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Bae, Sang Won ; Park, Heejin (Ed.)We present an O(n³ g² log g + m) + Õ(n^{ω + 1}) time deterministic algorithm to find the minimum cycle basis of a directed graph embedded on an orientable surface of genus g. This result improves upon the previous fastest known running time of O(m³ n + m² n² log n) applicable to general directed graphs. While an O(n^ω + 2^{2g} n² + m) time deterministic algorithm was known for undirected graphs, the use of the underlying field ℚ in the directed case (as opposed to ℤ₂ for the undirected case) presents extra challenges. It turns out that some of our new observations are useful for both variants of the problem, so we present an O(n^ω + n² g² log g + m) time deterministic algorithm for undirected graphs as well.more » « less
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null (Ed.)Abstract Many existing models that predict landslide hazards utilize ground-based sources of precipitation data. In locations where ground-based precipitation observations are limited (i.e., a vast majority of the globe), or for landslide hazard models that assess regional or global domains, satellite multisensor precipitation products offer a promising near-real-time alternative to ground-based data. NASA’s global Landslide Hazard Assessment for Situational Awareness (LHASA) model uses the Integrated Multisatellite Retrievals for Global Precipitation Measurement (IMERG) product to issue hazard “nowcasts” in near–real time for areas that are currently at risk for landsliding. Satellite-based precipitation estimates, however, can contain considerable systematic bias and random error, especially over mountainous terrain and during extreme rainfall events. This study combines a precipitation error modeling framework with a probabilistic adaptation of LHASA. Compared with the routine version of LHASA, this probabilistic version correctly predicts more of the observed landslides in the study region with fewer false alarms by high hazard nowcasts. This study demonstrates that improvements in landslide hazard prediction can be achieved regardless of whether the IMERG error model is trained using abundant ground-based precipitation observations or using far fewer and more scattered observations, suggesting that the approach is viable in data-limited regions. Results emphasize the importance of accounting for both random error and systematic satellite precipitation bias. The approach provides an example of how environmental prediction models can incorporate satellite precipitation uncertainty. Other applications such as flood and drought monitoring and forecasting could likely benefit from consideration of precipitation uncertainty.more » « less