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Ph.D. Theses

Data Analytics of Time-Series for Complex (Biological) Systems

By Nimit Dhulekar
Advisor: Bülent Yener
April 16, 2015

Complex time-series systems such as biological networks have been studied for many years using conventional molecular and cellular techniques. However, the multiscale nature of these networks make these techniques limited in their application. In this thesis, we present coupled interdisciplinary algorithms covering disparate concepts such as graph-theory, level sets, autoregressive modeling, and domain knowledge transfer - with a view to improving the modeling and prediction of the evolution of biological networks. Applying our approaches to various modalities such as image-based and signal-based data, we demonstrate the importance of coupling these various techniques for a much improved holistic algorithm.

We present a coupled cellular level set model for investigating cleft formation in the first round of branching morphogenesis in the mouse submandibular salivary gland. This model takes into account cellular spatial organization and provides a better method for gland evolution. We demonstrate that this coupled cellular level set model simulates the growth of the tissue much better than other models currently in use.

Next, we present a model for epileptic seizure prediction from scalp EEG recordings using graph-based methods coupled with an autoregressive process, domain knowledge transfer, and manifold alignment. We illustrate that our model can make reliable predictions more than 10 min prior to a seizure.

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