Step-Indexed Logical Relations for Probability (long version)

It is well-known that constructing models of higher-order probabilistic programming languages is challenging. We show how to construct step-indexed logical relations for a probabilistic extension of a higher-order programming language with impredicative polymorphism and recursive types. We show that the resulting logical relation is sound and complete with respect to the contextual preorder and, moreover, that it is convenient for reasoning about concrete program equivalences. Finally, we extend the language with dynamically allocated first-order references and show how to extend the logical relation to this language. We show that the resulting relation remains useful for reasoning about examples involving both state and probabilistic choice.Comment: Extended version with appendix of a FoSSaCS'15 pape

Evaluating the success of seed sowing in a New England grassland

Grassland habitat is declining in the northeastern United States, leading to a decline in associated native species. Consequently, there is considerable interest by land managers in conserving and restoring grassland habitats in the Northeast. However, unlike the Great Plains and Europe, quantitative monitoring of restoration sites is uncommon, making it difficult to improve new restoration projects. Here we evaluate a grassland restoration in Waterford, Connecticut to determine if mechanical clearing of woody vegetation combined with sowing 23 native grasses and forbs led to successful establishment of these species. We also compared cover, diversity, and colonization by exotic and woody species in planted and unplanted areas over time. In the third and fifth growing seasons after planting in 2006, we sampled the vegetation in the planted site, an unplanted zone within the planted grassland, and an adjacent unplanted grassland. Twenty of the 23 sown species established by 2010, and sown species dominated the planted area (70% of total cover). Despite the successful establishment of most sown species, species richness and diversity were no higher in the sown grassland than in adjacent unseeded areas. However, the sown grassland contained lower cover of non-native and invasive species. Big bluestem (Andropogon gerardii Vitman) established aggressively, potentially reducing both exotic colonization and native diversity. This study shows that sowing native grassland species can lead to the successful development of native-dominated grasslands. Results can inform future grassland restoration efforts in the Northeast and show that seeding with aggressive grass species may greatly impact restored plant communities

Friedmann Equations from Entropic Force

In this note by use of the holographic principle together with the equipartition law of energy and the Unruh temperature, we derive the Friedmann equations of a Friedmann-Robertson-Walker universe.Comment: latex, 8 pages, v2: minor modifications and to appear in PRD (Rapid Communication