Satellite rainfall products are often evaluated with gauges that sample different periods and spatial supports. We assessed daily Integrated Multi-satellitE Retrievals for GPM (IMERG) Final V07 rainfall over Malaysia from October 2015 to September 2025. National and six regional means were summarized with observed percentiles, leave-one-hydrological-year-out influence, and complete-year bootstrap uncertainty. Validation used a common seven-year period, gauges with at least 90% cell availability, and 2,420 dates meeting the coverage rule in all regions. Colocated gauges were averaged within each IMERG cell. We compared cell-aggregated gauges with IMERG on the same dates and cells, then compared gauge-footprint IMERG with full-region IMERG. The national 99th percentile was 25.24 mm day⁻¹; regional values ranged from 31.92 to 50.09 mm day⁻¹. East Coast and Southern Peninsular Malaysia together accounted for the highest P99 in 99.8% of full-archive year resamples, although their intervals overlapped. In the stable gauge design, footprint effects ranged from −6.2% to 11.5%, and gauge-to-footprint differences ranged from −27.2% to 12.8%. East Coast gauges ranked first in 99.8% of matched-period resamples. At 593 evaluable cells, median all-day P99 bias ranged from −13.3% to −24.2% and remained negative under two alternative event definitions and 12 spatial-block designs. Median probability of detection declined from 0.51–0.63 at 10 mm day⁻¹ to 0.09–0.31 at 50 mm day⁻¹. IMERG can screen regional rainfall patterns, but local high-intensity verification remains gauge-dependent.

A full-factorial experiment in the Public Goods Game shows that information regime and incentive strength explain 85.8% of cooperation-rate variance; algorithm choice accounts for just 3.8%. Agents with the least information cooperate most (83% vs 42% under full observation), attributable to state-space compression. TreeSHAP and Shapley-variance decomposition confirm information structure, not algorithm selection is the primary design lever for cooperation.

The execution of large portfolio transactions requires balancing market impact and adverse price drift. The Almgren-Chriss (2001) framework provides a mean-variance trade-off for martingale price processes, but practitioners often use short-term alpha signals. This paper re-evaluates optimal liquidation with Stochastic Optimal Control. Adding a mean-reverting alpha signal to the price dynamics produces a closed-form solution through the Hamilton-Jacobi-Bellman (HJB) equation. The resulting trading rate is affine in current inventory and the predictive signal, giving institutional execution desks a transparent additive framework.