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Welcome to the research group's web page.

The purpose of this web page is to contribute to the diffusion of some of the scientific communications of this research group. In addition, it serves to make available to others our resources or facilities which may be useful in different scientific and technical fields.

        Osvaldo Skliar
        Coordinator
        Applied Mathematics & Computer Simulation Group

1) Signal and Image Analysis2) Randomness3) Pattern Recognition and 4) Logic.

1. Signal and Image Analysis

     Analysis of time series and signals using the Square Wave Method
Skliar O., Monge R. E. and Gapper S. (2016). Analysis of time series and signals using the Square Wave Method. arXiv:1608.02166 [cs.NA].

Abstract

The Square Wave Method (SWM), previously introduced for the analysis of signals and images, is presented here as a mathematical tool suitable for the analysis of time series and signals. To show the potential that the SWM has to analyze many different types of time series, the results of the analysis of a time series composed of a sequence of 10,000 numerical values are presented here. These values were generated by using the Mathematical Random Number Generator (MRNG).

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     A New Method for Signal and Image Analysis: The Square Wave Method
Skliar O., Monge R. E. and Gapper S. (2015). A New Method for Signal and Image Analysis: The Square Wave Method. arXiv:1501.00680 [cs.NA].

Abstract

A brief review is provided of the use of the Square Wave Method (SWM) in the field of signal and image analysis and it is specified how results thus obtained are expressed using the Square Wave Transform (SWT), in the frequency domain. To illustrate the new approach introduced in this field, the results of two cases are analyzed: a) a sequence of samples (that is, measured values) of an electromyographic recording; and b) the classic image of Lenna.

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     A New Method for the Analysis of Signals: The Square Wave Transform
Skliar O., Monge R. E., Oviedo G. and Gapper S. (2016). A New Method for the Analysis of Signals: The Square Wave Transform, Revista de Matemática: Teoría y Aplicaciones 2016, Vol. 23(1), pp. 85-110.

Presented at: XIX International Symposium on Mathematical Methods Applied to the Sciences (XIX SIMMAC), San José, 25-28 February 2014.

Abstract

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.

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     A New Method for the Analysis of Images: The Square Wave Method
Skliar O., Oviedo G., Monge R. E., Medina V. and Gapper S. (2013). A New Method for the Analysis of Images, Revista de Matemática: Teoría y Aplicaciones 2013, Vol. 20(2), pp. 133-153.


Presented at: XVIII International Symposium on Mathematical Methods Applied to the Sciences (XVIII SIMMAC), San José, 21-24 February 2012.

Abstract

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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2. Randomness

    A Mathematical Random Number Generator (MRNG)
Skliar O., Monge R. E., Gapper S and Oviedo G. (2012). A Mathematical Random Number Generator (MRNG) arXiv:1211.5052 [cs.NA].

Abstract

A novel Mathematical Random Number Generator (MRNG) is presented here. In this case, "mathematical" refers to the fact that to construct that generator it is not necessary to resort to a physical phenomenon, such as the thermal noise of an electronic device, but rather to a mathematical procedure. The MRNG generates binary strings — in principle, as long as desired — which may be considered genuinely random in the sense that they pass the statistical tests currently accepted to evaluate the randomness of those strings. From those strings, the MRNG also generates random numbers expressed in base 10. An MRNG has been installed as a facility on this web page. This generator may be used for applications in tasks in: a) computational simulation of probabilistic-type systems, and b) the random selection of samples of different populations. Users interested in applications in cryptography can build another MRNG, but they would have to withhold information — specified in section 5 — from people who are not authorized to decode messages encrypted using that resource.

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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.

Abstract

The 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.

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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.

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.
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.

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3. Pattern Recognition

    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.

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:
a) a unique cluster which can be visualized as an object with no internal structure;
b) a set of n first-order subclusters—given they exist—which are constituents of the cluster mentioned in (a);
c) n sets of second-order subclusters—each of which are constituents of one of the first-order subclusters mentioned in (b)—and so on, successively.
Convexity is not required either for the cluster mentioned in (a) or for the subclusters of different orders. Although in this paper the method presented is applied to bidimensional objects, it may be generalized for the n-dimensional case.

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     A Variation of the Method Using the Simulation of a Diffusion Process to Characterize the Shapes of Plane Figures
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.

Abstract

This 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.

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4. Logic

     Using Inclusion Diagrams as an Alternative to Venn Diagrams to Determine the Validity of Categorical Syllogisms
Skliar O., Monge R. E. and Gapper S. (2015). Using Inclusion Diagrams as an Alternative to Venn Diagrams to Determine the Validity of Categorical Syllogisms. arXiv:1509.00926 [cs.LO].

Abstract

Inclusion diagrams are introduced as an alternative to using Venn diagrams to determine the validity of categorical syllogisms, and are used here for the analysis of diverse categorical syllogisms. As a preliminary example of a possible generalization of the use of inclusion diagrams, consideration is given also to an argument that includes more than two premises and more than three terms, the classic major, middle and minor terms in categorical syllogisms.

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    Propositional Calculus and Binary Calculus
Skliar O., Medina, V. (1990) Propositional Calculus and Binary Calculus, UNICIENCIA, Vol. 7 (1), pp. 43-57.

Abstract

We present an efficient method of propositional calculus which allows the manipulation of logical functions with an arbitrary number of propositional variables. This method is based on the use of binary sequences (in other words, sequences of digits that can only be either 0 or 1) and certain operations between them. This calculus is then implemented by using neural network type devices.

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