Occupancy distributions in Markov chains via Doeblin's ergodicity coefficient

We apply Doeblin's ergodicity coefficient as a computational tool to approximate the occupancy distribution of a set of states in a homogeneous but possibly non-stationary finite Markov chain. Our approximation is based on new properties satisfied by this coefficient, which allow us to approximate a chain of duration n by independent and short-lived realizations of an auxiliary homogeneous Markov chain of duration of order ln(n). Our approximation may be particularly useful when exact calculations via first-step methods or transfer matrices are impractical, and asymptotic approximations may not be yet reliable. Our findings may find applications to pattern problems in Markovian and non-Markovian sequences that are treatable via embedding techniques.Comment: 12 pages, 2 table

Enumerative properties of triangulations of spherical bundles over S^1

We give a complete characterization of all possible pairs (v,e), where v is the number of vertices and e is the number of edges, of any simplicial triangulation of an S^k-bundle over S^1. The main point is that Kuhnel's triangulations of S^{2k+1} x S^1 and the nonorientable S^{2k}-bundle over S^1 are unique among all triangulations of (n-1)-dimensional homology manifolds with first Betti number nonzero, vanishing second Betti number, and 2n+1 vertices.Comment: To appear in European J. of Combinatorics. Many typos fixe

SB65-16/17: Resolution Regarding the ASUM City Council Liaison

SB65-16/17: Resolution Regarding the ASUM City Council Liaison. This resolution passed 21Y-0N-0A by roll call vote at the March 1, 2017 meeting of the Associated Students of the University of Montana (ASUM)

SB40-15/16: Regarding the Davidson Honors College Director of External Scholarships and Advising

SB40-15/16: Regarding the Davidson Honors College Director of External Scholarships and Advising. This resolution was passed 22Y-2N by roll call vote at the March 9, 2016 meeting of the Associated Students of the University of Montana (ASUM)

SB66-16/17: Resolution Regarding the Campaigning in the UC

SB66-16/17: Resolution Regarding the Campaigning in the UC. This resolution was referred back to the Elections Committee at the March 15, 2017 meeting of the Associated Students of the University of Montana (ASUM)

Master of Science in Human Development and Social Policy

thesisThis study seeks to identify differences between preschool-aged boys and girls in their engagement in book browsing and book reading in a public library to investigate gender differences in early literacy and reading experiences. Sixty-eight child-caregiver dyads were observed in the children's area at five branches of the Salt Lake City Public Library System. Of this sample, 35 were girls and 33 were boys. Dyads were observed at various times of day (i.e., morning, early afternoon, late afternoon, evening, and weekend). Engagement was measured through time-sampled incidences of child book browsing and book reading. Using ANCOVA, the number and percentage of observed time intervals of each reading-related behavior of children in the library were analyzed to determine gender differences after controlling for age. Additional ANCOVA was conducted to analyze parent-reported reading behaviors at home so as to compare gender differences in book access, book reading, and shared reading interactions as observed versus reported. As observed in the library, girls were more involved in interactive browsing behaviors than boys and also spent a greater percentage of time in library on both general reading and shared reading. No gender differences were observed for verbatim reading, expanding discussion, or parents responding to child's talk. Girls were engaged for a higher percentage of time intervals over time spent in library reading in describing discussion and print referencing during shared reading. For parent-reported reading behaviors at home, girls were found to be more involved in reading discussion