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Magnetic structure of our Galaxy: A review of observations
The magnetic structure in the Galactic disk, the Galactic center and the
Galactic halo can be delineated more clearly than ever before. In the Galactic
disk, the magnetic structure has been revealed by starlight polarization within
2 or 3 kpc of the Solar vicinity, by the distribution of the Zeeman splitting
of OH masers in two or three nearby spiral arms, and by pulsar dispersion
measures and rotation measures in nearly half of the disk. The polarized
thermal dust emission of clouds at infrared, mm and submm wavelengths and the
diffuse synchrotron emission are also related to the large-scale magnetic field
in the disk. The rotation measures of extragalactic radio sources at low
Galactic latitudes can be modeled by electron distributions and large-scale
magnetic fields. The statistical properties of the magnetized interstellar
medium at various scales have been studied using rotation measure data and
polarization data. In the Galactic center, the non-thermal filaments indicate
poloidal fields. There is no consensus on the field strength, maybe mG, maybe
tens of uG. The polarized dust emission and much enhanced rotation measures of
background radio sources are probably related to toroidal fields. In the
Galactic halo, the antisymmetric RM sky reveals large-scale toroidal fields
with reversed directions above and below the Galactic plane. Magnetic fields
from all parts of our Galaxy are connected to form a global field structure.
More observations are needed to explore the untouched regions and delineate how
fields in different parts are connected.Comment: 10+1 pages. Invited Review for IAU Symp.259: Cosmic Magnetic Fields:
From Planets, to Stars and Galaxies (Tenerife, Spain. Nov.3-7, 2009). K.G.
Strassmeier, A.G. Kosovichev & J.E. Beckman (eds.
First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources with General Mixture
The first- and second-order optimum achievable exponents in the simple
hypothesis testing problem are investigated. The optimum achievable exponent
for type II error probability, under the constraint that the type I error
probability is allowed asymptotically up to epsilon, is called the
epsilon-optimum exponent. In this paper, we first give the second-order
epsilon-exponent in the case where the null hypothesis and the alternative
hypothesis are a mixed memoryless source and a stationary memoryless source,
respectively. We next generalize this setting to the case where the alternative
hypothesis is also a mixed memoryless source. We address the first-order
epsilon-optimum exponent in this setting. In addition, an extension of our
results to more general setting such as the hypothesis testing with mixed
general source and the relationship with the general compound hypothesis
testing problem are also discussed.Comment: 23 page
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