An exact algorithm for minimum distortion embedding

Let G be an unweighted connected graph on n vertices. We show that an embedding of the shortest path metric of G into the line with minimum distortion can be found in time 5^n+o(n). This is the first algorithm breaking the trivial n!-barrier.     

Spanners of bounded degree graphs

A k-spanner of a graph G is a spanning subgraph of G in which the distance between any pair of vertices is at most k times the distance in G. We prove that for fixed k,w, the problem of deciding if a given graph has a k-spanner of treewidth w is fixed-parameter tractable on graphs of bounded degree. In particular, this implies that finding a k-spanner that is a tree (a tree k-spanner) is fixed-parameter tractable on graphs of bounded degree. In contrast, we observe that if the graph has only one vertex of unbounded degree, then Treek-Spanner is NP-complete for k?4.     

Fast Minor Testing in Planar Graphs

Minor Containment is a fundamental problem in Algorithmic Graph Theory used as a subroutine in numerous graph algorithms. A model of a graph H in a graph G is a set of disjoint connected subgraphs of G indexed by the vertices of H, such that if {u,v} is an edge of H, then there is an edge of G between components C _u and C _v . A graph H is a minor of G if G contains a model of H as a subgraph. We give an algorithm that, given a planar n-vertex graph G and an h-vertex graph H, either finds in time $\mathcal{O}(2^{\mathcal{O}(h)} \cdot n +n^{2}\cdot\log n)$ a model of H in G, or correctly concludes that G does not contain H as a minor. Our algorithm is the first single-exponential algorithm for this problem and improves all previous minor testing algorithms in planar graphs. Our technique is based on a novel approach called partially embedded dynamic programming.     

DNA Break Mapping Reveals Topoisomerase II Activity Genome-Wide

Genomic DNA is under constant assault by endogenous and exogenous DNA damaging agents. DNA breakage can represent a major threat to genome integrity but can also be necessary for genome function. Here we present approaches to map DNA double-strand breaks (DSBs) and single-strand breaks (SSBs) at the genome-wide scale by two methods called DSB- and SSB-Seq, respectively. We tested these methods in human colon cancer cells and validated the results using the Topoisomerase II (Top2)-poisoning agent etoposide (ETO). Our results show that the combination of ETO treatment with break-mapping techniques is a powerful method to elaborate the pattern of Top2 enzymatic activity across the genome.     

Effect of oxide nanofillers on fabrication,structure, and properties of zirconia-based composites

We have studied the effect of NiO on the sintering of yttria-stabilized zirconia at temperatures ranging from 1300 °C to 1500 °C in air and argon environments. It was found that the addition of NiO stabilized the cubic phase of ZrO₂ independently from the sintering atmosphere. The monoclinic phase of ZrO₂ formed only during sintering within the air environment at temperatures higher than 1450 °C. The transformation of NiO to Ni by reversible decomposition depends on the sintering atmosphere, and this can lead to variations in the nature of inclusions and in changes of the structure and properties of nanocomposite materials in the system ZrO₂–NiO(Ni). NiO and Ni inclusions can increase the indentation fracture toughness of zirconia–nickel oxide composite material more than 50%, which can be compared with zirconia ceramics during sintering in a neutral atmosphere alone.     

Interplay between nitronates and nitriles accomplished in a PtIV-mediated reaction

Reaction between the coordinated propanenitriles in trans-[PtCl₄(EtCN)₂] and the cyclic nitronate

(1) gives the N-acylated iminocomplex

(2) which is unstable in wet solvents and undergoes hydrolysis to furnish

(3). The formulation of 2 and 3 was supported by satisfactory C, H, and N elemental analyses, agreeable HRESI⁺-MS, IR, ¹H NMR spectroscopies, and single-crystal X-ray diffraction (for trans-3).     

Novel Antitumor L‐Arabinose Derivative of Indolocarbazole with High Affinity to DNA

Novel indolocarbazole derivative 12‐(α‐L ‐arabinopyranosyl)indolo[2,3‐α]pyrrolo[3,4‐c]carbazole‐5,7‐dione (AIC) demonstrated high potency (at submicromolar concentrations) against the NCI panel of human tumor cell lines and transplanted tumors in vivo. In search of tentative targets for AIC, we found that the drug formed high affinity intercalative complexes with d(AT)₂₀, d(GC)₂₀ and calf thymus DNA (binding constants (1.6×10⁶) M ^?1≤K_a≤(3.3×10⁶) M ^?1). The drug intercalated preferentially into GC pairs of the duplex. Importantly, the concentrations at which AIC formed the intercalative complexes with DNA (C≤1 μM ) were identical to the concentrations that triggered p53‐dependent gene reporter transactivation, the replication block, the inhibition of topoisomerase I‐mediated DNA relaxation and death of HCT116 human colon carcinoma cells. We conclude that the formation of high affinity intercalative complexes with DNA is an important factor for anticancer efficacy of AIC.