Date of Award

8-27-2015

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Computer Science

First Advisor

Coskun Bayrak

Abstract

Positive electrical charges in a solid conductor generate an outward electrical field emanating from the charged conductor. In this context, overall cognitive decisions, which were initiated by the electrical activities of neural modules at different parts of the cerebrum, are completed at the highest spatial and hierarchical level. EEG systems are capable of detecting these electrical activities, however, a unified mathematical model of these highest-level cognitive interactions has not yet been stated. Recent studies support the theory that brain is composed of modules and certain nodes establish connections between the modules. Within the scope of this study, the highest spatial and hierarchical level of connectivity of neural communities is mathematically modeled integrating the “antipodal points” concept of the Borsuk-Ulam theorem. In order to apply the Borsuk-Ulam theorem and Riemann’s stereographic projection to the EEG data, a sophisticated computational tool was developed which transforms single dimensional EEG data to higher dimensions in a complex domain and captures the highly-correlated data pairs, called COGSIP. COGSIP analyzes the degree of similarity of the transformed EEG data pairs in a 3D environment to detect antipodal points, stemming from the electrical activity of neural communities. Highly correlated EEG data pairs are defined as Antipodal Connector Nodes (ACNs). Thus, the antipodal connectivity of the cognitive decision mechanism is detected by identifying the highest spatial and hierarchical level connections. In contrast to the many existing inductive methods, this new approach depends on deductive reasoning.

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