Conjuntos numéricos y aritmética

Conjuntos numéricos y aritmética, plantea, de manera descriptiva, un recorrido por los diferentes conjuntos numéricos. La pretensión inicialmente, ha sido partir del planteamiento y definición del conjunto numérico más elemental como lo es el conjunto de los números naturales, hasta llegar a su ampliación, por necesidades de cálculo y solución de operaciones, al conjunto de los números complejos. Por esta vía se transita, entonces, pasando por el conjunto de los números enteros, racionales, irracionales y reales, sin abordar, en ningún momento, estos conjuntos con enfoques o análisis axiomáticos. La colección Lecciones de matemáticas, iniciativa del Departamento de Ciencias Básicas de la Universidad de Medellín y del grupo de investigación SUMMA, incluye en cada número la exposición detallada de un tema matemático, tratado con mayor profundidad que en un curso regular. Las temáticas incluyen: álgebra, trigonometría, cálculo, estadística y probabilidades, álgebra lineal, métodos lineales y numéricos, historia de las matemáticas, geometría, matemáticas puras y aplicadas, ecuaciones diferenciales y empleo de software para la enseñanza de las matemáticas. Todas las carátulas de la colección vienen ilustradas, a manera de identificación, con diseños de la geometría fractal cuya fuente u origen se encuentra referenciada en las páginas interiores de los textos.

Modelos Arima - Arch. Algunas aplicaciones a las series de tiempo financieras

La colección de textos , iniciativa del Departamento de Ciencias Básicas de la Universidad de Medellín y su grupo de investigación SUMMA, incluye en cada número la exposición detallada de un tema matemático en particular, tratado con el rigor que muchas veces no es posible lograr en un curso regular de la disciplina. Las temáticas incluyen diferentes áreas del saber matemático como: álgebra, trigonometría, cálculo, estadística y probabilidades, álgebra lineal, métodos lineales y numéricos, historia de las matemáticas, geometría, matemáticas puras y aplicadas, ecuaciones diferenciales y empleo de softwares matemáticos. Todas las carátulas de la colección vienen ilustradas, a manera de identificación, con diseño de la geometría fractal cuya fuente y origen se encuentra referenciada en las páginas interiores de los textos. La finalidad de esta lección de matemáticas número 9 Modelos Arima-ARCH es proporcionarle al estudiante y lector interesado las herramientas que le permitan tomar decisiones a través de la construcción de los modelos Arima-ARCH para ser aplicados en Ingeniería Financiera, métodos cuantitativos y mercados de capitales, entre otros

Morphological traits of surveillant/activated microglia during an experimentally induced acute neuroinflammatory process

Several studies show that morphological changes of microglia over the course of inflammation are tightly coupled to function. However the progressive transformation into activated microglia is poorly characterized. AIMS: This study aimed to establish a spatiotemporal correlation between quantifiable morphological parameters of microglia and the spread of an acute ventricular inflammatory process. METHODS: Inflammation was induced by a single injection of the enzyme neuraminidase within the lateral ventricle of rats. Animals were sacrificed 2, 4 and 12 hours after injection. Coronal slices were immunostained with Iba1 to label microglia and with IL1β to delimit the spread of inflammation. Digital images were obtained by scanning the labelled sections. Single microglia images were randomly selected from periventricular areas of caudate putamen, hippocampus and hypothalamus. FracLac for ImageJ software was used to measure the following morphological parameters: fractal dimension, lacunarity, area, perimeter and density. RESULTS: Significant differences were found in fractal dimension, lacunarity, perimeter and density of microglia cells of neuraminidase injected rats compared to sham animals. However no differences were found in the parameter “area”. In hipoccampus there was a delay in the significant change of the measured parameters. These morphological changes correlated with IL1β-expression in the same areas. CONCLUSIONS: Ventricular inflammation induced by neuraminidase provokes quantifiable morphological changes in microglia restricted to areas labelled with IL1β. Morphological parameters of microglia such as fractal dimension, lacunarity, perimeter and density are sensitive and valuable tools to quantify activation. However, the extensively used parameter “area” did not change upon microglia activation.

Curvas clásicas. Enfoque geométrico, cartesiano y matemático

La colección de textos Lecciones de Matemáticas, iniciativa del Departamento de Ciencias Básicas de la Universidad de Medellín y su grupo de investigación SUMMA, incluye en cada número la exposición detallada de un tema matemático en particular, tratado con el rigor que muchas veces no es posible lograr en un curso regular de la disciplina. Las temáticas incluyen diferentes áreas del saber matemático como: álgebra, trigonometría, cálculo, estadística y probabilidades, álgebra lineal, métodos lineales y numéricos, historia de las matemáticas, geometría, matemáticas puras y aplicadas, ecuaciones diferenciales y empleo de softwares matemáticos. Todas las carátulas de la colección vienen ilustradas, a manera de identificación, con diseño de la geometría fractal, cuya fuente y origen se encuentra referenciada en las páginas interiores de los textos. Este número tiene por objeto mostrar, con claridad y en forma simple, temas de geometría que probablemente no han sido bien estudiados en los cursos normales de matemáticas como geometría, cálculo y ecuaciones diferenciales, entre otros, y que hacen referencia a las secciones cónicas y las curvas clásicas en general.

Os fractais no urbanismo

Dissertação para obtenção do grau de Mestre em Arquitectura com Especialização em Urbanismo, apresentada na Universidade de Lisboa - Faculdade de Arquitectura.

Caracterización geométrica de aglomerados granulados cuasi-fractales

En este trabajo de investigación se ha conseguido caracterizar la morfología de aglomerados granulados cuasi-fractales individuales. Por otro lado se ha demostrado que el prefactor de la ley de potencias junto a la dimensión fractal, caracterizan morfológicamente el aglomerado. De modo que el prefactor de la ley de potencias no solo es un coeficiente de proporcionalidad entre el número de partículas primarias y una distancia característica elevada a la dimensión fractal sino que representa la lagunaridad del aglomerado granular.

Atomic-level structure and deformation in metallic glasses

Metallic glasses (MGs) are a relatively new class of materials discovered in 1960 and lauded for its high strengths and superior elastic properties. Three major obstacles prevent their widespread use as engineering materials for nanotechnology and industry: 1) their lack of plasticity mechanisms for deformation beyond the elastic limit, 2) their disordered atomic structure, which prevents effective study of their structure-to-property relationships, and 3) their poor glass forming ability, which limits bulk metallic glasses to sizes on the order of centimeters. We focused on understanding the first two major challenges by observing the mechanical properties of nanoscale metallic glasses in order to gain insight into its atomic-level structure and deformation mechanisms. We found that anomalous stable plastic flow emerges in room-temperature MGs at the nanoscale in wires as little as ~100 nanometers wide regardless of fabrication route (ion-irradiated or not). To circumvent experimental challenges in characterizing the atomic-level structure, extensive molecular dynamics simulations were conducted using approximated (embedded atom method) potentials to probe the underlying processes that give rise to plasticity in nanowires. Simulated results showed that mechanisms of relaxation via the sample free surfaces contribute to tensile ductility in these nanowires. Continuing with characterizing nanoscale properties, we studied the fracture properties of nano-notched MGnanowires and the compressive response of MG nanolattices at cryogenic (~130 K) temperatures. We learned from these experiments that nanowires are sensitive to flaws when the (amorphous) microstructure does not contribute stress concentrations, and that nano-architected structures with MG nanoribbons are brittle at low temperatures except when elastic shell buckling mechanisms dominate at low ribbon thicknesses (~20 nm), which instead gives rise to fully recoverable nanostructures regardless of temperature. Finally, motivated by understanding structure-to-property relationships in MGs, we studied the disordered atomic structure using a combination of in-situ X-ray tomography and X-ray diffraction in a diamond anvil cell and molecular dynamics simulations. Synchrotron X-ray experiments showed the progression of the atomic-level structure (in momentum space) and macroscale volume under increasing hydrostatic pressures. Corresponding simulations provided information on the real space structure, and we found that the samples displayed fractal scaling (r^d ∝ V, d < 3) at short length scales (< ~8 Å), and exhibited a crossover to a homogeneous scaling (d = 3) at long length scales. We examined this underlying fractal structure of MGs with parallels to percolation clusters and discuss the implications of this structural analogy to MG properties and the glass transition phenomenon.

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Análise não linear de séries temporais e aplicações à Psicologia

Nesta dissertação estudámos as séries temporais que representam a complexa dinâmica do comportamento. Demos especial atenção às técnicas de dinâmica não linear. As técnicas fornecem-nos uma quantidade de índices quantitativos que servem para descrever as propriedades dinâmicas do sistema. Estes índices têm sido intensivamente usados nos últimos anos em aplicações práticas em Psicologia. Estudámos alguns conceitos básicos de dinâmica não linear, as características dos sistemas caóticos e algumas grandezas que caracterizam os sistemas dinâmicos, que incluem a dimensão fractal, que indica a complexidade de informação contida na série temporal, os expoentes de Lyapunov, que indicam a taxa com que pontos arbitrariamente próximos no espaço de fases da representação do espaço dinâmico, divergem ao longo do tempo, ou a entropia aproximada, que mede o grau de imprevisibilidade de uma série temporal. Esta informação pode então ser usada para compreender, e possivelmente prever, o comportamento. ABSTRACT: ln this thesis we studied the time series that represent the complex dynamic behavior. We focused on techniques of nonlinear dynamics. The techniques provide us a number of quantitative indices used to describe the dynamic properties of the system. These indices have been extensively used in recent years in practical applications in psychology. We studied some basic concepts of nonlinear dynamics, the characteristics of chaotic systems and some quantities that characterize the dynamic systems, including fractal dimension, indicating the complexity of information in the series, the Lyapunov exponents, which indicate the rate at that arbitrarily dose points in phase space representation of a dynamic, vary over time, or the approximate entropy, which measures the degree of unpredictability of a series. This information can then be used to understand and possibly predict the behavior.

Improving multivariate data streams clustering.

Clustering data streams is an important task in data mining research. Recently, some algorithms have been proposed to cluster data streams as a whole, but just few of them deal with multivariate data streams. Even so, these algorithms merely aggregate the attributes without touching upon the correlation among them. In order to overcome this issue, we propose a new framework to cluster multivariate data streams based on their evolving behavior over time, exploring the correlations among their attributes by computing the fractal dimension. Experimental results with climate data streams show that the clusters' quality and compactness can be improved compared to the competing method, leading to the thoughtfulness that attributes correlations cannot be put aside. In fact, the clusters' compactness are 7 to 25 times better using our method. Our framework also proves to be an useful tool to assist meteorologists in understanding the climate behavior along a period of time.