Rational Symplectic Field Theory for Legendrian knots

We construct a combinatorial invariant of Legendrian knots in standard contact three-space. This invariant, which encodes rational relative Symplectic Field Theory and extends contact homology, counts holomorphic disks with an arbitrary number of positive punctures. The construction uses ideas from string topology.Comment: 58 pages, many figures; v3: minor corrections; final version, to appear in Inventiones Mathematica

Proteinases in bone resorption: obvious and less obvious roles

Bone resorption is critical for the development and the maintenance of the skeleton, and improper regulation of bone resorption leads to pathological situations. Proteinases are necessary for this process. In this review, we show that this need of proteinases is not only because they are required for the solubilization of bone matrix, but also because they are key components of the mechanism that determines where and when bone resorption will be initiated. Moreover, there are indications that proteinases may also determine whether resorption will be followed by bone formation. Some of the proteinases involved in these different steps of the resorption processes were recently identified, as for instance cathepsin K, MMP-9 (gelatinase B), and interstitial collagenase. However, there is also increasing evidence showing that the critical proteinase(s) may vary depending on the bone type or on other factor