Majorization methods solve minimization problems by replacing a complicated problem by a sequence of simpler problems. Solving the sequence of simple optimization problems guarantees convergence to a solution of the complicated original problem. Convergence is guaranteed by requiring that the approximating functions majorize the original function at the current solution. The leading examples of...

The objective of this study is to develop a majorization-based tool to compare financial networks with a focus on the implications of liability concentration. Specifically, we quantify liability concentration by applying the majorization order to the liability matrix that captures the interconnectedness of banks in a financial network. We develop notions of balancing and unbalancing networks to...

two latin squares of order $n$ are orthogonal if in their superposition, each of the$n^{2}$ ordered pairs of symbols occurs exactly once. colbourn, zhang and zhu, in a seriesof papers, determined the integers $r$ for which there exist a pair of latin squares oforder $n$ having exactly $r$ different ordered pairs in their superposition. dukes andhowell defined the same problem for latin squares ...

Let n be a positive integer. We may write (or split) n as sums of n nonincreasing nonnegative integers p1, p2, . . . , pn in different ways (or partitions; see Section 2). For example, 3 = 3 + 0 + 0 = 2 + 1 + 0 = 1 + 1 + 1. If we denote by P (n) the number of different partitions of n, then P (3) = 3. One may check that P (5) = 7. As n gets large, P (n) increases rapidly. It is astounding that ...

The Latin American School of Human and Medical Genetics (ELAG) is the main course of its kind in the genetics field in Latin America. Here we describe the main challenges regarding the organization of such event, including how we obtain funding and how we proceed with student selection. Thus, we aim to share our experience with other groups that intend to follow this format to create similar ev...

Optimal power allocation for maximizing the sum capacity of multiple access channel (MAC) with quality-of-service (QoS) constraints is investigated in this paper. Majorization theory is the underlying mathematical theory on which our method hinges. It is shown that the optimal structure of the solution can be easily obtained via majorization theory. Furthermore, based on our new approach, an ef...

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...