Papers

Let $W_s=K_1+C_{s-1}$ denote the wheel on $s$ vertices. We give structural proofs that $R(C_{14},W_{11})=27$ and $R(C_{15},W_{11})=29$. Together with the theorem of Chen et al. for $n\ge16$, these equalities give $R(C_n,W_{11})=2n-1$ for every $n\ge14$. The two boundary values were included in an earlier survey announcement. We also give structural proofs of $R(C_8,W_7)=15$, $R(C_9,W_7)=17$, and $R(C_8,W_9)=15$. The common starting point is a Hamilton-connected core lemma. For the eleven-vertex wheel, bounds on vertex connectivity and on the matching number of a bipartite graph associated with a local cycle yield a vertex cut of order nine. Paths with prescribed endpoints then rule out every possible pair of orders of the two remaining vertex sets. For the smaller wheels, we use the structure of critical cycle colorings and local cycle-shortening arguments. We also give complete structural classifications of the $(C_8,C_6)$- and $(C_9,C_6)$-critical colorings, recovering the previously reported counts 24 and 26. All proofs are combinatorial and use no exhaustive graph enumeration.

General-purpose agents can plan, use tools, and revise their behavior from feedback, but it remains unclear whether these capabilities transfer from digital environments to embodied manipulation. To investigate this question, we introduce LIBERO-Agent, an agent-native benchmark for evaluating these agents in robot manipulation tasks. Rather than asking agents to submit task-level Python control programs or operate through high-level robot skills, LIBERO-Agent provides an interactive robotic environment where agents can select which observations to inspect, process them with their own tools, and issue native action commands. LIBERO-Agent integrates 200 tasks into a common interaction framework and provides a 30-task primary suite that separates perception, short-horizon execution, and long-horizon composition. Results reveal a pronounced reliability gap: while agents perform well on perception and easy short-horizon tasks, their performance degrades substantially on hard short-horizon and long-horizon tasks. Richer observations improve short-horizon manipulation, while demonstration benefits depend on the agent and format. Among these agents, GPT-6 Astra achieves the strongest overall performance. Further analysis shows its major advantage lies in mechanism interaction, especially when sustained physical contact is needed, while its remaining failures stem from cross-stage interference and geometric errors.

We consider a procedure for nonperturbative quantization based on an infinite system of nonperturbative Dyson–Schwinger equations. We propose a first approximation for truncating this infinite system of equations in the static case. The main ideas underlying this approximation are as follows: (a) the two-point Green's functions of vacuum gauge fields are factorized by introducing scalar fields; (b) in the non-vacuum case, the degrees of freedom of the $SU(3)$ gauge field can be divided into “almost classical” and “almost quantum” degrees of freedom; (c) the four-point Green's functions of the gauge fields are represented as bilinear combinations of two-point Green's functions; (d) an approximation for the three-point Green's function describing the interaction between quarks and gauge fields is proposed, which leads to the splitting of the original Dirac equation for the quark-field operators into two equations, one describing the expectation value of the fermion field and the other acquiring a nonlinear term and serving to describe a condensate composed of sea quarks bound by the vacuum gauge field. We consider the choice of gauge appropriate for this approximation to nonperturbative quantization. We point out that the emergence of a nonlinear Dirac equation within this approximation may lead to a mass gap in the energy spectrum of solutions of the corresponding systems of equations. The issue of the emergence of “dimensional transmutation” within this approximation is also discussed. We provide arguments in favor of the statement that the “closure constants” appearing in the finite truncation and giving rise to “dimensional transmutation” should survive in the transition to the infinite system of Dyson–Schwinger equations. An analogy between nonperturbative quantization and the stochastic theory of turbulence is also discussed.

For a quasi-projective arithmetic surface $\mathcal U/\mathbb Z$ and a compact subset $E\subset \mathcal U(\mathbb C)$ under mild regularity assumptions, we study algebraic integral points on $\mathcal U$ whose Galois orbits lie in $E$. We characterize the collections of local probability measures that arise simultaneously as the local limit distributions of Galois orbits of such points. Our result also works for measures prescribed at a subset of places. This generalizes the results of Smith and Orloski–Sardari on $\mathcal{U}=\mathbb{A}^1$ concerning the archimedean place. As a consequence, we prove an integral version of Szachniewicz's theorem on curves, which states that every integral GVF functional can be approximated by a sequence of algebraic integral points in the GVF topology. We also give several applications: we prove that the essential minimum of height functions on curves can be attained by algebraic integral points; we connect integer Chebyshev constants with the essential minima of certain height functions on $\mathbb{A}^1$ and prove a conjecture of Montgomery; we also answer affirmatively a question of Levenberg–Londhe by showing that the smallest limit of averaged trace of totally positive algebraic integers can be attained by a sequence of totally positive algebraic units.

We present PartiCam, a training-free Particle filtering rooted method for improved Camera controlled video generation. Generating videos that follow a precisely specified camera trajectory remains challenging for large video diffusion models. Training-free approaches are backbone-agnostic and avoid the need to construct large camera-annotated datasets by steering pretrained models toward the desired camera motion at test time. This enables the generation of camera-controlled video data that can subsequently be used to train camera-conditioned video diffusion models. Existing sampling-based guidance approaches often suffer from unstable trajectories: they either explore too broadly and fail to respect the target camera motion or collapse early and lose visual diversity over time. We introduce a global-local refinement framework for diffusion reward guidance, enabling accurate and consistent camera control during video generation. Our method builds on Sequential Monte-Carlo (SMC) guidance, but introduces a local refinement stage based on particle filtered resampling. Experiments show large improvements in camera trajectory adherence, reduced drift, and better visual quality, without requiring model retraining.

We discuss central exclusive production (CEP) of $\eta$ and $\eta'(958)$ mesons in high-energy proton-proton collisions using the tensor-pomeron approach, incorporating absorption effects at the amplitude level. Model parameters are constrained using WA102 experimental data measured at $\sqrt{s} = 29.1$ GeV. We present cross sections and differential distributions for the LHC energy of $\sqrt{s} = 13$ TeV. For $pp \to pp \eta$, the upper limit of the total cross section is 2.5 $\mu$b for $|\eta_{M}| < 1$ and 5.6 $\mu$b for $2 < \eta_{M} < 5$. For $pp \to pp \eta'$, the predicted cross sections are 0.3–0.7 $\mu$b and 0.9–2.1 $\mu$b in the respective pseudorapidity regions. These results demonstrate the feasibility of studying diffractive flavour singlet pseudoscalar meson production to probe the nature of the pomeron at the LHC.

The interaction between flame dynamics & hydrodynamic instabilities plays a fundamental role in determining the stability of swirl-stabilized combustors. In the present study, we investigate the hypothesis that spatial overlap between flame & wavemaker region is a necessary prerequisite for combustion stability in flows characterized by a wavemaker region. To test the hypothesis, a low-momentum secondary methane injection was introduced through circumferential holes located on the centerbody of a swirl-stabilized burner. The injection velocity was maintained below 5% of bulk flow velocity to minimize momentum-induced modifications of flow field while selectively redistributing heat release. In addition, an equivalent amount of fuel was diverted from primary fuel supply to secondary injection ports, known as fuel-staging, to isolate the effects of flame relocation from those of the total fuel flow rate. The introduction of secondary injection produced a transition of the flame from M-shaped to V-shaped structure, while fuel-staging yielded a similar flame response, demonstrating that observed behavior results primarily from redistribution of heat release. Linear stability analysis revealed that wavemaker region remains near inlet of the combustion chamber. Moreover, flame root transitions from a lifted M-flame to attached V-flame and consistently stabilizes at radial position corresponding to the identified wavemaker region. The coincidence of flame attachment & wavemaker location under stable operating conditions provides strong experimental evidence that flame stabilization is governed by their spatial overlap rather than by a modification of the underlying hydrodynamic instability. The proposed framework provides new insight into the coupling between flame stabilization & hydrodynamic instability & offers practical guidance for the design of stable, low-emission combustion systems.

How and when dust settles in young protostellar disks is a key open question for the dust concentration needed to form planetesimals and, ultimately, planets. However, directly measuring the vertical dust distribution in embedded (Class 0/I) systems remains challenging. We show that brightness asymmetry along the minor axis of highly inclined disks provides a simple, powerful geometric diagnostic of vertical dust structure. Using radiative transfer modeling with RADMC-3D, we generate synthetic continuum images showing that the observed asymmetry arises naturally from disk inclination, optical depth, and dust scale height. We apply this framework to nine Class 0 and I disks from the ALMA Large Program, Early Planet Formation in Embedded Disks (eDisk), using Markov Chain Monte Carlo (MCMC) fitting. Outflow observations independently validate the inferred near- and far-side geometries: all eight sources with useful outflow constraints agree with the orientations predicted by the dust continuum modeling. Our results indicate that most embedded disks show no strong evidence of significant dust settling, with dust scale heights comparable to the gas scale height. Given that the literature indicates Class II disks tend to be well settled, our results reinforce the notion that significant dust settling occurs during the Class I phase, when deeply embedded Class 0 disks transition to their more revealed Class II counterparts. Intriguingly, the timing of dust settling appears to broadly coincide with the development of widespread dust substructures, suggesting that gravitationally driven vertical dust concentration may have triggered substructure formation.

In graphene and other two-dimensional materials, periodic modulations of the electron density can significantly alter the energy spectrum and transport properties. Here, we report magnetotransport measurements in encapsulated monolayer graphene with ultra-high-quality patterned periodic antidot lattices that preserve the intrinsic electronic properties of the material. This lithographically defined platform enables controlled access to commensurability and superlattice phenomena at length scales otherwise difficult to achieve. By systematically tuning the lattice dimensions, we reveal a hierarchy of classical commensurability features arising from cyclotron orbits with comparable radii that follow multiple classical trajectories, resulting in broadened resistance peaks beyond the conventional single-orbit picture. Superimposed on these features, we observe pronounced Brown-Zak oscillations arising from the quantum commensurability between the magnetic flux quantum and the unit cell of the engineered Bravais lattices. We demonstrate that the intrinsic geometric phase of our system is directly measurable and show a precise matching of the magnetic field periodicity to the lithographic periodic patterning, where moiré-like electronic spectra can be geometrically generated in single-layer graphene without the need for twist, lattice mismatch, or multilayer stacking. Our results establish nanopatterned graphene as a clean, tunable, and scalable platform for realizing and exploring moiré physics through on-demand real-space design

This article develops a systematic characterization and exact computational framework for the maximal robust positively invariant set of linear difference inclusions. The maximal set is characterized as the greatest fixed point of the robust predecessor operator, leading to three equivalent set iterations for its computation. Under uniform exponential stability and bounded disturbances, the Kuratowski upper limit of the disturbance-reachable sets yields a necessary and sufficient condition for the maximal set to be nonempty under closed state constraints. Sufficient conditions for its finite determination are also established, together with an explicit bound on the determination index. For polyhedral state constraints, bounded disturbances, and finite or polytopic matrix families, exact half-space implementations of the three iterations are derived. Although these algorithms generate the same set sequence, complexity analysis and numerical experiments reveal substantial differences in their computational performance.

High-precision measurement of oscillating signal is a ubiquitous issue in fundamental science and a critical task in practical technologies. In quantum metrology, quantum lock-in detection provide an efficient method for measuring such signal. In general, when the initial phase of the oscillating signal is unknown,quantum double lock-in detection can effectively extract complete information about the signal's amplitude, frequency, and initial phase. Conventional quantum double lock-in detection requires two individual quantum interferometry, each of which must undergo state preparation and readout. However, the time for state preparation and readout need not be negligible in practical experiments. In particular, the time for state preparation is longer than the time for sensing. To save experimental resources, it is challenging to achieve quantum double lock-in detection just via a single quantum interferometry while still extracting complete information about the signal's amplitude, frequency, and initial phase. Here, we present a general protocol for achieving a quantum double lock-in detection just via a single quantum interferometry under a sequential orthogonal periodic multipulse sequences. In particular, if the input state is a Greenberger-Horne-Zeilinger state and two interaction-based operations are applied during interferometry, the measurement precisions for frequency, amplitude, and initial phase can both approach the Heisenberg limit. Our study paves a new way for measuring oscillating signals with a single quantum interferometry, and provides a feasible method for achieving Heisenberg-limited detection of alternating signals.

Randomized smoothing certifies the probability of a fixed output event as the center of Gaussian noise moves. Feasibility or confidence filtering reports label probabilities only among retained proposals, producing a ratio. Its numerator is a fixed Gaussian event mass, while its denominator is the probability of retention and can change with the center. Substituting this ratio into the ordinary smoothing formula can therefore certify a ball that contains a decision boundary. We separate the problem into a geometric question and a certification question. Geometry determines when conditioning preserves Gaussian comparisons. Convex retained sets preserve the full comparison, while general sets require geometric control of the retained law as the center moves. Without such control, conditional probabilities imply no positive universal radius. Joint retention-and-label probabilities always yield a valid certificate for the same filtered predictor. A uniform covariance bound transfers divergence certificates to the retained law and can yield larger radii even when the Gaussian event comparison fails. Both methods admit finite-sample bounds. For a learned image classifier with a training-selected nonconvex filter, conditional Rényi bounds certify more images than joint-mass bounds without additional model evaluations. A released confidence filter exhibits verified label changes inside radii obtained by conditional substitution. An application of adaptive Gaussian composition covers causal finite-horizon executions with history-dependent center shifts under a pathwise energy bound.

Typed decision models such as Jev offer an efficient alternative to generative LLMs in decision-making workflows by selecting directly from predefined options. When candidate sets contain no valid answer, TypeSafe recommends including an "other" or "none-of-the-above" option to enable rejection. In this report, however, we identify an arithmetic-dependent rejection bottleneck: Jev reliably selects correct numerical answers when available but frequently accepts incorrect alternatives when they are absent despite an explicit rejection option. On paired arithmetic problems, answer-present accuracy reaches 99%, while correct rejection falls to 7%. Moreover, this gap persists across numerical magnitudes, operation depths, contextual formulations, and rejection labels, and extends to scenarios such as time calculation and capacity rounding. Yet native Boolean verification achieves 99% exact-match accuracy on the same answer-absent arithmetic cases, showing that categorical rejection can fail even when the model successfully verifies candidate correctness. Finally, we show that a simple decision threshold selected on separate development problems raises arithmetic rejection accuracy from 7% to 79% while retaining 97% answer-present accuracy, substantially mitigating the failure without retraining or additional inference.

Interactive proof systems with a laconic prover, studied by Goldreich, Vadhan, and Wigderson (CC, 2002), capture problems verifiable with logarithmic prover communication in the classical setting. For two-message quantum analogs, even a single-bit prover response contains quantum statistical zero-knowledge ($\sf QSZK$), introduced by Watrous (FOCS 2002). However, restricting the verifier's question to classical public coins collapses the corresponding class to $\sf BQP$, as shown by Beigi, Shor, and Watrous (ToC, 2011). We further study two-message quantum interactive proof systems with a laconic prover. To this end, we introduce the class ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$, where $\ell$ is the length of the prover's response, and establish: 1. A natural complete characterization of ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$ by Multi-State Distinguishability. In particular, Quantum State Distinguishability (QSD) is ${\sf QIP}_{\rm bit}$-complete. Since QSD is $\sf QSZK$-hard, our result places ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$, for $\ell\geq 2$, in a landscape "just above" $\sf QSZK$. 2. Easy regimes for ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$ collapsing to $\sf QSZK$. We prove that QSD$[a,b]$ (and thus ${\sf QIP}_{\rm bit}[a,b]$) is in $\sf QSZK$ when $a(n)-b(n)\geq 1/O(\log n)$, and combine this with an answer compression from ${\sf QIP}_{\ell\text{-}{\rm bit}}[2,c,s]$ to ${\sf QIP}_{\rm bit}$ to obtain another easy regime when $2c>(1+2^{\ell/2})s$. Remarkably, our improved polarization applies to SD and $\sf SZK$, resolving an open problem in Sahai and Vadhan (JACM, 2003). 3. Quantum public coins also make the interaction useless: ${\sf qc}\text{-}{\sf QAM}[O(\sqrt{\log{n}})]$ with constant gap is in $\sf BQP$, where ${\sf qc}\text{-}{\sf QAM}[\ell]$ is a subclass of ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$ in which the verifier's question is exactly halves of EPR pairs.

Self-distillation with privileged context adapts a language model from demonstrations by letting the model, once conditioned on a reference response, teach its context-free copy token by token. Our taxonomy reveals existing methods differ along three entangled axes: (i) the rollout source (student or teacher), (ii) the teacher coupling (frozen, or an exponential moving average of the student at some coupling rate) and (iii) the KL direction (reverse or forward), yet these axes are usually studied in fixed combinations and have led to conflicting conclusions. We formalize a unifying framework to encompass all self-distillation methods vs classic supervised fine-tuning: we train every combination of the three axes, on Qwen2.5-7B and Ministral-3-3B across ordinary and contradictory tasks, totaling 1,200 adaptation runs, to systematically investigate the impact of the above axes. We propose a controlled model of the same objective to explain the resulting acquisition-retention trade-offs. We find that (i) the rollout source matters mostly where the task contradicts the pretrained behavior: there teacher rollouts raise acquisition well above what student rollouts achieve, with almost no change in retention; (ii) the teacher coupling changes acquisition most, on every task: acquisition rises with the coupling rate, then falls past a task-specific rate; (iii) switching the KL direction costs retention in one model but not the other so which axis to tune first depends on the model. The controlled model reproduces the three trends.

Spintronic terahertz emitters (STEs) are versatile sources of terahertz (THz) frequency radiation that offer high electric field strengths and gap-free bandwidths covering the THz (0.1-30 THz) band. In addition, they are low-cost to produce and easy to use in a variety of optical setups. However, an obstacle to their wider applicability is the recently reported decrease in optical fluence damage threshold when driven with high-repetition-rate lasers. Here, we use an asynchronous optical sampling (ASOPS) THz time-domain spectrometer (THz-TDS) to observe the degradation of the THz signal in real-time when driven by a 1 GHz repetition-rate laser. We demonstrate that the loss of THz emission is permanent and is likely the result of thermal damage to the STE structure. However, by utilizing substrates with high thermal conductivities, an increase of the damage threshold of over three orders of magnitude is observed enabling stable emission from a STE for the first time when driven by a high-repetition-rate laser.

Matching the same vehicle across front and rear cameras is difficult because the cameras do not share a view and the vehicle's appearance changes substantially. We introduce Front2Back-ReID, a benchmark of 500 manually verified vehicle handovers from 20 recording sequences in South Africa. Each example asks a model to match a vehicle highlighted in a front-camera image to the same vehicle among at least three candidates in a later rear-camera image. We evaluate seven zero-shot vision-language models, four image-retrieval baselines, and 25 human participants. Models are tested using full front RGB images, cropped target vehicles, and binary silhouettes. The strongest VLM achieved 76.6 percent Rank-1 accuracy on target crops, compared with 74.0 percent for the frozen SigLIP2 baseline; this difference was not statistically clear. Human participants achieved 94.0 percent accuracy with full images and 92.2 percent with target crops. Under our evaluation setup, enabling reasoning improved accuracy across all three input conditions for every model evaluated in both modes. We also found that VLMs generally performed worse on full scenes than on target crops. These results show that general-purpose VLMs do not yet consistently outperform strong visual retrieval for front-to-rear vehicle matching, while humans remain substantially more reliable.

In this paper, we study various aspects of perspectivity in modules. We prove that the following classes of modules satisfy the perspective-Schröder-Bernstein property: modules with transitive perspectivity, quasi-continuous modules, Harada (and hence discrete) modules and quasi-discrete modules with the (finite) exchange property. Furthermore, we prove that for a semiregular ring, the Schröder-Bernstein property implies the perspective-Schröder-Bernstein property. We prove that for $A,B \subseteq ^{\oplus} M$, if all complements of $A$ are perspective with $B$, then all complements of $B$ are perspective with $A$. We also provide new characterizations of weakly perspective modules and modules in which perspectivity is transitive. Some applications of these results are given. We finally prove that perspectivity is transitive in a ring $R$ if and only if every special clean element of $R$ is perspective.

Recent advances have enabled unified omni-modal models in understanding audio, vision, and language. However, existing benchmarks, training data, and learning methods largely treat the modalities independently, leaving the capability of audio-visual joint reasoning poorly evaluated and insufficiently elicited. We address this gap with a benchmark, data engine, and learning method. First, we introduce OmniReasoningBench, a benchmark where both audio and visual evidence are indispensable. It comprises 1,150 multiple-choice and open-ended questions across two tasks, reasoning over video and reasoning beyond video. Second, we develop a data engine OmniQA. It automatically constructs evidence-grounded QA pairs that explicitly necessitate audio-visual joint reasoning, together with time-stamped clue chains that guide the annotation of thinking process. Besides our benchmark, this engine produces training data OmniReasoning-SFT-112K and OmniReasoning-RL-19K. Finally, we propose an on-policy self-distillation method Modality-Factored Self-Distillation (MFSD). It evaluates each sampled response under modality-specific clue contexts, disentangling the contributions of individual clues and their cross-modal interactions for token-level credit assignment. With our training data and learning method, our model OmniReasoning-30B-A3B achieves 50.0% on OmniVideoBench and 42.5% on OmniReasoningBench, improving the base model Qwen3-Omni-30B-A3B-Thinking by 12.8 and 9.3 percentage points, respectively. Moreover, it delivers substantial gains on general and long-video benchmarks, including Video-MME-v2. We hope our work offers a solid step for facilitating future research in omni-modal joint reasoning.

Sample-level reliability heterogeneity is common in deep time series learning. Standard training pipelines apply a uniform regularization setting to all samples, which can under-regularize corrupted samples and over-restrict clean samples. Common robustness approaches filter observations in data space or impose priors on latent representations. We propose Capacity-Centric Modulation (CCM) as a complementary, sample-adaptive regularization principle. Under this principle, we introduce SACM (Sample-Adaptive Capacity Modulation), a task-agnostic framework that exploits spectral sparsity to assign sample-wise dropout probabilities along internal activation paths. SACM integrates into existing backbones without architectural redesign and preserves the deterministic inference pipeline. Across 301 real-world dataset-backbone pairs covering 9 forecasting, 32 classification, and 4 anomaly-detection datasets, SACM reduces forecasting MSE by 6.7% on average and improves classification accuracy and point-adjusted F1 by 3.04% and 17.05%, respectively, relative to unmodified backbones, with zero test-time overhead.

Flow matching generates samples by gradually transforming noise into data. In practice, using a finite number of sampling steps introduces a numerical error that depends on the chosen schedule. We study this dependence for Gaussian targets and the explicit midpoint sampling method, using the exact flow field. We measure sampling error by the squared Wasserstein distance between the target distribution and the final distribution produced by the midpoint sampler. We show that the standard conditional optimal transport (CondOT) schedule cancels the leading midpoint error and improves the general convergence bound, even when the sampling steps are unequally spaced. On a uniform grid of $S$ sampling steps, we fix the signal schedule at $\alpha_t=t$ and prove the existence of scalar noise schedules $\beta_t$ that approach the CondOT noise schedule $1-t$ at rate $1/S$ and yield exact Gaussian sampling for every sufficiently large $S$. Controlled Gaussian experiments illustrate the convergence rates and exact calibration.

Call a linear order type $\varphi$ Hagendorf if it shares two properties with additively indecomposable ordinal numbers without being one itself: $\varphi$ is strictly indecomposable to the right and whenever $\psi < \varphi$, then $\psi$ can be embedded into a proper initial segment of $\varphi$. In the 1970s, J. Hagendorf asked whether such types exist. F. Galvin observed that they must be uncountable, and soon thereafter, J. Larson proved that they cannot be scattered. We provide a simplification of her argument that might give additional insight into the $\sigma$-scattered case. We then show that consistently Hagendorf types exist and that this holds in many models of set theory, for instance under $\mathsf{BA}$ or $\mathsf{MA}_{\aleph_1}$. In fact, their non-existence has large cardinal strength. Furthermore, we construct real Hagendorf types from $\diamondsuit$ and from $\mathsf{PFA}$. This marks the first progress on this interesting problem since its description by Larson four dozen years ago.

Estimating accident mechanics from real-world crashes is important for vehicle-safety analysis, injury modeling, crash-severity prediction, and operational workflows such as insurance claim triage. In standard crash records, key metadata such as impact configuration, principal direction of force, and change in velocity ($\Delta V$) may be missing, delayed, or corrupted, while post-crash photographs are widely available and contain rich visual evidence of deformation. We study how much crash-mechanics information can be recovered directly from vehicle photos when structured signals are absent. We formulate crash understanding as supervised prediction from per-case multi-view photo sets. Targets include six Collision Deformation Classification (CDC) descriptors and the longitudinal and lateral components of reconstructed $\Delta V$. Each photo is encoded by a shared visual backbone, and the resulting view-level features are fused into a case-level representation from which target-specific heads predict crash descriptors. Using 15.2k training cases from the Crash Investigation Sampling System, drawn from about 1.5M photos before filtering, together with 1.15k validation and 1.15k test cases, we define an evaluation protocol for vision-based crash descriptor estimation from incomplete multi-view evidence. Post-crash imagery alone provides usable signal for several non-trivial crash-mechanics descriptors, while weakly observable and long-tailed targets remain challenging. Within the compared training regimes, the selected joint-training recipe reduces mean absolute angular error for principal direction of force from 20.1 to 14.05 degrees and longitudinal $\Delta V$ MAE from 8.04 to 7.45 km/h. Our work provides a reference point for future multimodal fusion with structured crash metadata.

Algorithms are increasingly being used to help automate and improve data-driven decisions, but care must be taken to prevent such algorithms from learning discriminatory patterns from historical data and perpetuating their biases. Statistical notions of fairness aim to mitigate either a model's disparate impact on disadvantaged groups (thus ensuring group fairness) or the resulting disparate treatment of individuals with similar features (thus ensuring individual fairness). Simultaneously mitigating disparate impact and disparate treatment is generally impossible for non-trivial models, necessitating a compromise. In this paper, we introduce the Fair Lasso and Fair Posterior as methods for selecting fair covariates in generalised linear models. By targeting variables that are simultaneously strong predictors of the response and weakly dependent on the sensitive group memberships, we aim to achieve favourable trade-offs between disparate treatment and disparate impact. Additionally, our selected set of fair features can be used as the conditioning set of legitimate features in the paradigm of Conditional Demographic parity (CDP) when no prescriptive legal framework exists.

Longitudinal clinical cohorts are multimodal, irregularly sampled and pervasively incomplete: in ADNI, positron emission tomography and cerebrospinal fluid assays are absent from roughly half of all visits. Linear state-space models handle irregular sampling gracefully but treat a missing modality by masking the input, leaving the transition operator untouched. We prove that this is a representational limitation: the latent state of any linear state-space layer whose transition operator does not depend on the availability pattern is an additive function of the availability indicators, so no such layer can represent an interaction between two modalities being jointly present or jointly absent. We propose CAMOS, which gives each modality a bank of second-order oscillators coupled through a matrix that sits inside the differential equation and is gated by availability, so the transition operator itself becomes a function of which measurements were taken. Coupling invalidates the analysis of uncoupled oscillatory models, and we restore it: a per-channel Gershgorin budget makes the effective stiffness positive definite uniformly over all $2^M$ availability patterns and all gaps, an energy argument charges amplification to availability transitions rather than sequence length, and a channel factorization preserves exact associative parallel scans. On ADNI, CAMOS outperforms uncoupled oscillatory state-space models and clinical fusion models on same-visit staging, landmark prediction and longitudinal forecasting, and under zero-shot transfer to OASIS-3 it is the only model that avoids collapse to the majority class.

Ownership establishes rights over the use, control, and transfer of objects. Understanding these relations is essential for AI systems to interact appropriately with people and their resources. Yet how large language models (LLMs) attribute ownership under competing claims remains unclear. We introduce the Competing Ownership Attribution Task (COAT), comprising 42 scenarios, and compare ownership allocations from 24 LLM configurations with those of 108 human participants. Overall, human-model similarity is close to human-human similarity, but models show greater homogeneity in their ownership judgments. Within individual answers, models also divide ownership more evenly among claimants than humans do. Pooling responses across model configurations reveals more scenarios with a shared judgment and fewer with distinct viewpoint groups than in humans. When humans form distinct groups, models may converge on one viewpoint or between competing viewpoints. Further comparisons reveal different contextual sensitivities. As material value increases across scenarios, allocations to creators decline less sharply in models than in humans. Across scenarios differing in public recognition of later holders as owners, allocations to these holders increase in models but decrease slightly in humans. Together, these findings suggest that the evaluated LLM responses do not fully capture the diversity of participants' ownership judgments or how those judgments vary across situations. Developing socially capable AI therefore requires moving beyond overall similarity to capture the diversity and context dependence of human judgments.

The Gottesman-Kitaev-Preskill encoding has emerged as a leading candidate for fault-tolerant quantum computation with continuous variables. For photonic architectures, the major challenge is preparing high-quality resource states, which can be deterministically synthesised from many large-amplitude cat states. Thus far, only modest-sized optical cat states have been prepared experimentally, and the implemented methods are highly probabilistic. We propose an all-optical scheme utilising quantum non-demolition interactions and photon-number measurements to prepare large-amplitude cat states with near-unity probability. Importantly, no particular photon-number outcome is postselected: all outcomes contribute to the accumulated photon number, with the protocol repeated until a required threshold is reached. We demonstrate that the scheme is robust to realistic levels of photon-loss, the dominant source of error in optical systems. Our results highlight the power of active Gaussian operations for state preparation and pave the way for efficient quantum error correction using bosonic codes.

Efficient resource provisioning for large-scale workflows on cloud infrastructures is a critical performance engineering challenge. These workflows are often structured as directed acyclic graphs (DAGs), where under-provisioning can cause critical bottlenecks and over-provisioning leads to unnecessary costs. Accurate, task-level prediction of resource intensity (e.g., CPU load and memory usage) is essential for mitigating these issues. While task-level features are commonly used for prediction, the performance impact of the workflow's overall topological structure is often overlooked or assumed. The central question of our work is: To what extent does what part of the DAG topology influence task-level resource intensity, and what is the most effective way to model this influence? This paper presents a comprehensive benchmark to systematically quantify the impact of graph topology on task intensity prediction. We evaluate and compare a spectrum of modeling approaches. Our findings demonstrate that topology is a critical feature for accurate prediction. Models incorporating important topological information, even through simple handcrafted features, significantly outperform baseline models. We show that graph-native models provide the highest accuracy, achieving low mean absolute errors for both CPU and memory predictions, and can still be combined with simple topological features that they do not learn for better performance.

This work investigates the spatially wideband (SWB) array factor (AF) of linear thinned antenna arrays. The SWB AF is formulated as a matched filter and expressed as a spatially variant convolution of a spatially narrowband (SNB) AF and a SWB kernel. Originally derived for uniform arrays, the SWB AF approximation is revisited and extended to thinned arrays. The approximation is shown to remain accurate across a wide range of parameters. Representing the SWB AF as a convolution offers an intuitive interpretation of how the bandwidth-aperture product modifies the SNB AF. Specifically, the SWB kernel acts as an averaging window for the SNB AF, suppressing the sidelobe levels (SL) of the SNB AF. In thinned arrays, the sidelobes away from the mainlobe can be treated as random, noise-like, making averaging and suppression particularly effective. Next, the analytical formulas for the expected SL and peak-to-sidelobe level (PSL) in SNB thinned arrays are first introduced and subsequently extended to the SWB regime. Finally, simple closed-form expressions for the expected SL and PSL levels of the uniformly thinned arrays with a uniform spectrum are provided. The expected SWB SL and PSL are formulated as functions of the bandwidth-aperture product and are shown to steadily decrease with distance from the mainlobe.

This paper investigates semantic secrecy in wireless status-update systems using Version Age of Information (VAoI). We model the fundamental tradeoff between informative updates and confidentiality (semantic asymmetry between the legitimate destination and the eavesdropper) using a three-node wiretap channel. To evaluate secrecy performance, we introduce the concept of a semantic secrecy region (SSR) and analyze it from a geometrical perspective. By developing a two-dimensional Markov chain, we derive closed-form expressions for the destination's average VAoI and the probability of semantic asymmetry at the eavesdropper. These results enable the joint optimization of transmission probability and power control. For Rayleigh fading channels, we characterize the optimal SSR boundary and power allocation. Numerical results validate our analysis, showing that optimized power allocation significantly enlarges the secrecy region compared with fixed-power benchmarks.