Lenstra-Hurwitz Cliques In Real Quadratic Fields

Let $K$ be a number field and let \OO_K denote its ring of integers. We can define a graph whose vertices are the elements of \OO_K such that an edge exists between two algebraic integers if their difference is in the units \OO_K^{\times}. Lenstra showed that the existence of a sufficiently large clique (complete subgraph) will imply that the ring \OO_K is Euclidean with respect to the field norm. A recent generalization of this work tells us that if we draw more edges in the graph, then a sufficiently large clique will imply the weaker (but still very interesting) conclusion that $K$ has class number one. This thesis aims to understand this new result and produce further examples of cliques in rings of integers. Lenstra, Long, and Thistlethwaite analyzed cliques and gave us class number one through a prime element. We were able to extend and generalize their result to larger cliques through prime power elements while still preserving our desired property of class number one. Our generalization gave us that class number one is preserved if the number field $K$ contained a clique that is generated by a prime power

U.S. Hispanic Country-of-Origin Counts for Nation, Top 30 Metropolitan Areas

Based on 2010 census data, summarizes trends in the countries of origin of Latinos/Hispanics compared with 2000, including the fastest-growing groups and their distribution across metropolitan areas

The Software and Information Services Sector in Argentina: Pros and Cons of an Inward-Orientated Development Strategy

software information services, developing countries, Argentina

Ignorance in Congressional Voting? Evidence from Policy Reversal on the Endangered Species Act

Objective: In 1978 Congress weakened several key provisions of the Endangered Species Act (ESA), which had been enacted only five years earlier. The objective is to compare alternative explanations for this policy reversal. Methods: Probit and multinomial logit models are used to explain empirically how senators voted in both 1973 and 1978, and to investigate why many senators switched their vote from supporting ESA to weakening it. Results: The findings here indicate that party affiliation and policymaker preferences were not important to the 1973 vote, but they were key variables in the 1978 votes and the vote-switching decision. Proxies for unexpected economic impacts of ESA on individual states have little explanatory power. Conclusions: Ignorance, as measured here, does not appear to explain this policy reversal. Rather, an influx of relatively conservative Democrats between 1973 and 1978 presents itself as the leading explanation.endangered species act, congressional voting

Personalized Automatic Estimation of Self-reported Pain Intensity from Facial Expressions

Pain is a personal, subjective experience that is commonly evaluated through visual analog scales (VAS). While this is often convenient and useful, automatic pain detection systems can reduce pain score acquisition efforts in large-scale studies by estimating it directly from the participants' facial expressions. In this paper, we propose a novel two-stage learning approach for VAS estimation: first, our algorithm employs Recurrent Neural Networks (RNNs) to automatically estimate Prkachin and Solomon Pain Intensity (PSPI) levels from face images. The estimated scores are then fed into the personalized Hidden Conditional Random Fields (HCRFs), used to estimate the VAS, provided by each person. Personalization of the model is performed using a newly introduced facial expressiveness score, unique for each person. To the best of our knowledge, this is the first approach to automatically estimate VAS from face images. We show the benefits of the proposed personalized over traditional non-personalized approach on a benchmark dataset for pain analysis from face images.Comment: Computer Vision and Pattern Recognition Conference, The 1st International Workshop on Deep Affective Learning and Context Modelin