The “Square-Wave Method” (SWM) presented here is a new method for the systematic analysis of signals – either locally or globally – depending on only one variable (time). The SWM is based on a technique (previously described elsewhere) for the representation of this type of signals using a sum of trains of square waves. The SWM is applied here to several analytically characterized signals and to an audio signal.
El presente trabajo busca evaluar la creación de empresas por parte de ex empleados de empresas multinacionales de inversión extranjera directa. En concreto, se busca dimensionar el fenómeno, caracterizarlo, asà como valorar el desempeño de las empresas creadas. El estudio se hizo mediante un muestreo aleatorio simple con margen de error del 7% y nivel de confianza del 95%, sobre una base de datos de 11.120 ex empleados de empresas multinacionales en Costa Rica (n = 175). Además se utilizó un grupo control ad hoc. Los resultados muestran cómo son estos emprendedores, el proceso creador experimentado, las caracterÃsticas y el desempeËœno de las nuevas empresas.
The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT is used to analyze a sequence of samples (that is, of measured values) taken from an electroencephalographic recording. A computational tool, available at www.appliedmathgroup.org/, has been developed and may be used to obtain automatically the SWTs of sequences of samples taken from registers of interest for biomedical purposes, such as those of an EEG or an ECG.
The notions "regularity index" and "randomness index" previously introduced for binary strings (2-ary) have been modified slightly and generalized for m-ary strings (m = 2, 3, 4, . . .). These notions are complementary and the regular/random dichotomy has been replaced by a gradation of values of regularity and of randomness. With this approach, the more regular an m-ary string, the less random it is, and vice versa. The distributions of frequencies of different length strings -2-ary and 3-ary strings-according to their indices of randomness, are shown by histograms.Keywords: regularity index, randomness index, m-ary strings.Resumen Las nociones deíndice de regularidad y deíndice de aleatoriedad previamente introducidas para cadenas binarias (2-arias) son modificadas ligeramente y generalizadas para cadenas m-arias (m = 2, 3, 4, . . .). Dichas nociones resultan complementarias y la dicotomía regular-aleatorio es sustituida por una gradación de valores de regularidad y de aleatoriedad. Con el enfoque utilizado, cuanto más regular es una cadena m-aria menos aleatoria debe ser considerada y viceversa. Las distribuciones de frecuencias de cadenas -de diversas longitudes-2-arias y 3-arias en función de susíndices de aleatoriedad son presentadas mediante histogramas.Palabras clave:índice de regularidad,índice de aleatoriedad, cadenas m-arias.Mathematics Subject Classification: 49J55.
The Square Wave Method (SWM)-previously applied to the analysis of signals-has been generalized here, quite naturally and directly, for the analysis of images. Each image to be analyzed is subjected to a process of digitization so that it can be considered to be made up of pixels. A numeric value or "level" ranging from 0 to 255 (on a gray scale going from black to white) corresponds to each pixel. The analysis process described causes each image analyzed to be "decomposed" into a set of "components". Each component consists of a certain train of square waves. The SWM makes it possible to determine these trains of square waves unambiguously. Each row and each column of the image analyzed can be obtained once again by adding all the trains of square waves corresponding to a particular row or to a particular column. In this article the entities analyzed were actually sub-images of a certain digitized image. Given that any sub-image of any image is also an image, it was feasible to apply the SWM for the analysis of all the sub-images.
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