#ISSS2018 Corvallis

3336 
TOWARDS FRACTAL PROPERTIES OF COGNITIVE PROCESSES IN THE HUMAN BRAIN UNDER THE COMPLEXITY SCIENCE APPROACH 
1 Lina Reyes Ixchel, 2 Contreras Troya T. Ivonne, 1 Morales Matamoros Oswaldo, 1 Tejeida Padilla Ricardo, 1 Moreno Escobar Jesús Jaime

1 Instituto Politécnico Nacional, 2 Universidad Autónoma del Estado de México, megamikurayami6@gmail.com, ticontrerast@uaemex.mx, omoralesm@ipn.mx, ricardotp75@hotmail.com, jemoreno@esimez.mx

The systems movement experienced four waves in 20th century: the first wave stemmed from the debate on the nature of life between vitalism and mechanicalism. The second was the interdisciplinary research arising after the World War II, with General System Theory and Cybernetics, with the help of Information Theory, Operational Research, and Systems Analysis. The third one was the establishment and development of the Theory of Self-Organization. And the fourth wave of systems movement was the rise of Complex Systems Science, which mainly referred to the systems research movement in 1980s with the Chaos Theory and Complexity Science, including some new concepts such as emergence and chaos, appeared with the accompaniment of some new methods of mathematics and computation such physical theories of nonlinear dynamics (e.g. Fractal geometry) and multi-agent-based computer simulation. 
The human brain has been the subject of study among different branches of knowledge, describing their physiological and cognitive processes from data treated with qualitative tools and linear quantitative variables, seeking to obtain a determined average behaviour and the causality of the same. However, living systems do not obey linear issues. The actions that emerge from them have complex characteristics, which explanations or understanding is far from being able to be represented from their components and their individual behaviour, reason why their study and understanding requires the application of Chaos Theory and Complexity Science.

Cognitive processes are the ones that allowed human beings to differentiate them from other animals in ways that give them the opportunity to own, modify and live in any environment on the planet. This research focuses on the nonlinear quantitative characterization of cognitive processes. In order to do this, it was applied fractal geometry as an alternative tool for the characterization of cognitive (non-linear) processes that emerge from human brain. With this quantitative tool it was studied data signals of EEG (voltage generated by the interrelation among neurons as a function of time) from cognitive processes.
Fractal geometry could allow to eliminate the biases and tendencies in the signals of the cognitive processes to increase the visualization and suggestion of the real dynamics of these processes, in order to complement the experts opinion in a discipline or medical field that interpret the results.

In this research it was applied fractal geometry to study the fluctuations dynamics of stochastic time series (EEG) of a patient with reading and spelling disorders, which can be a reflection of difficulties in some of the cognitive processes such as language, learning, memory, intelligence, perception sensation or attention. Data were taken from 19-channel EEG (electrodes), which were treated as time series: voltage vs. time, each time series was 6453 data length. For each channel it was constructed 198 time series of fluctuations (standard deviation), for different time lags (τ). From each fluctuation time series, there were constructed other 198 time series (fluctuation of deviation fluctuation), also for different τ. Based on all-time series of generated fluctuations (39,204), there were determined two scaling exponents: the roughness exponent (H) and the fluctuation growth, for each of the 19 channels.

By applying fractal geometry, it would be possible to establish (from statistical point of view) the probable future states of cognitive processes, that help to discovering new forms of treatment, therapies and contribute with ideas about the dynamics of cognitive processes