Lie Groups and mechanics: an introduction

The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and in a third section we apply these methods for the diffeomorphism group of the circle with two particular examples: the Burger equation and the Camassa-Holm equation

Effects of Poverty Funding on Math and Literacy Achievement in Arkansas

This research project was designed to provide a foundational study of the effectiveness of a state categorical fund directed at poverty students called NSLA funding on literacy and math achievement in Arkansas. Poverty funding for students in Arkansas is realatively new and there have not been any studies to examine the impact of this funding to date. Literacy and math achievement scaled scores were evaluated for one year for fourth, sixth, and eighth grades by four NSLA levels, NSLA level 1, NSLA level 2, NSLA level 3, and NSLA level 4. This causal comparative study was conducted with data from school districts in Arkansas. In the first phase of the study, two school districts were randomly chosen from each of the four NSLA levels (eight school districts in all). The NSLA levels were based on percentages of students who received free or reduced lunches in the districts. Math and literacy achievement were measured in these school districts using scaled scores from the Arkansas Augmented Benchmark Examination. The sample consisted of 720 students randomly chosen from the eight districts. Thirty students were chosen from each grade level in each district. Descriptive statistics were reported for the sample, but were not included in the statistical analysis. A series of six one-way analyses of variance (ANOVAs) were used to analyze the data, with NSLA level as the independent variable and math and literacy scores as the dependent variables. Significant differences were found among the different NSLA levels on all six hypotheses; therefore, all six null hypotheses were rejected. In the second phase of the study, the way in which NSLA program funds were spent in school districts was examined. Six districts were chosen from each of the four funding levels (24 school districts in all), and the percentages of fund expenditures among 11 categories of spending were determined. Descriptive statistics were used to examine the expenditures at each of the four NSLA levels to determine if spending patterns could be found, and if so, which patterns were most effective

A Cantor set of tori with monodromy near a focus-focus singularity

We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol'd determinant grows infinitely large near the pinched torus. Moreover, we prove that it is possible to globally parametrise the Liouville tori by their frequencies. If one perturbs this integrable system, then the KAM tori form a Whitney smooth family: they can be smoothly interpolated by a torus bundle that is diffeomorphic to the bundle of Liouville tori of the unperturbed integrable system. As is well-known, this bundle of Liouville tori is not trivial. Our result implies that the KAM tori have monodromy. In semi-classical quantum mechanics, quantisation rules select sequences of KAM tori that correspond to quantum levels. Hence a global labeling of quantum levels by two quantum numbers is not possible.Comment: 11 pages, 2 figure

Adiabatically coupled systems and fractional monodromy

We present a 1-parameter family of systems with fractional monodromy and adiabatic separation of motion. We relate the presence of monodromy to a redistribution of states both in the quantum and semi-quantum spectrum. We show how the fractional monodromy arises from the non diagonal action of the dynamical symmetry of the system and manifests itself as a generic property of an important subclass of adiabatically coupled systems

Age Differences in Reward Anticipation and Memory

Aging research on item- and associative-recognition memory has demonstrated that older adults are deficient in forming associations between two unrelated stimuli. Although older adult performance on tests of item-recognition is similar to younger adult performance, older adults perform worse than younger adults on tests of associative memory (Naveh-Benjamin, Hussain, Guez, & Bar-On, 2003). In addition to the idea that younger adult performance on associative-recognition tests is superior to that of older adults, research has shown that reward cues can enhance motivated learning and item memory performance of younger adults. In an fMRI study that examined the influence of reward anticipation on episodic memory formation, Adcock and colleagues (2006) examined memory performance in response to reward cues that preceded single stimuli and found that young adult participants remembered more stimuli associated with high value reward cues than those associated with low value reward cues. The aim of the current study was to examine whether reward cues that precede a stimulus pair might enhance an association between two stimuli and influence younger and older adult performance on tests of item- and associative-recognition. Our study confirms the idea that while older adult memory for individual items is intact, older adult memory for associations is impaired (Naveh-Benjamin et al., 2003). The results supported the idea that younger and older adult item-recognition is better for high versus low reward cues, but the reward cues had no influence on the associative-recognition of either age group. Therefore, the age-related associative deficit was not improved by reward cues that preceded each stimulus pair

Re-evaluating causal modeling with mantel tests in landscape genetics

The predominant analytical approach to associate landscape patterns with gene flow processes is based on the association of cost distances with genetic distances between individuals. Mantel and partial Mantel tests have been the dominant statistical tools used to correlate cost distances and genetic distances in landscape genetics. However, the inherent high correlation among alternative resistance models results in a high risk of spurious correlations using simple Mantel tests. Several refinements, including causal modeling, have been developed to reduce the risk of affirming spurious correlations and to assist model selection. However, the evaluation of these approaches has been incomplete in several respects. To demonstrate the general reliability of the causal modeling approach with Mantel tests, it must be shown to be able to correctly identify a wide range of landscape resistance models as the correct drivers relative to alternative hypotheses. The objectives of this study were to (1) evaluate the effectiveness of the originally published causal modeling framework to support the correct model and reject alternative hypotheses of isolation by distance and isolation by barriers and to (2) evaluate the effectiveness of causal modeling involving direct competition of all hypotheses to support the correct model and reject all alternative landscape resistance models. We found that partial Mantel tests have very low Type II error rates, but elevated Type I error rates. This leads to frequent identification of support for spurious correlations between alternative resistance hypotheses and genetic distance, independent of the true resistance model. The frequency in which this occurs is directly related to the degree of correlation between true and alternative resistance models. We propose an improvement based on the relative support of the causal modeling diagnostic tests

Effect of heifer calving date on longevity and lifetime productivity

Longevity and lifetime productivity are important factors in profitability of the beef cow herd. Therefore, a concern for many producers is the productivity and longevity of the individual cow in their herd. The 2007-08 survey from National Animal Health Monitoring System (NAHMS) reported that the largest percentages of cows (33%) are culled because they do not become pregnant during the breeding season. It also reported that 15.6% of all culled cows leave the herd before 5 years of age, and an additional 31.8% leave the herd between 5 and 9 years of age. Research has reported that it takes 5 calves to pay for the development costs and annual maintenance of a replacement heifer (E.M. Mousel, Unpublished data). Therefore, to be sustainable, producers need to manage their herd to reduce the number of cows that are culled at a young age