Abstract: In this project, a sequence of processing stages of a 2-digit mathematical comparison has been studied using the additive factors of visual noise, and digital distance. The behavioral data was recorded to interpret how reaction times (RTs) changed by the factors, whereas the further information obtaining from Event Related Potentials (ERPs) of continuous Electroencephalogram (EEG) signals were used to model processing stages and complexity of brain activities during the event-related task. The task was simply constructed by selecting twenty-four pseudorandom Arabic numbers from the numbers between 30 and 99 excluding the reference number 65. Two levels of visual noise were applied in order to degrade the same twenty-four numbers. While subjects were comparing the numbers as larger or as smaller than 65, ERPs from visual cortex (occipital lobes) and primary sensor cortex (parietal lobes) were examined.

In general, the experimental background of the project is based on earlier number sense studies by Stanislas Dehaene and his group at INSERM, Paris. He and his colleagues collected reaction time responses of several number comparison task using Arabic numbers (70) and semantic numbers (seventy) (Dehaene, 1997). Their findings showed that larger numbers are associated with right hand, while the numbers smaller associated by left hand. This finding is known as Spatial-Numerical Association of Response (SNARC) effect (Dehaene, 1997) in the literature. Later, Pinel (2001) focused on a number comparison task by adopting findings invented by Dehaene. 2-digit numbers between 30 and 99 with a fixed memorized reference value (65) were chosen, because of the smooth distance effect in reaction times meaning the more the number . In addition to the quantity effect of numbers, it is found that the quality of numbers reflects different effects on the number processing, therefore, verbal (fifty) versus Arabic (50) notations of numbers were presented in this study (Pinel et al,2001). Pinel recorded the behavioral and electro-physical brain activations of healthy subjects using simultaneous EEG and fMRI. While fMRI technique was spatially identifying the brain activations, EEG used to achieve temporal organization of these activations.

The hypothesis was structured as follows: “The complexity and connectivity map of brain activities can be manipulated quantitatively and qualitatively”. In order to prove this hypothesis a two-digit number comparison task was developed using Arabic number format and visual degradation adding visual noise in the represented stimuli. Based on Pinel et al.’s study, the numbers quantitatively were classified into three distance groups as close numbers (60-64 and 66-69), intermediate numbers (50-59 and 70-79) and far numbers (30-49 and 80-99), according to their distance from 65 . In order to prevent biases, subjects were instructed to press the left button for numbers smaller than 65 and the right button for the numbers larger than 65.  In addition to the quantity of numbers, the quality of numbers was the concern of our study. Thus, three levels of visual noise “Salt and Pepper Noise” were added to degrade the quality of visual recognition which was not studied before. Studying this aspect would give us a chance to define a brain connectivity and complexity model to find out which part of the brain is activated.

Therefore, brain images of children who are suffering from dyscalculae, which is difficulty learning and execution mathematics problems, would be diagnosed at different levels of perception. In addition to dyscalculae, Parkinson’s disease would be studied in this aspect. The current Parkinson’s studies have been only involved in the movement controlled tasks. The perceptual level of preparation would affect the motor execution, however. In this research the reactions are controlled by a two sided button box (left and right index fingers), therefore, the relationship between perceptual brain complexity and the motor execution would be modeled.

The current stage of the project is analyzing the EEG data obtained at University in Groningen, Holland. In this multidisciplinary area trying to understand the components and putting them all together is a challenging issue. Although the physiological aspects of the mathematical perception have been discussed by scientist, the brain dynamics and complexity behind neuronal activities is a very challenging and new question. The following stage of the project would be analyzing the datasets simultaneously obtained from EEG and fMRI. The expected outcome of the project is that developing a model supported by spatial and temporal components of brain imaging techniques. These findings would bring a new perspective about learning and motor perception involving disorders, such as Parkinson’s and Dyscalculae.

(1)Stanislas Dehaene, “The number sense”, Oxford University Press, Penguin press, New York, Cambridge (UK), 1997.

(2)Philippe Pinel, Stanislas Dehaene, D. Rivière, and Denis LeBihan, “Modulation of parietal activation by semantic distance in a number comparison task”, Neuroimage, 14:1013--1026, 2001.

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