Angle Bisectors of a Triangle in Lorentzian Plane

In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to study attributes of triangles. Using the new definition, this paper investigates the existence of the incenter and the isogonal conjugate of a triangle in Lorentzian plane.Comment: 15 pages, 7 figure

Perturbation and scaled Cook's distance

Cook's distance [Technometrics 19 (1977) 15-18] is one of the most important diagnostic tools for detecting influential individual or subsets of observations in linear regression for cross-sectional data. However, for many complex data structures (e.g., longitudinal data), no rigorous approach has been developed to address a fundamental issue: deleting subsets with different numbers of observations introduces different degrees of perturbation to the current model fitted to the data, and the magnitude of Cook's distance is associated with the degree of the perturbation. The aim of this paper is to address this issue in general parametric models with complex data structures. We propose a new quantity for measuring the degree of the perturbation introduced by deleting a subset. We use stochastic ordering to quantify the stochastic relationship between the degree of the perturbation and the magnitude of Cook's distance. We develop several scaled Cook's distances to resolve the comparison of Cook's distance for different subset deletions. Theoretical and numerical examples are examined to highlight the broad spectrum of applications of these scaled Cook's distances in a formal influence analysis.Comment: Published in at http://dx.doi.org/10.1214/12-AOS978 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Doctor of Philosophy

dissertationMelanoma is the most deadly skin malignancy and one of the most rapidly increasing cancers. Like other cancers, melanoma is known to exploit specific signaling pathways for growth and disease progression. The AKT pathway is aberrantly activated in upwards of 70% of melanomas and several lines of clinical evidence suggest that increased AKT signaling plays a role in melanomagenesis. However, in vivo experimental data directly testing the role of aberrant AKT activation in melanoma has been lacking. This dissertation addresses the role of aberrant AKT signaling in melanoma by expressing AKT isoforms and mutant protein in an established non-metastatic mouse model of melanoma. We report that expression of activated AKT1 in the context of BRAFV600E; INK4A/ARFNull melanomas result in highly metastatic disease with lung and brain metastasis. Interestingly, loss of Pten in this same context does not yield significant metastasis but in combination with activated AKT1 results in a significant increase in brain metastasis compared to AKT1 expressing melanomas with wild-type PTEN. Upregulation of mTOR pathway components is observed in AKT1 expressing melanomas compared to PTEN silenced counterparts. Expression of activated AKT3 in the context of BRAFV600E; INK4A/ARFNull melanomas results in significant metastatic disease to the brain while activated AKT2 expression in this same context does not result in observable brain lesions. Lastly, we investigated the role of AKT3E17K in iv melanoma growth and metastasis. We report no observable brain metastases and instead found that in vivo expression of AKT3E17K in BRAFV600E; INK4A/ARFNull melanomas yields highly aggressive lung lesions. In summary, this dissertation furthers our knowledge of melanoma by providing experimental evidence for the role of aberrant AKT signaling in melanoma metastasis to the lungs and brain. Mechanistically, our data reveal that PTEN silencing and AKT1 activation differs in terms of promoting melanoma metastasis, that preferential organspecific metastasis appears to be mediated through specific AKT isoforms, and that the melanoma relevant mutant protein, AKT3E17K, may play a role in promoting lung metastasis. These findings advance our knowledge of melanoma and provide valuable insights for the clinical management of this disease

Users Attitudes Toward Movie-Related Websites And E-Satisfaction

Numerous websites provide information, sell products, and offer services. However, not many websites have focused on usability issues, such as ease of use, usefulness, and customer satisfaction. Therefore, in this paper, the authors first consider what factors affect ease of use and usefulness and then how ease of use and usefulness affect attitudes toward websites and customer satisfaction. This study classified four different user groups based on their degree of involvement to measure different levels of perceived ease of use and usefulness. Uses and gratification theory (Herzog 1944; McGuire 1974; Luo 2002) has been applied in this study to explain users’ attitudes toward movie-related web sites and consumer satisfaction. This study found that online users’ positive attitudes towards movie-related websites impact their satisfaction, while their positive attitudes do not significantly lead to the actual purchase of tickets online. The findings of the study contribute to the development of the uses and gratification theory by applying it to the online users’ attitudes toward movie-related sites. Further, this study provides implications and offers suggestions to e-businesses dealing with movie-related products and services

Assessing Country-Of-Origin Effects: The Impact Of An International Event

This study is to investigate how consumers’ attitudes toward brands/products manufactured by a country are affected by an international event. Authors explored that consumers’ attitudes toward brand “made in ___” are affected by various constructs, such as prior beliefs about the products’ attributes, the country’s image along with the brand name, and attitudes toward the advertising during an international event