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...
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...
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...
Each second, living organisms take in sensory input from an ever-changing environment and respond appropriately. Identifying and contextualizing stimuli is critical for survival, and it often necessitates distinguishing between sensory experiences that are similar to each other. Pattern separation characterizes the mechanisms by which neuronal networks extract and highlight differences...
Deterministic models are used to explain and predict the dynamics of ecosystems featuring cyclic competition schemes. The models are systems of reaction-diffusion partialdifferential equations that account for species mobility via Fickian diffusion and interspecies interactions according to the competition scheme. Length and temporal scales are
chosen to be appropriate for...
Dynamical modeling aims to capture the essential mechanics at work in real-world systems while remaining tractable enough to yield mathematical insights for predictions and interventions. The work presented here first takes this approach to the system of political ideology and influence, establishing a model for the continuous-time evolution of individual...
Originally motivated by the emergence of networked systems lacking central coordination such as multiprocessors, wireless sensor networks and smart grids, the study of distributed optimization algorithms has been an active field of research spanning multiple decades. More recently, the rapid growth in the availability of high-dimensional datasets has posed the...