We provide new concentration inequalities for functions of dependent variables. The work extends that of Janson (2004), which proposes concentration inequalities using a combination of the Laplace transform and the idea of fractional graph coloring, as well as many works that derive concentration inequalities using the entropy method (see, e.g., (Boucheron et al., 2003)). We give inequalities f...

Feature transformation is an important process following feature extraction for improving classification performance. It has been frequently addressed in the kernel-based framework utilizing non-linear kernel functions, and the additive kernel equipped with explicit feature mapping works as efficient and effective (non-linear) feature transformation. The kernel functions, however, are defined i...

In this work we consider the Public-Private model of graphs introduced by Chierichetti et al [1]. In the first part, we briefly introduce the model and give the description of the shortest-path algorithm as described in their paper. In the second part we describe algorithms for Community Detection(Densest Subgraph problem), Max-Cut and Vertex Cover . We also briefly explain how the above algori...

Transformation of 3-propargylmercapto-6 methyl-1, 2,4-triazin- 5 (2H)- one (1; R=CH3) to 3,6- dimethyl-7H- thiazolo [3,2-b] [1, 2, 4] triazin -7- one (2) is performed under basic condition. The formation of (2) may be mainly due to the high reactivity of acetylenes towards nucleophiles and isomerization of the intermediate. 

In this article, we propose a new merit function based on sub-additive functions for solving a nonlinear complementarity problem (NCP). This leads to consider an optimization problem that is equivalent to the NCP. In the case of a concave NCP this optimization problem is a Difference of Convex (DC) program and we can therefore use DC Algorithm to locally solve it. We prove that in the case of a...