A somewhat gentle introduction to differential graded commutative algebra

Differential graded (DG) commutative algebra provides powerful techniques for proving theorems about modules over commutative rings. These notes are a somewhat colloquial introduction to these techniques. In order to provide some motivation for commutative algebraists who are wondering about the benefits of learning and using these techniques, we present them in the context of a recent result of Nasseh and Sather-Wagstaff. These notes were used for the course "Differential Graded Commutative Algebra" that was part of the Workshop on Connections Between Algebra and Geometry held at the University of Regina, May 29--June 1, 2012.Comment: 78 page

Quality Child Care Supports the Achievement of Low-Income Children: Direct and Indirect Pathways Through Caregiving and the Home Environment

Existing studies of child care have not been able to determine whether higher quality child care protects children from the effects of poverty, whether poverty and lower quality child care operate as dual risk factors, or whether both are true. The objective of the current study was to test two pathways through which child care may serve as a naturally occurring intervention for low-income children: a direct pathway through child care quality to child outcomes, and an indirect pathway through improvements in the home environment. Children were observed in their homes and child care settings at 6, 15, 24, and 36 months. An interaction between family income-to-needs ratio and child care quality predicted School Readiness, Receptive Language, and Expressive Language, as well as improvements in the home environment. Children from low-income families profited from observed learning supports in the form of sensitive care and stimulation of cognitive development, and their parents profited from unobserved informal and formal parent supports. Policy implications are discussed

Drivers of Change in a 7300-Year Holocene Diatom Record from the Hemi-Boreal Region of Ontario, Canada

A Holocene lake sediment record spanning the past 7300 years from Wishart Lake in the Turkey Lakes Watershed in the Hemi-Boreal of central Ontario, Canada, was used to evaluate the potential drivers of long-term change in diatom assemblages at this site. An analysis of diatom assemblages found that benthic and epiphytic taxa dominated the mid-Holocene (7300–4000 cal yr BP), indicating shallow, oligotrophic, circum-neutral conditions, with macrophytes present. A significant shift in diatom assemblages towards more planktonic species (mainly Cyclotella sensu lato, but also several species of Aulacoseira, and Tabellaria flocculosa) occurred ~4000 cal yr BP. This change likely reflects an increase in lake level, coincident with the onset of a more strongly positive moisture balance following the drier climates of the middle Holocene, established by numerous regional paleoclimate records. Pollen- inferred regional changes in vegetation around 4000 yrs BP, including an increase in Betula and other mesic taxa, may have also promoted changes in diatom assemblages through watershed processes mediated by the chemistry of runoff. A more recent significant change in limnological conditions is marked by further increases in Cyclotella sensu lato beginning in the late 19th century, synchronous with the Ambrosia pollen rise and increases in sediment bulk density, signaling regional and local land clearance at the time of Euro- Canadian settlement (1880 AD). In contrast to the mid-Holocene increase in planktonic diatoms, the modern increase in Cyclotella sensu lato likely indicates a response to land use and vegetation change, and erosion from the watershed, rather than a further increase in water level. The results from Wishart Lake illustrate the close connection between paleoclimate change, regional vegetation, watershed processes, and diatom assemblages and also provides insight into the controls on abundance of Cyclotella sensu lato, a diatom taxonomic group which has shown significant increases and complex dynamics in the postindustrial era in lakes spanning temperate to Arctic regions

Augmented generalized happy functions

An augmented happy function, $S_{[c,b]}$ maps a positive integer to the sum of the squares of its base-$b$ digits and a non-negative integer $c$. A positive integer $u$ is in a cycle of $S_{[c,b]}$ if, for some positive integer $k$, $S_{[c,b]}^k(u) = u$ and for positive integers $v$ and $w$, $v$ is $w$-attracted for $S_{[c,b]}$ if, for some non-negative integer $\ell$, $S_{[c,b]}^\ell(v) = w$. In this paper, we prove that for each $c\geq 0$ and $b \geq 2$, and for any $u$ in a cycle of $S_{[c,b]}$, (1) if $b$ is even, then there exist arbitrarily long sequences of consecutive $u$-attracted integers and (2) if $b$ is odd, then there exist arbitrarily long sequences of 2-consecutive $u$-attracted integers

Quantifying the Coastal Hazard Risk Reduction Benefits of Coral Reef Restoration in the U.S. Virgin Islands

Coastal habitat restoration, especially of coral reef ecosystems, can significantly reduce the exposure of coastal communities to natural hazards and, consequently, the risk of wave-driven flooding. Likewise, reef degradation can increase coastal flood risks to people and property. In this study, the valuation of coral reefs in the United States Virgin Islands (USVI), along the coasts of St. Croix, St. John, and St. Thomas, demonstrated the social and economic benefits provided by these natural defenses. Across the territory, more than 481 people and 31.2 million of infrastructure were estimated to receive protection from coral reefs per year (2010 U.S. dollars). In 2017, Hurricanes Irma and Maria significantly damaged coral reefs throughout the archipelago. By combining engineering, ecological, geospatial, social, and economic data and tools, this study provided a rigorous valuation of where potential coral reef restoration projects could help rebuild these damaged habitats and decrease the risks from coastal hazards faced by USVI’s reef-fronted communities. Multiple restoration scenarios were considered in the analysis, two of which are detailed in this report. These include (1) ‘Ecological’ restoration, where restoration creates a structure that is 0.25 m high and 25-m-wide reef, and (2) ‘Hybrid’ restoration, where restoration creates a structure that is 1.25 m high and 5 m wide. There are many ways that such structures could be developed. In the hydrodynamic analyses, there are no assumptions about how the restoration is developed. Many practitioners of both coral (and oyster reef) restoration consider that a reef height of 0.25 m might be delivered from planting corals alone and that 1.25 m might require a combination of artificial structures and coral planting. In a third scenario, the analysis investigated the reduction of protection benefits that would occur through the reduction of 1 meter of naturally occurring reef height due to reef degradation. The reduction of protection due to the loss of reefs can also be interpreted as the protection value of the existing reefs. In all studied restoration scenarios, it was assumed that the planting of corals would enhance hydrodynamic roughness, effectively dissipating incident wave energy and reducing the potential for coastal flooding. A standardized approach was employed to strategically locate potential restoration projects along the entire linear extent of existing reefs bordering the USVI, and to identify where coral reef restoration could offer valuable benefits in flood reduction. Potential restoration projects were only located within the existing distribution of reefs across the region, even though numerous sites were positioned far offshore (2-3 km), and some were at relatively deep depths (up to 7 m). Risk-based valuation approaches were followed to delineate flood zones at a 10 m2 resolution along the entire region's reef-lined shorelines for all the potential coral reef restoration scenarios. These were subsequently compared to flood zones without coral reef restoration. The potential reduction in coastal flood risk provided by coral reef restoration, and the protection value of existing reefs, were quantified utilizing the latest information available at the time of analysis from the U.S. Census Bureau, Federal Emergency Management Agency (FEMA), and Bureau of Economic Analysis for return-interval storm events. The change in Expected Annual Damages (EAD), a metric indicating the annual protection gained due to coral reef restoration, was calculated based on the damages associated with each storm probability. The findings suggest that the benefits of reef restoration are spatially variable within the USVI. In some areas, the analysis showed limited benefits from reef restoration, which may be attributed to the depth or offshore distances of proposed restoration sites. However, there were a number of key areas where reef restoration could have substantial benefits for flood risk reduction. The annual flood risk reduction attributed to potential ‘ecological’ coral reef restoration in the USVI was 99 people and 6.1 million (2010 U.S. dollars). The Benefit-to-Cost Ratio (BCR) for this restoration approach was found to be larger than 1 (i.e., cost-effective) along 11% of the St. Croix coastline, 4.9% of the St. John coastline, and 8.7% of the St. Thomas coastline. This analysis offers stakeholders and decision-makers a spatially explicit and rigorous evaluation that illustrates how, where, and when potential coral reef restoration efforts in St. Croix, St. John, and St. Thomas could be instrumental to reducing coastal storm-induced flooding. Understanding areas where reef management, recovery, and restoration could effectively reduce climate hazard-related risks is crucial to protect and enhance the resilience of coastal communities in USVI