Finite size corrections in random matrix theory and Odlyzko's data set for the Riemann zeros

Odlyzko has computed a data set listing more than $10^9$ successive Riemann zeros, starting at a zero number beyond $10^{23}$. The data set relates to random matrix theory since, according to the Montgomery-Odlyzko law, the statistical properties of the large Riemann zeros agree with the statistical properties of the eigenvalues of large random Hermitian matrices. Moreover, Keating and Snaith, and then Bogomolny and collaborators, have used $N \times N$ random unitary matrices to analyse deviations from this law. We contribute to this line of study in two ways. First, we point out that a natural process to apply to the data set is to thin it by deleting each member independently with some specified probability, and we proceed to compute empirical two-point correlation functions and nearest neighbour spacings in this setting. Second, we show how to characterise the order $1/N^2$ correction term to the spacing distribution for random unitary matrices in terms of a second order differential equation with coefficients that are Painlev\'e transcendents, and where the thinning parameter appears only in the boundary condition. This equation can be solved numerically using a power series method. Comparison with the Riemann zero data shows accurate agreement.Comment: 22 pages, 10 figures, Version 2 added some new references in bibliography, Version 3 corrected the scaling on the spacing distribution and some typo

Health Science Curriculum for Early Childhood: Teacher Implementation and Impact on Child Health Knowledge

This dissertation contains two secondary quantitative data analyses studies. In the first, implementation of the WannaBee Healthy? Be Smart! Be Active! Be a Leader! health science curriculum was examined to expand understanding about teacher usage of an integrated health curriculum. Specifically, researchers assessed the amount of activities within each curriculum domain (i.e., books, creative expressions, language/literacy, math, science) and the number of activities within each theme of the lessons (i.e., nutrition, physical activity, sleep) utilized by participating teachers. Prior to implementation, teachers (N = 68; M age = 35.5 years old) attended a one-hour training where use of the curriculum and supplemental material toolkit were exhibited. Participants were instructed to implement the curriculum over the course of a month and directed to record lessons implemented on a teacher usage checklist, indicating a “Y+” if they taught the lesson and would likely teach it again, a “Y-” if they taught the lesson, but would not likely teach it again, and an “N” if the lesson was not implemented. An overall total number of activities and a total number of activities within each curriculum domain (e.g., language/literacy) and within each theme (e.g., nutrition) was calculated using a frequency analysis. Results show that more than 20% of reporting teachers (n = 10; 21.8%) implemented all or almost all (i.e., 49 or 50 lessons) of the curriculum’s 50 activities. Children had more exposure to the book domain and the theme of nutrition, with less engagement in the domain of math and sleep-themed lessons. Based on the results of the first study, the second study examined the association between the dosage of the WannaBee Healthy? curriculum implementation within each classroom (i.e., frequency use of curriculum domains; frequency use of lesson themes) and child health knowledge outcomes (e.g., USDA MyPlate accuracy). Explicitly, is the dosage and type of content implementation directly associated with student’s gain in knowledge and the ability to successfully identify the following: (1) food from each of the five food groups, (2) healthy plate that includes all recommended food groups, (3) food origins, (4) four activities that increase heart rate, and (5) sleep, healthy plate, and physical activity as behaviors needed to keep our body healthy. Researchers utilized the information from the teacher usage checklist to determine dosage and content implementation of lessons. Pre- and post-assessments were randomly conducted on 252 pre-kindergarten (17.9%) and kindergarten (82.1%) students (M age = 5.02) whose parents had provided consent. Pearson correlations identified strong, positive correlations regarding implementation across the curriculum and within the domains and themes. A series of One-way ANOVAs were conducted, identifying a significance in outcomes of at least one child assessment and in both health themes (i.e., nutrition, physical activity). However, overall findings indicate that curriculum dosage alone was not related to changes in child health knowledge. Further testing did not show a significant difference in association between changes in child knowledge when controlling for time between pre- and post-assessments. Results suggest the effectiveness of the WannaBee Healthy? curriculum is not based on curriculum alone

Unbundling the “Big Deal”: One Library’s Experience in Rising to the Occasion

Background: Budgetary constraints at West Virginia University (WVU) in combination with the impending expiration/renewal of “big deal” contracts forced the WVU Collections Advisory Committee (CAC) to implement the unbundling of three major journal packages. Wiley was the first package unbundled in 2017, followed by Elsevier Science Direct and Springer packages in 2018-19. Methods: The CAC determined criteria to use to consider whether or not to keep specific journal titles, including total uses, cost per use, and number of papers published and references used from each title by WVU faculty members over a 3-year period. Journals were ranked for each of these criteria, and then a rank average was obtained. Journals were then placed in a spreadsheet in rank order of rank average with a rolling sum so that a cutoff point could be determined based upon what the institution could afford. Librarians had the opportunity to “plead the case” for certain titles. WVU’s Clinical Key contract had a major impact on which journals were kept from the Science Direct package. Results: For Springer, we retained 79 titles and lost access to 2,143; for Wiley, we retained 113 titles and lost access to 1,275 titles, and for Science Direct, we retained 247 titles plus 294 Clinical Key titles and lost access to 196 subscribed and 1,216 Freedom Collection titles. Usage statistics for Clinical Key journals have quadrupled since the unbundling, going from an average of 505/month in 2018 to an average of 2,192/month this year. An expected increase in interlibrary loan requests for canceled journals has not materialized, making ILL costs much more cost-efficient than the former subscription costs. Librarians have received few complaints about canceled titles. Conclusions: Unbundling the big deal has not been nearly as traumatic as we thought it might be

From respect to reburial: negotiating pagan interest in prehistoric human remains in Britain, through the Avebury consultation

The recent Avebury Consultation on reburial has drawn considerable public and professional attention to the issue of pagan calls for respect towards the care of human remains. Our work has pointed to the importance of archaeologists and others engaging seriously and respectfully with pagans as significant stakeholders in our heritage. The Avebury Reburial Consultation suggests this dialogue is increasing in strength, but we identify problems in the process. We focus here on approaches to the prehistoric dead and worldviews enabling communication from which calls or ‘claims’ for the reburial of prehistoric pagan human remains, versus their retention for scientific study, are articulated; frameworks for assessing and adjudicating such ‘claims’; and implications for the interest groups concerned. We argue that room must be made for philosophical debate and the emotional and spiritual views of pagans, in order to improve dialogue, develop common ground, and enable participatory decision-making and situational pragmatism