Hierarchical hyperbolicity of graphs of multicurves

We show that many graphs naturally associated to a connected, compact, orientable surface are hierarchically hyperbolic spaces in the sense of Behrstock, Hagen and Sisto. They also automatically have the coarse median property defined by Bowditch. Consequences for such graphs include a distance formula analogous to Masur and Minsky's distance formula for the mapping class group, an upper bound on the maximal dimension of quasiflats, and the existence of a quadratic isoperimetric inequality. The hierarchically hyperbolic structure also gives rise to a simple criterion for when such graphs are Gromov hyperbolic.Comment: 27 pages, 4 figures. Minor changes from previous version. Addition of appendix describing a hierarchically hyperbolic structure on the arc grap

The early career of Thomas, Lord Howard, Earl of Surrey and third Duke of Norfolk, 1474-c.1525

Why another thesis on the third duke of Norfolk, and why, in particular, a partial one? It is true that two competent studies of the duke have been made in relatively recent times; the first an M.A. thesis submitted in the University of Nottingham in 1961 by F.R. Grace, and the second, a Ph.D. in the University of Florida, submitted in 1978 by D. Head. Both of these suffer from one besetting problem. Because Norfolk lived to the age of eighty years, and from the age of thirty-eight occupied a very important position in the Tudor state, both were forced to deal almost exclusively with the massive bulk of material which survives concerning his actions in the public domain. The result is that we learned more about Norfolk the politician, but almost nothing new about Norfolk the man. Indeed, I would go further. The pressure to negotiate large quantities of material in the public records at speed forced both researchers to accept without question assumptions about the motivations of the duke which had been current for a very long time, and which a more detailed study of the early part of his life, and attention to private records might have modified.My approach to this task has been to focus attention on the least studied, early part of his life, in an effort to re-connect Norfolk with his family's past, the ideals which underpinned his own upbringing and training, and his early experience, which together shaped his outlook and his goals in life. I have ignored the artificial and often unhelpful dividing line drawn by historians between the late medieval and early modern periods, and availed myself of the considerable body of excellent modern scholarship on the nobility in the fifteenth and first half of the sixteenth centuries to examine Norfolk In his role as heir to a great landed estate, as well as in his other roles as courtier, warrior and councillor. My aim has been to present a complete picture of the man, his family (so intimately involved in the life of every nobleman of this period) and their affairs in the years which are covered here

Prevalence of vertebral fractures on chest radiographs of elderly African American and Caucasian women.

The prevalence of vertebral fractures on routine chest radiographs of elderly Caucasian women was only 1.3 times higher than in African American (AA) women, a difference considerably smaller than reported in population studies. AAs with medical problems may have higher risk of vertebral fractures than previously suspected.IntroductionEarlier studies noted a 1.9- to 3.7-fold higher prevalence of vertebral fractures in Caucasian (CA) compared to African American (AA) women. These studies, however, may have suffered from selection bias. We reported that among women referred for bone density testing, the prevalence of vertebral fractures in AA was the same as in CA women. Suspecting that the latter might have been due to a referral bias, we examined the racial difference in the prevalence of vertebra fractures on chest radiographs of patients seeking general medical care, not selected for osteoporosis.MethodsConsecutive chest radiographs (N = 1,200) of women over age 60 were evaluated using Genant's semi-quantitative method. Patients' race and the presence of diseases or medications associated with increased fracture risk were ascertained from the electronic medical records.ResultsAmong 1,011 women (76% AA) with usable radiographs, 11% had moderate or severe vertebral fractures. The prevalence of vertebral fractures was 10.3% in 773 AA and 13% in 238 CA women (p = 0.248 for difference between races). The lack of difference persisted after controlling for age, smoking, use of glucocorticoids, or presence of cancer, rheumatoid arthritis, organ transplantation, and end-stage renal disease. Among all subjects, CA women were more likely to be diagnosed and treated for osteoporosis (p <0.001).ConclusionAmong subjects seeking medical care, the difference in the prevalence of vertebral fractures between AA and CA women is smaller than previously suspected. Greater attention to the detection of vertebral fractures and the management of osteoporosis is warranted in AA women with medical problems