Capacitated Vehicle Routing with Non-Uniform Speeds

The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple vehicles having non-uniform speeds (that we call Heterogenous CVRP), and present a constant-factor approximation algorithm. The technical heart of our result lies in achieving a constant approximation to the following TSP variant (called Heterogenous TSP). Given a metric denoting distances between vertices, a depot r containing k vehicles with possibly different speeds, the goal is to find a tour for each vehicle (starting and ending at r), so that every vertex is covered in some tour and the maximum completion time is minimized. This problem is precisely Heterogenous CVRP when vehicles are uncapacitated. The presence of non-uniform speeds introduces difficulties for employing standard tour-splitting techniques. In order to get a better understanding of this technique in our context, we appeal to ideas from the 2-approximation for scheduling in parallel machine of Lenstra et al.. This motivates the introduction of a new approximate MST construction called Level-Prim, which is related to Light Approximate Shortest-path Trees. The last component of our algorithm involves partitioning the Level-Prim tree and matching the resulting parts to vehicles. This decomposition is more subtle than usual since now we need to enforce correlation between the size of the parts and their distances to the depot

Magnetic-field-induced Luttinger liquid

It is shown that a strong magnetic field applied to a bulk metal induces a Luttinger-liquid phase. This phase is characterized by the zero-bias anomaly in tunneling: the tunneling conductance scales as a power-law of voltage or temperature. The tunneling exponent increases with the magnetic field as BlnB. The zero-bias anomaly is most pronounced for tunneling with the field applied perpendicular to the plane of the tunneling junction.Comment: a reference added, minor typos correcte

The Influence of In Vitro Gastrointestinal Digestion on the Anticancer Activity of Manuka Honey

Manuka honey (MH) is a natural food with many beneficial properties to human health, thanks to its high variety of bioactive compounds; however, little is known about its bioaccessibility. The aim of this study was to evaluate and compare the polyphenol compounds, the antioxidant capacity and the anticancer activity of MH subjected to an in vitro gastrointestinal digestion in human HCT-116 colon cancer cells. Raw MH and digested MH (DMH) were assessed for total polyphenols and flavonoids by spectrophotometric and HPLC-ESI-MS/MS analysis, and total antioxidant capacity (TAC) using different methods. Cell viability, intracellular ROS production, apoptosis, cell cycle and colony formation capacity were tested after treatment with MH or DMH. Results showed that total polyphenols, total flavonoids and TAC were significantly (p < 0.05) reduced after in vitro digestion. In addition, MH and DMH at 8, 16 and 24 mg/mL had similar effects in inducing intracellular ROS production and in inhibiting the colon formation ability; MH induced a more marked apoptosis compared to DMH, while cell cycle was blocked in S phase by MH and in Sub G1 phase by DMH. Our results increase knowledge of the effect of gastrointestinal digestion on the biological effect of honey against colorectal cancer

Differential Photoelectron Holography: A New Approach for Three-Dimensional Atomic Imaging

We propose differential holography as a method to overcome the long-standing forward-scattering problem in photoelectron holography and related techniques for the three-dimensional imaging of atoms. Atomic images reconstructed from experimental and theoretical Cu 3p holograms from Cu(001) demonstrate that this method suppresses strong forward-scattering effects so as to yield more accurate three-dimensional images of side- and back-scattering atoms.Comment: revtex, 4 pages, 2 figure

Electron Correlation Effects in Resonant Inelastic X-ray Scattering of NaV2O5

Element- and site-specific resonant inelastic x-ray scattering spectroscopy (RIXS) is employed to investigate electron correlation effects in {$\rm NaV_2O_5$}. In contrast to single photon techniques, RIXS at the vanadium $L_3$ edge is able to probe $d-d^*$ transitions between V d-bands. A sharp energy loss feature is observed at -1.56 eV, which is well reproduced by a model calculation including correlation effects. The calculation identifies the loss feature as excitation between the lower and upper Hubbard bands and permits an accurate determination of the Hubbard interaction term $U= 3.0 \pm 0.2$ eV.Comment: 15 pages, four figures, accepted to Phys. Rev. Let

Spin-Peierls transition in NaV2O5 in high magnetic fields

We investigate the magnetic field dependence of the spin-Peierls transition in NaV$_2$O$_5$ in the field range 16T-30T. The transition temperature exhibits a very weak variation with the field, suggesting a novel mechanism for the formation of the spin-Peierls state. We argue that a charge ordering transition accompanied by singlet formation is consistent with our observations.Comment: 4 pages, 3 figures, final version to appear in Phys. Rev. B (RC