UC San Diego

The brain can be seen as an extremely high-dimensional dynamical system. Despite the great complexity of the brain and the diversity of its activity, only limited measures of brain function are in general possible to record--e.g. the electroencephalogram (EEG) or intracranial recordings. The problem of extracting relevant information from a limited measurement of a complex system, and thereby determining the invariant nonlinear properties of the underlying system, has been well-studied in the field of nonlinear dynamics. Delay Differential Analysis (DDA) is a powerful nonlinear tool for time-domain data classification. In DDA, a low-dimensional nonlinear functional embedding is built from the dynamical structure of the data; this serves as a basis onto which the data can be mapped. By constraining the models used to low dimensionality, we ensure that DDA is largely immune to overfitting, insensitive to noise, and generalizes well to new data. DDA has been successfully applied to a range of EEG classification problems. Cross-Dynamical DDA (CD-DDA) is a formulation of DDA which includes terms from multiple locations to study information flow or causal connections. Here, DDA and CD-DDA are applied to several EEG and and intracranial data sets. In Chapter 2, DDA is applied to EEG data from a large study of schizophrenia patients and nonpsychiatric comparison subjects. In Chapter 3, DDA is used to detect sleep spindles in human intracranial recordings. In Chapter 4, CD-DDA is applied to intracranial recordings from the hippocampus and remote cortical sites to study information flow. In Chapter 5, the system that has been developed for analysis of large volumes of intracranial data from epilepsy patients is described, along with preliminary results related to seizure timing and prediction. Each of these distinct applications illustrates the power of DDA to access the underlying dynamics of neural activity and provide new insights.