7,134 research outputs found
Using the kinematic Sunyaev-Zeldovich effect to determine the peculiar velocities of clusters of galaxies
We have investigated the possibility of inferring peculiar velocities for
clusters of galaxies from the Doppler shift of scattered cosmic microwave
background (CMB) photons. We find that if the core radius of the gas
distribution or the beam size of the instrument is larger than 3-7 arcminutes,
then the maximum attainable signal-to-noise ratio is determined by confusion
with primary fluctuations. For smaller angular scales, ``cosmic confusion'' is
less important and instrumental noise and/or foreground emission will be the
limiting factor. For a cluster with the optical depth of the Coma cluster and
for an optimal filtering technique, typical one-sigma errors span the wide
range from 400 to 1600 km/s, depending on the cosmological model, the
resolution of the instrument and the core radius of the cluster. The results
have important implications for the design of future high-resolution surveys of
the CMB. Individual peculiar velocities will be measurable only for a few fast
moving clusters at intermediate redshift unless cosmic fluctuations are smaller
than most standard cosmological scenarios predict. However, a reliable
measurement of bulk velocities of ensembles of X-ray bright clusters will be
possible on very large scales (100-500 Mpc/h).Comment: 34 pages, with 11 figures included. Postscript. Submitted to MNRAS.
Latest version (recommended) at http://www.mpa-garching.mpg.de/~max/sz.html
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Nagata compactification for algebraic spaces
We prove the Nagata compactification theorem for any separated map of finite
type between quasi-compact and quasi-separated algebraic spaces, generalizing
earlier results of Raoult. Along the way we also prove (and use) absolute
noetherian approximation for such algebraic spaces, generalizing earlier
results in the case of schemes.Comment: 49 pages, various clarifications and bugfixe
Complexity and Approximation of the Continuous Network Design Problem
We revisit a classical problem in transportation, known as the continuous
(bilevel) network design problem, CNDP for short. We are given a graph for
which the latency of each edge depends on the ratio of the edge flow and the
capacity installed. The goal is to find an optimal investment in edge
capacities so as to minimize the sum of the routing cost of the induced Wardrop
equilibrium and the investment cost. While this problem is considered as
challenging in the literature, its complexity status was still unknown. We
close this gap showing that CNDP is strongly NP-complete and APX-hard, both on
directed and undirected networks and even for instances with affine latencies.
As for the approximation of the problem, we first provide a detailed analysis
for a heuristic studied by Marcotte for the special case of monomial latency
functions (Mathematical Programming, Vol.~34, 1986). Specifically, we derive a
closed form expression of its approximation guarantee for arbitrary sets S of
allowed latency functions. Second, we propose a different approximation
algorithm and show that it has the same approximation guarantee. As our final
-- and arguably most interesting -- result regarding approximation, we show
that using the better of the two approximation algorithms results in a strictly
improved approximation guarantee for which we give a closed form expression.
For affine latencies, e.g., this algorithm achieves a 1.195-approximation which
improves on the 5/4 that has been shown before by Marcotte. We finally discuss
the case of hard budget constraints on the capacity investment.Comment: 27 page
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