A Note on 1-Edge Balance Index Set

A graph labeling is an assignment of integers to the vertices or edges or both, subject to certain conditions. Varieties of graph labeling have been investigated by many authors [2], [3] [5] and they serve as useful models for broad range of applications

Teaching of Critical Analysis of Drug Advertisements to Medical Students

Background: Medical practitioners utilize drug promotional materials from pharmaceutical companies as a major source of information especially in developing countries. These promotional materials can be highly informative as long as they are critically appraised but when they are accepted without question, they lead to irrational prescribing. Aim: To sensitize the students regarding WHO criteria for medicinal drug promotion and to determine the impact of teaching critical appraisal of medicinal drug promotion to medical students. Design: The medical students of second year were given a pre test questionnaire to identify the violations in generic labeling, pharmacological information, claims, relevance and references cited in the drug advertisements. Later they were sensitized about the WHO criteria for medicinal drug promotion and how to critically appraise a drug advertisement. This was followed by a post test questionnaire with the same drug advertisement. Result: The number of students answering the post test correctly was significantly (p<0.05) more than that of pre test. Conclusion: Education of medical students regarding critical analysis of drug advertisements should be a part of the medical curriculum

Quintuple product identity as a special case of Ramanujan's 1ψ1 summation formula.

In this note we observe an interesting fact that the well-known quintuple product identity can be regarded as a special case of the celebrated 1ψ1 summation formula of Ramanujan which is known to unify the Jacobi triple product identity and the q-binomial theorem

Stability of Influence Maximization

The present article serves as an erratum to our paper of the same title, which was presented and published in the KDD 2014 conference. In that article, we claimed falsely that the objective function defined in Section 1.4 is non-monotone submodular. We are deeply indebted to Debmalya Mandal, Jean Pouget-Abadie and Yaron Singer for bringing to our attention a counter-example to that claim. Subsequent to becoming aware of the counter-example, we have shown that the objective function is in fact NP-hard to approximate to within a factor of $O(n^{1-\epsilon})$ for any $\epsilon > 0$. In an attempt to fix the record, the present article combines the problem motivation, models, and experimental results sections from the original incorrect article with the new hardness result. We would like readers to only cite and use this version (which will remain an unpublished note) instead of the incorrect conference version.Comment: Erratum of Paper "Stability of Influence Maximization" which was presented and published in the KDD1

Griffiths phase-like behaviour and spin-phonon coupling in double perovskite Tb2_{2}NiMnO6_{6}

The Griffiths phase-like features and the spin-phonon coupling effects observed in Tb$_2$NiMnO$_6$ are reported. The double perovskite compound crystallizes in monoclinic $P2_1/n$ space group and exhibits a magnetic phase transition at $T_c \sim$ 111 K as an abrupt change in magnetization. A negative deviation from ideal Curie-Weiss law exhibited by 1/$\chi(T)$ curves and less-than-unity susceptibility exponents from the power-law analysis of inverse susceptibility are reminiscent of Griffiths phase-like features. Arrott plots derived from magnetization isotherms support the inhomogeneous nature of magnetism in this material. The observed effects originate from antiferromagnetic interactions which arise from inherent disorder in the system. Raman scattering experiments display no magnetic-order-induced phonon renormalization below $T_c$ in Tb$_2$NiMnO$_6$ which is different from the results observed in other double perovskites and is correlated to the smaller size of the rare earth. The temperature evolution of full-width-at-half-maximum for the {\it stretching} mode at 645 cm$^{-1}$ presents an anomaly which coincides with the magnetic transition temperature and signals a close connection between magnetism and lattice in this material.Comment: 17 pages, 8 figures; accepted in J. Appl. Phy

Boxicity of graphs on surfaces

The boxicity of a graph $G=(V,E)$ is the least integer $k$ for which there exist $k$ interval graphs $G_i=(V,E_i)$, $1 \le i \le k$, such that $E=E_1 \cap ... \cap E_k$. Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and Thomassen proved in 1986 that planar graphs have boxicity at most three. In this note we prove that the boxicity of toroidal graphs is at most 7, and that the boxicity of graphs embeddable in a surface $\Sigma$ of genus $g$ is at most $5g+3$. This result yields improved bounds on the dimension of the adjacency poset of graphs on surfaces.Comment: 9 pages, 2 figure