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

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 $\Lambda$-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 $1.5^\circ$. 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

Triangulum galaxy viewed by Planck

We used Planck data to study the M33 galaxy and find a substantial temperature asymmetry with respect to its minor axis projected onto the sky plane. This temperature asymmetry correlates well with the HI velocity field at 21 cm, at least within a galactocentric distance of 0.5 degree, and it is found to extend up to about 3 degrees from the galaxy center. We conclude that the revealed effect, that is, the temperature asymmetry and its extension, implies that we detected the differential rotation of the M33 galaxy and of its extended baryonic halo.Comment: 8 pages, 8 figures, in press on Astronomy and Astrophysics, main journa

From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking

The existence of quantum uncertainty relations is the essential reason that some classically impossible cryptographic primitives become possible when quantum communication is allowed. One direct operational manifestation of these uncertainty relations is a purely quantum effect referred to as information locking. A locking scheme can be viewed as a cryptographic protocol in which a uniformly random n-bit message is encoded in a quantum system using a classical key of size much smaller than n. Without the key, no measurement of this quantum state can extract more than a negligible amount of information about the message, in which case the message is said to be "locked". Furthermore, knowing the key, it is possible to recover, that is "unlock", the message. In this paper, we make the following contributions by exploiting a connection between uncertainty relations and low-distortion embeddings of L2 into L1. We introduce the notion of metric uncertainty relations and connect it to low-distortion embeddings of L2 into L1. A metric uncertainty relation also implies an entropic uncertainty relation. We prove that random bases satisfy uncertainty relations with a stronger definition and better parameters than previously known. Our proof is also considerably simpler than earlier proofs. We apply this result to show the existence of locking schemes with key size independent of the message length. We give efficient constructions of metric uncertainty relations. The bases defining these metric uncertainty relations are computable by quantum circuits of almost linear size. This leads to the first explicit construction of a strong information locking scheme. Moreover, we present a locking scheme that is close to being implementable with current technology. We apply our metric uncertainty relations to exhibit communication protocols that perform quantum equality testing.Comment: 60 pages, 5 figures. v4: published versio

Almost-Euclidean subspaces of ℓ1N\ell_1^N via tensor products: a simple approach to randomness reduction

It has been known since 1970's that the N-dimensional $\ell_1$-space contains nearly Euclidean subspaces whose dimension is $\Omega(N)$. However, proofs of existence of such subspaces were probabilistic, hence non-constructive, which made the results not-quite-suitable for subsequently discovered applications to high-dimensional nearest neighbor search, error-correcting codes over the reals, compressive sensing and other computational problems. In this paper we present a "low-tech" scheme which, for any $a > 0$, allows to exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$ while using only $N^a$ random bits. Our results extend and complement (particularly) recent work by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1) simplicity (we use only tensor products) and (2) yielding "almost Euclidean" subspaces with arbitrarily small distortions.Comment: 11 pages; title change, abstract and references added, other minor change