Alien Registration- Sylvester, John (Monroe, Waldo County)

https://digitalmaine.com/alien_docs/5188/thumbnail.jp

The Cover Time of a (Multiple) Markov Chain with Rational Transition Probabilities is Rational

The cover time of a Markov chain on a finite state space is the expected time until all states are visited. We show that if the cover time of a discrete-time Markov chain with rational transitions probabilities is bounded, then it is a rational number. The result is proved by relating the cover time of the original chain to the hitting time of a set in another higher dimensional chain. We also extend this result to the setting where $k\geq 1$ independent copies of a Markov chain are run simultaneously on the same state space and the cover time is the expected time until each state has been visited by at least one copy of the chain.Comment: 8 pages, 1 figure. The Proof of Proposition 8 has been simplifie

Developing and Assessing the Psychometric Properties Of a Multidimensional College Mental Health Assessment Inventory: A Mixed-Methods Study

The purpose of this study was to develop a multidimensional College Mental Health Assessment Inventory (CMHAI) specifically for the college student population. In the first phase, a conceptual and theoretical review of general existing scales was performed, followed by conducting exploratory semi-structured interviews with twelve participants. From the interviews, I identified themes/constructs (domains) comprised of 52 items to make up the initial inventory. Participants believed these themes to be worthy of note: (a) admission to college with pre-existing mental conditions; (b) students’ expectation about college versus the actual experience; (c) college as a new environment brings about feelings of loneliness; (d) ethical issues related to college students seeking mental health support; and (e) publicizing available supports on campus to students. The second qualitative research phase consisted of content and face validity processes on the 52 items developed from phase one, including conducting a readability test, expert reviews, and using think-aloud protocols. The content and face validity resulted in 45 items inventory that was then quantitatively tested in phase three and four. The third phase consisted of conducting exploratory factor analysis (EFA) on the 45-items inventory to explore, develop and refine the measure. The 45-item inventory was administered to the traditional college population in the United States (n=220). An EFA was conducted on the data and seven factors were extracted based on Kaiser’s criteria of eigenvalue \u3e1 rule (Kaiser, 1960). Five factors out of the seven extracted factors were identified, described, and retained based on factor loading \u3e .40 and with loaded items four and above (Izquierdo et al., 2014). The internal consistency reliability was assessed for each of the extracted factors and were all \u3e .70. The EFA resulted in a 34-item inventory with five factors (subscales). The fourth phase involved using the 34-item inventory from EFA. A different set of data was collected from another sample in the population of study to conduct a confirmatory factor analysis (CFA), which was used to validate how well the hypothesized model from EFA could adequately model scores from the population of study (construct validity). The results of the model fit information on the second data indicated that the data fit very well with the developed CMHAI model. The internal consistency reliability (Cronbach’s alpha) and McDonald Omega reliability were conducted on the CFA data for each of the subscale and the results met the acceptable standards. Considering the results of analyses reported by existing general measures reviewed and from the results of the analyses of this research, the developed CMHAI-34 shows a high promise of being a reliable and valid measure for college students’ mental health assessment