7,734 research outputs found
The Niceness of Unique Sink Orientations
Random Edge is the most natural randomized pivot rule for the simplex
algorithm. Considerable progress has been made recently towards fully
understanding its behavior. Back in 2001, Welzl introduced the concepts of
\emph{reachmaps} and \emph{niceness} of Unique Sink Orientations (USO), in an
effort to better understand the behavior of Random Edge. In this paper, we
initiate the systematic study of these concepts. We settle the questions that
were asked by Welzl about the niceness of (acyclic) USO. Niceness implies
natural upper bounds for Random Edge and we provide evidence that these are
tight or almost tight in many interesting cases. Moreover, we show that Random
Edge is polynomial on at least many (possibly cyclic) USO. As
a bonus, we describe a derandomization of Random Edge which achieves the same
asymptotic upper bounds with respect to niceness and discuss some algorithmic
properties of the reachmap.Comment: An extended abstract appears in the proceedings of Approx/Random 201
Nonlinear force-free coronal magnetic stereoscopy
Getting insights into the 3D structure of the solar coronal magnetic field
have been done in the past by two completely different approaches: (1.)
Nonlinear force-free field (NLFFF) extrapolations, which use photospheric
vector magnetograms as boundary condition. (2.) Stereoscopy of coronal magnetic
loops observed in EUV coronal images from different vantage points. Both
approaches have their strength and weaknesses. Extrapolation methods are
sensitive to noise and inconsistencies in the boundary data and the accuracy of
stereoscopy is affected by the ability of identifying the same structure in
different images and by the separation angle between the view directions. As a
consequence, for the same observational data, the computed 3D coronal magnetic
field with the two methods do not necessarily coincide. In an earlier work
(Paper I) we extended our NLFFF optimization code by the inclusion of
stereoscopic constrains. The method was successfully tested with synthetic data
and within this work we apply the newly developed code to a combined data-set
from SDO/HMI, SDO/AIA and the two STEREO spacecraft. The extended method
(called S-NLFFF) contains an additional term that monitors and minimizes the
angle between the local magnetic field direction and the orientation of the 3D
coronal loops reconstructed by stereoscopy. We find that prescribing the shape
of the 3D stereoscopically reconstructed loops the S-NLFFF method leads to a
much better agreement between the modeled field and the stereoscopically
reconstructed loops. We also find an appreciable decrease by a factor of two in
the angle between the current and the magnetic field which indicates the
improved quality of the force-free solution obtained by S-NLFFF.Comment: 9 pages, 7 figure
A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus
We compare the eigenvalues of the Dirac and Laplace operator on a
two-dimensional torus with respect to the trivial spin structure. In
particular, we compute their variation up to order 4 upon deformation of the
flat metric, study the corresponding Hamiltonian and discuss several families
of examples.Comment: Latex2.09, 28 pages, with figure
Distributed Channel Assignment in Cognitive Radio Networks: Stable Matching and Walrasian Equilibrium
We consider a set of secondary transmitter-receiver pairs in a cognitive
radio setting. Based on channel sensing and access performances, we consider
the problem of assigning channels orthogonally to secondary users through
distributed coordination and cooperation algorithms. Two economic models are
applied for this purpose: matching markets and competitive markets. In the
matching market model, secondary users and channels build two agent sets. We
implement a stable matching algorithm in which each secondary user, based on
his achievable rate, proposes to the coordinator to be matched with desirable
channels. The coordinator accepts or rejects the proposals based on the channel
preferences which depend on interference from the secondary user. The
coordination algorithm is of low complexity and can adapt to network dynamics.
In the competitive market model, channels are associated with prices and
secondary users are endowed with monetary budget. Each secondary user, based on
his utility function and current channel prices, demands a set of channels. A
Walrasian equilibrium maximizes the sum utility and equates the channel demand
to their supply. We prove the existence of Walrasian equilibrium and propose a
cooperative mechanism to reach it. The performance and complexity of the
proposed solutions are illustrated by numerical simulations.Comment: submitted to IEEE Transactions on Wireless Communicaitons, 13 pages,
10 figures, 4 table
Torus models for obscuration in type 2 AGN
We discuss a clumpy model of obscuring dusty tori around AGN. Cloud-cloud
collisions lead to an effective viscosity and a geometrically thick accretion
disk, which has the required properties of a torus.
Accretion in the combined gravitational potential of central black hole and
stellar cluster generates free energy, which is dissipated in collisions, and
maintains the thickness of the torus. A quantitative treatment for the torus in
the prototypical Seyfert 2 nucleus of NGC 1068 together with a radiative
transfer calculation for NIR re-emission from the torus is presented.Comment: 6 pages, 2 figures, contributed paper to Proceedings of the
Conference "Growing Black Holes" held in Garching, Germany, June 21-25, 2004,
edited by A. Merloni, S. Nayakshin and R. Sunyaev, Springer-Verlag series of
"ESO Astrophysics Symposia
A two parameter ratio-product-ratio estimator using auxiliary information
We propose a two parameter ratio-product-ratio estimator for a finite
population mean in a simple random sample without replacement following the
methodology in Ray and Sahai (1980), Sahai and Ray (1980), Sahai and Sahai
(1985) and Singh and Ruiz Espejo (2003).
The bias and mean square error of our proposed estimator are obtained to the
first degree of approximation. We derive conditions for the parameters under
which the proposed estimator has smaller mean square error than the sample
mean, ratio and product estimators.
We carry out an application showing that the proposed estimator outperforms
the traditional estimators using groundwater data taken from a geological site
in the state of Florida.Comment: 13 pages, 2 figures, 4 table
Polarization and Rising Wage Inequality: Comparing the U.S. and Germany
This paper compares trends in wage inequality in the U.S. and Germany using an approach developed by MaCurdy and Mroz (1995) to separate age, time, and cohort effects. Between 1979 and 2004, wage inequality increased strongly in both the U.S. and Germany but there were various country specific aspects of this increase. For the U.S., we find faster wage growth since the 1990s at the top (80% quantile) and the bottom (20% quantile) compared to the median of the wage distribution, which is evidence for polarization in the U.S. labor market. In contrast, we find little evidence for wage polarization in Germany. Moreover, we see a large role played by cohort effects in Germany, while we find only small cohort effects in the U.S. Employment trends in both countries are consistent with polarization since the 1990s. We conclude that although there is evidence in both the U.S. and Germany which is consistent with a technology-driven polarization of the labor market, the patterns of trends in wage inequality differ strongly enough that technology effects alone cannot explain the empirical findings.wage inequality, polarization, international comparison, cohort study, quantile regression
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