Papers

Let $E$ be the exterior algebra on $n$ generators over a field, and let $F$ be a graded free $E$-module with $r$ generators, of degrees $d_1 \le \dots \le d_r$. We determine the convex hull of the set of Hilbert functions of the quotients $F/M$, where $M$ runs over the monomial submodules of Amata and Crupi. The hull is the Minkowski sum of $r$ shifted copies of one and the same simplex: the Kozlov simplex, which Kozlov proved in 1997 to be the convex hull of the $f$-vectors of simplicial complexes on $n$ vertices. For $r=1$ the statement is Kozlov's theorem, so this is a rank-$r$ generalization of it. We give a self-contained proof, including a short proof of Kozlov's theorem from the local Lubell-Yamamoto-Meshalkin inequality, and an explicit facet description of the Kozlov simplex that appears not to be recorded in the literature. Along the way we isolate the class of submodules for which the argument works, the ideal-direct-sum modules, and show by example that the Hilbert function of a graded submodule outside that class need not be a shifted sum of $f$-vectors at all. The combinatorial content is stated separately, in language that uses no algebra, as a result on $r$-vectors of simplicial complexes and their $ff$-vectors. Finally we describe the vertex structure of the Minkowski sum – which sums of vertices of the summands survive as vertices – proving the answer for the all-ones leg vector at every rank and for the Kozlov leg vector at rank two.

Influence maximization asks for $k$ seed vertices that maximize the expected spread of a diffusion process in a network. Standard near-optimal-time algorithms based on reverse-reachable sampling achieve a $(1-1/e-\varepsilon)$ approximation, but their expected running-time bounds grow linearly with the seed budget $k$. We remove this multiplicative dependence: for the independent cascade model, our algorithm succeeds with probability at least $1-\delta$ in $O((m+n)\varepsilon^{-3}\log(2n/\delta))$ expected time. The result extends to triggering models with explicitly charged local sampling costs. We reserve $O(\varepsilon k)$ seed positions for cost-weighted random vertices, allowing reverse-reachable searches to stop as soon as they encounter a reserved seed. An independent sample-count estimation phase uses a statistic that also controls the expected search cost. Matching these quantities eliminates the multiplicative dependence on $k$ while preserving the approximation guarantee.

We study SC derandomizations for regular read-once branching programs (ROBPs) and computation models beyond BPL. For regular ROBPs with length $n$, width $w$, and multiple accept nodes, we attain the following results. 1. When $n \le w$, we show an SC derandomization with space $O(\log^2 n+\log w)$ and two-sided error $1/\text{poly}(nw)$. 2. When $n \ge w$, we show an SC derandomization with space $O(\log n \log w)$ and two-sided error $1/\text{poly}(w)$. In addition, when $w=O(\log n)$, we attain an optimal $O(\log n)$ space derandomization with two-sided error $1/\text{poly}(w)$. 3. When $w \le 2^{O(\sqrt{\log n})}$, we show that reachability of regular ROBPs (i.e. derandmization of one-sided unbounded small error ROBPs) can be computed in SC. We also show that when regular ROBPs are powering, optimal deterministic logspace can be attained for computing reachability and for bounded two-sided error derandomization, when $w = n^{1/c}$ for some constant $c$. We further show that two super sets of BPL can be computed in SC. 1. For probabilistic logspace TMs with a two-way access random tape, we show that it can be approximated in SC if each entry of the random tape is accessed for at most a constant number of times. 2. For probabilistic logspace TMs with a polynomial size stack, i.e. probabilistic logspace Auxiliary Push-down Machines (AuxPDMs), we show that it can be approximated in SC if the timings of push/pop/idle stack operations do not depend on the randomness. The first model is the read-multiplicity model considered by Impagliazzo, Nisan, Wigderson (STOC'94), in which they show that their INW generator can fool such computations. For the second model, we indicate that it contains candidate languages separating BQL from BPL considered by Apers and Edenhofer (CCC'25).

Autocatalysis, the ability of a chemical subsystem to sustain its own constituents when supplied with sufficient food molecules, has been closely related to the origin of life on Earth. Emerging from Wilhelm Ostwald's considerations about an explicit autocatalytic reaction, different notions of autocatalysis have been developed over the years. The two most prominent are reflexively autocatalytic F-generated sets (RAFs) and stoichiometric autocatalysis. After having shown that each RAFs is, under reasonable conditions, in general stoichiometrically autocatalytic, we examine here the relationship between the two notions of minimality: irreducible RAFs and autocatalytic cores. To this end, we overcome the obstacle that RAFs and stoichiometric autocatalysis have been formalized in distinct systems of chemical reactions, i.e., catalytic reaction systems (CRS) and chemical reaction networks (CRNs), respectively. We show that reactions in a CRS constitute equivalence classes of reactions of the corresponding CRNs w.r.t. their specific catalyzations. Using the fact that CRN and CRS can be canonically identified whenever each CRS reaction is associated with a single catalyzation, we demonstrate that the Kőnig graph of a monocatalyzed, irreducible RAF is composed of strong blocks devoid of food and waste species that are separated by reaction vertices, each of which contains an autocatalytic core. In fact, a single irreducible RAF can, in general, contain exponentially many autocatalytic cores.

Long-video understanding must capture transient visual evidence under strict token budgets, yet existing methods compress frames, append memory tokens, or alter internal key-value (KV) caches. We introduce Prefix-Steered Recurrent Memory (PREM), a memory-token-free framework for frozen vision-language models (VLMs). PREM separates video ingestion from query answering: a recurrent writer distills visual streams into a compact 256 KiB multi-slot associative state, while a question-conditioned readout adds memory-derived key/value (K/V) steering modulations to existing non-visual prompt prefixes during prefill. This enables write-once, query-many inference without extra prompt tokens or decoding recurrence. Across six long-video benchmarks in offline and streaming end-of-stream settings, PREM consistently outperforms frozen baselines at every evaluated visual budget. Under a constrained budget of 16 frames, PREM improves macro-average accuracy by 3.06% on Qwen2.5-VL-3B, with gains of 11.0% on action antonym identification and 9.9% on localized needle retrieval. These gains require tuning 0.24% of backbone parameters at 0.03 GiB of peak GPU memory overhead.

Prompt learning efficiently adapts vision-language models (VLMs) to downstream tasks, but gains on seen classes often come at the expense of generalization to unseen classes. To address this limitation, we propose prompt ensembling with training-free routing (PETR), whose key innovation is a carefully designed dual-prompt architecture: two complementary prompts are learned from different data and objectives to emphasize seen class discrimination and unseen-class generalization, respectively. During training, both prompts are fine-tuned using a shared frozen CLIP backbone, and statistical information is collected from the training set logits. At inference time, we determine the similarity of each test sample to seen data, and route the sample to the most appropriate prompt branch. To the best of our knowledge, this is the first prompt tuning framework that performs training-free adaptive routing based on statistical similarity. This design provides an interpretable routing signal and avoids common MoE-style routing pathologies, such as router training instability and load imbalance. Extensive experiments on 11 benchmark datasets demonstrate that our framework consistently outperforms previous methods on both seen and unseen classes, achieving new state-of-the-art results.

Phase change materials (PCMs) can enable non-volatile optical memory through the large refractive index and extinction coefficient contrast between crystalline and amorphous states. Among them, $\mathrm{Sb}_{2}\mathrm{Se}_{3}$ combines low optical attenuation at telecom wavelengths, making it promising for low-loss programmable phase shifters. Its non-volatility is particularly useful for cryogenic systems, where power dissipation and thermal load constrain scalability. However, its optical properties at cryogenic temperatures remains poorly understood. Here, we report the first cryogenic optical characterization of $\mathrm{Sb}_{2}\mathrm{Se}_{3}$ integrated on a foundry silicon photonic platform from 4K to 300K for both crystalline and amorphous states. We observe that the magnitude of the thermo-optic coefficient decreases upon cooling, whereas the optical attenuation changes only weakly for both the amorphous and crystalline phases. We report the stability of the material upon repeated thermal cycling. These measurements provide the material parameters and stability required to design low-loss, non-volatile photonic memory elements for scalable cryogenic information processing.

Intraday electricity markets enable participants to adjust energy positions close to delivery, with price forecasts necessary to support trading and the scheduling of flexible electricity resources as well as increasingly responsive consumers. Forecasting model specifications have progressed from using macro-features, such as renewable generation and load, to the micro-features of continuous orderbooks. A recent advanced deep learning model, OrderFusion, explicitly models micro-level buy-sell orderbook interactions. However, despite its superior comparative forecasting performance, it considers only one delivery product at a time, ignoring neighboring-product information. Moreover, when forecasting aggregated price indices such as the liquid German ID3, ID2, and ID1 products, it omits the information contained in price trajectories. In contrast, pretrained time-series foundation models have shown success in financial, renewable-energy, and day-ahead electricity price forecasting. However, their performance on intraday orderbook data remains an open research question of considerable practical importance. In this paper, we propose OrderFusion+, an open-source deep learning model that combines historical orders from the target and neighboring delivery products to forecast probabilistic buy-sell price trajectories. We benchmark OrderFusion+ against forecasting baselines and pretrained foundation models, and investigate dynamic market conditions through the designed dynamic masking mechanism, revealing insights into market efficiency. The implementation and forecasts can be found at: https://runyao-yu.com/OrderFusion/

We prove a rigidity theorem for closed Einstein manifolds of dimension $n\ge6$ under two lower bounds on the curvature operator of the second kind. More precisely, for $L_1, L_2\ge0$ and some real number $\alpha>1$ in a suitable range, we consider \[ \lambda_1\ge-L_1\bar\lambda, \qquad \frac1\alpha\sum_{j=1}^{\alpha}\lambda_j \ge-L_2\bar\lambda. \] Here $\lambda_1\le\cdots\le\lambda_N$ are the eigenvalues of the curvature operator of the second kind $\mathring R$, $N=(n-1)(n+2)/2$, and $\bar\lambda=N^{-1}\sum_{j=1}^N\lambda_j$. Let $\theta(n, \alpha)$ be the constant appearing in \cite[Theorem~1.1]{CW26}; see (2). In the parameter range considered here, $L_2>\theta(n, \alpha)$, so the second condition is strictly weaker than the corresponding condition in \cite{CW26}, while the first condition and that condition do not imply each other. Under an additional explicit relation between $L_1$ and $L_2$, we prove that the manifold is either flat or a spherical space form.

With face-recognition models now embedded in everyday authentication and surveillance, recent works have pinpointed a critical weakness: these models remain acutely vulnerable to adversarial semantic edits. I.e., adversarially produced semantic alterations to the input, such as slight aging or pose changes, can induce misclassifications. Certain existing attacks are powerful, but they can be computationally costly, rendering them inadequate for developing defenses (e.g., through adversarial training). To fill the gap, we introduce BoundStyle, a potent semantic attack operating in StyleGAN's rich latent space to maximize misclassification rates. Notably, BoundStyle achieves high attack success rates while being ${\sim}{\times}9.5$ faster than existing state-of-the-art attacks, making it suitable for adversarial training. Building on BoundStyle, we develop StyleAT, an efficient adversarial training scheme that incorporates low-budget attack variants yet defends against stronger and unseen semantic attacks. We evaluate on two datasets unseen during training and seven models, and find that StyleAT boosts robust accuracy against state-of-the-art attacks and outperforms common defenses in various settings.

We prove Kahn's flow conjecture, which is a strong form of Chvátal's conjecture on the largest intersecting subfamily of a downset.

Orthogonality in a LoRA factor does not by itself specify what the composed update protects: the answer depends on the task-start state, the parameterization, and the realized optimizer displacement. We formalize this question through Bilinear Optimization Divergence (BOD), an anchor-relative diagnostic of effective-update response on selected historical features. The finite-step analysis distinguishes two cases. In a shared adapter, protecting the routing displacement leaves a learned-anchor residual through the changing companion factor. In a fresh zero-output block, a feasible routing state can protect the composed update while both current factors remain trainable. These conditions yield Semi-Frozen Orthogonal Routing (SFOR) for shared adapters and current-block hard protection for cumulative O-LoRA; Weight Residual Projection (WRP) enforces the required displacement after the optimizer step. Controlled two-task traces verify the predicted residual paths, reducing normalized historical response from 19.12% to 0.005% in the shared family and from 7.72% to 0.002% in the cumulative family. Four-task experiments on Qwen3-8B characterize the resulting trade-offs: SFOR improves backward transfer (BWT) from -2.47 to -0.86 with nearly unchanged average accuracy (AA), while O-LoRA hard protection improves three-order mean AA from 80.27% to 81.30% and forgetting measure (FM) from 2.20 to 0.43. Component controls also show that stricter feasibility need not improve final task performance. Together, the analysis and evidence provide an architecture-conditioned account of which constraint to enforce, how to enforce it, and how to interpret its empirical value.

In this paper, we study the Dirichlet eigenvalue problem for the logarithmic Hardy operator, defined as the logarithmic Laplacian with a critical logarithmic potential, in a bounded Lipschitz domain containing the origin. We first establish a logarithmic Hardy inequality and use it to identify the associated energy space, showing that the embedding into \(L^2\) is compact when the perturbation parameter exceeds the endpoint value \(-1\), but fails to be compact at that endpoint. For parameters above \(-1\), we develop a complete variational spectral theory, prove that the problem admits a discrete sequence of eigenvalues tending to infinity, characterized by successive minimizations over orthogonal complements, whose eigenfunctions form a complete orthonormal basis of \(L^2\). We further establish a uniform lower bound for the first eigenvalue, a scaling property under domain dilation that determines a critical radius for the sign of the first eigenvalue and leaves the eigenvalue gaps invariant.

End-to-end document parsers increasingly offer an optional reasoning mode for complex pages. On a 180-page entropy-stratified discovery sample with one frozen 4B checkpoint, complexity is the wrong decision variable. Reasoning lowers mean quality by 2.21 Overall at 1.54x tokens; a preregistered input-only model cannot predict its signed benefit (held-out AUROC 0.47, indistinguishable from chance). The benefit concentrates on pages whose ordinary pass has already collapsed, and they do not look complex: shared collapses have lower layout entropy than healthy ones yet consume 19x the tokens as degenerate repetition that doubling the budget does not cure. Switching modes rarely repairs them: 83% recur under reasoning. We instead detect collapse from the ordinary-pass trace, decompose the page by projection, and re-parse each region. Repair gains 1.40 Overall (95% CI [0.68, 2.16]) at 1.13x tokens, replicates across three checkpoints, and, with all parameters frozen, gains 2.41 (CI [1.64, 3.46]) on the remaining 1,175 benchmark pages.

Strong and weak symmetries and their spontaneous breaking distinguish different forms of symmetry and order in mixed states. We show that complete one- and two-point correlation functions, equivalently all two-site reduced density matrices, determine exact strong symmetry for continuous onsite unitary actions of connected groups: states with identical correlations have the same strong symmetry and character. We also present an algorithm to determine the maximal connected strong-symmetry sub-Lie group and its character from two-point correlations. Because such correlations are more accessible than full-state tomography, the algorithm is readily applicable to experiments ranging from condensed-matter systems to quantum simulators and circuits. We also identify group and representation-specific cases in which fewer correlations suffice.

Battery energy storage system (BESS) dispatch must preserve operational feasibility while declining price spreads reduce the margin available to pay for cycling. We study a proximal policy optimization (PPO) controller whose pre-selection physical action mask and emergency projection are separated from a causal, forecast-informed economic advisory. All forecast-dependent methods receive the same causal 24-step forecast and grid-side settlement. Across five PPO seeds, advice-on net profit is 30.59 and 18.04 USD per 336-hour T1 and T2 window, versus 36.77 and 22.94 USD for proxy-cost MPC; PPO remains below this reference in both periods. Advice raises T2 profit from 16.45 to 18.04 USD while reducing throughput, but is immaterial in T1. On disjoint weekly blocks, PPO is stable under daily, weekly, and blended seasonal forecasts, weakens under persistence, and remains below proxy-cost MPC. Paired diagnostics localize changes to the observed 5-10 USD/MWh regime with mixed SoC-dependent effects. An M0-M6 ablation shows that mask removal sends thousands of infeasible requests to projection, while removing both physical layers exposes ramp violations. The evidence separates economic screening from feasibility enforcement without claiming formal safety, lifecycle-optimal aging, or RL dominance.

Large audio-language models (LALMs) are increasingly used for a broader range of audio reasoning tasks. These models typically incorporate audio representations into a large language model (LLM) backbone to enable multimodal reasoning. Recent test-time reinforcement learning (TTRL) methods further improve LLM reasoning capability by leveraging unlabelled test data after pre-training. However, the importance of the perceptual capability of LALMs remains underexplored, particularly how much acoustic evidence is integrated and relied upon during reasoning, and how this contributes to final task performance. This gap limits the development of effective post-training methods like TTRL for audio reasoning. In this work, we first analyse how audio information is integrated and utilised during reasoning process. We quantify layer-wise perceptual reliance and show that stronger acoustic reliance is associated with higher accuracy and a larger performance gain attributable to the audio input. Building on this, we propose Perception-Grounded TTRL (PG-TTRL), which aligns label-free test-time optimisation with perceptually grounded reasoning, encouraging the model to structure its reasoning more strongly on the audio input. Experiments across LALMs and benchmarks show that PG-TTRL consistently improves reasoning performance over both the base models and standard TTRL, showing the value of perceptual-grounding optimisation for test-time audio reasoning.

This paper investigates the $L_p$-dual mixed Euclidean-Gauss Minkowski problem associated with the $L_p$-dual mixed Euclidean-Gaussian curvature measure. The solvability of this problem is equivalent to that of a class of Monge-Ampère type equations on the unit sphere. Under smooth assumptions, We establish the existence of solutions for $p<1$, $q<0$, and $q<p$ and uniqueness of solutions for $p\geq q$ to the aforementioned Monge-Ampère type equations, respectively. Furthermore, we obtain a complete solution concerning the existence part of this problem when $p<1$ and $q<0$.

Large reasoning models (LRMs) incur high inference costs, often mitigated by efficiency techniques like quantization and pruning. However, the impact of these techniques on model adversarial robustness remains largely unexplored. This study provides the first comprehensive analysis of the interplay between efficiency, jailbreak vulnerability, and reasoning in LRMs. We find that while efficiency methods seemingly reduce the success rate of jailbreak attacks, this improvement is often superficial. It largely arises from degraded reasoning capabilities leading to "attempted but failed" malicious responses, rather than an increase in genuine alignment. Mechanistic analysis of representational drift confirms this, revealing a strict coupling between reasoning capability loss and the model's inability to maintain malicious semantic trajectories. Additionally, we identify quantization with pruning as the optimal strategy to balance efficiency and robustness. These findings clarify the distinction between true safety alignment and capability-induced failure, providing an empirical foundation for LRM deployment.

The rapid development of video generative models (VGMs) has enabled the generation of highly realistic synthetic videos, raising concerns about the intellectual property rights (IPR) of these models. In particular, two closely related forensic tasks remain largely unaddressed: synthetic video verification (determining whether a video was generated by a protected VGM) and model ownership verification (determining whether a suspect VGM is an unauthorized copy of a protected VGM). In this paper, we propose a new in-generation watermarking scheme that can address the two verification tasks. First, a novel video watermarking network named VidMark is presented, which incorporates a two-scale discrete wavelet transform (DWT) decomposition and a global temporal attention block (GTAB) to enhance watermark robustness and imperceptibility. Second, we present a decoder-guided fine-tuning procedure. By leveraging the frozen VidMark decoder, this process enables VGMs to synthesize videos carrying an imperceptible, robust, and model-specific watermark. Finally, two verification frameworks are established to perform synthetic video verification and model ownership verification. Extensive experiments on representative VGMs demonstrate that the proposed scheme achieves over 99% watermark extraction accuracy and 100% verification accuracy on both tasks, with negligible impact on video generation quality. Furthermore, the watermarks exhibit strong robustness against a comprehensive range of video-level and model-level attacks.

Sink-aware deployment may identify important first-token attention heads before a model is quantized, then reuse that map at the edge. We test when this shortcut is safe for 4-bit NF4 weight-only post-training quantization (PTQ). Our Sink Topology Consistency (STC) metrics separate global rank preservation, top-$k$ set overlap, and layerwise sink-mass shift, and distinguish per-input sensitivity from calibration-map transfer. Across Qwen2.5-0.5B, Qwen2.5-1.5B, and Llama-3.2-1B, global bf16-to-4-bit ranks remain high at 4,096 tokens ($\rho_s \geq 0.980$), yet top-$k$ Jaccard overlap is only 0.619-0.793, corresponding to 76.5-88.5% membership retention. The global statistic also masks local failures: terminal Qwen layers shift by 6.2-7.9x their model means, whereas Llama-3.2-1B shows low, nearly uniform drift. Under a C4-to-LongBench shift, cross-domain overlap degrades more than the within-domain precision comparison for both Qwen models, but not for Llama-3.2-1B. Matched-domain 4-bit recalibration reaches 90% of a split-half stability plateau at the smallest tested $n=8$ for both Qwen models and $n=32$ for Llama-3.2-1B, though not as a sharp threshold; for the two Qwen models, updating only selected layers does not reach the full-map stability criterion. On Jetson Orin NX, the 16-sample workload takes seconds for the two models with valid on-device sink measurements. The practical message is precise: global rankings often transfer, but discrete head sets, layer-local policies, and cross-domain calibration should be revalidated after quantization.

In the 1950s and 1960s, Agrawal introduced a class of experimental designs that later became known as triple arrays. Gordeev, Markström and Öhman proposed near triple arrays by relaxing all three intersection properties of triple arrays, allowing two values concentrated around the average intersection size, as well as two consecutive values for the replication numbers. They completely resolved the existence of near triple arrays with three rows, showing that there exists a $(3\times c,v)$-near triple array if and only if $v\geq c\geq 3$ except for $(c,v)\in\{(3,6),(4,6),(5,8)\}$. In this paper, we further investigate the existence of near triple arrays with four rows and prove that there exists a $(4\times c,v)$-near triple array if and only if $v\geq c\geq 4$ except for $(c,v)\in\{ (4,9),(5,7),(5,10),(6,8),(7,9),(10,12),(11,13)\}$.

Firmware fuzzing is an effective technique for discovering vulnerabilities in embedded systems. However, existing coverage-guided firmware fuzzers typically obtain feedback through firmware instrumentation, hardware debug interfaces, or firmware rehosting, which requires access to the firmware source code or binary image. Such requirements are often infeasible for off-the-shelf embedded devices, where firmware binaries are inaccessible, unrehostable, immodifiable, or undebuggable, necessitating fuzzing under black-box conditions. In this paper, we present POZZER, a power side-channel-guided fuzzer for black-box embedded systems. POZZER uses power traces as feedback to identify previously unseen behavior via an incrementally constructed graph-based representation of observed executions, guiding the fuzzer toward unexplored execution paths. Its non-profiling design requires neither prior firmware knowledge nor a clone device, extracting meaningful feedback from a single power trace per execution while remaining robust to measurement noise. We evaluate POZZER on 15 firmware targets across two platforms and two real-world commercial embedded devices. Across the resulting target-platform combinations, POZZER outperforms a blind fuzzer under the same time budget in 26 out of 30 target-platform combinations. Furthermore, POZZER discovers two previously unknown vulnerabilities in one of the commercial devices, both confirmed by the vendor, demonstrating its potential for identifying vulnerabilities in black-box embedded systems.

Maintenance work orders must often be processed offline on embedded hardware, yet downstream software requires predictable structured output. We present ARID (Aviation-inspired Routing for Industrial Deployment), which extracts component, failure mode, symptom, and maintenance action into fixed-schema JSON on an 8 GB NVIDIA Jetson Orin NX. ARID combines conservative dual-teacher filtering, targeted noise-aware synthesis, one routing decision per work order, 4-bit inference, and grammar-constrained decoding. From 2,326 unlabeled OMIn records, it retains 716 training pairs and adds 99 topology-constrained records targeting action extraction. On 300 human-labeled records, ARID reaches 84.8% token-F1 on the reference stack and 82.9% on the deployed Jetson. Resident serving achieves 5,310/5,656 ms P50/P99 at 12.5 W. On zero-shot MaintNet transfer, semantic F1 falls to 46.4% while parser success remains at least 99.8%, showing that output validity transfers but field semantics do not.

We study finite left-nested Jordan products of idempotents in finite-dimensional simple Jordan algebras over a field $\mathbb{F}$ of characteristic different from $2$. Over an algebraically closed field, the structure theorem reduces the problem to the scalar algebra, spin factors, the full matrix Jordan algebras $M_n(\mathbb{F})^+$, the symmetric matrix algebras $H_n(\mathbb{F})$, the symplectic Hermitian algebras $H_{2n}(\mathbb{F},\mathrm{sp})$, and the split Albert algebra. We determine exactly which elements are representable: except in $H_2(\mathbb{F})$, these are all nonscalar elements together with $0$ and $1$, whereas in $H_2(\mathbb{F})$ the nonzero square-zero elements are also not representable. We also study the minimal word length of representable elements. For $M_n(\mathbb{F})^+$ over an arbitrary field, the maximal word length grows logarithmically in $n$, and for $n=2$ we determine the exact length of every nonscalar matrix. The same logarithmic growth holds for $H_{2n}(\mathbb{F},\mathrm{sp})$. The spin-factor and symmetric-matrix results hold over quadratically closed fields, whereas the full matrix, symplectic Hermitian, and split Albert results hold over arbitrary fields of characteristic different from $2$.

Reactive vision-language-action (VLA) policies suffer from task-state aliasing in long-horizon manipulation, where identical multimodal inputs call for distinct, context-dependent actions. Given that pretrained VLAs already possess rich control primitives to express diverse behaviors, we hypothesize that the execution bottleneck lies not in policy capacity, but in input ambiguity. In this paper, we propose TaskAnchor, a lightweight adapter that grounds task state by injecting execution context into the VLA's native input space. During post-training, TaskAnchor learns to represent the semantic execution stage as a milestone-supervised coordinate prepended to the language instruction, while incorporating fine-grained historical evidence via a residual update to the current visual tokens. This formulation avoids generating complex subtask instructions and leaves the backbone architecture unchanged. Across long-horizon benchmarks, TaskAnchor delivers substantial gains, achieving approximately 6 times the average success rate of the pi0.5 and X-VLA baselines on RMBench and more than doubling the task success rate of pi0.5 on RoboMemArena. Real-robot experiments further validate reliable multi-stage execution, with the same policy adapting its subsequent behaviors using earlier human interactions as in-context cues. Our project website is available at https://taskanchor.netlify.app/.

Computational complexity is an inherent limitation of formal synthesis for networked systems, and decomposing the global specification into local ones relaxes this limitation at the cost of conservatism. Since the granularity of the partition governs this trade-off, it is reasonable to treat the partition as a design variable, which calls for local specifications that remain correct for every partition. To this end, this paper gives each agent a local specification, written as an assume-guarantee contract that the agent can establish from local information. We first derive a necessary and sufficient condition for these contracts to decompose the global specification under a given partition. Building on this, we then present a condition under which the decomposition is correct for every partition, so that the partition becomes a free design variable. For linear dynamics and signal temporal logic formulas with affine predicates, we further synthesize a controller for each coalition by a tube-based approach. Finally, simulations on a network of input-coupled tanks show how the choice of partition trades computational cost against conservatism.

As AI agents become increasingly capable, agent-driven robotic control is emerging as a compelling paradigm. However, prevailing vision-language-action (VLA) models and world action models (WAMs) still rely on natural-language instructions to specify manipulation tasks, an ill-suited interface for agent-driven control: referentially ambiguous, spatially imprecise, redundant with the agent's inherent language understanding, and entangling intent with execution. We present AR-WAM, a visual-conditioned, agent-ready world action model that replaces language with two complementary conditions: a visual grounding prompt (a bounding box of the target) denoting the interaction object and location, and a learnable operation token dictating the atomic skill to execute. Our compact 0.5B-parameter model, with a frozen pretrained visual encoder and no language encoder, predicts scene evolution within compact latent states while decoding actions, exposing the policy's intent through explicit, supervisable reasoning signals. A model-agnostic compatibility layer provides three primitives (detect, execute, and query) so that local VLMs or online agent APIs can drive the policy directly, with long-horizon memory and closed-loop error recovery delegated to the agent side. On RoboTwin 2.0, RMBench, and a real Astribot S1 dual-arm platform, AR-WAM attains the highest average success on standard manipulation (85.7% over the clean and randomized settings) and outperforms all baselines on memory-dependent and real-robot long-horizon tasks, improving success rates by 5.9% and 36.7%, respectively, while maintaining the lowest inference latency (14.1 ms). Project page is at https://ar-wam.github.io/.

We study randomized algorithms for the fully online allocation of indivisible goods among $n\ge2$ agents with nonnegative additive valuations. Goods arrive sequentially and must be allocated immediately and irrevocably, with only $n$ known in advance. Since exact ex-ante envy freeness and proportionality are readily achievable, while no positive ex-post approximation is possible for the fairness notions considered here, we study the intermediate notions of high-probability fairness and expected realized fairness. Against a non-adaptive adversary, we give a randomized algorithm for proportionality up to one good (PROP1) whose parameter depends only on $n$ and that preserves exact ex-ante envy-freeness and proportionality. At confidence $1-\delta$, its PROP1 guarantee improves on independent uniform allocation (Rand) by a factor of $\Omega(\log n)$, uniformly over $\delta\in(0,1/2]$. As $n\to\infty$, its expected realized PROP1 factor is at least $\frac{3-\sqrt5}{2}-o(1)$. We also show that the expected realized PROP1 factor of Rand is $(1+o(1))/\log n$, yielding an improvement of at least $\bigl(\frac{3-\sqrt5}{2}-o(1)\bigr)\log n$ for our algorithm. For every randomized online algorithm and every positive approximation factor, the success probability can be made arbitrarily small for envy freeness up to any good (EFX) and at most $\frac{n+1}{2n}$ for envy freeness up to one good (EF1). Consequently, every randomized fully online algorithm has an expected realized EFX guarantee of zero and an expected realized EF1 guarantee of at most $\frac{n+1}{2n}$.

In the framework of non-relativistic quantum chromodynamics (NRQCD), we systematically investigate the inclusive and exclusive production processes of spin-singlet \(^1S_0\) and spin-triplet \(^3S_1\) toponium at future muon colliders and in Pb–Pb ultraperipheral collisions (Pb–Pb UPC). Using the Coulomb-plus-linear potential and solving the Schrödinger equation, we obtain the wave function at the origin as $|R_{t\bar{t}}(0)|^2 = 2.507\ \text{GeV}^3$. The scattering cross sections and various kinematic distributions for two types of processes are calculated, and the corresponding event yields are estimated based on the expected integrated luminosities. Our study indicates that the detection prospects for toponium production through the aforementioned processes are unfavorable.