Papers

Observations by the Laser Interferometer Space Antenna (LISA) will contain time-varying, cyclostationary confusion noise from the Galaxy, which is naturally handled using time-frequency analysis methods. We present a fast, forward model that maps the parameterized Galactic gravitational-wave luminosity density onto the annually modulated, unresolved confusion foreground in the complete set of time-delay interferometry channels. The line-of-sight luminosity integral is evaluated on a HEALPix grid and decomposed into spherical harmonics, while the detector response is decomposed analytically, independent of the Galaxy model, such that a new Galactic model costs a single map evaluation, transformation, and contraction. We compute the modulated covariance beyond the standard low-frequency limit, expanding the LISA response to second order in finite armlength corrections, and to first order in the unequal-arm corrections. These effects change the normalized modulation curves by up to $\sim\!0.23\%$ and $0.64\%$ for finite armlength corrections at $3$ and $5$ mHz respectively, and by $\sim\!0.074\%$ and $0.71\%$ for unequal-arm corrections in the self and cross channels respectively. Using the fast, forward model and a notional disk-and-bulge Galaxy model, we construct a Fisher matrix from the time-dependent channel covariance and forecast that one year of observation constrains the disk scale width and scale height relative to the distance to the Galactic center at the $8\%$ and $12\%$ levels respectively, and leaves the strongly correlated bulge fraction and bulge radius individually unconstrained.

Operator-side network profiles derived from 5G/ORAN traffic carry personal data such as ephemeral subscriber identifiers, slice-level KPIs, and control-plane signalling, and must be anonymised before release to a federated-learning aggregator, threat-intelligence exchange, or ML training pipeline. We study how much re-identification risk remains after standard operator-side anonymisation. We quantify privacy posture with k-anonymity, l-diversity and t-closeness, aggregate them into a composite Privacy-Posture Index (PPI), and measure residual re-identification across eight transformation configurations on internal PCAP captures and the public Idaho Labs 5GAD corpus, under a full-QI syntactic bound and two simulated adversaries. The evaluation is modest in scale, and we read its trends as indicative rather than definitive. Three findings emerge. Pseudonymisation alone leaves re-identification unchanged; material privacy gains arise when quasi-identifiers are coarsened through generalisation, optionally combined with suppression. A downstream classification task then shows that suppression-heavy releases retain majority-class utility but sacrifice much of their minority-class recall, a cost the aggregate metrics hide. Finally, the standard kmin-based PPI correlates only modestly with the disclosure bound and not at all with the partial-knowledge attack, whereas a mean-class-size variant PPI correlates strongly with all three disclosure/attack measures; we therefore read PPI as a regulator-facing summary, not a security bound. The profiles are produced by passive operator-side monitoring with rule-based DPI; our contribution is the privacy-quantification layer that computes these metrics, applies the transformation policy, and exposes both through an inspectable dashboard.

Future gravitational-wave observatories such as the Einstein Telescope will detect tens of thousands of binary neutron star mergers per year, making gravitational waves a dominant probe of the neutron-star equation of state in the coming decades. However, extracting this information requires hierarchical inference across a rapidly growing catalog of events, and existing methods must restart from scratch whenever a new event arrives, making them impractical at this scale. In this Letter, we introduce a hybrid sequential Monte Carlo algorithm that combines data and likelihood tempering to adaptively update the equation-of-state posterior in batches, reusing previous inference results instead of restarting from a wide prior. Accelerated by GPU hardware, our method infers the equation of state from a simulated month of around 1500 binary neutron star mergers in a few hours on a single GPU, and we project that a full year of detections could be processed in a few days on current hardware. This establishes sequential Monte Carlo as a practical route for real-time hierarchical inference with future gravitational-wave detectors.

The middle-income trap is usually identified by comparing a country's income to a threshold. This reveals that convergence has stalled but not where the blockage lies, and it leaves unexplained why the trap is still debated in countries that have already passed the threshold. This study treats the trap as a configuration problem, measuring development along three dimensions - future, outside, and inside potential - with indices built from standardised indicators. The indices are calculated for 34 OECD members in 2000, 2010, and 2020, so that changes in configuration become visible, and the resulting country clusters are interpreted through factor analysis. Two traps and two transition strategies emerge. The first strategy attracts foreign investment and technology, but can itself become a trap: domestic value added stays limited and rising wages erode export competitiveness. The second adds a developmental state focused on the quality of education, building the human capital that raises productivity and innovation. All six CEE members of the OECD had adopted the first strategy by 2010; by 2020 only Estonia had completed the second. Configuration levels and changes track relative income convergence.

We study the problem of recovering the ranking of a fixed set of items according to their unknown numerical utilities. At each interaction with the environment, a learner presents the item set to a human and receives comparative feedback of two types. Under full-ranking feedback, each interaction reveals a noisy ranking of all items, whereas under winner-only feedback, it reveals only the item ranked first. In both settings, we model human feedback using a random utility model with log-concave noise and study the number of observations needed to recover an $\epsilon$-accurate ranking with high probability. This novel criterion tolerates ordering errors only between items whose utilities differ by less than $\epsilon$. For both feedback types, we establish worst-case sample-complexity lower bounds and develop algorithms that match these bounds up to logarithmic factors. Neither algorithm requires knowledge of the noise distribution, while only requiring an upper bound on its variance. Our results show that the ranking problem under winner-only feedback is intrinsically harder by exposing the sample complexity dependence on the minimum winning probability across the item set.

Mobile GUI agents increasingly operate on interfaces influenced by users' histories and preferences, but their reliability across different users remains underexplored. We introduce PAIR (Personalized Application-state Instantiation and Rendering), a pipeline for constructing user-conditioned application states that enables controlled evaluation of the same task across different users. We further introduce RePAIR (Reinforcement learning with Personalization-Aware Interaction Rewards), a training approach that learns from cross-user differences in subgoal outcomes to improve reliability across user-conditioned mobile environments. Across six agents, we find substantial variation in task success across users and consistently lower subgoal achievement in user-conditioned UI contexts (6.98 to 15.4 pp). This gap further increases for personal targets drawn from each user's own content (8.77 to 22.0 pp). Failures in these contexts frequently involve selecting another item instead of the intended target, particularly before target exposure. Finally, RePAIR improves user-conditioned SAR (+5.87 pp), all-success (+7.50 pp), and overall Task SR (+9.42 pp) over its supervised fine-tuning parent on unseen users, providing initial evidence that explicitly learning from cross-user variation can improve GUI-agent reliability.

In this work, we investigate three modified versions of the classic Hegselmann-Krause opinion dynamics model, incorporating features that are typical of many real-world systems, such as uncertainty in the selection of interacting agents and a weighted evaluation of the relevance of their opinions in the influence function to enhance confirmation bias. Through extensive simulations across different network topologies, ranging from stylized network models (Barabási-Albert, Erdős-Rényi, and Watts-Strogatz networks) to empirical networks with community structure, we identify the influence of each modification on opinion evolution and convergence. Our findings reveal that they exert opposite effects on the bounded confidence threshold required for consensus. We further explore an extension based on a data-driven opinion initialization on the empirical networks, where initial opinions are drawn from Gaussian distributions specific to each detected community. While the qualitative effects of the three modified models remain consistent, this new initialization strategy reveals distinct dynamics within the network communities. These insights provide a new and comprehensive perspective on how realistic variations of the Hegselmann-Krause model, in terms of both interaction rules and initial opinion distributions, affect opinion dynamics and shed light on the mechanisms of consensus formation within structured communities.

Background: Galleries, libraries, archives and museums (GLAM) increasingly produce scientific collection data whose digital state must remain identifiable, recoverable, and verifiable after acquisition. A staging architecture should provide redundancy without requiring every measurement to depend on one workstation or storage path. Methods: We evaluated a private seven-node InterPlanetary File System (IPFS) deployment at the Museum für Naturkunde Berlin. Five Raspberry Pi 5 edge peers and two archive-class peers contributed NVMe-backed repositories across two wired zones linked by a shared wireless path. Two real raw-acquisition folders were recovered by content identifier (CID), a large machine-learning model-weight folder was ingested, and sustained telemetry from two edge and two archive nodes was compared. Results: Raw acquisition A (6.20 GB) materialized in 34.0 s (182 MB/s effective logical rate) and raw acquisition B (5.19 GB) in 14.092 s (368 MB/s). A 156.1 GB model-weight folder was recursively added in approximately 300 s (520 MB/s logical ingest). Four sustained telemetry series comprised 857.3 logged node-hours and 27,616 valid block-stat probes, all reporting successful local block access. Conclusion: The prototype demonstrates a practical institution-local distributed file system (DFS) for content-addressed acquisition staging. Museum-specific object identifiers can remain stable at the collection-object level while each imported measurement automatically receives a content-derived state identity. Replication intentionally distributes identical blocks across failure domains, while content addressing enables reuse of unchanged blocks within repositories. This combination supports verifiable digital collection objects and a federated storage model for collaborating GLAM institutions.

Scaling robotic foundation models requires diverse training data and reliable evaluation environments. Simulation offers a scalable solution, yet existing generation pipelines remain constrained by predefined assets and skills, a disconnect between scene generation and task generation, and limited support for complex embodiments and physics. We introduce EmbodiedSmith, a framework for scalable embodied data generation through recursive self-improvement (RSI). EmbodiedSmith unifies asset, scene, and task generation in a pipeline that supports autonomous creation and language-driven customization. Its core is an agentic refinement loop: scene generation anticipates downstream task requirements, while task generation guides targeted scene edits, allowing scenes and tasks to iteratively improve one another. This joint refinement improves task generation success, including for long-horizon tasks. The framework further supports mobile manipulators, humanoids, and dexterous hands, as well as interactions involving deformable objects and fluids, broadening the range of behaviors and physical phenomena represented in generated data. Together, these capabilities provide a flexible simulation engine for both robot pretraining and evaluation. Extensive experiments validate the quality, diversity, and generation efficiency of the resulting data, while downstream policy experiments demonstrate that increased data diversity improves generalization.

We give an independent computer-assisted proof of the k=4 case of the Chen-Raspaud conjecture. We prove that every graph G with odd-girth(G) >= 9 and mad(G) < 9/4 admits a homomorphism to the Kneser graph K(9,4). The proof combines a minimal-counterexample argument with a rooted star replacement, exact finite computations in K(9,4), and a final charging argument. After all reducible local types are removed, the unique positive local type is (3,3,4). Its unit excess is transferred through its 4-thread to a relative with sufficient negative capacity. The computer-assisted statements used in the proof are certified by exact C++ bitset verifiers, and a separate Python implementation provides an independent cross-check; the complete source code and raw certificates accompany the manuscript.

As large language model (LLM) agents become increasingly autonomous, they may pursue task performance through deception, raising concerns about their reliable deployment. Existing evaluations show that LLM agents can deceive, but often examine isolated scenarios or narrowly defined conditions, limiting systematic understanding of when deception becomes more likely. To address this gap, we introduce DecepEval, a benchmark comprising 1,532 instances across 3 task families and 28 professional scenarios. Drawing on classical fraud theories, we propose the LLM Deception Diamond framework, which characterizes four external conditions that may induce deception: pressure, incentive, opportunity, and conflict. DecepEval pairs neutral and induced versions of each instance to measure condition-dependent changes in deception rates, while explicit task facts and observable agent behavior help distinguish deception from capability-related errors. Evaluations of nine frontier LLMs show that inducements increase deception across models and task families, even among models with low baseline deception rates. DecepEval makes these vulnerabilities measurable, providing a shared benchmark for progress toward trustworthy artificial intelligence.

Neural audio synthesis models like the Realtime Audio Variational autoEncoder (RAVE) achieve impressive genera tion quality, yet how their internal representations encode musical features remains poorly understood. We present a systematic layer-wise and cross-layer cluster analysis of RAVE decoder activations across three models trained on different musical domains, tested with four stimulus types. We then evaluate architectural generalization with a general purpose EnCodec model. For RAVE, we find that synthetic stimuli are encoded well across models and audio features (pitch |h̊o}|=0.45, 5.1x the null, BPM |h̊o}| = 0.76, 8.6x the null). These results are reduced but still substantively apparent when using natural audio (mean across features |h̊o}|=0.25, 2.8x the null). Natural audio sees a stronger encoding when nonlinear probes are used (mean across features R2=0.56, 18x the null, +0.152 nonlinear gain over the linear probe R2). Encoding strength varies throughout the layers of the decoder and an increased ability to joint-encode in the middle layers is seen across all audio features (e̱ta}2 all negative, p < 0.05). The general purpose EnCodec decoder also sees similar strong synthetic responses across audio features, similar nonlinear gains for natural audio joint encoding and similar depth profiles. We find the best cross-layer cluster improves the strength (r = 0.65, p = 0.006) and prevalence (r = 0.75, p = 0.001) of BPM encoding when compared against the best whole layers within the same section, with no effect for joint encoding. These findings advance the interpretability of neural audio models and inform targeted control strategies for neural synthesis.

Higher-order Laguerre-Gaussian modes can reduce test-mass thermal noise in gravitational-wave interferometers, but their implementation is limited by degeneracy-induced coupling losses in realistic high-finesse cavities. We mitigate these losses by optimizing the mirror curvature to break modal degeneracy. We develop a general framework for designing an axisymmetric corrective test-mass surface profile that lifts the degeneracy of the sixth-order Laguerre-Gaussian subspace while preserving an injected donut-shaped $\mathrm{LG}_{0,6}$ mode. Expanded in a Fourier-Bessel basis, the profile is optimized to maximize the frequency splitting from the nearest unwanted mode while minimizing target-mode loss. For a Virgo-like Fabry-Perot arm cavity, the optimized profile separates the $\mathrm{LG}_{0,6}$ resonance from the nearest same-order resonance, $\mathrm{LG}_{1,4}$, by 2.04% of the free spectral range, reducing unwanted-mode gains below unity at the target-mode resonance and suppressing their resonant enhancement. The profile introduces negligible target-mode loss and improves robustness against astigmatism and realistic mirror surface distortions. Monte Carlo simulations with realistic mirror imperfections yield an average contrast defect of 368 ppm and an average reflected optical loss of 979 ppm, equivalent to a round-trip loss of approximately 3.5 ppm for the modeled cavity. These results substantially improve upon the central anti-reflective mirror mask approach based on selective loss engineering, bringing reflected optical loss within a factor of two of that obtained with the fundamental Gaussian mode under the same simulation conditions. This approach offers a route toward robust donut-shaped Laguerre-Gaussian modes in future precision interferometers with realistic imperfections.

Despite purely local microscopic dynamics, nonequilibrium steady states can develop long-range correlations. We investigate this phenomenon in the boundary-driven symmetric simple exclusion process by relating its exact nonlocal large-deviation functional to finite-time thermodynamic irreversibility under weak time-dependent driving. Decomposing the long-range correlations into hydrodynamic modes, we find that the lag associated with the slowest mode satisfies an upper bound determined by the excess entropy production rate at each driving frequency. This bound is approached in the quasistatic limit, whereas progressively shorter-wavelength modes do not generally satisfy the corresponding bound. These results provide a quantitative connection between the curvature of the large-deviation functional, long-range correlations in the nonequilibrium steady state, and finite-time dissipation. Within the linear-response regime considered here, they indicate that the longest-wavelength hydrodynamic mode has a distinct relation between slow relaxation and thermodynamic irreversibility.

We study stability of semilinear exterior Dirichlet problems driven by possibly nonsymmetric Levy operators. Let $L^n$ and $L$ have Lévy-Khintchine symbols $\psi_n$ and $\psi$, respectively. Our basic assumption on the operators is that $\psi_n(\xi)\to\psi(\xi)$ for every $\xi\in\mathbb R^d$. Under mild regularity assumptions on the domain and an absolute-continuity condition for the resolvent of the limiting process, we prove pointwise and $L^p$-stability of solutions. No symmetry, uniform ellipticity, comparability of Lévy kernels, or common energy space is required; nonzero exterior data are allowed; and the monotone nonlinearity is subject to no growth restriction in the solution variable. The framework therefore covers local, nonlocal and mixed operators and, in particular, nonlocal-to-local limits, as well as fractional, relativistic, anisotropic and nonsymmetric stable-type operators. The proofs combine convergence of Lévy processes with a detailed analysis of exit times and exit positions and a stability theorem for monotone backward stochastic differential equations with varying terminal times. In the symmetric case, we also obtain Mosco convergence of the corresponding part forms on $C^0$ domains and give a counterexample showing that whole-space Mosco convergence need not pass to part forms on arbitrary open sets.

Where generalization capacity–the ability to extract context-invariant relational structures–first emerges remains a central question in AI and neuroscience. The foundation for this capacity lies upstream of the hippocampus, within the entorhinal cortex, where parallel pathways dissociate relational structure in the medial entorhinal cortex (MEC) from sensory content in the lateral entorhinal cortex. However, as Eichenbaum argued, such factorization likely originates earlier, driven by the segregation of the dorsal ('where') and ventral ('what') visual streams. Supporting this, grid-like firing patterns–a signature of MEC (context-invariant codes)–also appear in preceding neocortical regions along the dorsal pathway. Yet, how such representations are computationally formed along upstream pathways remains unknown. To investigate this in silico, we developed ReGraph, a recurrent dual-stream graph model with biological inductive biases, including retina-driven stream-specialized encoding, dorsal-to-ventral modulation, and dynamic lateral connectivity. Trained on the action benchmark Something-Something V2, ReGraph revealed a pathway-specific emergence of relational mapping: context-invariant codes and grid-like spatial bases uniquely co-emerged along the extended dorsal stream. In contrast, their absence in single-stream, unmodulated variants, and standard baselines implies that these inductive biases are prerequisites for relational structures. Crucially, our post-hoc analyses demonstrated that these grid-like bases serve as reusable routing templates for information processing via lateral connectivity. Together, our findings provide a computational account that generalization may not be a faculty that emerges abruptly within a dedicated region, but a property that already takes shape as sensory information is parsed into factorized streams of hierarchical visual processing.

Video Action Models (VAMs) couple visual dynamics modeling with action generation for robot manipulation. However, video representations are not naturally suited to action generation, as exposing the action policy to excessive visual detail can impair its generalization ability. Therefore, we introduce IronMan (Information-constRained videO-actioN learning for robot MANipulation), a robust video-action learning framework built on the information bottleneck principle. The core principle of this framework is to impose information constraints that suppress irrelevant visual information while preserving action-relevant dynamics cues. IronMan employs a dynamics-aware bottleneck that distills noisy, entangled one-step video features into compact world representations. Extensive simulation and real-world experiments demonstrate strong in-distribution (ID) performance and out-of-distribution (OOD) robustness while maintaining efficient inference. IronMan achieves success rates of 99.0% on LIBERO and 79.4% on RoboTwin clean2clean, outperforming all the evaluated baselines. Under OOD shifts, IronMan achieves a success rate of 79.1% on LIBERO-Plus, exceeding the strongest baseline by 10.4 percentage points. Project page: https://youngsoul0731.github.io/ironman-project-page/

Recent advances in agentic search have given large language model (LLM) agents finer control over corpus exploration. However, search interfaces often return matching passages even when feedback about the candidate set would suffice for the next decision, coupling candidate refinement with source-text exposure. We propose IndexAct, an interface for Index-Native Corpus Interaction that separates candidate-set refinement from text inspection. Agents construct and manipulate persistent candidate sets through lexical conditions and set operations over an inverted index, receiving reusable state references and statistics such as candidate counts rather than matching passages. This feedback guides further refinement, while separately requested passages provide new clues or evidence that can inform subsequent operations on retained candidate sets. Experiments on five benchmarks spanning agentic search and multi-hop question answering show that IndexAct outperforms the evaluated baselines on each benchmark. On BrowseComp-Plus, it also achieves higher evidence coverage with a smaller average live context than terminal-based corpus interfaces, and maintains answer accuracy as the corpus expands. Further analyses suggest that informative refinement feedback and state reuse support continued evidence discovery, while shorter contexts or fewer search steps alone do not ensure better performance.

We study reward design for delegated representatives who acquire costly information and vote on a binary governance proposal. Effort improves both private information and delegated voting weight. We show that no payment rule can make sincere voting strictly optimal at every positive effort profile under a non-neutral prior, while fixed budgets limit accuracy in large symmetric committees. We then compare proportional sharing with a conditional rule that rewards only members of a sufficiently large winning coalition. Unlike proportional sharing, which supports sincere voting only through indifference, the conditional rule makes sincere voting strictly optimal at symmetric positive effort profiles. It supports sincere equilibria with the same effort as proportional sharing and, under suitable reward-cost conditions, with strictly higher effort and decision accuracy. Insincere equilibria may nevertheless coexist.

Feed-forward 3D Gaussian Splatting (3DGS) reconstructs a scene in a single forward pass, replacing per-scene optimization with a network trained across many scenes. Its quality, however, degrades sharply as the number of input images drops. The bottleneck is upstream of the reconstruction heads: from a few unposed views, the internal representation they read carries no evidence for unobserved regions, leaving holes, floaters, and blur. The common remedy supplies that evidence as pixels, synthesizing extra views with an image or video generator and re-encoding them, which is costly and not 3D-consistent by construction. We instead densify the evidence itself. We present DensiTok, a plug-in module for pretrained feed-forward 3DGS models that densifies their internal geometry tokens directly, making a frozen backbone behave as though it had observed many more views than it was given. DensiTok compresses those tokens into a compact latent space, completes the latents of the unobserved viewpoints in a single flow-matching step conditioned on camera geometry, and decodes them back into tokens that the original reconstruction heads. The same module design can be integrated into different pretrained predictors while keeping each backbone and its reconstruction heads frozen. Completion in a low-dimensional latent space requires no image synthesis or additional encoder passes. Across three pretrained backbones and two benchmarks, DensiTok consistently improves sparse-view reconstruction and recovers much of the gap to dense-view reconstruction.

{For a matrix function $A(t)$, we study the normalisation of its Wiener–Hopf factorisation $A(t)=A_-(t)D(t)A_+(t)$ which guarantees the uniqueness of the factors $A_\pm(t)$. Previously, this problem was investigated for second-order matrix functions, the stable factorisation, and the factorisation of matrix functions with distinct partial indices. The main tools for solving the problem of normalisation are the theorem of I.C. Gohberg and M.G. Krein on a general form of the factors $A_\pm$, a Birkhoff factorisation of matrix functions, and a block PLU factorisation of the numerical matrix $A_-(\infty)$. To solve the normalisation problem, a concept of P-normalised factorisation is introduced. The Birkhoff factorisation of matrix functions plays a key role in defining this concept. The permutation matrix $P$ is determined by PLU factorisation of the numerical matrix $A_-(\infty)$. We proved that any invertible matrix function $A(t)$ admits P-normalisation. This normalisation guarantees the uniqueness of the Wiener–Hopf factorisation. The P-normalised factorisation of $A(t)$ allows us to find the Birkhoff factorisation of $A(t)$. Without normalisation, it is impossible to obtain explicit estimates of the absolute errors in the approximate computation of the factorisation factors.}

The Multilevel Markov chain Monte Carlo algorithm accelerates Bayesian inversion by exploiting correlations between discretized quantities of interest across a hierarchy of model resolutions. A key practical parameter is the subsampling rate used to generate coarse-level proposals for the finer-level chains. Existing practice sets this rate equal to an integrated autocorrelation time as a proxy for proposal decorrelation, but this choice can be overly conservative and lead to substantial computational overhead. In this work we treat finite subsampling as an error-budget question. We derive a cost-error criterion for selecting a computationally efficient subsampling rate using estimates of sample variances, integrated autocorrelation times, and per-level costs. The criterion balances multilevel sampling errors across levels rather than enforcing approximate independence of the coarse proposals. We clarify the theoretical role of independence through an ideal reset-reference kernel, for which independent coarse proposals may be replaced by proposals generated from a reversible coarse-level kernel. We derive a Poisson-equation representation of the perturbation bias resulting from finite subsampling. Under a state-averaged lower-level forgetting assumption, this yields a conditional geometric perturbation-bias bound; in computation, the corresponding projected diagnostic is used as an empirical error-budget check. Numerical experiments on a highly autocorrelated elasticity beam benchmark show substantial reductions in computational cost compared with IAT-based subsampling. A second Darcy-flow inverse problem gives supporting evidence of qualitatively similar finite-subsampling behaviour in another elliptic benchmark.

We study the diagonal Specht ideals $I_\lambda\subseteq\mathcal{R}_{m,n}:=\mathbb{C}[\mathbf{x}_1,\dots,\mathbf{x}_m]$, $\mathbf{x}_r=(x_{r,1},\dots,x_{r,n})$, generated by the $\lambda$-isotypic component of $\mathcal{R}_{m,n}$ for the diagonal action of $S_n$. We characterize the set of zeros of $I_\lambda$ as $V_\lambda=\bigcup_{\mu\not\trianglelefteq\lambda}H_\mu$ and prove that $\lambda\mapsto V_\lambda$ is an isomorphism of posets from $(\mathcal{P}_n,\trianglelefteq)$ to $(\{V_\lambda:\lambda\in \mathcal{P}_n\},\supseteq)$ for all $m$, while $\lambda\mapsto I_\lambda$ is an isomorphism of posets from $(\mathcal{P}_n,\trianglelefteq)$ to $(\{I_\lambda:\lambda\in \mathcal{P}_n\},\subseteq)$ if and only if $m=1$ or $n\leq3$. Unlike the case $m=1$, where Specht ideals are always radical, radicality in the diagonal setting depends on $\lambda$ and $m$. We prove radicality for hook partitions of length at most three by providing explicit Gröbner bases, and we develop three criteria for non-radicality via content, multidegree, and total degree, showing in particular that $I_\lambda$ is not radical for any non-hook partition $\lambda$ when $m\geq\operatorname{len}(\lambda)$. Using the $\operatorname{GL}_m(\mathbb{C})$-action on $\mathcal{R}_{m,n}$, we show that $I_\lambda$ is radical for all $m$ if and only if it is radical for $m=n$. Finally, for $m\geq2$, we prove that $\mathcal{R}_{m,n}/I_\lambda$ is Cohen-Macaulay if and only if $\lambda=(n)$ or $\lambda=(n-1,1)$, and the same is true for $\mathcal{R}_{m,n}/\operatorname{rad}(I_\lambda)$.

Language-based trajectory predictors represent coordinates as discrete tokens and learn auxiliary tasks such as destination and group reasoning. This formulation enables the model to capture behavioral intent and social context beyond coordinate dynamics alone. However, token-level objectives provide only indirect guidance for continuous coordinate-space dynamics. To address this limitation, we introduce MoRE (Mixture of Reward Experts), a refinement framework that transfers numerical forecasting priors into a pretrained language-based predictor through reinforcement learning. Five frozen numerical predictors provide complementary coordinate-level knowledge of motion and interactions. Their predictions are converted into expert rewards and combined through an uncertainty-weighted consensus that penalizes disagreement. A ground-truth reward anchors the prediction to the target trajectory. To focus refinement on difficult cases, MoRE refines the policy using the top 1% of training samples ranked by predictive entropy. Expert predictions are computed once and cached before PPO training, so the experts are not run during policy updates or inference. In this way, MoRE combines the contextual modeling of the language-based predictor with coordinate-level feedback from numerical experts. On ETH-UCY, MoRE reduces ADE from 0.22 to 0.20 m and FDE from 0.32 to 0.29 m. Relative to the base policy, ADE decreases by 17.9% on SDD and 12.7% on NBA. On ETH-UCY, MoRE also reduces collision rates and better matches ground-truth pedestrian spacing, without increasing measured inference memory or latency. The project page is available at https://jungyu0413.github.io/MoRE/.

Online moderation systems must apply changing platform policies, community rules, and prior decisions while producing decisions that can be audited and routed to human review. We evaluate whether System One Models, which accept natural-language context but return typed choices, probabilities, or scores, can support this setting. Across five moderation benchmarks, Jev is competitive with specialized reference systems, matching or exceeding them in several policy-grounded and harmful-content settings. We then use controlled information conditions to separate written rules, retrieved precedents, and restrictions on the candidate answer space. Jev generally benefits from retrieved precedents, improving exact policy selection and harmful-content discrimination when the answer space is held fixed. Laya is less consistent: retrieval often shifts its positive prediction rate or no-violation rate without improving discrimination. Jev confidence can support selective review in several settings, although it is not consistently calibrated; Laya confidence is less useful for ranking errors. These results show a promising future for SOM-powered content moderation.

Navier-Stokes (NS) equations lose accuracy in the transition regime when the Knudsen number is large, while the Boltzmann equation provides an adequate kinetic description with a substantially higher computational cost. In this work, a data-driven generalized Navier-Stokes (GNS) model is proposed to extend the applicability of the NS equations to the transition regime. A new relationship between the non-equilibrium variables, such as the stress tensor and the heat flux, and the equilibrium variables, including the density, macroscopic velocity, and the temperature, together with the Knudsen number, is learned from the data formed by the numerical solution to the Boltzmann equation. The standard end-to-end learning is utilized to construct the loss function, based on which, a long-term end-to-end learning method is proposed for the loss function to reduce accumulated error and improve long-term predictive accuracy. Several numerical examples, including one-dimensional wave and Riemann problems as well as two-dimensional isentropic vortex and Taylor-Green vortex problems, are studied to validate the efficiency of this new GNS model.

Hyperspectral imaging (HSI) enables spatial mapping of haemoglobin oxygenation and cytochrome-c-oxidase (CCO) redox changes in exposed neural tissue. In this study, we present a technical upgrade of an existing HSI platform by the integration of laser speckle contrast imaging (LSCI), enabling contemporaneous assessment of oxygenation, oxidative metabolism, relative perfusion and a derived relative oxygen metabolic index in exposed spinal cord in a rat preclinical model. The upgraded system (hNIR+) uses a shared optical path and a single camera to acquire HSI and LSCI images from the same field of view using a sequential acquisition workflow. Hyperspectral images are acquired at 11 discrete wavelengths (600, 630, 665, 784, 800, 818, 835, 851, 868, 881, and 894 nm) to estimate changes in oxygenated haemoglobin (HbO2), deoxygenated haemoglobin (HHb) and oxidized CCO (oxCCO). LSCI is implemented using 632.8-nm coherent illumination to generate relative blood-flow index (rBFI) maps. The LSCI subsystem was validated using a controlled blood-flow phantom, where the LSCI-derived inverse speckle contrast index showed a strong positive linear relationship with pump-controlled flow. The upgraded platform was then evaluated in proof-of-concept observations of the rat spinal cord under normoxia, hypoxia and recovery conditions. Representative multimodal maps and ROI-based time-course analysis showed clear dynamic responses in HbO2, HHb, oxCCO and rBFI during oxygen challenges that were consistent with the expected physiological responses of the spinal cord during hypoxia, hyperoxia and subsequent recoveries. Overall, these results demonstrate that integrating LSCI into HSI extends the platform to multimodal and simultaneous monitoring of haemodynamic-metabolic coupling.

We prove that the upper box dimension of an inhomogeneous attractor of a $C^1$ iterated function system in $\mathbb{R}^d$ is bounded above by the maximum of the singularity dimension of the system and the upper box dimension of the condensation set. This extends the upper bound of Burrell and Fraser (2020) for inhomogeneous self-affine sets to the $C^1$ setting. The covering argument of Burrell and Fraser does not apply directly to nonlinear compositions. We overcome this difficulty by combining their approach with an extension of the recursive covering estimate of Feng and Simon (2023). We also obtain the corresponding bound for orbital sets driven by arbitrary compact subshifts.

Action-chunking policies predict multi-step control sequences, but a fundamental question remains: how much of a predicted action chunk should be committed before replanning? Existing systems typically execute a fixed-length prefix, implicitly assuming that the same execution horizon remains trustworthy across states. Some adaptive methods estimate this horizon from the similarity or stability of predicted actions. However, different actions may lead to the same successful outcome, whereas similar actions can produce different futures, suggesting that commitment should be determined by agreement among imagined futures rather than by similarity in action space. To this end, we propose Consequence-Aware Adaptive Action Chunking (CA$^3$C), an inference-time framework built on a simple principle: commit while imagined futures agree, and replan when they diverge. Without modifying or retraining the base policy, CA$^3$C uses an action-conditioned world model to imagine the future consequences of multiple candidate action chunks under the same sampling noise. Using these imagined consequences, we formulate execution-horizon estimation as a Bayesian change-point inference problem and select the execution candidate through future consensus. Across multiple simulation benchmarks and real-world robot manipulation tasks, CA$^3$C consistently improves diverse action-chunking policies, achieving up to a 71.8% relative reduction in failure rate over the corresponding base policies.

When using an LLM agent in a consequential domain, making an informed decision about whether to trust its output or intervene requires calibrated confidence in the agent's success. Confidence estimation for agents is difficult because evidence about success is distributed across heterogeneous, interdependent steps of an agent's trajectory. Practical agentic deployments introduce further challenges: frontier LLMs often provide limited access to internal signals, agent roll-outs are costly, and training data may be unavailable or quickly become outdated. To address these challenges, we introduce Confidence Reasoning Graphs (CRGs), an inference-time framework that estimates the probability an agent accomplished its task from a single trajectory, without privileged model access or training data. Rather than compressing an execution into a single holistic judgment, a CRG begins with the claim that the agent accomplished its task, decomposes it into contextualized sub-claims grounded in trajectory evidence, estimates confidence for each terminal claim, and finally aggregates these into an overall confidence estimate. Across three agentic benchmarks, three backbone models, and three agent frameworks, CRGs yield better-calibrated confidence and stronger risk-aware decision making than verbalized, sampling-based, and white-box surrogate baselines. We further find that calibration error alone can be misleading: a white-box surrogate baseline appears well calibrated while providing near-chance discrimination. Ablations attribute CRG's improvements to claim-level confidence estimation and aggregation rather than graph construction alone. Finally, a CRG exposes the claims and trajectory evidence underlying each confidence estimate, enabling it to be audited at decision time.