Sets Characterized by Missing Sums and Differences in Dilating Polytopes

A sum-dominant set is a finite set $A$ of integers such that $|A+A| > |A-A|$. As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to be rare in some sense. In 2006, however, Martin and O'Bryant showed that the proportion of sum-dominant subsets of $\{0,\dots,n\}$ is bounded below by a positive constant as $n\to\infty$. Hegarty then extended their work and showed that for any prescribed $s,d\in\mathbb{N}_0$, the proportion $\rho^{s,d}_n$ of subsets of $\{0,\dots,n\}$ that are missing exactly $s$ sums in $\{0,\dots,2n\}$ and exactly $2d$ differences in $\{-n,\dots,n\}$ also remains positive in the limit. We consider the following question: are such sets, characterized by their sums and differences, similarly ubiquitous in higher dimensional spaces? We generalize the integers in a growing interval to the lattice points in a dilating polytope. Specifically, let $P$ be a polytope in $\mathbb{R}^D$ with vertices in $\mathbb{Z}^D$, and let $\rho_n^{s,d}$ now denote the proportion of subsets of $L(nP)$ that are missing exactly $s$ sums in $L(nP)+L(nP)$ and exactly $2d$ differences in $L(nP)-L(nP)$. As it turns out, the geometry of $P$ has a significant effect on the limiting behavior of $\rho_n^{s,d}$. We define a geometric characteristic of polytopes called local point symmetry, and show that $\rho_n^{s,d}$ is bounded below by a positive constant as $n\to\infty$ if and only if $P$ is locally point symmetric. We further show that the proportion of subsets in $L(nP)$ that are missing exactly $s$ sums and at least $2d$ differences remains positive in the limit, independent of the geometry of $P$. A direct corollary of these results is that if $P$ is additionally point symmetric, the proportion of sum-dominant subsets of $L(nP)$ also remains positive in the limit.Comment: Version 1.1, 23 pages, 7 pages, fixed some typo

Biomass of Submerged Aquatic Vegetation in the Chesapeake Bay

Information provided in existing field biomass and ground truth surveys of Chesapeake Bay submerged aquatic vegetation (SAV) were quantified along with 1985 to 1996 annual aerial surveys of SAV distribution and abundance to determine the community type and aboveground biomass for each SAV bed mapped in the bay during this 12 year period. Using species identifications provided through over 10,000 SAV ground survey observations the 17 most abundance SAV species found in the bay were clustered into four species associations: ZOSTERA, RUPPIA, POTAMOGETON and FRESHWATER. In addition, monthly aboveground biomass values were assigned to each bed based upon biomass models developed for each community. The biomass values of each SAV bed are now available for use along with the annual mapping measurements of bed area for evaluation of bay SAV standing stocks

Analysis of Historical Distribution of Submerged Aquatic Vegetation (SAV) in the York and Rappahannock Rivers as Evidence of Historical Water Quality Conditions

Historical black and white format photographs at scales of approximately 1:20,000, dating from 1952 to 1956 were used to delineate the maximum coverage of SAV in the study region. Coverage of photography from decades before and after this period were found to generally to be of poorer quality and show less SAV presence. Photo-interpretation of the aerial photographs was accomplished using a head-up, on-screen digitizing system at fixed image scale of 1:12,000 and followed as closely as possible the methods currently used to delineate SAV beds throughout the Chesapeake Bay as well as the delineation of historical SAV coverage for other region. A total of 16,340 hectares of sub-tidal bottom in the western shore bay region between the James and Potomac Rivers including all of the York and Rappahannock Rivers were found to display SAV signatures. Of this total approximately 11,260 ha, or 69%, were determined to be growing at depths shallower than 1 m MLW (Mean Low Water), 4,200 ha or 26% between 1 m and 2 m MLW, and 884 ha or 5% at depths below 2 m MLW. Comparison of the historical depths of growth with that of photography taken in 1999 reveal a general decrease in maximum depth of growth of approximately 0.5m in many areas. The most upriver areas of the York and Rappahannock, where SAV no longer are found, had SAV bed signatures to 1 m MLW, while downriver areas and regions along the Chesapeake Bay had maximum depths or 2 m or more in some areas. Losses of vegetation have been much more extensive in the Rappahannock than the York. In 1999, in the lower York River (YRKPH) approximately 23% of the historical SAV coverage remained while only 1% remained in the lower Rappahannock (RPPMH). Areas along the bay shoreline had the highest proportion of remaining beds with bay segments CB6PH and MOBPH exceeding 50% of historical coverage

The Relevance Of Discretionary Disclosures: Predictive Value Versus Feedback Value

This study contributes to the body of literature examining the role of discretionary disclosures. The primary theoretical contribution is a distinction between predictive value and feedback value. We use the Ohlson Model and examine the role of information as an endogenous variable in modeling the impact of disclosures on returns, which is a key methodological contribution to this stream of literature. Using a sample of 121 firms from the AIMR’s Corporate Information Committee for 1982-1994 we find that the expanded firm disclosures did possess predictive value, but they did not possess significant feedback value. These results have important policy implications since the relative costs and benefits of disclosures with predictive value differ from those with feedback value

Analysis of Historical Distribution of Submerged Aquatic Vegetation (SAV) in the James River

Analyses of historical photography and ground surveys dating from the 1930s indicate that approximately 1645 hectares of SAV have been historically present in shallow water regions throughout the James River. This compares to 77 hectares of vegetation reported in 1997 and a James River Tier I SAV restoration goal of 107 hectares (areas mappped with SAV from 1971- 1991). Overall, the temporal and spatial patterns of loss of SAV populations in the James River suggest declines occurred first in the tidal freshwater regions of the upper James beginning approximately 50 years ago, and then subsequently in the lower James beginning approximately 30 years ago. Since then regrowth has been limited to high salinity regions near the river’s mouth along the shoreline of Hampton and Newport News, and an apparent increase in the region of the Chickahominy River. In a series of surveys by boat during the summer of 1998, numerous beds of SAV, many too small to map with high altitude aerial photography, were found in a number of the tidal tributary creeks of the James including the Chickahominy River, Wards Creek, Upper Chippokes Creek, Grays Creek, and Lower Chippokes Creek, as well as along the HamptonNewport News shoreline. The SAV which occurs in the river system today was found to be dominated by three species. SAV in the tidal freshwater tributaries of the upper James consistes principally of Ceratophyllum demersum (coontail) and Najas minor (common naiad). Here the SAV was growing to depths of 0.5-1.5 m. The SAV in the high salinity region is the saltwater tolerant species Zostera marina (eelgrass). Water depths of the areas currently vegetated with eelgrass were found to be approximately 0.5 to 1.0 m at MLW, while historical photographs suggest that vegetation in the lower James formerly grew to depths of nearly 2.0 m

Analysis of Histocial Distribution of SAV in the Eastern Shore Coastal Basins and Mid-Bay Island Complexes as Evidence of Historical Water Quality Conditions and a Restored Bay Ecosystem

Historical black and white format photographs at scales of approximately 1:20,000, dating from 1952 to 1956 were used to delineate the maximum coverage of SAV in the study region. Coverage of photography from decades before and after this period were found to generally to be of poorer quality and show less SAV presence. Photo-interpretation of the aerial photographs was accomplished using a head-up, on-screen digitizing system at fixed image scale of 1:12,000 and followed as closely as possible the methods currently used to delineate SAV beds throughout the Chesapeake Bay as well as the delineation of historical SAV coverage for other region. A total of 13,046 hectares of sub-tidal bottom in the Eastern Shore bay region between the tip of Fisherman’s Island to the Virginia-Maryland border, including the mid-bay island complex, were found to display SAV signatures. Of this historical total, approximately 10,451 ha, or 80%, were determined to be growing at depths shallower than 1 m MLW (Mean Low Water), 2,511 ha or 19% between 1 m and 2 m MLW, and 84 ha o

A case study of the effects of privatization of child welfare on services for children and families: The Nebraska experience

Privatization, or contracting with non-governmental agencies for provision of state or federally funded services, is a strategy that has gained recent attention from policymakers as a potential tool for successful child welfare reform. The Child Welfare Privatization Initiatives Project was created in 2007 as a joint effort between the United States Department of Health and Human Services and the Office of the Assistant Secretary for Planning and Evaluation. The framework identified by this project produced twelve key considerations for states moving towards a privatized system. This case study considers these twelve considerations in a description of the large-scale effort to privatize child welfare services in the state of Nebraska that began in 2008. Problems leading to a need for child welfare reform and possible factors that motivated policymakers to shift services from the public to the private sector are also described. While proponents of privatization appeared to expect rapid increased efficiency and cost-savings, this case study explores multiple reductions in quality and availability of services for children and families served by the child welfare system that occurred during the effort. Further, the cost of child welfare services in Nebraska increased by 27% and the private agencies invested over $21 million of their own funds as they attempted to uphold contracts. Recommendations for practitioners and policymakers considering participating in efforts to privatize child welfare services in the future are made based on Nebraska’s recent experience