Mixing by cutting-and-shuffling (like that for a deck of cards or a Rubik's cube) is a paradigm that has not been studied in detail even though it can be applied in a variety of situations including the mixing of granular materials. Mathematically, cutting- and-shuffling is described by piecewise isometries (PWIs),...
Circadian rhythms — physiological, behavioral, and metabolic oscillations with an approximate 24-h period — are controlled by an evolutionarily conserved set of core clock genes operating at the transcriptional and protein level. Entrainable by Zeitgebers (external environmental stimuli such as light, temperature, and food) that modulate time-of-day specific functions, the...
Soft matter is the field of science concerning soft and deformable materials: such as liquids, gels, and foams. Active matter is a sub-field of soft matter that considers systems that contain active agents or particles that consume energy for self-propulsion or to exert mechanical stress on the surrounding system. In...
Perhaps because of the influence of the central limit theorem, it is common for scientists to assume distributions in the real world are singly peaked and unimodal. However, many quantities in nature are actually better represented by multimodal distributions. One must provide an explanation for this disconnect between the central...
This thesis focuses on applications of recurrent neural networks (RNNs) for three aspects of sequential classification. In the first chapter, a novel method to generate synthetic minority data generation to improve imbalanced classification is discussed. Generative Adversarial Networks (GANs) have been used in many different applications to generate realistic synthetic...
Many industrial fluid flow problems involve the interaction between heavy, rigid objects and one or more fluid phases. For several decades, there has been a vested interest in simulating these fluid-structure interaction (FSI) problems in order to improve engineering design processes. However, numerical simulations of these problems can be challenging...
The simplicity of morphogenesis, manifested as collective shape changes, emerges from complex biophysical regulations within a multicellular embryo. Constructing a spatio-temporal atlas of mechanical stresses is central for understanding the emergence of this simplicity. Developing a new mathematical theory for the static mechanics of three-dimensional multicellular aggregates involving pressures and...
Motivated by rhythms in the brain, we investigate the synchronization of noisy and all-to-all pulse-coupled oscillators. We consider a case where the oscillatory excursions are of varying amplitude and where only sufficiently large excursions result in the output pulses that drive the interactions between the oscillators. In the regime of...
This dissertation is a review of three projects I worked on during my time in the Computational Photography Lab at Northwestern University. First, a source separation problem for the X-Ray Fluorescence images of painted works of art is addressed through the incorporation of Hyperspectral Reflectance data. Following this, a discussion...
Motivated by rhythms in the brain, we investigate the synchronization of noisy and all-to-all pulse-coupled oscillators. We consider a case where the oscillatory excursions are of varying amplitude and where only sufficiently large excursions result in the output pulses that drive the interactions between the oscillators. In the regime of...