Duwamg Prada

Introducción. La demencia por enfermedad de Alzheimer representa una afectación cognitiva progresiva derivada de una patología cerebral que impacta en la autonomía y funcionalidad, por tanto, se planteó estudiar un modelo que integró indicadores cerebrales, autonómicos y cognitivos orientados a contribuir a la detección de casos con Alzheimer. Metodología. Estudio observacional conformado por 14 adultos mayores (controles) y 14 con diagnóstico de demencia (Alzheimer), seleccionados y examinados de manera intencional. Evaluación a través del examen cognitivo de Montreal, examen de resonancia magnética (dimensión fractal de cortes axiales y coronales), y la reactividad cardiaca ante una prueba de tolerancia ortostática. Resultados. Se identificaron diferencias en indicadores cognitivos, cerebrales y autonómicos entre ambos grupos (prueba t). Un análisis de regresión logística binomial reveló que el examen cognitivo de Montreal y la mínima frecuencia cardiaca constituyeron un modelo que explicó el diagnóstico en un 75.55% (R2 ajustado). La dimensión fractal cerebral de cortes axiales (r = -0.38, p = 0.046) y coronales (r = -0.42, p = 0.026) se correlacionó significativamente con el examen cognitivo de Montreal. Discusión. Los resultados se contrastaron con estudios que abordan el potencial de integrar medidas cognitivas y medidas autonómicas en el diagnóstico de las demencias; adicionalmente, se abordó la utilidad de la dimensión fractal cerebral como indicador derivado de la resonancia magnética. Conclusiones. La integración de indicadores (cognitivo y autonómico) explicó en mayor medida el diagnóstico, a diferencia de las variables aisladas. Adicionalmente, se demostró el uso potencial de la dimensión fractal cerebral, pues reveló una asociación con el funcionamiento cognitivo representado en el examen cognitivo de Montreal.

El análisis del índice MSCI COLCAP de la bolsa de valores en Colombia es crucial para comprender la dinámica del mercado y evaluar su estabilidad y riesgos, especialmente en pospandemia. Este estudio se justifica por la necesidad de examinar la persistencia y comportamiento de la volatilidad del índice colombiano en un contexto afectado por el covid-19, donde las fluctuaciones en los precios han sido notoriamente marcadas. Utilizando el coeficiente de Hurst, se determinó que el índice muestra una memoria histórica. El análisis de la volatilidad, basado en ventanas de 20 días, reveló una mayor inestabilidad tras la pandemia. Las pruebas de backtesting con modelos GARCH indicaron un aumento significativo en el riesgo durante la pandemia, con valores esperados de -1,14 % antes de esta; -7,4 % en marzo de 2020 y -1,95 %, posteriormente. Dado el anterior contexto, se puede indicar que el presente estudio permite comprender la dinámica y estabilidad del mercado colombiano pospandemia, y proporciona herramientas prácticas para mejorar la previsión y gestión del riesgo. Es relevante para inversores, reguladores y académicos interesados en mercados emergentes y su respuesta a eventos globales disruptivos.

Fractional Brownian motion allows you to see the correlation between past data increments in a shift with respect to future increments. Through this important physical property of fractional Brownian motion, it was possible to perform an analysis of the impact of suspended particles, also known as particulate matter, on the environment, which is a worldwide concern. The particulate matter produced in a coal mine is large and can be disastrous for neighboring communities, resulting in a decrease in their health and quality of life in general. In this work we analyze a time series of the values of total suspended particles registered by the “La Jagua” monitoring station located 5 km from the coal mine complex in the municipality of “La Jagua” de Ibrírico in Colombia, we do this by using the fractional Brownian motion calculated from Hurst’s coefficient to determine if there is persistence of the presence of this particulate material in the future. Initially a normality test is carried out, then the rescaled range and Hurst coefficient are computed with which it is possible to determine the increasing persistence and volatility of the series.

The air quality index shows the pollution of the air we breathe, a very low index indicates that we can have respiratory, eye or heart conditions. An index below the minimum levels declared, requires generating strategies such as days without the presence of private vehicles, among others, to reduce pollution. The city of Medellin, Colombia, has shown very low levels in the air quality index due to several factors, mainly the emission produced by vehicles and companies. Due to this, activities have been initiated to reduce the emission of 2.5 micron and 10 microns particulate material, classified as highly harmful to health. The city installed 12 air quality monitoring stations and designed a decontamination proposal for the year 2030. Conducting a study on the persistence of particulate matter in the air according to the data recorded by the stations, will strengthen the proposed strategy or modify it to achieve the goal. In this work, the data collected by a station from July to December 2018 in which a high persistence in the presence of particulate material was analyzed.

Chaotic population dynamics present interesting behaviors that are the object of study for biologists, microbiologists, ecologists, epidemiologists and bioanalysts. With the proposal of the mathematician and biologist Pierre Verhulst on the logistic equation as a population discrete mathematical model, studies were initiated on chaotic dynamics regarding the growth factor immersed in the equation. When assigning different values to the factor, orbits are observed that are initially convergent, however, there are values for which there is no convergence due to the bifurcations suffered by the orbit. For values greater than or equal to 3 and less than 4, the forks bend, but not consecutively. Through the logistic equation and the identity function it is possible to find the values of the orbit corresponding to a specific value of the growth factor, however, these data are evidenced graphically, so it is important to know the explicit calculation of these bifurcations. The calculation of the fixed points of the quadratic iterator of the logistic equation is shown by equations.

Population growth is a topic of great interest to biologists, epidemiologists, ecologists, microbiologists and bioanalysts. Describing the dynamics of a population system through mathematical models is very useful in order to predict the behavior of the study population. Chaos theory supports studies of this type through the analysis of the logistic equation which allows observing this behavior under the variation of the constant k that represents the rate of increase in the number of times of the population values in a given time and the orbit diagram that summarizes the asymptotic behavior of all orbits in which we have values of k between zero and four. These models work with discrete time under measurement by iteration in observation and not continuously. The objective is to show the relationship of the logistic equation and the orbit diagram with the Feigenbaum constant in order to show the order that exists in the population dynamics.

Urban population growth, together with the industrial advances, leads to consider time as one of the most precious goods and therefore, an indicator of quality of life. Larger cities usually have mobility challenges due to inefficient or insufficient transport means or inadequate design of the road layout. Therefore, people may spend large portions of their daytime moving around places. It is precisely in this type of cities, where it is more complicated to find solutions that really solve the problem because it would be harder to change the already existing infrastructure. Two roads compositions, from the cities of Barcelona, Spain, and La Plata, Argentina, were selected to incorporate a fractal analysis in order to relate it with homogeneity. This was performed using a box counting methodology which determines the fractal dimension. As a complement, fractal lagunarity was calculated to get a value of the existing voids in the magnetic resonance images. The results show that the images have similar fractal dimension regarding the differences in road structure. However, the lagunarity is not the same, La Plata, Argentina, has a lower value than Barcelona, Spain, which indicates more coherence in the road structure.

Alzheimer’s disease is a degenerative neurological disorder that comes with the aging process characterized by cognitive, affective and behavioral deficits. a possible method that can support the diagnosis and treatment of Alzheimer’s disease is called fractal geometry, given that the brain has fractal structure, therefore, Alzheimer’s disease is an observed progressive process of alterations within the groups of topographic voxels, which means that a geometrical fractal analysis can support the diagnosis of the disease. For this purpose, a double blind clinical trial study was designed, calculating the fractal dimension and the lagunarity of magnetic resonance imaging of the cerebral cortex of patients with the neurological report of Alzheimer’s disease, implementing the box-counting method or “entropy of kolmogorov”, by means of a software with logarithm FracLac (p=1.029). As a relevant result, a characteristic fractal pattern was evidenced in the images of patients with Alzheimer’s disease, which allowed to postulate the mathematical method as a possible analysis to complement the clinical order in the diagnostic assessment.

El Mercado Bursátil en Colombia se encuentra administrado por la Bolsa de Valores de Colombia, la cual evalúa el comportamiento del mercado a través de indicadores financieros, entre los cuales se encuentra el índice COLCAP, que mide el movimiento del precio de las acciones más liquidas en el mercado. Este indicador se actualiza de manera trimestral, tanto en las acciones que lo conforman como en la participación correspondiente de cada una de ellas, de modo que es importante comparar la variación de dicho índice de un trimestre a otro, y así determinar si existe evidencia significativa en la diferencia entre las variaciones trimestrales del índice. Para realizar este estudio se toma información del índice en el periodo comprendido desde el primero (01) de febrero de 2012 al treinta y uno (31) de enero de 2017 y se analizan los datos aplicando el modelo de análisis de varianza simple o de un solo factor partiendo de la hipótesis inicial de que la media de la volatilidad del periodo 1 es igual a los periodos restantes (2, 3 y 4), mostrando en los resultados que no existe suficiente evidencia estadística para rechazar esta hipótesis.

Flipped Classroom, Twenty first century teaching technique, oriented to transfer a slice of the learning component to the person within his comfort zone and/or family environment; it is an activity or transference that pretends to stimulate individual tasking of the learner through the use of the technologic element, in such a way that the face to face course time in the classroom is significant to deeply develop the topics object to study. This initiative is relevant to be applied in the teaching process of financial sciences, particularly the financial analysis learning, activity developed by means of reviewing accounting data, which is vital in order to manage and to understand companies, inasmuch as from the holistic understanding of the company itself, it is possible to build survival business strategies; therefore it is necessary that the apprentice deeply comprehends the business complexity and fragility, also that he can use the analysis to take different decisions to improve the business dynamics, with the application of this methodology within the subject of financial analysis, it was possible to demonstrate that it effectively brought visible, positive and general interest results for the professors and other members of the academic year, visualized these in significant improvements in both numerical and of participation and commitment on the part of the student.