Categorical Aspects of the Double Structure of a Module

In this work we develop some categorical aspects of the double structure of a module

The canonical econophysics approach to the flash crash of May 6, 2010

We carry out a statistical physics analysis of the flash crash of May 6, 2010 using data from the Dow Jones Industrial Average index sampled at a one-minute frequency from September 1, 2009 to May 31, 2010. We evaluate the hypothesis of a non-Gaussian Levy-stable distribution to model the data and pay particular attention to the distribution-tail behavior. We conclude that there is non-Gaussian scaling and thus that the flash crash cannot be considered an anomaly. From the study of tails, we find that the flash crash followed a power-law pattern outside the Levy regime, which was not the inverse cubic law. Finally, we show that the time-dependent variance of the DJIA-index returns, not tracked by the Levy, can be modeled in a straightforward manner by a GARCH (1, 1) process.flash crash; econophysics; stable distribution; extreme events

Real and complex integral closure, Lipschitz equisingularity and applications on square matrices

Recently the authors investigated the Lipschitz triviality of simple germs of matrices. In this work, we improve some previous results and we present an extension of an integral closure result for the real setting. These tools are applied to investigate classes of square matrices singularities classified by Bruce and Tari

Discriminating word senses with tourist walks in complex networks

Patterns of topological arrangement are widely used for both animal and human brains in the learning process. Nevertheless, automatic learning techniques frequently overlook these patterns. In this paper, we apply a learning technique based on the structural organization of the data in the attribute space to the problem of discriminating the senses of 10 polysemous words. Using two types of characterization of meanings, namely semantical and topological approaches, we have observed significative accuracy rates in identifying the suitable meanings in both techniques. Most importantly, we have found that the characterization based on the deterministic tourist walk improves the disambiguation process when one compares with the discrimination achieved with traditional complex networks measurements such as assortativity and clustering coefficient. To our knowledge, this is the first time that such deterministic walk has been applied to such a kind of problem. Therefore, our finding suggests that the tourist walk characterization may be useful in other related applications

Graded identities of block-triangular matrices

Let $F$ be an infinite field and $UT(d_1,\dots, d_n)$ be the algebra of upper block-triangular matrices over $F$. In this paper we describe a basis for the $G$-graded polynomial identities of $UT(d_1,\dots, d_n)$, with an elementary grading induced by an $n$-tuple of elements of a group $G$ such that the neutral component corresponds to the diagonal of $UT(d_1,\dots,d_n)$. In particular, we prove that the monomial identities of such algebra follow from the ones of degree up to $2n-1$. Our results generalize for infinite fields of arbitrary characteristic, previous results in the literature which were obtained for fields of characteristic zero and for particular $G$-gradings. In the characteristic zero case we also generalize results for the algebra $UT(d_1,\dots, d_n)\otimes C$ with a tensor product grading, where $C$ is a color commutative algebra generating the variety of all color commutative algebras.Comment: 24 pages and 39 references. We have added section 5 in the text about tensor products by color commutative superalgebra

A concepçâo do projeto corrida geográfica

O projeto Corrida Geográfica consiste em uma estratégia de ensino/aprendizagem voltada aos alunos do 7º ano do Ensino Fundamental da Escola Municipal Consulesa Margarida Maksoud Trad em Campo Grande-MS, Brasil. As metodologias empregadas no projeto buscam tornar o processo de aprendizagem dos alunos mais prazeroso por meio da organização de uma competição em equipe e do uso de jogos em sala de aula. Os objetivos do projeto são amplos e multidisciplinares, dentre eles: estimular e envolver os alunos no seu processo de aprendizagem tornando-os protagonistas na construção de seus conhecimentos, desenvolvendo a habilidade de trabalho em equipe e despertando o espírito de liderança. Para tanto, são utilizadas diversas metodologias a partir do uso de mapas temáticos, aplicativos virtuais, softwares como o Google Earth, o blog Mundo Geográfico e jogos analógicos e digitaisThe Geographic Running project consists of a teaching / learning strategy aimed at the 7th grade students of the Consulesa Municipal School Margarida Maksoud Trad in Campo Grande-MS, Brazil. The methodologies used in the project seek to make the students' learning process more enjoyable by organizing a team competition and using games in the classroom. The objectives of the project are broad and multidisciplinary, among them: to stimulate and involve students in their learning process making them protagonists in building their knowledge, developing the ability to work as a team and awakening the spirit of leadership. To do so, several methodologies are used from thematic maps, virtual applications, software such as Google Earth, the Geographic World blog and analogue and digital game