Fractal dimension in the evaluation of different treatments of muscular injury in rats

Garcia, Thiago Alves; Ozaki, Guilherme Akio Tamura; Castoldi, Robson Chacon; Koike, Tatiana Emy; Camargo, Regina Celi Trindade; Filho, José Carlos Silva Camargo

doi:10.1016/j.tice.2018.08.014

Cited by 14 publications

(9 citation statements)

References 29 publications

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“…In 1975, the mathematician Benoit Mandelbrot defined the concept of fractals as a semi-geometric element with a repetitive structure at different scales [1], with characteristics of self-similarity as seen in some natural formations such as snowflakes, ferns, peacock feathers, and Romanesque broccoli. Fractal theory has been applied to various fields such as biology [15,8], health sciences [3,13,12,5,11], stock markets [10], network communications [7,9,18], and others. Fractal theory is one of the methods used to analyze data and obtain relevant information in highly complex problems.…”

Section: (Communicated By Miguel Sanjuan)mentioning

confidence: 99%

Methodology for the characterization of the electrical power demand curve, by means of fractal orbit diagrams on the complex plane of Mandelbrot set

Tabares-Ospina¹,

Osorio²

2020

Discrete &Amp; Continuous Dynamical Systems - B

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The present article proposes a new geometric space in the complex plane of the Mandelbrot set, framed in the diagram of orbits and attractors, to characterize the dynamics of the curves of the demand of daily electrical power, with the purpose of discovering other observations enabling the elevation of new theoretical approaches. The result shows a different method to evaluate the dynamics of the electric power demand curve, using fractal orbital diagrams. This method is a new contribution that extends universal knowledge about the dynamics of complex systems and fractal geometry. Finally, the reader is informed that the data series used in this article was used in a previous publication, but using a different fractal technique to describe its dynamics.1. Introduction. The purpose of this article is to present a methodology for characterizing the dynamics of electric power demand curves using fractal orbit diagrams defined in the complex plane of the Mandelbrot set. On this subject, the present authors have published two (2) articles. The fractal geometrical pattern of the Julia set [16] was determined with respect to the signs in the complex plane of the active and reactive electrical power; with new data based on [17] the conclusions were extended with respect to the fractal geometric pattern that produces the daily hourly demand of electric power. The main contribution to the theory of fractal geometry consisted in the identification and qualitative interpretation of the rules of formation of the topologies of Julia sets that produce the demand of hourly daily electrical power. The article [21] focuses on presenting a new methodology to analyze the dynamics of the series in reference, using the curve formed by attractors that move

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Section: (Communicated By Miguel Sanjuan)mentioning

confidence: 99%

Methodology for the characterization of the electrical power demand curve, by means of fractal orbit diagrams on the complex plane of Mandelbrot set

Tabares-Ospina¹,

Osorio²

2020

Discrete &Amp; Continuous Dynamical Systems - B

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“…In 1975, the mathematic Benoit Mandelbrot was the responsible to define the concept of fractal as a semi geometric element with a repetitive structure at different scales [1], with characteristics of self-similarity as some nature elements such as snowflakes, ferns, peacock feathers, and romanesco broccoli. Fractal theory has been applied to various fields such as biology [2,3], health sciences [4][5][6][7][8], stock markets [9], network communications [10][11][12], and others. Fractal theory is one of the methods used to analyze data and obtain relevant information in a highly complex problem.…”

Section: Introductionmentioning

confidence: 99%

Topological Properties of Fractal Julia Sets Related to the Signs of Real and Reactive Electric Powers

Tabares-Ospina

Candelo-Becerra

2019

Fractals

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In AC electrical systems, the power depends on the real power (P) due to resistive elements and the reactive power (Q) due to the inductive and capacitive elements, which are commonly studied by using phasor and scalar methods. Thus, this paper focuses on applying the fractal Julia sets to observe the topological properties related to the signs and magnitudes of the real and reactive powers consumed or supplied by an electrical circuit. To perform this, different power combinations were used to represent the fractal diagrams with an algorithm that considers the mathematical model of Julia sets. The study considers three type of loads: the first study considers the change of real power when the reactive power is fixed; the second study deals with the change of the reactive power when the real power is fixed; and finally, the third study contemplates that both real and reactive powers change. Furthermore, the fractal diagrams of the power in the four quadrants of the complex plane are studied to identify the topological properties that each sign and magnitude represent. A qualitative analysis of the diagrams helps to identify that the complex power loads present some fractal graphic patterns, with respect to the signs and magnitudes considered in the different quadrants of the complex planes. The diagrams represented in the complex planes save a relation in the forms and structure with other points studied, concluding that the power is related to other figures in other quadrants. Thus, this result allows a new study of the behavior of the power in an electrical circuit, showing a clear relation of the different fractal diagrams that the Julia sets obtained.

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“…Benoit Mandelbrot defined the concept of fractals as a semi-geometric element with a repetitive structure at different scales [1], with characteristics of self-similarity as seen in some natural formations such as snowflakes, ferns, peacock feathers, and Romanesco broccoli. Fractal theory has been applied to various fields such as biology [2,3], health sciences [4][5][6][7][8], stock markets [9], network communications [10][11][12], and others. Fractal theory is one of the methods used to analyse data and obtain relevant information in highly complex problems.…”

Section: Introductionmentioning

confidence: 99%

Fractal representation of the power demand based on topological properties of julia sets

Tabares-Ospina¹,

Candelo-Becerra²,

Hoyos³

2019

IJECE

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In a power system, the load demand considers two components such as the real power (P) because of resistive elements, and the reactive power (Q) because inductive or capacitive elements. This paper presents a graphical representation of the electric power demand based on the topological properties of the Julia Sets, with the purpose of observing the different graphic patterns and relationship with the hourly load consumptions. An algorithm that iterates complex numbers related to power is used to represent each fractal diagram of the load demand. The results show some representative patterns related to each value of the power consumption and similar behaviour in the fractal diagrams, which allows to understand consumption behaviours from the different hours of the day. This study allows to make a relation among the different consumptions of the day to create relationships that lead to the prediction of different behaviour patterns of the curves.

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Fractal dimension in the evaluation of different treatments of muscular injury in rats

Cited by 14 publications

References 29 publications

Methodology for the characterization of the electrical power demand curve, by means of fractal orbit diagrams on the complex plane of Mandelbrot set

Methodology for the characterization of the electrical power demand curve, by means of fractal orbit diagrams on the complex plane of Mandelbrot set

Topological Properties of Fractal Julia Sets Related to the Signs of Real and Reactive Electric Powers

Fractal representation of the power demand based on topological properties of julia sets

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