Background/Objectives: Poly(lactide-co-glycolide) (PLGA) microspheres support long-acting drug delivery, but their release profiles are difficult to predict because burst release, diffusion, polymer degradation, and formulation-dependent effects interact across multiple time scales. This study aimed to develop a continuous-time model that combines accurate release prediction with physically admissible trajectories and release-component attribution. Methods: MC-NODE encodes ten drug, polymer, and formulation descriptors, decomposes the non-negative release rate into burst, diffusion, degradation-associated late-stage, and neural-residual components, and applies a formulation-dependent plateau through a semi-analytical state map. The model was evaluated on a literature-curated dataset containing 321 in vitro release curves, 4913 observations, 89 drugs, and 113 publications using DOI-grouped five-fold cross-validation, complementary extrapolation and sparse-sampling protocols, synthetic mechanism-recovery experiments, and retrospective orthogonal consistency analysis. Results: MC-NODE achieved an RMSE of $0.094\pm 0.005$ and an $R^2$ of $0.854\pm 0.018$, with all 321 out-of-fold trajectories satisfying monotonicity and range criteria. It recovered synthetic contribution labels more accurately than the ablated variants. The degradation-associated late-stage contribution showed positive associations with experimental degradation, molecular-weight loss, pore-evolution, and mass-loss indicators, while the diffusion contribution was positively associated with an experimental diffusion indicator. Dominant-process agreement was 83.3%, and matched external or out-of-fold trajectories achieved an RMSE of $0.108\pm 0.020$. Under drug-grouped, chemical-cluster, and alternative sparse-sampling evaluations, MC-NODE retained the lowest absolute trajectory-level errors among the compared models. Conclusions: MC-NODE improves formulation-level PLGA release prediction while preserving continuous, monotonic, and bounded trajectories. Its component outputs provide experimentally supported, model-attributed summaries for comparative formulation analysis.

Camera-based visual sensing for classroom behavior detection remains challenging because fine-grained behaviors often differ only in subtle posture and hand–object cues, while dense seating, occlusion, scale variation, and background interference further weaken discriminative visual evidence. To address these issues, this study proposes the Multi-scale Context, Hierarchical Integration, and Memory Enhancement Detector (MCHIME-Det), a lightweight, multi-scale context and memory-enhanced detector built on YOLO26n. The framework introduces three complementary components: C3k2PMM combines multi-scale local modeling with direction-aware selective state-space scanning; CGHFF performs channel-guided hierarchical feature interaction across adjacent feature levels; and C2MECM uses input-dependent memory experts to compensate for ambiguous high-level representations. For evaluation, two public classroom behavior datasets were combined into a corpus containing 11,879 images and 71,657 annotated instances across three categories: hand-raising, reading, and writing. On the curated image-level split, MCHIME-Det achieves 76.3% precision, 74.9% recall, 82.1% mAP${}_{50}$, and 61.4% mAP${}_{50:95}$, improving the YOLO26n baseline by 5.6 and 4.4 percentage points in mAP${}_{50}$ and mAP${}_{50:95}$, respectively. These gains are achieved with only 2.36 M parameters and 5.2 GFLOPs, while maintaining 182 FPS on an RTX 4090 and 17.1 FPS on a Jetson Orin Nano edge device. Ablation, cross-architecture, scale-, density-, and overlap-conditioned analyses, cross-source evaluation, image-corruption robustness tests, and cross-hardware benchmarks characterize model performance on the curated benchmark, three sampled external datasets, specified synthetic corruptions, and tested hardware platforms. These results support hierarchical local–global refinement and memory-assisted compensation as effective strategies for lightweight camera-based visual sensing under the evaluated image datasets and inference settings.

Regulatory instruments alter institutional payoffs, but they do not choose which equilibrium a decentralized financial system will realize. A policy that appears safe at one computed response can therefore coexist with an unobserved fire-sale or funding-run outcome. We pose policy construction as a set-containment requirement: every approximate Nash equilibrium of the regulated game must remain inside a buffered stability target. EquiImplement enforces this requirement with state-dependent mixtures of admissible unilateral deviations over the target complement. When policy features enter payoffs affinely, holding this proof object fixed gives affine inequalities in the regulatory vector and a concave minimum margin, producing a convex semi-infinite policy subproblem. A rigorous regional separator locates the weakest-covered state, and the same verified counterexample drives both the next policy solve and certificate revision. A preset outer-iteration budget gives finite execution and one of three outputs: globally certified containment, budget infeasibility within the prescribed incentive–certificate family, or an unresolved status. The evaluation covers 330 fire-sale and rollover/run games. At the default budget, EquiImplement attains full-stability rates of 95.0%, 85.6%, and 92.5%, while reducing the worst-equilibrium violation from 0.037 for the strongest non-oracle baseline to 0.016. The mean regulatory cost over returned budget-feasible evaluation policies decreases from 0.119 to 0.113. Further analyses relate certification difficulty to stability-target tightness, leverage, market depth, liquidity buffers, and coordination strength. The results show that a deviation-based proof object can serve directly as an optimization interface for financial regulation under equilibrium multiplicity.