Coloring vertices of a graph or finding a Meyniel obstruction

A Meyniel obstruction is an odd cycle with at least five vertices and at most one chord. A graph is Meyniel if and only if it has no Meyniel obstruction as an induced subgraph. Here we give a O(n^2) algorithm that, for any graph, finds either a clique and coloring of the same size or a Meyniel obstruction. We also give a O(n^3) algorithm that, for any graph, finds either aneasily recognizable strong stable set or a Meyniel obstruction

Micronesia in Modern Geopolitics

After the Second World War, the United States established full strategic control over the South Pacific region of Micronesia. Under a United Nations agreement, America held Micronesia as a “Strategic Trust Territory” during the Cold War, eventually acceding to the islanders’ demands for political self-determination. Throughout this period, the US failed to maintain coherent policy priorities and treated the islanders as second-class negotiating partners. Today, Micronesia is comprised of three states in “free association” with the United States: the Federated States of Micronesia, the Republic of the Marshall Islands, and the Republic of Palau, as well as the American territories of Guam and the Northern Mariana Islands. Micronesia lies geographically in the heart of the Asia-Pacific and continues to be of great strategic importance to the United States. In the coming decades, the rise of China will significantly alter the geopolitical status quo in Micronesia. The potential loss of Micronesia to China would be a substantial blow to America’s strategic position in the Asia-Pacific, and would be deeply damaging to American interests. US policymakers should consider the nature of this threat and create policy that meets the Chinese challenge in the Micronesia region. This thesis will provide a political history of Micronesia to the present day, describe the unique relationship between America and the freely associated states, and discuss the geopolitical issues currently facing the region. Overall, I intend for this thesis to provide a basic primer on Micronesia, and a broader look at the region’s role in global geopolitics.Plan II Honors Progra

The travelling preacher, projection, and a lower bound for the stability number of a graph

AbstractThe coflow min–max equality is given a travelling preacher interpretation, and is applied to give a lower bound on the maximum size of a set of vertices, no two of which are joined by an edge

The semantics, sociolinguistics, and origins of double modals in American English:New insights from social media

In this paper, we analyze double modal use in American English based on a multi-billion-word corpus of geolocated posts from the social media platform Twitter. We identify and map 76 distinct double modals totaling 5,349 examples, many more types and tokens of double modals than have ever been observed. These descriptive results show that double modal structure and use in American English is far more complex than has generally been assumed. We then consider the relevance of these results to three current theoretical debates. First, we demonstrate that although there are various semantic tendencies in the types of modals that most often combine, there are no absolute constraints on double modal formation in American English. Most surprisingly, our results suggest that double modals are used productively across the US. Second, we argue that there is considerable dialect variation in double modal use in the southern US, with double modals generally being most strongly associated with African American Language, especially in the Deep South. This result challenges previous sociolinguistic research, which has often highlighted double modal use in White Southern English, especially in Appalachia. Third, we consider how these results can help us better understand the origins of double modals in America English: although it has generally been assumed that double modals were introduced by Scots-Irish settlers, we believe our results are more consistent with the hypothesis that double modals are an innovation of African American Language.</p

A simple model for predicting snow albedo decay using observations from the Community Collaborative Rain, Hail, and Snow-Albedo (CoCoRAHS-Albedo) Network

The albedo of seasonal snow cover plays an important role in the global climate system due to its influence on Earth’s radiation budget and energy balance. Volunteer CoCoRaHS-Albedo observers collected 3,249 individual daily albedo, snow depth, and density measurements using standardized techniques at dozens of sites across New Hampshire, USA over four winter seasons. The data show that albedo increases rapidly with snow depth up to ~ 0.14 m. Multiple linear regression models using snowpack age, snow depth or density, and air temperature provide reasonable approximations of surface snow albedo during times of albedo decay. However, the linear models also reveal systematic biases that highlight an important non-linearity in snow albedo decay. Modeled albedo values are reasonably accurate within the range of 0.6 to 0.9, but exhibit a tendency to over-estimate lower albedo values and under-estimate higher albedo values. We hypothesize that rapid reduction in high albedo fresh snow results from a decrease in snow specific surface area, while during melt-events the presence of liquid water in the snowpack accelerates metamorphism and grain growth. We conclude that the CoCoRaHS-Albedo volunteer observer network provides useful snow albedo, depth, and density measurements and serves as an effective model for future measurement campaigns

Economic, Neurobiological and Behavioral Perspectives on Building America's Future Workforce

A growing proportion of the U.S. workforce will have been raised in disadvantaged environments that are associated with relatively high proportions of individuals with diminished cognitive and social skills. A cross-disciplinary examination of research in economics, developmental psychology, and neurobiology reveals a striking convergence on a set of common principles that account for the potent effects of early environment on the capacity for human skill development. Central to these principles are the findings that early experiences have a uniquely powerful influence on the development of cognitive and social skills, as well as on brain architecture and neurochemistry; that both skill development and brain maturation are hierarchical processes in which higher level functions depend on, and build on, lower level functions; and that the capacity for change in the foundations of human skill development and neural circuitry is highest earlier in life and decreases over time. These findings lead to the conclusion that the most efficient strategy for strengthening the future workforce, both economically and neurobiologically, and for improving its quality of life is to invest in the environments of disadvantaged children during the early childhood years.

Quantum critical behavior of a three-dimensional superfluid-Mott glass transition

The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional XY model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the 4D XY universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent $\nu = 1/2$ violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of $p_c = 0.688392$, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents $z=1.67(6)$, $\nu = 0.90(5)$, $\beta/\nu = 1.09(3)$, and $\gamma/\nu = 2.50(3)$. The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors and magnetic systems.Comment: 10 pages, 12 figures, published versio

Chytrid fungus infection in alpine tree frogs is associated with individual heterozygosity and population isolation but not population-genetic diversity

Chytridiomycosis, a disease caused by the emerging fungus Batrachochytrium dendrobatidis (Bd), has been implicated in the decline of over 500 amphibian species. Population declines could have important genetic consequences, including reduced genetic diversity. We contrasted genetic diversity among both long-Bd-exposed and unexposed populations of the south-east Australian alpine tree frog (Litoria verreauxii alpina) across its range. At the population level, we found no significant differences in genetic diversity between Bd-exposed and unexposed populations. Encouragingly, even Bd-infected remnant populations that are now highly isolated maintain genetic diversity comparable to populations in which Bd is absent. Spatial genetic structure among populations followed an isolation-by-distance pattern, suggesting restricted movement among remnant populations. At the individual level, greater heterozygosity was associated with reduced probability of infection. Loss of genetic diversity in remnant populations that survived chytridiomycosis epidemics does not appear to be a threat to L. v. alpina. We suggest several factors underpinning maintenance of genetic diversity: (1) remnant populations have remained large enough to avoid losses of genetic diversity; (2) many individuals in the population are able to breed once before succumbing to disease; and (3) juveniles in the terrestrial environment have low exposure to Bd, providing an annual ‘reservoir’ of genetic diversity. The association between individual heterozygosity and infection status suggests that, while other work has shown all breeding adults are typically killed by Bd, males with greater heterozygosity may survive longer and obtain fitness benefits through extended breeding opportunities. Our results highlight the critical role of life history in mitigating the impacts of Bd infection for some amphibian species, but we infer that increased isolation as a result of disease-induced population extirpations will enhance population differentiation and thus biogeographic structure