Marco Piangerelli
Complex systems, biological or artificial, are among us every day and every moment, and whether we want it or not, are part of our daily life. They continually generate data and having the right technology to record them, as well as innovative techniques to analyze them, could be the key to understanding their emerging behaviors. This is the inspirational principle of this work, where the complex study system - the main actor - is the human brain. In this thesis, first, a new, implantable and completely wireless device for the recording of electrocorticographic signals is presented. This could be the prototype of a closed-loop adaptive device able to learn from complex sistems-generated data and to react. In addition, an innovative method based on Topological Data Analysis (TDA) is introduced for classifying EEG recordings of patients affected by epileptic seizures and for detecting phase transitions. First of all, EEG signals (mutivariate time series) were used to build a topological space that is analyzed by Persistent Entropy, a global topological feature, in order to set up a linear classi er for discriminate non-epileptic and epileptic signals. The quality of classi cation is evaluated in terms of the Area Under Curve (AUC) of the Receiver Operating Characteristic Curve (ROC). It is shown that the proposed method has an AUC equal to 97.2%. Then, a set of weighted graphs were derived from the same multivariate time series as above in a way that preserves the temporal evolution. TDA and Persistent Entropy were, once again, applied on each graph in order to capture the occurrence of phase transitions in the brain. Numerical evidences that the methodology is able to detect the transition between the pre-ictal and ictal states were collected. Unfotunately in this case a statistical validation is lacking
