The Chiral Potts Model and Its Associated Link Invariant

A new link invariant is derived using the exactly solvable chiral Potts model and a generalized Gaussian summation identity. Starting from a general formulation of link invariants using edge-interaction spin models, we establish the uniqueness of the invariant for self-dual models. We next apply the formulation to the self-dual chiral Potts model, and obtain a link invariant in the form of a lattice sum defined by a matrix associated with the link diagram. A generalized Gaussian summation identity is then used to carry out this lattice sum, enabling us to cast the invariant into a tractable form. The resulting expression for the link invariant is characterized by roots of unity and does not appear to belong to the usual quantum group family of invariants. A table of invariants for links with up to 8 crossings is given.Comment: 32 pages + 9 figure

Corticosteroids and Open-Angle Glaucoma in the Elderly A Population-Based Cohort Study

Background It is largely unknown if corticosteroid-induced open-angle glaucoma (OAG) is an entity that is limited to a few susceptible individuals or whether it contributes significantly to the overall population burden of OAG. Objective The aim of this study was to determine whether there is an association between corticosteroid use and the incidence of OAG in the general elderly population. Methods A prospective population-based cohort study was conducted in a general community setting. 3,939 participants of the Rotterdam Study aged 55 years and older for whom data from ophthalmic examinations at baseline and follow-up were available and who did not have glaucoma at baseline were included (baseline examination from 1991 to 1993; follow-up examinations from 1997 to 1999 and from 2002 to 2006). Ophthalmic examinations, including measurement of the intraocular pressure, assessment of the optic nerve head and perimetry, were performed at baseline and follow-up. The use of corticosteroids was monitored continuously during follow-up. Corticosteroids were stratified into five groups: ophthalmic steroids, inhaled steroids, nasal steroids, oral steroids and steroid ointments. Associations between the use of corticosteroids and incident OAG were assessed using logistic regression models. The study outcome measures were the odds ratios (ORs) of associations between the use of corticosteroids and incident OAG. Results During a mean follow-up of 9.8 years, 108 participants (2.8 %) developed OAG. The median number of steroid prescriptions during follow-up was 2 for ophthalmic, 7 for inhaled, 2 for nasal and 2 for oral steroids, and 3 for steroid ointments. The OR of the use of ophthalmic steroids was 1.04 [95 % confidence interval (CI) 0.66, 1.65; p = 0.86], inhaled steroids 0.79 (95 % CI 0.42, 1.48; p = 0.46), nasal steroids 1.26 (95 % CI 0.74, 2.13; p = 0.40), oral steroids 1.03 (95 % CI 0.65, 1.64; p = 0.89) and steroid ointments 0.70 (95 % CI 0.47, 1.05; p = 0.086). These analyses were adjusted for age, sex, high myopia and family history of glaucoma. The small median numbers of prescriptions made it difficult to evaluate dose-response relationships. Conclusion None of the classes of steroids were associated with the incidence of OAG in this elderly population