Wiener Index and Remoteness in Triangulations and Quadrangulations

Let $G$ be a a connected graph. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. We provide asymptotic formulae for the maximum Wiener index of simple triangulations and quadrangulations with given connectivity, as the order increases, and make conjectures for the extremal triangulations and quadrangulations based on computational evidence. If $\overline{\sigma}(v)$ denotes the arithmetic mean of the distances from $v$ to all other vertices of $G$, then the remoteness of $G$ is defined as the largest value of $\overline{\sigma}(v)$ over all vertices $v$ of $G$. We give sharp upper bounds on the remoteness of simple triangulations and quadrangulations of given order and connectivity

Distance Related Graph Invariants in Triangulations and Quadrangulations of the Sphere

The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. I provide asymptotic upper bounds and sharp lower bounds for the Wiener index of simple triangulations and quadrangulations with given connectivity. Additionally, I make conjectures for the extremal triangulations and quadrangulations which maximize the Wiener index based on computational evidence. If σ(v) denotes the arithmetic mean of the distances from v to all other vertices of G, then the remoteness and proximity of G are defined as the largest and smallest value of σ(v) over all vertices v of G, respectively. I give sharp upper bounds on the remoteness and asymptotic upper bounds on the proximity of simple triangulations and quadrangulations of given order and connectivity

Sampling and Robustness in Multi-Robot Visibility-Based Pursuit-Evasion

Given a two-dimensional polygonal space, the multi-robot visibility-based pursuit-evasion problem tasks several pursuer robots with the goal of establishing visibility with an arbitrarily fast evader. The best-known complete algorithm for this problem takes time doubly exponential in the number of robots. However, sampling-based techniques have shown promise in generating feasible solutions in these scenarios. Existing sampling-based algorithms have long execution times and high failure rates for complex environments. We first address that limitation by proposing a new algorithm that takes an environment as its input and returns a joint motion strategy which ensures that the evader is captured by one of the pursuers. Starting with a single pursuer, we sequentially construct data structures called Sample-Generated Pursuit-Evasion Graphs to create such a joint motion strategy. This sequential graph structure ensures that our algorithm will always terminate with a solution, regardless of the complexity of the environment. Another aspect of this problem that has yet to be explored concerns how to ensure that the robots can recover from catastrophic failures which leave one or more robots unexpectedly incapable of continuing to contribute to the pursuit of the evader. To address this issue, we propose an algorithm that can rapidly recover from catastrophic failures. When such failures occur, a replanning occurs, leveraging both the information retained from the previous iteration and the partial progress of the search completed before the failure to generate a new motion strategy for the reduced team of pursuers. The final contribution is a novel formulation of the pursuit-evasion problem that modifies the pursuers\u27 objective by requiring that the evader still be detected, even in spite of the malfunction of any single pursuer robot. This novel constraint, whereby two pursuers are required to detect an evader, has the benefit of providing redundancy to the search, should any member of the team become unresponsive, suffer temporary sensor disruption/failure, or otherwise become incapacitated. The proposed formulation produces plans that are inherently tolerant of some level of disturbance. For each contribution discussed above, we describe an implementation of the algorithm and provide quantitative results that show substantial improvement over existing results

Senior Recital: Jacob Greifinger, trumpet

This recital is presented in partial fulfillment of requirements for the degree Bachelor of Music in Performance. Mr. Greifinger studies trumpet with Michael Tiscione.https://digitalcommons.kennesaw.edu/musicprograms/2224/thumbnail.jp

Observational Diagnoses of Extratropical Ozone STE from 2005-2010

The transport of ozone from the stratosphere to the extratropical troposphere is an important boundary condition to tropospheric chemistry. However, previous direct estimates from models and indirect estimates from observations have poorly constrained the magnitude of ozone stratosphere-troposphere exchange (STE). In this study we provide a direct diagnosis of the extratropical ozone STE using data from the Microwave Limb Sounder on Aura and output of the MERRA reanalysis over the time period from 2005 to the present. We find that the mean annual STE is about 275 Tg yr-1 and 205 Tg yr-1 in the NH and SH, respectively. The interannual variability of the magnitude is about twice as great in the NH than the SH. This variability is dominated by the seasonal variability during the late winter and spring. A comparison of the ozone flux to the mass flux reveals that there is not a simple relationship between the two quantities. This presentation will also examine the magnitude and distribution of ozone in the lower stratosphere relative to the years of maximum and minimum ozone ST

Restaurant cooking trends and increased risk for Campylobacter infection

In the United Kingdom, outbreaks of Campylobacter infection are increasingly attributed to undercooked chicken livers, yet many recipes, including those of top chefs, advocate short cooking times and serving livers pink. During 2015, we studied preferences of chefs and the public in the United Kingdom and investigated the link between liver rareness and survival of Campylobacter. We used photographs to assess chefs’ ability to identify chicken livers meeting safe cooking guidelines. To investigate the microbiological safety of livers chefs preferred to serve, we modeled Campylobacter survival in infected chicken livers cooked to various temperatures. Most chefs correctly identified safely cooked livers but overestimated the public’s preference for rareness and thus preferred to serve them more rare. We estimated that 19%-52% of livers served commercially in the United Kingdom fail to reach 70°C and that predicted Campylobacter survival rates are 48%-98%. These findings indicate that cooking trends are linked to increasing Campylobacter infections

Human Monoclonal Antibody HCV1 Effectively Prevents and Treats HCV Infection in Chimpanzees

Hepatitis C virus (HCV) infection is a leading cause of liver transplantation and there is an urgent need to develop therapies to reduce rates of HCV infection of transplanted livers. Approved therapeutics for HCV are poorly tolerated and are of limited efficacy in this patient population. Human monoclonal antibody HCV1 recognizes a highly-conserved linear epitope of the HCV E2 envelope glycoprotein (amino acids 412-423) and neutralizes a broad range of HCV genotypes. In a chimpanzee model, a single dose of 250 mg/kg HCV1 delivered 30 minutes prior to infusion with genotype 1a H77 HCV provided complete protection from HCV infection, whereas a dose of 50 mg/kg HCV1 did not protect. In addition, an acutely-infected chimpanzee given 250 mg/kg HCV1 42 days following exposure to virus had a rapid reduction in viral load to below the limit of detection before rebounding 14 days later. The emergent virus displayed an E2 mutation (N415K/D) conferring resistance to HCV1 neutralization. Finally, three chronically HCV-infected chimpanzees were treated with a single dose of 40 mg/kg HCV1 and viral load was reduced to below the limit of detection for 21 days in one chimpanzee with rebounding virus displaying a resistance mutation (N417S). The other two chimpanzees had 0.5-1.0 log(10) reductions in viral load without evidence of viral resistance to HCV1. In vitro testing using HCV pseudovirus (HCVpp) demonstrated that the sera from the poorly-responding chimpanzees inhibited the ability of HCV1 to neutralize HCVpp. Measurement of antibody responses in the chronically-infected chimpanzees implicated endogenous antibody to E2 and interference with HCV1 neutralization although other factors may also be responsible. These data suggest that human monoclonal antibody HCV1 may be an effective therapeutic for the prevention of graft infection in HCV-infected patients undergoing liver transplantation