A Graph Theoretic Approach To Food Combination Problems

Graph theory provides a useful representation of, and mathematical toolkit for, analyzing how things are connected together. This collection of research investigates the use of graph theory as a representation of how foods are connected together. The first two studies validate the subject questioning procedure used to create a graph model out of responses and the final study introduces a new approach to using this methodology to optimize field ration menus for the United States Army. In the first study, we began by asking subjects whether or not pairs of ingredients would be appropriate to combine on a salad. Next, using graph theoretic methods, we predicted which combinations of 3-8 components should go together. Subjects were then asked whether or not particular combinations were appropriate to combine on a salad. A paired Wilcoxon test between the predicted and non-predicted combinations was significant for all combination sizes. The second study tested the principle of supercombinatorality, i.e. that food combinations (of more than two items) that are fully compatible on a pairwise basis are more compatible than combinations that are not fully compatible pairwise. This study extended the previous findings to group data. Purchase intent responses to pairs of different pizza toppings were collected and used to predict pizzas (with one to 6 toppings) that would appeal to the entire group. Results showed purchase interest to be higher for the predicted pizzas than for non pre- dicted pizzas supporting the supercombinatorality principle. The final study extends the graph theory representation to military rations known as Meal-Ready-to-Eat or MREs. MRE menus are composed of 11 different food categories (entr´ e, side, snack, etc.) and there are multiple items e available in each category. From these items there are over 22 billion potential menus. Categories and items were screened to create a list of the most important ones and we asked soldiers whether or not pairwise combinations of components were appropriate to combine in a meal. Using graph theoretic tools, predictions were made of optimal MRE menus and rankings were attached to prediction in order to assist the product developers in screening old and new menu concepts

Perennial Filter Strips Reduce Nitrate Levels in Soil and Shallow Groundwater after Grassland-to-Cropland Conversion

Many croplands planted to perennial grasses under the Conservation Reserve Program are being returned to crop production, and with potential consequences for water quality. The objective of this study was to quantify the impact of grassland-to-cropland conversion on nitrate-nitrogen (NO3–N) concentrations in soil and shallow groundwater and to assess the potential for perennial filter strips (PFS) to mitigate increases in NO3–N levels. The study, conducted at the Neal Smith National Wildlife Refuge (NSNWR) in central Iowa, consisted of a balanced incomplete block design with 12 watersheds and four watershed-scale treatments having different proportions and topographic positions of PFS planted in native prairie grasses: 100% rowcrop, 10% PFS (toeslope position), 10% PFS (distributed on toe and as contour strips), and 20% PFS (distributed on toe and as contour strips). All treatments were established in fall 2006 on watersheds that were under bromegrass (Bromus L.) cover for at least 10 yr. Nonperennial areas were maintained under a no-till 2-yr corn (Zea mays L.)–soybean [Glycine max (L.) Merr.] rotation since spring 2007. Suction lysimeter and shallow groundwater wells located at upslope and toeslope positions were sampled monthly during the growing season to determine NO3–N concentration from 2005 to 2008. The results indicated significant increases in NO3–N concentration in soil and groundwater following grassland-to-cropland conversion. Nitrate-nitrogen levels in the vadose zone and groundwater under PFS were lower compared with 100% cropland, with the most significant differences occurring at the toeslope position. During the years following conversion, PFS mitigated increases in subsurface nitrate, but long-term monitoring is needed to observe and understand the full response to land-use conversion

The Impact of Unauthorized and Fake Social Medial Profiles on the Financial Performance of Top US-Based and International Companies

Facebook, Twitter, Google+, and Instagram are all popular social media networking sites. Companies use these sites to communicate with existing and potential customers to increase brand awareness and positively impact their image. So when unauthorized pages for companies are created, “these pages can make it difficult for consumers to find the official brand page, damage the brands, and even create liability for the brand owner.” (PR Newswire, 2011). Despite the knowledge that these fake pages can harm companies, no research was found that measures the actual financial impact of these fake sites on companies. This exploratory study is a step towards measuring that impact. The study uses four independent binary variables: US-based (1) versus international (0), airline industry (1) versus other (0), whether there was a hoax (1) or not (0), and if the hoax was on a major social media site, such as Facebook and Twitter (1) versus minor social media site, such as Instagram and Google+ (0) with major versus minor defined by the number of active users. The dependent variable tested will be the financial performance of the company for the prior year compared to the current year as normalized by the S&P performance and measured if the performance is higher or the same than the previous year (0) or lower (1). The expected outcome is that while the impact may not be large, there should be a measurable decline in financial performance

Chapter 15 - Projective Mapping and Sorting Tasks

International audienceProjective mapping and sorting tasks—often called “Holistic” Methods—are methods that directly obtain similarity measurements between products by asking participants (who could be novices, trained assessors, or experts, adults or children) to provide a global evaluation of a set of products of interest. In projective mapping, each participant is asked to place products on a sheet of paper in such a way that the positions of the products express the products’ similarity structure. In the sorting task, each participant is asked to sort the products in groups such that similar products are sorted together. For both projective mapping and sorting—in order to derive a better understanding of the similarity structure between the products—participants are also sometimes asked to verbally describe products or groups of products. The statistical analysis of projective mapping and sorting tasks used well know techniques such as: (multiple and simple) correspondence analysis, multiple factor analysis, principal component analysis, multidimensional scaling, and DISTATIS

Seeing a Meal is Not Eating It: Hedonic Context Effects Differ for Visually Presented and Actually Eaten Foods

A meal usually consists of several different foods presented together. This study investigates how side dishes (vegetables/starches) affect the hedonic ratings of the main food item (meat/meat substitute) when a plate of these foods is viewed and also after the meal is eaten. The main question is whether the hedonic rating of the main food item assimilates toward the hedonic rating of the side dishes or shows contrast, moving away from the hedonic rating of the side dishes. In Experiment 1, when subjects only viewed a picture of a meal consisting of an imitation chicken tender (main food item) with either hedonically positive or hedonically negative side dishes, no effect of the side dishes was seen on the hedonic rating of the main food item. In Experiment 2, when subjects ate the meal shown in the picture in Experiment 1, hedonic contrast was found. That is, the main food item was rated as less good when simultaneously presented with more hedonically positive side dishes than when presented with hedonically negative side dishes. Thus, when a meal is eaten, foods influence the evaluation of other foods on the same plate. The same is not true when foods are presented in a picture