Cohen-Macaulay Circulant Graphs

Let G be the circulant graph C_n(S) with S a subset of {1,2,...,\lfloor n/2 \rfloor}, and let I(G) denote its the edge ideal in the ring R = k[x_1,...,x_n]. We consider the problem of determining when G is Cohen-Macaulay, i.e, R/I(G) is a Cohen-Macaulay ring. Because a Cohen-Macaulay graph G must be well-covered, we focus on known families of well-covered circulant graphs of the form C_n(1,2,...,d). We also characterize which cubic circulant graphs are Cohen-Macaulay. We end with the observation that even though the well-covered property is preserved under lexicographical products of graphs, this is not true of the Cohen-Macaulay property.Comment: 14 page

Physiologically-based Pharmacokinetics in Critically Ill Children

Extracorporeal membrane oxygenation (ECMO) is used to support cardiorespiratory failure in critically ill infants, children, and adults. In these vulnerable populations, the effect of ECMO on drug disposition leaves clinicians with uncertainty about dosing. The goal of this dissertation research was to develop a physiologically-based pharmacokinetic (PBPK) modeling approach that translated results from ex vivo ECMO studies to bedside dosing recommendations. To determine optimal dosing, the impact of the ECMO circuit on antifungal disposition was first assessed in isolation through ex vivo studies of three antifungal drugs. These experiments showed variable degrees of extraction by the ECMO circuit with micafungin highly extracted and fluconazole and amphotericin B deoxycholate with limited extraction. These results were then used to parameterize drug-specific ECMO compartments in the PBPK models. Model building followed an established workflow whereby a PBPK model was developed in adults and scaled to children. Once the Pediatric PBPK Model met acceptance criteria, an ECMO compartment was added to the Pediatric PBPK Model to form the ECMO PBPK Model. The fluconazole ECMO PBPK Model over-predicted exposure (1.13 fold error) but was within the pre-specified acceptance criteria of 0.7-1.3 fold error. PBPK-predicted dosing recommendations showed good agreement with recommendations based on the Fluconazole ECMO PK Trial. The micafungin ECMO PBPK Model also over-predicted exposure (1.16 fold error), but, again, dosing recommendations were in close agreement with recommendations determined from the trial. The two clinical PK trials of fluconazole and micafungin in children on ECMO were performed in parallel with the PBPK model building. Both the Fluconazole and Micafungin ECMO PK Trials showed that exposure was significantly lower in children on ECMO compared to children not on ECMO. Although determining optimal dosing for these two commonly used drugs in children on ECMO was important, more importantly, the PBPK modeling developed in this dissertation demonstrated the utility of this approach to understand and quantify the physiologic alterations driving drug disposition in critically ill children. A more precise, refined, integrated approach for drug dosing in this pediatric sub-population will improve both the safety and efficacy of drug therapy in children supported with ECMO.Doctor of Philosoph

Palladium(II) Catalyzed C–H Functionalization Cascades for the Diastereoselective Synthesis of Polyheterocycles

C–H activation offers huge potential in the generation of complex structures from simple starting materials. Herein we report the development of a highly diastereoselective palladium­(II) catalyzed C–H functionalization cascade to produce novel, unsaturated polyheterocycles from simple diene-tethered heterocyclic starting materials. The reaction is applicable to both indole and pyrrole based substrates and tolerates a wide range of functional group substitutions around the heteroaromatic core. The polyheterocyclic products are formed as single diastereoisomers, with two new stereocenters formed in a single step

The ISOSAT Small Satellite: A Design in Isogrid Technology

ISOSAT, a small hexagonal shaped satellite structure, was designed and constructed in the Industrial Technology Department at Utah State University as a senior research project using automated manufacturing techniques and incorporating the Isogrid structure concept. Isogrid applications can be found in projects such as Skylab, most cylindrical structural elements of the Delta rocket and in the engine shrouds of Boeing\u27s new 777 commercial airliners. The basis of the Isogrid is the repeating pattern of equilateral triangles which make up the structure. This pattern, machined into solid aluminum plates, results in a substantial weight savings with an acceptable reduction in structural strength. The intersections of adjacent triangles are referred to as nodes. These nodes serve as uniformly distributed attachment points for the mounting of instrumentation and other hardware

Pharmacokinetics and Safety of Micafungin in Infants Supported With Extracorporeal Membrane Oxygenation

Candida is a leading cause of infection in infants on extracorporeal membrane oxygenation (ECMO). Optimal micafungin dosing is unknown in this population because ECMO can alter drug pharmacokinetics (PK)

Pd(II)-Catalyzed [4 + 2] Heterocyclization Sequence for Polyheterocycle Generation

A new Pd­(II)-catalyzed cascade sequence for the formation of polyheterocycles, from simple starting materials, is reported. The sequence is applicable to both indole and pyrrole substrates, and a range of substituents are tolerated. The reaction is thought to proceed by a Pd­(II)-catalyzed C–H activated Heck reaction followed by a second Pd­(II)-catalyzed aza-Wacker reaction with two Cu­(II)-mediated Pd(0) turnovers per sequence. The sequence can be considered a formal [4 + 2] heterocyclization

The tammar wallaby: a marsupial model to examine the timed delivery and role of bioactives in milk

It is now clear that milk has multiple functions; it provides the most appropriate nutrition for growth of the newborn, it delivers a range of bioactives with the potential to stimulate development of the young, it has the capacity to remodel the mammary gland (stimulate growth or signal cell death) and finally milk can provide protection from infection and inflammation when the mammary gland is susceptible to these challenges. There is increasing evidence to support studies using an Australian marsupial, the tammar wallaby (Macropus eugenii), as an interesting and unique model to study milk bioactives. Reproduction in the tammar wallaby is characterized by a short gestation, birth of immature young and a long lactation. All the major milk constituents change substantially and progressively during lactation and these changes have been shown to regulate growth and development of the tammar pouch young and to have roles in mammary gland biology. This review will focus on recent reports examining the control of lactation in the tammar wallaby and the timed delivery of milk bioactivity

Overexpression of Carnitine Palmitoyltransferase-1 in Skeletal Muscle Is Sufficient to Enhance Fatty Acid Oxidation and Improve High-Fat Diet–Induced Insulin Resistance

OBJECTIVE—Skeletal muscle insulin resistance is associated with lipid accumulation, but whether insulin resistance is due to reduced or enhanced flux of long-chain fatty acids into the mitochondria is both controversial and unclear. We hypothesized that skeletal muscle–specific overexpression of the muscle isoform of carnitine palmitoyltransferase 1 (CPT1), the enzyme that controls the entry of long-chain fatty acyl CoA into mitochondria, would enhance rates of fatty acid oxidation and improve insulin action in muscle in high-fat diet insulin-resistant rats