Abstract:
In a graph whose edges are colored, a parity walk is a walk that uses each color an even number of times. The parity edge chromatic number p(G) of a graph G is the least k so that there is a coloring of E(G) using k colors that does not contain a parity path. The strong parity edge chromatic number p'(G) of G is the least k so that there is a coloring of E(G) using k colors with the property that every parity walk is closed. Our main result is to determine p'(K_n). Specifically, if m is the least power of two that is as large as n, then p'(K_n) has value m - 1. As a corollary, we strengthen a special case of an old result of Daykin and Lovasz. Other results include determining p(G) and p'(G) whenever G is a path, cycle, or of the form K_{2,n}, and an upper bound on p'(G) for the case that G is a complete bipartite graph. We conclude with a sample of open problems.

Abstract:
We study the Maker-Breaker game on the hypergraph of chains of fixed size in a poset. In a product of chains, the maximum size of a chain that Maker can guarantee building is $k-\lfloor r/2\rfloor$, where $k$ is the maximum size of a chain in the product, and $r$ is the maximum size of a factor chain. We also study a variant in which Maker must follow the chain in order, called the {\it Walker-Blocker game}. In the poset consisting of the bottom $k$ levels of the product of $d$ arbitrarily long chains, Walker can guarantee a chain that hits all levels if $d\ge14$; this result uses a solution to Conway's Angel-Devil game. When d=2, the maximum that Walker can guarantee is only 2/3 of the levels, and 2/3 is asymptotically achievable in the product of two equal chains.

Abstract:
An {\it overlap representation} of a graph $G$ assigns sets to vertices so that vertices are adjacent if and only if their assigned sets intersect with neither containing the other. The {\it overlap number} $\ol(G)$ (introduced by Rosgen) is the minimum size of the union of the sets in such a representation. We prove the following: (1) An optimal overlap representation of a tree can be produced in linear time, and its size is the number of vertices in the largest subtree in which the neighbor of any leaf has degree 2. (2) If $\delta(G)\ge 2$ and $G\ne K_3$, then $\ol(G)\le |E(G)|-1$, with equality when $G$ is connected and triangle-free and has no star-cutset. (3) If $G$ is an $n$-vertex plane graph with $n\ge5$, then $\ol(G)\le 2n-5$, with equality when every face has length 4 and there is no star-cutset. (4) If $G$ is an $n$-vertex graph with $n\ge 14$, then $\ol(G)\le \floor{n^2/4-n/2-1}$, and this is sharp (for even $n$, equality holds when $G$ arises from $K_{n/2,n/2}$ by deleting a perfect matching).

Abstract:
My introduction to high altitude occurred in 1960 when I learned that Sir Edmund Hillary was planning a physiological expedition to the Himalayas. I applied to the scientific leader Dr. Griffith Pugh and was accepted in spite of the fact that I had previously never done any climbing. The Silver Hut Expedition as it was called was unique in that a small group of physiologists spent several months during the winter and spring of 1960–1961 at an altitude of 5,800 m (19,000 ft), about 16 km south of Mt. Everest. There, we carried out an extensive physiological program on acclimatization in a sophisticated, well-insulated wooden building that was painted silver. As far as we were aware, nobody had lived for such a long period at such a high altitude before. Subsequently, measurements were extended up to an altitude of 7,440 m (24,400 ft) on Mt. Makalu, which has an altitude of 8,481 m. These included the highest measurements of maximal oxygen uptake that have been reported to date [1]. The physiological program was very productive with many articles in top-level journals [2].The primary purpose of the physiological program was to obtain a better understanding of the acclimatization process of lowlanders while they were living continuously at a very high altitude. The main areas of study were the cardiorespiratory responses to exercise under these conditions of extreme hypoxia, but measurements of blood, renal, and neuropsychometric function were made as well [3]. However, in the event, there was an unrelenting rapid loss of body weight, and the conclusion was that we would not have been able to remain at that altitude indefinitely.The success of this expedition prompted me to wonder whether it might be possible to obtain physiological measurements at the highest point on earth. There was abundant evidence that at this altitude, humans are very close to the limit of oxygen deprivation, and so, it was a fascinating physiological problem to determine how the body responds.

Abstract:
This paper is devoted to proving that, in QCD, the lightest glueball state must be the scalar with $J^{PC} = 0^{++}$. The proof relies upon the positivity of the path integral measure in Euclidean space and the fact that interpolating fields for all spins can be bounded by powers of the scalar glueball operator. The problem presented by the presence of vacuum condensates is circumvented by considering the time evolution of the propagators and exploiting the positivity of the Hamiltonian.

Abstract:
Theoretical ideas related to the existence of glueballs in QCD are reviewed. These include non-perturbative phenomena such as confinement, instantons, vacuum condensates and renormalons. We also discuss glueball dominance of the trace of the stress-tensor, the mass content of the nucleon and a theorem on the lightest glueball state.

Abstract:
A proof of Bloom-Gilman duality which relates an integral over the low-mass resonances in deep inelastic structure functions to an integral over the scaling region near x = 1 is given. It is based on general analytic properties of the corresponding virtual Compton amplitude but is insensitive to its asymptotic behaviour.

Abstract:
Some of the basic concepts regarding asymptotic series are reviewed. A heuristic proof is given that the divergent QCD perturbation series is asymptotic. By treating it as an asymptotic expansion we show that it makes sense to keep only the first few terms. The example of e^+e^- annihilation is considered. It is shown that by keeping only the first few terms one can get within a per cent (or smaller) of the complete sum of the series even at very low momenta where the coupling is large. More generally, this affords an explanation of the phenomena of precocious scaling and why keeping only leading order corrections generally works so well.

Abstract:
Background The QuantiFERON？-TB Gold In-Tube test (QFT-GIT) is a viable alternative to the tuberculin skin test (TST) for detecting Mycobacterium tuberculosis infection. However, within-subject variability may limit test utility. To assess variability, we compared results from the same subjects when QFT-GIT enzyme-linked immunosorbent assays (ELISAs) were performed in different laboratories. Methods Subjects were recruited at two sites and blood was tested in three labs. Two labs used the same type of automated ELISA workstation, 8-point calibration curves, and electronic data transfer. The third lab used a different automated ELISA workstation, 4-point calibration curves, and manual data entry. Variability was assessed by interpretation agreement and comparison of interferon-γ (IFN-γ) measurements. Data for subjects with discordant interpretations or discrepancies in TB Response >0.05 IU/mL were verified or corrected, and variability was reassessed using a reconciled dataset. Results Ninety-seven subjects had results from three labs. Eleven (11.3%) had discordant interpretations and 72 (74.2%) had discrepancies >0.05 IU/mL using unreconciled results. After correction of manual data entry errors for 9 subjects, and exclusion of 6 subjects due to methodological errors, 7 (7.7%) subjects were discordant. Of these, 6 (85.7%) had all TB Responses within 0.25 IU/mL of the manufacturer's recommended cutoff. Non-uniform error of measurement was observed, with greater variation in higher IFN-γ measurements. Within-subject standard deviation for TB Response was as high as 0.16 IU/mL, and limits of agreement ranged from ？0.46 to 0.43 IU/mL for subjects with mean TB Response within 0.25 IU/mL of the cutoff. Conclusion Greater interlaboratory variability was associated with manual data entry and higher IFN-γ measurements. Manual data entry should be avoided. Because variability in measuring TB Response may affect interpretation, especially near the cutoff, consideration should be given to developing a range of values near the cutoff to be interpreted as “borderline,” rather than negative or positive.