Invariable generation of the symmetric group

We say that permutations $\pi_1,\dots, \pi_r \in \mathcal{S}_n$ invariably generate $\mathcal{S}_n$ if, no matter how one chooses conjugates $\pi'_1,\dots,\pi'_r$ of these permutations, $\pi'_1,\dots,\pi'_r$ generate $\mathcal{S}_n$. We show that if $\pi_1,\pi_2,\pi_3$ are chosen randomly from $\mathcal{S}_n$ then, with probability tending to 1 as $n \rightarrow \infty$, they do not invariably generate $\mathcal{S}_n$. By contrast it was shown recently by Pemantle, Peres and Rivin that four random elements do invariably generate $\mathcal{S}_n$ with positive probability. We include a proof of this statement which, while sharing many features with their argument, is short and completely combinatorial.Comment: 15 pages. Corrections and clarifications suggested by the referees. Added a reference to a paper of Raouj and Stef which solves related problems about divisor

The Pontem Path: A Case Study of a Catholic Bridge Program Focusing on College Readiness

The Department of Education’s 2018 report on the “Condition of Education” indicated nearly 60% of all children under the age of 18 had parents without a bachelor’s degree. When the statistics were broken down by race, the numbers were far higher. For Black children, that number was 74%; for Hispanic children, that number was 79%; for Pacific islander, it was 78%; and for American Indian/Alaska native, it was 80%. This gap in education has had a tremendous economic impact on families, reverberating through generations. According to Georgetown’s 2015 study on the economics of college majors, a college graduate makes $1 million more than a high school graduate (Carnevale et al., 2015). In addition, the study indicated a difference of$3.4 million in income between the highest and lowest paying majors. One way to bridge this gap is through improving college readiness of these students. Existing bridge programs like TRiO, Upward Bound, and summer bridge have shown success in improving college readiness. Upward Bound and Upward Bound math and science programs reported 86% of their participants from the 2013–2014 high school cohort immediately enrolled in a postsecondary education program. Current research has found programs focusing on college readiness have indeed helped. Many of these studies on college readiness programs have focused on student academic preparation, parental involvement, and school supports (e.g., college counseling, course selection). There has been comparatively less research focused on extracurricular programs aimed at fostering individual student traits, such as self-efficacy. This study focused on a college readiness program conducted at an area parochial school in San Diego County. The case study addressed the program’s role in fostering self-efficacy among student participants and examined organizational level factors leading to successful implementation. This research was important because it provided further insight into the role self-efficacy can play in a college bridge program and identified organizational factors that are barriers to or help with implementation

The American Police System (GHC)

This Grants Collection for The American Police System was created under a Round Eleven ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/criminal-collections/1003/thumbnail.jp

Constructing A Flexible Likelihood Function For Spectroscopic Inference

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints (pixels) into the residual spectrum. For the high signal-to-noise data with large spectral range that is commonly employed in stellar astrophysics, that covariant structure can lead to dramatically underestimated parameter uncertainties (and, in some cases, biases). We construct a likelihood function that accounts for the structure of the covariance matrix, utilizing the machinery of Gaussian process kernels. This framework specifically address the common problem of mismatches in model spectral line strengths (with respect to data) due to intrinsic model imperfections (e.g., in the atomic/molecular databases or opacity prescriptions) by developing a novel local covariance kernel formalism that identifies and self-consistently downweights pathological spectral line "outliers." By fitting many spectra in a hierarchical manner, these local kernels provide a mechanism to learn about and build data-driven corrections to synthetic spectral libraries. An open-source software implementation of this approach is available at http://iancze.github.io/Starfish, including a sophisticated probabilistic scheme for spectral interpolation when using model libraries that are sparsely sampled in the stellar parameters. We demonstrate some salient features of the framework by fitting the high resolution $V$-band spectrum of WASP-14, an F5 dwarf with a transiting exoplanet, and the moderate resolution $K$-band spectrum of Gliese 51, an M5 field dwarf.Comment: Accepted to ApJ. Incorporated referees' comments. New figures 1, 8, 10, 12, and 14. Supplemental website: http://iancze.github.io/Starfish

Women\u27s Choir with Lost Mountain Middle School 7th and 8th Grade Choruses

The KSU Women\u27s Choir, directed by Dr. Alison Mann, Associate Professor of Choral Music Education, and the Lost Mountain Middle School Choruses present a performance titled I Carry Your Heart With Me.https://digitalcommons.kennesaw.edu/musicprograms/2170/thumbnail.jp

The association between medical students\u27 motivation with learning environment, perceived academic rank, and burnout

Objectives: To assess the correlations between extrinsic and intrinsic motivation, personal growth and quality of life with learning environment perceptions, perceived academic rank and burnout among medical students. Methods: Cross-sectional questionnaires were administered to medical students at three medical schools in Israel, Malaysia, and China, at the end of one academic year. Surveys included demographic data, students\u27 perceived academic rank, two learning environment perceptions scales, and scales for personal growth, goal orientation, burnout and quality of life. Comparative analyses were made to determine the significance of relationships between the outcome measures and control variables, using a series of t-tests. Pearson correlation coefficients were used to test the hypothesis. Results: Sixty-four percent (400/622) of the students responded. Significant correlations were found between: intrinsic motivation (r(398) =.37, p\u3c.001); personal growth (r(398)=.62, p\u3c.001); and quality of life (r(398)= .48, p \u3c.001) with higher learning environment perceptions, intrinsic motivation (r(398)= .21, p\u3c.001); personal growth (r(398) =.21, p\u3c .001); and quality of life (r(398)=.18, p\u3c.001) with perceived academic rank, and negative correlation between personal growth (r(398) =-.38, p\u3c.001); and quality of life (r(398) =-.42, p\u3c.001) with burnout. Conclusions: Intrinsic motivation, personal growth and quality of life are correlated with higher learning environment perceptions and perceived academic rank. Burnout is influenced by personal growth and quality of life. We suggest focusing on motivation profiles before acceptance to medical school and during studies

34th Annual Cornell Real Estate Conference Recap

Every October, the Cornell Real Estate Conference draws together the real estate community of Cornell and other significant industry individuals to meet and discuss current issues in real estate. In 2016, the theme of the conference was Disruption in Real Estate. The central discussion was simple: as with many industries, the pace of change in real estate is accelerating. New technologies have affected every sector of real estate including property management, data analytics and investment sourcing