Investigating Antigram Behaviour using Distributional Semantics

Language is an extremely interesting subject to study, each day presenting new challenges and new topics for research. Words in particular have several unique characteristics which when explored, prove to be astonishing. Anagrams and Antigrams are such words possessing these amazing properties. The presented work is an exploration into generating anagrams from a given word and determining whether there exists antigram relationships between the pairs of generated anagrams in light of the Word2Vec distributional semantic similarity model. The experiments conducted, showed promising results for detecting antigrams.Comment: 4 page

Coloring Sums of Extensions of Certain Graphs

Recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted by $\chi(G).$ In this paper the concepts of $\chi$'-chromatic sum and $\chi^+$-chromatic sum are introduced. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. We further the concepts of $\chi$'-chromatic sum and $\chi^+$-chromatic sum to extended paths and cycles. The paper concludes with \emph{patterned structured} graphs.Comment: 12 page

Consistent estimation of the spectrum of trace class data augmentation algorithms

Markov chain Monte Carlo is widely used in a variety of scientific applications to generate approximate samples from intractable distributions. A thorough understanding of the convergence and mixing properties of these Markov chains can be obtained by studying the spectrum of the associated Markov operator. While several methods to bound/estimate the second largest eigenvalue are available in the literature, very few general techniques for consistent estimation of the entire spectrum have been proposed. Existing methods for this purpose require the Markov transition density to be available in closed form, which is often not true in practice, especially in modern statistical applications. In this paper, we propose a novel method to consistently estimate the entire spectrum of a general class of Markov chains arising from a popular and widely used statistical approach known as Data Augmentation. The transition densities of these Markov chains can often only be expressed as intractable integrals. We illustrate the applicability of our method using real and simulated data.Comment: 43 pages (including Appendix), 3 figures; final versio