This paper investigates a non-orthogonal multiple access assisted coordinated beam hopping (NOMA-CBH) scheme in multidimensional very low Earth orbit (VLEO) satellite communication systems, where multiple satellites employ CBH and coordinated beams jointly serve ground users and a dedicated ground station (GS). To characterize the VLEO-specific propagation environment, we develop a channel model that incorporates atmospheric attenuation, Doppler effects, and pointing perturbations. Building upon this architecture and channel model, a low-complexity decoupled (LCD) algorithm is designed to optimize beam scheduling and power allocation. We further derive closed-form outage probability expressions for the ground users and the GS, perform asymptotic analysis to characterize their diversity orders, and evaluate the delay-limited throughput. Simulation results demonstrate that: i) The NOMA-CBH with LCD algorithm achieves an enhanced system sum rate relative to orthogonal multiple access with coordinated beam hopping (OMA-CBH); ii) Across the considered heterogeneous traffic-demand operating points, the NOMA-CBH scheme achieves higher aggregate delivered traffic than the benchmark schemes; and iii) The outage performance of NOMA-CBH is better than that of OMA-CBH.
Stochastic simulators need suitable parameter values to reproduce observed behaviour in complex systems. Searching for these values through repeated simulations makes frequent recalibration computationally expensive. We develop an amortized optimizer that uses simulations collected in advance to learn how to choose parameters that make simulated outcomes agree with observations. Once fitted, it maps new observations to feasible parameters without further simulator calls. The method retains alternative parameter settings that can explain similar observations and compares their responses, avoiding the conflicting labels that arise when training a single parameter regressor. Historical observations also provide supervision by showing which simulated responses agree with the data, even when the underlying parameters are unknown. Experiments across four simulators compare calibration accuracy and query time. Dedicated cost analyses quantify traffic preparation and the recorded financial reuse costs. On new traffic targets, local correction more than halves query time relative to empirical and surrogate selection; a learned inverse is faster still, with similar mean error. In a retrospective comparison on real financial data, our method returns parameters about $1.07\times10^{7}$ times faster than a 10-minute Gaussian-process Bayesian optimization search, with mean calibration error 3.06% higher. Reusing simulation work across observations supports repeated parameter updates when the available time is too short for a new search.
Chain-of-thought reasoning has substantially advanced video understanding in multimodal large language models (MLLMs). However, language-based reasoning traces do not provide a reliable mechanism for models to revisit relevant visual evidence, leading to visual forgetting and impairing their ability to reason over video content. Existing approaches maintain visual grounding during reasoning in two main ways: they either refer to evidence using textual coordinates, which specify symbolic locations rather than the visual content itself, or reinsert cropped regions or frames into the multimodal context, preserving visual details at the cost of substantial context expansion. To address these limitations, we introduce VideoLVR, which constructs latent visual evidence from local regions at relevant video moments, thereby providing visual support for intermediate reasoning steps. To supervise latent visual evidence generation, we introduce a visual token prediction objective that formulates visual token reconstruction as prediction over a vocabulary derived from the input video, thereby unifying visual evidence reconstruction and text generation within the same token prediction framework. This shared prediction framework enables MLLMs to reason over interleaved text tokens and latent visual states while integrating evidence from different moments. We further extend VideoLVR to reinforcement learning by treating sampled visual tokens as actions alongside text tokens and jointly optimizing the policy using final-answer rewards. By efficiently revisiting task-relevant visual information during reasoning, VideoLVR improves video understanding without substantially expanding the multimodal context. Experiments on multiple video benchmarks demonstrate its effectiveness, especially on tasks requiring fine-grained visual evidence.