Szego limit theorem for operators with discontinuous symbols and applications to entanglement entropy

The main result in this paper is a one term Szego type asymptotic formula with a sharp remainder estimate for a class of integral operators of the pseudodifferential type with symbols which are allowed to be non-smooth or discontinuous in both position and momentum. The simplest example of such symbol is the product of the characteristic functions of two compact sets, one in real space and the other in momentum space. The results of this paper are used in a study of the violation of the area entropy law for free fermions in [18]. This work also provides evidence towards a conjecture due to Harold Widom.Comment: 18 pages, major revision, to appear in Int. Math. Res. No

Should we use early less invasive hemodynamic monitoring in unstable ICU patients?

In the previous issue of Critical Care, Takala and colleagues presented the results of a multicenter study to investigate whether the early presence of less invasive hemodynamic monitoring improves outcome in patients admitted with hemodynamic instability to the intensive care unit. The authors' results suggest that it makes no difference. We discuss these findings and compare them to the literature on early goal-directed therapy in which monitors are used early but with a protocol