Papers

Examples of one-sided balanced shifts which do not have variable specification are provided. On the other hand, under synchronization condition, bi-balancedness is proven to be equivalent to variable specification.

Molecular qubits held in conservative optical traps may lose coherence when they scatter photons from the trapping lasers. The rate for this process has two parts, one equal to the mean Raman scattering rate of the two qubit states, and the other proportional to the square of the difference in their Rayleigh scattering amplitudes. This paper calculates the decoherence rate, expressing results in terms of the vector and tensor parts of the molecular polarizability, $\alpha_1$ and $\alpha_2$. While the decoherence rate is generally much larger for molecules than for atoms, it is suppressed at wavelengths where $\alpha_1$ and $\alpha_2$ are both small. The wavelengths where this occurs are identified for CaF molecules.

The recent resolution of the Nisan–Ronen conjecture~\cite{NR,CKK} establishes that the optimal worst-case approximation ratio of deterministic truthful mechanisms for makespan on m unrelated machines is exactly m. We ask how prior information, Bayesian incentive compatibility (BIC), randomization, and machine-side resource augmentation change this barrier. We obtain three main results. First, we prove an asymptotic 4/3 lower bound for randomized BIC mechanisms with two machines, strengthening the previous 1.2 deterministic-BIC lower bound~\cite{MS}. Second, in the prior-free setting for two machines, randomization improves the known truthful ratio from 2 to 7/4~\cite{NR}. We show that randomized BIC scheduling mechanisms are likewise strictly more powerful than their deterministic counterparts, exhibiting an asymptotic BIC-integrality gap of 8/7. Thus, optimality in prior-dependent BIC scheduling can strictly require randomization. This parallels the role of lotteries in multidimensional revenue maximization, where randomization can strictly improve revenue~\cite{MV,BCKW}. Third, we show that when job assignments are sufficiently well spread across machines (more formally, when the pairwise collision parameter $\Delta_r$ is bounded by a constant independent of both the number of machines m and the number of sampled layers r), then $O(m/\varepsilon)$ sampled layers suffice for the standard truthful MinWork mechanism to achieve a $1+\varepsilon$-approximation to the original first-best benchmark. Equivalently, $O(m/\varepsilon)$ sampled replicas per machine suffice. This resource-augmentation result parallels the Bulow–Klemperer perspective~\cite{BK,EFFTW}. As a by-product, in the standard unaugmented model, MinWork achieves a $(1+\frac{\Delta_1(m-1)}{2})$-approximation to the first-best benchmark for every prior.

We classify the exact evaluation of $\operatorname{Holant}(f\mid=_3)$ for every fixed complex algebraic symmetric Boolean ternary signature $f$. An input is a cubic bipartite multigraph: every vertex on one side carries $f$, every vertex on the other side carries ternary equality, and no auxiliary signatures are freely available. The tractable signatures are precisely rank-one tensors, generalized equalities, and equality-preserving cube-root diagonal transformations of six affine signatures, together with nonzero scalings and reversal. Every other signature gives a $\#\mathrm{P}$-hard problem under polynomial-time Turing reductions. We also identify the exact real intersection: it consists of the same tractable families as in the rational classification, with real algebraic parameters. The proof preserves degree exactly three on both sides of every oracle instance. A rank-one matrix extracted by interpolation supplies one unary signature only after its unused factor has been absorbed in triples. Over the complex numbers this absorption has three exceptional projective directions. We combine this constraint with projective matrix-group orbits, explicit ternary replacements, and an exhaustive treatment of finite projective orders. The cases of orders three and five include exact polynomial certificates; the certificate identities and a rational-arithmetic verifier are supplied as supplementary material.

Decision-focused surrogates can recover downstream decisions without identifying the quotient report. We characterize the equality set of the convex Smart Predict-then-Optimize surrogate (SPO+) population risk. Under central symmetry, the centered mean class is the unique Bayes minimizer exactly when every nonzero effective displacement makes the old optimizer leave the shifted optimal face with positive probability. This condition separates face crossing from selected-oracle disagreement and gives quantitative local coercivity. Without symmetry, strict crossing alone need not identify the mean; selection balance with reflected crossing restores quotient-report identification, and conditional versions extend the result to measurable predictors. These are population statements, without finite-sample report-recovery or generic transfer-regret guarantees. Closed-form mechanisms reproduce the analytic identities and rates. Portfolio, complete-matrix KuaiRec, and Energy/Storage studies measure predictive fidelity, shifted regret, and fitted-report geometry. A known data-generating process (DGP) companion retains their application geometries while isolating conditional-mean recovery and crossing, without testing the original observational assumptions.

We study a fixed-normalization class of symmetric bimatrix games generated by a common kernel and show that it admits efficient approximation despite exact symmetric-equilibrium computation remaining PPAD-hard. For every rational game in the class, a single auxiliary zero-sum saddle computation yields a rational symmetric \(1/5\)-approximate Nash equilibrium in polynomial time. We also give exact recognition and unique kernel recovery, and an exact polynomial-time post-processing algorithm that minimizes regret along the segment joining the selected saddle strategies. For arbitrary rational square games, we formulate the nearest common-kernel projection as a linear program with an explicit dual certificate, obtaining a certified \((1/5+2\eta^*)\)-approximation guarantee. A separate selector result proves a sharp regret-to-uniformity constant for the full-subset construction. The results provide a tractable and certifiable structured-game regime and clarify which common-kernel reduction architectures cannot support certain fine-grained approximation-hardness objectives.

Large language models (LLMs) and multi-agent systems (MAS) have shown promise in financial decision-making, yet existing evaluations focus on equity trading and primarily assess directional prediction, overlooking the structural complexity of derivative markets. Option trading introduces fundamentally different challenges, including nonlinear payoffs and multi-leg strategy construction, requiring structured decisions rather than simple directional bets. We introduce LiveOption, an evaluation framework for LLM-based agents in option trading. LiveOption formulates the problem as structured sequential decision-making under realistic execution and capital constraints, and provides a reproducible environment with standardized interaction protocols. The framework includes three task suites covering portfolio overlays, event-driven earnings trading, and 0DTE intraday trading. We further propose a hierarchical metric suite that evaluates action validity, decision quality, risk characteristics, and outcome-level performance. Experiments show that current agents often fail to achieve competitive returns in most scenarios. LiveOption offers a principled testbed for evaluating structured decision-making beyond outcome-based metrics. Project Website: https://liveoption.github.io/

A noetherian form over a category enables one to formulate and prove homomorphism theorems in that category, such as the isomorphism theorems and the diagram lemmas of homological algebra. In this paper we develop a strategy for establishing existence of a noetherian form over a given category, which enables one to find noetherian forms for a broad range of concrete categories. While it was already known that all semi-abelian categories, Grandis exact categories and algebraic categories have noetherian forms, we now establish that so do wide classes of essentially algebraic and topological categories, which include the categories of small categories, groupoids, topological spaces, extended pseudometric spaces, approach spaces, graphs, measurable spaces and axiom-free relational structures.

Intelligent handover management is a key capability for future 6G networks. This paper investigates enhanced handover strategies in systems assisted by Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surfaces (STAR-RIS). In addition, it explores the optimal placement of multiple base stations (BSs) to further improve network performance. To eliminate coverage dead zones, a Deep Deterministic Policy Gradient (DDPG) framework is utilized to enforce a Max-Min Fairness objective, directly maximizing the worst-case Signal-to-Noise Ratio (SNR). This optimized topology is evaluated via a dynamic mobility stress test simulating 180 pedestrians executing A3-event handovers under stochastic transient blockages. Results demonstrate that the DDPG deployment outperforms random baselines by a 3.17 dB mean gap, achieving a 24 dB worst-case SNR and a 0.963 Jain's fairness index. Crucially, this optimal static placement drastically improves dynamic mobility resilience, ensuring a 100% successful handover rate and reducing post-failure outage time to a negligible 0.01%.

When post-training large language models on tasks with semi-verifiable rewards, there are many factors (training steps, base model size, training order, data quality, verifier accuracy, etc.) that practitioners must contend with to maximize model performance. Yet, it remains unclear how well verifier agreement predicts post-training performance on such tasks. In this paper, we explore this question with over 11k H100 GPU-hours, across HealthBench and PRBench tasks in medical, legal, and finance domains. Across the tested domains, Qwen3 trainees (1.7B-8B on HealthBench; 8B on PRBench), evaluation splits, and frontier LLM reference judges (which we call golden verifiers), higher verifier agreement does not consistently identify the best training verifier. Expensive verifiers need not outperform inexpensive ones, and open-weight Gemma verifiers produce strong training outcomes. We compare two low-cost choices retrospectively – a cost-reducing choice and a balanced choice – with estimated grading cost reductions of 98.8%-99.7% relative to the golden grading protocols and average post-training score gaps of 1-3 points from the best evaluated training verifier. These averages include larger losses in individual settings; they do not establish that verifier choices are interchangeable.

Infectious disease models that allow for reinfection, such as the SIS or SIRS frameworks, typically treat all infections as exchangeable and independent, erasing the temporal structure of individual reinfection histories. Here, we introduce a minimal "chain SIR" model that resolves this limitation by indexing compartments by reinfection count and allowing transmission, recovery, and waning rates to depend on that count. The dynamics generate an advective flux along the reinfection ladder, producing traveling waves in reinfection space and a coherent structure in the population's lifetime infection histories. We derive an analytical expression for the wave speed and identify the general conditions under which such cohort waves exist and persist, offering a new lens to interpret long-term prevalence patterns and the emergence of age- or immunity-structured endemicity. Finally, comparing the speed formula with longitudinal cohort data, we quantify the reduction in reinfection rate attributable to immunological responses for several seasonal viruses, including influenza A/H3N2 and respiratory syncytial virus (RSV).

Improving language model efficiency requires not only cheaper operations but also eliminating redundant computation. We argue that effective modeling requires information accessibility and computational depth, but not repeated historical retrieval across layers. Guided by this principle, we introduce the Global State Model (GSM), a causal encoder–decoder architecture that separates historical information acquisition from deep computation. The encoder progressively aggregates long-range information through multi-stage sparse retrieval into a fixed-size shared state, while decoder layers perform successive transformations over this state without repeated historical access. This design makes decoder attention and cache costs independent of history length, while dependency-aware pruning further reduces prefill computation. Experiments across multiple model scales show that GSM achieves downstream performance comparable to matched DeepSeek-V4.1-Flash-based baselines, with improvements at some scales, while preserving long-context retrieval capabilities. GSM also improves training and inference throughput and reduces cache overhead. These results demonstrate that eliminating architectural redundancy offers an effective path toward efficient language modeling without sacrificing information accessibility or computational depth.

World models learn internal representations of environment dynamics to predict future states, enabling agents to optimize action plans without physical interactions. However, developing world models that genuinely internalize underlying causal physical laws to explicitly reason about action preconditions and subsequent state transitions remains an open challenge. In this paper, we propose VIDEAS, a data distillation framework that transforms continuous physical dynamics from operational videos into explicit action semantics for foundation models. Specifically, it deconstructs visual demonstrations into discrete action trajectories and utilizes advanced vision-language models (VLMs) to extract structured knowledge encapsulating action preconditions and effects. To ensure physical consistency, we introduce a prior-guided trajectory simulation mechanism grounded within a text-based environment to rigorously validate the extracted knowledge. Notably, we incorporate negative trajectories to enrich knowledge completeness and enhance data diversity to mitigate cognitive bias. Furthermore, we present VIDEAS-WM, an 8B/9B-parameter suite of language-based world models trained on 34K high-quality samples derived from AgiBot-World dataset. Extensive experiments demonstrate that VIDEAS-WM establishes state-of-the-art performance in high-level embodied action semantic reasoning, exhibiting profound physical understanding and robust generalization across unseen scenarios.

Supervised fine-tuning (SFT) learns most aggressively from tokens that the model deems least likely. This helps acquire new behaviors, but also amplifies noisy or conflicting supervision and can overwrite useful pretrained knowledge. Through a unified policy-loss view, we revisit existing token-reweighting methods and show that they assign nonnegative coefficients to demonstrated tokens. Consequently, they can suppress or amplify supervised updates, but cannot reverse harmful features once learned. Moreover, larger training weights do not amount to feature extrapolation, since they change the optimization trajectory rather than scale a fixed SFT direction. We argue that reversal and extrapolation require a stable reference frame defined by a fixed SFT delta. Motivated by this, we propose SCALE (Selective Control of Adaptation via Local Entropy), an entropy-guided adaptation-strength-control method that freezes the pretrained model and the SFT delta and learns bounded token- and module-specific gates by minimizing predictive entropy alone. These gates suppress, reverse, or extrapolate frozen SFT features according to their alignment with entropy reduction. Across Qwen2.5-Math-1.5B, Qwen2.5-Math-7B, and Qwen3-4B-Base, SCALE achieves mathematical-reasoning averages of 37.84, 43.60, and 36.57, exceeding the strongest corresponding baselines while remaining competitive on general-retention benchmarks. It also attains the best average code-generation performance across HumanEval, HumanEval+, and MBPP for all three models. These results suggest that effective SFT correction can benefit from controlling how already learned residuals are used, rather than only modifying how they are learned.

Omnidirectional or 360 cameras provide embodied AI agents with a holistic, wide field-of-view (FoV) view of their surroundings, motivating the use of Multi-modal Large Language Models (MLLMs) for omnidirectional spatial reasoning. However, most MLLMs are trained on conventional 2D perspective images and struggle with the severe distortions and wrap-around discontinuities induced by spherical geometry. Enabling them to generalize to non-Euclidean 3D spaces without retraining therefore remains challenging. We propose SphMind, a training-free, plug-and-play framework that decouples semantic perception from geometric reasoning. Rather than requiring MLLMs to learn spherical geometry internally, SphMind preserves their semantic capabilities while handling geometry externally. We introduce a Spherical Harmonics-based Spatial Graph (SHSG) that models spatial relationships through equivariant transformations on the sphere, together with Inference-Time Geometric Grounding (IGG), a model-agnostic closed-loop optimization process that aligns MLLM representations with spherical geometric constraints during inference. Experiments on three benchmarks show that SphMind achieves over 21.4% average improvement in directional reasoning on MP3D and Stanford2D-3D, outperforms prompt-engineering baselines by 8.7% on the real-world ODI-Bench, and improves rotational invariance by 5.9% under panorama rotations, without additional training or dataset-specific tuning. In-the-wild evaluations further show that SphMind resolves directional reasoning queries that baseline vision-language models fail to answer correctly.

Runtime monitoring traditionally evaluates a specification that is fixed before execution or externally modified when requirements change. In learning-enabled and data-intensive systems, however, the temporal relationships represented by a specification may themselves evolve. Allowing an AI component to directly replace a formal specification is unsafe: it may overfit transient behavior, weaken protected requirements, or activate statistically unsupported revisions. We introduce an intersymbolic architecture in which an untrusted AI proposer suggests temporal specification revisions and a symbolic governor controls their activation. Two results organize the framework. First, origin-version semantics makes the outcome of each obligation invariant to later revisions. Second, aggregate certification can conceal systematic failures on protected triggers; simultaneous aggregate and core-conditional post-selection certification controls both targets. A structural invariant preserves designer-protected components, and a proposer-independent lifetime error bound supports repeated activation decisions. The statistical bound concerns the predictable means of completed certification samples; interpreting it as future operational validity requires an additional stability assumption. Controlled synthetic experiments use a frozen supervised AI proposer to illustrate the masked-core failure at one decision and across repeated governed revisions. The proposer is a supervised regressor trained offline on synthetic tasks and frozen before use; it ranks candidates by predicted aggregate margin and never observes the protected-trigger success rate, so the masked-core failure arises from optimising the aggregate rather than from an adversary constructed by hand.

Semiconductor electronic devices are increasingly constrained by fundamental quantum tunneling effects and charge-based mechanisms, which severely limit further miniaturization, write-speed scaling, and environmental robustness of silicon-based technologies. These limitations are particularly prohibitive for deep-space exploration, where extreme temperatures, ultra-strong magnetic fields, and intense radiation rapidly incapacitate conventional electronics without massive shielding. Here, we present an intrinsically resilient, strain-mediated antiferromagnetic MnIr/PMN-PT edge processor that operates reliably as a bare die under temperatures up to 500 K, magnetic fields of 55 T, and radiation doses of 1.5 Mrad. By exploiting an input-modulated in situ self-refreshing encoding mechanism, the device performs nonlinear feature extraction and classification directly from raw analog signals, enabling an analog computing architecture that requires no time-frequency transformation. This architecture achieves 99.8% accuracy in speech recognition without digital preprocessing and 100% accuracy in astronaut visual object recognition. Furthermore, an all-hardware integrated drone vision system demonstrates real-time in situ command execution and autonomous navigation, delivering a terahertz-level response frequency and an ultra-low energy consumption of approximately 0.2 fJ per operation. This work expands the functional scope of antiferromagnetic devices beyond memory and logic, establishing them as a promising materials platform for energy-efficient physical computing and autonomous intelligence in extreme environments.

It is shown that all solutions of the canonical equation y^a = 1 + a*x*y^b with arbitrary complex exponents a, b (case m = 1) and of its limiting cases - the binomial root y = (1 + a*x)^(1/a) at b = 0, the exponential y = e^x at a = 0, b = 0, and the Lambert equation y = e^(x*y^b) at a = 0 - as well as the logarithms of these solutions (case m = 0), are expressed by a single power master series M(m; a; b; x) = m + x + ((m - a + 2b)/2!) x^2 + ((m - a + 3b)(m - 2a + 3b)/3!) x^3 + ... For multivalued solutions beyond the radius of convergence, a geometric criterion for selecting the conjugate series (the same master series, but with a different set of parameters M(m; a'; b'; x')) is proposed, ensuring branch continuity on the complex plane. This representation of power series in terms of master numbers not only allows one to compute coefficients in degenerate cases where the gamma-function representation loses meaning, but also provides a transparent analytical algorithm for the merge operation on master series. The method is illustrated on problems in gas dynamics and plasma physics, where it is demonstrated that physically realizable states require the application of conjugate series beyond the radius of convergence of the basic expansion.

Multimodal large language models answer audio questions, but how they represent auditory semantics and use them in decisions remains unclear, limiting our understanding of response formation. We study dog barking in Qwen2.5-Omni-7B using Jacobian lens (J-lens) readout and directional interventions. We define the dog direction as a J-lens-derived hidden-state vector associated with dog; adding or removing its component modulates dog-related information. We find this information decodable without dog/bark prompt cues or animal-identification requirements. Directional interventions change response tendencies and some final answers, with effects concentrated in late-layer states immediately before generation across species classification, vocalization classification, and sound description. The dog direction shows no comparable advantage over controls in animal/other classification. These results provide causal-intervention evidence that the dog direction affects output scores in a task-dependent manner, most consistently at L22 and L24 immediately before generation.

Many dense-prediction benchmarks evaluate rare events by pooling prediction and target over spatial blocks, thresholding each, and scoring the contingency table. At a fixed rare operating point, the max-pooled Critical Success Index (CSI) confounds spatial discrimination with amplitude calibration: sharp observations promote many blocks above threshold, while attenuated predictions from squared-error regression leave the same blocks below it. We repurpose classical monotone calibration as a symmetric audit: a post-hoc transform fitted on held-out data and applied separately to each system. The transform cannot reverse pixel ordering, so any contrast it reproduces cannot establish improved spatial ranking. On SEVIR, two released checkpoints of one architecture differ by -29.5% in extreme-threshold CSI before the control and by +5.3% after it. Across 450 pairwise contrasts among 6 systems, the difference in pooled frequency-bias deviation is associated with how far the CSI contrast moves under the control (r = +0.796), and 51 contrasts reverse sign. At CasCast's published extreme-event operating point, the cascade-over-backbone CSI gap falls from 0.1601 to 0.0339, a 78.8% reduction; the remaining gap stays positive. The effect persists when the transform is fitted on a window before the test period, and calibration also reveals advantages hidden by a better-calibrated baseline. On geostationary infrared imagery the relative gain grows as events become rarer, crowd counting reproduces the bias-gain relationship under patch-sum pooling, and semantic segmentation, where frequency bias is already near one, shows little average change. The confound therefore requires both a fixed operating point and a training regime that leaves the output miscalibrated there. We recommend reporting pooled frequency bias and a symmetric held-out FreeKnob Audit alongside rare-event pool-and-threshold scores.

Weighted split conformal prediction reweights calibration scores by the likelihood ratio between the test and training covariate distributions and guarantees marginal coverage under covariate shift. We study its coverage conditional on the calibration data. An elementary argument, based on a single concentration inequality at a fixed population quantile, gives explicit training-conditional bounds without unspecified constants, and shows that the relevant scale is not the supremum of the likelihood ratio but a variance proxy built from the chi-squared divergence of the shift and from the average of the ratio over the part of the test population, of probability equal to the miscoverage level, where it is largest. A two-point lower bound shows that the root-m rate and the chi-squared contribution are intrinsic to the shift. Run at an explicitly inflated level, the weighted quantile becomes a deterministic PAC prediction set. We compare it with randomized rejection sampling and with importance-weighted learn-then-test and, through a certified choice of a clipping level for the likelihood ratio, map the regime in which each gives the narrower valid set. The analysis extends to estimated likelihood ratios and to tail functionals estimated from an unlabeled source sample, which yields a fully finite-sample certificate.

On-policy distillation (OPD) trains a student model on its own trajectories using dense token-level feedback from a stronger teacher model. Since each update is conditioned on the reasoning prefix already generated by the student, the prefix also shapes how effectively teacher feedback is converted into learning. We find that shared prefixes can lead to weak token-level updates, a phenomenon we call Prefix-Induced Supervision Attenuation (PISA). This attenuation arises in two common cases. (i) High student confidence can weaken corrective gradients even when the teacher disagrees. (ii) Tokens that rely on earlier reasoning can receive learning signals as weak as those for simple local continuations. To solve this problem, we propose Trajectory Dropout, a simple training-time intervention that exposes these weakened signals. The student first performs a standard full-context rollout to generate a complete trajectory. During training, we randomly drop a certain proportion of the student's reasoning trajectory, while the teacher continues to observe the complete trajectory for token-level supervision. This intervention strengthens corrections for overconfident predictions and introduces additional supervision at prefix-sensitive positions. Trajectory Dropout consistently improves average performance across teacher–student model pairs of different scales and six mathematical reasoning benchmarks, while also yielding gains on two out-of-domain benchmarks. It can also be flexibly integrated into existing OPD variants with negligible computational overhead, further improving their performance. These results demonstrate that Trajectory Dropout provides a simple mechanism for strengthening token-level supervision across model scales and OPD objectives.

We study the spin-$1/2$ Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice with a symmetry-preserving tri-coloring of the Kitaev exchanges. We focus on two cases: (i) the pure Kitaev model with anisotropic exchanges and (ii) the Kitaev-Heisenberg model with isotropic Kitaev exchange. In the absence of Heisenberg interactions, we use the standard mapping of the Kitaev model onto a quadratic Majorana-fermion problem in a $\mathbb{Z}_2$ gauge field. We find a gapped energy spectrum throughout the positive-coupling phase diagram, except at a single point where the twofold-degenerate energy bands form a Dirac cone. This unique gapped region corresponds to a toric code phase. However, depending on the couplings, vortex excitations on square, hexagonal, and dodecagonal plaquettes realize three distinct relative assignments to the $e$ and $m$ anyons. We determine these relative assignments from the physical fermion parity of the vortex sectors and locate their boundaries by tracking zero crossings of vortex-bound Majorana levels. For the isotropic Kitaev-Heisenberg model, we combine graph-based projected entangled-pair-state calculations, exact diagonalizations, and linear spin-wave theory to study the entire phase diagram. Apart from the toric code topological phases that are robust around the Kitaev limits, we obtain four collinear magnetically ordered phases that can be characterized by their local and relative orderings of hexagonal plaquettes. We also identify a special point at which the ground state is a product state.

Bell's theorem establishes that a local and spatially separable physical theory with no superdeterminism or retrocausality must be a theory of many local worlds. The local many worlds formalism of quantum mechanics is a transparent separable physical theory in spacetime with a Lorentz covariant causal structure. Unlike the Everett many worlds interpretation, there is no nonseparable universal wavefunction in configuration space, but like Everett, there is only local unitary evolution which conserves probability (fluid) current, and no wavefunction collapse. Each event in spacetime has its own local wavefunction which is built up using only the local wavefunctions and local unitary evolution operators within its past light cone, and which is entirely disconnected from spacelike separated local wavefunctions. We call this the local Schrödinger picture. Local many worlds can also be described in the Heisenberg picture by ascribing Deutsch-Hayden (DH) descriptors to each individual system, each of which evolves under local unitary operations. Both the local wavefunctions and DH descriptors contain records of past interactions, and while the local wavefunctions provide a clear and intuitive physical narrative, the descriptors contain all of the same information in a much more compact form. Unfortunately, the compact form is also somewhat cryptic, which has made the local Heisenberg picture relatively inaccessible. The purpose of this article is to show that the local wavefunctions for any $N$-qubit system can always be constructed directly from the DH descriptors, allowing us to combine the benefits of both pictures.

We study transition amplitudes of the quantum universe in $D$-dimensional spacetime within the de Sitter minisuperspace approximation in Einstein gravity. Using the Lorentzian path integral combined with Picard-Lefschetz theory, we identify the saddle points that contribute to the integral and derive a well-defined transition amplitude under Dirichlet boundary conditions. We further show numerically that a resurgence analysis based on Borel-Padé resummation is effective in resolving the residual Stokes ambiguities that arise in certain cases. Analyzing three-, four-, and five-dimensional cases, as well as the large-$D$ limit, we find that the tunneling proposal is commonly realized for the creation of the universe from nothing. This result implies a universal feature of quantum cosmology based on Einstein gravity across dimensions.

We present DAOCP, a dual active set solver for linear quadratic optimal control problems with stage-wise equality and inequality constraints. Active set methods are leading Model Predictive Control benchmarks for full-body robotics, but existing solvers operate on dense QPs, while typical problem dimensions favor methods that exploit the optimal control structure. DAOCP combines the warm-starting capabilities of active set algorithms with the better computational scaling of structure exploiting solvers, by relying on a generalization of the relationship between the Riccati recursion and the Cholesky factorization of the condensed Hessian. This result enables dual active set iterations to operate directly on the original optimal control problem through recursive computations, without explicitly forming the condensed quadratic program. On robotics benchmarks, DAOCP is the fastest of four solvers in four of five scenarios, cutting average solve time on a 58-state Atlas model by 9$\times$ relative to state of the art solvers DAQP and HPIPM.

Extracting who is where, on which team, wearing which number from a broadcast frame is typically done by stitching a detector, an OCR engine, and classifiers together – and the stitching step swaps identities under occlusion. We make association native instead: a 0.77B vision-language model (Florence-2) is fine-tuned to emit all per-person attributes as one grammar-constrained sequence, with each attribute generated inside its owner's block. Output is therefore schema-valid on every frame by construction, and no post-hoc binding step exists to attach a correctly read number to the wrong player: residual misassociation is pure perception error, $\approx4\times$ rarer than zero-shot-prompted frontier APIs' (0.057 vs. 0.21-0.24). On a frozen multi-sport test set, this single pass reaches 0.95 detection F1 (APIs: 0.65-0.75). A single extra forward pass yields a per-field confidence that supports a reject option (jersey precision $0.71\rightarrow0.96$ at half coverage) and routes a training-free zoom-and-re-read for small players. Surprisingly, once the grammar is learned, further parameter-efficient tuning yields no measurable gain under the adaptation configurations we test; the identical recipe on WIDER-Attribute reaches 93.1 mAP given-box, yields the first detection-coupled end-to-end results under its standard test protocol (84.5 mAP), and reproduces the same tuning result. In this regime, the gains live in the structure, not in added weights.

Historical manuscript illustrations preserve rich visual evidence of past cultures. They depict people, animals, plants, diagrams, music notations, and decorative forms. Although large digitization projects have made many manuscripts available online, the material itself remains difficult to explore at scale. Extraction systems can find illustrations on manuscript pages, but without meaningful categories, large collections remain hard to search and explore. We address this gap by introducing a manually labeled dataset of 15,000 illustrations from manuscripts dating back hundreds of years across 22 categories, and evaluating modern vision models for image classification on this task. The problem is challenging due to stylistic diversity, degradation, and semantic ambiguity, with many images that fit more than one category. We compare fine-tuned CNN and Transformer-based classifiers, zero-shot CLIP, embedding-based classifiers, and direct vision-language models. Results show that fine-tuned image classifiers perform best overall, with ConvNeXt reaching 88.9% accuracy and 81.3% macro-F1. Using CLIP embeddings with XGBoost provides a strong alternative. In contrast, zero-shot CLIP and direct vision-language classification perform substantially worse, highlighting the limits of general-purpose models in this domain. Beyond overall performance, the analysis reveals which categories are visually separable and where errors reflect genuine semantic overlap, suggesting that some limitations arise from the taxonomy itself.

We compute the Higgs thermal mass and the electroweak and colour Debye mass parameters to full $\mathcal{O}(g^6)$ in dimensional reduction, where $g$ represents a gauge coupling or the top Yukawa. We employ new methods to evaluate previously unknown mixed-signature sum-integrals.

Guideline documents are published as unstructured PDFs whose evidence is locked in visual structures—tables, flowcharts, and graded recommendations—that standard retrieval pipelines flatten into fixed-size text chunks. We cast evidence access as a document image analysis problem: parse each page image into typed structural elements, then retrieve structure-aware evidence units that follow the document's own layout (sections, table rows, flowchart paths, graded recommendations), each keeping its structural context so a result points to a specific element rather than a page. On 26 clinical practice guidelines from 9 sources (3,619 pages, Chinese and English) with 199 evidence queries, structure-aware units rank the gold element first under BM25, dense, and hybrid retrieval (hybrid Element Hit@1 of 0.382), with a significant element-level ranking gain over per-element OCR text (MRR_e +0.107, p=0.002; the Hit@5 gain is directional, p=0.17), while matching page-level recall (Page Hit@5 0.879 vs. 0.889, p=0.75) at 3.8x less context and clearly outperforming a ColPali visual-RAG baseline (PH@5 0.497).