Hadwiger's conjecture for graphs with forbidden holes

Given a graph $G$, the Hadwiger number of $G$, denoted by $h(G)$, is the largest integer $k$ such that $G$ contains the complete graph $K_k$ as a minor. A hole in $G$ is an induced cycle of length at least four. Hadwiger's Conjecture from 1943 states that for every graph $G$, $h(G)\ge \chi(G)$, where $\chi(G)$ denotes the chromatic number of $G$. In this paper we establish more evidence for Hadwiger's conjecture by showing that if a graph $G$ with independence number $\alpha(G)\ge3$ has no hole of length between $4$ and $2\alpha(G)-1$, then $h(G)\ge\chi(G)$. We also prove that if a graph $G$ with independence number $\alpha(G)\ge2$ has no hole of length between $4$ and $2\alpha(G)$, then $G$ contains an odd clique minor of size $\chi(G)$, that is, such a graph $G$ satisfies the odd Hadwiger's conjecture

The Kerry-Bush Health Care Proposals: A Characterization and Comparison of their Impacts on Connecticut (Full Report)

health care, connecticut, health insurance

The Kerry-Bush Health Care Proposals: A Characterization and Comparison of their Impacts on Connecticut (Executive Summary)

health care, connecticut, health insurance

The Kerry-Bush Health Care Proposals: A Characterization and Comparison of their Impacts on Connecticut (Technical Appendix)

health care, Connecticut, health insurance

The Chemistry of Flavonoids in Model Beverages and Human Milk

Interest in the chemistry and stability of flavonoids in foods has been generated by countless epidemiological, in vitro, and in vivo studies that suggest a variety of potential health promoting effects of diets rich in flavonoids. Flavonoids have been shown to interact with multiple components in beverages including macromolecules, minerals, certain vitamins, and other flavonoids. Furthermore, environmental conditions including light exposure, elevated temperatures, and relative humidity have been shown to modify flavonoid stability. However, specific mechanisms, relative kinetics of degradation reactions and the impact of macromolecules in model beverages and biological fluids on flavonoid stability remain largely unknown. Recently, interest in the application of natural pigments to replace synthetic dyes in beverages has grown. However, there is limited information concerning the impact of prominent beverage ingredients, photo and thermal stress, and the potential mechanisms involved in anthocyanin degradation. Chapter 2 of this dissertation investigates the stability of anthocyanin rich grape and purple sweet potato (PSP) extracts to photo and thermal stresses in ready-to-drink beverage models including hot-fill beverages with varying concentrations of ascorbic acid, a preserved beverage, and a vitamin enriched water beverage. Thermal and photo stress were induced at 40, 60, and 80 oC and 250, 500, and 750 W/m2, respectively. Increasing concentration of ascorbic acid resulted in more rapid degradation of anthocyanins through thermal stress, but had a protective effect through photo stress. Additionally, PSP was significantly less stable than grape extract in the vitamin enriched water model beverage through photo stress. Furthermore, a potential degradation mechanism involving the formation of monoacylated peonidins from diacylated peonidins under photo, but not thermal, stress was identified. The transfer of dietary flavonoids to human milk and the potential exposure to nursing infants quickly became of interest. Chapters 3 and 4 of this dissertation focuses on the presence of several flavonoids in human milk samples. In our initial screening, samples were collected from 17 women who delivered healthy term babies (37 wk of gestation) at 1, 4, and 13-wk postpartum intervals. Epicatechin (63.7-828.5 nmol/L), epicatechin gallate (55.7-645.6 nmol/L), epigallocatechin gallate (215.1-2364.7 nmol/L), naringenin (64.1-722.0 nmol/L), kaempferol (7.8-71.4 nmol/L),hesperetin (74.8-1603.1 nmol/L), and quercetin (32.5-108.6 nmol/L) were present in human milk samples with high inter/intraindividual variability. With the exception of kaempferol, the mean flavonoid content in human milk was not statistically different among lactation stages. In contrast, carotenoids in human milk significantly decreased from weeks 1 to 13 of lactation. In our follow up study, cohorts from the USA, China, and Mexico each comprised of 20 women in each country. Milk samples were collected at 2, 4, 13, and 26-wk postpartum intervals. Glucuronides of epicatechin, naringenin, kaempferol, hesperetin, and quercetin were the predominant metabolites detected. Despite all efforts, anthocyanins were not detected in any of the 4 cohorts between the 2 studies and their relatively low bioavailability and presence in tissue is likely a contributing factor. The presence of flavonoids in human milk suggested that select flavonoids maintained relative stability in protein rich fluid in order to avoid degradation between emptying through feeding. Previous studies indicated that polyphenols bind to proline rich segments, including those on caseins, and may have a stabilization effect. Chapter 5 investigates the impact of protein rich milk on tea flavan-3-ol degradation during thermal treatment. Single strength milk (36.2 protein per L), quarter strength milk (9.0 g protein per L), and a zero protein control models were incubated with isolated epigallocatechin gallate and green tea extract at 62 or 37oC for 180 minutes. Intact flavan-3-ols as well as auto-oxidation products including theasinesins (THSNs) and P-2 dimer concentrations were quantified by LC-MS. In general, greater polyphenol to protein ratios increased first order degradation rates, which consequently decreased the formation of THSNs and P-2 dimers. The presence of the galloyl and hydroxy moieties increased apparent affinity of flavan-3-ols to proteins, thereby stabilizing monomeric flavan-3-ols to processing conditions with increasing protein concentrations. In contrast, the absence of these moieties led to no observable interactions to proteins. A thorough understanding of protein-polyphenol interactions may provide further insight to their chemistry in protein rich beverages and biological fluid

Wireless Multi-User Communication System

The project’s ultimate goal is to send and receive information wirelessly from multiple unique users at once. Our design includes an antenna with beam-switching capabilities to serve multiple users at once. The project also focused on providing a more compact solution along with additional uplink capability and power indication. This has the potential to be used in the upcoming 5G machine to machine communication. The antenna and feed network were made smaller by making use of less conventional structures. The power indicator was made by using a digital logic circuit. These components form a proof-of-concept communication system

Emergence of Topologically Nontrivial Spin-Polarized States in a Segmented Linear Chain.

The synthesis of new materials with novel or useful properties is one of the most important drivers in the fields of condensed matter physics and materials science. Discoveries of this kind are especially significant when they point to promising future basic research and applications. van der Waals bonded materials comprised of lower-dimensional building blocks have been shown to exhibit emergent properties when isolated in an atomically thin form [1-8]. Here, we report the discovery of a transition metal chalcogenide in a heretofore unknown segmented linear chain form, where basic building blocks each consisting of two hafnium atoms and nine tellurium atoms (Hf_{2}Te_{9}) are van der Waals bonded end to end. First-principle calculations based on density functional theory reveal striking crystal-symmetry-related features in the electronic structure of the segmented chain, including giant spin splitting and nontrivial topological phases of selected energy band states. Atomic-resolution scanning transmission electron microscopy reveals single segmented Hf_{2}Te_{9} chains isolated within the hollow cores of carbon nanotubes, with a structure consistent with theoretical predictions. van der Waals bonded segmented linear chain transition metal chalcogenide materials could open up new opportunities in low-dimensional, gate-tunable, magnetic, and topological crystalline systems

Conceptual Design of a Manufacturing Process for an Automotive Microchannel Heat Exchanger

Calls for higher fuel efficiency in the United States and Europe are driving the need for waste heat recovery in automotive markets. While conventional heat exchangers can be designed to meet the heat duty requirement, the resulting volume, weight, and thermal mass are too large for rapid transient response and packaging of the device. The lightweight, compact form factor of microchannel heat exchangers with submillimeter flow passages is attractive for automotive applications. However, the industrial use of microchannel heat exchangers continues to be inhibited by high manufacturing costs. The objective of this paper is to develop a microchannel heat exchanger concept capable of meeting the cost and performance goals for an automotive application. So-called printed-circuit microchannel heat exchangers are produced using a stacked-lamina approach in which individual metal laminae are photochemically machined and diffusion bonded. Here, the conceptual design of a microchannel heat exchanger produced using more conventional stamping and joining technologies is discussed for an automotive application. The device is sized to provide waste heat recovery from an exhaust stream to engine coolant for a representative passenger vehicle with acceptable pressure loss. Using the specified design, a process-based cost model is presented showing cost modeling efforts to date including the capital investment and cost-of-goods-sold as a function of annual production volume. The initial results show a pathway for the cost effective integration of compact microchannel heat exchangers into advanced vehicle thermal management systems