N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds

We study the elliptic genera of hyperKahler manifolds using the representation theory of N=4 superconformal algebra. We consider the decomposition of the elliptic genera in terms of N=4 irreducible characters, and derive the rate of increase of the multiplicities of half-BPS representations making use of Rademacher expansion. Exponential increase of the multiplicity suggests that we can associate the notion of an entropy to the geometry of hyperKahler manifolds. In the case of symmetric products of K3 surfaces our entropy agrees with the black hole entropy of D5-D1 system.Comment: 25 pages, 1 figur

Increased Risk of Temporomandibular Joint Closed Lock: A Case-Control Study of ANKH Polymorphisms

Objectives: This study aimed to carry out a histological examination of the temporomandibular joint (TMJ) in ank mutant mice and to identify polymorphisms of the human ANKH gene in order to establish the relationship between the type of temporomandibular disorders (TMD) and ANKH polymorphisms.\ud \ud Materials and Methods: Specimens from the TMJ of ank mutant and wild-type mice were inspected with a haematoxylin and eosin staining method. A sample of 55 TMD patients were selected. Each was examined with standard clinical procedures and genotyping techniques.\ud \ud Results: The major histological finding in ank mutant mice was joint space narrowing. Within TMD patients, closed lock was more prevalent among ANKH-OR homozygotes (p = 0.011, OR = 7.7, 95% CI 1.6–36.5) and the elder (p = 0.005, OR = 2.4, 95% CI 1.3–4.3).\ud \ud Conclusions: Fibrous ankylosis was identified in the TMJ of ank mutant mice. In the human sample, ANKH-OR polymorphism was found to be a genetic marker associated with TMJ closed lock. Future investigations correlating genetic polymorphism to TMD are indicated