Square-tiled cyclic covers

A cyclic cover of the complex projective line branched at four appropriate points has a natural structure of a square-tiled surface. We describe the combinatorics of such a square-tiled surface, the geometry of the corresponding Teichm\"uller curve, and compute the Lyapunov exponents of the determinant bundle over the Teichm\"uller curve with respect to the geodesic flow. This paper includes a new example (announced by G. Forni and C. Matheus in \cite{Forni:Matheus}) of a Teichm\"uller curve of a square-tiled cyclic cover in a stratum of Abelian differentials in genus four with a maximally degenerate Kontsevich--Zorich spectrum (the only known example found previously by Forni in genus three also corresponds to a square-tiled cyclic cover \cite{ForniSurvey}). We present several new examples of Teichm\"uller curves in strata of holomorphic and meromorphic quadratic differentials with maximally degenerate Kontsevich--Zorich spectrum. Presumably, these examples cover all possible Teichm\"uller curves with maximally degenerate spectrum. We prove that this is indeed the case within the class of square-tiled cyclic covers.Comment: 34 pages, 6 figures. Final version incorporating referees comments. In particular, a gap in the previous version was corrected. This file uses the journal's class file (jmd.cls), so that it is very similar to published versio

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE

Morphine metabolism, transport and brain disposition

The chemical structures of morphine and its metabolites are closely related to the clinical effects of drugs (analgesia and side-effects) and to their capability to cross the Blood Brain Barrier (BBB). Morphine-6-glucuronide (M6G) and Morphine-3-glucuronide (M3G) are both highly hydrophilic, but only M6G can penetrate the BBB; accordingly, M6G is considered a more attractive analgesic than the parent drug and the M3G. Several hypotheses have been made to explain these differences. In this review we will discuss recent advances in the field, considering brain disposition of M6G, UDP-glucoronosyltransferases (UGT) involved in morphine metabolism, UGT interindividual variability and transport proteins

Pharmacokinetic Modeling of Non-Linear Brain Distribution of Fluvoxamine in the Rat

Introduction. A pharmacokinetic (PK) model is proposed for estimation of total and free brain concentrations of fluvoxamine. Materials and methods. Rats with arterial and venous cannulas and a microdialysis probe in the frontal cortex received intravenous infusions of 1, 3.7 or 7.3 mg.kg j1 of fluvoxamine. Analysis. With increasing dose a disproportional increase in brain concentrations was observed. Th

On The Rate and Extent of Drug Delivery to the Brain

To define and differentiate relevant aspects of blood–brain barrier transport and distribution in order to aid research methodology in brain drug delivery. Pharmacokinetic parameters relative to the rate and extent of brain drug delivery are described and illustrated with relevant data, with special emphasis on the unbound, pharmacologically active drug molecule. Drug delivery to the brain can be comprehensively described using three parameters: Kp,uu (concentration ratio of unbound drug in brain to blood), CLin (permeability clearance into the brain), and Vu,brain (intra-brain distribution). The permeability of the blood–brain barrier is less relevant to drug action within the CNS than the extent of drug delivery, as most drugs are administered on a continuous (repeated) basis. Kp,uu can differ between CNS-active drugs by a factor of up to 150-fold. This range is much smaller than that for log BB ratios (Kp), which can differ by up to at least 2,000-fold, or for BBB permeabilities, which span an even larger range (up to at least 20,000-fold difference). Methods that measure the three parameters Kp,uu, CLin, and Vu,brain can give clinically valuable estimates of brain drug delivery in early drug discovery programmes