Online k-taxi via double coverage and time-reverse primal-dual

We consider the online k-taxi problem, a generalization of the k-server problem, in which k servers are located in a metric space. A sequence of requests is revealed one by one, where each request is a pair of two points, representing the start and destination of a travel request by a passenger. The goal is to serve all requests while minimizing the distance traveled without carrying a passenger. We show that the classic Double Coverage algorithm has competitive ratio 2 k- 1 on HSTs, matching a recent lower bound for deterministic algorithms. For bounded depth HSTs, the competitive ratio turns out to be much better and we obtain tight bounds. When the depth is d≪ k, these bounds are approximately kd/ d!. By standard embedding results, we obtain a randomized algorithm for arbitrary n-point metrics with (polynomial) competitive ratio O(kcΔ 1/clog Δn), where Δ is the aspect ratio and c≥ 1 is an arbitrary positive integer constant. The only previous known bound was O(2 klog n). For general (weighted) tree metrics, we prove the competitive ratio of Double Coverage to be Θ (kd) for any fixed depth d, but unlike on HSTs it is not bounded by 2 k- 1. We obtain our results by a dual fitting analysis where the dual solution is constructed step-by-step backwards in time. Unlike the forward-time approach typical of online primal-dual analyses, this allows us to combine information from the past and the future when assigning dual variables. We believe this method can be useful also for other problems. Using this technique, we also provide a dual fitting proof of the k-competitiveness of Double Coverage for the k-server problem on trees

Efficient online weighted multi-level paging

We study the writeback-aware caching problem, a variant of classic paging where paging requests that modify data and requests that leave data intact are treated differently. We give an O(log^2 k) competitive randomized algorithm, answering an open question of Beckmann et al. [8] and Even et

Receptors for Hyaluronic Acid and Poliovirus: A Combinatorial Role in Glioma Invasion?

Background: CD44 has long been associated with glioma invasion while, more recently, CD155 has been implicated in playing a similar role. Notably, these two receptors have been shown closely positioned on monocytes. Methods and Findings: In this study, an up-regulation of CD44 and CD155 was demonstrated in established and earlypassage cultures of glioblastoma. Total internal reflected fluorescence (TIRF) microscopy revealed close proximity of CD44 and CD155. CD44 antibody blocking and gene silencing (via siRNA) resulted in greater inhibition of invasion than that for CD155. Combined interference resulted in 86 % inhibition of invasion, although in these investigations no obvious evidence of synergy between CD44 and CD155 in curbing invasion was shown. Both siRNA-CD44 and siRNA-CD155 treated cells lacked processes and were rounder, while live cell imaging showed reduced motility rate compared to wild type cells. Adhesion assay demonstrated that wild type cells adhered most efficiently to laminin, whereas siRNA-treated cells (p,0.0001 for both CD44 and CD155 expression) showed decreased adhesion on several ECMs investigated. BrdU assay showed a higher proliferation of siRNA-CD44 and siRNA-CD155 cells, inversely correlated with reduced invasion. Confocal microscopy revealed overlapping of CD155 and integrins (b1, avb1 and avb3) on glioblastoma cell processes whereas siRNAtransfected cells showed consequent reduction in integrin expression with no specific staining patterns. Reduced expression of Rho GTPases, Cdc42, Rac1/2/3, RhoA and RhoB, was seen in siRNA-CD44 and siRNA-CD155 cells. In contrast t

CD44v4 Is a Major E-Selectin Ligand that Mediates Breast Cancer Cell Transendothelial Migration

BACKGROUND: Endothelial E-selectin has been shown to play a pivotal role in mediating cell-cell interactions between breast cancer cells and endothelial monolayers during tumor cell metastasis. However, the counterreceptor for E-selectin and its role in mediating breast cancer cell transendothelial migration remain unknown. METHODOLOGY/PRINCIPAL FINDINGS: By assessing migration of various breast cancer cells across TNF-alpha pre-activated human umbilical vein endothelial cells (HUVECs), we found that breast cancer cells migrated across HUVEC monolayers differentially and that transmigration was E-selectin dependent. Cell surface labeling with the E-selectin extracellular domain/Fc chimera (exE-selectin/Fc) showed that the transmigration capacity of breast cancer cells was correlated to both the expression level and localization pattern of E-selectin binding protein(s) on the tumor cell surface. The exE-selectin/Fc strongly bound to metastatic MDA-MB-231, MDA-MB-435 and MDA-MB-468 cells, but not non-metastatic MCF-7 and T47D cells. Binding of exE-selectin/Fc was abolished by removal of tumor cell surface sialyl lewis x (sLe(x)) moieties. Employing an exE-selectin/Fc affinity column, we further purified the counterreceptor of E-selectin from metastatic breast cancer cells. The N-terminal protein sequence and cDNA sequence identified this E-selectin ligand as a approximately 170 kD human CD44 variant 4 (CD44v4). Purified CD44v4 showed a high affinity for E-selectin via sLe(x) moieties and, as expected, MDA-MB-231 cell adhesion to and migration across HUVEC monolayers were significantly reduced by down-regulation of tumor cell CD44v4 via CD44v4-specific siRNA. CONCLUSIONS/SIGNIFICANCE: We demonstrated, for the first time, that breast cancer cell CD44v4 is a major E-selectin ligand in facilitating tumor cell migration across endothelial monolayers. This finding offers new insights into the molecular basis of E-selectin-dependent adhesive interactions that mediate breast cancer cell transendothelial metastasis

Data for The role of nuclear quantum effects in the relative stability of hexagonal and cubic ice

At atmospheric pressure, hexagonal ice (Ih) is thermodynamically stable relative to cubic ice (Ic), although the magnitude and underlying physical origin of this stability difference are not well defined. Pure Ic crystals are not accessible experimentally, and hence computer simulations have often been used to interrogate the relative stabilities of Ih and Ic; however, these simulations are dominated by molecular interaction models that ignore the intramolecular flexibility of individual water molecules, do not describe intermolecular hydrogen-bonding with sufficient accuracy, or ignore the role of nuclear quantum effects (NQEs) such as zero-point energy. Here, we show that when comparing the relative stability of Ih and Ic using a flexible, anharmonic molecular interaction model, while also accurately accounting for NQEs, a new picture emerges: Ih is stabilized relative to Ic as a result of subtle differences in the intramolecular geometries and intermolecular interactions of water molecules which are modulated by NQEs. Our simulations hence suggest that NQEs are a major contributor to the stabilization of Ih under terrestrial conditions and thus contribute to the well-known hexagonal (sixfold) symmetry of ice crystals