In this research, I surveyed existing methods of characterizing Epilepsy from Electroencephalogram (EEG) data, including the Random Forest algorithm, which was claimed by many researchers to be the most effective at detecting epileptic seizures [7]. I observed that although many papers claimed a detection of >99% using Random Forest, it was not specified “when” the detection was declared within the 23.6 second interval of the seizure event. In this research, I created a time-series procedure to detect the seizure as early as possible within the 23.6 second epileptic seizure window and found that the detection is effective (> 92%) as early as the first few seconds of the epileptic episode. I intend to use this research as a stepping stone towards my upcoming Masters thesis research where I plan to expand the time-series detection mechanism to the pre-ictal stage, which will require a different dataset.
I conduct a simulation study, where I show that the approximation methods achieve the goals proposed while maintaining a similar level of out-of-sample prediction accuracy as LRP. I then illustrate and compare the methods using an applied data.
Revealing the underlying structure and dynamics of complex networked systems from observed data without of any specific prior information is of fundamental importance to science, engineering, and society. We articulate a Markov network based model, the sparse dynamical Boltzmann machine (SDBM), as a universal network structural estimator and dynamics approximator based on techniques including compressive sensing and K-means algorithm. It recovers the network structure of the original system and predicts its short-term or even long-term dynamical behavior for a large variety of representative dynamical processes on model and real-world complex networks.
One of the most challenging problems in complex dynamical systems is to control complex networks.
Upon finding that the energy required to approach a target state with reasonable precision
is often unbearably large, and the energy of controlling a set of networks with similar structural properties follows a fat-tail distribution, we identify fundamental structural ``short boards'' that play a dominant role in the enormous energy and offer a theoretical interpretation for the fat-tail distribution and simple strategies to significantly reduce the energy.
Extreme events and cascading failure, a type of collective behavior in complex networked systems, often have catastrophic consequences. Utilizing transportation and evolutionary game dynamics as prototypical
settings, we investigate the emergence of extreme events in simplex complex networks, mobile ad-hoc networks and multi-layer interdependent networks. A striking resonance-like phenomenon and the emergence of global-scale cascading breakdown are discovered. We derive analytic theories to understand the mechanism of
control at a quantitative level and articulate cost-effective control schemes to significantly suppress extreme events and the cascading process.