Explorations in Elementary and Analytic Number Theory

In this dissertation, we investigate two distinct questions in number theory. Each question is dedicated its own chapter. First, we consider arithmetic progressions in the polygonal numbers with a fixed number of sides. We will show that four-term arithmetic progressions cannot exist. We then describe explicitly how to find all three-term arithmetic progressions. Additionally we show that there are infinitely many three-term arithmetic progressions starting with an arbitrary polygonal number. Second, we will show certain irreducibility criteria for polynomials. Let f(x) be a polynomial with non-negative integer coefficients such that f(b) is prime for some integer 2 ≤ b ≤ 20. A. Cohn\u27s criteria states that if b=10 and each coefficient is ≤ 9, then f(x) is irreducible. In 1988, M. Filaseta showed that the bound 9 can be replaced by 1030. We will look at work that was done to further increase this bound and then generalize this for an arbitrary base b. Along the way, we will also establish additional irreducibility criteria

Trip Characteristics of Casino and Racino Visitors In A Midwestern State

Gaming is a revenue driver for many areas and can be an economic boost for businesses and tourism entities around gaming venues. This study seeks to provide a comprehensive overview of the characteristics profile and expenditures of casino and racino visitors in a Midwestern state as a valuable resource that could be used by those in tourism planning to better determine who is coming into their state for gaming purposes and how they might better attract and accommodate them. Suggestions will be made based on the findings to aid in determining effective marketing methods to attract visitors, as well as facility or program enhancements to increase visitor expenditures

Commentary: A new model for chronic care to improve patient\u27s skill

More effective treatment and increased survival from acute cardiometabolic conditions, such as heart attack and stroke, and an aging population has resulted in more people living with chronic conditions, such as coronary artery disease, heart failure, hypertension, high cholesterol, diabetes, and obesity1. With increased incentives to focus on the long-term outcomes of patients, we believe that there is an even greater need for more effective models for chronic care, both in research and in clinical practice2

Commentary: A new model for chronic care to improve patient\u27s skill

More effective treatment and increased survival from acute cardiometabolic conditions, such as heart attack and stroke, and an aging population has resulted in more people living with chronic conditions, such as coronary artery disease, heart failure, hypertension, high cholesterol, diabetes, and obesity1. With increased incentives to focus on the long-term outcomes of patients, we believe that there is an even greater need for more effective models for chronic care, both in research and in clinical practice2

Current Perspective on the Location and Function of Gamma- Aminobutyric Acid (GABA) and its Metabolic Partners in the Kidney.

Gamma-aminobutyric acid (GABA) is an inhibitory neurotransmitter located in the mammalian central nervous system, which binds to GABAA and GABAB receptors to mediate its neurological effects. In addition to its role in the CNS, an increasing number of publications have suggested that GABA might also play a role in the regulation of renal function. All three enzymes associated with GABA metabolism; glutamic acid decarboxylase, GABA ?-oxoglutarate transaminase (GABA-T) and succinic semialdehyde dehydrogenase (SSADH) have been localised to the kidney providing the necessary machinery for localised GABA synthesis and metabolism. Moreover GABA receptors have been localised to both tubular and vascular structures in the kidney, and GABA is excreted in urine (~3 ?M) in humans. Despite the collective evidence describing the presence of a GABA system in the kidney, the precise function of such a system requires further clarification. Here we provide an overview of the current renal GABA literature and provide novel data that indicates GABA can act at contractile pericyte cells located along vasa recta capillaries in the renal medulla to potentially regulate medullary blood flow

Playing the Game of Health: Best Practices for Health Optimization Program in a Worksite Setting, with Case Study of a Real World Example

While there have been multiple efforts to improve the health of the population, and simultaneously reducing the cost of healthcare and improving the quality of care, there is no single model for improving population health. Worksite health is a microcosm of the health of the nation and the results of been mixed. This paper considers the best practices associated with key worksite health. These best practices include the type of worksite intervention, attention to health literacy, engagement, onsite clinics, coaching and care plans, a digital platform, social support, population health, performance excellence, performance improvement, and an evaluation strategy. While each best practice is considered important, very few programs provide all of the components, and most emphasize one component over the other. A gap in the literature, therefore, is how these best practices can be combined into a single program. Following the review of literature of best practices, a case study, of the program design, of a comprehensive worksite program was conducted to demonstrate how these best practices are operationalized. The Game of Health, is a cognitive based program that focuses on stress management and behavior change in a program that provides onsite programs, a medical clinic, and a digital platform

Playing the game of health: Best practices for health optimization in a worksite setting with a case study of a real world example

While there have been multiple efforts to improve the health of the population, and simultaneously reducing the cost of healthcare and improving the quality of care, there is no single model for improving population health. Worksite health is a microcosm of the health of the nation and the results of been mixed. This paper considers the best practices associated with key worksite health. These best practices include the type of worksite intervention, attention to health literacy, engagement, onsite clinics, coaching and care plans, a digital platform, social support, population health, performance excellence, performance improvement, and an evaluation strategy. While each best practice is considered important, very few programs provide all of the components, and most emphasize one component over the other. A gap in the literature, therefore, is how these best practices can be combined into a single program. Following the review of literature of best practices, a case study, of the program design, of a comprehensive worksite program was conducted to demonstrate how these best practices are operationalized. The Game of Health, is a cognitive based program that focuses on stress management and behavior change in a program that provides onsite programs, a medical clinic, and a digital platform

Playing the game of health: Best practices for health optimization in a worksite setting with a case study of a real world example

While there have been multiple efforts to improve the health of the population, and simultaneously reducing the cost of healthcare and improving the quality of care, there is no single model for improving population health. Worksite health is a microcosm of the health of the nation and the results of been mixed. This paper considers the best practices associated with key worksite health. These best practices include the type of worksite intervention, attention to health literacy, engagement, onsite clinics, coaching and care plans, a digital platform, social support, population health, performance excellence, performance improvement, and an evaluation strategy. While each best practice is considered important, very few programs provide all of the components, and most emphasize one component over the other. A gap in the literature, therefore, is how these best practices can be combined into a single program. Following the review of literature of best practices, a case study, of the program design, of a comprehensive worksite program was conducted to demonstrate how these best practices are operationalized. The Game of Health, is a cognitive based program that focuses on stress management and behavior change in a program that provides onsite programs, a medical clinic, and a digital platform

Isoprenoids determine Th1/Th2 fate in pathogenic T cells, providing a mechanism of modulation of autoimmunity by atorvastatin.

3-hydroxy-3-methylglutaryl-coenzyme A (HMG-CoA) reductase is a critical enzyme in the mevalonate pathway that regulates the biosynthesis of cholesterol as well as isoprenoids that mediate the membrane association of certain GTPases. Blockade of this enzyme by atorvastatin (AT) inhibits the destructive proinflammatory T helper cell (Th)1 response during experimental autoimmune encephalomyelitis and may be beneficial in the treatment of multiple sclerosis and other Th1-mediated autoimmune diseases. Here we present evidence linking specific isoprenoid intermediates of the mevalonate pathway to signaling pathways that regulate T cell autoimmunity. We demonstrate that the isoprenoid geranylgeranyl-pyrophosphate (GGPP) mediates proliferation, whereas both GGPP and its precursor, farnesyl-PP, regulate the Th1 differentiation of myelin-reactive T cells. Depletion of these isoprenoid intermediates in vivo via oral AT administration hindered these T cell responses by decreasing geranylgeranylated RhoA and farnesylated Ras at the plasma membrane. This was associated with reduced extracellular signal-regulated kinase (ERK) and p38 phosphorylation and DNA binding of their cotarget c-fos in response to T cell receptor activation. Inhibition of ERK and p38 mimicked the effects of AT and induced a Th2 cytokine shift. Thus, by connecting isoprenoid availability to regulation of Th1/Th2 fate, we have elucidated a mechanism by which AT may suppress Th1-mediated central nervous system autoimmune disease