An Exact Universal Gravitational Lensing Equation

We first define what we mean by gravitational lensing equations in a general space-time. A set of exact relations are then derived that can be used as the gravitational lens equations in all physical situations. The caveat is that into these equations there must be inserted a function, a two-parameter family of solutions to the eikonal equation, not easily obtained, that codes all the relevant (conformal) space-time information for this lens equation construction. Knowledge of this two-parameter family of solutions replaces knowledge of the solutions to the geodesic equations. The formalism is then applied to the Schwarzschild lensing problemComment: 12 pages, submitted to Phys. Rev.

Cost-effective targeting of conservation investments to reduce the northern Gulf of Mexico hypoxic zone

A seasonally occurring summer hypoxic (low oxygen) zone in the northern Gulf of Mexico is the second largest in the world. Reductions in nutrients from agricultural cropland in its watershed are needed to reduce the hypoxic zone size to the national policy goal of 5,000 km2 (as a 5-y running average) set by the national Gulf of Mexico Task Force’s Action Plan. We develop an integrated assessment model linking the water quality effects of cropland conservation investment decisions on the more than 550 agricultural subwatersheds that deliver nutrients into the Gulf with a hypoxic zone model. We use this integrated assessment model to identify the most cost-effective subwatersheds to target for cropland conservation investments. We consider targeting of the location (which subwatersheds to treat) and the extent of conservation investment to undertake (how much cropland within a subwatershed to treat). We use process models to simulate the dynamics of the effects of cropland conservation investments on nutrient delivery to the Gulf and use an evolutionary algorithm to solve the optimization problem. Model results suggest that by targeting cropland conservation investments to the most cost-effective location and extent of coverage, the Action Plan goal of 5,000 km2 can be achieved at a cost of $2.7 billion annually. A large set of cost-hypoxia tradeoffs is developed, ranging from the baseline to the nontargeted adoption of the most aggressive cropland conservation investments in all subwatersheds (estimated to reduce the hypoxic zone to less than 3,000 km2 at a cost of$5.6 billion annually)

Least-cost Control of Agricultural Nutrient Contributions to the Gulf of Mexico Hypoxic Zone

In 2008, the hypoxic zone in the Gulf of Mexico, measuring 20 720 km2, was one of the two largest reported since measurement of the zone began in 1985. The extent of the hypoxic zone is related to nitrogen and phosphorous loadings originating on agricultural fields in the upper Midwest. This study combines the tools of evolutionary computation with a water quality model and cost data to develop a trade-off frontier for the Upper Mississippi River Basin specifying the least cost of achieving nutrient reductions and the location of the agricultural conservation practices needed. The frontier allows policymakers and stakeholders to explicitly see the trade-offs between cost and nutrient reductions. For example, the cost of reducing annual nitrate-N loadings by 30% is estimated to be US$1.4 billion/year, with a concomitant 36$370 million/year, with a concomitant 9% reduction in nitrate-N

LUMINATE: linking agricultural land use, local water quality and Gulf of Mexico hypoxia

In this paper, we discuss the importance of developing integrated assessment models to support the design and implementation of policies to address water quality problems associated with agricultural pollution. We describe a new modelling system, LUMINATE, which links land use decisions made at the field scale in the Upper Mississippi, Ohio and Tennessee Basins through both environmental and hydrological components to downstream water quality effects and hypoxia in the Gulf of Mexico. This modelling system can be used to analyse detailed policy scenarios identifying the costs of the policies and their resulting benefits for improved local and regional water quality. We demonstrate the model\u27s capabilities with a simple scenario where cover crops are incentivised with green payments over a large expanse of the watershed

Identifying amyloid pathology–related cerebrospinal fluid biomarkers for Alzheimer\u27s disease in a multicohort study

Introduction: The dynamic range of cerebrospinal fluid (CSF) amyloid β (Aβ1–42) measurement does not parallel to cognitive changes in Alzheimer\u27s disease (AD) and cognitively normal (CN) subjects across different studies. Therefore, identifying novel proteins to characterize symptomatic AD samples is important. Methods: Proteins were profiled using a multianalyte platform by Rules Based Medicine (MAP-RBM). Due to underlying heterogeneity and unbalanced sample size, we combined subjects (344 AD and 325 CN) from three cohorts: Alzheimer\u27s Disease Neuroimaging Initiative, Penn Center for Neurodegenerative Disease Research of the University of Pennsylvania, and Knight Alzheimer\u27s Disease Research Center at Washington University in St. Louis. We focused on samples whose cognitive and amyloid status was consistent. We performed linear regression (accounted for age, gender, number of apolipoprotein E (APOE) e4 alleles, and cohort variable) to identify amyloid-related proteins for symptomatic AD subjects in this largest ever CSF–based MAP-RBM study. ANOVA and Tukey\u27s test were used to evaluate if these proteins were related to cognitive impairment changes as measured by mini-mental state examination (MMSE). Results: Seven proteins were significantly associated with Aβ1–42 levels in the combined cohort (false discovery rate adjusted P \u3c .05), of which lipoprotein a (Lp(a)), prolactin (PRL), resistin, and vascular endothelial growth factor (VEGF) have consistent direction of associations across every individual cohort. VEGF was strongly associated with MMSE scores, followed by pancreatic polypeptide and immunoglobulin A (IgA), suggesting they may be related to staging of AD. Discussion: Lp(a), PRL, IgA, and tissue factor/thromboplastin have never been reported for AD diagnosis in previous individual CSF–based MAP-RBM studies. Although some of our reported analytes are related to AD pathophysiology, other\u27s roles in symptomatic AD samples worth further explorations