Papers

We prove the converse of the Serre-Grothendieck finiteness theorem for the cohomology of coherent sheaves, originally due to Lipman. This result characterizes proper morphisms as those morphisms whose derived pushforward preserves pseudo-coherent complexes. Although the derived pushforward does not reflect pseudo-coherence, we prove that it does after twisting by all perfect complexes. This provides a new characterization of properness.

We determine the sharp weighted power-mean comparisons for the family $\{H_a(r)\}_{r\in (0,1)}$ with the logarithmic interpretation at $a=0$. In the parameter ranges considered by Barnard, Richards and Tiedeman, we give a complete characterization of all orders $\lambda,\mu\in\mathbb{R}$ for which $$A_\lambda(w;1,1-r)\leq H_a(r)\leq A_\mu(w;1,1-r)$$ holds for every $r\in(0,1)$. In particular, our results settle completely their two power-mean conjectures. The two sharp orders are determined by the second-order expansion at $r=0$ and the endpoint matching as $r\to1$. A weighted Wronskian identity and a sign analysis of its residual establish the global inequalities.

The microservice architecture has been applied broadly in many mainstream computing environments. As one of the most prevalent environments, edge computing also widely employs microservices to handle diverse requests and tasks. In practical scenarios, microservices usually constitute workflows that are built based on service dependencies to execute tasks. This offers an opportunity to explore the offloading technology to better harness resources and accelerate task execution. Unfortunately, this problem has not been paid attention to by existing research, and thus some valuable resources (e.g., microservice image cache) remain obscure. To fill this gap, we innovatively study the problem of joint optimization for microservice workflow offloading and service image caching in edge. This problem is challenging due to several issues such as the complexity of its solution space, intricate relationships among shared image layers, long-range dependencies between workflow tasks, and the absence of a real-world collection of service images. To address these issues, this paper proposes an innovative dependency- and layer-aware workflow offloading and image caching framework for microservices. We collected a real-world collection of microservice image layer data and published both this collection and experimental codes on GitHub. Extensive results demonstrate that our framework achieves superior performances, for example, a 22. 38% reduction in average task completion time compared to baselines and significantly-increased image hit rates.

Personalized value alignment has become increasingly important as large language models (LLMs) are expected to accommodate diverse user preferences. However, existing methods typically align model outputs with a static value profile across prompts, overlooking that the salience of value dimensions varies substantially across contexts. Inspired by Lewin's Field Theory, which views human behavior as jointly shaped by personal dispositions and situational constraints, we model personal values as priors and context-dependent preferences as posteriors. We propose BaCVA, an inference-time Bayesian Context-aware personalized Value Alignment method that approximates posterior personalized preferences by integrating static personal values with scenario-specific value salience. BaCVA first estimates contextual value salience from generally normative responses, and then employs a dual-view personalization module to infer posterior preferences from complementary personal-value and scenario-driven perspectives. This Bayesian formulation enables more accurate and adaptive personalized value alignment while improving data efficiency via prior values. Extensive experiments on benchmarks demonstrate its superiority over strong baselines.

Let $F$ be the free group of rank two and, for a prime $p$, let $\mathbf H_p=\mathbf G_p*\mathbf{Ab}_{p-1}$ be the pseudovariety of finite groups having a normal $p$-subgroup with abelian quotient of exponent dividing $p-1$. For $H$ of rank two with $\ab_F(H)=F^{\ab}$ we determine the set $\mathfrak D(H)$ of primes $p$ where $H$ is $\mathbf H_p$-dense in $F$, and we show that this prime set is Frobenian in the sense of Serre: it is governed by a single Laurent polynomial $g$ attached to $H$. We prove that $p\in\mathfrak D(H)$ if and only if $g$ has no zero on the torus $(\F_p^\times)^2$, and hence that $\mathfrak D(H)$ possesses a computable natural density $d(H)$. Exactly one of three cases holds: $\mathfrak D(H)$ is the set of all primes, it is finite, or it is neither and $d(H)$ satisfies $\frac1{|G|}\le d(H)\le1-\frac1{|G|}$, where $G$ is the finite Galois group attached to $g$.

Autonomous penetration-testing harnesses use large language models (LLMs) for reconnaissance, exploitation, and reporting, but often rely on those same models to confirm findings, grade severity, and select agents. This can lead to false positives, inflated severity, and wasted compute. We examine how System One decision models, lightweight non-generative classifiers that return typed, calibrated verdicts, can support these decisions. We make five contributions. First, we define four decision points: finding adjudication, severity recalibration, agent pruning, and confirmation loops. Second, we present an exploratory NeuroSploit case study comparing one run with TypeSafe System One (Jev) and one without it against a web target containing 13 vulnerabilities. Differences in severity distribution, runtime, and grading by exposed data type motivate the architecture but do not establish statistical significance. Third, we review published specifications for Jev, Jev-Ultrafast, and the open-source Laya without assuming that results from other benchmarks transfer to penetration testing. Fourth, we discuss RLHF, RLAIF, RLCD, and RLHV as training approaches and their implications for trust in security decisions. Finally, we propose Rave, a domain-adapted System One model, and outline its training data, evaluation protocol, and potential effect on harness assurance.

We prove that a hyperkähler manifold of OG6 type is determined, up to isomorphism, by its integral second cohomology endowed with its Hodge structure and Beauville–Bogomolov–Fujiki form. The proof combines the monodromy and chamber theorems of Mongardi–Rapagnetta with the bimeromorphic Torelli theorem. In particular, bimeromorphic OG6 manifolds are biholomorphic.

We say that the Poisson operator $P_r$ is Schwarz-contractive from a space $X$ to a space $Y$ if $\|P_r\|_{X\to Y}\le r$ holds for all $0<r<1$. The classical Schwarz lemma is the case $H^\infty_0\to H^\infty$, the subscript indicating zero mean. We are concerned with the non-holomorphic case $L^\infty_0 \to L^p$. For real functions Schwarz-contractivity holds up to the sharp exponent $p_{\mathbb R}=4.109\ldots$. For complex functions we prove it for $p\le 3$ and conjecture that the critical exponent is $4$.

We consider a stochastic parabolic equation on the $n$-dimensional flat torus $\mathbb{T}^n=(\mathbb{R}/(2\pi\mathbb Z))^n$, $n\in\mathbb N$, whose only control acts in the drift. The multiplicative-noise coefficient is adapted and may depend jointly on the sample point, time, and space. Its spatial profiles are assumed to be real analytic with a uniform positive radius of analyticity, while the corresponding analytic norm is only required to be square integrable in time, uniformly along sample paths. We prove a state-only observability inequality with an $L^1$-in-time mean-square observation norm and deduce null controllability from every measurable spatial set of positive measure by one adapted drift control. The same one-time interpolation estimate also yields approximate controllability to arbitrary square-integrable random terminal targets. The proof is based on a direct analytic energy estimate for the adjoint state, followed by propagation of smallness and a telescoping argument.

Audio carries rich cues about human activities, and microphones are already built into most wearable devices. However, microphones also capture speech, and this privacy risk limits their use in Human Activity Recognition (HAR). We present AnomaSense, a sensor activation approach for wrist wearables that keeps the microphone off by default and turns it on for at most one second when an unsupervised anomaly detector flags an IMU segment that is likely to produce sound. The captured audio is further masked before it reaches the recognition model. We study 20 activities from 15 participants, organized into five groups in which activities share similar wrist motion but differ in the object or material involved. With IMU data alone, our recognition model reaches 78.98% accuracy in leave-one-participant-out validation. With the short, masked audio windows added, accuracy reaches 96.89% with no masking and stays above 86% when 90% of each one-second audio window is removed. On the same data, the anomaly detector triggers the microphone with 86.46% precision and 74.28% recall relative to sound events. We also report a small preliminary check of automatic speech recognition on masked speech, which shows that contiguous masking degrades recognition far more than point-wise masking at the same masking ratio. Our evaluation is a controlled, offline feasibility study. We describe the threat model, what the approach does and does not protect, and the steps needed before deployment.

Vibrational spectral prediction can become inaccurate when localized stereoelectronic environments perturb intermediate response states and high-risk response units dominate characteristic spectral fingerprints, making prediction across external chemical space difficult. SO(3) Equivariant Neural Kalman Networks (SENK) form a response-state cascade that combines an equivariant transformer backbone for Hessian, dipole-derivative and polarizability-derivative learning, an Equivariant Neural Kalman bridge for state-dependent refinement and reliability sensing, and an NBO-informed electronic-prior pathway coupling consistency regularization with bounded, branch-specific guided spectral calibration. SENK outperforms DetaNet on QM9S and QMe14S while preserving full-spectrum IR and Raman fidelity from small molecules to drug-like systems. SENK remains stable and selectively improves spectrally sensitive features in biomolecular systems with complex stereoelectronic effects. It therefore integrates tensor prediction, reliability diagnosis and physics-informed calibration, supporting transferable vibrational spectroscopy from molecular systems to functional molecular materials.

Bound states in the continuum (BICs) exhibit rich momentum-space dynamics, including merging, annihilation, and reconnection across symmetry directions and bands. Yet these phenomena have largely been explained case by case, without a unified framework to classify or predict them. Here we develop a global symmetry-equivariant theory for the dynamics of nondegenerate and degenerate BICs. We show that BIC dynamics can be classified into $\alpha$-, $\beta$-, and $\gamma$-processes according to root motion, which not only encompass the reported dynamics in $C_{2v}$, $C_{4v}$, and $C_{6v}$ systems but also include previously unrecognized ones. More importantly, we reveal that distinct dynamics are bridged by the criticality of BICs through a merging of merging, in which selected direction–band branches acquire higher-order radiation zeros. Such a theory predicts which branches become critical and how to tune system parameters to realize them. Following this framework, we construct high-order BICs in full-wave calculations, realizing $Q\sim k^{-10}$ nondegenerate criticality and $Q\sim k^{-8}$ single-branch and band-paired degenerate criticalities. Our framework provides a systematic route to understanding, discovering, and selectively controlling BIC dynamics and high-$Q$ states.

Outdoor robots require more than an accurate receiver and a path-tracking law: the navigation system must preserve geometric consistency from geographic waypoints to actuator commands, expose measurement validity and timing, and respond to invalid or stale state information. This work presents a ROS~2 navigation stack with interchangeable single-GNSS–IMU and dual-antenna-GNSS localization front ends. Both provide a common local East–North–Up state interface for pure pursuit, virtual-point cross-track PID, finite-horizon nonlinear model predictive control (NMPC), and a segment-dependent hybrid dispatcher. The architecture specifies coordinate conventions, datum initialization, asynchronous state construction, waypoint geometry, controller equations, quality gates, command arbitration, and watchdog behavior. Independent physical field runs collected during 2025 and 2026 grape-vineyard deployments support a balanced evaluation of 800 runs, with 100 runs for each of eight controller–localization combinations on an approximately 199.6-m route. The row-hybrid mode yields the lowest run-averaged post-acquisition mean absolute cross-track error (MAE) in the evaluated dataset: 0.00952~m with single GNSS+IMU and 0.00846~m with dual GNSS. These findings characterize deviations of the recorded positions from the reference route under the evaluated conditions. The open-source navigation software and deployment instructions are available in the https://github.com/YiyuanLinXX/PPBv2/tree/main/PPBv2_Navigation.

We report a hint of recurrent double-peaked $\gamma$-ray sub-flares in PKS~1424–418 during two similar major active epochs, MJD 56117–56498 and MJD 59669–59978. The candidate double-peaked sub-flares show a characteristic intra-subflare peak separation of $\sim 11.8$ d and a neighbouring-subflare spacing of $\sim 67$ d. Red-noise Monte Carlo tests indicate that the candidate recurrent double-peaked morphology is not easily reproduced by stochastic variability alone, with false-alarm probabilities of $p_{\rm a}=0.0216$ and $p_{\rm b}=0.0006$ for the two active epochs, respectively. In the simulations of the entire Fermi Large Area Telescope (LAT) light curve, no red-noise realisation reproduces both epoch-like structures. The spectral energy distribution (SED) modelling shows similar radiative properties for the two peaks of one double-peaked candidate, while changes in the Doppler factor appear to play an important role in the flaring activity. Together with the previously reported near-zero lag between the millimetre and $\gamma$-ray emission, these results suggest that the recurrent activity may be associated with the compact mm/sub-mm core region. We discuss a possible structured-jet scenario in which a single disturbance propagates through a chain of quasi-stationary recollimation shocks. In this picture, repeated interactions between the disturbance and the shock structure may qualitatively account for both the double-peaked sub-flare profiles and the observed $\sim 11.8$ d and $\sim 67$ d time-scales. Further active epochs are required to determine whether this similarity represents a recurrent long-term behaviour.

Driving world models provide a promising route toward scalable counterfactual data generation and interactive simulation beyond recorded driving logs. Realizing this potential requires a system that can generalize across diverse scenes, respond faithfully to prescribed controls, generate coherent multi-sensor observations, and operate efficiently under repeated inference. We present HelloWorld, a 2B driving world model system designed around these requirements. HelloWorld progressively specializes broad visual and motion priors from heterogeneous video data into controllable driving generation using ego pose, HD maps, and 3D boxes. A block-causal generation interface, together with adaptation to self-generated context, aligns the model with sequential simulation. The system further supports synchronized seven-camera RGB generation and conditional LiDAR synthesis, and is distilled toward few-step inference for efficient deployment. Experiments evaluate visual quality, control fidelity, cross-view consistency, robustness under repeated generation, inference efficiency, and LiDAR synthesis. Together, HelloWorld provides a unified framework for scalable driving data generation and interactive simulation.

Radiance field representations such as 3D Gaussian Splatting (3DGS) natively encode complex visual phenomena such as occlusions and view dependence, but they are inherently underconstrained. Independently optimized reconstructions converge to different primitive configurations, even in unchanged regions. We introduce Plenoptic CharacterIstics (PlenoCI), a novel feature built from the plenoptic field these representations approximate. PlenoCI directly captures rich visual behaviors while ignoring Lambertian textures. By deriving closed-form analytic plenoptic derivatives from a 3DGS representation, we efficiently detect these 5D structures. Our approach is robust to underconstrained representations by construction, reporting two orders of magnitude fewer false positives between independent reconstructions of unchanged scenes than concurrent work. We demonstrate PlenoCI's utility on change classification. First, we detect changes with an instance-aware 3DGS pipeline, achieving state-of-the-art results on CL-Splats with a 25.7% mIoU gain over the strongest competitor, while remaining competitive on the more challenging PASLCD benchmark. Leveraging PlenoCI, we classify changes as geometric or appearance-based with a balanced accuracy of 0.735, comparable to the best performing baseline. We believe plenoptic derivatives and PlenoCI open new directions for view dependence aware understanding in visually complex environments. Code and data are available at https://js0n-lai.github.io/plenoci.

We prove that a compact immersed disk of constant mean curvature in $\R^3$ whose boundary is mapped diffeomorphically onto a round circle is a planar disk or a spherical cap.

We study the quasinormal modes (QNMs) of Type II perturbations for dilaton-Euler-Heisenberg (dEH) black holes. These perturbations consist of coupled even-parity gravitational and dilaton perturbations together with odd-parity electromagnetic perturbations. The background is described by mass $M$, magnetic charge $Q_m$, and dilaton coupling difference $\zeta=\alpha-\beta$ to the Euler-Heisenberg term. To find the QNM frequencies, we need to find the parameter space of $(\zeta, Q_m/M)$ that is free from vector ghosts. For the $\ell=1$ mode, the radiative block couples the dilaton and axial electromagnetic amplitudes, whereas the $\ell=2$ mode also contains metric amplitudes, so the frequencies are obtained from matrix-valued boundary-value problems. We calculate QNM frequencies for the fundamental ($n=0$) branch with direct integration and the Chebyshev pseudospectral method, and compare the two computations wherever their charge intervals overlap. We find that the $\ell=1,2$ modes in the $n=0$ branch remain damped over the ghost-free parameter domain, supporting the stability of dEH black holes against Type II perturbations. The Type I sector will be presented elsewhere; no claim is made here about that sector, higher multipoles, or overtones.

World action models (WAMs) that use future visual prediction at inference time incur substantial generation costs. Asynchronous execution reduces waiting by overlapping inference with robot motion, but visual predictions used for subsequent action generation must anticipate the effects of actions already scheduled for execution during inference. We introduce Streaming-WAM, which couples action-conditioned world modeling with asynchronous robot control to account for committed actions in future visual prediction. At each streaming update, the model conditions future visual prediction on the latest observation and the committed actions, which form the fixed prefix of the next action chunk. The resulting action-conditioned visual features guide generation of the remaining actions within the same joint update, so the continuation is informed by the scene changes expected during execution of the fixed prefix. On LIBERO, Streaming-WAM achieves an average success rate of 98.35% and reduces mean episode time by a factor of 2.93 relative to Fast-WAM. On the real-world Stamp Paper task, mean episode time falls from 90 s with synchronous Joint-WAM to 38 s with Streaming-WAM. These results show that Streaming-WAM supports efficient asynchronous control while maintaining high task success rates.

The structure of a periodic multilayer X-ray mirror is obtained by fitting its X-ray reflectivity (XRR) curve, and the result depends on how the operator normalizes and trims the curve, frees parameters, and accepts a fit. The manual of the fitting program and the papers describing its engine leave these decisions to the operator, whose practice is tacit, so the fitting stays with the expert. To solve this problem, we proposed to develop a skill for a large language model (LLM) agent via elicitation: the expert's decisions were recorded during fitting and written as thirteen steps and a 22-item report template. The agent runs X-Ray Calc 3 through a Model Context Protocol (MCP) tool server. Fresh sessions, each given the skill, one curve, and a nominal design, were scored against fits the expert had withheld, under six tolerances fixed beforehand. The skill was developed on XRR curves of Co/C mirrors and of Ru/C mirrors from a public data deposit. The final version of the skill was tested on W/B4C multilayers. It was demonstrated that the skill recovered the mean period within 0.3 Å of the expert's fits and the period drift through the stack on both W/B4C specimens, and the W and B4C thicknesses within 1 Å on one of them.

Exploration seismic processing underpins subsurface imaging and resource exploration, but learning-based methods remain difficult to compare across studies. Our survey of 368 papers finds widespread reliance on private or difficult-to-reproduce datasets, with only 25 providing public code. This obscures whether reported gains arise from model design or experimental settings. We introduce the Seismic Processing Benchmark (SPBench), covering six tasks: random noise attenuation, trace interpolation, ground-roll suppression, multiple suppression, deblending, and first-arrival picking. We reproduce 24 supervised methods on 10 datasets under 43 standardized settings and release datasets, implementations, configurations, evaluation scripts, and results. To complement global scores and per-trace pick errors, we introduce signal-component-resolved evaluation (SCoRE) for reconstruction and a reference-free ridge-curvature score (RC_norm) for first-arrival picking. Our analyses show that synthetic rankings do not reliably predict field rankings, with task-dependent agreement when models train within each setting. As degradation strengthens, rankings reorder more under coherent ground roll than under random-like interference. The ridge score agrees with MAE-based model rankings in the evaluated settings, with a mean Kendall correlation of 0.881 across three field surveys, while SCoRE reveals frequency- and energy-dependent differences hidden by global scores. SPBench provides a reproducible basis for comparing learning-based seismic processing methods and characterizes how their relative advantages vary across data settings, degradation strengths, and evaluation criteria.

Spin is typically traced out in the description of quantum-dot-based Kitaev chains to simplify the construction of Majorana fermions. Yet the intrinsic spin structure of poor-man's Majorana modes in minimal Kitaev chains under finite Zeeman fields offers a natural interface for the Kitaev parity qubit to interact with other spinful systems. Here, we establish such a platform to bridge the parity qubit and a quantum-dot spin qubit, with the effective coupling governed by the spin-dependent delocalization of the Majorana modes. Depending on whether the spin qubit is coupled to one or two chains constituting the parity qubit, the parity-spin coupling exhibits distinct forms: an anisotropic parity-conserving exchange interaction or a nontrivial exchange tensor tunable via the interchain superconducting-phase bias. Leveraging fast spin-qubit manipulation, we further demonstrate universal parity-qubit control, high-fidelity qubit-state readout, and entangling operations between the parity and spin qubits. These results turn the spinful structure of poor-man's Majoranas from a finite-field imperfection into a resource for hybrid quantum control.

Few-step autoregressive (AR) video diffusion enables low-latency streaming generation, but existing post-training methods predominantly rely on Distribution Matching Distillation (DMD), requiring both a large pretrained teacher and an online critic to estimate distributional discrepancies through diffusion scores. In this work, we ask whether this resource-intensive teacher–critic stack can be eliminated by post-training only the generator against a precomputed target distribution. Drawing inspiration from representation distribution matching (RDM) for one-step image generation, we systematically study its transfer to few-step causal video generation and identify three key barriers: a memory-intractable gradient path, a distinct video optimization regime, and representation distributions that underconstrain temporal dynamics. We introduce ViRDM, a teacher- and critic-free video post-training recipe that addresses these barriers sequentially. By coupling RDM with stochastically truncated clean-exit supervision, a lightweight VAE decoder, and staged vector–Jacobian products, ViRDM makes representation distribution matching memory-feasible for multi-step causal video rollouts. We further establish effective generated-population and initialization regimes for video RDM, and introduce lightweight dynamics regularization to compensate for the underconstrained temporal dynamics. ViRDM turns three-network distillation into generator-only post-training, reducing GPU memory use and training time while improving video quality. With only 20 generator updates, the recipe reaches 84.87 on the official VBench evaluation, outperforming the previous best few-step causal baseline by 0.36, while requiring 16 A100 GPU-hours. We additionally report exploratory results demonstrating the potential of the same recipe for lower causal sampling budget and for one-, two-, and four-step bidirectional generation.

Let $X$ be a Banach space and let $\mathcal{N}(X)$ denote the family of equivalent norms on $X$. We study Hilbert projective metrics on its projectivization $\mathcal{N}'(X)$ induced by ambient cones of nonnegative functions, with particular attention to the intrinsic Hilbert metric induced by the cone $\mathcal{N}(X)\cup\{0\}$. First, we show that the symmetric logarithmic metric on $\mathcal{N}'(X)$ is the Hilbert projective metric induced by the cone of nonnegative real-valued functions, and we characterize the ambient cones that induce the same metric. We then study the intrinsic order on $\mathcal{N}(X)$. For this purpose, we introduce the triangular defect $\Delta_p(x,y)=p(x)+p(y)-p(x+y)$ and prove that two norms $p,q\in\mathcal{N}(X)$ belong to the same intrinsic part if and only if their triangular defects are uniformly comparable, that is, $a\Delta_p\leq\Delta_q\leq b\Delta_p$ for some $a,b>0$. This yields an explicit formula for the intrinsic Hilbert metric in terms of the pointwise comparison of the norms and of their triangular defects. Finally, the map $\Phi(p)=(p,\Delta_p)$ realizes the intrinsic cone order of $\mathcal{N}(X)$ inside a canonical product cone of nonnegative functions and preserves the Hilbert metric on each intrinsic part.

Protein modification requires navigating an immense sequence space, yet wet-lab validation remains low-throughput and costly. Although computational paradigms including protein language models (PLMs), large language models (LLMs), and LLM-based agents have shown promise in protein modification, their relative efficacy across realistic experimental decision-making settings remains unclear. To bridge this gap, we introduce PFArena, a benchmark comprising four controlled task interfaces that cover single-mutant generation and multi-mutant ranking. By providing varying levels of mutation fitness data, PFArena reflects four representative research scenarios characterized by differing degrees of prior experimental context. We assess six PLMs, six LLMs, and five LLM-based agents using complementary metrics to measure both peak and overall protein modification performance. Our evaluation reveals that model performance shifts systematically with the availability of target-specific experimental evidence: PLMs demonstrate proficiency in open-ended single-mutant generation by leveraging protein-specific priors, whereas LLMs and agents perform strongly in multi-mutant ranking, particularly when target-specific fitness data are available. Nevertheless, all model families face fundamental challenges with increasing search-space size and mutation depth. We release our code and benchmark suite to facilitate reproducible research in model-assisted protein modification.

Conventional model-based diffusion (MBD) achieves effective trajectory optimization by leveraging noise annealing. However, its high computational cost, primarily arising from repeated rollouts of the plant dynamics, has largely confined its use to offline settings. To address this limitation, this paper proposes bilinear Koopman model-based diffusion (BK-MBD). The proposed method lifts the robot's state into a high-dimensional space only once per control step and propagates all candidates in the lifted space thereafter, so each rollout reduces to a fixed number of matrix-vector multiplications. The lifted dynamics are bilinear, allowing the predicted input gain to vary with the robot's configuration, which a linear lifted model cannot represent. In simulation, BK-MBD completed each planning update in at most 14.7 ms within a 50 ms control period and reached the goal on every trial, whereas a linear lift almost never did. The annealed schedule improves closed-loop accuracy over fixed-noise schedules under the learned rollout. Under the exact rollout, both the annealed and fixed-narrow schedules reach every goal, indicating that annealing reduces sensitivity to surrogate-model error. BK-MBD also threaded a passage that no single convex region covers, whereas a convexified bilinear controller rarely succeeded. On a physical manipulator, BK-MBD tracked an initially unknown moving target within the control period and was the only method that met both the tracking task and the deadline. The project page is available at https://rcilab.khu.ac.kr/bkmbd/.

Harnesses, the products that run AI coding agents, are multiplying, and enterprises are rolling them out to their employees. What started as pilots with a few hundred seats is now scaling to tens of thousands. Enterprises rarely build these harnesses and usually adopt the ones model vendors bundle with their seats and APIs, such as Anthropic's Claude Code or OpenAI's Codex. A harness decides which model answers, what the model reads, how the prompt cache is used and which subagents run, so it picks the rate on the price sheet and sets the volume bought at it. Enterprises that keep a proprietary or untuned harness at its defaults inherit these choices and their bill. We build a fast, customisable router in which Jev, a classifier with calibrated probabilities, labels every prompt against a bring-your-own taxonomy of agentic requests. One user turn is many requests over a prompt cache that belongs to one model, so the router moves work only where no running conversation has to rebuild its cache. It routes at session start, in side lanes and at subagent launch. From the price sheet we derive when a mid-task switch pays back. We also find a crossover, in which the highest-priced model costs less than the next tier on long tool-heavy sessions, and repricing about 10,000 real sessions from public datasets confirms it. In an emulated enterprise of 10,000 seats with user behaviour taken from these datasets, the router recovers 13 to 21% of model spend at Anthropic's list prices of 21 September 2026, \$3.3M to \$5.1M a year. The paper also maps the risks across twenty-one harnesses, prices the dependence on one vendor's models, and proposes a control plane that enterprises can run from within, starting now, with a ladder for deciding later whether to own the harness.

Students increasingly turn to AI for help with problem-solving, yet too much AI support can undermine learning itself. To benefit from AI, students need to specify the necessary knowledge and scaffold type in their questions. However, they struggle to formulate such targeted questions because they lack metacognitive skills to recognize and select effective help options. We developed HelpCoach, an add-on for chat interfaces that helps students formulate knowledge- and scaffold-specific questions and receive targeted help during problem solving. HelpCoach continuously assesses students' help-seeking performance and prompts students to improve through an adaptive revision template. Whereas prior work has largely taught help-seeking skills apart from learning tasks, HelpCoach's in situ scaffold enables concrete practice on metacognitive skills and immediate revisions to help-seeking behavior. In a study with 40 college students learning web programming, HelpCoach led to more specific questions during chatbot interactions and greater knowledge retention than pre-task help-seeking training alone.

The first examples of asymmetric L-space knots were found by Baker and Luecke. Among Baker-Luecke knots, the simplest one has braid index 12. Later, it turned out that there are just 9 asymmetric hyperbolic L-space knots in the SnapPy census, and their braid indices take the values 4, 5, 6 and 7. It is known that asymmetric L-space knots have braid index at least 4. Recently, Baker and the second author give infinitely many asymmetric hyperbolic L-space knots with braid index 4. In this paper, we construct an asymmetric hyperbolic L-space knot with arbitrary braid index bigger than 4. In fact, there exist infinitely many such knots for each braid index.

Frame refresh rate estimation is a fundamental step in identifying compromising harmonic frequencies in electromagnetic side-channel attacks. Methods based on discrete linear autocorrelation (DLA) are robust across different scenarios and require a computational complexity of $O(N\log N)$ for a signal containing $N$ samples. This work proposes reducing this complexity to $O(N)$ by exploiting prior knowledge of the target system's display resolution, as is available for certain models of the Brazilian electronic voting machine. Experiments using software-defined radios show that the proposed method preserves the accuracy of the conventional approach in the evaluated scenarios.