Using the finite element method as a numerical approximation in solving for eigenvalues of the hyperbolic Laplacian, this research investigates the estimates of the first two eigenvalues with Dirichlet and Neumann boundary conditions on bounded domains in the upper half plane. Examples of finite element code using Matlab are presented to illustrate how to obtain these approximations for hyperbolic polygons. These values can further be used to shed light on the Selberg and Fundamental Gap conjectures.

In the past, Personality Psychologists have commonly applied clustering techniques on questionnaire data to analyze personality structure. The purpose of this research is to determine if techniques from topological data analysis can provide a greater understanding of personality. Specifically, persistent homology was used to determine clusters topologically and analyze the ‘shape’ of the data. Previous work we have done focused on seeing how persistent homology can provide insight on identifying the key (most persistent) clusters in the data. New analysis looks to see how the Big 5 Personality Factors cluster together as a function of age.

An algebraic curve is a one-dimensional set defined by polynomial equations, such as a parabola in the plane (given by y-x^2=0) or the z-axis in the space (given by x=y=0). Let Y be an algebraic curve. Then a multiplicity structure on Y is another curve Z, which as a set has the same points as Y but with a higher and fixed multiplicity at each point. For example, the y-axis in the plane is given by the equation x=0 and if we intersect it with horizontal lines, say with y-b=0, we get the points (0,b) on the y-axis. Now if we take the line given by x^2=0 and intersect it with the horizontal lines as above we get the points (0,b) with multiplicity 2. Hence we call the later curve a double structure on the previous one. Similarly the equation x^3=0 gives a triple structure on the y-axis in the plane and so on. Structures like these might sound naive but they are crucial to understand the behaviors of families of curves. For example, the family of parabolas ty-x^2=0 deforms into the double line x^2=0 as t approaches 0. Although the notion of multiplicity is pretty geometric, we can use tools from abstract algebra to make it rigorous. This makes the subject challenging and yet very interesting at the same time. Classifying the multiplicity structures on a curve is still a wide open field in algebraic geometry. It is now well understood how the double and triple structures on a line look. A natural question then arises how do the double and triple structures look on conics? It turns out that the answers are much more complicated than for lines. In this poster I am going to show some of my research in that direction.

An algebraic integer is a complex number that is a root of a polynomial with integer coefficients and a leading coefficient of 1. This includes numbers like the square root of 2 and the cube root of 10, for example. A field is a set in which we can add, subtract, multiply, and divide (among other details). Consider the set of all algebraic integers in any given field containing the rational numbers. The index of an algebraic integer in this set is a natural number that measures how close the algebraic integer is to generating the set. For instance, the imaginary number i (the square root of -1) is an algebraic integer which generates the set of all complex numbers of the form a + bi where a and b are integers, and so has index 1. The closer the index is to 1, the closer the algebraic integer is to generating the set. We investigate these indices in cubic fields, determining not only which numbers occur as indices in given families, but also that the minimal index is unbounded as one traverses the set of all cubic fields in those families.

Background: To replace milk fats and eggs commonly found in ice cream, vegan varieties substitute with vegetable fats and/or pureed fruits. Vegan ingredient substitutions for ice cream must contain similar structural components to milk fat to preserve the expected texture/mouthfeel of the product. The purposes of this study were 1) to measure university students’ preferences and sensory ratings of vegan ice cream substitutions and 2) to identify which ingredients act as the best replacements.

Methods: 54 students enrolled in one of two TCU Nutritional Sciences (NTDT) courses participated in this single-blind, cross-sectional study. Subjects completed sensory evaluation of three homemade vegan ice creams containing different structural/flavor components. Sample A included coffee, cashews, and coconut cream; B used coconut cream and dates, and C contained coconut milk. Evaluations took place on two separate occasions in the NTDT Laboratory Kitchens. Flavor, sweetness, texture, mouthfeel, eye appeal, color, and overall rating of vegan ingredient substitutions for ice cream recipes were assessed. Sensory criteria responses were analyzed using SPSS XIX. Frequency distributions, ANOVAs, correlations, and descriptive statistics were determined to meet study objectives (p≤0.05). Protocol was approved by the TCU IRB.

Results: 53% of participants preferred the flavor of sample A, 42% of participants reported that sample B was the preferred flavor, and sample C received the lowest overall acceptability rating, with 73% of the participants disliking the flavor. More than 50% of participants stated sample A was most similar to traditionally-prepared non-vegan ice cream, and 78% of participants stated that they would consume these ice creams outside of the study.

Conclusions: Acceptable vegan ice cream fat substitutes are available. Cashew, coconut cream, dates, and coffee contributed to the rich flavors, creamy textures, and overall desirable sensory qualities in samples A and B. Coconut milk, utilized in sample C, contributed to an undesirable and unacceptable crystallized texture.

Background: Research indicates individuals who follow plant-based diets make healthier food choices and have less chronic disease than those consuming the Standard American Diet. It is hypothesized that Texas Christian University (TCU) students have limited knowledge and/or exposure to vegan/plant-based lifestyles and diets. The purpose of this study was to determine whether knowledge level and attitudes/beliefs of vegan/plant-based diets/lifestyle changed with exposure and newly-gained knowledge in a semester-long three-hour course.

Methods: Subjects included 23 junior/senior multidisciplinary TCU students (56%/female; 44%/male) enrolled in a course about plant-based diets and lifestyles. Students completed a pre-assessment questionnaire on the first day of class before exposure to any content regarding vegan/plant-based diets and lifestyles. Students completed a post-assessment questionnaire at semester end to ascertain if changes in attitudes/knowledge/beliefs regarding vegan/plant-based diets and lifestyles changed over time with exposure and newly-gained subject knowledge in the course. Data was analyzed using SPSS (p<0.05).

Results: Prior to starting the course, 13% of students reported they were vegetarians, and 83% typically consumed animal protein in their diets (p=0.01); more students in health-related disciplines noted having friends/family members who followed vegan diets (p=0.01). Pre-assessment results showed that female students were more knowledgeable than male students about plant-based diets/veganism (p=0.01); whereas, post-assessment knowledge scores showed no differences among gender. Overall, post-assessment scores improved for all students in the following categories: reasons why people choose veganism, acceptable foods for vegans, nutrients at risk for vegans, availability of vegan ready-to-eat foods/grocery store and restaurant meals, and risk for chronic disease of vegans vs. people who consume animal products (p=0.01).

Conclusions: Students majoring in the sciences and nursing/health sciences possessed greater knowledge about vegan/plant-based diets/lifestyles than their counterparts majoring in other subjects. Although level of prior knowledge varied among all students, exposure to the topic through a vegan/plant-based studies course increased knowledge of participants.

Background:
Peanut butter is an all-American staple in nine out of 10 households. It’s estimated that each U.S. youth consumes an average of 1,500 peanut butter sandwiches by the time he/she graduates from high school. Although, the popularity of peanut butter alternatives such as tree nuts/seed butters has grown in recent years due to their rich source of nutrients, peanut butter continues to be the “nut butter” of choice for most people. This may be due to lack of knowledge about the health benefits of different nut/seed butters and/or lack of exposure to these products.

Methods:
The purpose of this study was to examine if taste-testing and increased awareness about the health benefits of tree nut/seed butters would influence their consumption among university students. 52 students enrolled in a multi-disciplinary introductory nutrition course participated in this single-blind, cross-sectional study. Participants completed a pre-study questionnaire identifying key nutritional benefits of peanut and alternative tree nuts/seeds butters and typical consumption of each. Following education about the nutrient content of peanuts compared to cashews, almonds, and sunflower seeds, participants taste-tested and evaluated a sample butter of each and completed a post-study questionnaire. Study procedures were approved by university IRB, and participants responses and sensory rankings were analyzed to meet study objectives (SPSS; p<0.05).

Results:
Significant improvement in pre and post-study knowledge of nutrient content in nut/seed butters was noted (p=0.01). Sensory evaluation showed that preferences for peanut butter were highest among participants, followed by almond butter and cashew butter. Sunflower seed butter was least preferred (p=0.01). Taste, color, and texture/mouthfeel sensory rankings correlated with overall acceptability for each sample (p=0.05). Following sensory evaluation, preferences for consuming almond butter increased by 38% compared to pre-tasting responses (p=0.01).

Conclusions:
Education and sensory evaluation are both important strategies for enhancing awareness of health benefits and acceptability of peanut butter alternatives.

Background: Among the many benefits associated with the consumption of probiotics, modulation of the immune system has recently received the most attention. Previously, researchers and scientists thought that the use of probiotics only improved the gastrointestinal tract, thereby aiding digestion. However, there is now evidence to support that intake of probiotics is effective in the prevention and/or management of many gastrointestinal diseases plus modulating immune functions in a person with normal immunological status and microbiota.
Methods: An online survey regarding knowledge of foods containing probiotics, consumption of these foods, frequency of probiotic supplementation, and recent illness was developed to determine the relationship between probiotic intake and immune health among college students. Researchers recruited Texas Christian University students through e-mail and social media. Once the target number of participants (>150) responded to the survey, data was analyzed using SPSS.
Results: Upon surveying participants (N=157), 58% (n=91) of respondents reported that they did not take a probiotic supplement, while 19.8% (n=31) reported taking a supplement every day or ≥3-4 times/week. There was a strong correlation between those who reported frequent probiotic supplementation and lower incidence of strep throat (p<0.01), lower incidence of nausea and vomiting (p<0.01), and lower incidence of constipation (p<0.05). There was also a correlation between the consumption of certain foods containing probiotics, yogurt specifically, and illness frequency, notably, lower incidence of fever (p<0.01) and cold (p<0.05).
Conclusions: There is a significant correlation between the consumption of probiotic supplements and positive effects with certain illnesses, but some foods containing probiotics show opposite or negligible results. For more conclusive results, further research should be conducted with controlled variables to determine the relationship between illness and intake of probiotic supplements versus probiotic-containing foods.

Background: Research indicates Millennials are more concerned about having healthy eating habits than following fad diets, and they exercise more than their Baby Boomer counterparts. The purposes of this study were 1) to determine reasons university students follow fad diets, and 2) to determine other methods students utilize for weight management.
Methods: In this un-blinded, randomized trial approved by TCU IRB, participants completed an online research questionnaire after providing informed consent. Population included 236 TCU male and female students, 18-22 years old. Analyses assessed students’ history of fad dieting and outcomes, perceived health status based on body weight and image, eating and exercise habits, and incidence of lifestyle practices such as smoking and alcohol use. Data was analyzed using SPSS (p<0.05). Frequency distributions and correlations were analyzed for trends in health maintenance behaviors.
Results: Participants self-identified as 76% females, 85% white, 6% Hispanic, and 4% other ethnicity. Only 32% of participants had followed a fad diet (p=0.01). Participants who followed fad diets included 30% Paleolithic®, 23% Gluten-Free®, 20% Weight Watchers®, and 14% Atkins®. Of those who followed the respective diets, 58% did not achieve desired results and reported feeling tired, had no change in health status, experienced temporary weight loss, and always felt hungry, and 56% of participants answered “no” when asked if fad diets work. Of those who followed a fad diet, 40% would not follow one again. Results also show a strong relationship between females and healthy eating habits, pressure to be a certain weight, and perceiving themselves to be a normal weight (p=0.01). Finally, weight loss behavior results show that 97% of participants exercise, while only 57% consciously eat less, and 55% count calories (p=0.01).
Conclusions: University students who followed fad diets experienced temporary or adverse results. Exercise was preferred rather than dieting to maintain weight.

Background: Up to 40% of food produced in America is wasted each year. Meanwhile over 42 million Americans are food insecure. The purposes of this study were to 1) identify contributing factors to local restaurant food waste, 2) describe barriers to restaurant food donations, and 3) describe barriers to donation acceptance by shelter employees.
Methods: Two electronic surveys were distributed to either local restaurant managers/owners or to employees involved in food donation acceptance in local shelters/kitchens following phone calls and/or personal visits by researchers to facilities. Data were coded into and analyzed using SPSS.
Results: There was a 17% (N=12/72) and 100% (N=14/14) response rate for restaurants and shelters requested to participate, respectively. While only 16% (N=2) of restaurant survey respondents (RSR) were concerned about food waste in their establishments, all RSR (N=12) agreed that reducing food waste in their facilities was important. Over 83% (N=10) reported having successful food waste prevention measures in their restaurants. There was a positive correlation with report of presence of prevention measures and knowledge of the Good Samaritan Act (r=.67, p<0.05). Approximately 42% (N=5) of RSR reported they would be interested in connecting with local shelters to donate food and also agreed that liability is a barrier to safe food donations.  Among shelter respondents, 81% (N=9) agreed that their facilities would benefit from excess restaurant food donations.
Conclusion: Although all RSR agreed that food waste prevention measures were important, the majority were not concerned about food waste in their facilities. Due to the overall poor response rates among restaurant owners/managers, the RSR in this survey may represent a segment that were more interested in food waste and more likely to respond to the survey.  The majority of respondents of both surveys agreed that partnering with restaurants and shelters for safe excess food donation was desirable.
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Funding Source: None