In this talk we deal with a more precise estimates for the matrix versions of Young, Heinz, and Hölder inequalities. First we give an improvement of the matrix Heinz inequality for the case of the Hilbert-Schmidt norm. Then, we refine matrix Young-type inequalities for the case of Hilbert-Schmidt norm, which hold under certain assumptions on positive semidefinite matrices appearing therein. Fin...

This article aims to prove that gender inequality still exists and is likely to remain in the region of Asia Pacific countries. In the first part, it will consider the data on three perspectives which are participation, wages and occupational composition of employment for women in order to understand the current situation of women employment. In the second part, it will focus on China and Japan...

In this paper, the problem of bridge consensus is presented and solved. Bridge consensus consists of a network of nodes, some of whom are participating and others are non-participating. The objective is for all the agents to reach average consensus of the participating nodes initial values in a distributed and scalable manner. To do this, the nodes must use the network connections of the non-pa...

Logistic regression learns a parameterized mapping from feature vectors to probability vectors and is for example central to estimating click rates for ads on web pages. The parameter is found by minimizing the logistic loss. However minimizing any convex loss summed over a set of examples is prone to outliers. We define a versatile method for designing non-convex losses that ameliorate the eff...