Abstract In General Secondary Education in Mozambique, the use of technological resources for learning Technical Drawing and Descriptive Geometry is still rare. The aim of this research is to see if Qubism 3D Modeling and GeoGebra software simulations, in the subjects of Orthogonal Projection and Section of Cylinders, contribute to improving students 3D spatial visualization, considering students previous difficulties in this type of skill. For the study of Orthogonal Projections, we adapted Qubism 3D Modeling to help clarify the representations of orthogonal views. For the study of cylinder sections, we used the dynamic geometry software GeoGebra, as it facilitates the perception of the shape of the figure resulting from the section. This is a quasi-experimental study, following a qualitative approach, conducted in a school in southern Mozambique. The techniques employed included observation, note-taking and photographic records, and the instruments used were satisfaction questionnaires. Fifty students took part, 25 of whom tried out the Qubism 3D Modeling software and the rest used the GeoGebra software. These students solved practical exercises in Technical Drawing and Descriptive Geometry during the didactic intervention. The analysis of the results suggests that the students developed spatial visualization skills, and the data also indicates that the software applied promoted significant learning, making it possible to verify the learning resulting from the computer simulations. From the research already carried out, there are some curiosities and perceptions that can serve as a bridge for further research into the applicability of technology in the study of various subjects in Technical Drawing and Descriptive Geometry. Mozambique rare D simulations Cylinders skill Projections views sections section quasiexperimental quasi experimental approach observation notetaking note taking records questionnaires part 2 intervention skills

Resumo No Ensino Secundário Geral em Moçambique, ainda é raro o uso de recursos tecnológicos para o aprendizado de Desenho Técnico e de Geometria Descritiva. O objetivo desta pesquisa é verificar se as simulações dos softwares Qubism 3D Modeling e GeoGebra, nos temas de Projeção Ortogonal e de Seção de Cilindros, contribuem para a formação de alunos nesse tipo de habilidade. Para o estudo das Projeções Ortogonais, adaptamos o Qubism 3D Modeling para ajudar na clarificação das representações das vistas ortogonais. Para o estudo das seções produzidas em cilindro, utilizamos o software de geometria dinâmica GeoGebra, por facilitar a percepção da forma da figura resultante da seção. Este estudo é quase-experimental, seguindo uma abordagem qualitativa, conduzido em uma escola do sul de Moçambique. As técnicas empregadas incluíram observação, tomadas de notas e registros fotográficos, e os instrumentos utilizados foram questionários de satisfação. Participaram 50 alunos, dos quais 25 experimentaram o software Qubism 3D Modeling e os 25 restantes utilizaram o software GeoGebra. Esses alunos resolveram exercícios práticos de Desenho Técnico e de Geometria Descritiva durante a intervenção didática. A análise dos resultados sugere que os alunos desenvolveram competências de visualização espacial, e os dados também indicaram que os softwares aplicados promoveram aprendizagens significativas, possibilitando verificar o aprendizado resultante das simulações computacionais. A partir da pesquisa já realizada, existem algumas curiosidades e percepções que podem servir de ponte para novas pesquisas sobre a aplicabilidade da tecnologia no estudo de diversos temas de Desenho Técnico e de Geometria Descritiva. Moçambique D GeoGebra Cilindros habilidade Ortogonais ortogonais cilindro seção quaseexperimental, quaseexperimental quase experimental, experimental quase-experimental qualitativa observação fotográficos satisfação 5 2 didática espacial significativas computacionais realizada

Extreme changes in climate, especially in temperature, could have implications for herbal plants in various world regions. Medicinal plants often produce a wide variety of natural phytochemicals to enhance their defence and survival mechanisms against harsh environmental conditions, and when these mechanisms fail, plants consequently die. We investigated the impact of high temperatures coupled with the specific duration of exposure on the yield and composition of essential oils and trichomes in leaves of Lippia javanica. Plants were exposed to increasing temperatures (25 °C to 47 °C) for different durations (48 h to 144 h). Response surface methodology was applied to assess the interaction between temperature and length of exposure on the essential oil yield, trichome length, and trichome diameter. Essential oils were recovered from the control and treated leaf samples using hydrodistillation and volatile compounds were identified through gas chromatography-mass spectrometry (GC-MS). Multivariate analysis modelling allowed different clustering patterns to be detected. That is, increasing temperatures raised the oil yield, trichome length, and diameter from 1.007 mg/100 g to 3.58 mg/100 g, 50 jm to 160 jm, and 25 jm to 60 jm, respectively. Significant chemical differences between the essential oils were confirmed by the principal component and orthogonal projections to latent structures, which identified separate clusters for the control and treated samples. The current findings indicate that L. javanica has coping mechanisms against high temperatures. SIGNIFICANCE: • High temperatures significantly alter the trichome morphology and secretion of essential oils in L. javanica, which adversely affects the shrub's medicinal properties. Regardless of climate change, this finding could have major implications for indigenous people who continue to use the shrub for therapeutic purposes. • L. javanica showed coping mechanisms against high temperatures for a maximum of six days; however, a prolonged exposure would be more detrimental. As a result, climate change will negatively influence the plant's developmental and defence mechanisms.

ABSTRACT: Background: FFR is a gold standard used evaluate the severity of coronary artery lesions. QFR is a new non invasive technique for the same purpose based on the analysis of flow directly derived from routine coronary angiography, without additional intervention and with no induction of hyperemia. The aim was to compare the results obtained by QFR to those obtained by FFR in in terms of its predictive value. Method: Retrospective analysis of FFR measurements in routine coronary angiographic studies were compared to results obtained by means of QFR. Main left lesions were excluded. FFR was evaluated using pressure guides across the lesion under hyperemia induced by intracoronary or intravenous adenosine. Two orthogonal projections with no more than 25o difference between them were analyzed. The analysis was performed by two independent and operators blind to the results of FFR. The QAngioXA (Medis ®, Netherland) software was used in the analysis. Results: 35 coronary arteries were analyzed: LAD 57.1%, RCA 20.9%; Cx 20%. QFR was available for 27 arteries, the rest being discarded due to inadequate orientation of the artery. Mean QFR was 0.81 (SD 0.118). Mean difference between QFR and DD FFR was 0,04 (SD 0,006) (NS). Interobserver correlation was good (r=0.95, P 0.07). In only 7.4% of arteries there was a notable though not statistically significant difference between FFR and QFR, either due to under estimation or overestimation of lesion severity by QFR compared to FFR. Using FFR as a gold standard method QFR revealed sensitivity 90.9%, specificity 93.8%, The respective numbers for either positive or negative predictive values were the same. Area under the ROC curve was 0.923 (95% C.I. 0.01-1.00). Conclusion: this study reveals similar results of QFR compared to FFE in the estimation of coronary lesion severity. Given that QFR is a significantly less invasive and less expensive method than FFR, it may lead to an increased use of flow analysis in the determination of coronary artery lesion severity.

RESUMEN: Introducción: La evaluación de lesiones coronarias mediante Reserva de Flujo Fraccional (FFR), es de elección para determinar su significancia funcional en el laboratorio de hemodinamia. La razón de flujo cuantitativo (Quantitative Flow Ratio, QFR) es una nueva técnica no invasiva para la evaluación de la significancia funcional de una estenosis coronaria, basada en el análisis de flujo a partir de la coronariografía diagnóstica, sin necesidad de hiperemia ni de la introducción de insumos adicionales. Objetivo: evaluar la correlación y valor predictivo del QFR comparado con FFR. Métodos: se seleccionaron arterias que contaban con medición de FFR realizados en nuestro centro y se analizó retrospectivamente el QFR a partir de las coronariografías de dichos estudios. Se excluyó lesiones de tronco y lesiones ostiales. La medición de FFR fue realizada con guía de presión ubicada distal al segmento afectado, mediante hiperemia con adenosina intracoronaria o intravenosa en infusión. Para el análisis de QFR se utilizan 2 proyecciones angiográficas ortogonales del vaso a interrogar con una separación de más de 25º entre ellas; ambas proyecciones deben coincidir en el eje para un correcto análisis. El análisis fue realizado por dos operadores, ciegos al resultado del FFR, utilizando el software QAngioXA (Medis ®, Netherland). Resultados: se analizaron 35 arterias, 57,1% Descendente Anterior (ADA), 20% Circunfleja (ACF) y 20% Derecha (ACD). El FFR promedio fue de 0,83±0,092 y 34,2% tuvieron como resultado un FFR ±0,80. El análisis retrospectivo del QFR se pudo realizar en 27 arterias; en las 8 restantes (22,9%) no fue posible su realización, ya sea por imágenes insuficientes o falta de perpendicularidad del segmento. El QFR promedio fue de 0,81±0,118. Hubo una buena correlación entre QFR y FFR (r =0,758; p<0,001), y excelente concordancia entre las dos medidas (diferencia de medias 0,0042±0,0646, 95%; p=0,74). Asimismo, en la medición del QFR existió una buena correlación Inter observadores (r=0,627, p<0,05). Sólo en 7,4% de las arterias hubo discordancia entre ambas mediciones: FFR>0,8 pero QFR±0,8 en 3,7%; y FFR ±0,8 y QFR >0,8 en 3,7%. Así, el QFR tuvo una Sensibilidad: 90,9%, Especificidad: 93,8%; Valor Predictivo Positivo: 90,9%; Valor Predictivo Negativo: 93,8%; Likelihood Ratio Positivo: 14,55 y Likelihood Ratio Negativo: 0,1. La curva ROC mostró un área bajo curva: 0,923; 95% IC: 0,801-1,00. Conclusión: Los resultados del QFR en nuestra serie son similares a las mediciones de FFR. El uso de QFR podría ser una alternativa, rápida, económica y segura, en la evaluación fisiológica de lesiones coronarias. Se requieren mayores estudios clínicos para comprobar estos resultados.

Two methodologies were developed to monitor the biodiesel content of mafurra in mixtures with diesel using hydrogen nuclear magnetic resonance (1H NMR) Spectroscopy combined with the multivariate regression by orthogonal projections to latent structure (OPLS) and partial least squares (PLS). The efficiency of these methodologies was analyzed based on the figures of merit and the fit of the models through the correlation of the measured and predicted values of the calibration and prediction sets. The results of the figures of merit in the OPLS model were better than in the PLS model. A high correlation between the measured and predicted values was evident in the OPLS model, with a correlation coefficient (R2) greater than 0.99, demonstrating a better fit of the OPLS model in relation to the PLS model which presented a correlation coefficient (R2) less than 0.98. The OPLS model is more robust and has good predictive capacity than the PLS model because it obtained a higher Q 2 value. The excellent results of the application of 1H NMR spectroscopy combined with multivariate regression by OPLS suggest that this analytical methodology is ideal, feasible, efficient and suitable for use by inspection agencies to control the quality of this fuel.

RESUMEN Se implementó un algoritmo de Búsqueda Voraz Ortogonal (OMP) y se muestran los resultados obtenidos usando esta técnica en el proceso de reducción de ruido e interpolación en datos sísmicos, bajo el esquema de representación poco densa de señales. El algoritmo OMP permite representar la señal poco densa basada en proyecciones ortogonales de la señal sobre un diccionario sobrecompleto. Los diccionarios sobrecompletos son diseñados usando k-veces descomposición en valores singulares (K-SVD). En cada iteración OMP calcula una nueva señal aproximada y el error es usado en la nueva iteración para determinar el nuevo elemento. Los nuevos elementos corresponden al valor máximo de los productos punto del residuo con los elementos iniciales del diccionario. El algoritmo implementado es aplicado a datos sísmicos VSP y a datos de sísmica de refracción, obteniéndose resultados satisfactorios en interpolación de trazas y reducción de ruido de forma simultánea.

ABSTRACT An implementation of the Orthogonal Matching Pursuit (OMP) algorithm was used and the results obtained therefrom are presented for simultaneous interpolation and denoising from seismic signals in the framework of sparse signal representation. OMP is an algorithm for sparse signal representation based on orthogonal projections underlying the signal over an over-complete dictionary. This over-complete dictionary was designed using K-times Singular Values Decomposition (K-SVD). In each iteration, OMP calculates a new signal approximation and the approximation error is used in the next iteration to determine the new element. The new element corresponds to the largest magnitude of the inner products between the current residual and the original elements in the dictionary. The implemented algorithm was applied to VSP seismic data and refraction seismic data; results for the application in restored missing traces and denoise signals are presented.

This paper presents a study done to find an interior point in the feasible region of linear programming problems is an aspect that should be solved in the initial stage of the implementation of the interior point algorithms used to optimize them. Consequently, it is proposed a methodology that starts with a formulation that does not require adding surplus or slack variables. It only includes an additional variable to generate a polyhedron in a new expanded space and with simple projections finds an interior point in the same polyhedron. It is demonstrated that the optimal solution of the extended linear programming problem allows obtaining a feasible point of the original problem or concluding that it has no feasible solutions.

Se presenta un estudio para encontrar un punto interior en la región factible de problemas de programación lineal, un aspecto que debe ser resuelto en la etapa inicial de la implementación de los algoritmos de punto interior empleados para optimizarlos. Para este fin, se propone un procedimiento que parte de una formulación que no requiere adicionar variables de holgura ni de exceso, solamente involucra una variable adicional para generar un poliedro en un nuevo espacio ampliado y que con proyecciones sencillas encuentra un punto interior en el mismo. Se demuestra que la solución óptima del problema de programación lineal ampliado permite obtener un punto factible del problema original o concluir que el mismo no tiene soluciones factibles.

The aim of this paper is to propose a procedure to create escape vectors specifically developed to perform an orthogonal projection from an Ax ≤ b type polyhedron’s edge tn its interinr. The prnpnsed prncedure can be implemented in interior-point methods for solving linear programming problems since in these methods various strategies are used to avoid reaching the borders of the polyhedron. A projection procedure was develnped tn the pnlyhedrnn’s interinr starting frnm three scenarins and it was used nn a cnntext case demonstrating its applicability. The results show that the projection carried out in the iteration in which the escape is done not only allows abandoning from a suboptimal solution but it also kept the same objective function value. Therefore, it can be concluded that interior-point methods do not need to avoid the frontier or to adjust values, as it occurs in other applications.

El objetivo de este trabajo es proponer un procedimiento para la creación de vectores de escape diseñados específicamente para realizar proyecciones ortogonales desde las aristas de poliedros Ax ≤ b hacia el interior de los mismos. El procedimiento propuesto puede ser implementado en algoritmos de punto interior para la optimización de problemas de programación lineal, pues en los mismos se emplean diversas estrategias para evitar llegar hasta la frontera de los poliedros. Para esto se desarrolló un procedimiento de proyección hacia el interior del poliedro desde tres situaciones y se probó con un ejemplo en contexto. Los resultados muestran que la proyección realizada en la iteración en que se aplica el escape no solo permite salir de un punto subóptimo sino que también mantuvo el último valor de la función objetivo. Por lo tanto, se puede concluir que no es necesario evitar la frontera del poliedro o ajustar valores de paso como ocurre en otras aplicaciones.

En este artículo se desarrolla el Análisis Factorial Interbaterías (AIB) mediante el uso de métodos PLS (Partial Least Squares). Ya que los métodos PLS son algoritmos que iteran hasta la convergencia, permiten ser intervenidos adecuadamente en algunas de sus etapas para tratar problemas tales como datos faltantes. Específicamente se toma la fase iterativa de la regresión PLS y se implementa el principio de "datos disponibles" del algoritmo NIPALS (Non-linear estimation by Iterative Partial Least Squares) para permitir el desarrollo algorítmico del AIB con datos faltantes, proporcionando los elementos básicos para el análisis e interpretación de los resultados. Este nuevo algoritmo para AIB elaborado bajo el entorno de programación R, fundamentalmente realiza secuencias iterativas convergentes de proyecciones ortogonales de vectores emparejados con los datos disponibles y funciona adecuadamente en bases con y sin datos faltantes. Para efectos de presentar los conceptos básicos del AIB y cotejar los resultados derivados de la aplicación algorítmica, se toma la base de datos completa de Linnerud para el análisis clásico; y luego esta base es contaminada con una muestra aleatoria que representa aproximadamente el 7% de los datos no disponibles (NA) para el análisis con datos faltantes. Se comprueba que con datos completos los resultados derivados del algoritmo son idénticos a los obtenidos mediante el desarrollo del método clásico para AIB, y que los resultados con datos faltantes son similares, aunque esto no siempre será así porque ello dependerá de que tanto se afecta la estructura de covarianza factorial ‘original’ ante la cantidad de información ausente; por tanto la interpretación será válida solo en relación con los datos disponibles.

In this article we develop the Inter-battery Factor Analysis (IBA) by using PLS (Partial Least Squares) methods. As the PLS methods are algorithms that iterate until convergence, an adequate intervention in some of their stages provides a solution to problems such as missing data. Specifically, we take the iterative stage of the PLS regression and implement the "available data" principle from the NIPALS (Non-linear estimation by Iterative Partial Least Squares) algorithm to allow the algorithmic development of the IBA with missing data. We provide the basic elements to correctly analyse and interpret the results. This new algorithm for IBA, developed under the R programming environment, fundamentally executes iterative convergent sequences of orthogonal projections of vectors coupled with the available data, and works adequately in bases with or without missing data. To present the basic concepts of the IBA and to cross-reference the results derived from the algorithmic application, we use the complete Linnerud database for the classical analysis; then we contaminate this database with a random sample that represents approximately 7% of the non-available (NA) data for the analysis with missing data. We ascertain that the results obtained from the algorithm running with complete data are exactly the same as those obtained from the classic method for IBA, and that the results with missing data are similar. However, this might not always be the case, as it depends on how much the ‘original’ factorial covariance structure is affected by the absence of information. As such, the interpretation is only valid in relation to the available data.

Resumo:As câmaras com objetiva olho de peixe permitem aumentar o campo de visada da câmara, e consequentemente é amplamente empregada na robótica. O uso desse tipo de câmara em aplicações de alta acurácia na Fotogrametria a curta distância, exige a sua calibração. O objetivo principal é calibrar a câmara Fuji Finepix S3pro com a lente olho de peixe Bower-Samyang 8mm usando modelos matemático rigorosos. Modelos matemáticos baseados nas projeções perspectiva, estereográfica, equidistante, ortogonal e do ângulo equi-sólido foram implementados e usados nos experimentos. As lentes olho de peixe são geralmente fabricadas seguindo um dos quatro últimos modelos, e a lente Bower-Samyang 8 mm é baseada na projeção estereográfica. Os modelos matemáticos foram usados em conjunto com os modelos de distorções radial simétrica, descentrada e de afinidade. Experimentos foram realizados para verificar o conjunto de parâmetros de orientação interior adequado para descrever a geometria interna da câmara. O modelo matemático de colinearidade, baseado na projeção perspectiva, apresentou o resultado menos acurado. As lentes olho de peixe não são fabricadas conforme a projeção perspectiva, o que justifica esse resultado. Os resultados obtidos com as projeções estereográfica, equidistante, ortogonal e do ângulo equi-sólido não apresentam diferenças significativas, embora a lente olho de peixe Bower-Samyang tenha sido construída conforme a projeção estereográfica. Verificou-se também uma baixa correlação entre os parâmetros de orientação interior e exterior para a lente Bower-Samyang

Abstract:Fisheye lens cameras enable to increase the Field of View (FOV), and consequently they have been largely used in several applications like robotics. The use of this type of cameras in close-range Photogrammetry for high accuracy applications, requires rigorous calibration. The main aim of this work is to present the calibration results of a Fuji Finepix S3PRO camera with Samyang 8mm fisheye lens using rigorous mathematical models. Mathematical models based on Perspective, Stereo-graphic, Equi-distant, Orthogonal and Equi-solid-angle projections were implemented and used in the experiments. The fisheye lenses are generally designed following one of the last four models, and Bower-Samyang 8mm lens is based on Stereo-graphic projection. These models were used in combination with symmetric radial, decentering and affinity distortion models. Experiments were performed to verify which set of IOPs (Interior Orientation Parameters) presented better results to describe the camera inner geometry. Collinearity mathematical model, which is based on perspective projection, presented the less accurate results, which was expected because fisheye lenses are not designed following the perspective projection. Stereo-graphic, Equi-distant, Orthogonal and Equi-solid-angle projections presented similar results even considering that Bower-Samyang fisheye lens was built based on Stereo-graphic projection. The experimental results also demonstrated a small correlation between IOPs and EOPs (Exterior Orientation Parameters) for Bower-Samyang lens.

La programación lineal (PL) es una de las herramientas de mayor aplicación en la investigación de operaciones. Se han desarrollado y se siguen proponiendo varios métodos para la resolución de problemas de este tipo, desde el famoso simplex hasta los algoritmos de punto interior. Este trabajo tiene como propósito principal presentar la propuesta de un nuevo procedimiento para la solución de problemas PL que, partiendo de un punto interior, realiza proyecciones ortogonales mediante rectas paramétricas y se mueve iterativamente entre el interior y la frontera del poliedro que define la región factible hasta llegar al punto extremo óptimo.

Linear programming (LP) is one of the most widely-applied techniques in operations research. Many methods have been developed and several others are being proposed for solving LP problems, including the famous simplex method and interior point algorithms. This study was aimed at introducing a new method for solving LP problems. The proposed algorithm starts from an interior point and then carries out orthogonal projections using parametric straight lines to move between the interior and polyhedron frontier defining the feasible region until reaching the extreme optimal point.

Efficacy and safety of dual-axis rotational coronary angiography versus conventional angiography Background Conventional coronary angiography (CA) is the gold standard for the diagnosis of coronary artery disease. However, this technique requires several orthogonal projections to determine the severity of the disease. Dual-axis rotational coronary angiography (DARCA) is a new technique which allows visualization of each coronary artery using a single contrast injection and obtains unique images. This technique has been shown to reduce both radiation and contrast exposure. Objective To determine the amount of contrast used, radiation exposure and diagnostic accuracy of DARCA compared to conventional CA. Methods We conducted a prospective, self-controlled study of consecutive patients undergoing elective coronary angiography to compare DARCA versus the conventional technique. All the angiographies were reviewed by two independent interventional cardiologists (observer 1 and observer 2) who evaluated agreement between both types of images. The observers evaluated firstly the DARCAs and three weeks later the conventional CAs to prevent bias in reading the images. Results The contrast volume used in the diagnostic procedure was significantly lower with DARCA (33.29±11.2 ml vs. 17±5.4 ml; p <0.01). Radiation exposure in patient (235.6±76.8 mGy vs. 82.7±46.6 mGy; p <0.01) and operator was also significantly lower (5.7±3.26 mSv vs. 2.48±1.47 mSv; p <0.04). A slight difference and a strong correlation were seen in the number of lesions, vessel diameter and percentage of stenosis between both observers and in both methods. Agreement for categorizing percentage of stenoses was also adequate. Conclusion DARCA reduces the use of contrast agent and radiation exposure compared to the conventional technique without modifying the diagnostic accuracy of the method.

Introducción La angiografía convencional (AC) es la técnica de referencia para el diagnóstico de la enfermedad coronaria. Sin embargo, requiere múltiples proyecciones ortogonales para determinar el grado de enfermedad. La técnica de angiografía rotacional dual (ARD) permite una única adquisición e inyección de contraste para cada coronaria, con potencial reducción del volumen de contraste y de la dosis de radiación. Objetivo Comparar ambas técnicas (AC vs. ARD) a través de la evaluación de cantidad de contraste, exposición a la radiación y eficiencia diagnóstica. Material y métodos El presente es un estudio prospectivo, consecutivo, autocontrolado de coronariografías electivas para comparar AC y ARD. Todas las angiografías fueron revisadas por dos hemodinamistas independientes (observador 1 y observador 2) para evaluar la concordancia entre ambos tipos de imágenes. Para prevenir un sesgo en la lectura de las imágenes, los observadores evaluaron primero las ARD y tres semanas más tarde hicieron lo propio con las AC. Resultados Con la ARD se observó una reducción en la utilización de contraste (33,29 ± 11,2 ml vs. 17 ± 5,4 ml; p < 0,01) y en la exposición a radiación del paciente (235,6 ± 76,8 mGy vs. 82,7± 46,6 mGy; p < 0,01) y del operador (5,7 ± 3,26 mSv vs. 2,48 ± 1,47 mSv; p < 0,04). Se observó una leve diferencia y una fuerte correlación en el número de lesiones, diámetro del vaso y porcentaje de estenosis entre ambos observadores y entre ambos métodos. La evaluación categórica del porcentaje de estenosis también demostró una concordancia adecuada. Conclusión La ARD reduce el uso de contraste y la exposición a radiación en comparación con la técnica convencional, sin alterar la eficiencia diagnóstica del estudio.

Muestreo compresivo es una rama emergente del procesamiento de señales, basada en el hecho de que un número pequeño de proyecciones lineales no adaptativas sobre una señal compresible contiene suficiente información para reconstruirla y procesarla. En este artículo se presentan los resultados obtenidos al evaluar cinco matrices de medición para la realización de muestreo compresivo en un sistema que utiliza el algoritmo orthogonal matching pursuit (OMP), para la recuperación de la señal original. Las matrices de medición están implicadas tanto en el proceso de muestreo-compresión de la señal, como en la reconstrucción de la misma. Dentro de este grupo de matrices estudiadas se destacó la matriz Hadamard aleatoria, con la cual es posible obtener el menor porcentaje de error en la recuperación de la señal. Adicionalmente se presenta una metodología para la evaluación de estas matrices, que permita posteriores análisis de la idoneidad de estas para aplicaciones específicas.

Compressive sensing is an emergent field of signal processing which states that a small number of non-adaptive linear projections on a compressible signal contain enough information to reconstruct and process it. This paper presents the results of evaluating five measurement matrices for applying them to compressive sensing in a system using orthogonal matching pursuit (OMP) to reconstruct the original signal. The measurement matrices were those implicated in compressive sensing as well as in reconstructing the signal. The Hadamard-random matrix stood out within this group of matrices because the lowest percentage of error in signal recovery was obtained with it. This paper also presents a methodology for evaluating these matrices, allowing subsequent analysis of their suitability for specific applications.

In this paper, a family of simple formulas for the calculation of the pseudo inverse of a rectangular matrix of less than maximum rank is derived using linear vector space methods. The principal result is that the pseudo inverse A+ of a matrix A can be calculated as A+ = Q(P T AQ)-1P T, where P and Q are rectangular matrices whose r columns are vectors that form a basis for the spaces spanned by the columns and rows, respectively, of matrix A. This leaves the user the liberty to choose the basis to take into consideration other questions such as amount of work needed and ill-conditioning of the matrix that has to be inverted. The formulas are particularized for rectangular matrices that have maximum rank and for the trivial case in which the original matrix is non-singular. Illustrative numerical examples are worked out for several choices of basis vectors and the results are compared with those provided by the program Mathematics through its function PseudoInverse[A].

En este artículo se deduce una familia de fórmulas simples para el cálculo de la seudo inversa de una matriz rectangular de rango menor que el máximo del número de filas y el número de columnas utilizando métodos de espacios vectoriales lineales. El resultado principal es que la seudo inversa A+ de una matriz A se puede calcular con la fórmula A+ = Q(P T AQ)-1P T, donde P y Q son matrices rectangulares cuyas r columnas ( r es el rango de la matriz A) son vectores que forman una base para los espacios generados por las columnas y filas respectivamente de la matriz A. Esto le deja al usuario la libertad de escoger la base y tomar en consideración otras cuestiones como la cantidad de trabajo requerida y el mal condicionamiento de la matriz A. Las fórmulas se particularizan para matrices rectangulares que tienen máximo rango y para el caso trivial en que la matriz original es no-singular. Se presentan las soluciones de ejemplos numéricos ilustrativos para varias selecciones de vectores base, y los resultados se comparan con los que proporciona el programa Mathematica a través de su función PseudoInverse[A].

Las proyecciones de demanda del servicio de banda ancha muestran un crecimiento vertiginoso en las próximas décadas. El esquema de modulación que soporta el nivel físico de tales servicios es el de multiplexión por división de frecuencias ortogonales (OFDM) que, gracias a sus características ortogonales, logran sobrepasar las barreras de transmisión impuestas por los canales de comunicaciones. Después de ilustrar los fundamentos del porqué OFDM logra su cometido, detallando el mapeamiento y modelo de comunicaciones en banda base, las aplicaciones potenciales actuales y futuras de OFDM son indicadas. Se prevé que surja un modelo para las nuevas generaciones, propuestas en espacios concurrentes en tiempo, frecuencia y código.

The projections of the demand of broadband services show a vertiginous growth in the next decades. The modulation scheme that supports the physical level of such services is the Orthogonal Frequency-Division Multiplexing (OFDM) that thanks to their orthogonal characteristics, overcome the transmission barriers imposed by the communication channels. After illustrating the fundamentals of why OFDM achieves its objective and detailing the mapping and model of communications in base band, the present and future of potential applications of OFDM are indicated. It is likely that a model for the new generations, in which time, frequency and code concur in space, will arise

An iterative method for finding the center of a linear programming polytope is presented. The method assumes that we start at a feasible interior point and each iterate is obtained as a convex combination of the orthogonal projection on the half spaces defined by the linear inequalities plus a special projections on the same half spaces. The algorithm is particularly suitable for implementation on computers with parallel processors. We show some examples in two dimensional space to describe geometrically how the method works. Finally, we present computational results on random generated polytopes and linear programming polytopes from NetLib to compare the centering quality of the center using projections and the analytic center approach.