Papers

In this paper, both the pointwise space-time structures of the solution for a three-dimensional model describing gas dynamics in thermal non-equilibrium and the corresponding background stabilities within the $L^p$ framework are investigated under the small initial perturbation assumption and the irrotationality condition. Our main tools are the modified Green's function according to the irrotationality condition, a priori energy method and a refined decay estimates of products composed of the entropy function and high-order derivatives.

We study the strategic design of learning algorithms in a canonical continuous-time pricing game. We introduce a meta-game in which firms select learning rates for a gradient dynamic, evaluating payoffs as the discounted sum of profits accrued along the entire learning path. We uncover a fundamental dichotomy driven by stage-game incentives: if the stage game exhibits strategic substitutability, each firm strictly prefers faster learning. Under strategic complementarity, however, an excessively fast algorithm accelerates the rival's competitive response, destroying transitional profit margins. Even though the competitive price is a dominant action in the stage game and convergence to this price is guaranteed, we prove that firms design sluggish algorithms in equilibrium.

Automated video surveillance analysis has become a critical component of intelligence infrastructures and Law Enforcement agencies. Traditional systems lack the semantic module for comprehensive situational awareness and forensic tasks, limiting their ability to interpret events meaningfully or support post-incident investigations. This slows operational insight and increases the burden on human analysts. Recent advances in Vision-Language Models (VLMs) offer promising pathways to bridge this gap. To address this, we propose VLM-Enhanced Support for Surveillance and Investigations (VESSI), a VLM-based framework designed to enhance automated video surveillance analysis through prompt-driven interrogation of video sequences where salient visual features are converted into textual descriptions. We test our framework with four state-of-the-art models. Since most datasets for this task are unlabeled, we also propose the Composite Model Utility Score (CMUS) to assess VLM performance. Experimental results show that our solution substantially improves the analysis capabilities of human operators and enhances the flexibility of automated surveillance systems. In our evaluation, the most reliable model flagged potentially relevant activity in more than 66% of the videos while reducing review time by more than 85%, offering a practical balance between selectivity and efficiency. The model ordering produced by the reference-free CMUS evaluation was reproduced by the normal-video CMUS evaluation and matched the false-positive-rate ordering obtained from 5,909 manually referenced frames. This agreement supports the operational use of the score within the evaluated setting.

Physics-informed neural solvers often struggle with multiscale behavior and sharp gradients due to the use of global approximation spaces and nonconvex training. We introduce AB-PIELM, an adaptive-basis physics-informed extreme learning machine that combines domain decomposition with joint optimisation of spatial and spectral hyperparameters while retaining deterministic normal-equation training. The method adapts both the number and placement of subdomains and the locality of radial basis functions, enabling problem-dependent allocation of representational capacity without modifying the underlying solver. Experiments on oscillatory function approximation and singularly perturbed advection-diffusion equations demonstrate accurate solutions across a wide range of stiffness regimes while using substantially fewer neurons than existing neural and PIELM-based approaches. The learned hyperparameters are interpretable, concentrating resolution near sharp gradients. The framework also supports inverse problems, successfully recovering diffusion coefficients from sparse noisy observations using Bayesian optimisation. These results indicate that adaptive-basis PIELM formulations provide an efficient and stable alternative to gradient-trained neural PDE solvers and naturally extend to broader classes of differential equations.

Evaluating generated music requires modeling perceptual quality, technical audio quality, and prompt alignment. Existing methods often overlook signal-level defects, produce compressed quality scores, and miss fine-grained musical attributes in text prompts. We propose CloudEar, a pairwise framework for evaluating musicality and prompt alignment. It comprises three components: i) a Perceptual Expert for song-quality assessment; ii) a Diagnostic Expert for learned and signal-level quality analysis; and iii) a Cross-modal Expert for prompt-song alignment based on musical attributes. Experiments show that CloudEar outperforms the compared baselines in pairwise preference accuracy and score correlation.

In this paper, we study the rational realization of the gap-two product $K(\mathbb{Q},n)\times K(\mathbb{Q},n+2)$ as the classifying space $B\mathrm{aut}_1(X)$ for a simply-connected $\pi$-finite space $X$ with rational homology of finite type. We prove that $K(\mathbb{Q},n)\times K(\mathbb{Q},n+2)$ can be realized as $B\mathrm{aut}_1(X)$ up to rational homotopy equivalence if and only if $n=3,4$ or $4m+2$ for $m\geq 1$. Moreover, we determine all their minimal Sullivan models up to isomorphism. The rational homotopy type of such $X$ is unique for $n=3$ or $4m+2$ for $m\geq 1$; there exist infinitely many rational homotopy types of such $X$ for $n=4$.

Diffusion models generalize early in training and later reproduce individual training samples. Standard tests detect memorization only once one-shot generation produces near-copies, leaving a released model unaudited until its outputs fail. We show that memorization is encoded in the geometry of the learned energy landscape before it appears in generated samples, a state we call latent memorization. Using score divergence and basin volume, we find that localized basins form around training samples and separate them from held-out samples before the first memorized sample appears, with an onset that follows the same $O(n)$ scaling as the memorization time. We probe these basins with cyclic denoising, which repeatedly applies partial noising and denoising. Under the exact empirical score, we prove that cycling started near an isolated training sample recovers it and returns to it over any finite number of cycles with high probability. In trained models, cycling recovers training images from CelebA and CIFAR-10 checkpoints whose one-shot samples contain no copies, and at a CelebA checkpoint with 0.1% one-shot copies, 500 cycles raise the memorized fraction above 30%. Cycling also reveals degenerate attractors that match no single training image and fade as training proceeds, so residence in a basin does not by itself imply memorization. These findings hold on a Gaussian mixture, CelebA, and CIFAR-10 across optimizers, architectures, noise schedules, and training-set sizes, and extend to off-the-shelf Stable Diffusion v1.4, where the cycled conditional-unconditional divergence gap separates memorized from non-memorized prompts with an AUC of 0.944 and a TPR of 0.866 at 1% FPR. More broadly, what a diffusion model has memorized is a property of the geometry and stability of its learned distribution, and assessing it requires examining this structure rather than generated outputs alone.

Holistic and semantics-aware co-speech gesture generation has advanced rapidly, yet evaluation remains behind: objective metrics do not consistently reflect human perception, and semantic appropriateness remains difficult to quantify. We present a perceptually grounded and semantics-aware benchmark that combines standardized model comparison, human-centered metric validation, and fine-grained semantic evaluation. We first curate a list of 13 objective metrics covering different aspects, including distributional similarity, geometric fidelity, kinematic quality, cross-modal synchrony, and semantic appropriateness. For the semantic-appropriateness category, we propose a new metric, Semantic Gesture Preservation (SGP), which measures how far semantic gestures in the ground truth are preserved in the generated gestures. For this, we augment the BEAT2 dataset's annotations using a multi-modal LLM. We then conduct a perceptual study where 101 participants score generated gestures among five dimensions, including human-likeness, motion diversity, absence of animation errors, speech timing and content match. We systematically analyze objective metric–subjective score correlations. Unlike Semantic Score (SC), which shows no significant association with the evaluated perceptual dimensions, SGP is selectively aligned with speech-aware human judgments. We construct five target-specific composite metrics aligned with the subjective dimensions. These composites improve perceptual alignment across all five dimensions, with the largest gains for absence of animation errors and content match, indicating that complementary objective signals can better approximate human judgments than individual metrics alone. Overall, our results show that objective metrics require validation against subjective evaluations.

Reliable predictive uncertainty in Laplace approximations depends critically on the prior precision, yet selecting it requires a posterior sweep that is prohibitively expensive for neural networks with billions of parameters. Under the Maximal Update Parametrization ($\mu\mathrm{P}$), we derive a rescaling of the prior covariance that makes the selected precision stable as model width grows. This leads to $\sigma\mathrm{Transfer}$: we select the precision on a smaller model and zero-shot transfer it to the much larger model, i.e., without searching for the precision on the larger model at all. We show convergence of the prior kernel, posterior covariance, selected precision, and posterior-derived decisions under explicit conditions, and verify $\sigma\mathrm{Transfer}$ across regression, image classification, and Transformer readouts. For example, measured precision-sweep speedups reach $\sim 5000\times$ when transferring from width 128 to 4096 on MNIST, at a target-NLL degradation of $0.002$; transferring from a public 1B to 7B model gives a median search speedup of $\sim 2.3\times$ (up to $\sim 330\times$), with a mean measured target-NLL increase below $10^{-4}$ across ten tasks. The same posterior stability also enables transfer of acquisition, OOD-detection, and abstention decisions without constructing a target posterior.

Thermodynamic cycles are the foundation of energy conversion across natural and engineered systems, transforming heat into useful work. However, these cycles traditionally operate between fixed thermal reservoirs, restricting them to specific locations and temperature differences. Here, we introduce autonomous thermodynamic cycles enabled by robotic mobility and sensing, allowing robots to perform thermodynamic cycles by accessing spatially varying temperature fields. We experimentally realize this concept using multistable gas-filled capsules that circulate within the system across a thermal gradient. Our model reveals that rapid transitions in the capsules' energy states allow the system to operate as a mobile heat engine that harvests and stores energy. By linking the capsule-scale internal energy dynamics to the robot's large-scale navigation strategy, we optimize locomotion paths that balance motion cost and energy harvesting. These findings demonstrate that thermodynamic cycles can emerge when autonomous systems navigate their environments, offering an artificial analog of organisms that forage for energy across spatial resources.

Universal multimodal retrieval typically encodes a query once and ranks independently indexed items by embedding similarity. This design supports efficient search, but leaves the query representation unchanged even when retrieved items could help clarify the information need. We introduce the AutoRegressive Retriever (ARR), a multimodal retrieval model that learns both to select informative items and to use their content to refine subsequent retrieval. ARR alternates between retrieving an item and updating the query embedding, then uses the final embedding to rank the collection. Supervised fine-tuning teaches the encoder to use feedback through stepwise contrastive supervision. Reinforcement learning treats feedback items as actions and optimizes their selection using the final reciprocal rank of a relevant item. A query-side adapter enables this optimization against a fixed item index. ARR demonstrates strong retrieval performance on both in-domain and zero-shot benchmarks, outperforming the compared baselines on average. Further analyses show that feedback improves retrieval at inference time and that training with feedback also improves the initial query embedding, before any item is observed.

Online platforms contain growing numbers of bots, deceptive reviewers, and scam accounts that imitate legitimate users. Such camouflage blurs graph neighborhoods and behavioral attributes, making it difficult for graph neural networks (GNNs) to distinguish both well-disguised fraudsters and legitimate users. Across diverse GNNs, we observe overlapping errors on a shared hard region, suggesting the presence of latent fraud evidence that graph topologies and standard features fail to capture. Fraud-specific GNNs can mitigate particular graph pathologies, yet they still make limited use of heterogeneous evidence such as structured records, text, images, and audio; uniform multimodal fusion may also disturb nodes already handled reliably by the graph. We propose Evi-VN to learn and correct these shared blind spots rather than build another fraud detector. To our knowledge, Evi-VN is the first graph fraud detection framework to use feature isolated evidence chains to correct hard regions shared across GNNs. Its evidence chains connect behavior, content, and context across structured, textual, visual, and acoustic sources, helping expose camouflage that graph neighborhoods may miss. Crucially, Evi-VN selectively applies this evidence only to likely hard samples via virtual class nodes, preserving both the reliable predictions and the input design of existing GNNs. Shared hard regions also let Evi-VN enhance generic, fraud-specific, and unseen GNNs even with imperfect evidence models. Experiments across bot, fake-review, refund-evidence, and telecom-fraud tasks validate these advantages.

We present a spacetime that serves as a horizonless mimicker of extremal black holes. Unlike previously studied mimickers of black holes with non-degenerate horizons, whose geometries are of the wormhole type and consist of two asymptotically flat regions connected by a very long throat, the mimicker of an extremal black hole possesses a single asymptotically flat region at one end and an infinitely long throat at the other. In the throat region, the spacetime approaches the direct-product geometry $M_{1,1} \times S^2$, where $M_{1,1}$ is two-dimensional Minkowski spacetime and $S^2$ is the two-sphere. We investigate scalar-field dynamics and the fate of the Aretakis instability. Although Aretakis-like modes arise in a local analysis of the throat, they do not lead to a physical instability of the mimicker. A scalar perturbation initially localized in the throat gives rise, at late times, to a sequence of signals with a characteristic separation $t_{\rm delay}\sim 1/\lambda$, where $\lambda\ll 1$ is a deformation parameter. This timescale is parametrically larger than the echo time $t_{\rm echo}\sim \ln(1/\lambda)$ characteristic of non-extremal black-hole mimickers. We refer to this sequence as a long-delay signal train. Geometrically, the periodicity of the long-delay signals is associated with periodic geodesics on $S^2$. We then extend the construction to extremal Kerr. In this case, the throat region approaches a generalized product geometry involving $M_{1,1}$ and a two-dimensional surface $\Sigma_2$. The corresponding signals are expected to form a quasi-periodic signal train, reflecting the quasi-periodic geodesic motion on $\Sigma_2$. We also comment on the generalization to wormhole mimickers of non-extremal black holes and on the implications of these results for unitarity in the context of the AdS/CFT correspondence.

Deep reinforcement learning agents reach strong performance in real-time strategy games but can be brittle against opponents outside their training distribution. Separating strategic command selection from learned unit control allows different strategies to be selected for different opponents while reusing the same execution policy. This requires an executor that can follow different commands and measurable criteria for assessing whether it does so. We introduce a constrained command-conditioned Proximal Policy Optimization (PPO) policy, the executor, for MicroRTS, a real-time strategy environment. Discrete commands specify strategic objectives and behavioral requirements for economy, army composition, military posture, and worker policy over multiple environment steps; the executor determines the unit-level actions used to fulfill them. A Thompson-sampling bandit acts as the strategist, selecting command tuples from an estimate of the opponent's strategy built from in-game observations rather than opponent identity. In a controlled comparison with a flat PPO baseline trained with the same architecture, budget, curriculum and self-play league, the strategist-executor system wins significantly more often against three of the four strongest opponents on a training map, including the two strongest held-out ones (0.55 to 0.97 and 0.01 to 0.34), with no significant difference against the others.

Autonomous driving capabilities depend strongly on the distribution of scenarios encountered during training. Existing methods commonly construct or dynamically adapt training scenario distributions using surrogate criteria such as realism, difficulty, or risk. However, these predefined surrogates may misrepresent training value, leading to inefficient use of training resources. To address this limitation, we propose a Lamarckian evolutionary framework that replaces surrogate-based guidance with competition among candidate distributions. We formulate training strategy discovery as a multi-stage bilevel optimization problem and use Lamarckian evolution algorithm to approximate its solution. At the outer level, Darwinian crossover, mutation, and selection explore the scenario distribution space; at the inner level, policy learning acquires new capabilities, and Lamarckian inheritance transfers them to subsequent stages, allowing scenario distributions and policy capabilities to co-evolve. The resulting evolutionary trajectories reveal recurring stage-wise regularities among high-value distributions, characterized by capability accumulation through stage-wise challenge rotation. We further distill these regularities into a lightweight, reusable Lamarckian Training Strategy. Experiments show that, compared with the baseline, the complete framework reduces performance loss by up to 25.07%, while the lightweight strategy still achieves a 19.13% reduction. These results demonstrate that evolutionary competition can both discover effective training strategies and reveal reusable stage-wise patterns in how the value of training distributions changes with policy capability. Code is available on GitHub.

Inspired from some works on constructions of algebraic structures from other ones, we purpose to give some construction theorems on BiHom-Poisson conformal superalgebras which unify the notion of the Z2 -graded Poisson algebras, the BiHom-Poisson algebras and their conformal setting. So, we introduce BiHom-Poisson conformal superalgebras and show that they are closed under twisting. We then prouve that any regular BiHom-associative conformal algebra leads to BiHom-Poisson conformal algebra via the commutator bracket. Then, we point out that any BiHom-Poisson conformal superalgebra together with Rota-Baxter operator give rises to another BiHom-Poisson conformal superalgebra. Next, we show that tensor prod- uct of any BiHom-associative superalgebra and any BiHom-Poisson conformal superalgebra is also a BiHom-Poisson conformal superalgebra. Contruction from Hom-post-Poisson conformal superalgebras is also given.

The central challenge in underdetermined models with bounded uncertainty, such as in nonlinear design and estimation, is certifying the solution sets. Conventional solution methodologies, such as those based on Newton's method or on sampling-based uncertainty quantification, are either not applicable due to the underdetermined nature or do not give guarantees that all solutions have been found, assuming they converge. We addressed this issue for a problem that arises in nonlinear design, where a target steady-state box is prescribed and the parameters have to be found. We developed a trapezoidal linearisation method that rigorously encloses all solutions and combined it with a tractable linear programming method to compute the component-wise bounds. We showed that the resulting families of linear programs can iteratively contract an initial parameter region. A subdivision of the target state and the initial parameter region can improve the contraction and provide tighter enclosures. The trapezoidal relaxation gives a family of linear programs that can also be used for finding solutions for interval linear systems via the Oettli-Prager characterisation. We demonstrate the generality of the method through different applications, including nonlinear design in biomolecular circuits, a sensitivity analysis method, and in a compressed sensing context, and discuss the trade-off between enclosure tightness and computational cost.

On-policy distillation (OPD) supervises student-generated trajectories with token-level teacher signals. Its sampled-token variant avoids the cost of full-vocabulary probabilities. Yet we find that training on fewer tokens can outperform full-token OPD, challenging the intuition that more supervision improves learning. This motivates selecting tokens by learning value. Existing disagreement-based criteria ignore probability scale: tokens assigned negligible probability by both models, termed low-low tokens, can receive large log-ratio rewards and hinder learning. We propose DIAL-OPD, a token-selection method that bridges log-probability and probability spaces by weighting reward magnitude with the logarithmic mean of teacher and student probabilities. A parameter beta controls this weighting, and the highest-scoring tokens are retained. Across 4 teacher-student pairs and 7 mathematical reasoning benchmarks, we compare DIAL-OPD with 9 baselines. Retaining only 40% of tokens, it outperforms Vanilla OPD and its full-token variants, with mean accuracy gains reaching 5.25 percentage points over Vanilla OPD, and doubles AIME25 Pass@16 from 13.33% to 26.67%. It also achieves up to an 18% relative improvement in mean accuracy over the strongest token-selection baseline at matched retention ratios. With a 4B teacher, DIAL-OPD surpasses the strongest full-token baseline using an 8B teacher at both student scales, showing that effective supervision allocation can outweigh teacher scaling. Further analysis shows that moderate beta balances suppressing low-low tokens against preserving useful disagreements. Token-level evidence reveals that DIAL-OPD filters high-reward tokens with limited reasoning value while preserving supervision critical to reasoning correctness.

Large quantum computations require high-fidelity error-corrected memory and fault-tolerant logical operations. To achieve these with superconducting circuits, quantum processors will need many components operating with low error rates. In practice, fabrication of monolithic superconducting devices produces unavoidable heterogeneity in component performance, which the quantum computer must accommodate. We implement strategies to operate a large dynamic compass code on an array of 156 superconducting qubits arranged on a heavy-hexagonal lattice, making use of the entire monolithic quantum processor and redesigning our measurement schedule to exclude underperforming components. We demonstrate improvements of up to $35\%$ in logical error probabilities for a memory experiment by using a noise-informed decoder combined with strategies to exclude the worst-performing qubits and couplers, along with post-selecting on shots with a low probability of leakage errors. In addition to these memory results, we also observe performance gains of up to $56\%$ when these strategies are applied to measurement-based logic, demonstrated by stability experiments. We furthermore demonstrate high-fidelity fault-tolerant logic through lattice surgery. Through pre-selection filtering techniques, we can obtain Bell fidelities above $77\%$, and further logical gap post-selection using exclusive decoding increases these fidelities to above $97\%$. Our experiments demonstrate that high performance can be maintained in key elements of fault-tolerant quantum memory and logic when working on monolithic superconducting quantum processors with underperforming components, by using a suite of noise-informed quantum error correction strategies.

Dexterous teleoperation requires reliable human-hand state estimations. However, common low-cost motion-capture gloves and markerless trackers often exhibit biases that vary across users, glove fit, and recording sessions, degrading retargeting and demonstration quality. We present YOCO, a fast few-shot, fine-tuning-free calibration framework that corrects biased hand-pose streams from a small set of paired raw and target poses. Instead of optimizing a separate model for every operator or session, YOCO conditions a calibration HyperNet on the paired examples and predicts LoRA-style updates for a frozen MANO hand-estimation module, turning per-user calibration into a lightweight feed-forward adaptation step while preserving the geometric prior of MANO and the efficiency of a compact estimator. We train YOCO with synthetic drift augmentations on InterHand2.6M and evaluate on augmented InterHand sequences, offline real glove data, and dexterous teleoperation tasks. Across these settings, YOCO improves calibration efficiency, hand-state estimation quality and teleoperation performance compared with uncalibrated input and standard calibration baselines.

Facial attractiveness prediction usually assigns one overall rating, leaving the roles of shape, appearance, and viewing conditions implicit. We propose DisFace3DNet, which uses 3D component disentanglement to learn seven component reference scores from overall ratings with auxiliary weak semantic supervision, without human-labeled component targets. Designated 3D representations and image cues feed jointly learned routes for identity, skin, hair, light, background, expression, and pose. A constrained fit then combines five static and two signed dynamic scores into the overall rating, exposing each component's numerical contribution and supporting component-specific comparisons across images. On SCUT-FBP5500, DisFace3DNet achieves a Pearson correlation of $0.8904\pm0.0063$ (mean $\pm$ standard deviation across five folds) with average human ratings; its component terms reconstruct every held-out prediction to numerical precision. Skin, hair, and facial shape account for the largest component-wise prediction variation. Human evaluation supports the score directions for facial shape, skin, and hair; expression agreement is weaker. DisFace3DNet thus connects overall prediction to quantitative analysis of the facial and contextual cues entering each estimate.

Improving a long-horizon LLM agent means evolving the harness around a frozen model or training its weights. We let a self-evolving harness make the system stronger first, then cross seed and evolved harnesses with base and trained weights to learn which gains the trained model keeps and which still need the runtime. We show that the right lever can be read off the agent's failure composition: labelling failed trajectories by the first signal that fires separates process failures (blocked calls, loops, exhausted step budgets) from content failures (a delivered plan that is poor). Harness evolution repairs the former, the behaviour it instils can be trained into the weights, and content failures are what weight training is for. On DeepPlanning, a self-evolving harness loop lifts the held-out score of Qwen3.5-4B from 0.16 to 0.30 and of Qwen3.5-9B from 0.32 to 0.44; for 4B, held-out delivery rises from 55% to 90% while content failures are left for the weights. LoRA adapters trained on evolved-harness trajectories internalise the gain: under the original harness they add +0.13 on held-out tasks for both sizes; on 4B they stack with the harness to more than double the held-out score, and on 9B the adapter alone matches the full evolution line, cutting content failures from a quarter of trajectories to one in twenty. A placebo adapter trained on answer-shuffled trajectories falls below the base model. The loop transfers to WebArena-Lite (+0.09 on 117 unseen tasks), where the gain lives in what the model sees and adapters do not add to it. The result is a diagnose-then-intervene rule applied twice: read the failure composition to choose between harness and weights, then read what the accepted edits changed to decide which gains to train in. Scores are four-rollout means against fresh anchors, same-night except where marked, across eight models from six families and two benchmarks.

The deposition of epitaxial films of WO3 by hot-filament metal-oxide deposition using CO2 as a precursor was demonstrated. The films were obtained at a low growth rate of 0.25 nm/min. The optical properties of the film were assessed by variable-angle spectroscopic ellipsometry, indicating transparency across the visible spectrum and high absorption above 3 eV.

We suggest a method to generate time-varying Gaussian noise with controlled variance and controlled temporal correlation. This noise is used in several downstream tasks for temporal control and temporal coherence. The core technical idea is to phrase this problem as joint Monte-Carlo estimation of both a classic pixel reconstruction and estimation of variance using the concept of "sketching" from the database literature. We demonstrate that our method allows temporal control for downstream tasks with simpler and faster code than previous methods.

We derive the triangular prism equations (TPE) for near-group fusion rules of type $G+|G|$, where $G$ is a finite abelian group. We prove that spherical categorification with trivial Frobenius–Schur indicator over any field in which $|G|$ is invertible is equivalent to the solvability of the TPE system. For every cyclic group, we construct an explicit solution to the TPE system using hyperbolic gamma functions, yielding both a spherical category with negative simple-object dimensions and, after Galois conjugation, a pseudo-unitary category with positive dimensions. For scalar solutions with positive dimensions, we establish an exact singular-value formula and a uniform gap, which provide explicit sufficient criteria for unitarity. Finally, we show that the unitarity of the cyclic Galois-conjugated coefficients for arbitrary orders corresponds to a specialization of a real-multiplication conjecture implied by the order-one abelian Stark conjecture, revealing a deep connection between categorical unitarity and Hilbert's twelfth problem for real quadratic fields.

Automated interviewers and conversational agents are increasingly used in research, recruitment, customer service, and education. However, many existing systems rely on fixed question sequences and provide limited context-based personalization without considering participants' knowledge, which can lead to repetitive or irrelevant follow-up questions. Therefore, there is a need for an adaptive interviewing system that can adjust question depth while maintaining conversational continuity and semantic progression. To address this, an Evidence-Traceable Dynamic Interviewer Architecture is presented using a locally hosted Large Language Model (LLM), with the interview continuously adapted throughout the entire conversation based on the participant's responses and evolving context. The interviewer profiles participants' expertise in real time to generate knowledge-appropriate questions, well-articulated responses, and smooth transition messages that support conversational continuity. A five-module prompt-driven architecture and persistent interview-state record support these functions. The interviewer was evaluated with 246 participants. Expertise Profiling module (M3) showed 78.9% exact agreement with independently reported participant expertise, with a weighted Cohen's K of 0.80. Generate Iterative Questions module (M4) showed a strong expertise-complexity association (p=.79, p<.001), and participants reported high relevance (mean 4.41), engagement (mean 4.32), and satisfaction (mean 4.38), providing evidence that the architecture's adaptive components operated consistently with their intended functions while participants reported a positive interview experience.

Similar agent skills can share instructions but differ in their conditions of use. Query-based text selection may retain shared instructions and omit these distinctions. We introduce SkillContrast, a training-free selector that compares retrieved skills and retains their differing text with local context for a pretrained reranker. On 1,235 requests from SameCapRisk-Bench, it yields 54-72 more clean hits (requests that retrieve a helpful skill without its marked risky sibling) than TF-IDF query selection at identical per-candidate input lengths, across 2 retrievers and 2 reranker sizes. Length-matched component replacements identify differing text as the main contributor in the primary setting, with smaller, mixed context effects. Relative to full skill bodies, SkillContrast uses 51.1-58.8% fewer model-input tokens, with 10-18 fewer clean hits at 0.6B and matching or higher observed clean-hit counts at 4B. Candidate-relative differences thus complement query relevance in selecting compact reranking inputs.

The Dolgov-Kawasaki instability tests the local scalaron response in metric $f(R)$ gravity, but does not determine strong-field horizon dynamics. We separate these questions using $F=f_R$ and the Legendre potential $\mathcal U(F)=FR-f$. The scalaron restoring coefficient is $m_{\rm sc}^2=(F-Rf_{RR})/(3f_{RR})$, whereas exact spherical Wald-area transport identities cancel the scalaron Hessian. Their Einstein-frame interpretation distinguishes longitudinal kinetic focusing from potential-dependent cross-focusing. We prove that, at fixed constant-curvature background with tracefree matter, transport depends only on $(f,f_R)$, while the scalaron mass depends on the independently adjustable $f_{RR}$. Reissner-Nordström in $f(R)=R+\alpha R^2$ gives an exact discriminator: identical background transport coexists with opposite scalaron mass signs. A charged solution with varying $F$ and a cosmological check test the identities beyond this constant-$F$ sector. For a nonzero massive scalaron tail transmitted to a nondegenerate Cauchy horizon, a conditional fixed-background estimate gives a nonintegrable contribution to generalized entropy focusing. This estimate does not establish nonlinear mass inflation or a particular extendibility class. The results provide a layered framework for coupling regularity, background transport, scalaron stability, and nonlinear inner-horizon evolution.

In this paper, we treat the problem of determining when a sequence $\{c_n\}_{n=0}^{\infty}$ with the exponential generating function $F(t)$ satisfies the congruence $c_{n+\ell p^k}\equiv c_n \pmod{p^{k+r}}$ for large $n$ and when its canonical interpolating functions are locally analytic. This type of congruence is often observed for several number-theoretic or combinatorial sequences, such as Bernoulli numbers, Euler numbers, and Fibonacci numbers. Traditionally, such congruences are proved by using $p$-adic integrations. In this paper, we present another approach to this problem. Instead of using $p$-adic integrals, we investigate an algebraic structure of the set of generating functions and establish some conditions on $F(t)$ that are equivalent to or sufficient for the congruence and smoothness of the interpolating functions. We also provide concrete applications of our framework to Genocchi numbers, generalized Euler numbers, and so on, which are outside the scope of the typical $p$-adic integration method.

Coding agents are extended with agent skills, directories whose SKILL.md tells the model when and how to perform a task. Because skills come from independent sources (teams, developers, plugins, copied collections), an installed skill can be co-installed with a similar skill doing the same job, and the model picks between them by name and description alone. In a conflict, the installed skill loses core functions (e.g., a ban on touching git) because the similar skill runs instead or changes what it does. The task still passes, so benchmarks that check only task completion miss such cases. We present the first empirical study of such conflicts. From snapshots of 20,947 repositories, we mine 822,109 candidate similar-skill pairs, have an LLM judge a stratified sample of 3,754, and run 312 confirmed pairs on three models (6,368 runs, 169,294 tool calls, 542 agent-hours). We report five findings. (1) Conflict-prone skills are common: nearly one in four installed skills is co-installed with one that does the same job, and 37% of judged skills sit inside copied collections. (2) Most such pairs involve normative skills, then capability skills. (3) Without lowering task completion, a similar skill takes one in five runs from the installed skill, and runs that open the similar skill first lose over a third of the exclusive core functions that only the installed skill fulfills. (4) Install location decides which skill runs, listing order barely matters, and the final reply names the skill used in only 0.9% of substituted runs. (5) Conflicts are decided at the first skill read, almost always before any file is changed, and a pre-tool hook at that read restores fidelity on exclusive core functions to the level of runs that open the installed skill first. Benchmarks should thus score exclusive core functions, and platforms should guard the first read and show which skill ran.