Another derivation of the geometrical KPZ relations

We give a physicist's derivation of the geometrical (in the spirit of Duplantier-Sheffield) KPZ relations, via heat kernel methods. It gives a covariant way to define neighborhoods of fractals in 2d quantum gravity, and shows that these relations are in the realm of conformal field theory

Refitting successful daily wear GP patients into thirty day continuous wear gas permeable lenses: A case series

Current rigid gas permeable lens wearers were refit into the thirty day continuous wear Menicon Z gas permeable lens. The purpose of the study was to evaluate how the subjects transitioned to the new Menicon Z lenses and the thirty day wearing schedule. Subjects were monitored for two months for an ocular health changes by assessing visual acuity, performing biomicroscopy and lens fit evaluation, and corneal topography

Extending Bauer's corollary to fractional derivatives

We comment on the method of Dreisigmeyer and Young [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems with fractional derivatives. It was previously hoped that using fractional derivatives in an action would allow us to derive a single retarded equation of motion using a variational principle. It is proven that, under certain reasonable assumptions, the method of Dreisigmeyer and Young fails.Comment: Accepted Journal of Physics A at www.iop.org/EJ/journal/JPhys

Nonconservative Lagrangian mechanics II: purely causal equations of motion

This work builds on the Volterra series formalism presented in [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems. Here we treat Lagrangians and actions as `time dependent' Volterra series. We present a new family of kernels to be used in these Volterra series that allow us to derive a single retarded equation of motion using a variational principle

Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

Confluence of geodesic paths and separating loops in large planar quadrangulations

We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minimal separating loops, i.e. paths of minimal length among all closed paths passing by one of the three vertices and separating the two others in the quadrangulation. We concentrate on the universal scaling limit of large quadrangulations, also known as the Brownian map, where pairs of geodesic paths or minimal separating loops have common parts of non-zero macroscopic length. This is the phenomenon of confluence, which distinguishes the geometry of random quadrangulations from that of smooth surfaces. We characterize the universal probability distribution for the lengths of these common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding paragraph and one reference added, and several other small correction

Patterns of initiation of second generation antipsychotics for bipolar disorder: a month-by-month analysis of provider behavior

Background: Several second generation antipsychotics (SGAs) received FDA approval for bipolar disorder in the 2000s. Although efficacious, they have been costly and may cause significant side effects. Little is known about the factors associated with prescribers’ decisions to initiate SGA prescriptions for this condition. Methods: We gathered administrative data from the Department of Veterans Affairs on 170,713 patients with bipolar disorder between fiscal years 2003–2010. Patients without a prior history of taking SGAs were considered eligible for SGA initiation during the study (n =126,556). Generalized estimating equations identified demographic, clinical, and comorbidity variables associated with initiation of an SGA prescription on a month-by-month basis. Results: While the number of patients with bipolar disorder using SGAs nearly doubled between 2003 and 2010, analyses controlling for patient characteristics and the rise in the bipolar population revealed a 1.2% annual decline in SGA initiation during this period. Most medical comorbidities were only modestly associated with overall SGA initiation, although significant differences emerged among individual SGAs. Several markers of patient severity predicted SGA initiation, including previous hospitalizations, psychotic features, and a history of other antimanic prescriptions; these severity markers became less firmly linked to SGA initiation over time. Providers in the South were somewhat more likely to initiate SGA treatment. Conclusions: The number of veterans with bipolar disorder prescribed SGAs is rising steadily, but this increase appears primarily driven by a corresponding increase in the bipolar population. Month-by-month analyses revealed that higher illness severity predicted SGA initiation, but that this association may be weakening over time