Convergence Analysis of Meshfree Approximation Schemes

This work is concerned with the formulation of a general framework for the analysis of meshfree approximation schemes and with the convergence analysis of the local maximum-entropy (LME) scheme as a particular example. We provide conditions for the convergence in Sobolev spaces of schemes that are n-consistent in the sense of exactly reproducing polynomials of degree less than or equal to n ≥ 1 and whose basis functions are of rapid decay. The convergence of the LME in W^(1,p)_(loc) (Ω) follows as a direct application of the general theory. The analysis shows that the convergence order is linear in h, a measure of the density of the point set. The analysis also shows how to parameterize the LME scheme for optimal convergence. Because of the convex approximation property of LME, its behavior near the boundary is singular and requires additional analysis. For the particular case of polyhedral domains we show that, away from a small singular part of the boundary, any Sobolev function can be approximated by means of the LME scheme. With the aid of a capacity argument, we further obtain approximation results with truncated LME basis functions in H^1(Ω) and for spatial dimension d > 2

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

Mycobacterium tuberculosis infection modulates adipose tissue biology

Mycobacterium tuberculosis (Mtb) primarily resides in the lung but can also persist in extrapulmonary sites. Macrophages are considered the prime cellular habitat in all tissues. Here we demonstrate that Mtb resides inside adipocytes of fat tissue where it expresses stress-related genes. Moreover, perigonadal fat of Mtb-infected mice disseminated the infection when transferred to uninfected animals. Adipose tissue harbors leukocytes in addition to adipocytes and other cell types and we observed that Mtb infection induces changes in adipose tissue biology depending on stage of infection. Mice infected via aerosol showed infiltration of inducible nitric oxide synthase (iNOS) or arginase 1 (Arg1)-negative F4/80+ cells, despite recruitment of CD3+, CD4+ and CD8+ T cells. Gene expression analysis of adipose tissue of aerosol Mtb-infected mice provided evidence for upregulated expression of genes associated with T cells and NK cells at 28 days post-infection. Strikingly, IFN-γ-producing NK cells and Mtb-specific CD8+ T cells were identified in perigonadal fat, specifically CD8+CD44-CD69+ and CD8+CD44-CD103+ subpopulations. Gene expression analysis of these cells revealed that they expressed IFN-γ and the lectin-like receptor Klrg1 and down-regulated CD27 and CD62L, consistent with an effector phenotype of Mtb-specific CD8+ T cells. Sorted NK cells expressed higher abundance of Klrg1 upon infection, as well. Our results reveal the ability of Mtb to persist in adipose tissue in a stressed state, and that NK cells and Mtb-specific CD8+ T cells infiltrate infected adipose tissue where they produce IFN-γ and assume an effector phenotype. We conclude that adipose tissue is a potential niche for Mtb and that due to infection CD8+ T cells and NK cells are attracted to this tissue

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

Phase diagram of bismuth in the extreme quantum limit

Elemental bismuth provides a rare opportunity to explore the fate of a three-dimensional gas of highly mobile electrons confined to their lowest Landau level. Coulomb interaction, neglected in the band picture, is expected to become significant in this extreme quantum limit with poorly understood consequences. Here, we present a study of the angular-dependent Nernst effect in bismuth, which establishes the existence of ultraquantum field scales on top of its complex single-particle spectrum. Each time a Landau level crosses the Fermi level, the Nernst response sharply peaks. All such peaks are resolved by the experiment and their complex angular-dependence is in very good agreement with the theory. Beyond the quantum limit, we resolve additional Nernst peaks signaling a cascade of additional Landau sub-levels caused by electron interaction

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