4,015 research outputs found
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
Emission Spectra from Internal Shocks in Gamma-Ray-Burst Sources
Unsteady activity of gamma-ray burst sources leads to internal shocks in
their emergent relativistic wind. We study the emission spectra from such
shocks, assuming that they produce a power-law distribution of relativistic
electrons and posses strong magnetic fields. The synchrotron radiation emitted
by the accelerated electrons is Compton up-scattered multiple times by the same
electrons. A substantial component of the scattered photons acquires high
energies and produces e+e- pairs. The pairs transfer back their kinetic energy
to the radiation through Compton scattering. The generic spectral signature
from pair creation and multiple Compton scattering is highly sensitive to the
radius at which the shock dissipation takes place and to the Lorentz factor of
the wind. The entire emission spectrum extends over a wide range of photon
energies, from the optical regime up to TeV energies. For reasonable values of
the wind parameters, the calculated spectrum is found to be in good agreement
with the burst spectra observed by BATSE.Comment: 12 pages, latex, 2 figures, submitted to ApJ
New Notions and Constructions of Sparsification for Graphs and Hypergraphs
A sparsifier of a graph G (Benczu´r and Karger; Spielman and Teng) is a sparse weighted subgraph ˜ G that approximately retains the same cut structure of G. For general graphs, non-trivial sparsification is possible only by using weighted graphs in which different edges have different weights. Even for graphs that admit unweighted sparsifiers (that is, sparsifiers in which all the edge weights are equal to the same scaling factor), there are no known polynomial time algorithms that find such unweighted sparsifiers. We study a weaker notion of sparsification suggested by Oveis Gharan, in which the number of cut edges in each cut (S, ¯ S) is not approximated within a multiplicative factor (1 + ǫ), but is, instead, approximated up to an additive term bounded by ǫ times d · |S| + vol(S), where d is the average
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
Gambling: Electronic friends or a threat to one's health and personal development?
Gambling has become quite common in Sweden. The Swedish National Institute of Public Health (2010) has reported that about 70% of the Swedish population has gambled at least once during the last 12 months. Half of the population had gambled with money by 18 years of age and about 11% had gambled for the first time when they were 12-years-old or younger. In the report from the Swedish National Institute of Public Health, gambling problems are related to health problems and risky alcohol consumption. The highest problem rate is found among men aged 18 to 24; almost 1 in 10 had some gambling problems. The share of problem gamblers is found to be twice as high among the under-age gamblers as it is among the population as a whole. Young people gamble less but develop gambling problems to a larger extent than adult gamblers. In this article young people's gambling and their gambling careers are analysed as a natural part of their internalisation of other adult habits
Uncertainty About the Persistence of Inflation
This paper offers several contributions to actual research and discussion on monetary policy. It clarifies the relationship between uncertainty of inflation persistence and optimal monetary policy and discusses the consequences of the recent Blanchard proposal to implement a higher inflation target in the light of parameter uncertainty. Furthermore, it provides insights of general interest on the methodological level by analyzing the interrelations between normalization of variables and their independence properties and by extending standard solution methods of dynamic programming problems to non-orthogonal parameter uncertainty
Effect of plasma elongation on current dynamics during tokamak disruptions
Plasma terminating disruptions in tokamaks may result in relativistic runaway
electron beams with potentially serious consequences for future devices with
large plasma currents. In this paper we investigate the effect of plasma
elongation on the coupled dynamics of runaway generation and resistive
diffusion of the electric field. We find that elongated plasmas are less likely
to produce large runaway currents, partly due to the lower induced electric
fields associated with larger plasmas, and partly due to direct shaping
effects, which mainly lead to a reduction in the runaway avalanche gain.Comment: 11 pages, 3 figure
Determination of the Bending Rigidity of Graphene via Electrostatic Actuation of Buckled Membranes
The small mass and atomic-scale thickness of graphene membranes make them
highly suitable for nanoelectromechanical devices such as e.g. mass sensors,
high frequency resonators or memory elements. Although only atomically thick,
many of the mechanical properties of graphene membranes can be described by
classical continuum mechanics. An important parameter for predicting the
performance and linearity of graphene nanoelectromechanical devices as well as
for describing ripple formation and other properties such as electron
scattering mechanisms, is the bending rigidity, {\kappa}. In spite of the
importance of this parameter it has so far only been estimated indirectly for
monolayer graphene from the phonon spectrum of graphite, estimated from AFM
measurements or predicted from ab initio calculations or bond-order potential
models. Here, we employ a new approach to the experimental determination of
{\kappa} by exploiting the snap-through instability in pre-buckled graphene
membranes. We demonstrate the reproducible fabrication of convex buckled
graphene membranes by controlling the thermal stress during the fabrication
procedure and show the abrupt switching from convex to concave geometry that
occurs when electrostatic pressure is applied via an underlying gate electrode.
The bending rigidity of bilayer graphene membranes under ambient conditions was
determined to be eV. Monolayers have significantly lower
{\kappa} than bilayers
u-RANIA: a neutron detector based on \mu -RWELL technology
In the framework of the ATTRACT-uRANIA project, funded by the European
Community, we are developing an innovative neutron imaging detector based on
micro-Resistive WELL ( -RWELL) technology. The -RWELL, based on the
resistive detector concept, ensuring an efficient spark quenching mechanism, is
a highly reliable device. It is composed by two main elements: a readout-PCB
and a cathode. The amplification stage for this device is embedded in the
readout board through a resistive layer realized by means of an industrial
process with DLC (Diamond-Like Carbon). A thin layer of BC on the copper
surface of the cathode allows the thermal neutrons detection through the
release of Li and particles in the active volume. This technology
has been developed to be an efficient and convenient alternative to the He
shortage. The goal of the project is to prove the feasibility of such a novel
neutron detector by developing and testing small planar prototypes with readout
boards suitably segmented with strip or pad read out, equipped with existing
electronics or readout in current mode. Preliminary results from the test with
different prototypes, showing a good agreement with the simulation, will be
presented together with construction details of the prototypes and the future
steps of the project.Comment: Prepared for the INSTR20 Conference Proceeding for JINS
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