The Four Color Theorem: A Possible New Approach

The goal of this thesis is to explore the topic of graph coloring and expand on existing ideas in the field of Graph Theory. These developments will then be used to provide a possible approach in proving the 4 – color theorem that was made famous by Guthrie in the 1800’s. Since the theorem was presented, many proofs were presented and eventually disregarded for one reason or another. Today, the types of proofs that are considered correct all rely on a computer. The first of this kind was set forth by Appel and Haken in 1977. The driving idea behind their proof was exhaustive analysis. A different approach will be taken here. The 4 – color theorem stated is: “Any finite, planar graph can be colored using 4 (at most) colors in such a manner that no adjacent vertices will share the same color.” While a complete proof of the theorem may not be possible to complete in this thesis, an intuitive idea will be presented that has potential to be expanded on in the future

A Help or Hindrance? Team Leader Behaviors and the Team Climate of Innovation

While the nature of teamwork in organizations is ever-evolving, the utilization of teams in some form has continued to increase over the past several decades. While creativity is generally regarded as an individual-level phenomenon, innovation tends to occur as an emergent process at the team level, so rather than only hiring and rewarding star performers, organizations should cultivate and protect the team’s climate for innovation. A particularly impactful contextual factor in team climate is the team leader’s behavior. Therefore, the team leader’s contribution to the climate should work to promote innovation rather than discourage it. A cross-sectional, correlational study surveyed participants who identified as part of a work-related team. They were asked about the motivational states their team leaders encourage (the motivational micro-climate created by the leader) and about their team’s climates of innovation and psychological safety. A regression-based analysis found the relationship between a psychologically diverse micro-climate encouraged by the team leader and the team’s climate of innovation to be significant (B = 0.11, 95.00% CI [0.10, 0.13], p \u3c .001). The analysis also considered the potential mediating role of psychological safety, and a significant indirect effect was found (β = 0.037, 95.00% CI [0.012, 0.07]). Additional relationships between selected aspects of the motivational micro-climate (specifically, purpose and change orientation) and selected factors of innovation (specifically, team orientation and vision) were examined with a moderated mediation model through conditional process analysis. Notable findings here were a positive relationship between the leader micro-climate of. iv change orientation and the team climate of innovation (B = 0.09, 95.00% CI [0.05, 0.13], p \u3c .001), that was partially mediated by the team climate of innovation factor, task orientation (B = 0.10, 95.00% CI [0.06, 0.13], p\u3c .001)

Exploring the use of the bass guitar as a clinical instrument within music-centered practice

There is limited research on the use of the bass guitar in music therapy. This study explored the use of the bass guitar as a clinical instrument from a music-centered perspective in clinical work with individuals with neurodevelopmental disorders and emotional challenges. Data were collected from filming individual music therapy sessions with three participants. Each participant had four sessions of music therapy. Data were analyzed using inductive thematic analysis. Five themes which reflect the interventions and social processes within music-centered work with the bass were identified: following the client’s lead, grounding, client and therapist as rhythm section, client and therapist as soloist and accompanist, and co-creative thematic development. These themes provided structure for further examining the role of the bass within clinical interventions. Clinical descriptions of musical interactions, with audio excerpts, are included to show how the bass guitar was used within improvisational interventions within each theme, as well as to provide context for clinical techniques and roles within the music. Understanding the role of the bass and its aesthetic qualities within the musical process can contribute to providing effective interventions, supporting the role of the client, and facilitating further development in music when working within these themes

Patterns in Abundance of Louisiana’s Avifauna Revealed by the Louisiana Bird Atlas Project

The Louisiana Bird Atlas Project is a multi-year citizen science effort designed to quantify bird distribution and abundance for all species regularly occurring in the state of Louisiana during two time periods: summer and winter. Data were collected by volunteers in a citizen science framework across eight years, from 2007 to 2014. A total of 351 species was recorded (254 during the Summer Bird Atlas and 315 during the Winter Bird Atlas). Maps showing distribution and relative abundance for each species were generated within a Geographical Information System, and were accompanied by short descriptions of status, distribution, abundance, and other patterns. Distributions of 116 species that were also recorded during a previous atlas effort, the Louisiana Breeding Bird Atlas (Wiedenfeld & Swan, 2000), were compared using the Chi-square statistical test to detect changes in distribution between 2000 and 2014. The Louisiana Bird Atlas Project generated a baseline snapshot of bird distributions and abundance from the early part of the 21st century that can be compared to future changes due to potential climate change, habitat degradation, and other factors

An In-depth Analysis of New England Mutual Savings Banks, 1870-1914

Scholars have studied the U.S. banking systems of the late 19th century, but the presence and influence of mutual savings banks has largely gone unexamined. A new annual database of New England banks shows that mutual savings banks had a significant presence in the postbellum banking system. Mutual savings banks accounted for about 75 percent of the region\u27s total bank deposits and largely avoided financial panics. The banks seemed to have complemented rather than competed with national banks. Mutual savings bank growth was correlated with agriculture and urbanization, whereas national bank growth was correlated with manufacturing. Mutual savings banks also channeled significant funds to national banks through the interbank network

Carte de visite, Confederate Generals Sterling Price, John Magruder, William Hardeman, Henry Allen, and Thomas C. Hindman in Mexico, in civilian dress, ca. 1866; print from negative by Matthew Brady.

These Confederate Generals left the United States for Mexico at the close of the Civil War. Standing in the rear (left to right) are John Bankhead Magruder and William P. Hardeman. Seated (left to right) are Henry W. Allen, Sterling Price, and Thomas C. Hindman. Verso indicates original negative by Matthew Brady. Verso annotations do not appear to be completely correct in identification of subjects. Source: http://ozarkscivilwar.org/photographs/confederate-generals-sterling-price-john-magruder-william-hardeman-henry-allen-and-thomas-c-hindman/https://digitalcommons.wofford.edu/littlejohnmss/1309/thumbnail.jp