TOPOLOGICAL AND COMBINATORIAL PROPERTIES OF NEIGHBORHOOD AND CHESSBOARD COMPLEXES

This dissertation examines the topological properties of simplicial complexes that arise from two distinct combinatorial objects. In 2003, A. Björner and M. de Longueville proved that the neighborhood complex of the stable Kneser graph SGn,k is homotopy equivalent to a k-sphere. Further, for n = 2 they showed that the neighborhood complex deformation retracts to a subcomplex isomorphic to the associahedron. They went on to ask whether or not, for all n and k, the neighborhood complex of SGn,k contains as a deformation retract the boundary complex of a simplicial polytope. Part one of this dissertation provides a positive answer to this question in the case k = 2. In this case it is also shown that, after partially subdividing the neighborhood complex, the resulting complex deformation retracts onto a subcomplex arising as a polyhedral boundary sphere that is invariant under the action induced by the automorphism group of SGn,2. Part two of this dissertation studies simplicial complexes that arise from non-attacking rook placements on a subclass of Ferrers boards that have ai rows of length i where ai \u3e 0 and i ≤ n for some positive integer n. In particular, enumerative properties of their facets, homotopy type, and homology are investigated

An overview of periodontal regenerative procedures for the general dental practitioner.

The complete regeneration of the periodontal tissues following periodontal disease remains an unmet challenge, and has presented clinicians with a remarkably difficult clinical challenge to solve given the extensive research in this area and our current understanding of the biology of the periodontal tissues. In particular as clinicians we look for treatments that will improve the predictability of the procedure, improve the magnitude of the effect of treatment, and perhaps most importantly in the long term would extend the indications for treatment beyond the need for single enclosed bony defects to allow for suprabony regeneration, preferably with beneficial effects on the gingival soft tissues. A rapid development in both innovative methods and products for the correction of periodontal deficiencies have been reported during the last three decades. For example, guided tissue regeneration with or without the use of bone supplements has been a well-proven treatment modality for the reconstruction of bony defects prior to the tissue engineering era. Active biomaterials have been subsequently introduced to the periodontal community with supporting dental literature suggesting that certain factors should be taken into consideration when undertaking periodontal regenerative procedures. These factors as well as a number of other translational research issues will need to be addressed, and ultimately it is vital that we do not extrapolate results from pre-clinical and animal studies without conducting extensive randomized clinical trials to substantiate outcomes from these procedures. Whatever the outcomes, the pursuit of regeneration of the periodontal tissues remains a goal worth pursuing for our patients. The aim of the review, therefore is to update clinicians on the recent advances in both materials and techniques in periodontal regenerative procedures and to highlight the importance of both patient factors and the technical aspects of regenerative procedures

Simplicial Complexes of Triangular Ferrers Boards

We study the simplicial complex that arises from non-attacking rook placements on a subclass of Ferrers boards that have ai rows of length i where ai> 0 and i ≤ n for some positive integer n. In particular, we will investigate enumerative properties of their facets, their homotopy type, and homology.

Characterization of LY3023414, a Novel PI3K/mTOR Dual Inhibitor Eliciting Transient Target Modulation to Impede Tumor Growth

The phosphoinositide-3 kinase (PI3K)/AKT/mammalian target of rapamycin (mTOR) pathway is among the most frequently altered pathways in cancer cell growth and survival. LY3023414 is a complex fused imidazoquinolinone with high solubility across a wide pH range designed to inhibit class I PI3K isoforms and mTOR kinase. Here we describe the in vitro and in vivo activity of LY3023414. LY3023414 was highly soluble at pH 2-7. In biochemical testing against approximately 266 kinases, LY3023414 potently and selectively inhibited class I PI3K isoforms, mTORC1/2, and DNA-PK at low nanomolar concentrations. In vitro, inhibition of PI3K/AKT/mTOR signaling by LY3023414 caused G1 cell-cycle arrest and resulted in broad antiproliferative activity in cancer cell panel screens. In vivo, LY3023414 demonstrated high bioavailability and dose-dependent dephosphorylation of PI3K/AKT/mTOR pathway downstream substrates such as AKT, S6K, S6RP, and 4E-BP1 for 4 to 6 hours, reflecting the drug's half-life of 2 hours. Of note, equivalent total daily doses of LY3023414 given either once daily or twice daily inhibited tumor growth to similar extents in multiple xenograft models, indicating that intermittent target inhibition is sufficient for antitumor activity. In combination with standard of care drugs, LY3023414 demonstrated additive antitumor activity. The novel, orally bioavailable PI3K/mTOR inhibitor LY3023414 is highly soluble and exhibits potent in vivo efficacy via intermittent target inhibition. It is currently being evaluated in phase 1 and 2 trials for the treatment of human malignancies