COMPLEXITY MEASURE: A QUANTUM INFORMATION APPROACH

In the past decades, all of the efforts at quantifying systems complexity with a general tool has usually relied on using Shannon's classical information framework to address the disorder of the system through the Boltzmann-Gibbs-Shannon entropy, or one of its extensions. However, in recent years, there were some attempts to tackle the quantification of algorithmic complexities in quantum systems based on the Kolmogorov algorithmic complexity, obtaining some discrepant results against the classical approach. Therefore, an approach to the complexity measure is proposed here, using the quantum information formalism, taking advantage of the generality of the classical-based complexities, and being capable of expressing these systems' complexity on other framework than its algorithmic counterparts. To do so, the Shiner-Davison-Landsberg (SDL) complexity framework is considered jointly with linear entropy for the density operators representing the analyzed systems formalism along with the tangle for the entanglement measure. The proposed measure is then applied in a family of maximally entangled mixed state.

Brazilian exchange rate complexity: Financial crisis effects

With the financial market globalization, foreign investments became vital for the economies, mainly in emerging countries. In the last decades, Brazilian exchange rates appeared as a good indicator to measure either investors' confidence or risk aversion. Here, some events of global or national financial crisis are analyzed, trying to understand how they influenced the "dollar-real" rate evolution. The theoretical tool to be used is the Lopez-Mancini-Calbet (LMC) complexity measure that, applied to real exchange rate data, has shown good fitness between critical events and measured patterns. (C) 2011 Elsevier B.V. All rights reserved.

Entropy, complexity and disequilibrium in compact stars

We used the statistical measurements of information entropy, disequilibrium and complexity to infer a hierarchy of equations of state for two types of compact stars from the broad class of neutron stars, namely, with hadronic composition and with strange quark composition. Our results show that, since order costs energy. Nature would favor the exotic strange stars even though the question of how to form the strange stars cannot be answered within this approach. (C) 2012 Elsevier B.V. All rights reserved.

IDM - A New Parallel Methodology to Calculate the Determinant of Matrices of the Order n, with Computational Complexity O(n)

This paper presents a new parallel methodology for calculating the determinant of matrices of the order n, with computational complexity O(n), using the Gauss-Jordan Elimination Method and Chio's Rule as references. We intend to present our step-by-step methodology using clear mathematical language, where we will demonstrate how to calculate the determinant of a matrix of the order n in an analytical format. We will also present a computational model with one sequential algorithm and one parallel algorithm using a pseudo-code.