Singular values of the Dirac operator in dense QCD-like theories

We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark condensate, in contrast to the complex Dirac eigenvalues whose scale is set by the chiral condensate at low density and by the BCS gap at high density. We identify three different low-energy effective theories with diquark sources applicable at low, intermediate, and high density, together with their overlapping domains of validity. We derive a number of exact formulas for the Dirac singular values, including Banks-Casher-type relations for the diquark condensate, Smilga-Stern-type relations for the slope of the singular value density, and Leutwyler-Smilga-type sum rules for the inverse singular values. We construct random matrix theories and determine the form of the microscopic spectral correlation functions of the singular values for all nonzero quark densities. We also derive a rigorous index theorem for non-Hermitian Dirac operators. Our results can in principle be tested in lattice simulations.Comment: 3 references added, version published in JHE

Drug dosing during pregnancy—opportunities for physiologically based pharmacokinetic models

Drugs can have harmful effects on the embryo or the fetus at any point during pregnancy. Not all the damaging effects of intrauterine exposure to drugs are obvious at birth, some may only manifest later in life. Thus, drugs should be prescribed in pregnancy only if the expected benefit to the mother is thought to be greater than the risk to the fetus. Dosing of drugs during pregnancy is often empirically determined and based upon evidence from studies of non-pregnant subjects, which may lead to suboptimal dosing, particularly during the third trimester. This review collates examples of drugs with known recommendations for dose adjustment during pregnancy, in addition to providing an example of the potential use of PBPK models in dose adjustment recommendation during pregnancy within the context of drug-drug interactions. For many drugs, such as antidepressants and antiretroviral drugs, dose adjustment has been recommended based on pharmacokinetic studies demonstrating a reduction in drug concentrations. However, there is relatively limited (and sometimes inconsistent) information regarding the clinical impact of these pharmacokinetic changes during pregnancy and the effect of subsequent dose adjustments. Examples of using pregnancy PBPK models to predict feto-maternal drug exposures and their applications to facilitate and guide dose assessment throughout gestation are discussed