In this paper, we obtain Markovian bounds on a function of a homogeneous discrete time Markov chain. For deriving such bounds, we use well known results on stochastic majorization of Markov chains and the Rogers-Pitman’s lumpability criterion. The proposed method of comparison between functions of Markov chains is not equivalent to generalized coupling method of Markov chains although we obtain...

We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111, 230401 (2013)] and [J. Phys. A. 46, 272002 (2013)]. The results give rise to state independent uncertainty relations satisfied by any nonnegative Schur-concave functions. On the other hand, a remarkable...

 In this paper, we study stochastic comparisons of order statistics of independent random variables with proportional hazard rates, using the notion of variance majorization.

The aim of this paper is using the majorization technique to identify the classes of trees with extermal (minimal or maximal) value of some topological indices, among all trees of order n ≥ 12

For vectors $X, Yin mathbb{R}^{n}$, we say $X$ is left matrix majorized by $Y$ and write $X prec_{ell} Y$ if for some row stochastic matrix $R, ~X=RY.$ Also, we write $Xsim_{ell}Y,$ when $Xprec_{ell}Yprec_{ell}X.$ A linear operator $Tcolon mathbb{R}^{p}to mathbb{R}^{n}$ is said to be a linear preserver of a given relation $prec$ if $Xprec Y$ on $mathbb{R}^{p}$ implies that $TXprec TY$ on $mathb...

The glmnet package by [1] is an extremely fast implementation of the standard coordinate descent algorithm for solving l1 penalized learning problems. In this paper, we consider a family of coordinate majorization descent algorithms for solving the l1 penalized learning problems by replacing each coordinate descent step with a coordinate-wise majorization descent operation. Numerical experiment...

To minimize the primal support vector machine (SVM) problem, we propose to use iterative majorization. To do so, we propose to use iterative majorization. To allow for nonlinearity of the predictors, we use (non)monotone spline transformations. An advantage over the usual kernel approach in the dual problem is that the variables can be easily interpreted. We illustrate this with an example from...

One of the most popular graph drawing methods is based of achieving graphtheoretic target ditsances. This method was used by Kamada and Kawai [15], who formulated it as an energy optimization problem. Their energy is known in the multidimensional scaling (MDS) community as the stress function. In this work, we show how to draw graphs by stress majorization, adapting a technique known in the MDS...