Coverings of Graphs and Tiered Trees

This dissertation will cover two separate topics. The first of these topics will be coverings of graphs. We will discuss a recent paper by Marcus, Spielman, and Srivastava proving the existence of infinite families of bipartite Ramanujan graphs for all regularities. The proof works by showing that for any d-regular Ramanujan graph, there exists an infinite tower of bipartite Ramanujan graphs in which each graph is a twofold covering of the previous one. Since twofold coverings of a graph correspond to ways of labeling the edges of the graph with elements of a group of order 2, we will generalize the content of the recent paper by discussing what happens when we label the edges of a graph by larger groups. We will give a version of their proof using threefold coverings instead of twofold coverings. We will also examine ways of reducing the size of the set of twofold coverings that we must consider when we follow the proof by Marcus, Spielman, and Srivastava. The other topic that will be covered in this dissertation will be alternating trees and tiered trees. We will define a new generalization of alternating trees, which we will call tiered trees. We will also define a generalized weight system on these tiered trees. We will prove some enumerative results about tiered trees that demonstrate how they can be viewed as being obtained by applying certain procedures to certain types of alternating trees. We also provide a bijection between the set of permutations in Sn and the set of weight 0 alternating trees with n+1 vertices. We use this bijection to define a new statistic of permutations called the weight of a permutation, and use this weight to define a new q-Eulerian polynomial

UC-491 Spectrum Analysis CLI Tool

The Spectrum Analysis CLI Tool takes in .mp4 recordings of a Spectrum Analyzer, converts them programmatically into values the application can understand and outputs this data into a .csv file. This file can be parsed/filtered by the user with commands during upload of the .mp4 recording, or anytime after the recording has been processed

Tiered trees, weights, and q-Eulerian numbers

Maxmin trees are labeled trees with the property that each vertex is either a local maximum or a local minimum. Such trees were originally introduced by Postnikov [12], who gave a formula to count them and different combinatorial interpretations for their number. In this paper we generalize this construction and define tiered trees by allowing more than two classes of vertices. Tiered trees arise naturally when counting the absolutely indecomposable representations of certain quivers, and also when one enumerates torus orbits on certain homogeneous varieties. We define a notion of weight for tiered trees and prove bijections between various weight 0 tiered trees and other combinatorial objects; in particular order n weight 0 maxmin trees are naturally in bijection with permutations on n−1 letters. We conclude by using our weight function to define a new q-analogue of the Eulerian numbers

Proceedings of Patient Reported Outcome Measure’s (PROMs) Conference Oxford 2017: Advances in Patient Reported Outcomes Research

A33-Effects of Out-of-Pocket (OOP) Payments and Financial Distress on Quality of Life (QoL) of People with Parkinson’s (PwP) and their Carer

Nebulized Tranexamic Acid in Secondary Post-Tonsillectomy Hemorrhage: Case Series and Review of the Literature

Introduction: Post-tonsillectomy hemorrhage is a serious postoperative complication, and its acute management can present a challenge for the emergency provider. Although various strategies have been proposed, guidance on the best approach for management of this condition in the emergency department (ED) setting remains limited. Anecdotal reports of the use of nebulized tranexamic acid (TXA) for management of tonsillar bleeding have emerged over the past two years. Two recently published case reports describe the successful use of nebulized TXA for stabilization of post-tonsillectomy hemorrhage in an adult and a pediatric patient.Case Series: Eight patients who presented to our ED with secondary post-tonsillectomy hemorrhage received nebulized TXA for hemostatic management. The most common TXA dose used was 500 milligrams, and all but one patient received a single dose of the medication in the ED. Hemostatic benefit was observed in six patients, with complete bleeding cessation observed in five cases. Interventions prior to nebulized TXA administration were attempted in three of the six patients and included ice water gargle, direct pressure with TXA-soaked gauze, and nebulized racemic epinephrine. All but one of the patients were taken to the operating room for definitive management after initial stabilization in the ED. Conclusion: Nebulized TXA may offer a hemostatic benefit and aid in stabilization of tonsillectomy hemorrhage in the acute care setting, prior to definitive surgical intervention.  Consideration of general principles of nebulization and aerosol particle size may be an important factor for drug delivery to the target tissue site