Extending the range of error estimates for radial approximation in Euclidean space and on spheres

We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both bounded subsets of R^d and spheres. As a step on the way to our ultimate goal we also show convergence of pseudoderivatives of the interpolation error.Comment: 10 page

Description of superdeformed bands in light N=Z nuclei using the cranked HFB method

Superdeformed states in light $N=Z$ nuclei are studied by means of the self-consistent cranking calculation (i.e., the P + QQ model based on the cranked Hartree-Fock-Bogoliubov method). Analyses are given for two typical cases of superdeformed bands in the $A \simeq 40$ mass region, that is, bands where backbending is absent ($^{40}$Ca) and present ($^{36}$Ar). Investigations are carried out, particularly for the following points: cross-shell excitations in the sd and pf shells; the role of the g$_{9/2}$ and d$_{5/2}$ orbitals; the effect of the nuclear pairing; and the interplay between triaxiality and band termination.Comment: 17 pages, 18 figures, accepted in Phys. Rev.

On the Approximability of Digraph Ordering

Given an n-vertex digraph D = (V, A) the Max-k-Ordering problem is to compute a labeling $\ell : V \to [k]$ maximizing the number of forward edges, i.e. edges (u,v) such that $\ell$(u) < $\ell$(v). For different values of k, this reduces to Maximum Acyclic Subgraph (k=n), and Max-Dicut (k=2). This work studies the approximability of Max-k-Ordering and its generalizations, motivated by their applications to job scheduling with soft precedence constraints. We give an LP rounding based 2-approximation algorithm for Max-k-Ordering for any k={2,..., n}, improving on the known 2k/(k-1)-approximation obtained via random assignment. The tightness of this rounding is shown by proving that for any k={2,..., n} and constant $\varepsilon > 0$, Max-k-Ordering has an LP integrality gap of 2 - $\varepsilon$ for $n^{\Omega\left(1/\log\log k\right)}$ rounds of the Sherali-Adams hierarchy. A further generalization of Max-k-Ordering is the restricted maximum acyclic subgraph problem or RMAS, where each vertex v has a finite set of allowable labels $S_v \subseteq \mathbb{Z}^+$. We prove an LP rounding based $4\sqrt{2}/(\sqrt{2}+1) \approx 2.344$ approximation for it, improving on the $2\sqrt{2} \approx 2.828$ approximation recently given by Grandoni et al. (Information Processing Letters, Vol. 115(2), Pages 182-185, 2015). In fact, our approximation algorithm also works for a general version where the objective counts the edges which go forward by at least a positive offset specific to each edge. The minimization formulation of digraph ordering is DAG edge deletion or DED(k), which requires deleting the minimum number of edges from an n-vertex directed acyclic graph (DAG) to remove all paths of length k. We show that both, the LP relaxation and a local ratio approach for DED(k) yield k-approximation for any $k\in [n]$.Comment: 21 pages, Conference version to appear in ESA 201

Social welfare in one-sided matchings: Random priority and beyond

We study the problem of approximate social welfare maximization (without money) in one-sided matching problems when agents have unrestricted cardinal preferences over a finite set of items. Random priority is a very well-known truthful-in-expectation mechanism for the problem. We prove that the approximation ratio of random priority is Theta(n^{-1/2}) while no truthful-in-expectation mechanism can achieve an approximation ratio better than O(n^{-1/2}), where n is the number of agents and items. Furthermore, we prove that the approximation ratio of all ordinal (not necessarily truthful-in-expectation) mechanisms is upper bounded by O(n^{-1/2}), indicating that random priority is asymptotically the best truthful-in-expectation mechanism and the best ordinal mechanism for the problem.Comment: 13 page

Regulation of peripheral inflammation by spinal p38 MAP kinase in rats.

BackgroundSomatic afferent input to the spinal cord from a peripheral inflammatory site can modulate the peripheral response. However, the intracellular signaling mechanisms in the spinal cord that regulate this linkage have not been defined. Previous studies suggest spinal cord p38 mitogen-activated protein (MAP) kinase and cytokines participate in nociceptive behavior. We therefore determined whether these pathways also regulate peripheral inflammation in rat adjuvant arthritis, which is a model of rheumatoid arthritis.Methods and findingsSelective blockade of spinal cord p38 MAP kinase by administering the p38 inhibitor SB203580 via intrathecal (IT) catheters in rats with adjuvant arthritis markedly suppressed paw swelling, inhibited synovial inflammation, and decreased radiographic evidence of joint destruction. The same dose of SB203580 delivered systemically had no effect, indicating that the effect was mediated by local concentrations in the neural compartment. Evaluation of articular gene expression by quantitative real-time PCR showed that spinal p38 inhibition markedly decreased synovial interleukin-1 and -6 and matrix metalloproteinase (MMP3) gene expression. Activation of p38 required tumor necrosis factor alpha (TNFalpha) in the nervous system because IT etanercept (a TNF inhibitor) given during adjuvant arthritis blocked spinal p38 phosphorylation and reduced clinical signs of adjuvant arthritis.ConclusionsThese data suggest that peripheral inflammation is sensed by the central nervous system (CNS), which subsequently activates stress-induced kinases in the spinal cord via a TNFalpha-dependent mechanism. Intracellular p38 MAP kinase signaling processes this information and profoundly modulates somatic inflammatory responses. Characterization of this mechanism could have clinical and basic research implications by supporting development of new treatments for arthritis and clarifying how the CNS regulates peripheral immune responses

Journal Staff

The aluminum–zinc-vacancy (Al Zn −V Zn ) complex is identified as one of the dominant defects in Al-containing n -type ZnO after electron irradiation at room temperature with energies above 0.8 MeV. The complex is energetically favorable over the isolated V Zn , binding more than 90% of the stable V Zn ’s generated by the irradiation. It acts as a deep acceptor with the (0/− ) energy level located at approximately 1 eV above the valence band. Such a complex is concluded to be a defect of crucial and general importance that limits the n -type doping efficiency by complex formation with donors, thereby literally removing the donors, as well as by charge compensation

Hydrogen induced optically-active defects in silicon photonic nanocavities

This work was supported by Era-NET NanoSci LECSIN project coordinated by F. Priolo, by the Italian Ministry of University and Research, FIRB contract No. RBAP06L4S5 and by the EPSRC UKSp project. Partial financial support by the Norwegian Research Council is also acknowledged.We demonstrate intense room temperature photoluminescence (PL) from optically active hydrogen- related defects incorporated into crystalline silicon. Hydrogen was incorporated into the device layer of a silicon on insulator (SOI) wafer by two methods: hydrogen plasma treatment and ion implantation. The room temperature PL spectra show two broad PL bands centered at 1300 and 1500 nm wavelengths: the first one relates to implanted defects while the other band mainly relates to the plasma treatment. Structural characterization reveals the presence of nanometric platelets and bubbles and we attribute different features of the emission spectrum to the presence of these different kind of defects. The emission is further enhanced by introducing defects into photonic crystal (PhC) nanocavities. Transmission electron microscopy analyses revealed that the isotropicity of plasma treatment causes the formation of a higher defects density around the whole cavity compared to the ion implantation technique, while ion implantation creates a lower density of defects embedded in the Si layer, resulting in a higher PL enhancement. These results further increase the understanding of the nature of optically active hydrogen defects and their relation with the observed photoluminescence, which will ultimately lead to the development of intense and tunable crystalline silicon light sources at room temperature.Publisher PDFPeer reviewe

InAs nanowire transistors with multiple, independent wrap-gate segments

We report a method for making horizontal wrap-gate nanowire transistors with up to four independently controllable wrap-gated segments. While the step up to two independent wrap-gates requires a major change in fabrication methodology, a key advantage to this new approach, and the horizontal orientation more generally, is that achieving more than two wrap-gate segments then requires no extra fabrication steps. This is in contrast to the vertical orientation, where a significant subset of the fabrication steps needs to be repeated for each additional gate. We show that cross-talk between adjacent wrap-gate segments is negligible despite separations less than 200 nm. We also demonstrate the ability to make multiple wrap-gate transistors on a single nanowire using the exact same process. The excellent scalability potential of horizontal wrap-gate nanowire transistors makes them highly favourable for the development of advanced nanowire devices and possible integration with vertical wrap-gate nanowire transistors in 3D nanowire network architectures.Comment: 18 pages, 5 figures, In press for Nano Letters (DOI below

Plasma Ejection from Magnetic Flares and the X-ray Spectrum of Cygnus X-1

The hard X-rays in Cyg X-1 and similar black hole sources are possibly produced in an active corona atop an accretion disk. We suggest that the observed weakness of X-ray reflection from the disk is due to bulk motion of the emitting hot plasma away from the reflector. A mildly relativistic motion causes aberration reducing X-ray emission towards the disk. This in turn reduces the reprocessed radiation from the disk and leads to a hard spectrum of the X-ray source. The resulting spectral index is Gamma=1.9B^{1/2} where B=gamma(1+beta) is the aberration factor for a bulk velocity beta=v/c. The observed Gamma=1.6 and the amount of reflection, R=0.3, in Cyg X-1 in the hard state can both be explained assuming a bulk velocity beta=0.3. We discuss one possible scenario: the compact magnetic flares are dominated by e+- pairs which are ejected away from the reflector by the pressure of the reflected radiation. We also discuss physical constraints on the disk-corona model and argue that the magnetic flares are related to magneto-rotational instabilities in the accretion disk.Comment: The final version, accepted for publication in ApJ Letter

Money in monetary policy design: monetary cross-checking in the New-Keynesian model

In the New-Keynesian model, optimal interest rate policy under uncertainty is formulated without reference to monetary aggregates as long as certain standard assumptions on the distributions of unobservables are satisfied. The model has been criticized for failing to explain common trends in money growth and inflation, and that therefore money should be used as a cross-check in policy formulation (see Lucas (2007)). We show that the New-Keynesian model can explain such trends if one allows for the possibility of persistent central bank misperceptions. Such misperceptions motivate the search for policies that include additional robustness checks. In earlier work, we proposed an interest rate rule that is near-optimal in normal times but includes a cross-check with monetary information. In case of unusual monetary trends, interest rates are adjusted. In this paper, we show in detail how to derive the appropriate magnitude of the interest rate adjustment following a significant cross-check with monetary information, when the New-Keynesian model is the central bank’s preferred model. The cross-check is shown to be effective in offsetting persistent deviations of inflation due to central bank misperceptions. Keywords: Monetary Policy, New-Keynesian Model, Money, Quantity Theory, European Central Bank, Policy Under Uncertaint