Papers

We introduce a family of metric outer measures whose critical exponents form a packing spectrum interpolating between Hausdorff and packing dimensions. For analytic sets, we characterize each spectral value as the supremum of the Hausdorff dimension of a product with a compact testing set minus the testing set's upper intermediate dimension at the complementary parameter. The associated product bounds refine the classical Hausdorff–packing inequalities and can give exact Hausdorff additivity when both factors have distinct endpoint dimensions. Below the packing endpoint, we prove a variational principle in terms of windowed local mass exponents and sharp parameter estimates implying local Lipschitz continuity; a jump at the endpoint is possible. We characterize all attainable profiles by monotonicity, continuity below the packing endpoint, and a sharp upper right Dini-derivative bound. Every admissible profile is realized by a compact binary digit set whose uniform measure attains the finite-window and classical packing variational suprema. Complementary digit positions yield reflected upper intermediate-dimension profiles and a single factor attaining the Hausdorff product bounds at every parameter, with an Ahlfors regular product measure.

A key challenge for multimodal large language models (MLLMs) is moving beyond visual recognition to constraint-aware cross-modal reasoning. This involves combining visual cues with information from other modalities to understand elements' relationships under domain-specific rules. This challenge is acutely evident in industrial design-to-code (D2C), which converts user interface (UI) designs into code and requires MLLMs to connect design images with disorganized layer metadata, infer component and layout implementation requirements, and realize them in code under target-library constraints. However, these capabilities remain insufficiently evaluated in realistic industrial settings. To fill this gap, we present TaoD2C-Bench, a benchmark for evaluating MLLMs' ability to generate UI code that satisfies implementation requirements in industrial applications. The TaoD2C dataset consists of 2,861 production designs from 17 commercial platforms with 97,652 expert annotations across four categories: Component, Group, Alignment, and Position. These annotations distinguish required constraints from permitted implementation choices. TaoD2C-Bench defines three tasks: end-to-end UI code generation, requirement inference, and requirement realization. Evaluating eight MLLMs reveals substantial gaps in generating UI code that satisfies implementation requirements, alongside distinct performance profiles in inference and realization. We further show that MLLMs' visual reconstruction ability does not necessarily imply an ability to generate code that meets these requirements. We release TaoD2C to support research on industrial UI code generation.

Circumnuclear structures in active galactic nuclei respond to accretion variability over different spatial and temporal scales, but whether compact narrow-line gas responds on decade timescales has not been systematically established. We use repeat Sloan Digital Sky Survey and Dark Energy Spectroscopic Instrument spectroscopy of 473 variability-selected galactic nuclei with evidence for recent nuclear brightening. We identify 19 sources whose narrow [O III] $\lambda5007$ flux increased by more than a factor of two over rest-frame baselines of 12.0-20.4 yr, which we term narrow-line ionization echoes (NIEs). In equal-weight stacked spectra, [O III] increased by $229\pm22\%$, while lower-ionization lines remained nearly unchanged or declined, indicating an ionization-dependent response rather than uniform spectral rescaling. The NIE hosts also moved coherently toward higher excitation in optical diagnostic diagrams, with mean increases of $0.46\pm0.18$ dex in $\log([\mathrm{O III}]/\mathrm{H}\beta)$ and $0.58\pm0.13$ dex in $\log([\mathrm{O III}]/[\mathrm{O II}])$. Photoionization models reproduce this evolution with a higher ionization parameter and a harder AGN-like ionizing spectrum at fixed gas abundance. For 13 sources with well-defined mid-infrared outbursts, the integrated W1+W2 excess energy correlates strongly with the absolute [O III] luminosity change ($r=0.87$), linking the dust and narrow-line responses to the same nuclear event. The mid-infrared timescale and spectroscopic baseline constrain the variable [O III]-emitting gas to characteristic scales of 1.5-5.2 pc. Compact narrow-line gas therefore appears to form an intermediate, decade-scale response layer between the infrared dust echo and the long-lived extended narrow-line region.

We extend the Nair–Tenenbaum estimates for short sums of nonnegative arithmetic functions at polynomial values to mixed moments involving Kloosterman sums. Combining these estimates with lower bounds obtained by refining the method of Fouvry and Michel, we prove that, for every fixed nonzero integer \(a\) and fixed \(z,\nu>0\), \[ \sum_{n\leq x}z^{\omega(n)} |\operatorname{Kl}(a;n)|^\nu \asymp_{a,z,\nu} x(\log x)^{z\mathfrak{s}(\nu)-1}, \] where \(\omega(n)\) counts distinct prime divisors and \(\mathfrak{s}(\nu)\) is the \(\nu\)-th absolute moment of the Sato–Tate measure. We also obtain upper bounds for mixed absolute moments of Hecke eigenvalues and Kloosterman sums, determine the frequency of large Kloosterman values on a logarithmic scale, and establish the order of magnitude predicted by Li and Sarnak for the diagonal second moment of classical Kloosterman sums. We obtain matching bounds for the smoothed spectral counting variance on the modular surface in a logarithmic range and the lower bound \(\int_T^{2T}S(t)^2\,dt\gg T^2/\log T\), where \(S(t)\) is the remainder in Weyl's law.

We introduce a method for efficiently computing multiple photofragmentation of atoms and molecules into photoelectrons and nuclear fragments. The method is a generalization of the time-dependent surface flux originally introduced for single and double photoionization.

As smart glasses and lightweight MR devices become increasingly practical, input remains a key challenge. The bare palm is an always-available, tactile, and proprioceptively accessible surface, but it has neither an explicit coordinate system nor embedded touch sensing. Prior on-palm systems typically expose isolated touch events, discrete regions, continuous trajectories, or task-specific gestures, limiting the palm's ability to support precise selection and gesture manipulation through a common input representation. We present PalmSpace, a wrist-worn infrared system that exposes mode-aware, body-referenced absolute input on the bare palm without per-user sensing calibration. At the interaction level, PalmSpace jointly represents contact occurrence, interaction mode, and palm-referenced absolute location; at the model level, it learns these coupled outputs through a shared real-time representation. In leave-one-participant-out evaluation with 17 participants, PalmSpace achieved 6.7 mm mean localization error, 98.9% contact detection accuracy, and 96.7% F1 for four-class interaction-state recognition. User studies further demonstrated absolute pointing and dragging, eyes-free digit input, and representative multi-finger controls including scrolling and pinch-based map manipulation. These results show that a morphologically variable bare palm can function as a transferable, mode-aware interaction surface.

The heavy-ball method can accelerate convergence near the minimizer, but it may also enter persistent oscillations on general strongly convex objectives. How should it be initialized to reliably realize this local advantage? We study the initialization neighborhood in which convergence can be guaranteed using only curvature and regularity bounds. This neighborhood shrinks as momentum approaches one; for Lipschitz-continuous Hessians, its radius is of the same order as damping. Matching upper and lower bounds show that this initialization requirement cannot be relaxed uniformly over the function class. We then derive a startup rule based on the current gradient: a finite gradient-descent warm-up enters the guaranteed region before switching to heavy-ball. With parameters optimal for strongly convex quadratics, the subsequent iterates satisfy an accelerated local asymptotic rate bound. Code is available at https://anonymous.4open.science/r/HeavyBall-811D/.

Adaptive computation aims to improve language-model inference by tailoring execution to each input. For layer programs, oracle evaluations use known answers to estimate the potential gain from this flexibility, before a practical selector is available. However, a gain from selection does not by itself explain why the chosen programs help. This study examines this distinction using 32 layer-skipping and repetition programs on two models and 4,413 multiple-choice items. The analysis compares their gains over a fixed action selected without the evaluation prompt with those of input-blind perturbations at the same sites, re-evaluating selections on another prompt. With shared option order, the controls give 10.2-11.8 and 15.6-19.4 percentage points of headroom on Qwen3-4B-Base and Llama-3.1-8B, exceeding the real programs' 9.0 and 10.1 in all three random-direction draws per model. They match answer-change rate only, and the ordering depends on the menu: in post hoc comparisons, real programs lead on Llama's repeat-only menu in every draw. A smaller KL-calibrated comparison, including an input-dependent control, favours real programs in point estimate, with inconclusive corrected tests. Fixed letter offsets produce headroom of similar scale. Rotating options sharply reduces both families' headroom, while leaving positive real-minus-control differences of 1.4-2.3 and 3.7-4.5 points; their magnitudes and statistical support depend on further adjustments and the reference. A supplementary generated-answer test finds that search-selected programs keep a 26.0-point advantage over programs selected for other problems after rewording, without a placebo comparison. These results show that substantial headroom can persist across prompts with shared option order without establishing a benefit specific to the selected layer computation; neither ordering against these controls identifies that benefit.

Interpretability offers a solution to safe autonomy by providing transparency into an agent's underlying decision-making model. Within sequential-decision making tasks, differentiable decision trees (DDTs) are one approach to such interpretability, maintaining automatic-differentiable policies while providing humans with a discrete tree-based visualization. Nonetheless, current implementations of DDTs are not well-suited for sequential-decision making domains, as there exists an inherent mismatch between a tree's single-timestep behavior and a human's multi-timestep planning. Our work thus introduces time as a new dimension of interpretability, coined as temporal interpretability, and demonstrates how temporal abstractions via action chunking improve it. We achieve this by first introducing two novel policy gradient algorithms that incorporate action chunking. Additionally, to maintain parameter-efficient trees, we develop an information-theoretic tree restructuring algorithm that modifies the tree during training. Across four simulation environments, we find that warm-starting action chunked DDTs from a distilled action chunked policy is the most effective way to obtain temporally interpretable trees: they match neural network policies in three of the four domains while using up to 80$\%$ fewer parameters. Our code is available at https://github.com/ei5uke/temp-interp.

Feature caching accelerates diffusion sampling by replacing expensive network evaluations with predictions from previously computed activations. However, forecasts based only on past features cannot directly incorporate changes in the current denoising state. We investigate whether inexpensive, freshly computed features can serve as observations for correcting these predictions. We introduce an observation-corrected Koopman framework for accelerating frozen diffusion models. Using calibration trajectories, we identify finite-dimensional, time-dependent Koopman approximations that jointly describe the increments of shallow and deep network features. During accelerated sampling, these operators predict the evolution of expensive deep features, while innovations in the observed shallow features correct the predicted state. Periodic full evaluations refresh the observer, and all generative-model parameters remain unchanged. This formulation enables controlled comparisons of temporal prediction and observation correction. Across three 10,000-image runs per dataset, our method reduces paired Inception-feature MSE by $19.9\%$ on CIFAR-10 and $11.9\%$ on a ten-class ImageNet subset relative to channelwise affine prediction under the same four-partial-step schedule. Matched ablations attribute additional reductions of $4.54\%$ and $4.67\%$ to observation correction. The observer achieves $1.89\times$ and $1.85\times$ measured speedups over DDIM-50, supporting improved reference-sampler fidelity without retraining the denoiser.

Recent work of Bergeron-Charollois-García proposed a conjectural analytic expression for elliptic units for complex cubic fields as the special values of smoothed quotients of elliptic Gamma functions. These values depend on the conductor ideal, ray class group element, smoothing ideal, and an admissible element $h$. If this analytic expression is to fit into the framework of explicit class field theory, then, as in the case of torsion points on CM elliptic curves, the resulting complex number should depend only on the congruence class of $h$ modulo a fractional ideal. This conjecture has been supported by much numerical evidence. In this paper, we use the cocycle relations of the smoothed elliptic Gamma function to prove that the construction is indeed independent of $h$.

We present a comprehensive analysis combining multi-epoch mid-infrared (MIR) photometric and optical spectroscopic observations of young stellar candidates associated with elongated, elephant trunk-like structures (ETLSs) in the IC 1848E star-forming region. A sample of 15 candidate YSOs, initially identified by Chauhan et al. (2011), was investigated using multi-epoch NEOWISE $W1$ and $W2$ photometry to characterize their variability properties. After imposing stringent positional and photometric quality constraints, a final set of eight robust YSOs was retained and classified into three variability categories: non-variable, secular, and stochastic. One source, Star #9, exhibits a pronounced curved variability in the MIR light-curve and color-magnitude domains, indicative of systematic evolution of its circumstellar disk and/or accretion processes. Optical spectroscopic data for this object show strong H$\alpha$ emission and prominent forbidden lines, providing clear evidence of active mass accretion and outflow phenomena. The combined photometric and spectroscopic diagnostics establish a close link between infrared variability, circumstellar disk evolution, and accretion-driven activity in YSOs associated with ETLSs in IC 1848E.

In the upper half-space model of the hyperbolic space $\mathbb{H}^{n+1}$, a translation hypersurface of type I is a graph $x_{n+1}=f_1(x_1)+\cdots+f_n(x_n)$ and a translation hypersurface of type II is a graph $x_n=f_1(x_1)+\cdots+f_{n-1}(x_{n-1})+g(x_{n+1})$. We classify the minimal translation hypersurfaces of both types for every $n\geq 2$. We obtain these results as particular cases of a classification of the singular minimal translation hypersurfaces of $\mathbb{R}^{n+1}$ for an arbitrary exponent $\alpha\neq 0$, with respect to a direction orthogonal (type I) or parallel (type II) to the hyperplane over which the hypersurface is a graph. The minimal translation hypersurfaces of type I are exactly the parabolic cylinders over a one-parameter family of arches, which contradicts a nonexistence theorem in the literature. The minimal translation hypersurfaces of type II are the parabolic cylinders, the vertical totally geodesic hyperplanes and, when $n\geq 3$, the vertical cylinders over the Scherk surface.

We study decentralized adaptive sensing, where multiple agents choose measurements from evolving local beliefs while exchanging information over a communication graph. We ask whether the measurements actually selected by an adaptive policy have collected enough evidence to distinguish the true target from every plausible alternative. We develop a pathwise certificate based on the Rényi–Chernoff information accumulated along the realized sensing trajectory. It yields nonasymptotic MAP-error bounds and an anytime, network-wide stopping rule for arbitrary history-dependent sensing policies, while separating accumulated statistical information from a bounded network-mixing transient. Linear growth of the information against the least-resolved competitor implies exponential decay of MAP and squared-localization error. A classical pairwise KL converse, specialized to the adaptive decentralized transcript, shows that insufficient information on any pair prevents a positive uniform error exponent, confirming the hardest competitor as a fundamental bottleneck. Across policies, graph topologies, sensor profiles, and seeds, the worst-competitor score correlates more strongly with localization speed than an average-pair proxy in both 1D ($r=0.89$ versus $0.40$) and structured 2D sensing ($r=0.77$ versus $0.48$). Our results provide a practical way to certify and diagnose adaptive multi-agent sensing systems using the evidence they actually collect.

Personalized federated learning combines shared representations with client-specific predictors, but the contribution of a server weighting rule can be obscured by local training and evaluation choices. We study ORDERS, a configuration that combines a shared backbone, a private residual adapter and classifier, geometric weights assigned by descending update norm, feature alignment, and private-parameter perturbations. The server computes a weighted sum of updates obtained from the same broadcast model; it does not obtain an additional optimization effect from sequential addition. A fully specified evaluation comprises 80 final runs: eight configurations, two datasets, and five training seeds on one fixed partition per dataset. On two-class-per-client CIFAR-10, ORDERS achieves $80.51 \pm 0.79\%$ native mean client accuracy, compared with $79.02 \pm 1.42\%$ for FedPer-R1 and $80.27 \pm 0.73\%$ for the matched uniform-weight control. After common local fine-tuning, the difference from FedPer-R1 narrows to 0.32 percentage points. On Sent140, ORDERS reaches $74.71 \pm 0.49\%$, only 0.69 points above a post hoc client training-majority diagnostic. Ablations provide limited, endpoint-dependent evidence for norm ranking and alignment, and no clear benefit from perturbations. Parameter-payload savings are 5.47% and 0.78%, respectively.

Federated learning lets a UAV fleet train a shared GPS spoofing detector without raw receiver data leaving any aircraft, and several recent UAV-FL designs weight each client by the validation accuracy it reports about itself. We show this self-report is an exploitable attack lever: two compromised clients of ten that poison part of their data, scale their updates, and inflate their reported accuracy raise backdoor lift to +0.3036, higher than the same attack achieves without lying. We propose receiver-domain behavioral probing, in which the coordinator evaluates every submitted model on counterfactual spoofed samples built by driving each discriminative GPS feature to a benign value, weighting clients by what their models do rather than what they claim. Under independent and identically distributed clients this reduces attacker-induced lift to -0.0265, statistically indistinguishable from an honest fleet, while flagging the compromised aircraft. Unlike Byzantine-robust aggregation it needs no exact attacker count, only an honest majority: when the true count exceeds the configured value, Multi-Krum degrades from +0.0061 to +0.2837 while ours stays near baseline. Evaluation uses one public single-receiver dataset partitioned into simulated clients; we also report where the mechanism fails, under strong client heterogeneity.

We introduce MultiFly, a real-world, low-altitude UAV dataset for semantic perception across RGB, thermal, LiDAR, and radar modalities. MultiFly provides 17,272 synchronized samples from four suburban scenes with frame-wise annotations for 15 semantic classes, together with calibration and GNSS-RTK/IMU measurements. To avoid costly and inconsistent modality-specific annotation, we propagate labels from only 115 manually annotated RGB images through shared geometric representations to all four modalities. This approach generates semantic labels for 17,157 additional RGB images, 17,272 thermal images, 840M LiDAR points, and 3.4M radar points. Transferred annotations achieve 89.93% average agreement with held-out manual annotations, and 90.94% average semantic consistency across all six modality pairs. We further establish semantic segmentation benchmarks for all four modalities, revealing distinct architectural behavior for dense LiDAR and sparse radar data. Taken together, MultiFly provides a scalable foundation for multimodal aerial perception and, to the best of our knowledge, the first public real-world low-altitude aerial benchmark that combines consistent frame-wise semantic annotations for RGB, thermal, LiDAR, and radar. Data at https://github.com/markus-42/multifly.

As multimodal large language models (MLLMs) become more capable and widely deployed, concerns about privacy and safety have become increasingly pressing. Machine unlearning offers one approach to addressing these concerns by removing designated information from trained models while preserving unrelated capabilities. However, fragmented implementations and evaluation protocols, incomplete robustness testing, and limited understanding of metric reliability make progress in MLLM unlearning difficult to assess systematically. We introduce Open-MMUnlearning, an open-source, extensible framework that integrates target-model preparation, multimodal data processing, unlearning, and evaluation through shared interfaces and structured configurations. The framework supports five benchmarks spanning privacy, safety, and copyright, eight MLLMs from four model families, and twelve unlearning methods. Its evaluation suite jointly assesses forgetting effectiveness, retained utility, and robustness to model interventions, adversarial inputs, and membership inference attacks. Using a common evaluation protocol, we compare ten representative unlearning methods. In this comparison, GD and MIP-Editor tie for the highest overall score: GD achieves the highest Forget Quality, while MIP-Editor preserves more Model Utility. We further introduce a metric meta-evaluation protocol that tests faithfulness using models with controlled exposure to target knowledge and robustness under quantization and relearning. Among the thirteen evaluated metrics, BLEU achieves the highest aggregate reliability score. KS-Test attains the highest faithfulness AUC but performs less well on robustness. Together, the framework and these findings support reproducible comparison of MLLM unlearning methods and systematic assessment of evaluation reliability.

A major application of analog quantum hardware is quantum simulation, where a system evolves over time according to a given Hamiltonian. One challenge when implementing the Hamiltonian on a programmable quantum simulator is the availability of distinct coupling types, many of which go beyond the conventional ZZ-couplings found in Ising Hamiltonians that are naturally implemented by various platforms. In prior work, we have developed a method based on domain wall encoding to simulate one-dimensional spin chains using only Ising Hamiltonians, which would otherwise require XX+YY-couplings as well. Here, we implement the method on a commercially accessible Rydberg atom quantum device, and simulate the time evolution of the Heisenberg XXZ model with various anisotropies. We successfully probe the XY and Ising phases of the model and reproduce the qualitative behavior of several one- and two-body observables in both phases, as well as at the critical point. Our work augments the toolbox to simulate canonical quantum many-body systems on analog quantum simulators.

This paper extends Goodwin's (1967) predator-prey growth-cycle model to incorporate the negative impact of Opioid Use Disorder (OUD) on labor productivity. Using U.S. state-level data for 1998–2019, we first document that deteriorations in the labor share are followed by rising drug-induced mortality. We then build this link into the model through a novel discrete-choice mechanism in which the probability of OUD decreases with the wage share, so when real wages fail to keep pace with productivity growth, opioid use rises. This behavioral health channel feeds back into the economy through a productivity damage function. Applying the existence part of the Andronov-Hopf bifurcation theorem, we show that the resulting three-dimensional nonlinear system admits a limit cycle, as confirmed by our numerical simulations. Along the cycle, rising OUD paradoxically raises the employment rate, as falling productivity requires more labor per unit of output; across steady states, however, higher OUD prevalence is associated with a lower employment rate, consistent with evidence that opioid use disorder reduces labor force participation. Moreover, our numerical experiments show that OUD sensitivity to income widens fluctuations, while productivity sensitivity to OUD counterintuitively compresses them through a self-correcting feedback that speeds the recovery of the wage share. Policies that weaken the link between income and OUD, such as stronger social safety nets, stabilize the resulting dynamics.

Text-to-music systems produce increasingly convincing audio, yet evaluation reveals little about whether the result matches user intent. A global text-audio relevance score can overlook the implicit intent in underspecified prompts and mask failures in specific requirements, such as instrumentation, structure, rhythm, or mood progression. To bridge this gap, we formulate text-to-music intent alignment as satisfying a per-request rubric of independently verifiable items covering both a request's explicit requirements and its implied musical intent. Scoring items individually makes evaluation diagnostic by intent source and musical dimension, rather than a single opaque score. We instantiate this as MuRA-Bench, a benchmark of real-world platform requests curated by music experts. We further propose MIRA (Musical Intent Refinement Agent), a test-time agent that first grounds a request's intent into rubrics, then searches over prompt revisions for a black-box generator under a bounded budget, iteratively generating music, verifying it against the rubrics, and using this feedback to guide a trajectory-aware tree search. Experiments across open-source and commercial backends show that MIRA improves intent alignment, enabling an open-source generator to achieve performance comparable to representative commercial systems (e.g. Suno and Mureka). Project page: https://mirareview.github.io/.

Min-Plus Convolution is a central problem in fine-grained complexity, and the associated Min-Plus Convolution Hypothesis forms the basis for a wide range of conditional lower bounds for fundamental problems. It is closely connected to the APSP and 3SUM Hypotheses, and in fact implies both, making it a unifying hypothesis for two of the main pillars of the area. In this work we establish several strong results related to Min-Plus Convolution. We design a universe reduction, showing, under a plausible additive combinatorics assumption, that the Min-Plus Convolution Hypothesis is equivalent to the Strong Min-Plus Convolution Hypothesis. We also obtain tight conditional lower bounds for multiple long-standing problems, including Min-Max Convolution and Bounded Monotone Min-Plus Convolution. Our approach is inspired by Fischer's recent equivalence between several variants of APSP [STOC '26], but extending that technique to the arithmetic setting requires overcoming deep obstacles. To this end, we develop a novel additive structure theorem that can be viewed as a higher-order substitute of the Balog-Szemerédi-Gowers (BSG) theorem, allowing us to extract strong additive structure even from weakly structured sets. Building on this structural result, we show that certain structured 3SUM instances (namely, sets with low rank) can be solved in truly subquadratic time. This algorithm forms the main algorithmic ingredient in our reductions. Besides, it generalizes all previously known truly subquadratic-time special cases of 3SUM, and is therefore of independent interest.

Self ion doping in ZnO nanorods offers a powerful route to dynamically control excitonic states and light matter interactions. Here, vertically aligned hexagonal ZnO nanorods were irradiated with 250 keV oxygen ions to establish a direct link between irradiation induced defects and excitonic and optical responses. Increasing ion fluence progressively quenches the near band edge emission at 380 nm, leading to a complete exciton OFF state, while thermal annealing restores the emission, yielding a reversible exciton OFF or ON response. This switching originates from defect mediated modification and thermal recovery of excitonic states. The defect band emission, between 400 to 750 nm, exhibits quasi periodic whispering gallery mode like resonances that are progressively suppressed as irradiation alters nanorod geometry and optical confinement. Low-temperature photoluminescence resolves D0X, FX 1LO, and FX 2LO transitions, whose temperature evolution follows the Bose Einstein model. The non-monotonic variation of excition phonon coupling strength reveals a competition among irradiation induced defects, lattice distortion, and exciton localization in determining exciton phonon coupling. These results establish Oxygen ion irradiation as a means to simultaneously engineer excitonic switching, exciton phonon interactions, and optical resonances, providing a pathway toward defect programmable ZnO nanophotonic and optoelectronic devices.

Human-machine systems rarely operate at a fixed level of AI autonomy. As operators and AI systems collaborate over time, control must shift: the AI can take on more responsibility when collaboration is stable, maintain its current role when evidence is ambiguous, or return control to the human when conditions deteriorate. Existing work on adaptive automation, supervisory control, trust in automation, and deskilling explains parts of this problem, but provides no auditable, multi-signal criterion for governing when autonomy should change across multi-cycle workflows. We formalise this challenge as the Handover Problem: deciding, at each operational cycle, whether to escalate, maintain, or revert AI autonomy while keeping the process reversible, recoverable, and auditable. We introduce the Handover Readiness Score (HRS), a transparent composite measure that integrates four signal dimensions: operator readiness, human-AI trust, learning stability, and operational performance. It is combined with a hysteresis-based transition policy that requires sustained positive evidence before increasing autonomy but reverts promptly when conditions worsen. Across software engineering and manufacturing domains, the HRS and hard safety guards address complementary failure regimes: guards enforce immediate corrective action when a single indicator breaches a critical threshold, while the HRS detects the slow, multi-signal erosion of operator readiness that no individual guard can observe. The framework establishes autonomy handover as a governance problem requiring explicit, composite, and auditable criteria. This provides a conceptual and formal foundation that adaptive automation research has not previously provided.

Differentiable quantum architecture search (DQAS) is a promising framework for the automated design of quantum circuits, particularly for variational quantum optimization algorithms. However, its practical deployment on quantum hardware is limited by the large number of circuit measurements required during optimization, making hardware execution costly. In this work, we show that for a broad class of combinatorial optimization problems and commonly used rotational gate parameterizations, the measurement cost of DQAS can be significantly reduced without changing the optimization objective. We derive the proposed measurement reduction scheme theoretically and validate it experimentally on 3-SAT and MaxCut benchmark problems. Our approach reduces the requested gradient measurement cost by about 39 to 41% while introducing only negligible classical post-processing overhead, lowering the practical cost of executing DQAS on quantum hardware.

We present results from a detailed finite-size scaling analysis of the $3$-$d$, $Z(2)$ and $O(2)$ spin models in an external field $H$. Using high statistics Monte Carlo data, we obtain the leading finite-size scaling correction to the infinite volume scaling functions. We show that these corrections are proportional to $\widetilde{z}_L^2=1/(H L^{3/(1+1/\delta))})^{2}$. This provides the parametric form for finite-size corrections to bulk thermodynamic observables as well as the pseudo-critical temperatures determined at non-vanishing $H$. In particular, it allows to eliminate systematic errors in the analysis of the chiral phase transition temperature in (2+1)-flavor QCD, that arose from the previously not well-controlled ansatz for infinite volume extrapolations. We also establish the validity range of this leading order correction and point out that there are significant differences between the $3$-$d$, $O(2)$ and $Z(2)$ universality classes.

Instruction-tuned models are deployed into environments where domains are heterogeneous and evolve, yet adding new domains or data typically requires costly retraining. We present AutoAdapt, a modular framework that incorporates new domains and data via targeted single-adapter training without modifying other adapters. The framework automatically discovers latent domains, uses them to train per-domain Low-Rank Adaptation (LoRA) adapters independently in parallel and performs parameter-free routing. Across 14 domain-specific benchmarks and GPT-4o pairwise judgements, AutoAdapt achieves parity with a LoRA adapter trained on all domains without requiring full-model retraining. We also find evidence of specialisation effect convergence across independent discovery methods. Overall, training each adapter on its own domain prevents domain interference by construction, thus enabling modular, taxonomy-free domain specialisation without aggregate performance loss or full model retraining.

We analyze the existence of static black hole solutions with maximally symmetric horizons and nontrivial torsion in five-dimensional Lovelock gravity. For each symmetry class, we obtain a black hole solution characterized by two independent constants. We also determine the conserved charges associated with these solutions.

Dataset pruning reduces a large training set to a representative subset while preserving model performance. Existing geometry-based methods typically assume that nearby points in embedding space share similar properties. Rather than imposing this assumption, we derive geometric selection criteria by reformulating unbiased subset selection as a variance minimization problem. Unbiasedness ensures that unweighted subset averages recover full-dataset averages in expectation, including losses and gradients at fixed model parameters. Specifically, we characterize a family of unbiased subset selection algorithms as a high-dimensional polytope. In this context, minimizing the expected sampling variance is a linear objective. Differences in sampling variance, averaged over rigid motions, admit closed-form pairwise expressions. Because the polytope has high dimension, directly applying standard linear programming is impractical. We instead use these expressions to construct an efficient vertex walk that optimizes an approximation of the variance objective while preserving unbiasedness, yielding a method that requires neither labels nor model training during selection. Across CIFAR-10, MNIST, and CelebA benchmarks, our method matches or exceeds uniform sampling in mean test accuracy at every evaluated budget and outperforms competing geometric methods in several settings, particularly at small selection budgets. Beyond dataset pruning, the same framework reduces stochastic-gradient variance by increasing diversity within mini-batches while keeping the batch size unchanged.

Robotic minimally invasive surgery has revolutionized surgical practice. However, as the surgeons are mechanically separated from the surgical tools, loss of tactile feedback occurs. We present a compact force sensor with three, millimeter scale sensing elements (taxels) that can be affixed to the grasping face of a robotic surgical tool. The sensor features a miniaturized design using Hall effect sensors and magnets embedded in a deformable elastomer contact layer. Sensor calibration is achieved with a 6 degree of freedom (DoF) parallel robot. Each taxel can detect applied normal and shear forces with average RMSE of 2.133 kPa. The calibrated sensor was validated on phantom and ex vivo porcine tissue, demonstrating tactile sensing during retraction as well as slip. This work introduces a small-scale Hall effect based tactile sensor, enabling sensing for force-sensitive robotic surgical applications.