The Lifting Properties of A-Homotopy Theory

In classical homotopy theory, two spaces are homotopy equivalent if one space can be continuously deformed into the other. This theory, however, does not respect the discrete nature of graphs. For this reason, a discrete homotopy theory that recognizes the difference between the vertices and edges of a graph was invented, called A-homotopy theory [1-5]. In classical homotopy theory, covering spaces and lifting properties are often used to compute the fundamental group of the circle. In this paper, we develop the lifting properties for A-homotopy theory. Using a covering graph and these lifting properties, we compute the fundamental group of the 5-cycle , giving an alternate approach to [4].Comment: 27 pages, 3 figures, updated version. Minor changes to the introduction and clarification that the computation of the fundamental group of the 5-cycle originally appeared in [4]. Title changed from "Computing A-Homotopy Groups Using Coverings and Lifting Properties" to "The Lifting Properties of A-Homotopy Theory

Collaborative research and sharing data ahead of paper publication: A case study of De Montfort University’s Dr. Fabio Caraffini

Figshare data• By sharing his high-resolution, multispectral images prior to a paper publication on DMU Figshare, Fabio and his colleagues are building public engagement with their research. • Storing large amounts of data in DMU Figshare allows Fabio and his colleagues to link to that data in a paper, which they would have otherwise just had to describe in the body of the paper

Effects of Swine Manure Management Options on Groundwater Quality

In 1994, there were 31 hog farms across the United States owning at least 10,000 sows and in 1995, there were 44 (Freese, 1994). This increasing number of large hog farms is evidence of the growing swine industry. This growth, however, has independent farmers, neighbors, environmentalists, and legislators in a quandary as to how the industry will evolve. These growing pains are of both an economic and environmental nature. Many topics need to be addressed as the production expands. One of the primary concerns of the growing hog industry is the issue of swine (Sus spp.) manure production

A Burkean Analysis of Eighteenth, Nineteenth, and Twentieth Century Christian Hymns

Hymns are one of the most popular forms of Christian worship, dating back to biblical times. Throughout history, hymns have been a way for people from all backgrounds and beliefs to express themselves in song. Hymnists have based their hymns on scriptures from the Bible, but have also written their hymns based on inspiration from scripture or divine revelation as well as their own earthly experience. To this day, hymns are still very present in both traditional and contemporary places of Christian worship, suggesting they are continually influential to the masses. My analysis looks at how hymns inform Christians’ theological framework, specifically how hymns shape and influence Christians’ perspective of God and Jesus, as well as their faith. To do this, I analyze hymns from three centuries: the eighteenth, nineteenth, and twentieth. Within each century I analyze four hymns using rhetorician Kenneth Burke’s theory, terministic screens. This theory examines how terms shape reality for humans and filter how humans perceive and understand the world around them. More specifically, terministic screens focus on how terms select, reflect, and deflect ideas about any given phenomenon, thus creating a variety of “screens” through which humans to understand reality. In my analysis, Burke’s theory enables me to examine how the hymns create different screens that inform Christians’ theological framework. My analysis reveals that each century has different screens to offer and provides a variety of perspectives for Christians to adopt, whether those screens inform their reality of who God and Jesus are, what their experience on Earth can or should be, what heaven looks like beyond this world, or how they should go about their daily lives. I hope that this analysis serves as a stepping stone for how Christians should evaluate the types of media they consume and how it informs their lives