Cyclic derangements

A classic problem in enumerative combinatorics is to count the number of derangements, that is, permutations with no fixed point. Inspired by a recent generalization to facet derangements of the hypercube by Gordon and McMahon, we generalize this problem to enumerating derangements in the wreath product of any finite cyclic group with the symmetric group. We also give q- and (q, t)-analogs for cyclic derangements, generalizing results of Brenti and Gessel.Comment: 14 page

A bijective proof of Kohnert's rule for Schubert polynomials

Kohnert proposed the first monomial positive formula for Schubert polynomials as the generating polynomial for certain unit cell diagrams obtained from the Rothe diagram of a permutation. Billey, Jockusch and Stanley gave the first proven formula for Schubert polynomials as the generating polynomial for compatible sequences of reduced words of a permutation. In this paper, we give an explicit bijection between these two models, thereby definitively proving Kohnert's rule for Schubert polynomials.Comment: 8 pages, 7 figures (examples added, minor corrections

A Littlewood-Richardson rule for Grassmannian Schubert varieties

We propose a combinatorial model for the Schubert structure constants of the complete flag manifold when one of the factors is Grassmannian.Comment: 6 pages, 2 figures - Final versio

Chemopreventive effect of corosolic acid in human hepatocellular carcinoma cells

Anticancer effects of corosolic acid have been demonstrated earlier in human cervix adenocarcinoma and osteosarcoma cells, but the exact underlying molecular mechanisms have not been studied. Hence, an attempt was made to identify the anticancer mechanism of corosolic acid in human hepatocellular carcinoma cells [HepG2]. The anticancer activity of corosolic acid through cell growth inhibition by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide (MTT) assay, reactive oxygen species (ROS) generation, mitochondrial membrane potential and apoptotic fragmentations by fluorescence microscope was evaluated. In addition, the cleavage of PARP, NF-κB, cytochrome c (cyt. C) release, and Bax and Bcl2 expression was analyzed by Western blot. The results clearly indicate that corosolic acid was involved in the alteration of mitochondrial membrane potential resulting in the release of cyt. C from mitochondria and increased ROS generation. The corosolic acid treatment causes the induction of apoptosis in a dose dependent manner (IC50, 40 μM). In conclusion, corosolic acid had chemopreventive effect on HepG2 cells by apoptosis.Keywords: Corosolic acid, hepatocellular carcinoma, reactive oxygen species (ROS), apoptosis, lipid peroxidationAfrican Journal of Biotechnology Vol. 12(19), pp. 2733-274

A coral-on-a-chip microfluidic platform enabling live-imaging microscopy of reef-building corals

Coral reefs, and the unique ecosystems they support, are facing severe threats by human activities and climate change. Our understanding of these threats is hampered by the lack of robust approaches for studying the micro-scale interactions between corals and their environment. Here we present an experimental platform, coral-on-a-chip, combining micropropagation and microfluidics to allow direct microscopic study of live coral polyps. The small and transparent coral micropropagates are ideally suited for live-imaging microscopy, while the microfluidic platform facilitates long-term visualization under controlled environmental conditions. We demonstrate the usefulness of this approach by imaging coral micropropagates at previously unattainable spatio-temporal resolutions, providing new insights into several micro-scale processes including coral calcification, coral-pathogen interaction and the loss of algal symbionts (coral bleaching). Coral-on-a-chip thus provides a powerful method for studying coral physiology in vivo at the micro-scale, opening new vistas in coral biology