Complementary vertices and adjacency testing in polytopes

Our main theoretical result is that, if a simple polytope has a pair of complementary vertices (i.e., two vertices with no facets in common), then it has at least two such pairs, which can be chosen to be disjoint. Using this result, we improve adjacency testing for vertices in both simple and non-simple polytopes: given a polytope in the standard form {x \in R^n | Ax = b and x \geq 0} and a list of its V vertices, we describe an O(n) test to identify whether any two given vertices are adjacent. For simple polytopes this test is perfect; for non-simple polytopes it may be indeterminate, and instead acts as a filter to identify non-adjacent pairs. Our test requires an O(n^2 V + n V^2) precomputation, which is acceptable in settings such as all-pairs adjacency testing. These results improve upon the more general O(nV) combinatorial and O(n^3) algebraic adjacency tests from the literature.Comment: 14 pages, 5 figures. v1: published in COCOON 2012. v2: full journal version, which strengthens and extends the results in Section 2 (see p1 of the paper for details

Enhancing Tc in field-doped Fullerenes by applying uniaxial stress

Capitalizing on the two-dimensional nature of superconductivity in field-effect doped C60, we show that it should be possible to increase the transition temperature Tc by applying uniaxial stress perpendicular to the gate electrode. This method not only holds the promise of substantially enhancing Tc (by about 30 K per GPa), but also provides a sensitive check of the current understanding of superconductivity in the doped Fullerenes.Comment: 3 pages RevTe

CpG-A and B oligodeoxynucleotides enhance the efficacy of antibody therapy by activating different effector cell populations

Immunostimulatory CpG oligodeoxynucleotides (ODNs) can enhance the therapeutic effect of monoclonal antibodies (mAbs) by enhancing antibody-dependent cell-mediated cytotoxicity (ADCC). Distinct classes of CpG ODNs have been found recently to stimulate different effector cell populations. We used murine cancer models to explore the role of various effector cell populations in the antitumor activity seen with mAbs combined with CpG ODNs of the A and B classes. In the 38C13 syngeneic murine lymphoma model, both CpG A and CpG B enhanced the efficacy of murine antilymphoma mAb. Depletion of natural killer (NK) cells alone markedly decreased the efficacy of therapy with mAbs plus CpG A. In contrast, depletion of both NK cells and granulocytes was required to decrease the efficacy of mAb plus CpG B. A human (h) Fc gamma receptor I (FcgammaRI)-expressing transgenic (Tg) mouse model was used to explore the role of FcgammaRI in therapy with mAb and CpG ODN. CpG B induced up-regulation of FcgammaRI in hFcgammaRI Tg mice, whereas CpG A did not. In vitro CpG B also enhanced ADCC of HER-2/neu-expressing tumor cells by the FcgammaRI-directed bispecific antibody MDX-H210 using hFcgammaRI-positive effector cells. In a solid tumor model, tumor growth was inhibited in Tg mice treated with a combination of MDX-H210 and CpG B. These data suggest that CpG A enhance ADCC largely by activating NK cells. In contrast, other effector cell populations, including granulocytes, contribute to the antitumor activity of CpG B and mAbs. FcgammaRI plays an important role in this activity