Papers

We study a class of complex-valued KdV-type equations with cubic second-order derivative nonlinearities and arbitrary complex coefficients. For sufficiently small initial data in $L^2$, we prove local well-posedness in $H^s(\mathbb R)$ for $s\ge3/4$. The key ingredient is a family of dyadic resolution spaces $Z_k=X_k+Y_k$, designed to overcome the logarithmic divergence arising from high$*$low$*$low interactions in which both derivatives fall on the highest-frequency factor. For the completely integrable third-order Kaup–Newell flow, we establish global-in-time $H^s(\mathbb R)$ bounds for $0\le s<1$ and global well-posedness in $H^s(\mathbb R)$ for every $s\ge3/4$, with no smallness assumption on the initial data.

Post-training quantization (PTQ) reduces the cost of on-device text-to-speech (TTS), but published evaluations cover one system or method. We evaluate PTQ across TTS architectures under one protocol with three core models, weight and activation ablations of eight more, and two held-out models quantized blind. Four-bit per-channel weights reduce UTMOS, a predicted mean opinion score, by 2.8 on Supertonic and 0.07 on Kokoro, and per-tensor scaling can cause severe degradation even at 8 bits. The same bit width yields different outcomes, because the sensitive component is model-specific and not reliably predicted from the model class. A staged ablation procedure identifies it, and per-layer GPTQ can restore it to within 0.1 UTMOS. Real int8 and int4 kernels reproduce the simulated ordering at hardware-dependent cost. On a Mac mini, a 4-bit weight kernel runs Supertonic at 0.60x the fp32 latency while int8 is slower, so each configuration requires validation on the target runtime.

Physical changes or sensing errors can invalidate embodied agents' task-relevant beliefs. AquaMend compares re-probing, rollback, and supported continuation on a probe-belief-action graph under an expected-loss objective covering sensing, physical recovery, and uncorrected failures. A joint posterior guides a one-step policy with conditional detection-power screening. The per-belief three-way optimum requires independence, separability, and fully resolving probes; the general policy has no global optimality guarantee. Across 32 paired scenarios in a self-constructed simulation benchmark, AquaMend recovers in 28/32 cases and reduces mean complete loss by 21.6% versus restart. Its paired loss difference from decision-theoretic troubleshooting (DTT) is not statistically significant after Holm correction. Against the all-candidate ablation, online decision time decreases by 12.3% overall but increases by 3.4% in the uncovered late stage.

Cross-country recommendation on modern e-commerce platforms is typically deployed with disjoint user and item ID spaces across markets, removing the shared anchors that conventional cross-domain methods rely on. Generative recommendation (GR) mitigates this by mapping items into a shared token space and training a unified model, but existing approaches keep behavior sequences strictly country-specific, so knowledge transfer occurs only at the parameter level and remains absent at the data level. Inspired by code-switching corpora in multilingual natural language processing, we propose CMRec, a cross-country GR framework that injects cross-country supervision at the data level via dual-constrained, context-aware code-mixing. CMRec first learns a shared semantic codebook from multi-modal content and behavioral co-occurrence across countries. It then uses this codebook to synthesize mixed-country sequences via token-level substitutions that satisfy both static (content) and dynamic (e.g., price, audience, popularity) constraints. Finally, it introduces a context-aware loss that reweights mixed samples according to their plausibility in the current sequence. Experiments on two real-world multi-country datasets and an online A/B test show that CMRec substantially improves recommendation quality in data-sparse countries while preserving performance in data-rich countries, achieving +1.77% advertising revenue and +2.64% orders on a large-scale e-commerce platform.

This paper is devoted to the non-diffusive computation of solutions to $N$-dimensional hyperbolic systems of conservation laws (HCL) and more specifically the accurate approximation of simple waves. We develop the LeafNet algorithm, which relies on: i) a reformulation of HCL as a coupled system involving smooth solutions, and ii) an accurate physics informed algorithms approximating smooth functions. An error estimate analysis and two-dimensional numerical experiments are proposed to illustrate the presented strategy.

Quasi-brittle fracture is prevalent in concrete, rock, ceramics, composites, and masonry, and its simulation faces a trade-off among accuracy, efficiency, and simplicity. The classical Lattice Spring Model (LSM) captures cracking via bond breakage without remeshing, but its elements are empirical and limited to a few tessellable shapes with fixed Poisson's ratios. We propose a tessellated Isotropic Elastic Lattice Spring Model (IELSM) that discretizes continua into polygonal elements with axial springs and a volumetric constraint, achieving isotropic elasticity on arbitrary polygonal tessellations. Macroscopic isotropy reduces to governing equations whose solvability gives a theoretical criterion for element admissibility, proving conventional tessellable elements and extending to arbitrary regular N-gons and concave elements. Exploiting boundary interpolation compatibility with finite elements, IELSM is assembled by direct node sharing, without interface elements or kinematic constraints. Coupled with an isotropic damage model, a pure bending test and four fracture benchmarks show that the coupling preserves displacement accuracy, yields crack paths and load-displacement curves agreeing with experiments and outperforming standard FEM, and is insensitive to mesh refinement. IELSM can also be restricted to damage-prone regions, with the remainder modeled by finite elements via node sharing. For the benchmarks, this reduces nodes by 41.2-80.9% and CPU time by 34.2-85.2% versus full-domain IELSM. The framework advances IELSM element construction from empirical trial and error to theoretical determination and simplifies coupling to node sharing, offering a balanced route for complex quasi-brittle fracture analysis.

While end-to-end autonomous driving systems show promise, their application to micromobility vehicles is hindered by simulators failing to capture specific kinematics, such as differential drives and omni-wheels. This paper pro- poses a sim-to-real-aware, vehicle-specific end-to-end learning environment for the WHILL Model CR on AWSIM and ROS 2. To minimize the sim-to-real gap, physical parameters are optimized via Bayesian optimization using real-world data, reducing trajectory errors across various driving scenarios. Additionally, this study introduces a synchronized architecture tailored for the stable training of world model-based agents. An end-to-end policy trained with DreamerV3 exhibited learning progress and achieved task completion in a simulated obstacle avoidance setting. Furthermore, this policy demonstrated direct sim-to-real transfer to the physical vehicle, enabling the vehicle to navigate around a cardboard box in a real-world corridor replica without fine-tuning. This paper provides a practical foundation for sim-to-real micromobility policy studies.

Kagome FeSn exhibits an occupied flat band at its terminated surface, whereas bulk FeSn adopts A-type antiferromagnetic order and does not display the same feature. Here, we combine density functional theory with primitive- and doubled-cell analysis and a double-layer tight-binding model to determine how interlayer electronic coupling and magnetic stacking control flat-band formation in FeSn. We identify an occupied Fe-$d_{z^2}$-derived flat-band manifold in the ferromagnetic state that is consistent with the experimentally observed surface feature. Brillouin-zone folding reveals that its flat branch originates from the $k_z=\frac{\pi}{c}$ sector of the primitive cell, demonstrating that it cannot be understood as an isolated kagome-layer state. Instead, the state depends on coupling between neighboring kagome layers and can be seen as a result of antibonding coupling between nearest neighbor kagome layers. A double-layer tight-binding analysis identifies interlayer Fe-Fe hopping as the dominant microscopic coupling responsible for this behavior, while a contrasting unoccupied flat-band-related manifold is governed primarily by intralayer Fe-Sn hybridization. These results establish interlayer coupling and magnetic stacking as key control parameters for kagome flat bands and highlight how coupling between layers can generate and tune extended correlated-electron states in quantum materials.

Passive long-wave infrared (LWIR) hyperspectral ranging enables distance estimation in low-light and nighttime scenes by exploiting atmospheric absorption features in thermal radiance received through the atmosphere.Joint estimation of temperature, emissivity, and distance is computationally expensive. Reference-range joint inversion also uses a distance-invariant effective attenuation coefficient, which can bias range estimates.We introduce transmittance extraction and distance alignment (TEDA), which decouples range estimation from temperature–emissivity inversion. In the first stage, a baseline estimator with a data-fidelity term invariant to the known absorption direction yields two closed-form smoothing branches for the slowly varying thermal continuum. An observation-derived gate combines the branches, and subtracting the blended baseline in the log domain recovers atmospheric transmittance. The second stage estimates range by matching the recovered transmittance to sensor-domain transmittance models recomputed for each candidate distance. Monte Carlo simulations show that TEDA effectively reduces the ranging bias caused by the distance-invariant attenuation coefficient approximation. In a measured scene, TEDA's mean range estimates are closer to the LiDAR medians than those of reference-range joint inversion in both evaluated patches. TEDA processes a complete $256\times256$ region of interest in 8.19~s versus 159.47~s for reference-range joint inversion, an approximately 20-fold speedup.

Using refined absorption, we prove that for every integer $g\ge 1$ and real $\gamma > 0$, and for sufficiently large $n$, there exists an $n^{-1+\gamma}$-spread distribution on Latin squares of order $n$ and girth at least $g$ that have no proper subsquares. This implies a combinatorial proof of Hilton's conjecture from the 1970s (recently proved algebraically by Allsop and Wanless) that for all sufficiently large $n$, there exists a subsquare-free Latin square of order $n$; indeed, it implies there exist at least $n^{(1-o(1))n^2}$ subsquare-free squares. Simultaneously it also implies the existence of high girth Latin squares (recently proved by Kwan, Sah, Sawhney and Simkin) and even an $n^{-1+\gamma}$-spread distribution on high girth Latin squares.

Prediction markets combine trading with public discussion of the same events. We examine whether comment-derived signals predict subsequent activity, buying direction, and changes in the leading outcome. A correlation sweep across 79 non-political Polymarket markets guides six classification experiments comparing comment features, trading features, and their combinations. On live blocks containing comments, attention nearly matches trading history in predicting heavy trading within 18 hours (PR-AUC 0.786 versus 0.790, against prevalence 0.606), with its relative advantage concentrated in short markets. Comment content carries directional information: toxicity ranks future buying direction above chance in 43 of 53 scored markets, while adding attention, sentiment, and stance to flow history increases ROC-AUC from 0.780 to 0.788. Leadership changes are predicted primarily by market state. Stance shifts against the leader before reversals in 23 of 27 evaluable markets, but adds no clear improvement in individual-block forecasting. These results distinguish attention from directional support and price uncertainty. They establish predictive associations consistent with discussion and trading responding to shared information, without identifying a causal effect of comments on markets.

Minimal strings offer two ways to study quantum surfaces: through a spectral curve or through a differential equation. We ask how much of the quantum equation can be recovered once the classical curve and its motion with the background are known. Our starting point is the resolvent of a scalar differential operator. We require its one-boundary integral to have poles only at branch points, with the resulting differential regular at infinity. These conditions give a finite reconstruction procedure at each genus. When the branch points are simple and their energy values move, we prove that the quantum corrections are unique whenever the procedure is consistent. A specified string equation provides a solution if its trace primitive satisfies the same analytic conditions. The scalar construction also leads to amplitudes with several boundaries. We introduce the method through pure gravity and Ising, then explore higher-order, dual and nonunitary models. Higher-Airy examples connect the calculation to $r$-spin theory on a degenerate locus that requires a separate treatment of the inverse problem.

Group-based reinforcement learning (RL) methods, such as GRPO and its variants, have become a leading paradigm for training reasoning and agentic large language models (LLMs). While their group-normalized advantage estimation is reliable at the response level, it becomes systematically biased at the step level, since coarse-grained trajectory-level advantages are hard to accurately reflect the contribution of individual steps (i.e, failed trajectories may contain valuable steps). Revisiting the foundational RL definition, we notice that GRPO's success on single-turn tasks stems from its advantage estimation strategy, which adheres to the basic definition: the mean reward of multiple actions sampled from the same state constitutes a credible state-value estimate. Extending the faithful estimation to step-level would in principle demand sampling multiple actions from each intermediate state, which is too costly on a per-state basis. To mitigate this issue, we propose a Graph-based Faithful sTep-level credit-assignment framework (GRAFT) that grafts all rollout trajectories into a trajectory graph, recovering node state-values via Bellman iteration on the graph, and assigning credit to each edge by the node value difference. Theoretically, the estimated step-level advantage faithfully adheres to the basic advantage definition in RL. To further ensure the reliability of step-level advantage estimation, we further propose Graph GAE, which extends GAE to the trajectory graph for reducing the impact of state-value estimation bias. Experiments across a range of multi-turn agentic benchmarks show consistent gains over GRPO and superior performance compared to recent agentic RL algorithms. Code will be available at https://github.com/xcyao00/GRAFT.

What happens to information carried through an evaporating black-hole horizon? We introduce a solvable model of evaporation built from coupled Sachdev-Ye-Kitaev systems, in which an initially two-sided black hole is coupled at a finite time to a larger, colder bath. Evaporation is rapid in this model, so we refer to the process as “blast freezing” of a black hole. In an appropriate large-$N$ and large-$p$ limit, the two-point functions and certain four-point probes can be computed analytically. Using the two-point functions as input to a generalized HKLL reconstruction, we obtain the emergent bulk geometry of the evaporation process. We then track the information carried by an infalling particle using operator size and Renyi-2 mutual information, showing how it is preserved in nonlocal many-body degrees of freedom after the blast-freezing transition.

A novel second-order consistent splitting scheme is proposed for the natural convection equations. The scheme is constructed using Taylor expansions about the time level $t^{n+k}$, where $k$ is a parameter to be determined. It is proved to be stable for all $k>4$, with the present study focusing primarily on the case $k=5$. Compared with the conventional splitting scheme based on Taylor expansions about $t^{n+1}$, the proposed scheme exhibits improved stability. By employing the Sobolev inequality and Gronwall's lemma, we rigorously establish stability of the proposed scheme and derive error estimates in both two and three spatial dimensions. Finally, several numerical experiments are presented to verify the stability and accuracy of the proposed scheme and to demonstrate its effectiveness.

While recent advances in perceptive locomotion have enabled humanoid robots to traverse structured terrains, agile parkour in highly discontinuous environments remains an open challenge. In particular, crossing sparse footholds and narrow support regions requires precise foothold selection, effective use of visual observations, and consistent alternating foot placement during fast transitions. In this paper, we present a perceptive humanoid parkour framework that enables stable traversal across terrains with limited foothold availability using only onboard depth observations. The framework features a saliency-guided temporal perception module that combines a saliency prior with gated memory. It retains informative depth features across frames, enabling reliable foot placement from partial observations. By introducing an alternation loss, our symmetry regularization encourages alternating gait patterns and improves traversal robustness. Extensive experiments show that our method significantly improves success rate and foothold accuracy on challenging terrains in both simulation and the real world.

Humanoid parkour policies can traverse various terrains, but task completion may mask challenges of harsh landings, edge contacts, and unstable stance contacts. Humans naturally regulate foot-terrain interaction through tactile feedback, modulating contact compliance according to terrain stiffness. This highlights a key domain gap between humans and humanoid robots: the absence of rich tactile sensing in most humanoid systems. We address this problem with TactileStep, a deployable tactile learning framework that brings sole pressure sensing into humanoid locomotion control for softer touchdowns and more stable support. TactileStep aligns tactile simulation with the real pressure insole, allowing the policy to learn from the same contact features available on hardware. During training, we use tactile and motion cues to recognize different foot-contact phases and apply phase-aware rewards that encourage safer landing and more stable stance. Evaluated in simulation and on a Unitree G1 humanoid across diverse terrains, TactileStep reduces peak touchdown force by up to 48.8% and peak A-weighted impact noise by up to 30.1 dB over a strong perceptive baseline, while increasing stance contact area by up to 23.8%.

Diffusion MRI microstructure mapping (MM) is conventionally solved voxel by voxel, ignoring the fact that tissue microstructure forms a spatially organized field. This isolation leaves each estimation problem ill-posed and nonconvex. We instead cast MM as a single global inverse problem, reconstructing the entire parameter field jointly from all measurements of a subject. An untrained neural representation supplies implicit spatial priors and eases the nonconvex optimization, requiring no training data, while coregistered T1-weighted anatomy contributes structural guidance that is freely available in standard protocols. On both synthetic and in-vivo data, our method compares favorably with established voxel-wise and learning-based baselines, suggesting global inversion is a promising alternative.

Tambara-Yamagami categories are among the simplest fusion categories beyond the pointed case: one adds a single noninvertible simple object to a finite group of invertible ones. We ask what remains of their (diagrammatic) calculus when the group is replaced by a finite semigroup, and develop the resulting (diagrammatic) calculus.

Recent advances in video object segmentation with Multimodal Large Language Model (MLLM) reasoning have demonstrated the effectiveness of using a single textual token, such as SEG, to predict segmentation masks across images and videos. However, we observe that this single-token strategy lacks the granularity required to precisely localize multiple objects across time in video segmentation tasks. To address this limitation, we develop Multi-Token Reasoning for Video Object Segmentation, or MoVISA. MoVISA uses multiple segmentation tokens, such as SEG0 and SEG1, to represent an object across different frames. This design enables more fine-grained alignment between language prompts and spatio-temporal mask predictions, improving both performance and interpretability. On the challenging MeViS, DAVIS17, ReVOS, and Ref-Youtube-VOS benchmarks, our model achieves a 13.2 percent J and F improvement on MeViS and an 8.4 percent J and F improvement on ReVOS. Code and models will be released.

Current Vision-Language-Action (VLA) models often struggle with high-precision robotic manipulation. We attribute this limitation primarily to their visual attention being dispersed across task-irrelevant regions. To address this issue, we propose ActGaze, a training approach that guides VLA policies to gaze on task-relevant regions, much like humans gaze on critical visual cues while executing precise movements. Unlike prior methods that rely on external labels for gaze supervision, ActGaze derives spatial supervision directly from the VLA's own action objective by using counterfactual visual interventions to identify regions that are critical for action prediction. Extensive real-robot experiments on four high-precision robotic manipulation tasks demonstrate that ActGaze induces more focused visual attention on task-relevant regions and consistently outperforms the base VLA policy and other visual-grounding approaches.

A finite difference numerical scheme is proposed and analyzed for the Cahn-Hilliard-Navier-Stokes system, combined with a dynamical boundary condition. Such a physical system has potential applications in the moving contact line problem. The boundary profile is governed by a lower-dimensional energy potential, coupled with a non-homogeneous boundary condition for the phase variable. In the numerical design, a convex-splitting approach is applied to the chemical potential in both bulk and surface levels, which leads to a highly coupled nonlinear system. A semi-implicit discretization is taken in the nonlinear fluid convection, as well as the coupled terms between the fluid motion and phase variable evolution. A careful finite difference approximation and convexity analysis reveals that such a numerical system could be represented as a non-symmetric and monotone mapping associated with the fluid convection. In turn, the unique solvability is valid based on the monotonicity argument. The total energy stability analysis is obtained through a careful summation-by-part calculation. In particular, an optimal rate convergence analysis is theoretically established in this work. The discrete mass conservation of the exact solution is required to preserve the mean-zero property of the error function, so that the associated discrete H_h^{-1} norm is well-defined. A combination of the Fourier projection and an auxiliary function is applied to overcome this difficulty. Furthermore, an approach of rough and refined error estimates concludes the desired convergence result. Some numerical results are presented in this article, which demonstrate the robustness of the proposed numerical scheme. In our knowledge, this work provides a theoretical proof of convergence analysis and error estimate for a numerical scheme to the moving contact line problem, for the first time in the literature.

Detecting quadratic quasi-normal modes in black hole ringdowns would provide evidence for nonlinear gravitational dynamics, while measuring their properties would enable tests of the corresponding predictions of general relativity. Specifically, second-order black hole perturbation theory predicts that their amplitudes scale with the product of the amplitudes of their parent linear modes, with a coupling coefficient that depends on the spin of the remnant black hole. This mode-specific coupling coefficient has not yet been directly measured from gravitational wave data. Here, we use Bayesian inference on the GW250114 ringdown, modeled with the $220$, $221$, and $220\times220$ modes, to infer the amplitude-coupling coefficient of the $220\times220$ mode. The inferred coefficient is consistent with predictions from numerical relativity fits and second-order perturbation theory; no comparison shows a deviation exceeding $1.3 \sigma$. Although the current data cannot distinguish among these spin-dependent predictions, this measurement establishes a basis for more stringent observational tests of nonlinear gravitational dynamics in black-hole ringdowns.

Robot-policy benchmarks increasingly cover diverse tasks and preset out-of-distribution conditions, but typically evaluate complete trajectories from predefined initial states. These evaluations often focus on the initialized scene and the final outcome, while paying less attention to the dynamic interaction process. During closed-loop execution, actions and contacts can alter object relations and task progress, producing off-nominal intermediate states that need recovery. Recovery requires a policy to infer how task progress has changed, correct the relevant relations, and continue the original goal. We introduce RoboRecover, a benchmark for robot policy recovery under execution deviations. RoboRecover selects deviation states from trajectories, reconstructs them by replaying action prefixes, and evaluates policies on the original task. RoboRecover contains 2,000 scenarios across RoboTwin and LIBERO, with 1,000 scenarios and a fixed 800/200 train/test split on each platform. Results show that initial-state performance does not determine recovery performance and policies exhibit different recovery strengths across scenarios. Using its training split, RoboRecover further supports study on recovery interventions. RoboRecover establishes recovery from execution-induced intermediate states as a distinct dimension of robot policy evaluation.

Wide-field surveys now report thousands of transients per month, while spectra are obtained for only a few per cent of them. We present DETECT (DESI–Transient Event Cross-matching Tool), a pipeline that turns each Transient Name Server (TNS) alert into a distance-informed candidate within an hour by placing it in the context of the Dark Energy Spectroscopic Instrument (DESI) archive. DETECT cross-matches every new report against the 22 million spectra of DESI EDR and DR1 through a HEALPix index, associates the transient with a host galaxy by a directional-light-radius rule whose morphology-dependent thresholds are calibrated on 4,474 supernovae with known redshifts (92.5% completeness, 0.4% wrong hosts), and passes ambiguous cases to a reviewer through a web interface. With a validated host redshift it derives the peak absolute magnitude, the projected offset and basic host properties of each event, and ranks it for spectroscopic follow-up. Applied retrospectively to ~1.2x10^5 TNS reports from 2020–2024, DETECT recovers a spectroscopic host for 15% of them, from these we build a Gold Sample of ~5,400 well-sampled light curves whose luminosity distributions by class reproduce those of untargeted surveys. Because the absolute magnitude is known at discovery, intrinsically overluminous events stand out immediately: in the prospective 2025 run this is how the lensed superluminous supernova SN~2025wny was flagged within hours of its report, and how faint, fast-declining kilonova candidates were screened against model grids and archival photometry. DETECT shows how an archival spectroscopic survey can make host redshifts a routine part of transient triage ahead of the Rubin Observatory's LSST.

Anderson acceleration (AA) is an effective technique for accelerating fixed point iterations, but it generally lacks global convergence guarantees. We propose a nonmonotone globalized Anderson acceleration framework that retains the local acceleration of AA while ensuring global convergence. For contractive mappings, without requiring prior knowledge of the contraction factor, we prove that the proposed method reduces exactly to pure AA after finitely many iterations and enjoys global $r$-linear convergence for memory size $m\geq1$ and global residual $q$-linear convergence for $m=1$, with convergence factors no greater than the contraction factor of the underlying fixed point mapping. For nonexpansive mappings, we prove that the fixed point residuals converge globally to zero. A class-agnostic parameter selection rule is further developed to ensure these convergence properties in both settings. Numerical experiments demonstrate the robustness and efficiency of the proposed method.

Few-shot segmentation (FSS) aims to segment unseen object categories with a few (e.g., one or five) labeled examples, enabling efficient adaptation to novel classes. Conventional models typically rely on appearance-based visual matching between support and query images for segmentation. While straightforward, these methods often struggle to handle significant appearance discrepancies and occlusions in the query image due to insufficient target knowledge. To mitigate this, we introduce a novel framework that mines target knowledge using the strong reasoning capacity of Multimodal Large Language Models (MLLMs) and employs it to enhance FSS. Specifically, building on SAM 2, our method, named MK-FSS, exploits two forms of complementary knowledge derived from a query image by an MLLM for FSS, including spatial knowledge, which provides a spatial prior indicating the potential target location, and semantic knowledge, which describes the target using text. The spatial knowledge is first encoded into a memory representation, and then resulting memory is integrated with the support-guided memory feature from query image through a carefully designed dual-memory debate-fusion (DMDF) module, yielding a more robust target memory feature. In parallel, the semantic knowledge is encoded into the textual feature, which is fused with multi-scale query features via a progressive cross-modal prompt generator (PCPG), producing a target-aware multimodal prompt for segmentation. Working together, the dual-memory feature and the multimodal prompt provide a comprehensive representation of the target, enabling more robust segmentation. In our extensive experiments, MK-FSS shows promising results and largely surpasses existing methods. Code will be released.

We test whether collisions involving Titan can eject enough water-rich material onto sufficiently distant Saturn-bound orbits to form Iapetus, while also accounting for Titan's orbital eccentricity. Three-dimensional impact calculations and post-impact trajectories examine initially Saturn-unbound and bound impactors. In the oblique unbound case with a differentiated impactor roughly a tenth the mass of Titan at a speed of 10 km s\(^{-1}\), outgoing predominantly icy material from a selected population totaling about 3.5 times Iapetus's mass remains Saturn-bound for days after impact. We track an icy sample whose orbital apoapsis extends beyond Iapetus's distance. After impact, Titan's eccentricity increases to near 0.13, while the impactor's rocky core escapes Saturn. In another case, a bound companion one quarter Titan's mass collides at \(45^\circ\) and about 3.7 km s\(^{-1}\), ejecting 0.60 Iapetus masses of ice. The rocky impactor core initially skips past Titan; an orbital continuation reaches return contact after 6.9 yr. This run also retains 0.48 Iapetus masses of ice. Titan's eccentricity evolves due to the initial impact and debris scattering. The merger results in a Titan with an eccentricity of about 0.10. These results establish the collisional production of an icy debris reservoir, with some material on orbits of large semimajor axis; raising Iapetus's periapse would require gas drag or dynamical friction.

Misinformation is widely reported to propagate faster on engagement-based platforms, yet prior work largely focused on empirical analysis, without identifying a specific algorithmic mechanism that results in this phenomenon. Thanks to the open-sourcing of X's recommendation algorithms, we conduct what is, to our knowledge, the first component-level study of the recommendation algorithm deployed by a social media platform, which examines how each of its components affects misinformation propagation. Specifically, we identify the engagement fungibility mechanism in the algorithm, where the final recommendation score is constructed as a weighted sum of all predicted user activities. As a result, a tweet can be repeatedly recommended simply because it is predicted to draw many instant reactions (e.g., likes and retweets), even when it is not expected to draw thoughtful responses (e.g., replies and quotes). Since misinformation typically draws a larger share of its engagement from instant reactions, this mechanism enables it to receive more recommendation exposure and to propagate faster. To empirically validate this mechanism, we re-implement X's recommendation algorithm on the USC X 2024 election corpus, and build a calibrated simulation study to analyze the impact of different scoring rules. We find that re-tuning the metric weights has little or even a negative impact on reducing the credibility exposure gap, while those scoring rules that set a precondition of thoughtful engagement for amplification would be able to alleviate the gap significantly, across 46 robustness checks. Our diagnosis, therefore, yields a simple and deployable fix, a reflective-threshold gate that withholds amplification until a tweet is predicted to draw thoughtful engagement, which we find to reallocate exposure away from low-credibility content at no cost to mainstream exposure and with no loss of engagement.

National-scale digital health platforms generate usage data that reveal population healthcare needs. MediVerify, Sri Lanka's online medicines information platform providing access to National Medicines Regulatory Authority (NMRA)-approved medicines, recorded over 1.49 million queries in its first year. Large-scale medicine search behaviour in low- and middle-income countries (LMICs) remains poorly characterised. Objectives: To characterise medicine information-seeking behaviour, identify mismatches between public demand and essential medicines policy, and evaluate technical performance. Methods: We retrospectively analysed 1,497,304 anonymised queries submitted between July 2024-2025. Queries were normalised and mapped to 11,933 approved medicines using fuzzy matching based on Levenshtein distance (threshold <=5). Therapeutic categories were assigned using an Anatomical Therapeutic Chemical (ATC)-aligned classification. Query patterns and system performance were analysed, and energy consumption was estimated from processing times. Results: Vitamins/minerals (11.74%), antibiotics (10.57%), anti-diabetes (7.02%), and antihypertensives (6.84%) dominated searches. The top 20 accounted for 37.3% of queries, while approximately 40%-50% of registered medicines were never queried. Zero-result queries (~ 1%) indicated unmet information needs. Frequently searched medicines diverged from essential medicines lists. Median latency was 8ms, with >99% query resolution. Estimated energy consumption was approximately 0.12 kWh per million queries. Conclusions: Large-scale medicine search data provide insights into healthcare information demand and policy alignment. MediVerify demonstrates that a national digital health platform can achieve high utilisation at low computational and environmental cost. Usage analytics could strengthen pharmaceutical policy and digital health infrastructure in LMICs.