Papers

GeoAI increasingly produces reusable Earth representation s, physical forecasts, multimodal systems, and reasoning a gents. Their progress exposes two distinct limitations. Geo graphic completeness asks whether the represented world ex tends beyond readily observed land surfaces and atmospher ic fields to oceans, biogeography, economies, institutions, and human agency. Geographic intelligence asks whether model outputs preserve place, scale, relations, process, un certainty, and the limits of valid inference. The first con cerns what exists in a model; the second concerns what may responsibly be claimed about it. This critical integrative review argues that geography provides the organizing gram mar that connects these dimensions. Seven structural gaps, propositions, and corresponding review questions translate the argument into testable requirements. The resulting re search agenda advances Living Geospatial Models as federat ed, continually updated systems that couple specialist Earth and human-domain models through shared geographic iden tity, support, relations, provenance, and uncertainty. The objective is not a single universal network, but geospatial intelligence that can explain connections and change, antic ipate plausible futures, and support accountable decisions across places and scales.

Higher twists in deep-inelastic scattering (DIS) and related hard scattering processes provide a unique window on nonperturbative QCD dynamics, encoding quark-gluon correlations and multiparton interactions beyond the leading-twist parton model. We present an overview of the theoretical foundations of higher twists in QCD, based on the operator product expansion, and discuss their intimate connection with quark-hadron duality in the transition between the resonance and scaling regimes. We review the phenomenology of higher-twist effects in unpolarized and polarized DIS, emphasizing their extraction from precision data through modern global QCD analyses that simultaneously determine both leading-twist parton distribution functions and higher-twist contributions. Finally, we discuss recent developments in the study of higher twists in semi-inclusive and exclusive reactions, and conclude by highlighting future opportunities to study QCD dynamics beyond leading twist at Jefferson Lab and the Electron-Ion Collider that promise to deepen our understanding of hadron structure.

We construct a restricted Boltzmann machine (RBM) whose visible input is a quantum state rather than a classical configuration. Each hidden unit carries a trainable quantum template prepared by a parametrized circuit and converts its overlap with the input into a feature. Treating quantum states as high-dimensional continuous visible objects creates nontrivial normalization and scaling problems. We regularize the continuous likelihood and derive two controlled high-dimensional limits, yielding a Hopfield-type network with continuous Hilbert-space patterns and a data-augmented Gram likelihood. The resulting algorithms are compact and use trainable circuit-prepared templates as measurement intermediaries between quantum data and classical optimization. Numerical simulations across several many-body systems demonstrate effective quantum-phase recognition and multicomponent feature extraction.

Multicomponent order can melt in stages, leaving a composite order after its primary constituents become short ranged. We study this possibility for commensurate three-$Q$ loop-current order on the kagome lattice. Large-scale cluster and parallel-tempering Monte Carlo simulations reveal direct and two-stage melting regimes in an effective fixed-amplitude sign model. In the latter regime, translation-sector domain walls proliferate before chirality-changing walls, restoring lattice translational symmetry while preserving long-range time-reversal-odd order. The primary $M$-point correlations are short ranged in this intermediate phase. The two-stage regime begins when the lowest-energy chirality-changing wall is only about $12$–$13\%$ more costly than a same-chirality translation wall. Finite-size scaling of a stable amplitude-resolved Ginzburg–Landau theory shows that the phase survives amplitude relaxation. Our results establish a quantitative domain-wall criterion for vestigial loop-current order and a fluctuation route to time-reversal symmetry breaking without long-range loop-current Bragg order. This separation provides a possible thermodynamic framework for time-reversal-odd responses recently reported above the critical temperature for conventional charge-density-wave ordering in kagome metals.

Business analytics education requires diverse datasets to support different learning objectives, student backgrounds, and analytical tasks. Real-world data can be difficult to obtain and offer limited flexibility for adapting a case to a particular course. Even when suitable data are available, instructors must investigate the patterns, verify the results, and prepare assignments and reference solutions, requiring substantial time and effort. The use of large language models (LLMs) introduces an additional concern about training data contamination. Widely used public datasets often have extensive tutorials and worked analyses that models may have encountered during training. Students may therefore receive explanations drawn from existing analyses without practicing how to investigate unfamiliar data in collaboration with AI. This paper presents DataCanvas-EDU, an agentic framework for instructor-guided synthetic data generation in business analytics education. Instructors specify teaching goals and intended patterns through conversation, while an AI agent writes generation code, checks the resulting data, and prepares assignments, reference analyses, and rubrics. Four phases, Plan, Create, Verify / Test Analysis, and Evaluate, organize the process and support instructor review and revision. The framework is intended to simplify case preparation while creating opportunities for students to investigate newly designed patterns with AI. We illustrate the approach with WindowDash, a food delivery case containing 15,000 orders and nine designed patterns. DataCanvas-EDU is packaged as a reusable AI Agent Skill for compatible agent environments, with the package and installation instructions available at https://github.com/BANG23333/datacanvas-edu

Measuring complexity from a model's own code is biased by failure: a hard prompt can produce a short, broken program that looks simple. We instead score each prompt's structure on six dimensions from the prompt alone, never from generated code or test results. We draw 5,000 Python prompts across six bands of a preliminary single-rater score, and four out-of-panel LLM judges rescore every prompt (composite ICC(2,1) = 0.872). Twenty-one models answer every prompt (105,000 generations), and an independent LLM auditor, checked against known-answer cases, reviews each unit-test verdict. Averaged over models, pass rate has a nonmonotone breakpoint at composite 14.0: 83.4% at or below, 90.1% above. That jump is not a law of difficulty: with task-type fixed effects the breakpoint stays at 14.0 but the adjusted jump shrinks from 6.8 to 0.4 points, and neither of the benchmark's two prompt sources reproduces it on its own. Nineteen models pass more often above their own breakpoint and two less often; one of those declines comes from API calls that returned nothing. In post hoc follow-up, Kimi K2.5 shows the clearest decline, at 14.25, under a prompt-source control and within the later source alone. Among failed generations with measurable output complexity, 25.0% pair a prompt composite above 8 with output complexity of at most 10, twice the share among passing ones. The pooled breakpoint moves to 11.25 on raw test outcomes. Human agreement with the index is moderate, paraphrase and cross-language rescoring preserve its ordering, and overidentification tests reject the six dimensions as instruments, so we make no causal claim. The contribution is a prompt-side way to locate where each model's pass rate changes and to test how much that depends on the prompt mix and on how success is scored.

Modern applications generate massive volumes of raw telemetry data, but translating those noisy, heterogeneous event streams into actionable business insights remains a fundamental challenge. Data engineers and analysts expend substantial effort reconciling semantic discrepancies, hand-crafting parsing logics, and maintaining fragile mappings between raw data and business KPIs. In this paper, we present an end-to-end framework that fully automates the construction of a business semantic layer from application raw logs. Our approach introduces a two-stage semantic abstraction: first, high-level business features are identified via LLM inference augmented with domain-specific industry knowledge; second, fine-grained business nodes are derived through a structured pipeline comprising data refinement, hybrid retrieval, multi-stage filtering, semantic clustering, and canonical naming. Evaluation on production-scale telemetry demonstrates that our system improves human-assessed semantic quality from 50 to 80+ on a 100-point scale, reduces maintenance effort by 80%, filters out 74% of noise, and achieves 0.87 Cohen's kappa via an integrated LLM-as-Judge evaluation, enabling continuous, scalable quality assurance. Overall, our work distinguishes itself from prior work by addressing the novel problem of business semantic layer induction from raw telemetry, operating without labeled training data or manual rule engineering.

The coercivity of rare-earth permanent magnets originates from the crystal field acting on localized 4f electrons, yet how grain boundaries modify the underlying single-ion Hamiltonian remains largely unknown. Here we determine the 4f crystal field in bulk and grain-boundary environments of Nd2Fe14B using embedded multireference electronic-structure calculations for the substitutional series Ce, Pr, Nd, Gd, Tb, and Dy. Grain-boundary distortion produces a crossover across the lanthanide series: the crystal field weakens by up to 36% for light lanthanides but strengthens by about 25% for heavy lanthanides, with Nd marking the crossover. The ground-state doublet of Dy becomes more isolated and axial, whereas Ce exhibits a collapsed low-lying excitation that suppresses anisotropy. The local easy axis rotates from the bulk c axis toward the basal plane, identifying grain-boundary sites as favorable nucleation centers for magnetization reversal. These results provide an atomistic basis for heavy rare-earth grain-boundary diffusion and furnish transferable single-ion parameters for spin-lattice simulations.

Dexterous food manipulation requires control under deformation, occlusion, and uncertain contact. We present TacSushi, a tactile-grounded, Cosmos3-based world-action policy that learns from recorded future consequences while acting on current observations. The backbone encodes current RGB, language, and hand state, and feature-wise gated fusion incorporates fingertip tactile features into the action representation. During training, a decoder conditioned on demonstrated action chunks predicts logged future visual observations, task progress, relative contact risk, and tactile summaries; this decoder is removed at deployment. Failed trials provide consequence supervision, but their actions are excluded from imitation. We train TacSushi on 340 successful and 50 failed real-robot trials and compare six methods in 600 separate rollouts across three in-distribution tasks and two out-of-distribution ingredient variants. To assess food quality beyond a single geometric threshold, we score terminal outcomes using an anchored visual-quality protocol that equally weights five human ratings and three vision-language-model ratings per rollout. Full TacSushi achieves 68.3% average in-distribution success and 37.5% out-of-distribution success, compared with 36.7%/10.0% without future-consequence supervision and 25.0%/17.5% with direct tactile concatenation in place of gated fusion. These comparisons support complementary benefits of feature-wise gated tactile fusion and training-only predictive supervision.

We prove that every countable meet-continuous lattice is Scott sober. For any family of such lattices, the Scott topology on the product equals the product of the factor Scott topologies, and the product Scott space is sober. These results answer affirmatively Questions 7.1 and 7.2 of Xu (arXiv:2609.18032v1), extending the countable-frame results beyond finite distributivity. A diagonal argument on meet coordinates extracts directed punctured intervals from nonprincipal ideals. Join translates of these intervals form a countable family detecting Scott openness and yield Scott open rectangles by successive finite choices. We also show that the cardinal spectrum of Scott non-sober meet-continuous lattices is upward closed and, under the Continuum Hypothesis, consists of all uncountable cardinals.

Tensor programs, as used in deep learning models, are a prime target for optimization, as small performance improvements can have a large impact across training or inference workloads. However, such optimizations are complicated and can produce subtle bugs. Traditionally, correctness is assumed when differential testing against a reference on random inputs fails to reveal bugs. However, the inputs to these programs are massive tensors, and finding bugs can require generating extremely low likelihood inputs with precise relationships among their values. We propose a novel way to find bugs more consistently by flipping the quantifiers. Rather than generating a single input and checking all output tensor locations for equivalence, what if you could check a single output tensor location's equivalence for all inputs? We implement this idea in a system, \dirigo, by using a novel symbolic execution strategy. We demonstrate that \dirigo can find bugs effectively in a public dataset of 6,988 AI-written CUDA kernels that are all marked correct by differential testing. Of these, \dirigo finds 600 kernels that are actually buggy, and finds 97.3% of those bugs within two minutes.

Understanding humans over long horizons requires agents to infer not only what people need in the moment, but also how routines form, why they repeat, and when they change. We introduce SimLife, a scalable platform for simulating long-term household life with rich visual observations, ground-truth action logs, and synthetic dialogues with audio. Built on SimLife, SimLife-BP evaluates long-context pattern understanding: the ability to infer latent behavioral rules from weeks or months of everyday observations. The benchmark contains 106 episodes averaging 15.49 hours and 38.57 in-game days, and 1,439 question-answer pairs. Each task probes direct, counterfactual, noisy, and inverse reasoning under different levels of rule hints. Evaluating frontier models and architectures, we find that current models often achieve surface-level prediction without comprehensive rule understanding, rely on frequency-based heuristics rather than if-then reasoning over evidence, and struggle to adapt when behavioral patterns change. These findings suggest that long-context pattern understanding remains a major bottleneck for future embodied agents, while SimLife opens a broader space for studying memory, personalization, adaptation, and long-horizon planning in everyday human-AI interaction.

We study harmonic maps \(F:\D\to G\) into bounded domains in real Hilbert spaces, prescribing \(F(0)\) and \(dF_0(\R^2)\) when \(dF_0\) is nonzero and conformal. We prove a target-independent identity for the Möbius-weighted Hilbert pairing. After normalization, the pairing is affine in \(\|dF_0\|\) with positive slope, yielding an exact equivalence between the derivative extremal problem and a boundary-pairing problem. For a round affine section, this gives a necessary and sufficient integral criterion for the Möbius parametrization to be extremal. A supporting-hyperplane condition guarantees the required integral inequality and characterizes equality. Examples show that roundness alone is insufficient and that the supporting condition is not necessary. For unit balls of real Hilbert spaces of dimension at least two, including infinite-dimensional spaces, we obtain the sharp prescribed-value Schwarz-Pick estimate, all equality cases, and quantitative \(L^2\) boundary stability. We also prove a Cayley-Klein contraction under pointwise distortion. For \(K\geq1\), let \(M_K\) denote the supremum of \(L_F(0)\) over harmonic maps \(F:\D\to\B_H\) satisfying \(F(0)=0\) and \(0<\ell_F(0)\leq L_F(0)\leq K\ell_F(0)\), where \(L_F(0)\) and \(\ell_F(0)\) are the maximal and minimal stretchings at the origin, respectively. We determine \(M_K\), identify the unique optimizing parameter, and characterize all extremals. The function \(K\mapsto M_K\) is strictly increasing, with \(M_1=1\) and \(M_K\to4/\pi\) as \(K\to\infty\).

Let $\mathpzc K$ be an arbitrary commutative ring containing an invertible element $\varepsilon$. Let ${\mathcal H}_{{\!\vartriangle\!}}(r)_{\mathpzc K}$ be the extended affine Hecke algebra of type $A$ with Hecke parameter $\varepsilon$, let $\Omega_{\mathpzc K}^{\otimes r}$ be the affine tensor space, and let ${\mathcal S}_{{\!\vartriangle\!}}(n,r)_{\mathpzc K}$ be the corresponding affine quantum Schur algebra. We first prove that the natural right action of ${\mathcal H}_{{\!\vartriangle\!}}(r)_{\mathpzc K}$ on $\Omega_{\mathpzc K}^{\otimes r}$ is always faithful. Assume further that $\mathpzc K$ is a field of characteristic $0$ and that $\varepsilon$ is not a root of unity. We prove that, for any $n\geq 2$, the natural algebra homomorphism $\xi_r:{\mathcal H}_{{\!\vartriangle\!}}(r)_{\mathpzc K}\rightarrow\operatorname{End}_{{\mathcal S}_{{\!\vartriangle\!}}(n,r)_{\mathpzc K}}(\Omega_{\mathpzc K}^{\otimes r})^{\mathrm{op}}$ is an isomorphism. This proves Conjecture~3.8.8 of \cite{DDF}. As an application, we prove the conjecture formulated in \cite[5.2.4]{DDF} concerning the center of the affine quantum Schur algebra. We also prove that ${\mathcal S}_{{\!\vartriangle\!}}(n,r)_{\mathpzc K}$ is left and right Noetherian whenever $\mathpzc K$ is a Noetherian commutative ring, which verify a conjecture in \cite[Rem. 1.7]{DY}.

Coding-agent benchmarks are built for broad and comprehensive comparisons, not frequent development decisions. Individual runs vary, full suites are expensive, and the benchmark harness may differ from the harness used in practice. In a resampling analysis of DeepSWE's published trials, only 19.5% of tasks (22 of 113) had a fifth-percentile Pearson correlation of at least 0.50 with full-benchmark performance. The paper presents DeltaSelect, an open-source method that identifies tasks whose one-run results consistently track full-benchmark performance using Pearson correlation, maps fractional verifier results to a common score using linear regression, and selects a fixed task set within a dollar budget. DeltaSelect is intended for repeated baseline-versus-candidate comparisons during development, not model rankings. In a gpt-5.6-luna low-reasoning case study, DeltaSelect was used to revise custom skills and instructions. Across 13 evaluations, the recorded cost was USD 27.86 at rates published August 16, 2026. The adopted version cost 58.1% less than the initial version (USD 1.75 versus USD 4.18; p=0.008), while the calibrated score was higher (42.36% versus 36.46%; published-analog variance p=0.326).

This empirical study is an independent reproduction of the dissociation Zhao reported in 2026. The shape of a large language model's chain-of-thought entropy trajectory predicts whether the final answer is correct, while the magnitude of its total entropy drop does not. The dissociation merits reproduction because the magnitude half rests on a single 300-problem run with one model at one seed, while the shape half was reported at full scale on both benchmarks and on a second model family. Registered at OSF before any confirmatory run, the reproduction crosses the complete GSM8K and MATH-500 benchmark test sets with four open-weight models including one reasoning-distilled model of a kind the original did not test. The shape signal replicates. The magnitude signal divides by setting. On the anchor model the accuracy gap between monotone and non-monotone chains is +9.6 percentage points on GSM8K and +27.5 on MATH-500, while the rank correlation of the total entropy drop with correctness is -0.018 on GSM8K and +0.414 on MATH-500. On the reasoning-distilled model the binary form of the shape signal fires on about one chain in a hundred, too few to estimate the registered contrast, while the graded violation count remains predictive there. In an exploratory comparison the final-step entropy alone outperforms the binary shape flag in all eight model-by-benchmark cells by ROC area, and in six or seven by the risk-coverage area the original reports, depending on an integration range the original does not state. The study contributes a reproduction of the shape signal at full test-set scale under seven documented protocol differences, a map of the settings where the magnitude signal holds and fails, and measurements of four protocol dependencies the original does not report.

Hydrogen is known to form stable compounds with a variety of simple molecular solids under high pressure. However, ammonia hydride has not been experimentally observed. Here, through a series of laser-heating diamond anvil cell (LHDAC) experiments, we observed the transparent ionic ammonia transformed into an opaque phase above 150 GPa and 1000 K. Raman spectroscopy reveals a pronounced structural change, accompanied by the emergence of two distinct asymmetric H$_2$ vibrons ($\nu_1$ and $\nu_2$). A new ionic phase produced following thermally induced dissociation and hydrogen reorganization in hot dense ammonia. The combination of experimental results and first-principles calculations identify this phase as the theoretically predicted ionic $P4_12_12$ phase of NH$_7$ , which consists of NH$_4^+$, H$^-$and H$_2$ units. Our results suggest that the formation of ammonia hydrides follows a thermodynamic pathway distinct from those of other H$_2$-containing mixtures, revealing a new ionic transformation pathway driven by hydrogen reorganization in hot dense ammonia.

We study the Friedrichs Laplacian associated with the pullback of the round metric on \(\mb P^1\) by a nonconstant meromorphic function \(\varphi:X\to\mb P^1\) on a compact Riemann surface. For arbitrary ramification profiles, including several ramification points over the same branch value, we prove the local formula \[ \operatorname{Det}_{\zeta}(\Delta_{[\varphi],\mc F}) =C\,\det\operatorname{Im}B\,|\tau_B|^2 \prod_{k=1}^N\rho(z_k,\overline{z_k})^{c_k}. \] The zero eigenvalue is omitted. Here \(B\) is the period matrix, \(\tau_B\) is the local Bergman tau-function, \(z_k\) are the branch-value coordinates, \(\rho(z,\overline z)=4(1+|z|^2)^{-2}\), and \(c_k=\frac1{12}\sum_j(n_{kj}-n_{kj}^{-1})\), where \(n_{kj}\) are the ramification indices over the \(k\)-th branch value. The constant \(C>0\) is independent of the Hurwitz coordinates, and \(\det\operatorname{Im}B\) is taken to be \(1\) in genus zero. The proof combines smooth trivializations and trace-norm variation of resolvent powers with matrix comparison to spherical conic models. The Davies–Gaffney estimate provides the required uniform high-energy control, while the zero-energy terms are identified through the Schiffer bidifferential and Rauch variational formulas.

This paper presents novel approaches to tackle two key challenges in topology optimization problems with buckling constraints: determining how many eigenvalues to aggregate and identifying the eigenvalue modality at the optimal design. We demonstrate the mathematical inconsistencies that arise when choosing an arbitrary fixed number of eigenvalues for aggregation. Specifically, if the multiplicity of the critical eigenvalues is smaller than the chosen subset size, coalescence with higher-order eigenvalues can occur. Neglecting these during aggregation causes incorrect sensitivities, while simply increasing the preselected eigenvalue count unnecessarily raises computational costs. To resolve this issue, we propose an approach that dynamically determines the exact number of eigenvalues required at each optimization iteration. The proposed approach reduces computation time significantly while maintaining competitive performance relative to the conventional method across the numerical experiments presented. Additionally, accurately predicting modality at the optimal point is crucial for understanding the buckled mode shapes of optimized designs. A new optimization formulation is proposed using the difference between eigenvalues to capture the true eigenvalue modality. This formulation is first validated on a classical 1D clamped column, successfully predicting both the bimodal solution and the optimal eigenvectors. The approach demonstrates that the optimal solutions for the wall reinforcement and shear-loaded hinged plate problems for the given set of parameters are trimodal and tetramodal, respectively.

Recent measurements of cosmic expansion have renewed interest in dark-energy scenarios in which the effective equation of state exhibits phantom-like evolution and may cross $w=-1$. Such behavior, however, does not require a fundamental phantom field: in coupled dark-energy-dark-matter~(CDEDM) models, energy exchange between a canonical scalar field and cold dark matter, happens Lagrangian labels, can reproduce the same effective equation of state evolution as that of phenomenological $w_0w_a$CDM model. We show that this microscopic interaction leaves distinctive, testable signatures in structure growth by forming a two-fluid system in which only cold dark matter feels the scalar-mediated fifth force (and an associated drag term), while baryons remain uncoupled. When combined with neutrino-free streaming, this setup generates a characteristic coupling, neutrino-mass degeneracy, whose leading scaling $\sum m_\nu \propto f_c^2 \alpha^2$ follows analytically from the two-fluid growth equations. Using DESI DR2 BAO, CMB distance information, ACT DR6 lensing, redshift-space distortions, and three supernova compilations, we find that this scaling is recovered for both exponential and inverse-power-law potentials. We further show that the dominant contribution to the growth response arises from the coupling-induced modification of the background evolution, with the fifth force enhancing growth and the drag partially counteracting it. Finally, the interaction induces a running dark-matter mass, changing it at recombination by $4.3\%$–$5.5\%$, so CMB distance calculations must account for the evolving dark-matter density. These correlated growth and recombination effects provide a route to distinguish interaction-driven phantom crossing from purely kinematic dark-energy parametrizations.

Retrieval-Augmented Generation (RAG) is increasingly used to ground large language model (LLM) outputs in scientific literature. However, in open-ended literature exploration, the evidence context used for generation is often produced through hidden retrieval, reranking, assessment, and filtering steps. Users may receive retrieval summaries without knowing how the system constructed the evidence context, which evidence units were retained or discarded, or whether potentially useful evidence was excluded before synthesis. We present FootprintRAG, an LLM-agent-powered visual analytics system for evidence context refinement in RAG-based scientific literature exploration. The core idea is to treat the RAG evidence context as an explicit, inspectable, and revisable analytical object before generation. FootprintRAG parses scientific literature into text and figure evidence units, expands an initial query into parallel query variants, retrieves and assesses evidence across iterative rounds, and surfaces ERS-ranked supplementary candidates from the corpus-level evidence space. Through coordinated views, the system connects retrieval trajectories, evidence-state revision, and provenance-aware summary generation into a user-steerable workflow. We evaluate FootprintRAG through two case studies, a user study, and a workflow-level comparison with representative RAG systems. The results show that FootprintRAG helps users compare retrieval directions, revise candidate evidence, recover potentially overlooked evidence, and trace generated summaries back to supporting evidence units. FootprintRAG is available at https://github.com/meteorshowering/FootprintRAGVA.git.

Adapting robots to new objects and tasks requires interaction experience that can be costly to obtain. We present WorldContact, a contact-centric world model for deformable-object manipulation, constructed from a limited set of high-quality trajectories to generate additional training data efficiently. It predicts object dynamics using larger time steps than the source numerical simulator, which requires small integration steps to resolve rapid motion and prevent interpenetration. We evaluate WorldContact across 16 shopping-bag manipulation tasks. State-rollout measurements on a single H100 GPU show a $10\times$ speedup over the source simulator, excluding rendering and disk I/O. We use the generated data to fine-tune an existing vision-language-action policy and deploy it directly on a real robot. In bag lifting, the same policy achieves 65% single-attempt success when fine-tuned on source simulation data alone, compared with 95% when fine-tuned on the dataset expanded with WorldContact. These results support efficient data generation with WorldContact for robot policy adaptation.

Human pairwise comparisons provide a reference for evaluating large language models (LLMs), but collecting sufficient judgments for each new release is costly and time-consuming. LLM judges offer a scalable alternative, although their comparisons may differ systematically from human preferences and across judges. We study the ranking of a new model that has received LLM-judge comparisons but no human comparisons. We propose ANCHOR (ANchored Comparisons for Human-reference inference with Orthogonal Riesz correction), which uses historical human and LLM comparisons to learn judge-specific sensitivities to human score differences and feature-dependent judge biases. These estimates are then used to infer the new model's human-reference score from its judge comparisons. The framework allows the feature distribution to change between historical and new-model comparisons. For inference, we construct a Neyman-orthogonal estimator through a joint Riesz correction that removes the first-order effects of estimating the historical human scores, judge sensitivities, and bias functions. We establish identification, convergence rates, and asymptotic normality with consistently estimable variance, and show that ANCHOR attains the semiparametric efficiency bound. Simulations demonstrate gains in score estimation and ranking accuracy. On Chatbot Arena, ANCHOR achieves the lowest score RMSE and insertion MAE among competing methods, with narrower score intervals on average.

What kind of thing is a “theory of mind”? We propose to formalize theories of mind as domain-specialized programming languages, which can be used to reason about the mental states of other agents. Our proposal builds on the longstanding idea that thinking is akin to programming in an internal “language of thought.” But rather than positing a single general-purpose language for all of thought, we posit a collection of domain-specific languages of thought, whose respective syntaxes and semantices encode the theories of various domains. We make this idea concrete in the domain of intuitive psychology using a real-world programming language called memo, which is specialized for theory-of-mind reasoning via domain-specialized syntactic constructs like “knows,” “wants,” and “thinks.” In our view, using one's theory-of-mind to think about a social situation is analogous to using memo to write a program that models that situation. Through a series of worked examples, we show how formally representing a theory of mind as a memo-like programming language can lend insight into a variety of theoretical issues in theory-of-mind research: (1) how a single, fixed intuitive theory can be used to reason about social situations with unbounded structural variation; (2) how a modular, domain-specialized, and informationally-encapsulated system for social cognition might interface with external world knowledge, as well as other cognitive systems like intuitive physics; and (3) how different theories of mind, such as those of children and adults, differ, what exactly is gained as theories grow over the course of development, and how that growth might occur.

In this article, we give various real-variable properties of local Muckenhoupt matrix weights $W$ and establish the quantitative boundedness of several operators on local matrix-weighted Lebesgue spaces $L^p(W)$, including local (fractional) maximal operators, local fractional integral operators, local Haar square functions, and Calderón–Zygmund operators with exponential decay. For the local maximal operators, we obtain the sharp quantitative bounds when $p\in(1,2]$, while, for local fractional integral operators, we obtain the quantitative bounds matching the global best known exponents, whose scalar case is known to be sharp. The key used strategies include giving a new extension property (which can clarify their relationships with global ones) and an optimal scale lifting property (which can balance the locality of weights and operators under consideration) of local matrix weights. As an application, we establish the quantitative boundedness on $L^p(W)$ of the Riesz transform associated with Schrödinger operators $-\Delta+m^2I$ with $m\in(0,\infty)$ being large enough, whose quantitative bound when $p=2$ is precisely $[W]_{\mathscr{A}^{\operatorname{loc}}_{2}(r)}^{\frac 32}$.

Full-duplex speech models listen and speak at once, promising always-on assistants. Yet they must also decide when they should speak. Human listeners speak when addressed or when the speaker stops, but also self-select to correct a false claim, supply a missing word, or warn of danger. We ask whether full-duplex models do the same. To separate the reason to speak from the opportunity, we construct context-matched English monologues in which only the trigger utterance varies within a topic, define 10 conditions from turn-allocation rules, and compress inter-word pauses to limit opportunities created by silence. Across five model families, being addressed and silence are far more reliable triggers than false facts or hazards. Frame-level text-token probabilities in Moshi and PersonaPlex are lower for false facts than for Neutral when averaged over the first 2\,s after trigger end. Pauses or permission to interrupt do not close this gap either. Given the floor, Moshi and PersonaPlex answer most direct questions, yet the proportion of non-empty false-fact replies that challenge the claim is only .14–.15, and the proportion of hazard replies that warn of danger is .04–.07. This paper thus identifies a gap in both speech initiation and response content. Closing it requires genuine content understanding and intervention decisions grounded in it.

Let $P$ be a group, $L(P)$ be the free multiplicative Lie algebra with normal subgroup $\Gamma_n(P)$ generated by Lie bracket “commutators” of weight $n$ and $\{ \gamma_n(P) \}$ be the lower central series of $P$. We prove that $\Gamma_n(P) \simeq \gamma_n(P)$ for arbitrary $n \geq 1$ and $P$ a finitely generated parafree group such that $H_2(P, \mathbb{Z}) = 0 = H_3(P, \mathbb{Z})$ (e.g. $P$ satisfies the Strong Parafree Conjecture), in particular Ellis's conjecture holds i.e. the above isomorphism holds for finitely generated free group $P$ but this easily implies it holds for any free group.

We consider the elastic wave equation in three-dimensional isotropic medium with up to quadratic nonlinear terms. We show that five out of the six elastic parameters can be uniquely determined by boundary measurements under the assumption that the wavespeeds are non-trapping, while the last one can also be determined in a generic setting.

The Kemeny rule aggregates multiple strict rankings into a single strict ranking that minimizes the sum of its distances from the input rankings. The resulting optimization problem, called the Kemeny problem (KP), is a special case of the linear ordering problem (LOP). The Kemeny rule satisfies several desirable properties in social choice theory, including the extended Condorcet criterion (XCC). Ando et al. strengthened this result by introducing the strong Condorcet criterion (SCC) and showing that it holds for every optimal solution to an arbitrary LOP instance. Yoo and Escobedo extended the Kemeny rule to rankings with ties and showed that the resulting rule satisfies the non-strict extended Condorcet criterion (NXCC). This criterion gives a condition under which one candidate must be ranked strictly above another in every optimal solution. In this paper, we introduce the non-strict strong Condorcet criterion (NSCC), a counterpart of the SCC for rankings with ties, and show that it holds for every optimal solution to an arbitrary instance of the linear ordering problem with ties (LOPT). We also establish a complementary structural property that gives conditions under which two candidates must be tied in every optimal solution to an arbitrary LOPT instance.

This study developed and evaluated a deep-learning-based perception framework for selective robotic cotton picking. The dataset contained 1,008 annotated field images collected using three cameras under varying natural lighting and weather conditions. Object-detection models from the YOLOv8 through YOLOv13 families were evaluated using their default configurations, while segmentation performance was assessed using YOLOv8-seg, YOLOv11-seg, YOLOv12-seg, the Segment Anything Model (SAM), SAMv2.1, FastSAM, and Grounded-SAM with the Recognize Anything Model (RAM). Among the detection models, GELAN-s achieved the most favorable balance between mean average precision (mAP) and inference speed, obtaining an mAP of 86.1%, precision of 81.6%, recall of 76.6%, and an F1-score of 79.0%, with an average inference time of 42.3 ms per image. Among the direct segmentation models, YOLOv12-m-seg provided the most favorable balance between AP@0.5 and FPS, achieving a segmentation AP@0.5 of 83.7% with an inference time of 20.4 ms per image. In the detection-prompted segmentation approach, bounding-box prompts generated by GELAN-s improved the localization of cotton bolls for SAM and SAMv2.1, while SAMv2.1 Tiny consistently outperformed FastSAM and Grounded-SAM with RAM. In the area-based evaluation against manually annotated segmentation masks, YOLOv12-m-seg achieved an $R^2$ value of 0.966, compared with 0.860 for GELAN-s + SAMv2.1 Tiny. Field experiments conducted using a UR5e robotic manipulator, a custom end-effector, and a ZED2i stereo camera further validated the effectiveness of the YOLOv12-m-seg model for real-time cotton boll detection, segmentation, and selective picking under varying confidence levels. These results demonstrate that YOLOv12-m-seg provides an efficient perception model for robotic cotton harvesting and has strong potential for field deployment.