Papers

Let $G$ be a finite abelian group of order $n$ and $X$ a finite $G$-set. We give a necessary and sufficient condition on $G$ for any $X$ to be determined up to isomorphism by certain combinatorial data. Specifically, if $M_H^X$ is the number of $H$-orbits in $X$, and $a_d^X$ is the number of $G$-orbits in $X$ of cardinality $d$, we characterize when equalities $M_H^{X_1} = M_H^{X_2}$ and $a_d^{X_1}=a_d^{X_2}$ for all $H \leq G$ and $d|n$, respectively, force an isomorphism $X_1 \simeq X_2$. Our main result is that this occurs if and only if $G$ is cyclic or $G$ is the direct sum of a finite cyclic group and a cyclic group of prime order. We conclude with an arithmetic application to $L$-function factorization.

The rapid spread of face forgeries on the Web challenges the credibility of visual content. In practical Web environments, manipulated media originate from evolving generation pipelines and undergo diverse processing during dissemination, making reliable authenticity assessment under unseen manipulations and visual changes a critical challenge. We observe that a standard LoRA-adapted CLIP detector exhibits uneven patch-level decision dependence, concen trating a disproportionate share of class-specific relevance on a small fraction of visual patches. To improve robustness to variations in such highly dependent evidence, we propose EviStress, a two-stage framework for generalizable face forgery detection with textual explanations. In the first stage, Evidence-Targeted Patch Perturbation (ETPP) estimates patch dependence from global, relational, and semantic cues and assigns positively correlated perturbation probabilities, explicitly stress-testing highly dependent visual evidence during training. We further introduce Discriminative Variation Preservation (DVP), which constrains the residual between clean and perturbed representations to retain authenticity discriminative information. In the second stage, Intrinsic Evidence Instruction Tuning (IEIT) transfers the adapted CLIP encoder into LLaVA as its vision tower and performs parameter-efficient multimodal instruction tuning, enabling authenticity prediction and textual explanation directly from the learned forgery-sensitive representation without an external detector. Experiments demonstrate improved cross-dataset and cross-method generalization and corruption robustness, with the multimodal model providing authenticity predictions and human-readable explanations.

Autoregressive electronic health record (EHR) foundation models predict the next event token in patient trajectories: sequences of structured medical events. A typical pretraining strategy is to concatenate all trajectories into a global stream and sample token windows from it. This gives patients with longer sequences more training exposure and allows tokens to attend across patient boundaries. We argue that these choices create a misalignment between pretraining and downstream clinical tasks. To explore this, we investigate how the composition of pretraining sequences affects clinical prediction performance. Using the global-stream approach as a baseline, we propose alternative sequence composition methods that control how patient trajectories contribute to pretraining sequences. Across four MIMIC-IV v2.2 tasks, our best method improves macro AUROC, AUPRC, F1, and balanced accuracy, with relative gains of 9.3% in F1 and 2.7% in AUPRC under a fixed training recipe. We find that these gains generalize across four additional evaluation settings, including the INSPIRE and eICU-CRD datasets, with improvements in macro AUROC, AUPRC, and F1 score. Our results show that simply changing how EHR data are presented to the model during pretraining can improve downstream performance, without changing the model or collecting additional data.

Let $F$ be a nonarchimedean local field of characteristic zero and residue characteristic $p$. Let $E$ be a quadratic field extension of $F$. Let $D$ be the unique quaternion division algebra defined over $F$. Let $G=\GL_{2}(E)$ and $H=D^\times$. This paper studies the modulo distinction problem for the pair $(G,H)$ with $\ell\neq p$, which gives a complete classification of $H$-distinguished representations of $G$, including the cases $\ell=2$ and $p=2$. In terms of type theory, we give a complete classification of $H$-distinguished supercuspidal representations when $p$ is odd.

Target-aware multimodal instruction selection requires useful examples and an appropriate balance of supervision. Sample-level rankings can overrepresent similar content without optimizing this balance; group-level methods face coarse units, predefined set-level validation signals, and costly or inaccurate mixture search. We propose CLIVO, a target-aware framework connecting fine-grained semantic allocation, automatically learned validation objectives, and differentiable mixture search. Specifically, semantic clusters provide independently adjustable shares at the hundred-cluster scale. Correlations between per-example merged-proxy losses and real probe performance identify target-relevant validation examples; learned nonnegative weights combine their losses into an objective. A single backward pass through the merged proxy supplies gradients for all shares, avoiding an additional mixture-response regression model. Selecting 100K instructions from an 8M pool, CLIVO attains 97.2% of the full-data four-target average score with only 1.25% of the data. It improves on the strongest evaluated selection baseline by 1.16 points using random within-cluster sampling; combining learned quotas with sample ranking increases this advantage to 1.55 points. Analyses show that finer units benefit most targets, short-trained experts preserve mixture responses, sample weighting retains useful validation information, and direct search consistently reduces the learned objective. CLIVO also supports interpretable allocation, modular selection, and reuse across targets and granularities.

Can the Alexander-Orbach conjecture hold on hierarchical lattices? We construct Gromov-Hausdorff-Prokhorov scaling limits of critical percolation clusters on hierarchical lattices in the chemical metric and determine the typical spectral dimensions of the associated diffusions. These dimensions are dense in $(1,2)$; however, outside a narrow region in dimension space, we prove that the Alexander-Orbach conjecture fails on every hierarchical lattice under consideration.

We establish the existence and uniqueness, up to translation, of monotone viscous-dispersive shock profiles for the one-dimensional Navier-Stokes-Fourier-Korteweg system, provided the two end states satisfy the Rankine-Hugoniot and Lax entropy conditions and the shock strength is small. Taking the shock strength as a singular perturbation parameter, we reduce the profile equations by Fenichel's geometric singular perturbation theory to a scalar equation on a slow manifold and obtain the profile as a heteroclinic orbit. We also give pointwise estimates of the profiles and their derivatives up to fourth order, with explicit leading-order terms for the first derivatives.

We study quotients of free associative algebras by the two-sided ideals generated by positive-degree symmetric, quasisymmetric, or free quasisymmetric polynomials. Free quasisymmetric functions give a word realization of the Malvenuto-Reutenauer Hopf algebra of permutations. For quotients on $n$ variables, finiteness in the symmetric and quasisymmetric cases follows from a theorem of Bergman–Isaacs when $n!$ is invertible in the field. Our main result is a nilpotence criterion for families of relations compatible with restriction to subalphabets. The criterion proves finiteness over every field for quasisymmetric, $r$-quasisymmetric, and free quasisymmetric coinvariants, with explicit degree bounds exponential in $n$ for fixed $r$. In the quasisymmetric and $r$-quasisymmetric cases, these improve the bounds inherited from Bergman–Isaacs. A principal application is to the free quasisymmetric case, where, for $n\geq3$, the group-invariant argument used for the symmetric case does not apply. For the symmetric quotient $C_n$, we prove that invertibility of $n!$ is also necessary for finiteness. In characteristic zero, an auxiliary presentation and the Golod–Shafarevich inequality give $\log\dim C_n\geq(1-o(1))n^5(\log n)^2$ as $n\to\infty$. The same inequality shows that quasisymmetric and free quasisymmetric coinvariant dimensions grow faster than every fixed power of $n!$. For all three families on several freely noncommuting alphabets, we determine all multigraded Hilbert series and, for symmetric coinvariants in characteristic zero, Frobenius characteristics from one-alphabet data. In characteristic zero, projection gives stable Schur multiplicities for compatible quotients in mixed commuting, anticommuting, and free alphabets.

In Operational Technology (OT) environments, Federated Learning (FL) is increasingly adopted to train Intrusion Detection Systems (IDSs) without sharing raw operational data across facilities. However, model updates may still leak sensitive information about industrial processes, creating privacy risks that remain largely invisible within current OT security architectures. Existing reference models, including the Purdue hierarchy, do not explicitly represent the FL learning lifecycle, making privacy leakage difficult to observe and evaluate. To address this gap, we introduce the ML Plane, a novel architectural abstraction that integrates FL workflows within OT systems, enabling visibility of learning-related information flows that are not explicitly represented in traditional OT architectures. Building on the proposed ML Plane, we outline a privacy auditing framework for FL-enabled OT systems. The framework uses Federated Membership Inference Attacks (FedMIA) as an initial assessment mechanism and is being instantiated within a Smart Grid testbed to support the future evaluation of privacy risks under realistic OT deployment constraints.

Weak measurements are used to amplify small signals, to address foundational questions, and to characterise quantum states without tomography. In direct state reconstruction each amplitude of the state vector is proportional to a single complex weak value, which for a temporal pointer is read from the mean arrival time and the mean frequency of the postselected pulse. Such an experiment requires three quantities to be fixed, the coupling, the angular resolution demanded of the reconstruction, and the set of states over which the method remains usable, and these are commonly set by the available apparatus rather than derived. We derive all three for a Gaussian temporal pointer and an arbitrary postselection state. The states that cannot be reconstructed form a spherical cap centred on the state orthogonal to the postselection, whose geodesic half-angle follows from the largest of three independent thresholds and involves no adjustable parameter. Two states are distinguishable only if they differ by more than a minimal step fixed by the coupling, by the number of incident photons and by the sensitivity of the weak value along the path followed. For an inversion at first order in the coupling the systematic and statistical errors are opposed and fix an optimal coupling that varies as the inverse sixth root of the number of incident photons, whereas an exact inversion at finite coupling removes the systematic error, the remaining bound being one on the two-centroid readout rather than on the inversion, since below an amplitude equal to a quarter of the coupling two states give the same pair of centroids while their profiles differ. These results allow a direct reconstruction experiment to be dimensioned before the apparatus is assembled.

As coding agents become more capable, tests remain the primary evidence for judging whether their code is correct. Yet passing available tests does not establish that an implementation satisfies its natural language specification. Reliable validation requires checks that faithfully capture the specification and scenarios that thoroughly exercise the code, but current benchmarks provide limited insight into whether agents can construct such evidence themselves. We introduce SpecGuardBench, a benchmark of 291 tasks from 13 real-world repositories, covering 8 types of verification logic such as functional postconditions and interaction protocols. Given a natural language specification, repository context, and a reference implementation, an agent constructs a validation harness comprising executable checks and test scenarios. The checks should reject implementations that violate the specification while accepting those that satisfy it, and the scenarios should thoroughly exercise the code. Across four proprietary and open-weight coding agents, none constructs a harness scored as faithful on the benchmark's implementations for more than 63% of the tasks. The bottleneck lies less in exploring test scenarios than in constructing checks that faithfully reflect the specification. Specifically, the agents show a clear tendency to write checks that mirror the reference implementation rather than the specification, and therefore reject implementations that the specification permits.

Eulerian digraphs retain the directional structure of general digraphs while exhibiting a symmetry of cuts reminiscent of undirected graphs. We show that this symmetry extends beyond individual cuts to two fundamental techniques in parameterized algorithms for undirected cut problems: treewidth reduction and recursive understanding and randomized contractions. Both of these techniques have proved useful for dealing with undirected graph cut problems as each of them reduces the problem at hand on general undirected instances to ones that have bounded treewidth or that are highly connected, respectively. In this work we prove an edge-cut analogue of the treewidth-reduction theorem of Marx, O'Sullivan, and Razgon [ACM TALG 2013], and an Eulerian analogue of the reduction of CMSO model checking to unbreakable instances due to Lokshtanov, Ramanujan, Saurabh, and Zehavi [ICALP 2018]. Both these results allow us to reduce several problems on general Eulerian digraphs to Eulerian digraphs whose underlying undirected graph has bounded treewidth, or to Eulerian instances that are highly connected, thus bringing to Eulerian digraphs two fundamental tools from the undirected parameterized cut toolkit for which no counterparts are known on arbitrary digraphs. Beyond their structural significance, these results have substantial algorithmic consequences: they yield FPT algorithms for several directed cut problems that are W[1]-hard in general. We show that Directed Multicut and Directed Edge Odd Cycle Transversal are FPT on Eulerian digraphs when parameterized by the solution size and the number of terminal pairs, and just the solution size, respectively. This is in sharp contrast to general digraphs, where the first problem is W[1]-hard even for 4 terminal pairs, and the second is W[1]-hard in general. We also obtain FPT algorithms for Directed Edge Multiway Cut-Uncut and Directed Steiner Cut.

Simplicity bias, which can arise from sequential feature learning during training, has been proposed as a general explanation for the success of deep learning. An important driver of this phenomenon is saddle-to-saddle behavior, in which the gradient flow trajectory remains close to a sequence of saddle manifolds while learning one feature at a time. However, Muon, a state-of-the-art optimizer based on spectral descent, does not exhibit such dynamics in the full-batch setting and instead learns features in parallel. How is it then that Muon is so successful in deep learning settings? We show that stochastic gradient noise fundamentally changes this behavior: small-batch noise restores sequential feature learning, providing a mechanism for simplicity bias that is absent from full-batch Muon. We explain this transition through stochastic smoothing of the spectral descent operator underlying Muon. When gradients are small relative to the noise scale, the expected spectral update becomes approximately proportional to the actual gradient, which restores gradient-flow-like dynamics. We formalize this mechanism for deep linear models by deriving the effective continuous dynamics of noisy spectral descent. Experiments on low-rank matrix reconstruction, vision transformers, and large language models (LLMs) support these findings.

Reliable agentic tool use requires training data that pair diverse multi-step workflows with executable evidence that the requested outcomes were achieved. Scaling either trajectory coverage or verification alone is insufficient as new environments introduce distinct states, rules, and dependencies that must also be reflected in the success criteria. To address this challenge, we introduce Davinci-Tool, a 30B tool-use model, and Davinci-ToolData, an execution-grounded dataset designed to scale environment coverage and outcome verification together. Davinci-ToolData preserves restorable states, execution traces, outcomes, and verifiers as a unified substrate for supervision. Two complementary pipelines populate this substrate: Execution-Grounded Task Synthesis (EGTS) derives verified demonstrations from independently authored systems, and Executable Environment Synthesis (EES) synthesizes auditable environments, state-grounded tasks, and executable verifiers across single and coordinated domains. These pipelines yield 30,395 verified trajectories spanning 2,260 invoked tool names. We first train on these demonstrations with supervised fine-tuning, then reuse EES states and verifiers to compare alternative actions and construct outcome-grounded preferences for Direct Preference Optimization. Davinci-Tool improves Qwen3-Coder-30B-A3B-Instruct from 52.4 to 88.2 on $\tau^2$-bench, from 30.4 to 62.8 on BFCL v4 multi-turn, and from 16.9 to 56.2 on MCP-Atlas, outperforming Qwen3-Coder-480B-A35B-Instruct on all three benchmarks with only 1/16 of its total parameters. Code is available at https://github.com/MassLab-SII/Davinci-Tool.

Reinforcement learning (RL) post-training with generative reward models (GenRM) has become a central recipe for improving large language models (LLMs), and it is also increasingly resource-intensive: policy rollout, GenRM-based reward evaluation, and policy training all compete for GPU resources. However, existing colocated and disaggregated systems rely on static resource allocation for these roles. Such allocation cannot adapt as each role's workload changes during RL and therefore leaves a role's resources underutilized. We present PivotRL, an RL post-training system that dynamically shifts resources among different roles according to their runtime demands. PivotRL introduces a resource-shiftable runtime built on a Global Parameter Storage, together with a unified mechanism that efficiently shifts role-specific context. A shift-aware scheduler enables sequence migration upon a shift, while a planner considers the aggregate throughput benefit and the shift overhead to determine when and how to shift. We evaluate PivotRL on a 128-GPU cluster using four model groups spanning dense and mixture-of-experts models. PivotRL enables resource shifting within seconds and improves end-to-end throughput by 1.81-2.05 times over colocated deployment and 1.50-1.95 times over disaggregated deployment, while preserving RL convergence.

Software agents built on large language models act by issuing tool calls, some of which cannot be undone. To control theory the model is an opaque feedback controller, replaced every few months, whose closed loop cannot be analyzed directly. We propose a runtime filter, or shield, between any such controller and its environment that certifies a bound on the probability of reaching an unsafe condition during a bounded task. Given a predicate abstraction and candidate successor sets, everything else comes from logs: the loop becomes a finite controlled Markov chain, the estimated kernel is surrounded by a distribution-free confidence region, and robust reach-avoid value iteration runs over it. The certificate is probably approximately correct and uniform over controllers respecting the filter, so one model may replace another without recomputation. In all tested datasets the true risk stayed within certificate and budget; in a file-system sandbox the filter stays sound against a hazard the logs barely covered, where a plug-in baseline certifies safety and fails; and it holds seven controllers, three of them open-weights models, to zero unsafe outcomes in 1050 episodes.

In the Meyer–Miller–Stock–Thoss mapping representation, the Liouville operator of the quantum–classical Liouville equation contains an excess coupling term in addition to the Poisson bracket. Neglecting this term yields the Poisson bracket mapping equation (PBME). We expand the mapping dependence of the density in Hermite functions about the Gaussian factor common to all physical mapping densities. In this basis, the excess coupling term acts purely as a raising operator and exactly cancels the raising contribution generated by the back–reaction force. Consequently, the exact dynamics does not generate higher Hermite orders and closes on a finite, sparse system of equations for the coefficient fields. Within the physical sector, these equations reduce to the subsystem quantum–classical Liouville equation. In contrast, the PBME retains the raising contribution of the force, modifying the back reaction within the physical sector while continuously generating higher Hermite orders. For Tully's dual avoided crossing model, direct propagation of the coefficient equations confirms this finite closure and agrees with independent solutions of the subsystem equation. Comparison with converged full quantum dynamics further shows that, across all regimes examined, the PBME is less accurate than the quantum–classical description for populations, coherences, and momentum distributions.

Organizations pairing a human and a machine on a task decide, often by default, which executes each instance and what happens when both do. We account for what this attains under the squared rule, with performance distributed over instances to capture generalization difficulty. A gross stake lies between the skills' mean and best per instance. It splits at the best single skill into a systematic part, known from separate assessments and secured by commitment, and a residual, the expected value of perfect information on which skill each instance favors, known only from paired observation and split further by classes. Skills set the stake; workflows decide the take, via two channels. Routing directs work, weighting or selecting responses; with binary truth it is capped by the best skill per instance. Reading responses as joint evidence is not routing; what they jointly reveal caps it. Synergy lets skills interact before responding; bounded by no skill either way, its lift over independent responses must clear a break-even and can fall below one. As algorithms, arrangements form a ladder stating what each reads, holds and records, and a procedure whose checks keep earlier gains when class means are known and lose little on finite records given a margin. The theory extends to many skills, each worth what it adds where it beats all others held, and to competing skills, where at parity a single failure's allowed cost decides. In a public chest-radiograph study with 227 radiologists, they are near parity with the model and the stake is mostly residual; assisted reading, no better on average originally, returned less than averaging both responses; recalibrating the model alone beats any deployable arrangement of raw responses. Organizations can learn from their records what is at stake, which arrangement collects it and what evidence each step needs; pricing costs and errors is future work.

Optical music recognition (OMR) for medieval chant lacks training data linking manuscript images to musical symbols across notational families. Using existing Volpiano transcriptions from the Cantus Database, we created 30,567 image-target pairs from ten sources in eleven exports, including 339 verse fragments. Their target sequences contain 1,952,143 tokens. The pipeline locates staff systems, infers clefs and maps known pitches to staff positions. Six detector families handle the different layouts and notations. Where heuristics failed, two small U-Nets learned staff lines and clef letters from manual annotations. Reviews of sampled export lines found zero to four pitch or clef errors, but used different error definitions and do not provide a uniform audit of the corpus. A CRNN trained from scratch achieved a symbol error rate of 9.6 % on 3,086 test lines. The earlier model, trained mainly on Austrian sources of the 15th and 16th centuries, scored 45.3 %. In three separate training runs, each excluding one manuscript, error rates on the excluded manuscript were 21.5-31.0 %. Model-assisted alignment recovered a further 2,686 lines.

This paper presents GpFlash, a Gaussian process library that is focused on fast training and posterior evaluations, minimal memory usage, and scalability to high-dimensional problems. GpFlash was compared to the popular GP libraries scikit-learn, GPy, GPflow, GPyTorch, and SMT on a MacBook Pro and the supercomputer Trillium. GpFlash was found to use less memory and to be faster for training and posterior evaluations relative to the other GP libraries for all cases considered. For example, when using $\nx = 10^4$ training points in a 10-dimensional space GpFlash required 9.6 to 35 times less memory and was 2.6 to 54 times faster than the other GP libraries for the evaluation of the marginal log likelihood and its gradient. The memory reduction was achieved by only using one matrix of size $\nx \times \nx$ to store different symmetric matrices in its lower and upper triangular entries. The computational speedup was the result of designing algorithms to access memory efficiently, using BLAS and LAPACK methods extensively, and factoring kernel equations so that expensive exponential calculations could be reused. GpFlash was more than 440 times faster than all of the other GP libraries considered when evaluating the posterior mean together with its gradient for the case with $10^4$ training points and 10 dimensions. GpFlash is available at https://github.com/marchildon/gpflash.

How the relationship between image-text aligned and vision-only models changes across development remains unknown. We applied time-resolved representational similarity analysis to EEG data from 8-year-olds, 12-year-olds, and adults. CLIP showed significant model-brain alignment already in children, whereas vision-only models aligned more strongly later in development. Residual analyses revealed complementary structure, with CLIP retaining alignment beyond an architecture-matched vision-only model from age 8. Much of the model-brain alignment reflected semantic structure, with EEG representations of category and animacy strengthening toward adulthood, while alignment with low-level image properties remained weak across age. Together, these findings suggest that image-text aligned and vision-only models capture complementary aspects of developing visual representations and may provide useful constraints for AI systems that aim to learn and adapt over time.

For repository-grounded coding agents, a functionally correct patch is not necessarily an acceptable one: developers also constrain how the task must be carried out-modification scope, workflow order, validation, tool use, and reporting. This capability, which we call engineering constraint following, remains largely invisible to current evaluations. We introduce ANCHOR (Assessing Naturalistic Constraint Hierarchies and Ordering in Repository-Grounded Agentic Coding), a benchmark built on naturalistic, multilingual repository tasks spanning eight language groups. ANCHOR combines (i) a hierarchical taxonomy of 10 categories and 78 leaf types distilled from real developer interactions, (ii) an automated pipeline that instantiates task-grounded atomic constraints and composes them into typed AND/THEN/PRIORITY relations, and (iii) a trajectory-grounded evaluation framework that checks both the code diff and the execution trajectory with rule-based and LLM judges. Across 19 agent configurations spanning 2 scaffolds and 10 foundation models on 358 tasks, the strongest measured system, Claude Opus 4.8 under Cline, reaches 70.1% atomic compliance and 63.7% relation compliance, while 19.0% of tasks pass every scored checklist item under the strict all-item FCCR criterion. A five-engineer audit of constraints from 50 instances reports 94% feasibility, 94% repository consistency, and 96% realism. In the primary paired set (14 configurations), the mean signed change in task completion after adding constraints is +0.7 percentage points; individual changes vary in both directions. These results distinguish functional success from constraint compliance, with failures concentrated in workflow ordering, tool-use discipline, and reporting, and substantial interactions between models and scaffolds.

Target speaker extraction (TSE) aims to recover a target speaker's speech from a speech mixture using an enrollment utterance. Recent codec-based generative approaches formulate TSE as conditional speech token generation and achieve promising perceptual quality. However, most existing systems rely on unified codec tokens that entangle linguistic content, speaker characteristics, and acoustic details, forcing a single model to jointly handle target selection, content semantic, and acoustic reconstruction. In this paper, we investigate whether disentangled semantic-acoustic codec representations are better suited to TSE. We first show that simply replacing unified codec tokens with semantic-acoustic tokens is insufficient and can even degrade performance when both remain handled by a unified generative model. Motivated by this observation, we propose a task-aware discriminative-generative framework, where a discriminative branch extracts target-related semantic information, while a generative branch predicts coarse acoustic tokens and refines them under semantic guidance. This specialization separates what is said from how it sounds while coordinating both factors in a factorized codec space. Experiments on Libri2Mix show that our method reduces dWER from 0.388 to 0.118 compared with a unified-codec baseline, while maintaining competitive perceptual quality and speaker consistency. Ablation studies confirm that the gains arise from task-aware semantic-acoustic modeling rather than representation disentanglement alone.

Research on video classification models has witnessed significant growth recently, accompanied by a significant increase in the demand for datasets to train such models. Existing video dataset curation approaches share a common bottleneck: candidate videos must be downloaded before any relevance judgment is made, which results in storage, time and annotation costs. In this work, we present a filtering step, using Large Language Models (LLMs) to pre-screen videos based on their metadata, before actually downloading these videos, thereby saving on these costs. We evaluate the LLMs against a strict human majority vote derived from four independent annotators and validate the reliability of the annotations through inter-annotator agreement analysis (Gwet's AC1). We compare the LLM pre-filter against two no-LLM baselines, namely two keyword heuristics. Via a Leave-One-Rater-Out (LOO) mechanism and an Add-One-Rater-In (AORI), we evaluate the performance of the LLMs as virtual annotators. Finally, we report cost comparisons relative to existing approaches. To ensure reproducability, we made our implementation available on github.

We report a comprehensive experimental study including density functional theory calculations detailing the magnetic ground state of the $S = 1/2$ Mo$^{5+}$ pyrophosphate, LiMoOP2O7, and its magnetic excitations. Neutron powder diffraction measurements confirm the $P2_1/n$ structural model which is comprised of a three-legged ladder of distorted Mo$^{5+}$ octahedra. Magnetometry and specific heat reveal a long-range magnetic ordering transition at $T_\textrm{N} = 3.5$~K and a field-induced transition at $\mu_{0}$H$_\textrm{c}$ = 1 T. This zero-field long-range magnetic order was determined to be a commensurate $\kappa = 0$ order with an ordered moment that is reduced from the full $S = 1/2$ magnetic moment by 30%. Through inelastic neutron scattering measurements and density functional theory calculations, we define the minimal microscopic model and resolve the spin Hamiltonian up to the seventh leading exchange parameter, resulting in a model with dominant antiferromagnetic leg interactions, weaker ferromagnetic rung interactions, and a significant interlayer ferromagnetic coupling.

Real-time bimanual humanoid teleoperation requires accurate wrist tracking while keeping arm configurations predictable. Because a 7-DoF arm admits multiple elbow configurations for the same wrist pose, wrist-only tracking can cause elbow drift or abrupt configuration changes. Fixed anthropomorphic constraints can stabilize elbow posture, but they can also block the redundant adjustments needed near singular configurations. We propose a human-like redundancy-resolution framework that combines adaptive elbow guidance with singularity-robust wrist tracking. Shoulder-wrist geometric retargeting generates robot-scale wrist targets. An adaptive elbow-offset criterion uses the offset direction to guide posture and scales this guidance by the offset magnitude, so the redundant degree of freedom is progressively released as the human arm straightens. A hierarchical velocity solver prioritizes wrist tracking and projects the adaptive elbow guidance into the wrist-task null space. In a fixed-wrist-target ablation, adaptive guidance reduces mean elbow-direction error by 54.4% compared with removing this guidance. In a workspace-boundary stress test, singularity-robust tracking reduces peak raw joint-velocity demand by 97.9% compared with the undamped pseudoinverse. Real-world bimanual tasks and cross-platform retargeting show applicability across robot morphologies.

We describe an optimal-control strategy designed to accelerate the dissipative preparation of complex, highly entangled quantum many-body states. Analogous to optimal steering of isolated quantum systems, our scheme identifies control pulses that guide the evolution of open quantum systems along trajectories of instantaneous steady states while minimizing leakage resulting from non-adiabatic transitions. In many cases of interest, these control parameters can be derived analytically and without the need for computationally expensive numerical simulations of the full many-body master equation. We apply this technique for the preparation of bi- and multipartite entangled states in qubit systems coupled to a common photonic waveguide or a distributed squeezed reservoir. In both scenarios, our optimal-control strategy significantly outperforms the bare relaxation dynamics after a quench, reducing preparation times of near-maximally entangled states by orders of magnitude. This drastic speedup makes dissipative entanglement distribution protocols compatible with high-fidelity quantum information processing applications and illustrates more broadly the potential of leakage minimization for accelerating reservoir-engineering schemes.

We prove that every Lawson surface $\xi_{k,l}\subset\mathbb S^3$ of genus $kl>1$ is non-algebraic: any real polynomial vanishing on $\xi_{k,l}$ vanishes identically on $\mathbb S^3$. This answers a question posed by Hsiang in 1967 and proves Lawson's 1970 conjecture for $\xi_{2,2}$. The proof uses a reflection principle for the monodromy of the associated family of flat connections.

We derive explicit formulas for the dual Moore–Penrose generalized inverse (DMPGI) of dual complex matrix sums under some conditions. We first express the DMPGI of a matrix partitioned into column blocks in terms of these blocks and associated projectors, and then derive two formulas for matrix sums. Two examples illustrate the results. We further apply the formulas to rigid-body motion estimation with two observation points subject to a first-order perturbation of their positions that preserves the rank-deficient observation geometry. The DMPGI recovers the observable motion components from the velocity data.

Diffusion and flow-matching models may struggle to accurately represent distributional tails, especially for heavy-tailed data. Existing approaches often use heavy-tailed noise or modify the generative dynamics, requiring dedicated retraining and more difficult estimation. We take a simpler approach: rather than relearning the full distribution, we correct only the model's behavior in the extreme regime. Our method builds on the radial-angular decomposition of multivariate heavy tails, where radius and direction become asymptotically independent. This allows us to preserve the directional structure learned by the pretrained model and correct only its radial tail. We estimate the tail onset from reference and generated samples, then rescale generated extremes so that their radial survival matches the target distribution. The resulting method is a lightweight post-training correction applied to a frozen diffusion or flow-matching model, requiring neither retraining nor changes to its sampling dynamics. Experiments on challenging synthetic heavy-tailed distributions and real weather and wildfire datasets show that this simple correction substantially improves extreme-tail coverage using only a small number of fitting samples.