Papers

General-purpose multimodal foundation models are increasingly capable of directly controlling robots, yet improving their manipulation capabilities through autonomous interaction remains challenging. A key challenge to such self-improvement is learning from failures in complex manipulation tasks involving cross-stage dependencies, where an action may succeed locally but cause a later stage to fail. To address this challenge, we introduce ReTrace, a self-improvement framework for robotic manipulation through autonomous physical interaction and retrospective reasoning, without provided demonstrations or model-parameter updates. ReTrace retrospectively traces downstream failures to earlier decisions, proposes targeted corrections, and evaluates them through subsequent interactions. Across attempts, ReTrace progressively consolidates validated corrections into a reusable manipulation skill that guide subsequent execution. We evaluate ReTrace on four real-world manipulation tasks using a Franka Research 3 robot. On the two tasks with strong cross-stage dependencies, GPT-6 Astra-low improves from 0% to 80% success on plug insertion and from 0% to 100% on ball pouring, while GPT-6 Sol-xhigh improves from 0% to 10% and 0% to 90%, respectively. The learned skills also transfer across model and reasoning configurations and reduce inference-time decision cost in most evaluated settings.

Bitemporal remote sensing change detection requires representations that preserve spatial detail while capturing contextual information relevant to changes between acquisitions. Visual test-time training offers an alternative to explicit token-to-token attention by adapting a compact inner model to each image. This letter describes ChangeT$^3$, a vanilla Siamese configuration combining the existing hierarchical ViT$^3$-Tiny encoder with the multiscale ChangeFormer decoder. The two image streams share learned encoder parameters, while their fast weights are computed independently from their respective spatial features. Each encoder block retains the inherited global simplified SwiGLU and local adaptive depthwise-convolution branches. Temporal comparison is performed by the decoder through learned fusion of paired features at four resolutions, followed by coarse-to-fine aggregation and binary prediction. This separation provides a direct setting for examining image-conditioned inner updates without introducing an additional temporal interaction module. Trained from scratch on LEVIR-CD+ with the same decoder, recipe, and budget as a ChangeFormer control, ChangeT$^3$ reaches an F1 of 80.61$\pm$0.90 against 78.84$\pm$0.21 for ChangeFormer (three seeds each); as in the standard protocol for this dataset, checkpoints are selected on the test split. Trained with both inner updates disabled, the same encoder reaches 78.63$\pm$0.20. Neither model transfers zero-shot to SYSU-CD, DSIFN-CD, or WHU-CD, and ChangeT$^3$ is the slower of the two at small inputs despite similar parameter and operation counts.

Taylor bubble flows with nanoparticle suspensions are regularly encountered in non-isothermal chemical synthesis and microfluidics. Despite this, a complete mechanistic insight into the coupled thermal and hydrodynamic interactions remains unresolved. Here, a Eulerian-Lagrangian framework has been developed to address this, capturing two-way momentum, energy exchange, and nanoparticle interactions under non-isothermal conditions. We find that Brownian motion acts in two opposing ways, enhancing local particle-fluid energy exchange yet driving a thermophoretic drift away from the heated wall that strengthens as particle diameter is reduced below 100 nm. At particle volume fractions of $\phi \sim 10^{-2}$, Taylor flow departs from the Nusselt scaling with dimensionless slug length, $\tilde{L}_s$, observed for particle-free flows. This coincides with alterations to bubble topology that co-benefit nanoparticle momentum and energy exchange with the carrier fluid. Examining both Poiseuille and Taylor flow problems, we observe contrasting, often opposing dimensionless heat transport behaviours, questioning the suitability of traditionally accepted mixture approaches. This work reveals that, in the visco-inertial regime ($Re > 500$), it is the interplay of hydrodynamic, Brownian, and interfacial forces, combined with the Taylor bubble and slug flow topology, which determine positive or negative $Nu$ outcomes. Interestingly, short-range particle forces at the liquid-gas interface work synergistically with the convective motion in the slug to alter local particle concentration and energy exchanges within downstream thin film and near-wall regions. The intensity of this convective flow was found to impact both slug and film transport phenomena, improving the redistribution of nanoparticles when $\tilde{L}_s \leq 1.6$ and with increasing $Re$.

Context: Low polarization in an unresolved source may reflect weak local polarization or spatial cancellation between strongly polarized regions. An occultation can break this spatial degeneracy by differentially sampling the source as the occulting boundary moves. Aims: We develop a general theoretical framework for occultation polarimetry and determine what information can be inferred directly from unresolved full Stokes light curves, without reconstructing a polarization image or prescribing a source model. Methods: For a stationary, spatially incoherent source undergoing monotonic occultation, we relate Stokes variations to the polarization sampled by an arbitrarily curved occulting boundary and derive an exact variance decomposition of the normalized Stokes vector. Results: The polarization deficit decomposes exactly into three non-negative contributions: local polarization deficit, mixing within limb samples, and mixing between their mean polarization states. The last is directly measurable and provides a sharp, model-independent lower bound on total spatial mixing. The associated covariance tensor further characterizes the direction and correlations of the resolved polarization variations, including those between linear and circular polarization. Finite sampling preserves the bound, which can be strengthened through complementary occultation trajectories. Conclusions: Occultation polarimetry provides a powerful observational technique for extracting quantitative, model independent constraints on spatial polarization mixing directly from unresolved Stokes light curves. It offers a means to reveal both the extent and the form of polarization structure otherwise inaccessible at the available angular resolution.

The introduction of long chain-of-thought (CoT) reasoning and external tools has substantially improved the performance of multimodal large language models (MLLMs) on general and reasoning tasks. However, existing fast-slow reasoning paradigms mainly regulate textual reasoning length, while visual computation introduced by external tools or visual tokens is often treated as an auxiliary component. This separation prevents MLLMs from jointly optimizing visual perception and textual reasoning. To address this issue, we propose L2T (adaptive Look, flexible Thought), a unified reasoning framework that jointly optimizes the form and depth of computation. L2T first discretizes tool-produced visual states into visual tokens, bringing visual perception and textual reasoning into a shared autoregressive space. Based on this unified representation, L2T introduces a modality-aware routing reward to select appropriate reasoning modes and a difficulty-aware fast-slow strategy to adapt reasoning depth according to task complexity. Experiments on general perception and reasoning-intensive tasks demonstrate the effectiveness of L2T. Compared with explicit tool-calling approaches, L2T maintains competitive performance while achieving 1.7–3.6 times higher throughput.

Bugeaud, Haynes and Velani (2011) resolved a metric version of the $p$-adic Littlewood conjecture. We establish a fully inhomogeneous generalisation of their result, as well as a partially inhomogeneous generalisation of a result of Harrap and Haynes (2013) in the more general mixed setting.

Data flow underlies deep learning (DL) framework execution, including automatic differentiation and operator-fusion optimization. Bugs involving data flow can cause incorrect results or unexpected behavior. Existing testing methods represent models primarily by operator topology, omitting runtime tensor values and properties and operator input requirements. They therefore cannot distinguish data flows in models with similar topologies, even when these differences affect framework behavior. We introduce the Tensor Flow Graph (TFG) to capture runtime tensor states and operator input requirements. Its nodes represent operators and their input requirements, while its edges record tensor values and properties. Building on the TFG, we propose FlowMuT, a mutation-based testing method grounded in data flow. Mutations are represented as constrained subgraph replacements, with mutation operators derived from prior work and an analysis of mutable data flow objects. In each round, FlowMuT builds a TFG for the seed model, pairs mutation operators with TFG sites, and filters illegal candidates using data flow constraints. It uses LinUCB to select a candidate based on coverage and impact, executes the mutant, updates selection feedback, and uses each accepted mutant as the next seed. We evaluate FlowMuT on PyTorch and MindSpore using representative models from diverse application scenarios. FlowMuT submitted 55 bug reports for cases missed by all baseline methods; developers confirmed 41 reports and fixed the bugs described in 7 reports. FlowMuT achieves 43.4% higher data flow diversity than the strongest baseline and a legal mutant rate of 96.7%, compared with 86.4% without constraints. These results show that testing from a data flow perspective is practical and effective.

Generating coherent videos grounded in a unified underlying world remains a major challenge, particularly under large viewpoint changes, where existing methods often struggle to maintain stable representations of individual objects. To this end, we introduce Totem, an object-centric 3D memory framework for world-consistent video generation. Totem first represents each selected object as a persistent 3D memory aligned to a shared world frame, assigning it a dedicated state. Based on these memories, we design a dual-stream 3D conditioning architecture that combines object memories with scene geometry for target-view synthesis. Moreover, these object memories constrain the model's attention with 3D structural information, thereby preserving object surfaces and relative spatial layouts. Extensive experiments on world-generation and object-centric benchmarks demonstrate that Totem generates videos depicting a more object-consistent 3D world under challenging camera trajectories, while supporting versatile applications.

Recovering visually faithful content from damaged video bitstreams is important for reliable multimedia communication and storage. Existing methods exploit local residuals and non-local RGB references of the input video sequence, but both sources can become unreliable after decoding, while processing additional references increases receiver computation and memory. This paper studies multimodal bitstream-corrupted video recovery (MBSCVR) using RGB and depth information, where pre-transmission depth-based geometry aids reconstruction when the received appearance is corrupted. We propose a novel MBSCVR framework that selects and effectively utilizes a single selected non-local RGB reference per recovery window to achieve higher performance. It integrates a reliability-aware multimodal selector that combines valid appearance with depth compatibility before reference encoding. Depth-Conditioned Reference Adaptation (DCRA) introduces selected RGB evidence into feature completion and content generation, while frame-aligned depth conditions completion queries. On the complete BSCV benchmark with oracle masks, MBSCVR uses one selected reference to achieve 32.30 dB on YouTube-VOS and 28.93 dB on DAVIS, surpassing full-reference B2SCVR by 0.27 and 0.33 dB and improving SSIM on both subsets. Matched receiver-forward measurements show 36.8% lower latency and 40.8% lower peak memory. These results demonstrate how compact geometric guidance and adapted appearance processing improve the quality–resource trade-off of multimedia recovery.

We develop an $N$-adic modification of the construction of David-Jeznach-Julia for compact subsets of the real line $\mathbb{R}\subset\mathbb{C}$ for which harmonic measure for the complementary domains has no dimension drop. In particular, we show that for every $s\in(0,1/2)$, there exists an $s$-Ahlfors regular compact set $K\subset\mathbb{R}\subset\mathbb{C}$ such that $\mathrm{dim}\omega^\infty=s$, where $\omega^\infty$ denotes harmonic measure for $\mathbb{C}\setminus K$ with pole at infinity. Combined with a result of the third author, this shows that the threshold $1/2$ is sharp.

Large language model (LLM) that retrieve internal documents within an organization must decide who may receive them. Existing approaches based on Contextual Integrity ask the model to make that decision, so access depends on probabilistic reasoning. We present Privacy Conductor, an architecture that removes the decision from the model: a deterministic gate enforces a policy written by an authority, and the model receives only what the requester may already see. On a synthetic clinical corpus of 2,520 requester–document flows, the gate reproduces its policy exactly, so the remaining risk lies in the document labels it reads. As label source is of primary importance, we compare LLM and human generated labels. Across seven configurations of six models from two model families, LLM-written labels degrade the policy in every case. Models assign a document's sensitivity tier correctly on 78–86% of documents, but reproduce its access-control list on as few as 23%. Relabeling the same documents five times with an identical request changes 13 to 124 access decisions per configuration, a result that does not depend on our own labels. On 214 flows from HIPAA court cases, the most accurate configuration (87.8%) still permits 11 of the 20 disclosures the law prohibits. LLMs can describe what a document contains, but not decide who should receive it. Hence, we recommend privacy policy should be authored by accountable personnel and enforced outside the model.

Let $X$ be a smooth compact irreducible hyperkähler manifold of dimension six. We prove that the second Betti number satisfies $b_2(X) \le 23$. Furthermore, we show that the third cohomology vanishes whenever $b_2(X) \ge 19$, and that all odd cohomology vanishes when $b_2(X) = 23$. If the second Chern class lies in the subalgebra generated by $H^2(X,\mathbb{Q})$, then $b_2(X) \in \{5,8,23\}$. The proof uses the Looijenga–Lunts–Verbitsky decomposition, curvature inequalities for Segre classes, and the Hodge–Riemann bilinear relations on the projective cotangent bundle.

Generating a full song from lyrics and a style description requires long-range musical planning without sacrificing vocal and instrumental detail. Low-rate discrete semantic tokens make this tractable, but quantization constrains the information available to acoustic rendering, while separately optimized stages prevent downstream generation objectives from shaping the planner. We propose joint discrete and continuous modeling for high-fidelity song generation. A VQ tokenizer supplies tokens for autoregressive planning, and a separately trained SSL-derived variational encoder supplies continuous semantic targets. Conditioned on the completed token plan and differentiable readouts of the planner's predictive states, a full-sequence flow model generates semantic features for acoustic rendering. Its flow-matching gradients reach the language model through the readouts, without differentiating through token sampling; the standard pathway keeps continuous features out of autoregressive feedback. On 192 shared prompts, its 48D configuration improves SongEval from 4.152 to 4.269 and reduces micro-PER from 20.26% to 14.47% relative to a discrete baseline, while receiving substantially higher expert listening scores. We further analyze the system through downstream semantic probes and conditioned reconstruction.

We study the problem of fair allocation when agents have dichotomous submodular preferences over groups of, rather than individual, items. These preferences naturally extend existing models, and have a natural interpretation in settings such as course allocation. We show that this seemingly minor extension results in computational intractability barriers: computing a utilitarian or Nash-optimal allocation with item complements is NP-hard. However, when agents' complementary bundles have size at most $k$, there exist poly-time algorithms that compute $\frac1k$-$\texttt{maxUSW}$ allocations and approximate Nash-welfare-maximizing allocations. While PO+EF-1 allocations may not exist in the complementary preference setting, it is possible to compute $\frac1{k+1}$-approximately $\texttt{maxUSW}$ EF-X allocations in polynomial time; furthermore, these allocations offer each agent $i$ a utility of at least $\frac{\texttt{MMS}_i - k}{k+1 + \frac1n}$, where $\texttt{MMS}_i$ is agent $i$'s maximin share guarantee. While the standard dichotomous binary submodular setting admits simple sequential techniques for computing fair and efficient allocations, our results for the complements setting require more complex tools from combinatorial optimization.

Oral health is vital for overall well-being, yet many users brush different tooth surfaces for insufficient or excessive durations. Toothbrushing monitoring systems can help improve brushing habits by reminding users of under-brushed and over-brushed surfaces, but existing approaches often rely on external sensors, increasing cost and reducing practicality. We observe that the intrinsic motor signals of electric toothbrushes can reflect the brushing surfaces and durations. When brushing different tooth surfaces, the brush head experiences different constraints from the surrounding oral cavity, changing the motor's driving currents and position feedback. Based on this observation, we propose FreeBrush, a toothbrushing monitoring system that uses the intrinsic motor signals of electric toothbrushes to recognize brushed tooth surfaces and estimate brushing durations without any external sensors. We prototype the system on a commercial off-the-shelf electric toothbrush and conduct a comprehensive evaluation with 18 participants. FreeBrush achieves 92.8% accuracy for 16-surface recognition and 92.0% accuracy for brushing duration estimation. The system further shows robustness across different toothpastes, brush heads, vibration modes, usage scenarios, and long-term use, and is capable of running on edge devices. By recognizing brushed tooth surfaces and estimating the brushing duration, FreeBrush can help users identify under-brushed and over-brushed surfaces and build balanced brushing habits.

We investigate the problem of uncertainty quantification in the mean estimation framework. Given an i.i.d. sample from a distribution with unknown mean $\mu$ and variance $\sigma^2$, we want to construct an estimator $\wh\mu_n$ and provide a computable and size-optimal upper bound for the error $|\wh \mu_n - \mu|$. While estimators possessing strong deviation guarantees are well known, no data-dependent non-asymptotic upper bounds for their performance exist in general. We show that this gap can be bridged by introducing a parameter that characterizes the “effective sample size” available for uncertainty quantification. This parameter captures the difficulty of the problem, interpolating between “easy” cases where sub-Gaussian confidence intervals exist and “hard" cases where their construction is impossible. Using this characterization, we design confidence intervals of optimal length that are fully adaptive to the unknown variance. Numerical experiments confirm that our approach maintains nominal coverage even in asymmetric and heavy-tailed regimes where other existing methods fail.

Proton exchange membrane water electrolysis (PEMWE) is among the most promising techniques to provide hydrogen as both energy carrier and feedstock for the chemical industry, due to its compatibility with intermittent renewable electricity sources. However, a major bottleneck in scaling up PEMWE is the limited supply of the anode catalyst Ir. This work shows a novel approach to tailoring ionomer-free catalyst layers based on custom-made microporous substrates and two different atomic layer deposition (ALD) processes, both using Ir(EtCp)(CHD) precursor. Thermal ALD using O3 as counter-reactant yields mostly metallic Ir/IrOx and an electrode Ir loading of 0.21 mg/cm2. The PEMWE cell-level performance is comparable to a commercial catalyst-coated membrane anode despite 7x lower loading, and is maintained over an accelerated durability test equivalent to 600 h of intermittent operation. Moreover, using a low-loading ALD-made cathode, the total platinum group metal loading is only 0.24 mg/cm2. Plasma-enhanced ALD reduces the Ir loading to 0.04 mg/cm2 by tailoring the catalyst distribution, however, yields lower-activity IrO2. Finally, direct ALD catalyst deposition needs no ionomer-bearing ink. The anodes are therefore compatible with various membrane materials, as demonstrated in a CO2 electrolysis experiment with an anion exchange membrane.

Planning and revision are intended to bring generated code closer to the task specification. Yet a mistaken interpretation can persist across the plan, implementation, and tests - a pattern we call interpretive lock-in. We investigate this risk on 30 DataFrame tasks derived from TPC Benchmark DS, comparing Frozen One-Pass, Test-Guided Revision, and PlanAudit-Guided Revision. Test-pass counts rose from 22/30 to 29/30 and 30/30, yet no generated solution matched its stored reference output. Evaluator controls returned the expected outcome in 57/57 cases. Same-engine SQL re-execution reproduced 28/30 references; all 77 test-passing runs on these tasks still failed reference agreement. PlanAudit-Guided Revision improved code scores on 3/30 tasks and test coverage on 11/30, but the median paired change was zero for both measures. Failure analysis revealed tests that omitted requirements, adopted candidate-defined schemas, used nondiscriminating fixtures, or repeated the implementation's incorrect logic. Fresh generation on ten targeted tasks produced 0/30 reference matches and 25/25 false passes among test-passing runs. These findings are diagnostic rather than causal: the pipelines differ in feedback, grounding, call budgets, and editing permissions, and the study uses one model and one primary generation per eligible task. Because pre-adjudication human labels were not retained, inter-rater agreement cannot be reconstructed and the mechanism analyses remain exploratory. Overall, increasingly successful self-generated tests did not establish semantic correctness, even after excluding unreproduced references.

Epidemiological models often take the form of systems of differential equations of varying levels of complexity. In multi-strain models, complexity arises from the interaction of diverse pathogen types that may exhibit different patterns of cross-immunity due to the host's immune system. Where previous work has tended to focus on theoretical analysis of this complexity, or model simplification, less effort has been given to efficient numerical exploration of full multi-strain disease dynamics. Here, we propose a computational framework for representing multi-strain disease transmission models, through a mathematically transparent hard-coded mapping between sets and integers. By mapping infection histories into Boolean matrices, the framework eliminates explicit iteration over strain combinations while preserving key biological processes, including sequential infection and partial cross-immunity. Benchmark comparisons of numerical solutions of our matrix formulation and a set-indexed implementation demonstrate substantial performance gains. Across models with increasing numbers of strains, the matrix formulation consistently reduces runtime, with a speedup exceeding two orders of magnitude for systems with 11 strains. We present an application of this approach to the case of COVID-19 in Indonesia, focusing on the replacement of the Delta variant by Omicron. We hope that our approach represents a robust computational approach to automatically generate diverse multi-strain epidemic models that can be solved in a computationally efficient manner for a variety of scientific and public-health questions.

Automated moderation systems are deployed at scale, yet they remain opaque to the users and moderators affected by their decisions, and their coverage is almost entirely confined to English. For Urdu written in the Nastaliq script, no such system exists, and the annotated resources it would be built on are drawn largely from Twitter/X, where character limits constrain how users write. Interpretability has received little attention, leaving it unclear what such models actually learn. This study addresses these gaps in three steps. First, we curate and publicly release a corpus of 7604 Nastaliq Urdu Facebook comments, extending an earlier corpus by correcting text-level inconsistencies and re-examining the original labels. Second, we fine-tune four Urdu-capable transformers under a common grid-search protocol and compare them against twelve feature-classifier baselines on identical data partitions. The best configuration, Multilingual Representations for Indian Languages (MuRIL), reaches 87.05% accuracy and 87.06% macro F1, improving on the strongest baseline by 5.52 percentage points, a margin that exceeds the 95% confidence interval on test accuracy; the two leading transformers differ by less than the test set can resolve, and performance is stable across five optimizers. Third, we compute word-level SHAP attributions adapted to right-to-left rendering. Attribution mass concentrates on high-frequency slurs but extends to syntactically neutral function words and to political vocabulary characteristic of the source pages, indicating that aggregate performance may rest partly on lexical and topical regularities rather than a generalizable representation of offensiveness.

Flow matching is a common generative recipe for robot foundation models. Vision-language-action models (VLAs) generate action chunks, while world-action models (WAMs) additionally generate future visual states. Both start generation from a fixed Gaussian prior, despite temporal continuity between past and future states and actions. This requires costly training and iterative sampling, especially for WAMs with an additional visual branch. We introduce $\Delta$-flow, which constructs the source from recent history with mild noise rather than from a fixed Gaussian prior. This moves the source closer to the target, reducing transport to a small residual $\Delta$ that can be learned efficiently and enables single-step inference. We integrate $\Delta$-flow into the VLA policy $\pi_{0.5}$ and the WAM policies ImageWAM and Fast-WAM. On LIBERO, ImageWAM reaches 90% success in one epoch rather than six, and Fast-WAM reaches 95% in two epochs rather than eight. With LoRA fine-tuning, $\pi_{0.5}$ exceeds its baseline's five-epoch performance after one epoch. Single-step inference gives $1.54\times$, $2.49\times$, and $4.45\times$ speedups on $\pi_{0.5}$, ImageWAM, and Fast-WAM, respectively. It preserves action smoothness, achieving a $4.5\times$ reduction in action jerk compared with one-step Gaussian sampling. $\Delta$-flow reaches state-of-the-art generalization performance on LIBERO-Plus. Action-history sources can be applied to pretrained WAM policies without retraining. Replacing the Gaussian action source at inference largely preserves task success with a single sampling step and can slightly improve it. We further study how action representation and visual information in action learning affect history-to-future prediction in $\Delta$-flow. These results show that $\Delta$-flow is simple yet effective, improving the efficiency and generalization of robot foundation models.

Multi-version concurrency control (MVCC) has been the dominant concurrency protocol in modern database management systems (DBMSs). However, cloud-native HTAP architectures shift many of MVCC's traditional advantages from the primary transaction engine to the deployment architecture. Now, transactional and analytical processing are decoupled into loosely synchronized engines, while cloud deployment primitives provide the workload isolation required for this design. In this paper, we challenge the status quo, arguing that single-version concurrency control (SVCC) is better suited to cloud transaction processing than MVCC. Through a systematic analysis of MVCC's limitations, we show that SVCC avoids these shortcomings through a more lightweight and efficient design. Beyond arguing for a lighter transaction processing, we use this SVCC effort as a blueprint to advocate for a broader rethinking of cloud-native architectures and to outline a research roadmap to shape next-generation DBMSs.

We study the rank-twelve potential modular datum denoted $12^{39,406}_{4,1276.}$ in the low-rank classification tables. Its global dimension is $(1287+351\sqrt{13})/2$, and its fusion ring agrees with that of the known rank-twelve Haagerup modular category. The datum satisfies the modular relations, has nonnegative integral Verlinde coefficients, and passes several familiar genus-one necessary tests. We prove, nevertheless, that it cannot be realized by a unitary modular tensor category. The obstruction already occurs in the representation of the three-strand braid group on $\operatorname{Hom}(C_{[10]},B^{\otimes3})$. Generalized Frobenius–Schur indicators determine the eigenvalues of the two-strand generator on this twelve-dimensional space. The central relation in $B_3$ then reduces the problem to a product of three prescribed unitary conjugacy classes. A sixfold symmetry reduces the $1302$ determinant-compatible cases to $217$ representatives. Rank-one inequalities leave only $17$ of these, and ten explicitly displayed degree-zero rank-two Schubert inequalities exclude the remaining cases. A violated inequality with gap $2/117$ is worked out explicitly. All calculations used in the obstruction are exact. The argument uses unitarity essentially and leaves non-unitary categorification open.

Ordinal optimization selects designs that are good enough rather than optimal when evaluation is expensive and the budget is small. The alignment probability measures the chance that the selected set contains at least a prescribed number of truly good designs. We formulate quantum ordinal optimization as a class of problems that maximize this probability under a fixed oracle budget. We study exact, coherent pairwise comparisons with one selected design as a first instance, with the budget counted in comparison queries. For every classical comparison budget smaller than the number of designs, we prove that a knockout among uniformly sampled designs attains the optimum. The sample is drawn without replacement and contains one more design than the number of comparisons. For a uniformly random order, the selected design's rank has a polynomial probability law. At the same comparison budget, the maximum quantum degree is at most twice the classical maximum, a factor attained whenever there are more than twice as many designs as comparisons, so a quantum algorithm can realize rank laws that no classical algorithm with the same budget can. We determine the exact quantum optimum with one comparison for every number of designs and every good-enough set. For selecting the best of n designs, the optimal success probability with one quantum comparison is approximately 3.30/n for large n, compared with 2/n for one classical comparison. When the best design is sought, one quantum comparison gives a higher alignment probability than two classical comparisons whenever there are more than nine designs.

Magpie is a fully graphical linear spin-wave software which has its main focus on 3-d visualisation of magnetic models and magnon dispersion relations. The software is distributed under an open-source license and is written in high-performance, portable C++. Its modular architecture allows for a rapid development of new calculation modules and permits the inclusion into external applications. Included code generators ensure seamless interoperability with other linear spin-wave libraries.

In this paper, we develop an asymptotically normal estimator for the value of policy improvement (VPI) under adaptively collected data. This value, which is defined as the gap between the value of the best treatment policy in a class and that of a baseline policy, gauges whether or not it is worth deploying a personalized treatment policy. Building an estimator for the VPI is naturally more difficult than estimating the value of a fixed policy. This is because, in addition to contending with the correlated data and decaying propensities associated with adaptive experiments, any estimator must also handle the non-regularity, or lack of pathwise differentiability, of the underlying estimand when the optimal policy is non-unique. Our proposed estimator works by sequentially fitting a weighted empirical welfare maximizing policy on historical data and then evaluating it using inverse propensity weighting on future samples. We neither assume that the optimal policy is unique nor make a margin assumption on the underlying heterogeneous treatment effects. A key difficulty in analyzing our estimator is showing that the regret incurred through policy learning is asymptotically smaller than the standard error of the estimator. We accomplish this by showing faster regret rates for policy learning under decaying propensities, which may be of independent interest. We not only evaluate the coverage of our estimator on a mix of synthetic and semi-synthetic data, but also employ it to estimate the VPI in an adaptive experiment evaluating the efficacy of job assistance programs in Jordan due to Caria et al. Although our estimates are generally more conservative than their hierarchical Bayesian analysis, which assumes that the optimal policy is unique, we still corroborate the benefits of personalization amongst Syrian refugees.

Large language model (LLM) agents are increasingly deployed as teams, yet they fail in characteristically social ways: information holders stay silent, dominant speakers anchor groups on wrong answers, and norm violations go unsanctioned. We present Agent Sociodrama, a framework for modeling and validating evolving social dynamics in LLM agent teams. Under fixed personas, agents' emotional states and directed, asymmetric relationships are updated every round by a unified external LLM judge and shape their subsequent interactions. Across six LLM backbones and five social scenarios, we assess social fidelity through classical social-theory patterns and agreement with human judgments. The resulting trajectories exhibit structured social patterns and model-specific differences. We then introduce Trajectory-Guided Persona Recasting (TPR), which diagnoses group-dynamic failures from interaction transcripts and social trajectories and recasts agent personas before rerunning the task. Across four collaborative benchmarks, TPR improves performance from both heterogeneous and randomly initialized agent persona compositions, yielding up to 83.3%p of accuracy improvement over the initial casting. On representative distributed-information cooperation and mixed-motive bargaining tasks, we outperform SOTOPIA and AgentVerse in three of four comparisons, by up to 37.5%p in Pareto rate. These results show that validated social trajectories provide actionable signals for repairing LLM agent teams.

Frank and Loss proposed critical Sobolev inequalities for the Dirac operator and for vector fields. They conjectured optimality of their spinorial family and wrote that it is conceivable that the higher-dimensional Loss-Yau potential is an optimizer. Wang and Zhang recently disproved both optimizer claims using direct comparison and instability arguments. We compute closed-form quotients for two elementary families of explicit competitors with strictly smaller quotients. For every $d\geq2$, the spinorial competitor is a constant spinor multiplied by a scalar Aubin-Talenti optimizer. For every $d\geq3$, the vector competitor is the planar azimuthal field \[ A_d(x)=\frac{d}{(1+\lvert x\rvert^2)^2} (-x_2,x_1,0,\ldots,0). \] It lies in the nonlinear gauge and its quotient is computed in closed form. For every odd $d\geq3$, it gives an explicit proof of nonoptimality of the higher-dimensional Loss-Yau-Dunne-Min potential. In dimension three, this field is a specific member of the competitor family of Wang and Zhang: it is a linear combination of the Loss-Yau potential and its reflected twin. Its axisymmetry gives a negative answer to their question about minimization within the $\mathrm{SO}(2)\times 1$-invariant class.

A principal funds an agent's project over two periods, with a midterm review providing a public signal about project quality. The agent privately knows the project's quality and always prefers more funding, while the principal wants to match funding to quality. A natural benchmark uses the review only after it arrives, to update beliefs and improve the second-period allocation. The optimal mechanism instead frontloads the review's information value: it also uses the review as an incentive device to elicit truthful reporting up front, thereby strictly improving the principal's first-period expected payoff. In the optimal mechanism, higher-quality projects receive more funding initially but face larger cuts after a bad review, leaving them with less funding than lower-quality projects. A good review increases funding, but the resulting allocation need not preserve the initial ranking of projects and eventually declines with quality.

The periodic tiling conjecture asserts that if a bounded set $\Omega\subset \mathbb R^d$ of finite measure tiles $\mathbb R^d$ by translations, then it admits at least one fully periodic tiling. This conjecture was proved to hold in $\mathbb R$ by Lagarias and Wang, and was recently disproved by Greenfeld and Tao in sufficiently high dimensions. Its discrete analogue in $\mathbb Z^2$ was proved by Bhattacharya, whereas the conjecture in $\mathbb R^2$ remains open. In this paper, we analyze the structure of tilings by axis-parallel polygonal sets: bounded open sets in $\mathbb R^2$ whose boundary is a finite union of line segments parallel to the axes. We prove that every such tiling that is topologically minimal is weakly periodic. Moreover, we show that if an axis-parallel polygonal set $\Omega$ tiles $\mathbb{R}^2$ then it admits a quasi-periodic tiling (i.e., a finite union of translated lattices). The proofs combine geometric decompositions of tilings with rational approximation and discrete tiling theory. As a consequence, we obtain that the translational tiling problem for axis-parallel polygonal sets with real algebraic vertex coordinates is decidable.