403 research outputs found
Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits
It is well known that R^N has subspaces of dimension proportional to N on
which the \ell_1 norm is equivalent to the \ell_2 norm; however, no explicit
constructions are known. Extending earlier work by Artstein--Avidan and Milman,
we prove that such a subspace can be generated using O(N) random bits.Comment: 16 pages; minor changes in the introduction to make it more
accessible to both Math and CS reader
To the center of cold spot with Planck
The structure of the cold spot, of a non-Gaussian anomaly in the cosmic
microwave background (CMB) sky first detected by Vielva et al. is studied using
the data by Planck satellite. The obtained map of the degree of stochasticity
(K-map) of CMB for the cold spot, reveals, most clearly in 100 GHz band, a
shell-type structure with a center coinciding with the minima of the
temperature distribution. The shell structure is non-Gaussian at a 4\sigma
confidence level. Such behavior of the K-map supports the void nature of the
cold spot. The applied method can be used for tracing voids that have no
signatures in redshift surveys.Comment: A & A (in press), 4 pages, 5 figures; to match the published versio
Expected Supremum of a Random Linear Combination of Shifted Kernels
We address the expected supremum of a linear combination of shifts of the
sinc kernel with random coefficients. When the coefficients are Gaussian, the
expected supremum is of order \sqrt{\log n}, where n is the number of shifts.
When the coefficients are uniformly bounded, the expected supremum is of order
\log\log n. This is a noteworthy difference to orthonormal functions on the
unit interval, where the expected supremum is of order \sqrt{n\log n} for all
reasonable coefficient statistics.Comment: To appear in the Journal of Fourier Analysis and Application
Elliptic CMB Sky
The ellipticity of the anisotropy spots of the Cosmic Microwave Background
measured by the Wilkinson Microwave Anisotropy Probe (WMAP) has been studied.
We find an average ellipticity of about 2, confirming with a far larger
statistics similar results found first for the COBE-DMR CMB maps, and then for
the BOOMERanG CMB maps. There are no preferred directions for the obliquity of
the anisotropy spots. The average ellipticity is independent of temperature
threshold and is present on scales both smaller and larger than the horizon at
the last scattering. The measured ellipticity characteristics are consistent
with being the effect of geodesics mixing occurring in an hyperbolic Universe,
and can mark the emergence of CMB ellipticity as a new observable constant
describing the Universe. There is no way of simulating this effect. Therefore
we cannot exclude that the observed behavior of the measured ellipticity can
result from a trivial topology in the popular flat -CDM model, or from
a non-trivial topology.Comment: 10 pages, 5 figures, the version to appear in Mod.Phys.Lett.
Messier 81's Planck view vs its halo mapping
This paper is a follow-up of a previous paper about the M82 galaxy and its
halo based on Planck observations. As in the case of M82, so also for the M81
galaxy a substantial North-South and East-West temperature asymmetry is found,
extending up to galactocentric distances of about . The temperature
asymmetry is almost frequency independent and can be interpreted as a
Doppler-induced effect related to the M81 halo rotation and/or triggered by the
gravitational interaction of the galaxies within the M81 Group. Along with the
analogous study of several nearby edge-on spiral galaxies, the CMB temperature
asymmetry method thus is shown to act as a direct tool to map the galactic
haloes and/or the intergalactic bridges, invisible in other bands or by other
methods.Comment: 5 pages, 3 figures, in press in Astronomy and Astrophysics, Main
Journa
Planck's confirmation of the M31 disk and halo rotation
Planck's data acquired during the first 15.4 months of observations towards
both the disk and halo of the M31 galaxy are analyzed. We confirm the existence
of a temperature asymmetry, previously detected by using the 7-year WMAP data,
along the direction of the M31 rotation, therefore indicative of a
Doppler-induced effect. The asymmetry extends up to about 10 degrees (about 130
kpc) from the M31 center. We also investigate the recent issue raised in Rubin
and Loeb (2014) about the kinetic Sunyaev-Zeldovich effect from the diffuse hot
gas in the Local Group, predicted to generate a hot spot of a few degrees size
in the CMB maps in the direction of M31, where the free electron optical depth
gets the maximum value. We also consider the issue whether in the opposite
direction with respect to the M31 galaxy the same effect induces a minimum in
temperature in the Planck's maps of the sky. We find that the Planck's data at
100 GHz show an effect even larger than that expected.Comment: 4 pages, 1 table, 2 figures, in press as a Letter in A&
Planck view of the M82 galaxy
Planck data towards the galaxy M82 are analyzed in the 70, 100 and 143 GHz
bands. A substantial north-south and East-West temperature asymmetry is found,
extending up to 1 degree from the galactic center. Being almost
frequency-independent, these temperature asymmetries are indicative of a
Doppler-induced effect regarding the line-of-sight dynamics on the halo scale,
the ejections from the galactic center and, possibly, even the tidal
interaction with M81 galaxy. The temperature asymmetry thus acts as a
model-independent tool to reveal the bulk dynamics in nearby edge-on spiral
galaxies, like the Sunyaev-Zeldovich effect for clusters of galaxies.Comment: 4 pages, 3 figures, in press on A&
Planck revealed bulk motion of Centaurus A lobes
Planck data towards the active galaxy Centaurus A are analyzed in the 70, 100
and 143 GHz bands. We find a temperature asymmetry of the northern radio lobe
with respect to the southern one that clearly extends at least up to 5 degrees
from the Cen A center and diminishes towards the outer regions of the lobes.
That transparent parameter - the temperature asymmetry - thus has to carry a
principal information, i.e. indication on the line-of-sight bulk motion of the
lobes, while the increase of that asymmetry at smaller radii reveals the
differential dynamics of the lobes as expected at ejections from the center.Comment: 4 pages, 3 figures, Astronomy & Astrophysics, Letter to the Editor
(in press
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