Linear recurrence relations for cluster variables of affine quivers

We prove that the frieze sequences of cluster variables associated with the vertices of an affine quiver satisfy linear recurrence relations. In particular, we obtain a proof of a recent conjecture by Assem-Reutenauer-Smith.Comment: 20 pages, references updated and completed, acknowledgment adde

The Integral Cluster Category

Integral cluster categories of acyclic quivers have recently been used in the representation-theoretic approach to quantum cluster algebras. We show that over a principal ideal domain, such categories behave much better than one would expect: They can be described as orbit categories, their indecomposable rigid objects do not depend on the ground ring and the mutation operation is transitive.Comment: 17 pages, new section added, references adde

Creativity as a Gateway to Mental Health: A Burnout Recovery Journey

This research explored creativity and flow state as a means of overcoming symptoms of burnout and supporting mental wellness. In this self-study the subject participated in creating art using a variety of media for seven weeks. Additionally, the subject kept multiple streams of data to closely examine the main symptoms of stress and burnout, including an in-depth look at sleep patterns. Other data collected included flow achievement, pre and post study surveys, daily journals, and individual session check-ins. Data suggested that over the seven-week period, sleep became more regular and the subject felt better immediately after participating in creative activities. Additional research over a longer period of time, along with a holistic recovery plan, may prove to be a form of stress reduction and burnout recovery

Inscape, the inshape of the trinity : a genetic analysis of Gerard Manley Hopkins' "God's Grandeur" and "The Windhover"

Les théories poétiques de l’inscape et du sprung rhythm établies par le poète britannique Gerard Manley Hopkins (1844-1889) ont dérouté les critiques des années durant. La plupart d’entre eux se sont appuyés sur les poèmes publiés en quête d’indices quant à la signification de ses théories. Cette thèse approfondit l’analyse mise de l’avant en révélant que la genèse de la théorie de l’inscape provient des notes de Hopkins — alors étudiant de premier cycle — sur le philosophe présocratique Parménide, et est influencée par les commentaires sur l’oeuvre De la nature du philosophe. Un examen des lettres de Hopkins à ses collègues poètes Robert Bridges et Richard Watson Dixon révèle que le sprung rhythm découle de l’inscape, sa théorie de base. La technique du sprung rhythm consiste donc en l’application de l’inscape au schéma métrique de la poésie. Cette étude établit d’abord une définition opérationnelle de chacune de ces théories pour ensuite les appliquer aux manuscrits afin de déterminer dans quelle mesure Hopkins y adhérait et les exploitait lors de la rédaction de deux de ses poèmes canoniques, God’s Grandeur et The Windhover. L’étude s’inscrit ainsi dans le champ de la critique génétique, une approche mise au point en France, particulièrement à l’Institut des textes et manuscrits modernes (ITEM). Ce sont donc sur des oeuvres littéraires françaises ou sur des textes en prose qu’ont porté la majorité des analyses à ce sujet. Suppressions, ajouts, substitutions et constantes entre différentes versions témoignent de ce qu'étaient les priorités de Hopkins dans sa quête pour atteindre l’effet désiré. Par conséquent, cette thèse s’efforce de dévoiler la signification des théories poétiques de Hopkins en établissant leur genèse et leur application respectives dans deux de ses poèmes selon une perspective de critique génétique. Elle contribue également à enrichir la critique génétique en l’appliquant à des oeuvres littéraires écrites en anglais et sous forme de poésie plutôt que de prose. Enfin, son objectif ultime est de raviver l’intérêt pour le poète Hopkins en tant que sujet viable d’étude, et de favoriser l’appréciation de ses prouesses tant comme théoricien poétique que comme poète.The poetic theories of inscape and sprung rhythm developed by British poet Gerard Manley Hopkins (1844-89) have baffled critics for years. Most critics have relied upon the published poems for clues to their significance. This study advances the analysis further by revealing the genesis of the theory of inscape to be Hopkins’ undergraduate notes on the pre-Socratic philosopher Parmenides and is influenced by commentaries on Parmenides’ work “On Nature.” A study of Hopkins’ letters to fellow poets Robert Bridges and Richard Watson Dixon reveals that sprung rhythm emanates from his overarching theory of inscape; sprung rhythm is, thus, the application of inscape to the metrical patterns of poetry. After determining a working definition of both poetic theories, this study applies these terms to the manuscripts to determine to what extent Hopkins’ adhered to and developed the theories when writing two of his canonical poems: “God’s Grandeur” and “The Windhover.” It thus fits in the field of genetic criticism, a critical approach developed in France and centered at the Institut des Textes et Manuscrits Modernes (ITEM). Most analyses conducted have thus been done on French works and to prose. Deletions, additions, and substitutions, as well as the consistencies from one version to another, reveal Hopkins’ priorities as he strove to attain the desired effect. Therefore, this study endeavours to unveil the meaning of Hopkins’ poetic theories by determining their geneses and their application to two of his best known poems, “God’s Grandeur” and “The Windhover, ” through the practice of genetic analysis. It contributes to genetic criticism in applying it to works written in the English language and to poetry rather than prose. The hope is to renew interest in Hopkins as a viable poet to study and to incite further appreciation in his prowess as both poetic theorist and poet

Reading Education Issues: Principals’ and Teachers’ Perceptions

The purpose of this study was to examine middle school principals’ and teachers’ perceptions of the current issues in middle school reading education and to identify the sources of information that these educators use and find helpful to keep informed reading issues. Participants were employed in the 14 middle schools of the Knox County School System (KCS) in Knoxville, Tennessee. Questionnaires were completed in March and April 2004 by the14 middle school principals and 14 teachers who were reading chairpersons for their schools. The questionnaire used in this study, Middle School Principals and Teachers: Knowledge of the Reading Program, consists of five tasks. A chi- square analysis was used for three of the tasks and percentages of responses were compared to analyze two tasks. Principals and teachers agreed more than they disagreed on their responses to all tasks in the questionnaire. There were three items in which participants’ responses showed statistically significant differences: (a) the two groups’ classification and ranking of importance of one issue, providing a supportive learning community including teachers who serve as role models of active literacy via apparent relish for reading (teachers classified and ranked this as unresolved more often than did principals), and (b) one source of information, journals for educators (reported as used more by principals than teachers). Principals and teachers agreed that three issues are unresolved: (a) meeting the criteria of No Child Left behind for “Highly Qualified” teachers, (b) effects of public accountability, which foster teaching to the test, on reading instruction, and (c) planning reading instruction for struggling readers. Analysis of participants’ rating of understanding of reading issues showed similarity in their reported level of understanding. Participants identified three sources of information most often used in the last 12 months to keep informed about issues in reading education: (a) Informal contacts with specialists in the field, (b) formal contacts with specialists in the field, and (c) popular national magazines and/or newspapers. Participants rated the helpfulness of these sources of information similarly

Trends and interannual variability in snowpack and spring season hydroclimatology in the southwestern United States

By virtue of its relatively low latitude and already marginal snowpack, especially in Arizona and much of New Mexico, the southwestern U.S. is a compelling location in which to study how temperature and seasonal snowpack interact to affect spring hydroclimatology. Understanding snowpack-mediated spring soil moisture and how observed, current changes in the regional climate affect the snowpack-soil moisture relationship will provide important insights into the current and future hydrology of the southwestern U.S. In this study, we use newly available data from the North American Land Data Assimilation System (NLDAS-2) Phase 2, run with the Mosaic land surface model, to investigate the effects of recent historical trends and interannual variability (1979-2009) on land surface hydroclimatology in the Southwest U.S. There are multiple feedback mechanisms by which snowpack in the southwestern U.S. may indirectly influence short term and/or long-term climate variability. This study represents the first attempt to use newly available land surface data to describe the processes by which snowpack alters soil moisture and surface energy fluxes, thus characterizing the potential for land surface-atmosphere interactions to proceed in the southwestern U.S. We study the period between snow ablation and monsoon onset and find positive linear trends in spring temperature, decreasing linear trends in total precipitation, linear trends towards earlier snowmelt, decreasing linear trends in soil moisture and latent heat flux and increasing linear trends in sensible heat flux and the Bowen Ratio. We find that snowpack alters the magnitude and timing of soil moisture and the surface energy balance, though our sample sizes are small and the sizes of the uncertainties in the means are large. While monsoon onset negates these effects later in the year, decreased snowpack will likely exacerbate temperature-driven warming and drying, months after the complete ablation of snowpack. NLDAS-2 provides a unique opportunity to consider potential large-scale interactions of land surface hydrologic variables. With additional quantification of how the land surface behaves under changing climate conditions, we may be better able to anticipate future land surface variability and feedbacks and assess model projections with a better foundation of results from current climate change