10,295 research outputs found
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
On the Approximability of Digraph Ordering
Given an n-vertex digraph D = (V, A) the Max-k-Ordering problem is to compute
a labeling maximizing the number of forward edges, i.e.
edges (u,v) such that (u) < (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
, Max-k-Ordering has an LP integrality gap of 2 -
for 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 . We prove an LP rounding based
approximation for it, improving on the
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 .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
Kinetics of electron-positron pair plasmas using an adaptive Monte Carlo method
A new algorithm for implementing the adaptive Monte Carlo method is given. It
is used to solve the relativistic Boltzmann equations that describe the time
evolution of a nonequilibrium electron-positron pair plasma containing
high-energy photons and pairs. The collision kernels for the photons as well as
pairs are constructed for Compton scattering, pair annihilation and creation,
bremsstrahlung, and Bhabha & Moller scattering. For a homogeneous and isotropic
plasma, analytical equilibrium solutions are obtained in terms of the initial
conditions. For two non-equilibrium models, the time evolution of the photon
and pair spectra is determined using the new method. The asymptotic numerical
solutions are found to be in a good agreement with the analytical equilibrium
states. Astrophysical applications of this scheme are discussed.Comment: 43 pages, 7 postscript figures, to appear in the Astrophysical
Journa
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
Time dependent numerical model for the emission of radiation from relativistic plasma
We describe a numerical model constructed for the study of the emission of
radiation from relativistic plasma under conditions characteristic, e.g., to
gamma-ray bursts (GRB's) and active galactic nuclei (AGN's). The model solves
self consistently the kinetic equations for e^\pm and photons, describing
cyclo-synchrotron emission, direct Compton and inverse Compton scattering, pair
production and annihilation, including the evolution of high energy
electromagnetic cascades. The code allows calculations over a wide range of
particle energies, spanning more than 15 orders of magnitude in energy and time
scales. Our unique algorithm, which enables to follow the particle
distributions over a wide energy range, allows to accurately derive spectra at
high energies, >100 \TeV. We present the kinetic equations that are being
solved, detailed description of the equations describing the various physical
processes, the solution method, and several examples of numerical results.
Excellent agreement with analytical results of the synchrotron-SSC model is
found for parameter space regions in which this approximation is valid, and
several examples are presented of calculations for parameter space regions
where analytic results are not available.Comment: Minor changes; References added, discussion on observational status
added. Accepted for publication in Ap.
Older people and local public transit: Mobility effects of accessibility improvements in Sweden
JTLU vol. 2, no. 2, (2009) pp 49-65Several transportation factors concerning older and disabled people are under transition in Sweden at present. By the year 2010, the public transit system must be fully accessible for all passengers. The present survey studied older people, in order to assess the perceived travel opportunities. Questionnaires were sent to a sample of older citizens (75+) in three Swedish mid-sized municipalities. The general conclusions were that even though older people show appreciation of the existing travel opportunities, there was evidence for restricted mobility for some sub-groups of these older people, due to various perceived barriers. These groups have few optional modes, and despite various accessibility measures, special transportation services – the mandatory demand-responsive transport service – continues to provide crucial mobility. Hence, there is more to be done regarding accessibility and usability in public transit for older people. Further studies have to clarify reasons for bus travel cessation. Even larger efforts have to be put into accessibility improvements, in particular intermediate transit solutions in order to meet the regulations and policies
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