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OBJECTIVE: Hunger relief agencies have a limited capacity to monitor the nutritional quality of their food. Validated measures of food environments, such as the Healthy Eating Index-2010 (HEI-2010), are challenging to use due to their time intensity and requirement for precise nutrient information. A previous study used out-of-sample predictions to demonstrate that an alternative measure correlated well with the HEI-2010. The present study revised the Food Assortment Scoring Tool (FAST) to facilitate implementation and tested the tool's performance in a real-world food pantry setting. DESIGN: We developed a FAST measure with thirteen scored categories and thirty-one sub-categories. FAST scores were generated by sorting and weighing foods in categories, multiplying each category's weight share by a healthfulness parameter and summing the categories (range 0-100). FAST was implemented by recording all food products moved over five days. Researchers collected FAST and HEI-2010 scores for food availability and foods selected by clients, to calculate correlations. SETTING: Five food pantries in greater Minneapolis/St. Paul, Minnesota, USA. SUBJECTS: Food carts of sixty food pantry clients. RESULTS: The thirteen-category FAST correlated well with the HEI-2010 in prediction models (r = 0·68). FAST scores averaged 61·5 for food products moved, 63·8 for availability and 62·5 for client carts. As implemented in the real world, FAST demonstrated good correlation with the HEI-2010 (r = 0·66). CONCLUSIONS: The FAST is a flexible, valid tool to monitor the nutritional quality of food in pantries. Future studies are needed to test its use in monitoring improvements in food pantry nutritional quality over time.

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OBJECTIVE: To demonstrate the feasibility of applying the Healthy Eating Index-2010 (HEI-2010) to the hunger relief setting, specifically by assessing the nutritional quality of foods ordered by food shelves (front-line food provider) from food banks (warehouse of foods). DESIGN: This Healthy FOOD (Feedback On Ordering Decisions) observational study used electronic invoices detailing orders made by 269 food shelves in 2013 and analysed in 2015 from two large Minnesota, USA food banks to generate HEI-2010 scores. Initial development and processing procedures are described. RESULTS: The average total HEI-2010 score for the 269 food shelves was 62·7 out of 100 with a range from 28 to 82. Mean component scores for total protein foods, total vegetables, fatty acids, and seafood and plant proteins were the highest. Mean component score for whole grains was the lowest followed by dairy, total fruits, refined grains and sodium. Food shelves located in micropolitan areas and the largest food shelves had the highest HEI-2010 scores. Town/rural and smaller food shelves had the lowest scores. Monthly and seasonal differences in scores were detected. Limitations to this approach are identified. CONCLUSIONS: Calculating HEI-2010 for food shelves using electronic invoice data is novel and feasible, albeit with limitations. HEI-2010 scores for 2013 identify room for improvement in nearly all food shelves, especially the smallest agencies. The utility of providing HEI-2010 scores to decision makers in the hunger relief setting is an issue requiring urgent study.

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We construct solutions of the paraxial and Helmholtz equations that are polynomials in their spatial variables. These are derived explicitly by using the angular spectrum method and generating functions. Paraxial polynomials have the form of homogeneous Hermite and Laguerre polynomials in Cartesian and cylindrical coordinates, respectively, analogous to heat polynomials for the diffusion equation. Nonparaxial polynomials are found by substituting monomials in the propagation variable z with reverse Bessel polynomials. These explicit analytic forms give insight into the mathematical structure of paraxially and nonparaxially propagating beams, especially in regard to the divergence of nonparaxial analogs to familiar paraxial beams.