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Research Interests for Hamza M Ghadyali

Research Interests: Topological Data Analysis (TDA)

Did you know that over 50 million people worldwide suffer from Epilepsy? What is Epilepsy? Epilepsy is a neurological disorder characterized by recurrent but unexpected seizures. People with epilepsy and their families often suffer from stigma and discrimination: even in the United States of America, until the 1970s, it was legal to deny people with seizures access to restaurants, theatres, recreational centres and other public buildings! Imagine if there was a medical device which could consistently and accurately give a warning that a seizure is about to happen. My goal is to make this a reality. My primary research interest is to improve the lives of these people by producing a seizure prediction algorithm. To do this requires tools from many disciplines, and collaboration. ------------------------------------------------ Methods of describing geometric structure in data ------------------------------------------------ In any given field, once data has been collected and processed, it often takes the form of a 'point cloud' in Euclidean space (R^n). The fundamental open-ended question is then, "What is the 'shape of this point cloud?" The methods of TDA help to identify certain aspects of the shape --for example detecting and quantifying 'loops.' Depending on where the data comes from, geometric features such as 'loops' can be significant.

Current projects:
Seizure Detection Algorithm
Detecting Hidden Periodicity in Signals
Geometry of Delay-Maps
Areas of Interest:

Topological Data Analysis
Machine Learning
Statistical Learning Theory
Early Warning Detection Systems
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320