This paper proposes k-medoids clustering method to reveal the distinct groups of 1318 variable stars in the Galaxy based on their light curves, where each light curve represents the graph of brightness of the star against time. To overcome the deficiencies of subjective traditional classification, we separate the stars more scientifically according to their geometrical configuration and show that our approach outperforms the existing classification schemes in astronomy. It results in two optimum groups of eclipsing binaries corresponding to bright, massive systems and fainter, less massive systems. © 2019, © 2019 Informa UK Limited, trading as Taylor &amp; Francis Group.

TANUKA CHATTOPADHYAYKANJILAL

Applied Mathematics

Asis Kumar Chattopadhyay

Statistics

S MODAK

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Journal of Applied Statistics

We consider the problem related to clustering of gamma-ray bursts (from “BATSE” catalogue) through kernel principal component analysis in which our proposed kernel outperforms results of other competent kernels in terms of clustering accuracy and we obtain three physically interpretable groups of gamma-ray bursts. The effectivity of the suggested kernel in combination with kernel principal component analysis in revealing natural clusters in noisy and nonlinear data while reducing the dimension of the data is also explored in two simulated data sets. © 2018, © 2018 Taylor &amp; Francis Group, LLC.

Communications in Statistics: Simulation and Computation

Clustering of gamma-ray bursts through kernel principal component analysis

Area of study is the formation mechanism of the present-day population of elliptical galaxies, in the context of hierarchical cosmological models accompanied by ac- cretion and minor mergers. The present work investigates the formation and evolution of several components of the nearby massive early-type galaxies (ETGs) through cross- correlation function (CCF), using the spatial parameters right ascension (RA) and declination (DEC), and the intrin- sic parameters mass (M&lowast;) and size. According to the as- trophysical terminology, here these variables, namely mass, size, RA and DEC are termed as parameters, whereas the un- known constants involved in the kernel function are called hyperparameters. Throughout this paper, the parameter size is used to represent the effective radius (Re). Following Huang et al. (2013a), each nearby ETG is divided into three parts on the basis of its Re value. We study the CCF between each of these three components of nearby massive ETGs and the ETGs in the high redshift range, 0.5 &lt; z &le; 2.7. It is found that the innermost components of nearby ETGs are highly correlated with ETGs in the redshift range, 2 &lt; z &le; 2.7, known as &lsquo;red nuggets&rsquo;. The intermedi- ate and the outermost parts have moderate correlations with ETGs in the redshift range, 0.5 &lt; z &le; 0.75. The quantitative measures are highly consistent with the two phase formation scenario of nearby massive ETGs, as suggested by various authors, and resolve the conflict raised in a previous work (De et al. 2014) suggesting other possibilities for the forma- tion of the outermost part. A probable cause of this improvement is the inclusion of the spatial effects in addition to the other parameters in the study.

Astrophysics and Space Science

Two phase formation of massive elliptical galaxies: study through cross-correlation including spatial effect

A stochastic model has been developed to study the hierarchical fragmentation process of young massive clusters in external galaxies considering close binary components along with individual ones. Stellar masses for individual ones have been generated from truncated Pareto distribution and stellar masses for close binary components have been generated from a truncated Bi-variate Gumbel Exponential distribution. The above distribution is identified by fitting the observed bi-variate distribution of masses of eclipsing binary stars computed from the light curves catalogued in the package Binary Maker 3.0. The resulting mass spectra computed at different projected distances, show signature of mass segregation. Degree of mass segregation becomes reduced due to the inclusion of binary fraction. This might be due to the reduction of massive stars and inclusion of less massive stars rather than inclusion of single massive stars and the effect of line of sight length projected to an observer. © 2016, Springer Science+Business Media Dordrecht.

Journal	Data powered by TypesetJournal of Applied Statistics
Publisher	Data powered by TypesetTaylor and Francis Ltd.
ISSN	0266-4763
Open Access	Yes