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Our Voices Matter
Lydia G. Artz, Heather E. Ashley, Kayla N. Burdette, Morgan Couture, Elizabeth Licata Gallagher, Ayla Marie Garman, Cameron Cristina Nowlin, Christina Marie Reynolds, Cameron Rutherford, Allison Shaw, Shyanne Smith, Beck Lee Trumbull
Expressing oneself is one of the core values of the LGBTQ+ community, as to combat the years the community has spent with their voices oppressed and silenced. College specifically is a time for students to not only come to understand themselves, but to also find how they communicate their identities to the rest of the world-- and this applies even more strongly to LGBQT+ students. Our Voices Matter highlights the voices of LGBTQ+-identifying students and their narratives, giving those students a chance to freely express themselves. We have collected anonymously-submitted writings and artworks from LGBTQ+ students at UD. These will be shared by volunteer members of the LGBTQ+ community. This is the fourth annual Our Voices Matter event, and the second year that it will be facilitated as a part of the Stander Symposium.
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Panel Discussion: An Introduction to "The Magic Flute"
Mariah Joanna Berryman, Alyssa C. Boldt, Clare Rose Carey, Juliana Christine Hake, Mary Clare Hake, John Carter Herzog, Trinity Peace Hines-Anthony, Michaela Ann Miller, Angelo N. Moore-Knight, Arianna Maria Ranallo, Olivia Easton Redwine, Anna Jean Simmons, Blaise C. Stephens, Beck Lee Trumbull
Meet the cast and creative team who created the University of Dayton's 2020-2021 production of Mozart's The Magic Flute. Stream the episodes or binge watch the full version at the UD Music Department's YouTube channel.
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Parental Hostility and Youthful Offending
Shannon Elizabeth Powers
Research shows that parenting styles are associated with children’s behavior and adjustment. One type of parenting style is parental hostility, which has been found to be correlated with delinquency. This relationship is more pronounced when parental hostility includes physical aggression towards the child or teenager. The current study aims to examine the link between parental hostility and delinquency among adjudicated juveniles. The Pathways to Desistance data was used to examine this relationship. The sample consisted of 1,354 serious juvenile offenders between the ages of 14 years old to under 18 years old from Philadelphia and Phoenix. The participants were 86% males, 41.4% African American, 20% White, and 33.5% of the rest of the sample consisted of other races. A bivariate correlation was used to examine the association. The findings show a weak statistically significant association between mother’s and father’s parental hostility and total offending, which is aligned with previous research. Findings and implications will be discussed.
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Perception of Police Canines on a Midwest Campus
Tyera J. Brown, Noah Nietz
Officials at Midwest universities have often shied away from the idea of bringing police canines onto campuses in fear of the perceptions from students. The study used a phenomenological strategy to explain students' and officers' perceptions of police canines on a Midwest university campus. Participants enrolled in a Midwest university and officers employed at a Midwest university were interviewed using a snowball sampling method. Participants were asked a series of open-ended questions on their views of policing and bringing police canines on campus. Participant experiences and feedback were analyzed to answer the research questions in the study. Data collected from interviews was reviewed to identify themes.
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Persistent Developmental Delays in Children Born with Neonatal Abstinence Syndrome and In Utero Drug Exposure
Elizabeth Renee Staley
Children born with Neonatal Abstinence Syndrome (NAS) and In Utero Drug Exposure (IUDE) may experience delays that can impact cognition, motor skills, speech and language, attention and behavior development. Further, children born with NAS are more likely to be referred for evaluation and subsequently qualify for special education when compared with non-exposed peers. This quantitative study involved an evaluation of existing visual motor and receptive/expressive language data from birth to 24 months for 106 children born with NAS and IUDE. Results indicated that these children had significant deficits in visual motor scores and receptive and expressive language scores. Significant differences in visual motor and language scores were found between the NAS & IUDE and IUDE only groups. Children in the IUDE only groups had lower scores on visual motor and language assessments; the IUDE only group demonstrated a significant positive rate of change.
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Perspectives of Pre-service Art Educators
Brooke Ann Henry, Hannah Elyse Kelly, Shayna Rauch
In this presentation the authors -- Brooke Henry and Hannah Kelly, together, paint a conceptual portrait of their evolving relationships with art education. This is conducted through the Currere method of research where educators (or pre-service educators) can reconsider the meaning of curriculum. Through this method there have been findings through question and answer sessions as well as personal reflective writing, the conclusion is still being unpacked. The method consists of four steps: the regressive, progressive, analytical, and synthetical. Participating in autoethnographic research, such as the Currere method, reduces the distance between the researcher and subject by making the researcher the subject. It allows for deeper and clearer understanding of the present by outlining the past, present, and future. A third perspective comes from Shayna Rauch, who discusses her own autoethnographic research about incorporating mindfulness into the classroom as a pre-service educator. Initially her research focused solely on teacher mindfulness as a solution to lowering stress in order to improve teacher performance and classroom environment. Rauch practiced daily meditation, brain breaks in between classes, and reflected on the effects in a daily data log including a visual or written rumination. Through the course of the study student mindfulness was incorporated as well, where students engaged in mindful visual journaling. The results of this study found that over time daily meditation lowered stress, increased mental clarity, heightened empathy for students, and improved classroom climate. The improvements from meditation alone were moderate, but through the daily reflections and inclusion of student mindfulness, a greater effect on the classroom environment was seen.
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Pervasive Communal Trauma in Higher Education: The Effects of COVID-19 Trauma on U.S. Higher Education Professionals
Shane Borah
The COVID-19 pandemic has disrupted campus life in unprecedented ways. In response, higher education professionals have adapted, reframed, and provided support to students and colleagues while navigating the unknown world of the pandemic themselves. To better understand the effect COVID-19 may have on higher education professionals, this study introduces a conceptual form of connective trauma experience in the form of communal pervasive trauma. This research study examined (1) How does COVID-19 affect higher education professionals’ relationship with their work? (2) What effects does a pervasive communal traumatic experience, such as COVID-19, have on higher education professionals? Utilizing a phenomenological approach, nine mid- to senior-level higher education professionals across three different institutions in the Midwest, West, and Pacific and varying functional areas were interviewed. Results indicate an explorative developmental experience with one’s work across the pandemic, feelings of exhaustion from impossible expectations and limited resources, and personal disconnection and grief of sense of community and identity outside of work. This study provides implications for higher education and student affairs professionals in supporting their often overworked staff, notions of healing after tragedy, and how to continue functioning once the pandemic has ceased.
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Possible pharmacologic glioma treatment in Drosophila model
Catherine Martini, Anthony Latronica, Sadie Salmone, Angela Murrin, Nathan Haulthus, Kaitlynn Alleman, Elizabeth Conley, Kathleen Mcaslin, Laura Ann Bute, Molly Herr, Sofia Sacchetti, Karishma Gangwani
Glioma is a lethal brain cancer, and current treatment strategies have limited effects by extending life only by a few months. Thus, efforts should be made to discover better inhibitors of glioma growth. Ideally such inhibitors will suppress the progression of glioma by (a) inhibiting the underlying molecular pathways activated in glioma, or (b) prevent rapid proliferation of the glia and other cells that encompass the glioma tumor. We have developed a glioma model by co-activating PI3K and Ras/MAPK specifically in the Drosophila CNS glia. The Drosophila glioma cause the larval brain to appear enlarged due to rapid increase in the stem cells and their glial and neural progeny. These tumors cause the larvae to enter a prolonged larval phase, and eventually kill the organism. We are conducting a chemical screen using Tyrosine kinase inhibitors (Selleck Biochem.) in which we feed early third instar (72h old) larvae 10 or 300uM chemicals in DMSO and then see effects on glioma growth, and survival in mature third instar stage (120h old). Using these metrics, here we present data from our screen on B1-B11 of the library. Once we identify potential glioma inhibitors in the primary screens, we will validate them in secondary screens.
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Post-freeze recovery is delayed with repeated freeze-thaw cycles in Cope's gray treefrog Dryophytes chrysoscelis
Elizabeth R. Evans
Cope’s gray treefrog Dryophytes chrysoscelis is among a unique group of freeze tolerant vertebrates that can successfully freeze and thaw up to 70% of extracellular fluids. Previous studies have shown that the accumulation of cryoprotectants such as glycerol is vital to surviving the physiological stresses associated with freezing and thawing. Though D. chrysoscelis certainly experiences several freeze-thaw cycles annually in a natural setting, studies prior to this work have included one round of freeze-thaw in experimental protocols only. The objective of this study, therefore, is to document the post-freeze recovery of D. chrysoscelis with multiple rounds of freeze-thaw in a laboratory setting by observing several morphological and physiological factors associated with post-freeze recovery. Before freezing, animals were first cold acclimated and maintained at an environmental temperature of 5°C. Environmental temperature was lowered to -2.5°C over 7 days, at which point animals were inoculated with ice to initiate crystallization. After 24 hours in a frozen state, animals were permitted to thaw at 5°C, concluding a single freeze-thaw cycle. Of this cohort, a subset was selected for two additional rounds of freeze-thaw in which animals were rapidly cooled to -2.5°C and frozen over 24 hours then permitted to thaw at 5°C for 24 hours. Each thawing period was documented by observation and digital photography to characterize changes in skin color, respiratory function, neurological function, and muscular function associated with post-freeze recovery. Preliminary data suggests that post-freeze recovery of most morphological and behavioral factors observed were delayed in animals that had been repeatedly frozen and thawed compared to animals that had been frozen and thawed once. The trends observed in this study suggest that animals may experience increased physiological stresses with repeated freeze-thaw, providing novel and ecologically relevant insights into the natural freeze tolerance of D. chrysoscelis.
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Predation in the prairie “canopy”: What happens when leashed grasshoppers meet invasive tawny crazy ants?
Samantha Johnson, Ryan W. Reihart
Biological invasions have become a global concern, as invasive species are one of the leading causes for loss of biodiversity. Invasive ants, for example, often rapidly reach numerical dominance in invaded ecosystems, which results in a reduction in the abundance and diversity of native ants and small, non-ant arthropods. Because invasive ants are small, relatively few studies have considered the potential effect of invasive ants on the abundance of large, mobile aboveground insects. Here, we report evidence of grasshopper predation and the diet of an invasive ant, Nylanderia fulva, in a coastal tallgrass prairie. While working at the University of Houston’s Coastal Center in July 2016, we observed a large number of dead grasshoppers that were covered by N. fulva. To determine if grasshopper mortality was due to predation by N. fulva, we conducted a tethering experiment. We tethered 40 grasshoppers, 10 individuals of 2 grass feeding species and 10 individuals of 2 mixed feeding species, with a modified “leash” that was secured to the ground. Within the first 4 hours of the experiment, we found that 50% of the grasshoppers were dead and were covered by N. fulva. Following this experiment, we conducted a stable isotope analysis in 2017 to determine the trophic position and relative importance of grasshoppers in the diet of N. fulva. Across 20 different colonies of N. fulva, we found that workers had little variation in their average δ15N (mean ± SD; 5.44 ± 0.49), δ13C (-21.78 ± 0.86), and trophic position (2.29 ± 0.14). These results indicate that N. fulva are omnivores, but obtain most of their N from basal resources, like plants. Our data demonstrate some of the complexities of the diets of invasive ants and highlight their potential to reduce the abundance and richness of large, mobile insects like grasshoppers.
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President Donald Trump’s Rhetoric and its impact on Students
Lastacia Lanae Patterson
The overall purpose of the study is to look at Former President Trump’s rhetoric and its impact on racial tensions from the viewpoint of College students. This research looked to understand its impact on college students and their thinking about how to overcome racism. The study research consisted of ten questions: 2 collecting basic demographic of the participants, 7 Likert scale questions determining attitudes, and one open-ended question asking for suggestions for reducing racial tensions. . The survey received 28 responses. Eighty-nine percent of all respondents agree or strongly agreed that the election of Donald Trump worsened racial tensions. Almost 80% agreed or strongly agreed that Donald Trump is racist. Also, seventy-one percent agreed or strongly agreed that Donald Trump supports white supremacy. I noticed 8 themes in the open response question. These included education, equality, Laws & policy, Positive Coverage, Diversity, nonviolence, unknown. However, Education, Equality, and Law & policy were most prevalent. In conclusion, this research demonstrates that a strong majority of College students perceived Trump’s rhetoric as racist and they have suggestions on how to reduce racial tensions.
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Pretreating Anaerobic Listeria monocytogenes with Propionate Enhances Subsequent Intracellular Infection
Laura Marie McFarland
Listeria monocytogenes is a Gram-positive facultative intracellular pathogen, responsible for the foodborne illness listeriosis. During the infection process, L. monocytogenes is commonly exposed to propionate, a short chain fatty acid found in our gut and used as a food preservative. Although propionate is known to exhibit antimicrobial and anti-inflammatory properties, its role in L. monocytogenes pathogenesis is not clear. Therefore, I seek to further establish the effect of L. monocytogenes propionate exposure on subsequent infection. RAW264.7 macrophages infected with L. monocytogenes strain 10403s were used to assess intracellular growth. Plaque assays were performed with L fibroblasts to determine long-term impact of propionate exposure. Anaerobic L. monocytogenes pretreated with propionate was exhibited a significant increase in intracellular growth compare to untreated anaerobic L. monocytogenes. Furthermore, plaque sizes of propionate-treated anaerobic L. monocytogenes were significantly larger than plaque sizes from untreated L. monocytogenes. However, propionate pretreatment of aerobic L. monocytogenes exhibited no effect on subsequent intracellular growth or spread. These results indicate that propionate exposure of anaerobic L. monocytogenes prior to infection has a long-lasting impact on enhancing subsequent intracellular infection and cell-to-cell spread.
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Professional Office Personnel in Dayton
Caroline Anne Cochran, Emily V. Quick, Delaney Strzyz
Our topic is a HRS200 Project on advocacy work that has been done at the school through an organization called The Professional Office Personnel. Our team’s research focus is looking at how secretarial staff at the University of Dayton worked through an organization called POP to advocate for their working condition rights. The presentation will highlight research we have completed for HRS200 in the University Archive files. This will reflect Human rights issues here at the University such as gender equality and ones put forth by UDHR article 23. Research is important to the team and course because it allows us to build knowledge and apply what we have learned in class for advocacy of these issues. Researching POP can help us to spread awareness about gender equality and the workplace conditions that need to be addressed/changed and how they succeeded in doing so.
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Propeller and Propeller-in-Wing Thrust Vectoring
Grace Gabrielle Culpepper
In this study, we investigate the efficiency of a thrust vectoring system utilizing a set of vanes designed to create forward force at a minimum loss in net thrust, the system itself placed in both a stand-alone propeller configuration and a propeller-in-wing configuration. Both static and wind-on force-based experiments were conducted at the University of Dayton Low Speed Wind Tunnel (UDLSWT) with off-the-shelf R/C propellers. A square propeller sheath was incorporated for static testing and a propeller-wing integrated setup was the focus of wind-on experiments. Sensitivity analysis was conducted to determine the effect on thrust vectoring of vane tilt angle and propeller placement with respect to the upper surface of the integrated wing. Static test results indicated notable improvement in vane performance when placing the vane system in a wing as compared to the stand-alone sheathed design. Thrust vectoring was achieved, along with subsequent changes in pitching moment, by increasing vane deflection angle. Wind tunnel test results of the integrated propeller-in-wing system for the standard 90° pitch orientation indicated successful thrust vectoring below the advance ratio of 0.3, which is practical for most relevant applications. The 75° pitch orientation of the propeller-vane system observed increased thrust vectoring capabilities extending to an advance ratio of 0.7. Sensitivity analysis results revealed that the case of the propeller exposed to the flow freestream outperformed that of the propeller embedded in the test wing in overall efficiency, though the embedded featured a better thrust vectoring capability.
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Public Health Worker Perceptions of Black Infant Mortality in Dayton
Shyanne Smith
Constructing a study around the perceptions of black infant mortality from the very public health workers of Dayton allows a look at what rates currently exist and why it should matter. I sat down with several employees of the Public Health Department of Montgomery County for a 25-30 minute interview to get their perceptions of why black infant mortality is so high. Looking at black infant mortality rates from other states and cities gives a wider scope of the factors that contribute to them. Dayton Public health workers see preterm birth, high blood pressure, and racism, to name a few, as the major issue(s) here and express a hope that providing adequate resources and education can help stabilize and lower black infant mortality rates. If the rates are so high and worrisome that similar issues from research studies all over the country, and from earlier years, are being repeated in Dayton and are well known by the health workers here, it sheds a light on those causes and ultimately points people towards the main issues.
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Public Relations Theory: COM 555 Class Presentations
LNU Arshi Ara Khan, Christian Jesus Cabrera, Ziyi Chen, Kaellyn Joy Duerr, Pat M. Enright, Ian A. Evans, Claire B. Mahoney, Nicholas D. Orrill, Alyssa L. Reed, Colin P. Riordan, Sara K. Sweeterman, Rebecca Westphal, Erin Whalen
Students in the graduate course COM 555: Public Relations Theory will present their final research projects that examine and analyze emerging theories, principles, concepts, and research methods in the field of public relations. Research focusing on social media integration, nonprofit-public relationship building, integration of dialogic communication in community policing, and more will be presented.
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Reconstruction and Solvability
Sarah Josephine Herr
A graph is a mathematical object that consists of two sets: a set of vertices and a set of edges. An edge joins two vertices and depicts a relationship between those vertices. The following is a project for MTH 466 - Graph Theory and Combinatorics. The Reconstruction Conjecture states that any unknown graph that has at least five vertices can be reconstructed from knowing the “deck” of all its induced subgraphs that have one vertex removed. We will explore the validity of this conjecture. We will also consider ways of determining that a given deck of graphs is either an incorrect set or not the full set of induced subgraphs of a fixed graph and therefore unusable in reconstruction.
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Recurrence Interval of Hurricane Level Flooding in the Florida Panhandle
Ripken James Pacovsky
Hurricane Sally’s landfall in the Gulf Coast marked the fourth consecutive year of a slow-moving tropical system devastating the region with insurmountable rainfall, flooding and storm surge. With an estimated cost of over $7 billion in total damage and being the direct cause of 8 fatalities, Hurricane Sally broke storm records along the southern coasts of Alabama, Mississippi and the Florida panhandle. Using daily water discharge data from the USGS 02375500 station in the Escambia River near Century, FL, the river recorded nine consecutive days above its flood stage. The majority of the inundation and flood damage occurred between the 16th and 20th of September 2020 as the hurricane passed over Escambia County, FL. Peak discharge (in cubic feet per second) of the river occurred on the 17th and slowly declined after. Using historical data from the United States Geological Survey and National Oceanic and Atmospheric Administration, it is possible to estimate how often comparable levels of flooding will occur in the area. Knowing the recurrence of severe flooding is beneficial for homeowners, businesses and municipalities to make preparations and be insured. Compiling all daily discharge and gage height measurements of the Escambia River from 1934-2021, the recurrence interval of Hurricane Sally-level flooding was found to be ~6.8 years. In a given year, the probability of Hurricane Sally level flooding is about 15 in 100. Flood levels just below Hurricane Sally were found to have a much greater probability. With a predicted rise in sea level, this recurrence interval can be expected to shorten in the future. The outdated flood control systems from the 1900s will need to be updated this century to keep on pace with frequent and more extreme flood events.
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Religion and Food Justice
Emillie Anna Boyd, Josie K. Forsthoff, Abby Danae Hentz, Sebastián Edniel Serrano Préstamo
This collaborative study asks about the intersection of religious belief and food insecurity. The purpose was to explore the connections between food practices, religious belief, religious identity, food insecurity, and food justice. A literature review of relevant scholarly articles in sociology, psychology, anthropology, and interdisciplinary social sciences revealed that religious identity can be expressed and affirmed by food practices. Food justice advocates and volunteers often attribute their service with their religious beliefs, and providing adequate food can be an opportunity for religious or spiritual dialogue. Religious minorities in the United States, like Islam, especially rely on access to specific food for religious dietary rules that express their faith in a sometimes harsh environment. This harsh environment makes food practices more psychologically and religiously significant but also more difficult to follow when access to the specific foods is considered niche. In secular and religious organizations alike we found that religious beliefs motivated workers in food justice and food banks who worked in service of their community. Another study showed evidence that being more religious did not necessarily make a society more likely to share, but the presence of need and food supply stress predicted increased sharing of labor and food. While the service is attributed to religious belief, the need is the main catalyst. Lastly, religious dialogue has been seen to thrive in areas of community service, and food banks and justice movements are not an exception. All of these points and sources suggest that food insecurity is much more closely related to religious belief and identity than expected.
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Religion and Technology: Working for the Common Good
Tyler J. Delahanty, Emily Melissa Foppe, Benjamin M. Grawe, Emily Eileen Nugent
Many individuals believe that religion and science oppose each other, one working for morality and the other supporting the rejection of God and practice of actions that are immoral. This study investigates specifically how religious groups interact with technology. The literature review explored whether religious groups utilize technology as a tool that can help them achieve their goal, or if they view technology as the enemy that they are opposing. Seeing how different religious groups interact with technology is an extremely interesting subject. Our article analysis explored the interactions of various religious groups with technology and found that specific religious groups interact with specific technological advancements differently. Groups utilize and oppose specific technological advancements based on their own beliefs and contexts.
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Religion's Influence on Political Behavior in the U.S.
Matthew Michael Austin, Rosalie Ann Hopkins, Jacob M. Mantle, Matthew S. Ostermueller
The topic of study is to examine the relationship between religion and politics in the United States from a sociological, anthropological, and psychological perspective. More specifically, the three major groups studied were Christianity, Islam, and unaffiliated to see what their positions were on the different political ideas in the United States. Previous research has indicated that there is a strong relationship between religion and politics, and, in most cases, most peoples’ religious beliefs influence the ways in which they vote and the political ideologies they possess. This literature review examined the ways in which this relationship has changed in today’s volatile political climate. Several studies used methods including surveys, implicit association tests, and immersion to collect solid data to inform our research. The findings were as expected--religion is a major determining factor in the way people vote. However, the differences come when different religions are contrasted with each other (e.g., Catholicism and Islam) and we are able to see how their different beliefs lead them to take on different political beliefs.
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Resolving the gene regulatory network for a fruit fly pigmentation trait whose modification underlies climate-driven phenotypic variation
Jenna Rose Rock
Species are in the midst of surviving changing climates that require ancestral trait phenotypes to convert to derived states better adapted to the present conditions. Adaptations can occur through genetic differences, raising questions how such differences translate into phenotypic change. A prerequisite to answering these evolutionary questions is to understand the genetic basis for trait development. In animals, traits are made by developmental programs known as gene regulatory networks (GRNs) that are hardwired in genomic DNA sequence. Each GRN includes a fraction of the genes within an organism’s genome, notably some that encode transcription factors that regulate the expression of the trait-making differentiation genes. This regulation occurs by certain transcription factors interacting with short DNA sequences, called binding sites, in gene regions known as cis-regulatory elements (CREs). For any CRE, its ability to activate gene expression in specific cell types and developmental times is due to the binding sites it possesses for a particular combination of transcription factors. To date, a GRN for a climate adapted trait has not been resolved. Thus, understanding how GRNs and their genes and CRE constituents facilitate or stymie adaptation remains speculative. For the Berry Summer Thesis Institute research, I propose to resolve the GRN responsible for a pigmentation pattern on the abdomen of Drosophila melanogaster fruit flies. Preliminary work has revealed many of the genes for this GRN, though the connections between transcription factors and CRE binding sites remain largely unknown. By using genetic, bioinformatic, and microscopy approaches, I will resolve the important connections that orchestrate this GRN’s operation. Success here will enable future efforts to reveal how this GRN has been reformulated to deal with differing climates, findings that bear upon the genetic underpinnings of animal adaptations more broadly.
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Revitalization of the Hero's Journey
Mary Kathryn Caserta
My practicum Capstone will provide an analysis of Joseph Campbell’s work to understand why Campbell’s model has been commonly employed in the classroom and involve a unit plan that modernizes the hero’s journey. The overarching goal of my proposed research will allow young, secondary school readers to more deeply connect with the hero’s journey and, through their narrative work and literary analyses, more deeply consider the importance of literature in their personal lives when the protagonists are more diverse. An updated model that accounts for these discriminatory practices that heroes face allows for contemporary discourse about the various steps of the hero’s journey; therefore, allowing the heroes in question to be critiqued and analyzed through a modern lens. In secondary education, the hero’s journey can allow for deeper engagement with texts when students are able to broaden their view as to who a hero truly is- is the hero always the muscled Hercules, or can it also be a scrawny girl from a novel who rises above the expectations set before her? Joseph Campbell’s hero’s journey is missing elements that should be included to update his seventeen-step model for contemporary audiences; in this practicum, I combine Campbell’s framework with some missing elements and stages that modern readers face on their personal hero’s journeys. An updated model of the hero’s journey will include a variety of heroic protagonists, specifically protagonists that further align with contemporary views regarding intersectional texts which explore gender, race, age, and preconceived abilities.
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Riemann Sum Construction to Obtain the Power Rule for Integral Calculus
Siobhan R. Chawk, Alison L. Hardie
The power rule for integration is highly studied and applied in calculus. Integral calculus is widely used in various fields outside of mathematics including science and engineering. There are multiple methods of solving integrals and this poster will demonstrate a proof of the power rule for integration through the construction of a Riemann sum. The integral that this poster will focus on is the integral of x to the power of k, in which k is assumed to be positive and rational. The sum constructed in this poster utilizes a geometric partition. Following the construction of the lower Riemann sum the limit as n approaches infinity is taken to eliminate the dependence on n. An upper Riemann sum is constructed, and the sandwich theorem is applied to the two sums to complete the proof of the original statement.
The Brother Joseph W. Stander Symposium recognizes and celebrates academic excellence in undergraduate and graduate education. This annual event provides an opportunity for students from all disciplines to showcase their intellectual and artistic accomplishments and embody the University's mission to be a "community of learners." This collection contains a sampling of the more than 200 projects presented each year during the symposium.
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