All trees are six-cordial

For any integer $k>0$, a tree $T$ is $k$-cordial if there exists a labeling of the vertices of $T$ by $\mathbb{Z}_k$, inducing a labeling on the edges with edge-weights found by summing the labels on vertices incident to a given edge modulo $k$ so that each label appears on at most one more vertex than any other and each edge-weight appears on at most one more edge than any other. We prove that all trees are six-cordial by an adjustment of the test proposed by Hovey (1991) to show all trees are $k$-cordial.Comment: 16 pages, 12 figure

Inner City Artscape

The research of this project deals with multiple disciplines such as art, culture, and social connection that ultimately benefits human development and well-being. Through the architectural urban design of the main street of Hapeville, GA, this thesis aims to solve the issues of vitalization and attraction to a main city street in a design of a residential community to activate public spaces through the work and input of the creative class and local community. Ultimately, this redesign of the main street will be a catalyst of economic growth and well-being of the local community, revitalizing a home into an urban art district

The Effects of Crude Oil on the Marine Diatom, Phaeodactylum tricornutum, Grown in Silica-Enriched and Silica-Limited Conditions

This experiment was designed to determine the effects that crude oil and dispersants have on a marine diatom, Phaeodactylum tricornutum. This species was chosen as it has a siliceous frustule, which may increase its resilience to pollutant exposure. We hypothesized that P. tricornutum grown without their siliceous frustule would be more susceptible to pollutants compared to those grown with their siliceous frustule. We analyzed estimated oil equivalents, growth, photosynthetic efficiency, and macromolecular composition to examine the effects of oil and oil and dispersant exposure. P. tricornutum exhibited a high level of robustness in response to WAF and DCEWAF and a high sensitivity to CEWAF. Silica-limitation proved to be a major factor in the sensitivity of P. tricornutum to the oil and dispersants, which can be explained by significant differences in treatments with and without the presence of silica. We found that the effect of oil and dispersants on phytoplankton vary based on the environmental conditions and oil concentrations and that the effects of oil exposure are not always detrimental. These data provide an understanding of the response of this phytoplankton following an oil spill. In future studies, it would be beneficial to expand the parameters being tested to gain more insight into the physiological changes in phytoplankton cells resulting from crude oil exposure

Characterizing A Signaling Network That Maintains Hematopoietic Stem Cells

Hematopoietic stem cells (HSCs) are able to self-renew and to differentiate into all blood cells. HSCs reside in a low-perfusion niche and depend on local signals to survive and to maintain the capacity for self-renewal. HSCs removed from the niche can survive if they receive hematopoietic cytokines, but they then lose the ability to self-renew. However, we showed previously that simultaneous inhibition of glycogen synthase kinase-3 (GSK-3) and mammalian target of rapamycin complex 1 (mTORC1) maintains HSC function ex vivo without the need for exogenous cytokines. As these experiments were initially done in heterogeneous cell populations, I then showed that purified HSCs can also be maintained under these conditions, demonstrating a direct effect of GSK-3 and mTORC1 inhibition on HSCs. Although Wnt/β-catenin signaling downstream of GSK-3 is required for this response, the downstream effectors of this network remained otherwise undefined. I therefore explored targets downstream of GSK-3 and mTORC1. I found that HSCs express a pro-autophagic gene signature and accumulate LC3 puncta only when both mTORC1 and GSK-3 are inhibited, identifying autophagy as a signature for a signaling network that maintains HSCs ex vivo. In contrast, I did not find evidence to support a role for other downstream targets of mTORC1, such as protein translation and mitochondrial biogenesis. I also report a significant reduction in total RNA content in cultured HSCs and describe a method to perform transcriptional profiling of these cells. Together, these findings provide new insight into the relative contributions of various mTORC1 outputs toward the maintenance of HSC function and build upon the growing body of literature implicating autophagy and tightly controlled protein synthesis as important modulators of diverse stem cell populations

Low Dose Ketamine for Opioid Refractory Cancer Pain

Background: Sub-anesthetic ketamine is used in the hospice and palliative setting to provide analgesia for opioid refractory cancer pain. While there are case reports supporting its use for this indication, results from the few studies done are mixed. Additionally, there are no widely agreed upon guidelines for dosing. The heterogeneous results may be attributed to small sample sizes and differing doses and routes of administration of ketamine. The objectives of this case presentation is to describe the successful use of sub-anesthetic ketamine in the management of high dose opioid refractory cancer pain and to propose a new area of study in the use of sub-anesthetic ketamine for management of an opioid refractory cancer pain. Case: A 32 year old male, receiving home hospice, with stage IV gastric adenocarcinoma, complicated by severe cancer-related abdominal pain presented to the ED in a pain crisis, agitated, confused and drowsy. His pain had been managed with a fentanyl PCA at home, with a 650 mcg/hr continuous infusion and a 200mcg demand dose with a 10 minute lockout. His fentanyl use escalated over the preceding days with 31,600 mcg of fentanyl (5266 oral morphine equivalents) in the 24 hours leading up to presentation. In the ED, his fentanyl PCA was continued and he was given hydromorphone 6mg IV and dexamethasone 10mg IV without effect. He was then given a 0.3 mg/kg ketamine bolus with improvement of his pain. He was subsequently admitted to the inpatient hospice unit for further pain management. He was initiated on a low dose ketamine infusion at 0.1mg/kg/hr and was rotated to a hydromorphone PCA at a continuous infusion of 13mg/hr (which is a 25% dose reduction from total fentanyl use) and a 10mg demand dose and 10 minute lockout. His ketamine infusion was titrated upwards to 0.2mg/kg/hr with improvement of his pain. He was maintained at this rate with adequate pain control while his hydromorphone PCA was able to be tapered down to a continuous infusion of 6mg/hr (decreased by 2mg/hr daily) and demand dose of 8mg with a 10 minute lockout. He was subsequently weaned off the ketamine infusion with sustained pain control and a 50% decrease in his opioid requirement. He experienced mild non-disturbing hallucinations and vivid dreams which were adequately controlled with haloperidol and lorazepam. The patient was able to be discharged home with adequate pain control on the hydromorphone PCA with home hospice. Conclusion: This case presentation adds to the other case reports supporting the utility of sub-anesthetic ketamine in the treatment of opioid refractory cancer pain. It also identifies the use of an initial sub-anesthetic ketamine bolus as a means to identify patients that are more likely to benefit from an infusion. Current studies in the medical literature are of small scale, vary in regards to dosing and routes of administration and provide heterogeneous results. Further studies are needed with larger sample sizes, consistent dosing and consistent routes of administration to draw more definitive conclusions regarding the utility of sub-anesthetic ketamine for opioid refractory cancer pain and to guide clinical practice. It is our suggestion that these studies also investigate the use of a sub-anesthetic ketamine bolus as a means to identify patients more likely to benefit from an infusion.https://scholarlycommons.henryford.com/merf2020caserpt/1093/thumbnail.jp