On the Optimality of Tape Merge of Two Lists with Similar Size

The problem of merging sorted lists in the least number of pairwise comparisons has been solved completely only for a few special cases. Graham and Karp \cite{taocp} independently discovered that the tape merge algorithm is optimal in the worst case when the two lists have the same size. In the seminal papers, Stockmeyer and Yao\cite{yao}, Murphy and Paull\cite{3k3}, and Christen\cite{christen1978optimality} independently showed when the lists to be merged are of size $m$ and $n$ satisfying $m\leq n\leq\lfloor\frac{3}{2}m\rfloor+1$, the tape merge algorithm is optimal in the worst case. This paper extends this result by showing that the tape merge algorithm is optimal in the worst case whenever the size of one list is no larger than 1.52 times the size of the other. The main tool we used to prove lower bounds is Knuth's adversary methods \cite{taocp}. In addition, we show that the lower bound cannot be improved to 1.8 via Knuth's adversary methods. We also develop a new inequality about Knuth's adversary methods, which might be interesting in its own right. Moreover, we design a simple procedure to achieve constant improvement of the upper bounds for $2m-2\leq n\leq 3m$

High-resolution transport-of-intensity quantitative phase microscopy with annular illumination

For quantitative phase imaging (QPI) based on transport-of-intensity equation (TIE), partially coherent illumination provides speckle-free imaging, compatibility with brightfield microscopy, and transverse resolution beyond coherent diffraction limit. Unfortunately, in a conventional microscope with circular illumination aperture, partial coherence tends to diminish the phase contrast, exacerbating the inherent noise-to-resolution tradeoff in TIE imaging, resulting in strong low-frequency artifacts and compromised imaging resolution. Here, we demonstrate how these issues can be effectively addressed by replacing the conventional circular illumination aperture with an annular one. The matched annular illumination not only strongly boosts the phase contrast for low spatial frequencies, but significantly improves the practical imaging resolution to near the incoherent diffraction limit. By incorporating high-numerical aperture (NA) illumination as well as high-NA objective, it is shown, for the first time, that TIE phase imaging can achieve a transverse resolution up to 208 nm, corresponding to an effective NA of 2.66. Time-lapse imaging of in vitro Hela cells revealing cellular morphology and subcellular dynamics during cells mitosis and apoptosis is exemplified. Given its capability for high-resolution QPI as well as the compatibility with widely available brightfield microscopy hardware, the proposed approach is expected to be adopted by the wider biology and medicine community.Comment: This manuscript was originally submitted on 20 Feb. 201

Knockdown of TIGAR by RNA interference induces apoptosis and autophagy in HepG2 hepatocellular carcinoma cells

AbstractApoptosis and autophagy are crucial mechanisms regulating cell death, and the relationship between apoptosis and autophagy in the liver has yet to be thoroughly explored. TIGAR (TP53-induced glycolysis and apoptosis regulator), which is a p53-inducible gene, functions in the suppression of ROS (reactive oxygen species) and protects U2OS cells from undergoing cell death. In this study, silencing TIGAR by RNAi (RNA interference) in HepG2 cells down-regulated both TIGAR mRNA (∼75%) and protein levels (∼80%) and led to the inhibition of cell growth (P<0.01) by apoptosis (P<0.001) and autophagy. We demonstrated that TIGAR can increase ROS levels in HepG2 cells. The down-regulation of TIGAR led to the induction of LC-3 II (specific autophagic marker), the formation of the autophagosome, and increased Beclin-1 expression. 3-MA (3-Methyladenine), an inhibitor of autophagic sequestration blocker, inhibited TIGAR siRNA-enhanced autophagy, as indicated by the decrease in LC-3 II levels. Consequently, these data provide the first evidence that targeted silencing of TIGAR induces apoptotic and autophagic cell death in HepG2 cells, and our data raise hope for the future successful application of TIGAR siRNA in patients with hepatocellular carcinoma (HCC)

Rice black-streaked dwarf virus P6 self-interacts to form punctate, viroplasm-like structures in the cytoplasm and recruits viroplasm-associated protein P9-1

<p>Abstract</p> <p>Background</p> <p><it>Rice black-streaked dwarf virus </it>(RBSDV), a member of the genus <it>Fijivirus </it>within the family <it>Reoviridae</it>, can infect several graminaceous plant species including rice, maize and wheat, and is transmitted by planthoppers. Although several RBSDV proteins have been studied in detail, functions of the nonstructural protein P6 are still largely unknown.</p> <p>Results</p> <p>In the current study, we employed yeast two-hybrid assays, bimolecular fluorescence complementation and subcellular localization experiments to show that P6 can self-interact to form punctate, cytoplasmic viroplasm-like structures (VLS) when expressed alone in plant cells. The region from residues 395 to 659 is necessary for P6 self-interaction, whereas two polypeptides (residues 580-620 and 615-655) are involved in the subcellular localization of P6. Furthermore, P6 strongly interacts with the viroplasm-associated protein P9-1 and recruits P9-1 to localize in VLS. The P6 395-659 region is also important for the P6-P9-1 interaction, and deleting any region of P9-1 abolishes this heterologous interaction.</p> <p>Conclusions</p> <p>RBSDV P6 protein has an intrinsic ability to self-interact and forms VLS without other RBSDV proteins or RNAs. P6 recruits P9-1 to VLS by direct protein-protein interaction. This is the first report on the functionality of RBSDV P6 protein. P6 may be involved in the process of viroplasm nucleation and virus morphogenesis.</p