Papers

We present a low-cost miniature Ackermann vehicle for embedded neural-driving research, organized as a hardware-partitioned perceive-decide-act agent: an ESP32 camera node streams frames over Wi-Fi to a host computer, where neural inference and state estimation run, while an ESP32-S3 chassis controller executes safety-critical actuation in a 100 Hz per-wheel proportional-integral-derivative (PID) loop beneath a micro-ROS client. The partition isolates real-time control and safety on the vehicle while learning-based components run off-board, supervised by an operator from a gamepad. We characterize the complete pipeline during real closed-loop neural driving. Wireless sensing, rather than neural inference, dominates latency, with a 59.5 ms median capture-to-actuation delay; the platform absorbed wireless variability by holding the last safe command under a firmware watchdog, operating across twelve autonomous sessions with zero collisions or manual interventions; and encoder-inertial-measurement-unit (IMU) fusion cut odometry loop-closure error by 22%. These results indicate that carefully partitioned microcontroller-class vehicles support reproducible experiments in embedded AI, wireless control, and operator-supervised autonomous driving. The platform software is open source.

We study pretraining when compute is abundant but unique training data are finite, requiring repeated training on the same data. We first revisit infinite-compute pretraining (Kim et al. 2026) and show that its frontier depends critically on choices previously fixed or studied only in isolation. In particular, optimizing batch size together with epoch counts reveals a U-shaped relationship between validation loss and batch size, favoring smaller batches than typical pretraining, likely because small-batch gradient noise provides implicit regularization. We further find that training recipes, previously optimized under a single-pass assumption, can be tuned, e.g., repacking documents into new sequences every epoch, weight tying, and positive embedding weight decay. We then relax the infinite-compute assumption. In particular, smaller-than-typical batch sizes can require prohibitively long sequential training, motivating to treat GPUs and time as separate resources. Tighter deadlines favor larger batches, and latency-oriented parallelism can trade additional GPUs for shorter training. Nevertheless, even under a fixed time budget, a smaller batch with fewer GPUs can achieve lower validation loss than a larger batch with more GPUs, challenging the common practice of increasing data parallelism to maximize GPU utilization under a deadline. Together, our results identify underexplored factors in repeated-data training and provide concrete guidance on how training recipes and resource allocation should change from single-pass pretraining.

A self-evolving agent rewrites its own harness and must decide which rewrites to keep, so its improvement signal is the check a rewrite has to pass. Verifying a rewrite by agent rollout is expensive and subjective, while executable checks such as the repository's own tests are too sparse to catch behavior-changing rewrites, rejecting only a quarter of them. We instead take test feedback as the executable signal, and search for test suites that are both small and strong with a quality-diversity evolutionary algorithm, so that the signal is dense and informative. TeSearch treats suite size as a behavior descriptor, so that quality is pursued at every size and a small, strong suite is reachable, and learns a transition kernel during the search that denoises the LLM as an actuator on that descriptor. Across 129 real-world modules and three backbones, TeSearch delivers the highest-quality suites of any method compared, LLM-driven evolutionary search included, and the smallest of any LLM-based one. Used as the improvement signal of a self-evolving agent, it rejects 59.9% of behavior-changing rewrites against 25.3% for the repository's tests, at a 4.0% false-alarm rate and 3.5 s per decision. The code and data are available at https://github.com/ccsnow127/TeSearch.

High-pileup conditions in CMS during the HL-LHC era make charged-particle tracking increasingly challenging as detector occupancy and combinatorics grow. We present a hybrid approach that exploits Line Segment Tracking (LST) objects rather than individual hits to enable the first CMS ML-based track reconstruction algorithm. The LST objects, namely the triplets used in this study, are built according to geometry- and physics-driven criteria and carry richer local structure, geometrical cues, and physics quantities such as transverse momentum, which helps the model incorporate detector-level information from the start. We apply a Transformer encoder with geometrically masked sparse self-attention to embed these objects in a learned latent space, and use object condensation to assemble full tracks in a single inference step. This object-based representation reduces complexity in dense environments and makes the model less sensitive to ambiguities introduced by high pileup. Evaluated on CMS Phase-2 simulation of $t\bar{t}$ events at $\langle \mu \rangle = 200$, the approach achieves reconstruction efficiency comparable to the LST quintuplet baseline while reducing the fake rate by roughly a factor of three and suppressing duplicates almost entirely, demonstrating the promise of advanced ML architectures for next-generation particle tracking.

Fracture in polymer networks is strongly influenced by how network architecture and topology organize damage in space. Although these materials can sustain large deformations under homogeneous loading, they often fail in a brittle and flaw-sensitive manner once defects are present. Here we show that network heterogeneity is one key architectural parameter controlling this transition. Using a discrete mesoscale network model that explicitly resolves strand-level prestretch, force transmission, and irreversible bond scission, we demonstrate that heterogeneity in prestretch and strand lengths broadens crack-induced deformation, delocalizes bond rupture, and enlarges the fracture process zone. In polydisperse networks, increasing contour-length disorder broadens the prestretch distribution and systematically increases both toughness and the intrinsic length scale governing flaw sensitivity. Bimodal networks amplify this mechanism further through combined contrasts in prestretch and strand lengths, producing the largest damage zones and the highest toughness among the architectures studied. Inspired by the results, we derive a scaling estimate relating the emergent fracture-active length to the spatial range of crack-induced deformation and the logarithmic spread of strands' remaining stretch to rupture.

Emergent misalignment (EM) occurs when fine-tuning a language model to a narrow task makes it misaligned on unrelated ones. Because organizations now routinely fine-tune models on their own data, it matters which kinds of training data cause EM. So far, studies have induced EM with data containing recognized safety failures, such as insecure code or harmful advice, while biased training data is typically examined by fairness research for the bias models learn from it rather than for its effects on safety. In real-world text, much of this bias, such as demographic stereotypes, appears not as derogatory language but politely, embedded in judgments about people. We ask whether learning such polite stereotypes can itself cause EM. We find that fine-tuning on polite answers that rely on stereotypes makes models less safe and less truthful on unrelated tasks. The effect holds across four open-weight model families (7B to 12B), both gender and race stereotypes, and repeated training runs, relative to controls trained on the same questions without the stereotype. We further show that the learned stereotype has its own direction in model activations, distinct from directions for generic misaligned traits such as deception. This direction exists before fine-tuning and can both control the learned stereotype and monitor its acquisition. Existing defenses against EM improve safety while leaving the stereotype largely intact. Beyond this controlled setting, fine-tuning on political news coverage also triggers EM, apparently amplified by partisan framing, and stereotype models acting as tool-using agents can carry out harmful tasks and blame people without evidence. Our results show that biased training data is not only a fairness problem but also a safety one. We argue that EM is studied too narrowly, and that fairness concerns and methods offer a natural way to broaden the search for its triggers.

Text-conditioned symbolic music generation has attracted growing interest with the development of generative models. Yet two questions remain underexplored: what aspects of music the conditioning text should describe, and how the corresponding data should be collected and trained to improve controllability and text-music alignment. We address these challenges with TASTE, a taxonomy-aware framework for symbolic music generation with a main focus on piano pieces. First, we introduce a taxonomy of musical elements that specifies how a piece can be captured through textual description in a musically grounded way. The taxonomy comprises a set of metadata tags (genre, emotion, section plan, etc.) together with a free-form description of music imagery. This structure decomposes textual input to match the generation goal more coherently and precisely. Second, we build a data pipeline for collecting, annotating, and retrieving public symbolic piano resources, yielding a corpus of 432K MIDI files labeled at multiple levels of granularity. Finally, we design a staged training procedure that leverages this multi-granularity data across two model families: an autoregressive model and a non-autoregressive diffusion model. Both objective and subjective evaluations show that our models achieve superior musical-element control, text-description alignment, and overall music quality. We will release the full pipeline, all annotated datasets, and the model checkpoints.

In this short note we give a Khintchine-type inequality involving non-independentrandom variables. The basic setting is inspired by Breuer-Major theorem and the proof is based on a hypercontractivity argument.

Large language models (LLMs) are increasingly evaluated across ophthalmic tasks, yet the methodological quality of these evaluations has received little attention. Most studies report accuracy while overlooking design features required for valid and clinically meaningful inference. We critically reviewed published ophthalmic LLM evaluation studies covering knowledge assessment, patient education, diagnostic reasoning, triage, clinical documentation, multimodal image interpretation, and uncertainty estimation. We used the methodological weaknesses that recurred across study designs to develop the SIGHT framework, which has five domains: Sample and item provenance, Independence and blinding, Ground truth and comparator fairness, Handling of paired and repeated-measures data, and Transparency and trustworthiness. Current evaluations rely heavily on benchmark accuracy, synthetic clinical vignettes, and curated datasets, and real-world clinical validation remains rare. Common limitations include potential training-data contamination, inadequate handling of paired data, limited assessment of inter-rater reliability, inconsistent reference standards, insufficient evaluation of calibration and uncertainty, and frequent overinterpretation of benchmark performance as evidence of clinical readiness. SIGHT provides twenty structured appraisal items to evaluate internal validity, interpretability, and applicability across diverse ophthalmic LLM study designs. It offers a practical way to appraise ophthalmic LLM studies and may improve the methodological quality, interpretability, and clinical relevance of future evaluations.

Transformer models trained on symbolic music have become remarkably capable. However, it is yet unclear how they represent music structure, and whether understanding their internal representations can be used to unlock methods for model control. We examine this through a case study of harmonic analysis: when a music transformer navigates a cadence, what does it internally "know" about its harmonic context, and can that knowledge be used to affect the generation? Using Aria, a LLaMA-based symbolic music transformer evaluated on Bach chorales, we find that harmonic decisions are causally localized progressively from middle layers onward. Linear probes show that mode becomes decodable in the same layer range where patching identifies growing causal effect, while key identity emerges later. We then confirm these representations are actionable for music generation control: steering via latent directions corresponding to harmonic changes reliably produces a deceptive or minor resolution, while preserving structural coherence and generation quality. This demonstrates that, at inference time, the model's internal harmonic knowledge can be directly manipulated to control the harmonic output.

Vision-language-action models for embodied navigation typically rely on RGB observations, limiting their applicability in lights-out industrial environments where visible illumination may be unavailable. We study illumination-independent navigation using spatial audio for target localization and depth for obstacle-aware geometry. To support this setting, we introduce DarkNav-Bench, a benchmark with 24 industrial scenes and four progressively challenging acoustic conditions. We further propose ADAPT, an audio-depth action-planning framework equipped with spatial-audio perception and optimized for closed-loop navigation through reinforcement learning (RL). Our key RL contribution, transition-aware reward shaping (TARS), defines a pose-aware shortest-action potential over a position-heading graph. Unlike conventional geodesic-progress rewards, TARS accounts for both feasible movements and in-place rotations, providing action-consistent feedback for policy optimization. Experiments show that ADAPT consistently outperforms training-based navigation baselines and zero-shot multimodal models on both seen and unseen scenes. On unseen environments, it achieves 90.6% success under Clean conditions and retains 60.0% success under the most challenging Localized Noise setting. These results demonstrate the potential of spatial audio and depth as complementary modalities for reliable RGB-free navigation in lights-out industrial environments.

A multiple-access channel transmits messages from several senders to one receiver. For quantum outputs, the receiver must distinguish states depending on all messages, while tests for different decoding errors may not commute. In this paper, we give a self-contained account of simultaneous decoding, in which one joint measurement recovers the messages at the established achievable rates using independent codebooks. The proof combines Sen's tilted-subspace method with Cheng's analysis of the pretty-good measurement, a standard measurement for distinguishing quantum states. Auxiliary labels close to a common reference state separate the geometric directions associated with different errors. A Gram-matrix bound then allows separately chosen binary tests to certify the performance of one measurement. The labels are removed from the completed decoder, leading to a deterministic packing theorem that applies to finite state ensembles, including unequal priors. We develop the two-sender case first, with worked examples and figures, before treating any fixed number of senders. Sharper finite-error guarantees for the same decoder are developed separately, with sharp bounds for two specified steps of the analysis rather than a claim of globally optimal decoding. Applications recover known achievable rates for unassisted and entanglement-assisted classical communication, distributed classical compression with quantum side information, and coherent-state communication through a beamsplitter or passive multiport device. The common proof makes the geometric mechanism and its quantitative consequences available without repeating the construction for each application.

We study online multiclass multicalibration over $T$ rounds, and give an algorithm with beyond-worst-case guarantees. With $n$ possible outcomes, forecasts lie in a simplex of dimension $d=n-1$. In the worst case, cumulative $\ell_1$ multicalibration error scales with $\widetilde\Theta(T^{(d+1)/(d+2)})$, which becomes untenable once $d$ exceeds a small constant. Our algorithm adapts to the geometry of the realized sequence: if the sequence of adversarially selected outcome means lies in an affine subspace of dimension $s$, it obtains error $\widetilde O(n^{1/(s+2)}T^{(s+1)/(s+2)})$ with high probability. The algorithm adapts to this structure without knowing the subspace or its dimension. For $T\ge n\ge2$, this rate is minimax optimal up to polylogarithmic factors. For a stochastic instance with a fixed conditional mean, the bound specializes to $\widetilde O(\sqrt{nT})$, giving a square-root dependence on the horizon.

Small area estimation (SAE) traditionally borrows strength across domains through a prespecified working model. We introduce small area learning (SAL), a learner-agnostic framework that formulates SAE as a multi-target semi-supervised learning problem and treats outcome prediction as a nuisance task. Areas may differ through unrestricted covariate shift and structured conditional shift, with information shared through common and area-specific components. We develop standard and cross-fitted estimators for low-complexity and flexible learners, unifying synthetic, model-based, and fully residual-corrected estimation. For area means, we establish consistency and asymptotic normality and provide variance estimators and confidence intervals. We extend the theory to settings with only aggregated population covariates and characterize the resulting aggregation bias. SAL reveals a bias–variance trade-off: partial residual correction can reduce mean squared error, whereas full correction yields estimators robust to working-model misspecification, potentially at higher variance. Simulations yield RMSE reductions of 34%–49% relative to direct estimation, with the best configuration varying across settings. An empirical application favours a cross-fitted estimator using a flexible learner under the chosen validation criterion. The numerical studies also illustrate how shrinkage can produce overly optimistic confidence intervals at the expense of strong modeling assumptions.

We prove several regularity theorems concerning Lipschitz viscosity solutions to the minimal surface system. The main lemma (i.e. “Decoupling Lemma") says that the component functions of such solutions satisfy the homogeneous Pucci inequalities. This allows us to apply the regularity theory for scalar viscosity solutions for elliptic PDE component-wise to a viscosity solution for the system. As a result of the Decoupling Lemma, we deduce that 2D Lipschitz viscosity solutions to the system are analytic in the interior, and obtain a quantitative partial regularity theorem. We also prove a geometric Harnack inequality for Lipschitz solutions. The Harnack inequality yields a strong maximum principle and half-space Liouville theorem. Another significant consequence of the lemma is a boundary regularity theorem for Lipschitz viscosity solutions. Notably, our theorem does not require any density assumption at the graph boundary, and we do not assume stationarity. This is used to prove a classification theorem for the singular set of a 4D stationary solution on a bounded domain. We also prove an $\varepsilon$-regularity theorem extending a result of the author. To conclude, we survey open problems. As an example, we have included a Bernstein-type theorem for 3D homogeneous entire Lipschitz viscosity solutions. Taken together, our results suggest that viscosity methods are a useful tool for studying the regularity of minimal graphs.

Ransomware is a fast-escalating privacy threat causing significant financial and data losses worldwide. As attacks grow more sophisticated, traditional static signatures and dynamic behavior analysis struggle to defend. In this paper, we propose an novel framework that couples software-level scanning with hardware-level microprocessor activity monitoring to achieve efficient ransomware detection and mitigation. The contributions are threefold: (1) we employ adversarial training to harden static analysis against obfuscation and leverage hardware-assisted monitoring for real-time detection; (2) we integrate neural architecture search (NAS) to automatically tailor models for stronger generalizability; and (3) We validate the proposed approach through extensive experiments, demonstrating substantially improved detection accuracy and reduced latency compared with existing methods. Moreover, it provides trace-level interpretability that explains the underlying decision process.

We study particle approximations of maximum mean discrepancy (MMD) flows with the Coulomb kernel on the torus $\mathbb{T}^d$, $d\ge2$, driven by thermal noise of strength $\tau\ge0$. For smooth, strictly positive initial and target densities and i.i.d. initial positions, we prove that the expected Wasserstein-1 distance between the empirical measure and the mean-field solution is at most of order $N^{-1/d}$ for $d\ge3$ and $\sqrt{(\log N)/N}$ for $d=2$, uniformly in time and in the temperature $\tau\ge0$, including the deterministic case $\tau=0$. At each fixed $\tau>0$, we also prove propagation of chaos in total variation for any $k$-fold marginal distributions of particles, uniformly in time, with a bound of order $\sqrt{k/\tau}$ times the empirical convergence rate. Our proof uses the modulated free-energy method of Bresch, Jabin, and Wang to reduce the particle convergence estimate to a relaxation estimate that controls the time integral of the mean-field velocity gradient uniformly in $\tau\ge0$. Near zero temperature, where the smoothing effect of the noise degenerates, we obtain this estimate by recentering the dynamics at thermal equilibrium and using the damping generated by the Coulomb interaction.

With the rapid increase in interest towards large scale earth observing satellite constellations, the problem of properly commanding and utilizing these systems has become increasingly relevant. This work focuses on a complete distributed approach to this problem, incorporating an observation task allocation and scheduling algorithm in addition to a sensor data fusion algorithm for end-to-end target coverage and processing. Observation task allocation and scheduling is performed in this work through the combination of the bid warped consensus based bundle algorithm (BWCBBA) and a lightweight observation scheduler for bid scoring. This method produces a unique mapping of tasks to command agents when allowed to iterate sufficiently. The approach to distributed data fusion in this work occurs primarily through an ownership model in which one satellite takes ownership of a system track in the constellation. After local information is shared between the sensing nodes to create the system tracks, the dedicated fusion nodes assume ownership for further information fusion and track information is disseminated throughout the constellation for data association. This paper analyzes the performance of these two algorithms over a set of increasingly decentralized architectures to highlight the performance losses compared to more traditional centralized methods.

Proactive Smart Assistants (PSAs) increasingly use general knowledge, learned patterns from group-level data, patterns from individual user's data, and recent sensor observations to anticipate which action a user may prefer. Existing systems typically select actions from predicted user preference likelihoods, but these likelihoods alone do not reveal how reliable the prediction is, which evidence supports it, or why ambiguity remains. In this vision paper, we argue that uncertainty estimation can provide this missing information and substantially change appropriate downstream behavior. Using the example of a home assistant, we introduce the questions that uncertainty estimation aims to answer, i.e. how sure is the assistant about the predicted preference likelihood, whether the confidence come from group-level assumptions or individual's data, and whether likelihood ambiguity reflect the user's intrinsic preference variability or insufficient data for the particular situation. We further introduce uncertainty estimation applications in neighboring domains, such as human trajectory prediction, personalized activity recognition, information-collection, and model-based control. Finally, we draw on insights from neighboring domains to envision how future uncertainty-aware proactive assistants may address key challenges in proactive interaction.

Heap-leaching hydraulics vary between regions of an ore bed, motivating fast prediction models that accommodate different material properties. This study develops a parameter-conditioned physics-guided machine-learning (PGML) surrogate and demonstrates its use in simulated saturation control. A dataset of 4096 numerical Richards-equation trajectories was divided into 2867 training, 614 validation and 615 evaluation cases. The network predicts hourly saturation profiles from the current profile, irrigation rate and four hydraulic parameters, and is trained with an approximate Gardner mass-balance penalty. A daily predictive controller compared 200 constant irrigation rates over a 24-hour horizon. Across the evaluation cases, the median full-cycle tracking deviation was 4.9% of a 0.70 saturation target, equal to that of a tuned proportional-integral (PI) controller, while the PGML controller reached the target without overshoot in the median and applied approximately 4% less irrigation. Moderate physics guidance reduced long-horizon prediction error by approximately 30% relative to data-only training and reduced irrigation-bound activity, but slightly worsened closed-loop tracking. For a matched prediction workload, the surrogate was approximately 70 times faster than the numerical solver, and batched evaluation cost under 2 ms per column for 5000 columns. The results support a reusable physics-guided surrogate for large-scale saturation control in simulation.

The ancient stellar populations and simple structure of the local dwarf spheroidal galaxies (dSphs) make them excellent laboratories for studying the chemical evolution of the early universe. In this paper, we fit one-zone galactic chemical evolution models to C, Mg, Si, Ca, Fe, Sr, Y, Ba, and Eu abundances in the dSphs Sculptor and Draco. By including the s- and r-processes in our model, we are able to place constraints on the timescale of r-process enrichment in these dSphs. We find that neutron star mergers cannot be the only source of the r-process in Sculptor and Draco, and that a prompt r-process source is required to explain the observed stellar abundances. When neutron star mergers are the only source of the r-process in our models, their minimum delay time must be just 14-16 Myr. The neutron-capture abundances in Sculptor and Draco can also be fit by models with a longer neutron star merger minimum delay time combined with a prompt r-process source that operates on the same timescale as massive star evolution, such as magneto-rotational supernovae. Additionally, the Sr and Y abundances in the dSphs set limits on the Sr and Y yields per r-process event. We find that theoretical r-process yields overestimate Sr and Y production by a factor of up to 100.

Short-wavelength spin waves are central to miniaturizing magnonic devices and to studying exchange-dominated magnetization dynamics. Yet the wave-vector range between roughly 30 and 300 radians per micrometre has remained difficult to access experimentally, posing challenges for both excitation and detection. This Perspective reviews recent advances in emerging measurement techniques and discusses prospects for their future development. Optical and microwave techniques are restricted to the vicinity of the Brillouin-zone centre. Inelastic neutron, electron and resonant hard x-ray scattering cover the full Brillouin zone but lack the energy resolution needed for low-frequency magnons at intermediate wave vectors. This Perspective examines five emerging approaches that are beginning to close this gap: Mie-enhanced Brillouin light scattering, colour-centre magnetometry, magnon momentum microscopy, extreme-ultraviolet transient-grating spectroscopy, and time-resolved scanning transmission x-ray microscopy. For each, we discuss the physical principle, demonstrated capabilities, current limitations and prospects for development. Compared side by side, the techniques give complementary access to magnon frequencies, local stray fields, real-space dynamics and momentum-space distributions, and they differ in their sensitivity to coherent and incoherent excitations. We therefore discuss the main advantages and use cases of each technique and consider the practical requirements for addressing different scientific questions. We highlight opportunities for further development, including higher sensitivity, improved spatial and temporal resolution, and broader frequency and wave-vector coverage. Together, these advances could enable, for example, systematic studies of nonlinear magnon interactions at nanoscale wavelengths and investigations of emerging magnetic materials such as altermagnets.

Projection-based model-order reduction (MOR) offers a promising approach for accelerating expensive full-order model (FOM) by constructing reduced-order models (ROMs) that retain the majority of FOM accuracy while significantly reducing the computational cost. However, conventional static ROMs, often following offline/online training strategy, can exhibit limited predictive capability for convection-dominated problems featuring strongly evolving physics such as shocks. Adaptive ROMs emerge as a promising alternative and address such limitation by dynamically updating the low-dimensional subspace during online simulation to track locally evolving system dynamics, thereby enabling accurate predictions even for shock-dominated flows. However, such online adaptation introduces additional computational overhead, and frequent basis and sampling-point updates can substantially reduce their computational advantage relative to their static counterpart. To reconcile this tradeoff, the current work introduces a self-adaptive MOR framework that dynamically constructs and deploys the most appropriate ROM formulation (either adaptive or static) on the fly according to the evolving characteristics of the solution. to achieve optimal computational efficiency while maintaining high modeling accuracy of the local physics during the online model execution. In this regard, the proposed framework seeks to exploit the advantages of both adaptive- and static-ROM approaches to achieve an optimal computational efficiency and predictive accuracy while reducing reliance on extensive offline training. The framework is developed and evaluated for modeling rotating detonation engines (RDEs), which provide a challenging test environment involving strongly convection-dominated, transient, and multiscale reacting-flow dynamics.

Among Navier–Stokes systems, the Rayleigh–Bénard layer, a fluid between two horizontal plates heated from below and cooled from above, is the benchmark of hydrodynamic instability that manifests itself as the unsteady convection phenomenon, which in turn can be interpreted as the onset of chaos: the Lorenz equations represent the Fourier–Galerkin approximation coefficients for the minimal three-mode truncation of it. Its instability has no mean flow behind it. The fluid is at rest, the velocity and the temperature are each stable alone, and buoyancy closes a positive loop between them. The linearization is self-adjoint, its unstable spectrum real, and the number of unstable modes grows without bound in the Rayleigh number; at $\Ra=10^6$ the layer has $85$ of them, with growth rates up to $2137$. We stabilize the conductive state at every Rayleigh and Prandtl number, with any prescribed decay rate, by explicit feedback of the full state to the tangential velocity, temperature, and normal velocity of the upper plate. The feedback laws are obtained by Fredholm backstepping of the coupled velocity–temperature system, with pole placement for the lowest modes.

We consider the problem of computing Taylor approximations to the optimal feedback law and value function for infinite-horizon finite-dimensional nonlinear optimal control problem—also known as Al'brekht's method. The scalability of existing Al'brekht-based approaches to computing approximate solutions to the Hamilton-Jacobi-Bellman equation associated with the optimal control problem has been severely limited by computational resources. The computational time issue has been partially mitigated by recent works leveraging tensor-structure to develop efficient numerical methods. However, RAM requirements still have remained a major hindrance to scaling beyond state dimensions of a few hundred or low thousands. We propose an acceleration to compute the expensive higher-order terms in a reduced space, mitigating the curse of dimensionality. A fast and scalable Matlab implementation is provided open-source for general purpose use, with the ability to accommodate arbitrary polynomial nonlinearities in the control-affine state equation, as well as polynomial state-dependence in the cost function, and the ability to handle systems in generalized form with a non-identity mass matrix, such as finite element models. Combined with the exploitation of sparsity and modern low-rank Riccati solvers, this permits computing approximations to polynomial feedback laws based on Al'brekht's method in hundreds of thousands of states.

Curriculum teams often lack time to check whether assigned readings support learning objectives (LOs) and whether topic coverage is balanced. We present a natural language processing (NLP) workflow to support evidence-informed curation of reading lists. The workflow combines PubMedBERT sentence embeddings and cosine similarity for retrieval, natural language inference (NLI) for evidence checking, and topic modeling for coverage analysis. We tested the approach in dental education using 13 course-level LOs and a PubMed-derived corpus of 3,837 LO-abstract pairs. Median cosine similarity ranged from 0.86 to 0.91 across the 13 LOs, showing generally high semantic similarity. Topic modeling showed broad but uneven coverage, with one or two dominant topics per domain. Similarity alone was not enough for selecting readings: among high-similarity pairs (cosine 0.90-1.00), 22.9% were classified by NLI as neutral or contradictory. In a 49-pair expert-labeled validation set, cosine-based retrieval (cosine >= 0.90) achieved 0.69 accuracy, while the combined cosine and NLI approach achieved 0.73 accuracy against expert alignment labels. Overall, the workflow shows how AI can support curriculum alignment by reducing false positives and helping select readings that better match intended LOs.

This paper introduces an adjoint Krylov method for parameter inference in large, sparse linear evolution equations whose system matrices depend affinely on unknown coefficients. We estimate these coefficients from discrete observations by constructing one forward and one adjoint Krylov approximation on each observation interval. Quadrature of the resulting bilinear form gives the full coefficient gradient through sparse matrix-vector products, without evaluating a separate Frechet derivative in every operator direction. We separate the gradient error into forward, adjoint, and quadrature terms and derive residual-based bounds for Markov and Lindblad generators. We also identify cases in which heuristic stopping estimates become small before the gradient has converged. With workspace reuse, we compute library gradients for a 12-qubit Lindblad generator with dimension 1.7 x 10^7 on a single machine with 16 GB of memory. Experiments on chemical master, Kuramoto-Sivashinsky, and Lindblad equations demonstrate accurate gradients and parameter recovery.

Asteroseismology of $\delta$ Sct stars has strong potential for determining the ages of young stars through individual mode fitting. We present a neural-network emulator trained on approximately 46 million rotating pulsation models. From stellar mass, metallicity, age, and equatorial rotation velocity, it predicts 12 classical observables, two asteroseismic scalars, and the p mode, f mode and low-order g mode frequencies for degrees $\ell=0$-3, including the individual $m$ components of rotationally split multiplets. We couple the emulator to nested sampling through a multivariate likelihood that propagates correlated emulator residuals, making full Bayesian posterior exploration practical. Applied to five $\delta$ Sct stars in the Pleiades observed by TESS, the framework gives mutually consistent individual asteroseismic ages of 107-117 Myr. Combining their age posteriors gives a cluster age of $113.3\pm4.5$ Myr (statistical), consistent with the $112 \pm 5$ Myr lithium-depletion-boundary age and the 110-160 Myr range from rotating-isochrone fitting. Together with spectroscopic $v\sin i$, the inferred equatorial velocities also provide post-fit inclination estimates. Separate perturbed-grid tests using 100 matched synthetic pairs per input-physics variation give median absolute age shifts of $2.1$, $2.3$, and $5.2$ Myr for $|\Delta f_{\rm ov}|=0.005$, $|\Delta\alpha_{\rm MLT}|=0.1$, and $|\Delta Y|=0.02$, respectively; the corresponding 90th percentile shifts are $6.5$, $7.6$, and $16.2$ Myr. These tests describe conditional population sensitivities, not a systematic uncertainty on the Pleiades age. Together, the cluster-age agreement and the scale of these input-physics sensitivities support $\delta$ Sct asteroseismology as a complementary age estimation method for young stars.

Evaluation of text generated by large language models (LLMs) is increasingly delegated to LLMs acting as judges, yet what such a judge must be shown remains unresolved. We treat a judge whose reports are acted on as a regulator, in the sense of cybernetics, and ask what it must be shown, how much, in what form, and what its reports must get right. On seven public benchmarks we varied only what the judge was shown. Across three judges whose prices differ 10- to 17-fold, what the judge was shown mattered more than which judge it was. When a system revised its answers on feedback from a judge denied the material they had to respect, it ended below its starting point on instruction following and question answering. On instruction following the loss grew with each round, and it persisted when the judge saw the user's request but not the constraints and with a second judge family. On news summarisation, a correct reference summary beside the source undid most of the source's contribution, whereas on single-answer questions a reference helped. About a tenth of the source did almost all of its work, and a small entailment graph matched an LLM judge at finding errors in grounded text. We committed 83 testable clauses before running; of the 81 that ran, 32 met their bar and 50 went in the predicted direction, and most quantitative predictions from the theory failed. We report every shortfall and derive design rules tied to measured effects.

We infer kinetic rates of stochastic reaction networks from molecular-state pairs separated by a fixed time lag, without constructing the large state space of the Chemical Master Equation. Extended dynamic mode decomposition estimates the finite-time evolution of selected functions of the molecular state. A matrix logarithm then gives a projected generator whose species rows determine the rates through the known reaction stoichiometry. A finite set of functions introduces a systematic bias. We construct additional functions from the reaction channels and prove that each level of closure moves the first bias term to higher order. Spectral formulas identify the omitted modes responsible for this bias and show when the logarithm amplifies sampling error. Exact calculations and experiments on five reaction networks confirm the predicted error behavior and show when the added functions improve finite-sample rate recovery.