• The Uncertainty Principle in Harmonic Analysis and Bourgain's Theorem 

  Powell, Alexander M. (2003)

  We investigate the uncertainty principle in harmonic analysis and how it constrains the uniform localization properties of orthonormal bases. Our main result generalizes a theorem of Bourgain to construct orthonormal bases ...

• A latent variable modeling framework for analyzing neural population activity 

  Whiteway, Matthew (2018)

  Neuroscience is entering the age of big data, due to technological advances in electrical and optical recording techniques. Where historically neuroscientists have only been able to record activity from single neurons ...

• Consistency of Spectral Clustering with Functional Magnetic Resonance Image Data 

  Moon, Jessie (2018)

  Functional magnetic resonance imaging (fMRI) is a non-invasive technique for studying brain activity. It uses the amount of blood flowing through a brain, referred to as the blood oxygenation level dependent (BOLD) signal. ...

• Hydrodynamic Limits of the Boltzmann Equation 

  Lu, Chunting (2018)

  This dissertation studies two problems that are related to the question of how solutions of the Boltzmann equation behave in various fluid dynamic regimes. The Boltzmann equation models so-called rarefied gases of identical ...

• Fast Solvers and Preconditioners for Multiphase Flow in Porous Media 

  Bui, Quan Minh (2018)

  Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this pro- cess is modeled by a nonlinear system of ...

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