelastic cross sections suppresses the pion multiplicity by reducing the probability of $N\Delta$ production in dense matter. The HMT, on the other hand, enhances the high-momentum components of nucleons and modifies the available energy in individual $NN$ collisions, thereby affecting $NN\rightarrow N\Delta$ reactions and the subsequent pion production. With the simultaneous inclusion of these two effects, the pion yields and the $\pi^-/\pi^+$ ratio data can be better reproduced. These results highlight the importance of both the in-medium reaction cross sections and short-range correlation induced high-momentum components in pion production in intermediate energy HICs.

The timeliness and accuracy of edge-based video analytics can be hindered by drastic reductions in available bandwidth (ABW) at last-mile edge routers, causing prolonged queuing delays. This work proposes Lizard, a system that leverages video-content-aware packet discarding to mitigate the negative effects of drastic ABW degradation that may frequently occur at a last-mile edge router by judiciously discarding packets that contain frame blocks less important to the analytics at the destination. To achieve this, we first devise a frame-block-aware RTP header extension to effectively decouple packet dependencies to encode frame blocks. Second, Lizard uses a priority-based feedback mechanism that dynamically evaluates packet priorities based on relative accuracy impacts. Third, we develop an adaptive phase-transition-based packet discarding strategy at the router to discard packets that represent unimportant blocks. Our evaluation of Lizard shows improvements over existing methods are substantial: 53.2% reduction in latency and 27.1% increase in analysis accuracy.

A boolean function $f$ has Fourier dimension $k$ if its strings with nonzero Fourier coefficients span a subspace of dimension $k$. We first consider the property testing task of determining whether a function has Fourier dimension at most $k$, or is $\epsilon$-far from being so. We show that there is an $O(k/\sqrt{\epsilon})$-query quantum property tester for this problem, which we show to be almost optimal. Combined with Gopalan \etal's classical lower bound of $\Omega(2^{k/2})$, this demonstrates an exponential quantum advantage for this task. We complement this result with a $\tilde{O}(2^{k/2}/\epsilon)$ classical tester, giving a quadratic improvement over the previous best tester, and essentially settling the classical query complexity. We then introduce and study the tolerant version of this problem. That is, determining whether a function is $\alpha\epsilon$-close to having Fourier dimension at most $k$, or is $\epsilon$-far from being so. Perhaps surprisingly, we show that this tolerant version of the problem is essentially just as hard as the standard version of the problem. That is, we show this problem has a $\tilde{O}(k/\epsilon)$ quantum tester, and a $\tilde{O}(2^{k/2}/\epsilon)$ classical tester.

Visual attribution methods typically explain predictions using pixels, superpixels, or regular patches. These representations can localize important regions, but provide limited information about their structure. We introduce MorphoSHAP, a model-agnostic post-hoc method that instead uses morphological shapes as the players of a Shapley attribution game. Using the Tree of Shapes, each shape is described by its scale, geometry, and signed contribution, providing explanations of where the evidence lies, what type of structure carries it, and how strongly it affects the prediction. This shared morphological vocabulary enables spatial, textual, and global class-level explanations beyond image-specific heatmaps. To the best of our knowledge, MorphoSHAP is the first SHAP-based image attribution framework to combine these different forms of explanation. Across five diverse datasets and three architectures, MorphoSHAP achieves strong insertion/deletion performance and outperforms competing attribution methods on several benchmarks. Finally, a user study shows that MorphoSHAP provides explanations that are easy to use and are preferred over standard attribution baselines.

Dynamic graphs are widely used to model time-evolving relational systems in real-world applications. Dynamic graph neural networks provide an effective framework for capturing both structural dependencies and temporal dynamics in such data. However, they typically intertwine temporal graph propagation with every optimization epoch and often maintain large trainable representations for each node-time pair. This design repeatedly recomputes largely unchanged historical structures, leading to substantial training and parameter overhead. To address this critical issue, we propose CacheDyG, a Cache-refine framework for efficient Dynamic Graph learning. Specifically, it decouples temporal propagation from routine parameter updates by constructing a time-ordered temporal dependency cache that stores graph-aware node-time representations in non-trainable buffers. During standard training epochs, CacheDyG reads from the cache and updates only a lightweight cache refiner, an adaptive residual gate, and the link predictor. Selective cache refresh further keeps cached representations aligned with the supervised objective while avoiding epoch-wise sparse propagation. Experiments on five dynamic graph benchmarks show that CacheDyG adopts substantially fewer trainable parameters and lower runtime to obtain more competitive predictive performance than baselines. These results demonstrate that cache-based decoupling provides an effective principle for scalable dynamic graph learning.

This short report documents our entry to the COMFORT Localization Benchmark (IROS 2026), evaluated on the GrandTour dataset recorded with the Boxi payload. It extends MOLA-LO into a LiDAR-inertial system that also ingests IMU and, optionally, legged kinematic odometry. We describe the architecture, the streams consumed, the local protocol that selected the submitted configuration, and the measurements backing our real-time claim.

Let $[a_1(x),a_2(x),\ldots,a_n(x),\ldots]$ be the continued fraction expansion of irrational $x\in[0,1)$, and let $q_n(x)$ be the denominator of the $n$-th convergent. In this paper, we study how the growth rate of $a_{n+1}(x)$ on a prescribed logarithmic size interacts with its upper growth rate relative to $q_n(x)$. For $\psi:\mathbb N\to\mathbb{R}_{\ge0}$ satisfying $\psi(n)\to \infty$ and $\alpha, \beta\in [0, \infty]$, define the joint level set \[F_{\alpha,\beta}:=\Big\{x\in [0,1)\colon \liminf_{n\to\infty}\frac{\log (a_{n+1}(x))}{\psi(n)}=\alpha,\ \limsup_{n\to\infty}\frac{\log (a_{n+1}(x))}{\log q_n(x)}=\beta\Big\}. \] We determine the Hausdorff dimension of $F_{\alpha,\beta}$ for all values of $ \alpha$ and $\beta$. Our results is related to several earlier results on the metric theory of continued fractions, including those of Bugeaud [Math. Ann. {327} (2003)] on irrationality exponents, Wang–Wu [Adv. Math. {218} (2008)] on the growth of partial quotients, and Song–Tan–Zhang [Nonlinearity {37} (2024)] on the joint distribution of convergence and irrationality exponents.

Multi-view clustering (MVC) aims to uncover latent cluster structures by exploiting complementary information from multiple views. Despite substantial progress in clustering performance, fairness remains an important concern when MVC is applied to socially sensitive scenarios. Recent fair multi-view clustering methods have introduced fairness constraints into representation learning or clustering assignments. However, these methods generally treat different views under a largely uniform fairness mechanism, without explicitly distinguishing their varying levels of sensitive dependence during cross-view learning. In practice, different views may encode substantially different levels of sensitive information. Ignoring such cross-view discrepancy can allow highly sensitive-dependent views to influence less sensitive-dependent ones during cross-view learning, potentially degrading both clustering performance and fairness. To address this issue, we propose a novel multi-view fair clustering framework guided by cross-view sensitive information discrepancy. Specifically, we estimate the sensitive dependence of each view and develop a bias-ranked asymmetric alignment mechanism that encourages views with higher sensitive dependence to learn from those with lower sensitive dependence, while cross-view discrepancies are further exploited to adaptively regulate the alignment process. Moreover, fairness regularization is imposed on the consensus soft assignments to further promote group fairness. Extensive experiments on benchmark datasets demonstrate that the proposed method achieves a favorable balance between clustering quality and group fairness.

Fast radio bursts (FRBs) are millisecond-duration radio transients of extragalactic origin, whose emission mechanisms and progenitors remain unresolved. Statistical analyses of the rapidly growing samples provide a promising means to constrain the underlying physics. In this review, we synthesize the statistical properties derived from current FRB catalogs, encompassing constraints on dispersion measure, redshift, energy/luminosity functions, repetition rate, and host-galaxy demographics. For repeating FRBs, we examine the statistics of energy, fluence/flux, waiting time, and discuss time-series analyses that reveal memory effects and chaotic dynamics. We further discuss the observational discovery and theoretical interpretation of periodic activity, and survey polarization properties that probe the magneto-ionic environments of FRB sources. Throughout, we emphasize robust empirical trends, account for observational biases and selection effects, and outline outstanding open questions regarding the physical origin of these enigmatic bursts.

Fine-grained mixture-of-experts (MoE) architectures have become a mainstream design for open-weight LLMs, with hundreds of experts and increasingly many selected per token. This shift makes dynamic expert pruning an attractive route to cheaper inference. Yet existing evidence comes largely from coarser architectures and likelihood-scored multiple-choice benchmarks, leaving three central questions open in the fine-grained regime: how redundant per-token expert selection is, how effectively existing pruning methods exploit that redundancy, and what governs a model's sensitivity to pruning. We fill this gap with a systematic empirical study of twelve fine-grained MoE checkpoints spanning nine architecture families, with a core suite of eleven benchmarks covering knowledge QA, mathematics, code generation, and general reasoning. We find that expert selection is far more redundant than the field's operating points assume: uniformly retaining about two thirds of the selected experts preserves 98.8% of unpruned performance on average, requiring only a one-integer change and delivering 1.2-1.7x measured speedup across two serving backends. This simple baseline leaves little room for dynamic allocation at conservative budgets: even the best published rules differ from it by under 1% at matched expert budgets. Their value emerges under aggressive pruning, where the best rules recover up to 3.0% over uniform truncation, with gains concentrated in the generative tasks that suffer the sharpest degradation. Sensitivity to aggressive pruning also depends on the model: larger and thinking models are more resilient, whereas multimodal models are more vulnerable. Together, these findings reveal how much expert computation fine-grained MoEs can dispense with, and establish when dynamic allocation earns its complexity, informing both practical deployment and future pruning methods.

Evaluation scores are often validated by their agreement with inexpensive proxy labels. When the score and the proxy are computed from the same text span, however, that agreement can arise from surface evidence the two share rather than from the semantic construct the proxy is meant to represent. We make the distinction explicit by declaring the score, its span, the proxy and the target construct as a validation contract, then re-evaluating that proxy rule strictly outside the scored span. In a controlled HotpotQA correctness experiment varying only the shared text boundary, the score agrees with its proxy far better than with correctness at a 50-character prefix: the gap is +0.184, collapsing to at most +0.045 from 120 characters onward. At that short prefix the score still predicts whether the answer string appears later (AUC 0.634) while an equivalence test places its agreement with correctness at chance, so the reported proxy agreement does not establish that the score ranks correctness. On OR-Bench, suppressing each model's recurring opening templates removes most of the score's association with the refusal proxy, while matched-volume deletion removes almost none and construct agreement stays at chance. Only three of eleven external contracts support the off-span control, and none of the routing studies we sampled released the generations it needs. We therefore ask that a proxy-based validation claim declare the span each label is read from, report the construct agreement beside the proxy agreement, and release the generations that let the proxy be re-read off the scored span.

We construct the moduli space of marked polystable $\mathrm{SL}_r(\mathbb C)$-Higgs bundles via analytic methods. The resulting space is normal and Hausdorff, and its local models are products of a Teichmüller neighbourhood with a quotient of a quadratic cone. These models preserve the curve parameter and identify the stabilizers. We prove agreement with the complex and unitary gauge-quotient topologies and establish the coarse moduli property for semistable families over reduced analytic bases. The mapping class group and Higgs scaling act holomorphically. Besides, on the stable locus, the moduli spaces that we consider agree with the joint moduli constructed by Collier, Toulisse and Wentworth.

Runtime traces can appear transparent, but a closed-loop policy determines which states are visited and which failures become visible. We study a simulated hotel-pricing agent mapping time, inventory, and market state to discrete price actions under varying demand regimes. A fault may leave no aggregate trace when the policy rarely visits affected cells. We treat entry into aggregate-only fault interpretation as a diagnosability decision preceding scoring or localization. A reference-map gate requires repeated clean-policy support; a matched runtime gate then requires joint support in clean and current streams. Signal analysis occurs only after both pass. We calibrate false admission on a disjoint clean stream at the physical-component level and model detection by affected clean traffic rather than nominal cell coverage. In a frozen one-shot heldout, 55/72 (76.4%) regime-component units were reference-admitted, representing 20 physical components; 54/55 passed matched runtime admission, while the rejected unit abstained. Stable false admission was 0/20, with a one-sided exact 95% upper bound of 0.1391, meeting the frozen 0.20 criterion. Across 540 repeated unit-arm rows nested in those 20 clusters, affected clean traffic reduced negative log likelihood by 29.3% relative to cell coverage, a gain of 0.1264 nats per row (cluster-bootstrap 95% interval [0.0593, 0.1918]). Adding mask family and its interaction improved log loss by 0.0015 nats per row (one-sided upper bound 0.0066), below the frozen 0.01 practical-sufficiency margin. A development audit found that exact minimum hitting set and greedy selection chose identical supports in 12/12 scenarios because singleton evidence had resolved the conflicts. The result is a bounded rule for interpreting aggregate agent behavior: first establish exposure, then score change, and abstain when the trace cannot support the claim.

Finite monodromy provides a bridge between group representations and algebraic solutions of differential equations. We study this connection for the Katz-Long-Moody construction, which transforms representations of the semidirect product of a free group and a braid group into new representations of the same group and is related to Knizhnik-Zamolodchikov (KZ)-type equations. For a fixed finite-image input, we classify the parameter values for which the resulting representations have finite image, both on the semidirect product and on its free-group and braid-group subgroups. In particular, finiteness of the braid-group image is independent of the admissible parameter. These results give necessary and sufficient conditions for all solutions of the corresponding regular-singular KZ-type equations to be algebraic. On restriction to the free group, they also characterize finite monodromy and algebraicity of all solutions of the associated Fuchsian systems, connecting the classification to classical questions about algebraic hypergeometric functions.

LLM agents increasingly work on long-horizon tasks, and the decisions they make along the way, such as which hypothesis to test or which implementation to build on, determine the outcome of the whole run. Making these decisions well is becoming a key capability for both engineering and research agents. We refer to the ability to make good long-horizon decisions as the taste of an agent. While existing benchmarks measure the end-to-end success of agents on long-horizon tasks, none of them measures the taste of an agent. To address this problem, we build Taste-Bench, a benchmark of taste questions constructed automatically from trajectories that agents produced in engineering and research tasks. Each question presents a decision fork, a point in a trajectory where multiple directions are available and one of them leads to a better outcome, and the evaluated model chooses among these directions without seeing what happens after the fork. We mine these forks automatically from parallel attempts at the same task and from detours inside a single trajectory, without needing human annotation. We evaluate frontier models on Taste-Bench and find that the best model answers only 59.7% of the questions correctly. We further find that forks whose deciding evidence appears later in the trajectory are much harder for every model, and that a larger reasoning budget does not improve the accuracy. Finally, we show that taste can be trained. We distill the judgment of a teacher that has seen the outcome into a student model, and the student makes better decisions on unseen tasks and improves end-to-end success on held-out SWE-bench Pro tasks.

High-rate dense perception in dynamic environments is limited by the low update rate of RGB cameras, as rapid scene changes can occur between frames. Event cameras offer temporally dense but spatially sparse measurements, complementary to spatially dense RGB observations. Direct fusion cannot fully exploit this complementarity, while event-guided propagation fails on newly appearing or disoccluded regions without valid RGB support. We present LiFR v2, a unified propagation-completion-memory framework for causal anytime and streaming dense prediction from an RGB keyframe and events. LiFR v2 introduces an Event-Guided Completion Module (EGCM) to recover task-relevant representations where propagation is unsupported, and a History Retrieval Module (HRM) to reuse completed representations across successive queries. The framework supports semantic segmentation, monocular depth estimation, and multi-task dense prediction, and we further introduce SHF-Emerge to evaluate rapid object emergence and disocclusion. LiFR v2 achieves 74.37% mIoU on DSEC and 56.13% on SHF-Emerge, improving LiFR-Seg by 1.85 percentage points on the latter, while reducing SHF-Emerge depth RMSE from 1.564 m to 1.118 m over the propagation baseline. It also exceeds 100 FPS for both segmentation and depth, demonstrating accurate and efficient high-rate perception beyond RGB frame rates.

We introduce latest exact match attention (LEMA), an attention variant for transformers where queries and keys are binarized and each query attends only to the latest exactly matching key. We prove that LEMA transformers with chain of thought can simulate word-RAMs, as was recently shown for the less restrictive rightmost hard attention. In contrast to prior hard attention variants, the restriction to exact matches enables an efficient converse direction: word-RAMs can simulate LEMA transformers at a cost per token independent of the context length. Together, these results yield a close correspondence between the two computational models in terms of both compute and memory. Beyond the theory, we propose a training method for LEMA transformers that handles their non-differentiable operations with a straight-through estimator for the binarization and a soft attention surrogate annealed towards LEMA. On a synthetic associative recall task, LEMA models trained this way use their growing state to store and recall a large number of associations, outperforming gated DeltaNet (GDN) with its fixed state size. As a first scaling test, we train LEMA language models with up to 834 million parameters. They match softmax transformers of around half their size in loss and, on repeated rare phrases and a needle-retrieval task, remain behind softmax transformers but recall across longer distances than GDN models of comparable size. Finally, we implement dictionary-based inference for LEMA transformers and show constant generation speed comparable to GDN despite their growing state, with the dictionaries residing in main memory rather than VRAM. Code is available at https://github.com/moritzbroe/latest_exact_match_attention.

We study harmonic mappings between the source domain in the $\alpha$-Grushin plane and the target domain in the $\beta$-Grushin plane for $\alpha$ not necessarily equal to $\beta$ and $\alpha\in [0,1)$. Our harmonic mappings arise as a Euler–Lagrange system of equations related to the Dirichlet energy and are studied in weak and strong forms. The key results enclose the second order regularity of harmonic mappings, the Bochner identity, the weak Harnack estimates for coordinate functions of a harmonic mapping, as well as the Caccioppoli estimates and the Liouville type theorem. Furthermore, we discuss several examples of (Grushin) harmonic mappings and, in particular, relate them to holomorphic mappings in the plane.

We study the cyclic steepest descent method (CSD) for strictly convex quadratic minimization. CSD repeats, for j consecutive iterations, the exact steepest-descent step size computed at the beginning of each cycle. The only rigorous result for the real algorithm has so far been restricted to two dimensions, where the cycle-starting gradient sequence is known to converge doubly exponentially. For the simplified ("simple") model obtained by discarding bounded logarithmic terms, Dai and Fletcher predicted that CSD is superlinear whenever the number n of distinct eigenvalues is below twice the cycle length m, and linear otherwise. Let A be symmetric positive definite with q distinct eigenvalues, and suppose 2j > q. We prove the superlinear side of this threshold for the real algorithm in arbitrary dimensions, and in fact obtain a faster, doubly exponential, decay. Except for a Lebesgue-null set of initial points, for every kappa below an explicit positive threshold kappa_0, the cycle-starting gradient satisfies ||g_k|| <= exp(-C exp(kappa k)), and the full gradient and iterate errors satisfy analogous bounds with exponent kappa/j after m iterations. This is the first rigorous proof for the real CSD in arbitrary dimensions, including repeated eigenvalues, and confirms the threshold 2j > q (the simple-model prediction n < 2m); the doubly exponential rate is faster than the superlinear one predicted by the simple model. The proof combines arbitrary-reference ratio coordinates, inverse-image volume contraction, thin-band estimates, and a per-component Borel-Cantelli argument.

Probably not. For Airy-type initial data, although nearly all lobes accelerate, the principal lobe remains essentially stationary. Moreover, the overall wave packet gradually disperses.

This paper investigates the joint protection of confidential data and legitimate-user directional information in integrated sensing and communication (ISAC) networks. We consider a multiuser downlink in which passive multi-antenna eavesdroppers (Eves) attempt to decode confidential signals while exploiting legitimate-user reflections for unauthorized angular sensing. To address both threats, we develop a robust covariance-design framework that jointly limits Eve decoding, maintains the transmitter's accuracy in estimating the Eves' directions and shifts the dominant passive-sensing response toward prescribed deceptive directions. A Bayesian angular prior and the corresponding Bayesian Cramer-Rao bound (BCRB) characterize the transmitter's eavesdropper-angle estimation accuracy. Angular uncertainty is represented through geometry-consistent samples, such that each candidate Eve direction jointly determines the corresponding transmitter-Eve channel, user-Eve bearing, and deceptive direction. The resulting design balances worst-user secrecy, sensing accuracy, sensing privacy, and deception power. Robust Eve-decoding constraints are handled through finite sufficient conditions with intersample margins, while continuous ghost dominance is enforced using interval sum-of-squares (SOS) constraints. The resulting nonconvex problem is addressed through successive convex approximation (SCA) and semidefinite relaxation. Numerical results show that the proposed design effectively preserves secrecy and sensing privacy under Eve-angle uncertainty, provides controlled angular deception in single- and multiple-Eve scenarios, and outperforms benchmarks.

We reply to the comments by M. Sienicki and K. Sienicki (arXiv:2512.07881) and by K. Sienicki (arXiv:2601.06104) on our work on quantum-mechanical statistics in human language (arXiv:2407.14924) and on quantum structure in AI-generated language (arXiv:2511.21731). We thank the authors for their careful reading and address what we consider to be the main points of criticism: the exploratory nature of the protocol used in the experiments with large language models; the role of marginal-law violations, and of the Contextuality-by-Default criterion, in the identification of entanglement; the limited diagnostic value of a Bose-Einstein fit taken in isolation; the meaning of assigning the lowest energy levels to the most frequent words; and the relation between the vector spaces used by LLMs and quantum state spaces. We also correct a typographical error in Table 3 of arXiv:2511.21731, which does not affect the reported CHSH value.

We study various discretisation schemes for the regular Sturm–Liouville operator on a bounded interval and for the Laplace operator on an arbitrary planar domain, in both cases subject to zero Dirichlet boundary conditions. The objective is to identify a discretisation scheme such that the corresponding discretised operator—a matrix of size $N \times N$—produces $N$ eigenvalues that approximate as closely as possible the first $N$ eigenvalues of the corresponding operator at the continuous level. By means of numerical experiments we examine several conventional discretisation schemes, and we corroborate the known fact that the conventional discretisations fail to achieve the objective, with the failure attributable to the poor approximation of high-index eigenvalues, and, as a result, to the non-uniform spectrum approximation. In contrast, the newly proposed discrete sine transform based discretisation scheme is designed in such a way that it replicates the asymptotic behaviour of high-index eigenvalues, thereby providing the sought uniform spectrum approximation. Of equal significance is the fact that the proposed discrete sine transform based scheme can be, unlike many Fourier transform based methods, applied to non-rectangular domains.

Device-independent quantum key distribution (DIQKD) can guarantee security without trusting the internal workings of the measurement devices, but extending it to fiber networks demands high-quality entanglement, reliable heralding, and faithful photon transmission simultaneously. Here, we address these requirements in an event-ready asymmetric atom-photon architecture implemented over $25\,\mathrm{km}$ of spooled telecom fiber. A single trapped $^{40}\mathrm{Ca}^{+}$ ion forms one party of the protocol while a single transmitted photon measured at the remote station forms the other. Double quantum frequency conversion and active polarization stabilization preserve the atom-photon quantum correlation across the full link. We obtain a Clauser-Horne-Shimony-Holt parameter of $|S|=2.75^{+0.16}_{-0.15}$, exceeding the threshold $|S|=2.362$ required for a positive asymptotic secret-key fraction under the DIQKD model used. Within the same asymptotic model, this corresponds to a conservative estimate of 69 secret-key bits out of 10908 detected Bell states. The demonstrated architecture establishes a route towards DIQKD in heterogeneous, repeater-compatible quantum networks.

Let $\tau(G)$ denote the maximum number of edge-disjoint spanning trees in a connected graph $G$ of order $n$, and let $\rho_D(G)$ denote its distance spectral radius. For an integer $k\ge2$, Fan, He and Zhao [Discrete Appl. Math. 376 (2025) 31–40] obtained a sharp distance spectral radius condition for $\tau(G)\ge k$ when $n\ge2k+6$. In this paper, we fill the gap $2k\le n\le2k+5$ and thus complete the result for all $n\ge2k$. The extremal graph given by Fan, He and Zhao remains valid for $n\ge2k+2$, while we determine the unique extremal graph for each of the orders $n=2k$ and $n=2k+1$. We further obtain sharp distance spectral radius conditions and characterize all extremal graphs under the minimum degree condition $\delta(G)\ge k$ for all $n\ge2k$. Finally, for graphs with the stronger minimum degree condition $\delta(G)\ge6k-4$ and order $n\ge2\delta(G)+2$, we obtain a sharp distance spectral radius condition ensuring $\tau(G)\ge k$ and determine the unique extremal graph.

Zero-shot multimodal anomaly detection commonly assumes that RGB and point cloud modalities are equally reliable and can contribute uniformly to anomaly localization. We challenge this assumption. Using a set of recently proposed stringent metrics that penalize false anomaly responses in normal regions, we find that point clouds are substantially more reliable than RGB under zero-shot category shift. Motivated by this observation, we propose WOOPS (When Point Clouds Outperform Pixels), a reliability-aware zero-shot multimodal anomaly detection framework. To strengthen the more reliable geometric modality, we design a Multi-view Information Decoupling module to suppress heterogeneous information from multi-view point cloud projections and enhance point cloud feature quality. To avoid unconditional fusion, we further introduce a Modality Reliability Calibration module to adaptively calibrate modality contributions according to their reliability. Extensive experiments show that our method achieves the best or competitive performance under the new metrics in both unimodal and multimodal settings. Further analysis demonstrates that point cloud information also improves RGB-only inference, while ablations verify the effectiveness of both modules. Code will be released upon acceptance.

All-optical diffractive neural networks (DNNs) offer low latency, low energy consumption, and massive parallelism. However, their scalability in terms of network scale and multi-task processing remains limited. Here, we experimentally demonstrate a large-scale metasurface-based diffractive learning machine for angle-multiplexed multi-task processing. Our system employs a metasurface-based reflection cavity to realize a five-layer DNN comprising 115 million fixed, untrained diffractive nodes within a compact volume of 216 mm^3. By integrating this large-scale, untrained DNN with a lightweight, trainable digital backend containing only 7,680 parameters, our system experimentally achieves an accuracy of 95.3% on the standard full-scale CIFAR-10 dataset, significantly outperforming previous optical neural networks and rivaling large-scale digital models. Using a novel incident-angle-multiplexing scheme, our system experimentally achieves parallel processing of 11 tasks with negligible performance degradation, representing the largest multi-task processing capacity reported to date. Our work provides a scalable and energy-efficient solution for high-performance edge computing.

We establish a functional central limit theorem for locally stationary time series in a separable Banach space $B$. The result requires no type-2 or cotype assumptions and thus covers spaces central to functional data analysis, such as $C([0,1])$ and $L^p([0,1])$. Under moment conditions, summable physical dependence coefficients and a bracketing entropy condition controlling the infinite-dimensional tails, the centered partial sum process converges weakly in $D([0,1],B)$ to a centered Gaussian process, whose covariance is the integrated local long-run covariance, an element of the projective tensor product. We also obtain a stochastic integral representation with respect to a cylindrical Brownian motion. As the limit depends on the unknown long-run covariance, we prove consistency of a block multiplier bootstrap for the partial sum process. This yields CUSUM tests for a constant mean of the full process, based on arbitrary continuous seminorms and valid under a time-varying long-run covariance. For linear projections, we derive a self-normalized test with a pivotal limit. In simulations, the supremum norm test detects localized changes that its $L^2$ counterpart largely misses, and applications to EEG and temperature data illustrate the methodology. Examples in $C([0,1])$ and $W^{1,p}_0([0,1])$ show how the entropy condition can be verified.

This study aimed to automate hierarchical diagnostic reasoning (HDR), a constructive method for evaluating practical judgment skills, by developing and testing an evaluation process using a large language model. HDR is a descriptive task that measures higher-order cognitive skills by requiring students to identify and explain errors in case-study-based problems. However, it requires expertise and effort to develop and evaluate. Hence, we proposed and empirically validated the automatic (1) generation of case problems containing errors aligned with educational intentions, (2) scoring of descriptive answers, and (3) generation of structured feedback based on incorrect answers, achieved solely through prompt design without fine-tuning. The internal consistency and construct validity of the generated problems were supported by the experimental score distribution and Cronbach's alpha (0.78). The agreement between automated and human ratings reached 100% under some conditions. The feedback was rated as being as convincing and useful as that from human instructors, demonstrating a practical framework for implementing HDR-based constructive assessment with reproducibility, immediacy, and low cost. The flexibility of large language models will also enable repeated and longitudinal assessments while maintaining structure, showing broad potential for application in educational settings.