Searcharxiv⌕ Search

arXiv subjects

Shamik Ghosh

Publications and source records attributed to Shamik Ghosh.

47 records · Page 3Linked to original sources
arXiv2017

Dipole Modulation of Cosmic Microwave Background Temperature and Polarization

We propose a dipole modulation model for the Cosmic Microwave Background Radiation (CMBR) polarization field. We show that the model leads to correlations between l and l+1 multipoles, exactly as in the case of temperature. We obtain results for the case of TE, EE and BB correlations. An anisotropic or inhomogeneous model of primordial power spectrum which leads to such correlations in temperature field also predicts similar correlations in CMBR polarization. We analyze the CMBR temperature and polarization data in order to extract the signal of these correlation between l and l+1 multipoles. Our results for the case of temperature using the latest PLANCK data agree with those obtained by an earlier analysis. A detailed study of the correlation in the polarization data is not possible at present. Hence we restrict ourselves to a preliminary investigation in this case.

astro-ph.CO↗
arXiv2017

Imprint of Inhomogeneous and Anisotropic Primordial Power Spectrum on CMB Polarization

We consider an inhomogeneous model and independently an anisotropic model of primordial power spectrum in order to describe the observed hemispherical anisotropy in Cosmic Microwave Background Radiation. This anisotropy can be parametrized in terms of the dipole modulation model of the temperature field. Both the models lead to correlations between spherical harmonic coefficients corresponding to multipoles, l and l \pm 1. We obtain the model parameters by making a fit to TT correlations in CMBR data. Using these parameters we predict the signature of our models for correlations among different multipoles for the case of the TE and EE modes. These predictions can be used to test whether the observed hemispherical anisotropy can be correctly described in terms of a primordial power spectrum. Furthermore these may also allow us to distinguish between an inhomogeneous and an anisotropic model.

astro-ph.CO↗
arXiv2017

Testing the isotropy of the log N - log S slope for the NVSS radio catalogue

The cumulative number count $N$, of sources above a threshold is known to approximately follow a power law behaviour $N\propto S^{-x}$. We study the variation of spectral index $x$ across the sky in order to look for possible signals of violation of isotropy. We develop a rigorous algorithm of likelihood maximisation to accurately fit for the spectral index. We divide the sky into upper and lower hemispheres for a particular choice of $z$-axis and determine the difference $Δx$ between the best fit values of the spectral indices between the two hemispheres. The maximum value of this difference obtained by varying over the $z$-axis provides us with a measure of departure from isotropy. We find that the data support isotropy of the spectral index. The maximum difference is found to be 1.3\% of the full sky best fit value of $x$. The deviation is found to be significant only at 2$σ$ level which indicates a weak departure from isotropy. We also perform a dipole fit to the spectral index as a function of the angular coordinates. The result is found to be consistent with isotropy.

astro-ph.CO↗
arXiv2016

Probing statistical isotropy of cosmological radio sources using SKA

There currently exist many observations which are not consistent with the cosmological principle. We review these observations with a particular emphasis on those relevant for Square Kilometre Array (SKA). In particular, several different data sets indicate a preferred direction pointing approximately towards the Virgo cluster. We also observe a hemispherical anisotropy in the Cosmic Microwave Background Radiation (CMBR) temperature fluctuations. Although these inconsistencies may be attributed to systematic effects, there remains the possibility that they indicate new physics and various theories have been proposed to explain them. One possibility, which we discuss in this review, is the generation of perturbation modes during the early pre-inflationary epoch, when the Universe may not obey the cosmological principle. Better measurements will provide better constraints on these theories. In particular, we propose measurement of the dipole in number counts, sky brightness, polarized flux and polarization orientations of radio sources. We also suggest test of alignment of linear polarizations of sources as a function of their relative separation. Finally we propose measurement of hemispherical anisotropy or equivalently dipole modulation in radio sources.

astro-ph.CO↗
arXiv2016

An introduction to coding sequences of graphs

In his pioneering paper on matroids in 1935, Whitney obtained a characterization for binary matroids and left a comment at end of the paper that the problem of characterizing graphic matroids is the same as that of characterizing matroids which correspond to matrices (mod 2) with exactly two ones in each column. Later on Tutte obtained a characterization of graphic matroids in terms of forbidden minors in 1959. It is clear that Whitney indicated about incidence matrices of simple undirected graphs. Here we introduce the concept of a segment binary matroid which corresponds to matrices over $\mathbb{Z}_2$ which has the consecutive $1$'s property (i.e., $1$'s are consecutive) for columns and obtained a characterization of graphic matroids in terms of this. In fact, we introduce a new representation of simple undirected graphs in terms of some vectors of finite dimensional vector spaces over $\mathbb{Z}_2$ which satisfy consecutive $1$'s property. The set of such vectors is called a coding sequence of a graph $G$. Among all such coding sequences we identify the one which is unique for a class of isomorphic graphs. We call it the code of the graph. We characterize several classes of graphs in terms of coding sequences. It is shown that a graph $G$ with $n$ vertices is a tree if and only if any coding sequence of $G$ is a basis of the vector space $\mathbb{Z}_2^{n-1}$ over $\mathbb{Z}_2$. Moreover considering coding sequences as binary matroids, we obtain a characterization for simple graphic matroids and found a necessary and sufficient condition for graph isomorphism in terms of a special matroid isomorphism between their corresponding coding sequences. For this, we introduce the concept of strong isomorphisms of segment binary matroids and show that two simple (undirected) graphs are isomorphic if and only if their canonical sequences are strongly isomorphic segment binary matroids.

math.CO↗
arXiv2014

Generating Intrinsic Dipole Anisotropy in the Large Scale Structures

There have been recent reports of unexpectedly large velocity dipole in the NRAO VLA Sky Survey data. We investigate whether the excess in the NVSS dipole reported can be of cosmological origin. We assume a long wavelength inhomogeneous scalar perturbation of the form αsin (κz) and study its effects on the matter density contrasts. Assuming an ideal fluid model we calculate, in the linear regime, the contribution of the inhomogeneous mode to the density contrast. We calculate the expected dipole in the LSS for two cases, first assuming that the mode is still superhorizon everywhere, and second assuming the mode is subhorizon, but has crossed the horizon deep in matter domination and is subhorizon everywhere in the region of the survey (NVSS). In both cases we find that such an inhomogeneous scalar perturbation is sufficient to generate the reported values of dipole anisotropy in LSS. For the superhorizon modes we find values which are consistent with both CMB and NVSS results. We also predict signatures for the model which can be tested by future observations.

astro-ph.CO↗
arXiv2013

On certain classes of graceful lobsters

A graph G=(V,E) with m edges is graceful if it has a distinct vertex labeling f, a map from V into the set{0,1,2,3,...,m} which induces a distinct edge labeling |f(u)-f(v)| for edges uv in E. The famous Ringel-Kotzig conjecture (1964) is that all trees are graceful. The base of a tree T is obtained from T by deleting its one-degree vertices. A caterpillar is a tree whose base is a path and a lobster is a tree whose base is a caterpillar. Paths and caterpillars are known to be graceful. Next it was conjectured by Bermond (1979) that all lobsters are graceful. In this paper we describe various methods of joining graceful graphs and α-labeled graphs using the adjacency matrix characterization that initiated by Bloom (1979) and others. We apply these results to obtain some classes of graceful lobsters and indicate how to obtain some others.

math.CO↗
arXiv2008

Counting number of factorizations of a natural number

In this note we describe a new method of counting the number of unordered factorizations of a natural number by means of a generating function and a recurrence relation arising from it, which improves an earlier result in this direction.

cs.DM↗
arXiv2008

Characterizations of probe interval graphs

In this paper we obtain several characterizations of the adjacency matrix of a probe interval graph. In course of this study we describe an easy method of obtaining interval representation of an interval bipartite graph from its adjacency matrix. Finally, we note that if we add a loop at every probe vertex of a probe interval graph, then the Ferrers dimension of the corresponding symmetric bipartite graph is at most 3.

cs.DM↗