Terrapene

Number of Pages: 6Integrative BiologyGeological Science

Enclosings of Decompositions of Complete Multigraphs in 22-Edge-Connected rr-Factorizations

A decomposition of a multigraph $G$ is a partition of its edges into subgraphs $G(1), \ldots , G(k)$. It is called an $r$-factorization if every $G(i)$ is $r$-regular and spanning. If $G$ is a subgraph of $H$, a decomposition of $G$ is said to be enclosed in a decomposition of $H$ if, for every $1 \leq i \leq k$, $G(i)$ is a subgraph of $H(i)$. Feghali and Johnson gave necessary and sufficient conditions for a given decomposition of $\lambda K_n$ to be enclosed in some $2$-edge-connected $r$-factorization of $\mu K_{m}$ for some range of values for the parameters $n$, $m$, $\lambda$, $\mu$, $r$: $r=2$, $\mu>\lambda$ and either $m \geq 2n-1$, or $m=2n-2$ and $\mu = 2$ and $\lambda=1$, or $n=3$ and $m=4$. We generalize their result to every $r \geq 2$ and $m \geq 2n - 2$. We also give some sufficient conditions for enclosing a given decomposition of $\lambda K_n$ in some $2$-edge-connected $r$-factorization of $\mu K_{m}$ for every $r \geq 3$ and $m = (2 - C)n$, where $C$ is a constant that depends only on $r$, $\lambda$ and~$\mu$.Comment: 17 pages; fixed the proof of Theorem 1.4 and other minor change

Terrapene carolina

Number of Pages: 13Integrative BiologyGeological Science

Levels of C-reactive protein associated with high and very high cardiovascular risk are prevalent in patients with rheumatoid arthritis.

ObjectiveC-reactive protein (CRP) levels>3 mg/L and>10 mg/L are associated with high and very high cardiovascular risk, respectively, in the general population. Because rheumatoid arthritis (RA) confers excess cardiovascular mortality, we determined the prevalence of these CRP levels among RA patients stratified on the basis of their RA disease activity.MethodsWe evaluated physician and patient global assessments of disease activity, tender and swollen 28 joint counts, erythrocyte sedimentation rate (ESR), and CRP measured in a single clinic visit for 151 RA patients. Disease activity was calculated using the Clinical Disease Activity Index (CDAI) and the Disease Activity Score 28 Joints (DAS28-ESR and DAS28-CRP).ResultsMedian CRP level was 5.3 mg/L. 68% of patients had CRP>3 mg/L, and 25% had CRP>10 mg/L. Of those with 0-1 swollen joints (n = 56), or 0-1 tender joints (n = 81), 64% and 67%, respectively, had CRP>3 mg/L, and 23% and 20%, respectively, had CRP>10 mg/L. Of those with remission or mildly active disease by CDAI (n = 58), DAS28-ESR (n = 39), or DAS28-CRP (n = 70), 49-66% had CRP>3 mg/L, and 10-14% had CRP>10 mg/L. Of patients with moderate disease activity by CDAI (n = 51), DAS28-ESR (n = 78), or DAS28-CRP (n = 66), 67-73% had CRP>3 mg/L, and 25-33% had CRP>10 mg/L.ConclusionEven among RA patients whose disease is judged to be controlled by joint counts or standardized disease scores, a substantial proportion have CRP levels that are associated high or very high risk for future cardiovascular events in the general population

Kompaneets Model Fitting of the Orion-Eridanus Superbubble

Winds and supernovae from OB associations create large cavities in the interstellar medium referred to as superbubbles. The Orion molecular clouds are the nearest high mass star-forming region and have created a highly elongated, 20 degree x 45 degree, superbubble. We fit Kompaneets models to the Orion-Eridanus superbubble and find that a model where the Eridanus side of the superbubble is oriented away from the Sun provides a marginal fit. Because this model requires an unusually small scaleheight of 40 pc and has the superbubble inclined 35 degrees from the normal to the Galactic plane, we propose that this model should be treated as a general framework for modelling the Orion-Eridanus superbubble, with a secondary physical mechanism not included in the Kompaneets model required to fully account for the orientation and elongation of the superbubble.Comment: 15 pages, 5 figures, 2 tables, accepted by MNRAS, minor grammatical change