Heat Determinant on Manifolds

We introduce and study new invariants associated with Laplace type elliptic partial differential operators on manifolds. These invariants are constructed by using the off-diagonal heat kernel; they are not pure spectral invariants, that is, they depend not only on the eigenvalues but also on the corresponding eigenfunctions in a non-trivial way. We compute the first three low-order invariants explicitly.Comment: 41 page

Assessment of Selected Reef Sites in Northern and South-Central Belize, Including Recovery from Bleaching and Hurricane Disturbances (Stony Corals, Algae and Fish)

The condition of coral. algal. and fish populations in fore reefs. patch reefs, and coral reef ridges was investigated at 13 sites along the northern and south-central Belize barrier reef during May 1999, documenting effects of the 1998 warming episode and Hurricane Mitch. We found high percentages of partial, or even complete, colony mortality of major reef-builders (Acropora palmata, the Montastraea annuluris species complex and Agaricia tenuifolia) that were rarely censused as recruits. A. tenuifolia, formerly a space-dominant coral in reef ridges, had incurred nearly 100% mortality after bleaching. Nearly 45% of the M. annurluris complex was still discolored (50% had been bleached in January 1999) on some south-central patch reefs where the total (recent + old) partial mortality exceeded 60% of colony surfaces. Although turf algae dominated patch reefs and coral reef ridges, macroalgae were quite prevalent representing \u3e30% cover at six sites. Parrotfish densities exceeded surgeontishes at most sites (11/13). Consistent patterns of lower partial-colony mortality of stony corals and greater fish densities and sizes near and within the Hol Chan Marine Reserve highlight the ecological benefits of protected areas for the maintenance of reef corals and attendant fish populations

Discovery of Danoprevir (ITMN-191/R7227), a Highly Selective and Potent Inhibitor of Hepatitis C Virus (HCV) NS3/4A Protease

HCV serine protease NS3 represents an attractive drug target because it is not only essential for viral replication but also implicated in the viral evasion of the host immune response pathway through direct cleavage of key proteins in the human innate immune system. Through structure-based drug design and optimization, macrocyclic peptidomimetic molecules bearing both a lipophilic P2 isoindoline carbamate and a P1/P1′ acylsulfonamide/acylsulfamide carboxylic acid bioisostere were prepared that possessed subnanomolar potency against the NS3 protease in a subgenomic replicon-based cellular assay (Huh-7). Danoprevir (compound <b>49</b>) was selected as the clinical development candidate for its favorable potency profile across multiple HCV genotypes and key mutant strains and for its good in vitro ADME profiles and in vivo target tissue (liver) exposures across multiple animal species. X-ray crystallographic studies elucidated several key features in the binding of danoprevir to HCV NS3 protease and proved invaluable to our iterative structure-based design strategy