Papers

Tracking the 6DoF pose of a moving rigid object is fundamental to robotics and autonomous driving, but existing trackers assume that object appearance is stable across a sequence, an assumption that breaks down on reflective surfaces whose appearance changes as they mirror the environment. We introduce a light field based reflection-robust 6DoF tracker that turns this apparent nuisance into a pose cue. Per frame, our method recovers depth robustly against reflections, back-projects it into a point cloud, and estimates surface normals. It then decomposes the object's view-dependent appearance into a diffuse albedo and the environment map it reflects, resulting in a relightable surface light field. Starting from a coarse initialization, we relight it by the recovered environment map and optimize the pose on the photometric loss. Because a moving object mirrors new parts of the scene, the environment map fills in as the sequence proceeds, sharpening this signal over time. To evaluate this approach, we introduce a light field tracking dataset re-rendered from a robotic manipulation benchmark at four controlled reflectivity levels, each paired with simulated depth that reproduces how consumer RGB-D sensors fail on shiny surfaces. Additionally, we evaluate on two captured light field sequences. Our method trails the strongest baselines on diffuse objects and is the only one that holds its accuracy on fully reflective objects, where every baseline degrades.

On-policy distillation (OPD) trains a student model on self-generated trajectories, but transmitting dense teacher distributions across long reasoning traces creates prohibitive communication and memory bottlenecks. Practical systems therefore rely on sparse teacher interfaces, typically transmitting either the sampled-token score or a small Top-$k$ distribution. However, this sparse setting faces a fundamental dilemma: sampled-token estimators are unbiased but suffer from severe gradient variance, whereas directly optimizing Top-$k$ objectives introduces systematic bias. To improve this trade-off, we propose ResOPD (On-Policy Distillation with Tail Residualization), which provides unbiased full-vocabulary reverse KL gradient estimation under on-policy sampling, with substantial variance reduction under the same sparse payload in the evaluated settings. ResOPD aggregates the unobserved vocabulary into an observable coarse tail event, computes its exact aggregate gradient, and samples only the fine-grained within-tail residual, which requires no additional teacher queries or forward passes. Extensive experiments demonstrate that ResOPD substantially reduces gradient variance, stabilizes online training dynamics, and improves downstream performance across the evaluated settings. These results establish ResOPD as an efficient, plug-and-play variance reduction primitive for sparse on-policy distillation.

Data centers consume a large amount of energy, much of which is wasted due to idle servers. Turning off idle servers might be an effective power-saving solution; however, there is a trade-off between energy savings and system performance. Hence, we propose a setup queueing model with a batching policy that allows servers to process a set of jobs simultaneously to minimize power consumption while maintaining acceptable performance. We consider an M/M/c/SET–BATCH queue, a multi-server batch service queue with a fixed batch size and setup times, and some variants, including systems in which idle servers delay before turning off or systems in which the batch size is dynamic. We analyze the steady-state probabilities and system performance of the M/M/c/SET–BATCH system and its variants. Our analysis of the M/M/c/SET–BATCH system with lower computational complexity is made possible by utilizing the special structure of the model. In addition, we use simulations to compare the M/M/c/SET–BATCH model with some other variants with different setup time distributions. The results suggest that the model performs better when the setup time has a larger coefficient of variation. Our results indicate that the batching policy enhances the system performance, especially when we allow servers to be idle before turning them off.

We develop a high-order discontinuous Galerkin formulation of the general synthetic iterative scheme (GSIS) for steady rarefied gas mixture flows. The resulting GSIS-DG discretizes the mesoscopic kinetic equations for monatomic gas mixtures and the macroscopic synthetic equations with the same polynomial degree and solves them alternately. The kinetic solution supplies nonequilibrium corrections to the stress and heat flux, while the synthetic equations accelerate the convergence toward the steady state. Asymptotic analysis shows that GSIS-DG recovers the continuum limit without requiring the spatial mesh to resolve the molecular mean free path. Numerical results over a wide range of Knudsen numbers demonstrate high-order spatial accuracy and rapid steady-state convergence, with more than an order-of-magnitude reduction in computational cost relative to conventional kinetic iteration in the near-continuum regime. Comparisons with second-order finite-volume GSIS further demonstrate that GSIS-DG achieves comparable or better accuracy on coarser physical meshes with fewer total spatial degrees of freedom.

The quasi-static Biot system, which governs coupled fluid-solid interactions in poroelastic media, poses significant computational challenges due to its strong coupling and multiscale nature. To address these, we propose a hybrid fixed-stress transferable neural network (HFS-TransNet) method. In HFS-TransNet, a data-driven TransNet module first approximates observed data on an initialization domain to supply a high-quality starting point for the subsequent physics-informed stage, which then drives fixed-stress splitting iterations via TransNet and admits an error bound. After each iteration, a greedy update strategy on a validation domain prevents model degradation and a relative tolerance criterion governs convergence termination. HFS-TransNet thereby inherits the robustness of the fixed-stress splitting scheme, the flexibility of data-driven modeling, and the transferability of TransNet, effectively overcoming the strong coupling and locking instability inherent in the Biot system. Ablation studies and comparisons with FS-FEM and FS-PINN confirm HFS-TransNet's superior performance in capturing multiscale coupled physics across varying physical parameters and boundary conditions. By bridging classical decoupled iterative schemes with hybrid scientific machine learning, HFS-TransNet offers a novel perspective for complex poroelastic simulations, as demonstrated by its successful application to brain edema simulations.

Human-agent evaluations often compress interaction into a single performance score, even when human and automated policies adapt differently over time. We study this in a sequential cyber-defense game on an attack graph, where a human or reinforcement-learning defender protects cloud assets against a Deep Q-Network (DQN) attacker. We compare four defender settings: a human reward-only game operationalizing the DQN information structure, a human reward-plus-transition game operationalizing the Cognitive Hierarchy Theory-driven DQN (CHT-DQN) information structure, an automated DQN defender, and an automated CHT-DQN defender. In the reward-only game, participants receive payoff and reward feedback. In the reward-plus-transition game, they also see attacker-aware transition probabilities from the CHT-DQN model. Across 80 Mechanical Turk participants and matched automated simulations, human defenders adapted to outcomes in a way the automated defenders did not: they were more likely to reselect a node after a successful defense than after a failure, in both games, an asymmetry we interpret as consistent with Prospect Theory and Cumulative Prospect Theory. The 40-round average also mixes early rounds, where the DQN attacker acts mostly at random, with late rounds, where it mostly exploits; in the final stage, mean protection ranks the reward-plus-transition human game above the reward-only human game, then the automated CHT-DQN defender, then the automated DQN defender, an ordering the overall mean hides. By contrast, the reward-plus-transition game does not produce a statistically reliable overall gain in weighted data protection over the reward-only game. These results suggest that evaluating human-agent cyber-defense systems only by an averaged task score can miss behaviorally meaningful differences in adaptation, action allocation, and bounded human reasoning.

The transition toward decentralized digitalized and lowcarbon electricity systems is fundamentally changing the role of electricity consumers Traditionally passive endusers are increasingly expected to integrate distributed energy resources DERs and participate in energy management and demand response This paper examines consumer empowerment CE in electricity networks with a specific focus on small consumers connected to distribution networks The paper first discusses the technical economic and societal drivers underlying the growing need for CE including increasing DER penetration electrification of heating and transportation network congestion and flexibility requirements A comprehensive definition of CE is then proposed based on six elements active participation enhanced choice information and control automation and controllability selfsufficiency and resilience and energy communities with shared ownership The proposed CE definition is an explicit consideration of weakgrid where security of supply is not guaranteed To support consistent assessment across different electricity systems a framework for quantifying CE is developed based on the availability of technology and policy enablers and consumers ability to ensure security of supply The paper further reviews global experiences and implementation practices across different continents highlighting variations in technological readiness regulatory support and securityofsupply considerations Finally the expected outcomes and challenges of CE are discussed The expected outcomes of CE are improving affordability flexibility resilience market efficiency DER integration and decarbonization while its successful implementation requires overcoming barriers related to information access digital literacy affordability regulation interoperability privacy cybersecurity and consumer engagement

For an odd prime power $q$, a BLT-set $\mathcal B$ is a set of $(q+1)$ points of $\mathcal Q(4,q)$ such that every point of $\mathcal Q(4,q)$ is collinear with at most two points of $\mathcal B$. We complete the classification of BLT-sets of $\mathcal Q(4,q)$ admitting a non-solvable transitive automorphism group. Nelson and Penttila completed the classification of BLT-sets $\mathcal B$ with a non-solvable transitive automorphism group acting irreducibly on the underlying $5$-dimensional vector space. In this paper, we prove that a BLT-set with a non-solvable transitive full automorphism group acting reducibly on the underlying $5$-dimensional vector space is either a classical BLT-set or a Kantor semifield BLT-set.

Diffusion large language models (DLLMs) generate text through iterative block denoising, and multi-branch speculative decoding accelerates this process by verifying a main branch together with multiple draft branches in a single forward pass. While prior DLLM acceleration methods primarily exploit temporal redundancy across denoising steps, we identify a complementary redundancy axis within each speculative verification step: multi-branch computational redundancy. During speculative verification, draft branches inherit most tokens from their parents while unmasking a small set of additional positions, causing large portions of hidden states to remain highly similar across branches. We propose SpecFold, an algorithm-system co-design that exploits this multi-branch redundancy to reduce the cost of multi-branch speculative verification. Algorithmically, SpecFold performs token-level residual gating and selectively reuses parent computation through folded attention and FFN while preserving residual hidden states. Systemically, a Triton kernel implementation translates this fine-grained reuse into end-to-end throughput gains through efficient sparse multi-branch execution. SpecFold is orthogonal to temporal caching and compatible with existing DLLM speculation strategies. Across two DLLM families, five models, and five standard benchmarks, SpecFold achieves up to 1.64x throughput over Spiffy and up to 1.99x over vanilla decoding, while maintaining comparable task performance.

In this note, we prove that the noncommutative AM-GM inequality holds if $n\ge 2\lceil m/2 \rceil^2$. The motivation comes from counterexamples constructed in [De Sa, Random reshuffling is not always better, NeurIPS2020]. The proof constructs a vertex measure based on the Chebyshev nodes on the Boolean cube to extract the distinct indices. The main difficulty is that the measure is not positive on non-integer nodes. The key technique comes from [Grigoriev, Complexity of Positivstellensatz proofs for the knapsack, Computational Complexity (2001)] and eventually transforms the problem into a quadrature estimate.

The Hamilton-Jacobi-Bellman (HJB) equation of a nonlinear system is a nonlinear partial differential equation, and in that form it gives little away. This paper shows that it hides a Riccati equation. Carleman linearization reveals this structure. For scalar input-affine systems with analytic data, the lifted HJB equation is a single infinite-dimensional Riccati equation in a lower-triangular Toeplitz matrix. Its first entry is the Riccati equation of the standard linearization at equilibrium. Its remaining entries hold the nonlinear terms. Nothing about this is an approximation. Under controllability of the standard linearization and detectability of the cost, the equation has exactly one solution with positive diagonal entries, and it can be computed one entry at a time. This solution is the derivative of the value function. We prove that finite-sections of the solution are exact and converge exponentially to the derivative of the value function near the origin. The scalar case has a closed-form solution. This closed form is our benchmark: every result on the lifted equation is checked against it. Nothing in this structure depends on the state dimension. Our methodology points to a general theory of optimal control in which the HJB equation of analytic nonlinear systems becomes an infinite-dimensional Riccati equation.

We prove strong ill-posedness for the two-dimensional incompressible Euler equation in the endpoint velocity space $W^{3,1}_\sigma(\mathbb R^2)$. Given any compactly supported smooth divergence-free background and any $\delta>0$, we construct a single compactly supported divergence-free datum within $\delta$ of the background in $W^{3,1}$. The perturbation can be localized inside any prescribed nonempty open neighborhood of the background support while remaining disjoint from that support. The associated unique global finite-energy solution $u$ satisfies ${\rm curl} u\in C([0,\infty);W^{2,1}(\mathbb R^2))$, but \[ \operatorname*{ess\,sup}_{0<t<T}\|u(t)\|_{W^{3,1}}=\infty \qquad\text{for every }T>0. \] The proof combines localized hyperbolic insertion, the Bonami–Poornima nonmultiplier mechanism, and many-packet dilution. Moment cancellation and positive material separation control the nonlocal Biot–Savart interactions, allowing a nested construction inside one fixed compact region. Without the compact-support requirement on the limiting datum, a complementary far-field argument yields a dense $G_\delta$ set of data whose solutions leave $W^{3,1}$ at every positive rational time and on a residual set of times, with unbounded essential supremum on every nonempty open time interval.

Tonality is a fundamental organizing principle of Western music. However, the gradual transition from common-practice tonality to atonality around the turn of the twentieth century cannot be captured by binary labels. To characterize intermediate tonal states and trace this evolution, we propose a multidimensional framework for quantifying tonal strength, grounded in tonal theory and mechanisms underlying tonal dissolution. This framework operationalizes the global statistical regularity, temporal coherence, and local perceptual alignment of tonal organization through three complementary features: pitch-class distribution uniformity, temporal stability of tonal centers, and local tonal clarity, respectively. To validate the model, we introduce two new datasets: a binary dataset comprising 196 tonal and atonal pieces, and a historical MIDI corpus of 1,561 compositions by 21 composers spanning the Baroque era to the early twentieth century. The proposed model achieves high discriminative performance on the binary classification task (F_1=0.985), and quantitatively reveals a continuous historical trajectory from established tonality through progressive weakening to eventual dissolution. Computational analysis of representative composers further confirms significant declines in tonal strength throughout the careers of late-Romantic and modernist figures. Additionally, analysis of EMOPIA dataset reveals a weak but statistically significant positive correlation between higher tonal strength values and positive emotional valence. This work establishes a unified quantitative model for analyzing tonal evolution and provides a continuous measure for future behavioral and neurophysiological investigations of the relationships among tonal organization, musical emotion, and cognition.

Motivated by the EPPA problem for finite tournaments,we consider various extension properties for partial permutations. We show that for any set $\Pi$ of prime numbers, the $\Pi$-extension property is equivalent to the $\Pi$-LERF. As a consequence of known results, the odd-extension property is then equivalent to the EPPA for finite tournaments. To study the $\Pi$-extension property, we reformate the property using the concepts of EP problems and $\Pi$-solutions. We then show that the existence of a $\Pi$-solution for an EP problem depends entirely on its fundamental group. In particular, when the fundamental group is trivial or cyclic, the EP problem has a $\Pi$-solution for any $\Pi$. These extend some known results of Huang, Pawliuk, Sabok and Wise [HPSW19]. We give examples of EP problems without nilpotent-solutions; they witness that the $p$-extension property and the $p$-LERF fail for any prime $p$. Then we consider a special kind of EP problems whose fundamental groups have two generators. We show that any 1-weakly wandering problem has a $\Pi$-solution for any $\Pi$. For 2-weakly wandering problems, we show that they all have odd-solutions and we completely characterize those without nilpotent-solutions.

An interaction has two parts: someone decides to act, and then chooses whom to act on. Temporal link prediction has concentrated on the second, and we show that it is blind to the first by construction: a standard negative keeps the real source and swaps the destination, and we prove that this cancels the source's activity exactly from the optimal score, so no model trained and evaluated this way is ever rewarded for learning it. Under the harder historical and inductive negatives, whose sources differ, the same factor becomes the dominant signal. We model it with Source Node Activity Modeling (SNAM), a self-exciting event intensity fitted by an exact point-process likelihood to decayed interaction counts the history states already contain; it has fewer than 20 parameters. On their own, never looking at the destination, these parameters beat DyGFormer and TPNet on four of five datasets under historical negatives. Added to the frozen scores of TPNet, TGN, DyGFormer and DSRD, four models of different design, without retraining anything, they raise AP on almost every backbone-dataset pair in both settings, by up to 25 points. Our full model ranks first overall against eleven baselines on 13 datasets and three protocols, and on million-event streams trains an epoch 9-100x faster than TPNet and DyGFormer. We conclude that source activity is a blind spot of temporal link prediction, and a cheap, transferable one to close. Code is available at https://github.com/Erutaner/Your-Temporal-Link-Predictor-Is-Blind-to-Who-Is-Active.

Memory-augmented agents typically integrate procedural knowledge by injecting retrieved skills directly into text prompts. This approach dangerously equates readable text with reliable execution. To bridge this gap, we introduce From Memory to Guide, a novel paradigm that transitions procedural memory from passive text delivery to active, inference-time policy adaptation. We instantiate this paradigm through the Spatio-Temporal Composer, an active policy compiler that explicitly manages exactly how and when retrieved knowledge should be applied. Rather than treating skills as plug-and-play modules, Composer dynamically aligns historical knowledge with current environmental constraints (spatial adaptation) and precisely dictates its applicable lifecycle (temporal orchestration). It actively transforms static memories into strictly bounded Runtime Guides—equipping the agent with localized objectives and behavioral guardrails without requiring a single parameter update. Extensive evaluations on 13 demanding, long-horizon software engineering tasks in EngramBench demonstrate the clear advantages of this architecture. Composer not only robustly prevents context mismatch but drives an absolute pass-rate increase of 7.2 percentage points on the most complex tasks, while simultaneously slashing the main agent's token usage by 32.2%.

Greedy block-wise local learning splits a network into gradient-isolated blocks trained by local auxiliary losses, deleting the backward pass between blocks: inter-stage communication becomes forward-only and every block can step its optimizer independently, properties directly relevant to decentralized model-parallel training. Local learning is competitive with end-to-end backpropagation on image classification, and on small Transformers it is known to trade a worse best loss for parallel speedup. How this loss gap behaves in autoregressive language model (LM) pretraining at larger scale, and which auxiliary designs reduce it, has not been measured. We present a token-budget-matched empirical study at 125M and 400M parameters with $K \in \{1,2,4\}$ blocks at Chinchilla-optimal budgets, factorizing the auxiliary design into network architecture and training objective. We observe: (i) the gap to end-to-end training more than doubles from $K=2$ to $K=4$, but at $K=4$ shrinks from 125M to 400M; (ii) replacing an MLP auxiliary with a Transformer-based one is a strong network-side intervention, recovering 22-41% of the gap; (iii) a multi-token-prediction (MTP) auxiliary objective helps at the first block boundary, whereas adding it at deeper boundaries hurts, and restricting it to the first block yields the best $K=4$ configuration ($+0.062$ vs. $+0.075$ nats at 400M); and (iv) deployment-style per-block execution reduces activation memory by up to $2.2\times$. We frame these results as an empirically grounded method direction rather than a finalized method: local objectives should apply future-predictive pressure selectively across boundaries while resisting shortcuts that bypass predictive content.

Here we introduce a phenomenon-first framework for materials discovery in which an LLM receives separate descriptions of guest physics, host capabilities and operating context and proposes an unusual qualitative behavior with its mechanism, distinguishing signature and falsifier. Across 80 guest-host combinations in metal-organic frameworks, the model generated 57 proposals that were frozen before evaluation or materials selection; assessment identified nine computationally tractable candidates. In a repeat and guest-only baseline, structured formulation reproducibly broadened mechanistic exploration: the original and repeat runs each covered 21 broad mechanism families versus eight for guest-only formulation despite fewer proposals. From the original run, MC-010 yielded reproducible hydration-driven reorientation of retained ethanol in experimentally reported MOFs, while MC-015 yielded a quantum-corrected reversal of H$_2$ adsorption-region preference relative to the matched classical description. These results show how structured LLM reasoning can move upstream from executing supplied objectives toward prospectively formulating qualitative materials phenomena.

The transverse motion of a gravitational potential induces frequency shifts in photons propagating through it, giving rise to the moving-lens effect and providing a probe of transverse peculiar velocities. Statistical evidence for this effect has recently been reported using cross-correlations between cosmic microwave background temperature maps and large-scale-structure tracers. Here, we investigate a complementary spectroscopic approach based on wide-separation lensed quasars, for which different lensed images probe distinct deflection geometries through a moving foreground lens. We focus on SDSS J1004+4112 and assess the differential redshift that could be measured from its broad emission-line spectra. Using an estimator that combines information across the line profiles, we perform Monte Carlo forecasts for C IV and C III] under an ELT-like configuration, considering photon noise only. For an assumed lens transverse velocity of $500\,{\rm km\,s^{-1}}$ and the orientation maximizing the signal, the expected differential redshift reaches $|\Delta z_{\rm ML}|\simeq6.7\times10^{-7}$. At an integration time of 40 hr, the joint photon-noise-limited precision is $\sigma_z\simeq2.5\times10^{-7}$. C IV dominates the constraint, while C III] provides only a modest additional improvement, and integrations of tens of hours reach the $10^{-7}$ precision regime. These results show that photon statistics alone can reach the characteristic moving-lens signal scale, although practical detectability will depend on controlling astrophysical and instrumental systematics.

Long-video embedding requires capturing sparse query-relevant evidence under a limited visual-token budget. Uniform sampling can miss brief events in videos spanning minutes or hours, whereas encoding more frames in a single context increases memory and computation. We introduce Query-Aware Streaming Latent Reasoning (QASLR), a post-training framework that accumulates evidence across clips while keeping the embedding size fixed. QASLR selects a bounded set of frames, restores their temporal order, and processes them clip by clip with a vision-language backbone. A compact set of persistent think tokens cross-attends to each clip's features, while an embed token reads out a normalized representation after every update. This design integrates evidence across multiple backbone calls without requiring all selected frames to share a single context. Training combines final contrastive learning, step-wise contrastive supervision, and final-embedding self-distillation. Intermediate supervision trains partial-video readouts for retrieval, while self-distillation regularizes them toward the final representation. Query-aware selection produces query-conditioned representations for candidate-set scoring and reranking, whereas query-independent selection enables reusable corpus indexing. Under the full training recipe, HourVideo retrieval Hit@1 increases from 54.2 to 70.7 and from 57.4 to 72.8 for 2B and 8B Qwen3-VL-Embedding backbones, respectively. Gains extend to the evaluated moment-retrieval and video-QA tasks, and the streaming head transfers to a second Qwen-family embedding backbone. These results support streaming latent aggregation as an effective approach to integrating long-video evidence into fixed-dimensional representations.

The fate of quantum coherence following photoexcitation is a central problem in nonequilibrium condensed-matter physics, especially in low-dimensional solids where electronic, structural and many-body energy scales are strongly coupled. Here, we investigate this interplay in ferroelectric $\alpha$-In$_{2}$Se$_{3}$ using broadband transient-grating spectroscopy with $\sim$5 fs laser pulses. Photoexcitation launches pronounced oscillations dominated by a $\sim$104 cm$^{-1}$ mode that persists for several picoseconds. Measurements from 10 to 300 K show that its frequency remains nearly unchanged while its coherence is progressively suppressed, distinguishing the lattice coordinate from thermally activated dephasing. Varying excitation energy reveals a distinct crossover in which increasing photoexcitation progressively modifies and damps the coherent response. First-principles calculations assign the dominant oscillation to a 101.47 cm$^{-1}$ $\Gamma$-point optical phonon involving collective In-Se displacement, while quantum-dynamical simulations reproduce the main transient-grating oscillations. These results establish $\alpha$-In$_{2}$Se$_{3}$ as a model system for independently probing lattice coherence, thermal fluctuations and carrier-density-dependent interactions, revealing how a polar van der Waals semiconductor evolves from coherent lattice motion toward an incoherent many-body state after ultrafast excitation.

Long-horizon problem solving and scientific research require computation to accumulate across successive attempts. Partial solutions, experimental findings, and unsuccessful approaches can inform later work, yet most inference-time computation is organized around individual trajectories or candidates rather than a persistent body of reusable work. We call this paradigm compounding inference: organizing inference-time computation so that intermediate work persists and can be inspected, extended, combined, or challenged by subsequent computation. We instantiate compounding inference in GitSwarm, an asynchronous system where homogeneous agents independently decide how to advance a task while collaborating through structured persistent memory. Agents explore, experiment, verify, refine, and synthesize previous work in a shared, branch-able Git repository. Atomic commits preserve intermediate artifacts, while explicit semantic dependencies record how later contributions build on work across branches. We evaluate GitSwarm on long-horizon problem solving and sustained GPU-backed experimental research. On IMOProofBench-Advanced, GitSwarm solves all 30 problems in one run using GPT-5.5. On ProgramBench, it achieves a $79.4\%$ mean score, versus $65.1\%$ for the strongest reported baseline under the stated budget. On three neural architecture research tasks (Residual Matrix Transformer, Looped Transformer, NanoChat), GitSwarm improves upon the starting architectures through successive experimentation. Beyond final performance, we measure whether computation accumulates: on ProgramBench, $94.7\%$ of contributions are subsequently built upon, while the selected solution's ancestry covers $82-93\%$ of the contribution graph. These results show that inference-time computation can accumulate across otherwise independent episodes, forming an evolving body of work that subsequent inference can reuse.

Real-time directed acyclic graph (DAG) scheduling provides a rigorous basis for timing analysis and efficiency in component-oriented real-time systems (CORTS) such as autonomous driving systems, yet challenges remain from the perspectives of both theorists and practitioners. For theorists, no OS natively supports the DAG task model; algorithms are therefore evaluated only analytically or in simulation, ignoring real-hardware overheads. For practitioners, today's CORTS platforms (ROS~2 and AUTOSAR Adaptive Platform) are designed for service composition rather than timing analyzability; adopting DAG scheduling research therefore demands substantial code changes and developer discipline. This paper proposes Awkernel, the first open-source real-time operating system (RTOS) that natively supports real-time DAG scheduling research, bridging DAG scheduling theory and CORTS practice. For theorists, Awkernel is a real-hardware testbed: it exposes a modular OS-native DAG scheduler for easy algorithm implementation, plus a random workload generator and built-in metrics for evaluation. For practitioners, Awkernel is not a full replacement for today's platforms but a CORTS platform maximizing timing analyzability: its familiar publish/subscribe model keeps porting mechanical, mapping each callback to one subtask. Moreover, its function-as-subtask (FasS) API enforces DAG semantics (precedence constraints) without programmer discipline, yielding applications that match the theoretical DAG model and directly inherit its efficiency and safety guarantees. On a Raspberry Pi~4, microbenchmarks confirm microsecond-level scheduling overheads; a global earliest deadline first (GEDF) scheduler fits in 226~lines; and a practitioner ports part of an autonomous driving system using only the FasS API, without reasoning about DAG semantics.

Text watermarking helps identify AI-generated content, but its effect on factual reliability remains underexplored. In this paper, we study watermarking hallucination: factual errors induced or amplified by watermarking even when the required evidence is present in the context and the unwatermarked model can answer correctly. Using a controlled retrieval-augmented generation setting, we compare unwatermarked and watermarked generations under the same context, query, and decoding configuration, and quantify their factual accuracy decrease. Across six representative watermarking methods, including KGW, SWEET, DiPmark, GumbelSoft, Gumbel-Max, and SynthID watermarking, we consistently observe watermark-induced hallucination. Watermarked outputs can remain fluent while introducing factual errors. We attribute this failure mode to two mechanisms: (1) token perturbations in the current-step arising from method-specific reweighting or keyed sampling, and (2) prefix-induced attention drift, which accumulates through autoregressive decoding and weakens later attention to the factual context. Motivated by this analysis, we propose two plug-in interventions at the token and attention levels that can be integrated into existing watermarking methods to improve factuality. At a matched TPR of 0.90 at 1% FPR, combining the two interventions reduces factual errors by approximately 90% relative to watermark-only decoding while preserving fluency and comparable decoding efficiency. Overall, this work highlights factuality as a first-class criterion in watermark evaluation, alongside detectability and robustness, and calls for careful factuality validation before deploying watermarks in fact-critical applications.

Noisy matrix completion is a fundamental problem in statistical learning and has attracted a substantial amount of interest over the last two decades. In a variety of applications, the missingness pattern is highly informative, yet it has received relatively less attention. Most existing methods either overlook this source of information or oversimplify its generating process, with few attempting to model the association between the data matrix and its informative missingness. In this study, we propose a general modeling framework that jointly models the data matrix and its missingness pattern using a pair of low-rank models coupled by a flexible shared linear structure. This joint low-rank approach incorporates the informative missingness to improve matrix completion and can flexibly capture various associations between the two modes of data. We develop an efficient joint estimation procedure for this framework based on projected gradient descent, and establish local convergence guarantees that unveil its computational and statistical properties. We further demonstrate, through extensive simulation studies and real-world data analysis, that our proposed approach outperforms competing methods, achieving substantial improvements in prediction accuracy on missing entries.

We study the refined de Sitter conjecture (RdSC), the Trans-Planckian Censorship Conjecture (TCC) and the species scale $\Lambda_s$ in the multifield flux potential of type IIB string theory compactified on one-parameter Calabi–Yau threefolds. The scalar potential depends on the axio-dilaton and on the single complex-structure modulus, and is no-scale along the Kähler directions. Restricting to $h^{2,1}=1$ allows us to work with the exact periods obtained from the Picard–Fuchs equations rather than with their large-complex-structure expansion, and therefore to probe the conifold region. For the mirror quintic, $(h^{2,1},h^{1,1})=(1,101)$, we scan 200 flux configurations and find unstable extrema in $96\%$ of the cases, with $c'=0.18$. Once the Kähler runaway is taken into account, the no-scale structure fixes the logarithmic slope of the potential at every critical point to the universal value $\sqrt6$, so that the first RdSC condition is satisfied throughout. Statistically, the complex structure is the heavier sector and the axio-dilaton dominates the unstable directions. For the TCC we obtain analytic results valid for the whole class of one-parameter models: the slope approaches the universal value $2$ at large complex structure, diverges at the conifold, and equals exactly $\sqrt2$ in the axio-dilaton directions, where the leading potential takes a single $SL(2)$-covariant form, as the multifield evolutions confirm numerically. The TCC further translates into a lower bound on the compactification volume, $v>v_0\sim e^{N}$, controlled by the number of e-folds. Finally, the field displacements along our trajectories are compatible with the species-scale field-range bound, and restoring the volume dependence of $\Lambda_s$ shows that $V\lesssim3\Lambda_s^2$ is implied by the TCC volume bound, which is thus the genuine constraint on these models.

We study relative completions of fundamental groups of moduli stacks of curves of compact type and of partial compactifications of the smooth moduli stack. For $g\geq3$, the compact-type completion has commutative prounipotent radical with Lie algebra $\Lambda^3_0H\oplus H^{\oplus n}$. Fix $1\leq h\leq g-1$. We show that adjoining the one-node loci of the separating divisors whose genus-$h$ side carries at most two markings gives the same relative completion. The proof uses explicit separating-twist calculations in weight $-2$, pointed Johnson homomorphisms, and the lantern relation. Functorial specialization gives the corresponding results in positive characteristic for odd $\ell$ different from the characteristic. As a consequence, extension to compact type of iterated extensions of algebraic symplectic local systems can be tested on these selected divisors. We also prove that any collection of separating divisors giving the same relative completion contains at least $\binom n2$ divisors.

We study permutation and monomial equivalence for one-point codes on weighted superelliptic curves. On strata where $H_m\simeq \Z/n\Z\times\Z/m\Z$ acts regularly on the evaluation set, we prove that these codes are Cartesian character codes and determine their primal and dual minimum distances. We compute the projective monomial normalizer of the regular action and classify the compatible permutation and monomial equivalences through the induced actions on the defining sets. When $d > n$ and $m \geq 2$, the common permutation automorphism group of the full filtration is exactly $H_m$, and the regular action can be recovered from its two lowest nonconstant members. We determine the full permutation automorphism group in closed form at the top of the filtration and give a field-independent finite certificate for $\PAut ( \CC_s ) = H_m$ in the remaining primitive cases treated here. The hull dimension is bounded by the genus on every regular stratum, apart from the type $(3,3,3)$. Explicit examples show that length, dimension, and hull dimension do not determine monomial equivalence, and that the hull profile together with the regular automorphism subgroup does not determine the curve up to isomorphism. As an application, we determine the corresponding hull-based invariants and punctured signatures used in support-splitting methods.

Coupling two strongly correlated layers opens a distinct route to repulsion-driven superconductivity. Yet the same interlayer coupling makes the optimization of superconductivity highly nontrivial. Using the dynamical vertex approximation, we determine the superconducting landscape in the enlarged parameter space spanned by filling and interlayer hopping. We identify an optimal regime at intermediate interlayer hopping and moderate doping away from half filling, where the system exhibits high superconducting transition temperatures ($T_{\rm c}$) with an interband $s_{\pm}$-wave gap structure. Toward half filling, however, strong self-energy effects can suppress the superconducting tendency by reducing the low-energy spectral weight. We further show that a Fermi-surface distortion induced by longer-range hoppings can weaken this suppression and enhance $T_{\rm c}$. Our results establish how filling, interlayer hopping, and Fermi-surface geometry jointly optimize the superconducting regime in the strongly correlated bilayer Hubbard model.

This paper studies privacy-preserving distributed optimization using gradient tracking with one communication-free local update between consecutive communication rounds. Since local computation alone does not protect gradient information, we perturb both the primal state and the gradient-tracking direction at communication iterations while keeping local updates noise-free. We establish an aggregate variable for tracking, characterize the limiting consensus point in the presence of added random noise, and prove convergence in mean under certain parameter conditions. We also establish infinite-horizon pure differential privacy for the complete communication transcript under an affine objective adjacency relation and geometrically decaying Laplace perturbations. Simulation results illustrate the advantages of the proposed method in terms of the convergence and optimization accuracy given a privacy budget.