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The purpose of this web page is to contribute to the diffusion of some of the scientific communications of this research group. |
A New Method for the Analysis of Images: The Square Wave Method Presented at: XVIII International Symposium on Mathematical Methods Applied to the Sciences (XVIII SIMMAC), San José, 21-24 February 2012. By: Osvaldo Skliar, Guillermo Oviedo, Ricardo Monge, Víctor Medina and Sherry Gapper. AbstractThe 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. Size: 3.7M Download |
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A Characterization of the Notion of Fluctuation Presented at: XVIII International Symposium on Mathematical Methods Applied to the Sciences (XVIII SIMMAC), San José, 21-24 February 2012. By: Osvaldo Skliar, Ricardo Monge, Guillermo Oviedo, Víctor Medina and Sherry Gapper. Abstract
When it is said that "something" fluctuates, what is usually meant is that it randomly increases at times and decreases at other times. The nature of that "something" undergoing those changes can be quite varied: There are
fluctuations of the difference in electric potential, in pressure, in temperature, in the number of members
in a population, etc. The characterization presented here of the notion of fluctuation makes
possible not only the analysis of fluctuations in diverse types of systems but also an
adequate comparison of the values of the
fluctuations taking place in different systems. |
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A Hybrid Random Number Generator (HRNG) Skliar O., Monge R. E., Medina V., Gapper S. and Oviedo G. (2011) A Hybrid Random Number Generator (HRNG), Revista de Matemática: Teoría y Aplicaciones, Vol. 18 (2), pp. 265-297. Presented at: XVII International Symposium on Mathematical Methods Applied to the Sciences (XVII SIMMAC), San José, 16-19 February 2010. By: Osvaldo Skliar, Ricardo Monge, Víctor Medina, Sherry Gapper and Guillermo Oviedo. AbstractThe purpose of this paper is to present a novel Hybrid Random Number Generator (HRNG). Here "hybrid" refers to the fact that to construct this generator it is necessary to use 1) physical components — texts — and a physical process, and 2) a mathematical procedure. This HRNG makes it possible to generate genuine random numbers which may be used both for computer simulation of probabilistic systems and in the field of cryptography. The results of a comparative study of the binary strings generated by this HRNG and of those generated by two highly used implementations of a congruential algorithm designed to generate pseudorandom numbers are given here. One of the latter is the implementation incorporated into the Java 2 platform (version 1.6), and the other is the implementation incorporated into the runtime library of Microsoft's Visual C++ 2008 compiler. Size: 375K Download (2011 version)Size: 428K Download (2010 version) |
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Indices of Regularity and Indices of Randomness for m-ary Strings Skliar O., Monge R. E., Oviedo G. and Medina V. (2009) Indices of Regularity and Indices of Randomness for m-ary Strings, Revista de Matemática: Teoría y Aplicaciones, Vol. 16 (1), pp. 43-59. Presented at: XVI International Symposium on Mathematical Methods Applied to the Sciences (XVI SIMMAC), San José, 19-22 February 2008. By: Osvaldo Skliar, Ricardo Monge, Guillermo Oviedo and Víctor Medina. Abstract
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. |
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A New Method for the Analysis of Signals: The Square Wave Method Skliar O., Medina V. and Monge R. E. (2008) A New Method for the Analysis of Signals: The Square Wave Method, Revista de Matemática: Teoría y Aplicaciones, Vol. 15 (2), pp. 109-129. By: Osvaldo Skliar, Víctor Medina and Ricardo Monge. Abstract
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.
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| | A New Method for the Characterization of Clusters Skliar O., Oviedo G. and Monge R. E. (2007) A New Method for the Characterization of Clusters, Revista de Matemática: Teoría y Aplicaciones, Vol. 14 (2), pp. 123-136. Presented at: XV International Symposium on Mathematical Methods Applied to the Sciences (XV SIMMAC), San José, 21-24 February 2006. By: Osvaldo Skliar, Guillermo Oviedo and Ricardo Monge. Abstract
This new method for characterizing clusters is based on the simulation of a diffusion-like
process. A resolution-parameter—R—is introduced such that when assigned successive values
from an increasing sequence, it is possible to detect the following:
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| | A Variation of the Method Using the Simulation of a Diffusion Process to Characterize the Shapes of Plane Figures By: Osvaldo Skliar,Tatiana Láscaris-Comneno, Víctor Medina and José Poveda. Published in Spanish as: Skliar, O., T. Láscaris-Comneno, V. Medina, J. S. Poveda, (2003), Una variante del método que utiliza la simulación de un proceso de difusión para la caracterización de formas de figuras planas, Revista de Matemática: Teoría y Aplicaciones, Vol. 10, 1-2, pp. 107-121. AbstractThis is a variation of a previously presented method for characterizing the shapes of plane figures. In addition to retaining the advantages of the original method, this variant includes one more: It is no longer necessary to halt a (simulated) diffusion process during the transient stage; that is, before arriving at an equilibrium. On the contrary, the longer the process takes, the more noticeable the difference becomes between the concave parts and the convex parts of the contours of the figures analyzed. Size: 200K DownloadSize: 220K Download Spanish Version |