The 2-distance coloring of the Cartesian product of cycles using optimal Lee codes

AbstractLet Cm be the cycle of length m. We denote the Cartesian product of n copies of Cm by G(n,m):=Cm□Cm□⋯□Cm. The k-distance chromatic number χk(G) of a graph G is χ(Gk) where Gk is the kth power of the graph G=(V,E) in which two distinct vertices are adjacent in Gk if and only if their distance in G is at most k. The k-distance chromatic number of G(n,m) is related to optimal codes over the ring of integers modulo m with minimum Lee distance k+1. In this paper, we consider χ2(G(n,m)) for n=3 and m≥3. In particular, we compute exact values of χ2(G(3,m)) for 3≤m≤8 and m=4k, and upper bounds for m=3k or m=5k, for any positive integer k. We also show that the maximal size of a code in Z63 with minimum Lee distance 3 is 26

Kaon mixing matrix elements from beyond-the-Standard-Model operators in staggered chiral perturbation theory

Models of new physics induce K-Kbar mixing operators having Dirac structures other than the "left-left" form of the Standard Model. We calculate the functional form of the corresponding B-parameters at next-to-leading order in both SU(3) and SU(2) staggered chiral perturbation theory (SChPT). Numerical results for these matrix elements are being generated using improved staggered fermions; our results can be used to extrapolate these matrix elements to the physical light and strange quark masses. The SU(3) SChPT results turn out to be much simpler than that for the Standard Model B_K operator, due to the absence of chiral suppression in the new operators. The SU(2) SChPT result is of similar simplicity to that for B_K. In fact, in the latter case, the chiral logarithms for two of the new B-parameters are identical to those for B_K, while those for the other two new B-parameters are of opposite sign. In addition to providing results for the 2+1 flavor theory in SU(3) SChPT and the 1+1+1 flavor theory in SU(2) SChPT, we present the corresponding continuum partially quenched results, as these are not available in the literature.Comment: 16 pages, 3 figures. Typos corrected--published versio

Long-term outcomes of children after solid organ transplantation

Solid organ transplantation has transformed the lives of many children and adults by providing treatment for patients with organ failure who would have otherwise succumbed to their disease. The first successful transplant in 1954 was a kidney transplant between identical twins, which circumvented the problem of rejection from MHC incompatibility. Further progress in solid organ transplantation was enabled by the discovery of immunosuppressive agents such as corticosteroids and azathioprine in the 1950s and ciclosporin in 1970. Today, solid organ transplantation is a conventional treatment with improved patient and allograft survival rates. However, the challenge that lies ahead is to extend allograft survival time while simultaneously reducing the side effects of immunosuppression. This is particularly important for children who have irreversible organ failure and may require multiple transplants. Pediatric transplant teams also need to improve patient quality of life at a time of physical, emotional and psychosocial development. This review will elaborate on the long-term outcomes of children after kidney, liver, heart, lung and intestinal transplantation. As mortality rates after transplantation have declined, there has emerged an increased focus on reducing longer-term morbidity with improved outcomes in optimizing cardiovascular risk, renal impairment, growth and quality of life. Data were obtained from a review of the literature and particularly from national registries and databases such as the North American Pediatric Renal Trials and Collaborative Studies for the kidney, SPLIT for liver, International Society for Heart and Lung Transplantation and UNOS for intestinal transplantation

How to know when little kidneys are in trouble: a review of current tools for diagnosing AKI in neonates

Due to a plethora of risk factors, including prematurity, neonates are at risk for acute kidney injury (AKI) and, once established, AKI is associated with poor outcomes. The most widely used AKI biomarker is creatinine, despite research demonstrating creatinine to be a suboptimal tool for diagnosing neonatal AKI. This article uses an amalgamated case study to illustrate the inadequacies of creatinine for detection of preterm AKI and to present a range of novel AKI biomarkers relevant to the neonatal population. Clinical evaluation of novel AKI biomarkers is needed to improve precision and rapidity of AKI management in neonates